Finite Group Databasebeta

← C83×#36817 #35264641

Subgroups — C83×#36817 #35264641

Order 21248.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#2851C211yesmaximal, characteristic, complemented
2C83×#2850C211yesmaximal, characteristic, complemented
3C83×#2778C211yesmaximal, characteristic, complemented
4C83×#2763C211yesmaximal, characteristic, complemented
5C83×#2762C211yesmaximal, characteristic, complemented
6C83×#2756C211yesmaximal, characteristic, complemented
7C83×#2753C211yesmaximal, characteristic, complemented
8C83×#2728C211yesmaximal, characteristic, complemented
9C83×#2723C211yesmaximal, characteristic, complemented
10C83×#2723C211yesmaximal, characteristic, complemented
11C83×#2711C211yesmaximal, characteristic, complemented
12C83×#2708C211yesmaximal, characteristic, complemented
13C83×#2704C211yesmaximal, characteristic, complemented
14C83×#2700C211yesmaximal, characteristic, complemented
15C83×#2686C211yesmaximal, characteristic, complemented
16C83×#2676C211yesmaximal, characteristic, complemented
17C83×#2676C211yesmaximal, characteristic, complemented
18C83×#2671C211yesmaximal, characteristic, complemented
19C83×#2653C211yesmaximal, characteristic, complemented
20C83×#2649C211yesmaximal, characteristic, complemented
21C83×#2602C211yesmaximal, characteristic, complemented
22C83×#2589C211yesmaximal, characteristic, complemented
23C83×#2559C211yesmaximal, characteristic, complemented
24C83×#2549C211yesmaximal, characteristic, complemented
25C83×#2474C211yesmaximal, characteristic, complemented
26C83×#2470C211yesmaximal, characteristic, complemented
27C83×#2430C211yesmaximal, characteristic, complemented
28C83×#2407C211yesmaximal, characteristic, complemented
29C83×#2335C211yesmaximal, characteristic, complemented
30C83×#2318C211yesmaximal, characteristic, complemented
31C83×#2297C211yesmaximal, characteristic, complemented
32C22×#41×C83C2211yescharacteristic
33C2×#126×C83C2211yescharacteristic
34C2×#125×C83C2211yescharacteristic
35C2×#124×C83C2211yescharacteristic
36C2×#124×C83C2211yescharacteristic
37C2×#123×C83C2211yescharacteristic
38C2×#123×C83C2211yescharacteristic
39C2×C22⋊Q8×C83C2211yescharacteristic
40C2×C22⋊Q8×C83C2211yescharacteristic
41C2×C22⋊Q8×C83C2211yescharacteristic
42C2×C22⋊Q8×C83C2211yescharacteristic
43C2×#121×C83C2211yescharacteristic
44C2×#121×C83C2211yescharacteristic
45C2×#121×C83C2211yescharacteristic
46C2×#121×C83C2211yescharacteristic
47C2×#121×C83C2211yescharacteristic
48C2×C4×D4×C83C2211yescharacteristic
49C2×#117×C83C2211yescharacteristic
50C22×C42×C83C2211yescharacteristic
51#401×C83C2211yescharacteristic
52#400×C83C2211yescharacteristic
53#400×C83C2211yescharacteristic
54#400×C83C2211yescharacteristic
55#400×C83C2211yescharacteristic
56#400×C83C2211yescharacteristic
57#399×C83C2211yescharacteristic
58#399×C83C2211yescharacteristic
59#398×C83C2211yescharacteristic
60#398×C83C2211yescharacteristic
61#398×C83C2211yescharacteristic
62#398×C83C2211yescharacteristic
63#397×C83C2211yescharacteristic
64#397×C83C2211yescharacteristic
65#397×C83C2211yescharacteristic
66#397×C83C2211yescharacteristic
67#397×C83C2211yescharacteristic
68#397×C83C2211yescharacteristic
69#397×C83C2211yescharacteristic
70#396×C83C2211yescharacteristic
71#396×C83C2211yescharacteristic
72#396×C83C2211yescharacteristic
73#395×C83C2211yescharacteristic
74#395×C83C2211yescharacteristic
75#395×C83C2211yescharacteristic
76#395×C83C2211yescharacteristic
77#394×C83C2211yescharacteristic
78#394×C83C2211yescharacteristic
79#394×C83C2211yescharacteristic
80#394×C83C2211yescharacteristic
81#394×C83C2211yescharacteristic
82#394×C83C2211yescharacteristic
83#394×C83C2211yescharacteristic
84#394×C83C2211yescharacteristic
85#394×C83C2211yescharacteristic
86#394×C83C2211yescharacteristic
87#394×C83C2211yescharacteristic
88#394×C83C2211yescharacteristic
89#394×C83C2211yescharacteristic
90#394×C83C2211yescharacteristic
91#393×C83C2211yescharacteristic
92#393×C83C2211yescharacteristic
93#393×C83C2211yescharacteristic
94#393×C83C2211yescharacteristic
95#392×C83C2211yescharacteristic
96#392×C83C2211yescharacteristic
97#392×C83C2211yescharacteristic
98#392×C83C2211yescharacteristic
99#391×C83C2211yescharacteristic
100#391×C83C2211yescharacteristic
101#391×C83C2211yescharacteristic
102#391×C83C2211yescharacteristic
103#391×C83C2211yescharacteristic
104#391×C83C2211yescharacteristic
105#390×C83C2211yescharacteristic
106#390×C83C2211yescharacteristic
107#390×C83C2211yescharacteristic
108#390×C83C2211yescharacteristic
109#390×C83C2211yescharacteristic
110#389×C83C2211yescharacteristic
111#389×C83C2211yescharacteristic
112#389×C83C2211yescharacteristic
113#389×C83C2211yescharacteristic
114#389×C83C2211yescharacteristic
115#388×C83C2211yescharacteristic
116#388×C83C2211yescharacteristic
117#388×C83C2211yescharacteristic
118#388×C83C2211yescharacteristic
119#388×C83C2211yescharacteristic
120#388×C83C2211yescharacteristic
121#388×C83C2211yescharacteristic
122#388×C83C2211yescharacteristic
123#388×C83C2211yescharacteristic
124#388×C83C2211yescharacteristic
125#388×C83C2211yescharacteristic
126#388×C83C2211yescharacteristic
127#388×C83C2211yescharacteristic
128#388×C83C2211yescharacteristic
129#388×C83C2211yescharacteristic
130#388×C83C2211yescharacteristic
131#388×C83C2211yescharacteristic
132#387×C83C2211yescharacteristic
133#387×C83C2211yescharacteristic
134#387×C83C2211yescharacteristic
135#387×C83C2211yescharacteristic
136#387×C83C2211yescharacteristic
137#387×C83C2211yescharacteristic
138#387×C83C2211yescharacteristic
139#387×C83C2211yescharacteristic
140#387×C83C2211yescharacteristic
141#386×C83C2211yescharacteristic
142#386×C83C2211yescharacteristic
143#386×C83C2211yescharacteristic
144#386×C83C2211yescharacteristic
145#386×C83C2211yescharacteristic
146#386×C83C2211yescharacteristic
147#386×C83C2211yescharacteristic
148#386×C83C2211yescharacteristic
149#386×C83C2211yescharacteristic
150#386×C83C2211yescharacteristic
151#386×C83C2211yescharacteristic
152#386×C83C2211yescharacteristic
153#386×C83C2211yescharacteristic
154#386×C83C2211yescharacteristic
155#386×C83C2211yescharacteristic
156#386×C83C2211yescharacteristic
157#385×C83C2211yescharacteristic
158#385×C83C2211yescharacteristic
159#385×C83C2211yescharacteristic
160#385×C83C2211yescharacteristic
161#385×C83C2211yescharacteristic
162#385×C83C2211yescharacteristic
163#385×C83C2211yescharacteristic
164#385×C83C2211yescharacteristic
165#385×C83C2211yescharacteristic
166#385×C83C2211yescharacteristic
167#385×C83C2211yescharacteristic
168#385×C83C2211yescharacteristic
169#385×C83C2211yescharacteristic
170#385×C83C2211yescharacteristic
171#383×C83C2211yescharacteristic
172#382×C83C2211yescharacteristic
173#382×C83C2211yescharacteristic
174#382×C83C2211yescharacteristic
175#381×C83C2211yescharacteristic
176#380×C83C2211yescharacteristic
177#380×C83C2211yescharacteristic
178#380×C83C2211yescharacteristic
179#380×C83C2211yescharacteristic
180C4×C4⋊C4×C83C2211yescharacteristic
181C4×C22⋊C4×C83C2211yescharacteristic
182C4×C22⋊C4×C83C2211yescharacteristic
183C4×C22⋊C4×C83C2211yescharacteristic
184C4×C22⋊C4×C83C2211yescharacteristic
185C4×C22⋊C4×C83C2211yescharacteristic
186C2×#95×C83C2211yescharacteristic
187C2×#41×C83—24no—
188C2×#41×C83—42no—
189C2×#41×C83—42no—
190C22×Q8×C83C2311yescharacteristic
191C22×Q8×C83C2311yescharacteristic
192C22×Q8×C83C2311yescharacteristic
193C22×D4×C83C2311yescharacteristic
194C22×D4×C83C2311yescharacteristic
195C22×D4×C83C2311yescharacteristic
196C22×D4×C83C2311yescharacteristic
197C22×D4×C83C2311yescharacteristic
198C22×D4×C83C2311yescharacteristic
199C22×D4×C83C2311yescharacteristic
200C22×D4×C83C2311yescharacteristic
201C22×D4×C83C2311yescharacteristic
202C22×D4×C83C2311yescharacteristic
203C23×C4×C83C2311yescharacteristic
204C23×C4×C83C2311yescharacteristic
205C23×C4×C83C2311yescharacteristic
206C23×C4×C83C2311yescharacteristic
207C23×C4×C83C2311yescharacteristic
208C23×C4×C83C2311yescharacteristic
209C23×C4×C83C2311yescharacteristic
210C23×C4×C83C2311yescharacteristic
211C23×C4×C83C2311yescharacteristic
212#126×C83—42no—
213#125×C83—42no—
214#124×C83—42no—
215#124×C83—42no—
216#123×C83—24no—
217#123×C83—42no—
218C22⋊Q8×C83—42no—
219C22⋊Q8×C83—42no—
220C22⋊Q8×C83—42no—
221C22⋊Q8×C83—42no—
222#121×C83—42no—
223#121×C83—42no—
224#121×C83—42no—
225#121×C83—42no—
226#121×C83—42no—
227C4×D4×C83—24no—
228#117×C83—42no—
229C2×C4⋊C4×C83C2311yescharacteristic
230C2×C4⋊C4×C83C2311yescharacteristic
231C2×C4⋊C4×C83C2311yescharacteristic
232C2×C4⋊C4×C83C2311yescharacteristic
233C2×C4⋊C4×C83C2311yescharacteristic
234C2×C4⋊C4×C83C2311yescharacteristic
235C2×C4⋊C4×C83C2311yescharacteristic
236C2×C4⋊C4×C83C2311yescharacteristic
237C2×C4⋊C4×C83C2311yescharacteristic
238C2×C4⋊C4×C83C2311yescharacteristic
239C2×C4⋊C4×C83C2311yescharacteristic
240C2×C4⋊C4×C83C2311yescharacteristic
241C2×C4⋊C4×C83C2311yescharacteristic
242C2×C4⋊C4×C83C2311yescharacteristic
243C2×C4⋊C4×C83C2311yescharacteristic
244C2×C4⋊C4×C83C2311yescharacteristic
245C2×C4⋊C4×C83C2311yescharacteristic
246C2×C4⋊C4×C83C2311yescharacteristic
247C2×C4⋊C4×C83C2311yescharacteristic
248C2×C4⋊C4×C83C2311yescharacteristic
249C2×C4⋊C4×C83C2311yescharacteristic
250C2×C4⋊C4×C83C2311yescharacteristic
251C2×C4⋊C4×C83C2311yescharacteristic
252C2×C4⋊C4×C83C2311yescharacteristic
253C2×C4⋊C4×C83C2311yescharacteristic
254C2×C4⋊C4×C83C2311yescharacteristic
255C2×C4⋊C4×C83C2311yescharacteristic
256C2×C4⋊C4×C83C2311yescharacteristic
257C2×C4⋊C4×C83C2311yescharacteristic
258C2×C4⋊C4×C83C2311yescharacteristic
259C2×C4⋊C4×C83C2311yescharacteristic
260C2×C22⋊C4×C83C2311yescharacteristic
261C2×C22⋊C4×C83C2311yescharacteristic
262C2×C22⋊C4×C83C2311yescharacteristic
263C2×C22⋊C4×C83C2311yescharacteristic
264C2×C22⋊C4×C83C2311yescharacteristic
265C2×C22⋊C4×C83C2311yescharacteristic
266C2×C22⋊C4×C83C2311yescharacteristic
267C2×C22⋊C4×C83C2311yescharacteristic
268C2×C22⋊C4×C83C2311yescharacteristic
269C2×C22⋊C4×C83C2311yescharacteristic
270C2×C22⋊C4×C83C2311yescharacteristic
271C2×C22⋊C4×C83C2311yescharacteristic
272C2×C22⋊C4×C83C2311yescharacteristic
273C2×C22⋊C4×C83C2311yescharacteristic
274C2×C22⋊C4×C83C2311yescharacteristic
275C2×C22⋊C4×C83C2311yescharacteristic
276C2×C22⋊C4×C83C2311yescharacteristic
277C2×C22⋊C4×C83C2311yescharacteristic
278C2×C22⋊C4×C83C2311yescharacteristic
279C2×C22⋊C4×C83C2311yescharacteristic
280C2×C22⋊C4×C83C2311yescharacteristic
281C2×C22⋊C4×C83C2311yescharacteristic
282C2×C22⋊C4×C83C2311yescharacteristic
283C2×C22⋊C4×C83C2311yescharacteristic
284C2×C22⋊C4×C83C2311yescharacteristic
285C2×C22⋊C4×C83C2311yescharacteristic
286C2×C22⋊C4×C83C2311yescharacteristic
287C2×C22⋊C4×C83C2311yescharacteristic
288C2×C22⋊C4×C83C2311yescharacteristic
289C2×C22⋊C4×C83C2311yescharacteristic
290C2×C22⋊C4×C83C2311yescharacteristic
291C2×C22⋊C4×C83C2311yescharacteristic
292C2×C22⋊C4×C83C2311yescharacteristic
293C2×C22⋊C4×C83C2311yescharacteristic
294C2×C22⋊C4×C83C2311yescharacteristic
295C2×C22⋊C4×C83C2311yescharacteristic
296C2×C22⋊C4×C83C2311yescharacteristic
297C2×C22⋊C4×C83C2311yescharacteristic
298C2×C22⋊C4×C83C2311yescharacteristic
299C2×C22⋊C4×C83C2311yescharacteristic
300C2×C22⋊C4×C83C2311yescharacteristic
301C2×C22⋊C4×C83C2311yescharacteristic
302C2×C22⋊C4×C83C2311yescharacteristic
303C2×C22⋊C4×C83C2311yescharacteristic
304C2×C22⋊C4×C83C2311yescharacteristic
305C2×C22⋊C4×C83C2311yescharacteristic
306C2×C42×C83—42no—
307C2×C42×C83C2311yescharacteristic
308C2×C42×C83C2311yescharacteristic
309C2×C42×C83C2311yescharacteristic
310C2×C42×C83C2311yescharacteristic
311C2×C42×C83C2311yescharacteristic
312C2×C42×C83C2311yescharacteristic
313C2×C42×C83C2311yescharacteristic
314C2×C42×C83C2311yescharacteristic
315C2×C42×C83C2311yescharacteristic
316C2×C42×C83C2311yescharacteristic
317#95×C83C2311yescharacteristic
318#95×C83C2311yescharacteristic
319#95×C83C2311yescharacteristic
320#95×C83C2311yescharacteristic
321#95×C83C2311yescharacteristic
322#95×C83C2311yescharacteristic
323#95×C83C2311yescharacteristic
324#95×C83C2311yescharacteristic
325#95×C83C2311yescharacteristic
326#95×C83C2311yescharacteristic
327#95×C83C2311yescharacteristic
328#95×C83C2311yescharacteristic
329#95×C83C2311yescharacteristic
330#95×C83C2311yescharacteristic
331#95×C83C2311yescharacteristic
332#95×C83C2311yescharacteristic
333#95×C83C2311yescharacteristic
334#95×C83C2311yescharacteristic
335#95×C83C2311yescharacteristic
336#95×C83C2311yescharacteristic
337#95×C83C2311yescharacteristic
338#95×C83C2311yescharacteristic
339#95×C83C2311yescharacteristic
340#95×C83C2311yescharacteristic
341#95×C83C2311yescharacteristic
342#95×C83C2311yescharacteristic
343#95×C83C2311yescharacteristic
344#95×C83C2311yescharacteristic
345#95×C83C2311yescharacteristic
346#95×C83C2311yescharacteristic
347#95×C83C2311yescharacteristic
348#95×C83C2311yescharacteristic
349#95×C83C2311yescharacteristic
350#95×C83C2311yescharacteristic
351#95×C83C2311yescharacteristic
352#95×C83C2311yescharacteristic
353#95×C83C2311yescharacteristic
354#95×C83C2311yescharacteristic
355#95×C83C2311yescharacteristic
356#95×C83C2311yescharacteristic
357#95×C83C2311yescharacteristic
358#95×C83C2311yescharacteristic
359#95×C83C2311yescharacteristic
360#95×C83C2311yescharacteristic
361#95×C83C2311yescharacteristic
362#95×C83C2311yescharacteristic
363C24×C83C2411yescharacteristic
364C24×C83C2411yescharacteristic
365C24×C83C2411yescharacteristic
366C24×C83C2411yescharacteristic
367C24×C83C2411yescharacteristic
368#41×C83—416no—
369C2×Q8×C83—22no—
370C2×Q8×C83—22no—
371C2×Q8×C83—22no—
372C2×Q8×C83—41no—
373C2×Q8×C83—41no—
374C2×Q8×C83—41no—
375C2×Q8×C83—41no—
376C2×Q8×C83—41no—
377C2×Q8×C83—41no—
378C2×D4×C83—22no—
379C2×D4×C83—22no—
380C2×D4×C83—22no—
381C2×D4×C83—22no—
382C2×D4×C83—22no—
383C2×D4×C83—22no—
384C2×D4×C83—22no—
385C2×D4×C83—22no—
386C2×D4×C83—22no—
387C2×D4×C83—22no—
388C2×D4×C83—22no—
389C2×D4×C83—41no—
390C2×D4×C83—41no—
391C2×D4×C83—41no—
392C2×D4×C83—41no—
393C2×D4×C83—41no—
394C2×D4×C83—41no—
395C2×D4×C83—41no—
396C2×D4×C83—41no—
397C2×D4×C83—41no—
398C2×D4×C83—41no—
399C2×D4×C83—41no—
400C2×D4×C83—41no—
401C2×D4×C83—41no—
402C2×D4×C83—41no—
403C2×D4×C83—41no—
404C2×D4×C83—41no—
405C2×D4×C83—41no—
406C2×D4×C83—41no—
407C2×D4×C83—41no—
408C22×C4×C83—22no—
409C22×C4×C83—22no—
410C22×C4×C83—22no—
411C22×C4×C83—22no—
412C22×C4×C83—22no—
413C22×C4×C83—22no—
414C22×C4×C83—22no—
415C22×C4×C83—41no—
416C22×C4×C83—41no—
417C22×C4×C83—41no—
418C22×C4×C83—41no—
419C22×C4×C83—41no—
420C22×C4×C83—41no—
421C22×C4×C83—41no—
422C22×C4×C83—41no—
423C22×C4×C83—41no—
424C22×C4×C83—41no—
425C22×C4×C83—41no—
426C22×C4×C83—41no—
427C22×C4×C83—41no—
428C22×C4×C83—41no—
429C22×C4×C83—41no—
430C22×C4×C83—41no—
431C22×C4×C83—41no—
432C22×C4×C83—41no—
433C22×C4×C83—41no—
434C22×C4×C83#4114yes—
435C22×C4×C83C2411yescharacteristic
436C22×C4×C83C2411yescharacteristic
437C22×C4×C83C2411yescharacteristic
438C22×C4×C83C2411yescharacteristic
439C22×C4×C83C2411yescharacteristic
440C22×C4×C83C2411yescharacteristic
441C22×C4×C83C2411yescharacteristic
442C22×C4×C83C2411yescharacteristic
443C22×C4×C83C2411yescharacteristic
444C22×C4×C83C2411yescharacteristic
445C22×C4×C83C2411yescharacteristic
446C22×C4×C83C2411yescharacteristic
447C22×C4×C83C2411yescharacteristic
448C22×C4×C83C2411yescharacteristic
449C22×C4×C83C2411yescharacteristic
450C22×C4×C83C2411yescharacteristic
451C22×C4×C83C2411yescharacteristic
452C22×C4×C83C2411yescharacteristic
453C22×C4×C83C2411yescharacteristic
454C22×C4×C83C2411yescharacteristic
455C22×C4×C83C2411yescharacteristic
456C22×C4×C83C2411yescharacteristic
457C22×C4×C83C2411yescharacteristic
458C22×C4×C83C2411yescharacteristic
459C22×C4×C83C2411yescharacteristic
460C22×C4×C83C2411yescharacteristic
461C4⋊C4×C83—22no—
462C4⋊C4×C83—22no—
463C4⋊C4×C83—22no—
464C4⋊C4×C83—22no—
465C4⋊C4×C83—22no—
466C4⋊C4×C83—22no—
467C4⋊C4×C83—22no—
468C4⋊C4×C83—22no—
469C4⋊C4×C83—22no—
470C4⋊C4×C83—41no—
471C4⋊C4×C83—41no—
472C4⋊C4×C83—41no—
473C4⋊C4×C83—41no—
474C4⋊C4×C83—41no—
475C4⋊C4×C83—41no—
476C4⋊C4×C83—41no—
477C4⋊C4×C83—41no—
478C4⋊C4×C83—41no—
479C4⋊C4×C83—41no—
480C4⋊C4×C83—41no—
481C4⋊C4×C83—41no—
482C4⋊C4×C83—41no—
483C4⋊C4×C83—41no—
484C4⋊C4×C83—41no—
485C4⋊C4×C83—41no—
486C4⋊C4×C83—41no—
487C4⋊C4×C83—41no—
488C4⋊C4×C83—41no—
489C4⋊C4×C83—41no—
490C4⋊C4×C83—41no—
491C4⋊C4×C83—41no—
492C22⋊C4×C83—22no—
493C22⋊C4×C83—22no—
494C22⋊C4×C83—22no—
495C22⋊C4×C83—22no—
496C22⋊C4×C83—22no—
497C22⋊C4×C83—22no—
498C22⋊C4×C83—22no—
499C22⋊C4×C83—22no—
500C22⋊C4×C83—22no—
501C22⋊C4×C83—22no—
502C22⋊C4×C83—22no—
503C22⋊C4×C83—22no—
504C22⋊C4×C83—22no—
505C22⋊C4×C83—22no—
506C22⋊C4×C83—22no—
507C22⋊C4×C83—22no—
508C22⋊C4×C83—22no—
509C22⋊C4×C83—41no—
510C22⋊C4×C83—41no—
511C22⋊C4×C83—41no—
512C22⋊C4×C83—41no—
513C22⋊C4×C83—41no—
514C22⋊C4×C83—41no—
515C22⋊C4×C83—41no—
516C22⋊C4×C83—41no—
517C22⋊C4×C83—41no—
518C22⋊C4×C83—41no—
519C22⋊C4×C83—41no—
520C22⋊C4×C83—41no—
521C22⋊C4×C83—41no—
522C22⋊C4×C83—41no—
523C22⋊C4×C83—41no—
524C22⋊C4×C83—41no—
525C22⋊C4×C83—41no—
526C22⋊C4×C83—41no—
527C22⋊C4×C83—41no—
528C22⋊C4×C83—41no—
529C22⋊C4×C83—41no—
530C22⋊C4×C83—41no—
531C22⋊C4×C83—41no—
532C22⋊C4×C83—41no—
533C22⋊C4×C83—41no—
534C22⋊C4×C83—41no—
535C22⋊C4×C83—41no—
536C22⋊C4×C83—41no—
537C22⋊C4×C83—41no—
538C42×C83—22no—
539C42×C83—22no—
540C42×C83—22no—
541C42×C83—41no—
542C42×C83—41no—
543C42×C83—41no—
544C42×C83—41no—
545C42×C83—41no—
546C42×C83—41no—
547C42×C83—41no—
548C23×C83—21no—
549C23×C83—21no—
550C23×C83—21no—
551C23×C83—21no—
552C23×C83—21no—
553C23×C83—21no—
554C23×C83—21no—
555C23×C83—21no—
556C23×C83—21no—
557C23×C83—21no—
558C23×C83—21no—
559C23×C83—21no—
560C23×C83—21no—
561C23×C83—21no—
562C23×C83—21no—
563C23×C83—21no—
564C23×C83—21no—
565C23×C83—21no—
566C23×C83—21no—
567C23×C83—21no—
568C23×C83—21no—
569C23×C83—21no—
570C23×C83—21no—
571C23×C83—21no—
572C23×C83—21no—
573C23×C83—21no—
574C23×C83—21no—
575C23×C83—21no—
576C23×C83—21no—
577C23×C83—21no—
578C23×C83—21no—
579C23×C83—21no—
580C23×C83—21no—
581C23×C83C2×#4112yes—
582C23×C83H(5,𝔽2)12yes—
583C23×C83C2511yescharacteristic
584Q8×C83—44no—
585Q8×C83—82no—
586Q8×C83—82no—
587D4×C83—44no—
588D4×C83—44no—
589D4×C83—44no—
590D4×C83—44no—
591D4×C83—82no—
592D4×C83—82no—
593D4×C83—82no—
594D4×C83—82no—
595D4×C83—82no—
596D4×C83—82no—
597C2×C4×C83—28no—
598C2×C4×C83—21no—
599C2×C4×C83—21no—
600C2×C4×C83—21no—
601C2×C4×C83—21no—
602C2×C4×C83—21no—
603C2×C4×C83—21no—
604C2×C4×C83—21no—
605C2×C4×C83—21no—
606C2×C4×C83—21no—
607C2×C4×C83—21no—
608C2×C4×C83—21no—
609C2×C4×C83—21no—
610C2×C4×C83—21no—
611C2×C4×C83—21no—
612C2×C4×C83—21no—
613C2×C4×C83—21no—
614C2×C4×C83—21no—
615C2×C4×C83—21no—
616C2×C4×C83—21no—
617C2×C4×C83—21no—
618C2×C4×C83—21no—
619C2×C4×C83—21no—
620C2×C4×C83—21no—
621C2×C4×C83—21no—
622C2×C4×C83—21no—
623C2×C4×C83—21no—
624C2×C4×C83—21no—
625C2×C4×C83—21no—
626C2×C4×C83—21no—
627C2×C4×C83—21no—
628C2×C4×C83—21no—
629C2×C4×C83—21no—
630C2×C4×C83—21no—
631C2×C4×C83—21no—
632C2×C4×C83—21no—
633C2×C4×C83—21no—
634C2×C4×C83—21no—
635C2×C4×C83—21no—
636C2×C4×C83—21no—
637C2×C4×C83—21no—
638C2×C4×C83—21no—
639C2×C4×C83—21no—
640C2×C4×C83—21no—
641C2×C4×C83—21no—
642C2×C4×C83—21no—
643C2×C4×C83—21no—
644C2×C4×C83—21no—
645C2×C4×C83—21no—
646C2×C4×C83—21no—
647C2×C4×C83—21no—
648C2×C4×C83—21no—
649C2×C4×C83—21no—
650C2×C4×C83—21no—
651C2×C4×C83—21no—
652C2×C4×C83—21no—
653C2×C4×C83—21no—
654C2×C4×C83—21no—
655C2×C4×C83—21no—
656C2×C4×C83—21no—
657C2×C4×C83—21no—
658C2×C4×C83—21no—
659C2×C4×C83—21no—
660C2×C4×C83—21no—
661C2×C4×C83—21no—
662C2×C4×C83—21no—
663C2×C4×C83—21no—
664C2×C4×C83—21no—
665C2×C4×C83—21no—
666C2×C4×C83—21no—
667C2×C4×C83—21no—
668C2×C4×C83—21no—
669C2×C4×C83—21no—
670C2×C4×C83—21no—
671C2×C4×C83—44no—
672C2×C4×C83—44no—
673C2×C4×C83—44no—
674C2×C4×C83—44no—
675C2×C4×C83—82no—
676C2×C4×C83—82no—
677C2×C4×C83—82no—
678C2×C4×C83—82no—
679C2×C4×C83C2×#4112yes—
680C2×C4×C83C2×#4112yes—
681C2×C4×C83H(5,𝔽2)12yes—
682C2×C4×C83H(5,𝔽2)12yes—
683C2×C4×C832−1+412yes—
684C22×C83—22no—
685C22×C83—22no—
686C22×C83—22no—
687C22×C83—22no—
688C22×C83—22no—
689C22×C83—22no—
690C22×C83—41no—
691C22×C83—41no—
692C22×C83—41no—
693C22×C83—41no—
694C22×C83—41no—
695C22×C83—41no—
696C22×C83—41no—
697C22×C83—41no—
698C22×C83—41no—
699C22×C83—41no—
700C22×C83—41no—
701C22×C83—41no—
702C22×C83—41no—
703C22×C83—41no—
704C22×C83—41no—
705C22×C83—41no—
706C22×C83—41no—
707C22×C83—41no—
708C22×C83—41no—
709C22×C83—41no—
710C22×C83—41no—
711C22×C83—41no—
712C22×C83—41no—
713C22×C83—41no—
714C22×C83—41no—
715C22×C83—41no—
716C22×C83—41no—
717C22×C83—41no—
718C22×C83—41no—
719C22×C83C22×#4111yescharacteristic
720C22×C83C2×H(5,𝔽2)11yescharacteristic
721C22×C83C2×H(5,𝔽2)11yescharacteristic
722C22×C83C2×H(5,𝔽2)11yescharacteristic
723C22×C83C2×2−1+411yescharacteristic
724C22×C83#58511yescharacteristic
725C22×C83#58511yescharacteristic
726C4×C83—22no—
727C4×C83—22no—
728C4×C83—22no—
729C4×C83—22no—
730C4×C83—22no—
731C4×C83—41no—
732C4×C83—41no—
733C4×C83—41no—
734C4×C83—41no—
735C4×C83—41no—
736C4×C83—41no—
737C4×C83—41no—
738C4×C83—41no—
739C4×C83—41no—
740C4×C83—41no—
741C4×C83—41no—
742C4×C83—41no—
743C4×C83—41no—
744C4×C83—41no—
745C4×C83—41no—
746C4×C83—41no—
747C4×C83—41no—
748C4×C83—41no—
749C4×C83—41no—
750C4×C83—41no—
751C4×C83—41no—
752#36817C8311yesmaximal, characteristic, direct product factor, Sylow
753C2×C83—42no—
754C2×C83—42no—
755C2×C83—81no—
756C2×C83—81no—
757C2×C83—81no—
758C2×C83#345511yescharacteristic
759C2×C83#349011yescharacteristic
760C2×C83#351111yescharacteristic
761C2×C83#354111yescharacteristic
762C2×C83#354211yescharacteristic
763C2×C83#355811yescharacteristic
764C2×C83#355911yescharacteristic
765#2851C2×C8311yescharacteristic, complemented
766#2850C2×C8311yescharacteristic, complemented
767#2778C2×C8311yescharacteristic, complemented
768#2763C2×C8311yescharacteristic, complemented
769#2762C2×C8311yescharacteristic, complemented
770#2756C2×C8311yescharacteristic, complemented
771#2753C2×C8311yescharacteristic, complemented
772#2728C2×C8311yescharacteristic, complemented
773#2723C2×C8311yescharacteristic, complemented
774#2723C2×C8311yescharacteristic, complemented
775#2711C2×C8311yescharacteristic, complemented
776#2708C2×C8311yescharacteristic, complemented
777#2704C2×C8311yescharacteristic, complemented
778#2700C2×C8311yescharacteristic, complemented
779#2686C2×C8311yescharacteristic, complemented
780#2676C2×C8311yescharacteristic, complemented
781#2676C2×C8311yescharacteristic, complemented
782#2671C2×C8311yescharacteristic, complemented
783#2653C2×C8311yescharacteristic, complemented
784#2649C2×C8311yescharacteristic, complemented
785#2602C2×C8311yescharacteristic, complemented
786#2589C2×C8311yescharacteristic, complemented
787#2559C2×C8311yescharacteristic, complemented
788#2549C2×C8311yescharacteristic, complemented
789#2474C2×C8311yescharacteristic, complemented
790#2470C2×C8311yescharacteristic, complemented
791#2430C2×C8311yescharacteristic, complemented
792#2407C2×C8311yescharacteristic, complemented
793#2335C2×C8311yescharacteristic, complemented
794#2318C2×C8311yescharacteristic, complemented
795#2297C2×C8311yescharacteristic, complemented
796C83#3681711yescharacteristic, direct product factor, Sylow
797C22×#41C22×C8311yescharacteristic
798C2×#126C22×C8311yescharacteristic
799C2×#125C22×C8311yescharacteristic
800C2×#124C22×C8311yescharacteristic
801C2×#124C22×C8311yescharacteristic
802C2×#123C22×C8311yescharacteristic
803C2×#123C22×C8311yescharacteristic
804C2×C22⋊Q8C22×C8311yescharacteristic
805C2×C22⋊Q8C22×C8311yescharacteristic
806C2×C22⋊Q8C22×C8311yescharacteristic
807C2×C22⋊Q8C22×C8311yescharacteristic
808C2×#121C22×C8311yescharacteristic
809C2×#121C22×C8311yescharacteristic
810C2×#121C22×C8311yescharacteristic
811C2×#121C22×C8311yescharacteristic
812C2×#121C22×C8311yescharacteristic
813C2×C4×D4C22×C8311yescharacteristic
814C2×#117C22×C8311yescharacteristic
815C22×C42C22×C8311yescharacteristic
816#401C22×C8311yescharacteristic
817#400C22×C8311yescharacteristic
818#400C22×C8311yescharacteristic
819#400C22×C8311yescharacteristic
820#400C22×C8311yescharacteristic
821#400C22×C8311yescharacteristic
822#399C22×C8311yescharacteristic
823#399C22×C8311yescharacteristic
824#398C22×C8311yescharacteristic
825#398C22×C8311yescharacteristic
826#398C22×C8311yescharacteristic
827#398C22×C8311yescharacteristic
828#397C22×C8311yescharacteristic
829#397C22×C8311yescharacteristic
830#397C22×C8311yescharacteristic
831#397C22×C8311yescharacteristic
832#397C22×C8311yescharacteristic
833#397C22×C8311yescharacteristic
834#397C22×C8311yescharacteristic
835#396C22×C8311yescharacteristic
836#396C22×C8311yescharacteristic
837#396C22×C8311yescharacteristic
838#395C22×C8311yescharacteristic
839#395C22×C8311yescharacteristic
840#395C22×C8311yescharacteristic
841#395C22×C8311yescharacteristic
842#394C22×C8311yescharacteristic
843#394C22×C8311yescharacteristic
844#394C22×C8311yescharacteristic
845#394C22×C8311yescharacteristic
846#394C22×C8311yescharacteristic
847#394C22×C8311yescharacteristic
848#394C22×C8311yescharacteristic
849#394C22×C8311yescharacteristic
850#394C22×C8311yescharacteristic
851#394C22×C8311yescharacteristic
852#394C22×C8311yescharacteristic
853#394C22×C8311yescharacteristic
854#394C22×C8311yescharacteristic
855#394C22×C8311yescharacteristic
856#393C22×C8311yescharacteristic
857#393C22×C8311yescharacteristic
858#393C22×C8311yescharacteristic
859#393C22×C8311yescharacteristic
860#392C22×C8311yescharacteristic
861#392C22×C8311yescharacteristic
862#392C22×C8311yescharacteristic
863#392C22×C8311yescharacteristic
864#391C22×C8311yescharacteristic
865#391C22×C8311yescharacteristic
866#391C22×C8311yescharacteristic
867#391C22×C8311yescharacteristic
868#391C22×C8311yescharacteristic
869#391C22×C8311yescharacteristic
870#390C22×C8311yescharacteristic
871#390C22×C8311yescharacteristic
872#390C22×C8311yescharacteristic
873#390C22×C8311yescharacteristic
874#390C22×C8311yescharacteristic
875#389C22×C8311yescharacteristic
876#389C22×C8311yescharacteristic
877#389C22×C8311yescharacteristic
878#389C22×C8311yescharacteristic
879#389C22×C8311yescharacteristic
880#388C22×C8311yescharacteristic
881#388C22×C8311yescharacteristic
882#388C22×C8311yescharacteristic
883#388C22×C8311yescharacteristic
884#388C22×C8311yescharacteristic
885#388C22×C8311yescharacteristic
886#388C22×C8311yescharacteristic
887#388C22×C8311yescharacteristic
888#388C22×C8311yescharacteristic
889#388C22×C8311yescharacteristic
890#388C22×C8311yescharacteristic
891#388C22×C8311yescharacteristic
892#388C22×C8311yescharacteristic
893#388C22×C8311yescharacteristic
894#388C22×C8311yescharacteristic
895#388C22×C8311yescharacteristic
896#388C22×C8311yescharacteristic
897#387C22×C8311yescharacteristic
898#387C22×C8311yescharacteristic
899#387C22×C8311yescharacteristic
900#387C22×C8311yescharacteristic
901#387C22×C8311yescharacteristic
902#387C22×C8311yescharacteristic
903#387C22×C8311yescharacteristic
904#387C22×C8311yescharacteristic
905#387C22×C8311yescharacteristic
906#386C22×C8311yescharacteristic
907#386C22×C8311yescharacteristic
908#386C22×C8311yescharacteristic
909#386C22×C8311yescharacteristic
910#386C22×C8311yescharacteristic
911#386C22×C8311yescharacteristic
912#386C22×C8311yescharacteristic
913#386C22×C8311yescharacteristic
914#386C22×C8311yescharacteristic
915#386C22×C8311yescharacteristic
916#386C22×C8311yescharacteristic
917#386C22×C8311yescharacteristic
918#386C22×C8311yescharacteristic
919#386C22×C8311yescharacteristic
920#386C22×C8311yescharacteristic
921#386C22×C8311yescharacteristic
922#385C22×C8311yescharacteristic
923#385C22×C8311yescharacteristic
924#385C22×C8311yescharacteristic
925#385C22×C8311yescharacteristic
926#385C22×C8311yescharacteristic
927#385C22×C8311yescharacteristic
928#385C22×C8311yescharacteristic
929#385C22×C8311yescharacteristic
930#385C22×C8311yescharacteristic
931#385C22×C8311yescharacteristic
932#385C22×C8311yescharacteristic
933#385C22×C8311yescharacteristic
934#385C22×C8311yescharacteristic
935#385C22×C8311yescharacteristic
936#383C22×C8311yescharacteristic
937#382C22×C8311yescharacteristic
938#382C22×C8311yescharacteristic
939#382C22×C8311yescharacteristic
940#381C22×C8311yescharacteristic
941#380C22×C8311yescharacteristic
942#380C22×C8311yescharacteristic
943#380C22×C8311yescharacteristic
944#380C22×C8311yescharacteristic
945C4×C4⋊C4C22×C8311yescharacteristic
946C4×C22⋊C4C22×C8311yescharacteristic
947C4×C22⋊C4C22×C8311yescharacteristic
948C4×C22⋊C4C22×C8311yescharacteristic
949C4×C22⋊C4C22×C8311yescharacteristic
950C4×C22⋊C4C22×C8311yescharacteristic
951C2×#95C22×C8311yescharacteristic
952C2×#41—24no—
953C2×#41—42no—
954C2×#41—42no—
955C22×Q8C23×C8311yescharacteristic
956C22×Q8C23×C8311yescharacteristic
957C22×Q8C23×C8311yescharacteristic
958C22×D4C23×C8311yescharacteristic
959C22×D4C23×C8311yescharacteristic
960C22×D4C23×C8311yescharacteristic
961C22×D4C23×C8311yescharacteristic
962C22×D4C23×C8311yescharacteristic
963C22×D4C23×C8311yescharacteristic
964C22×D4C23×C8311yescharacteristic
965C22×D4C23×C8311yescharacteristic
966C22×D4C23×C8311yescharacteristic
967C22×D4C23×C8311yescharacteristic
968C23×C4C23×C8311yescharacteristic
969C23×C4C23×C8311yescharacteristic
970C23×C4C23×C8311yescharacteristic
971C23×C4C23×C8311yescharacteristic
972C23×C4C23×C8311yescharacteristic
973C23×C4C23×C8311yescharacteristic
974C23×C4C23×C8311yescharacteristic
975C23×C4C23×C8311yescharacteristic
976C23×C4C23×C8311yescharacteristic
977#126—42no—
978#125—42no—
979#124—42no—
980#124—42no—
981#123—24no—
982#123—42no—
983C22⋊Q8—42no—
984C22⋊Q8—42no—
985C22⋊Q8—42no—
986C22⋊Q8—42no—
987#121—42no—
988#121—42no—
989#121—42no—
990#121—42no—
991#121—42no—
992C4×D4—24no—
993#117—42no—
994C2×C4⋊C4C23×C8311yescharacteristic
995C2×C4⋊C4C23×C8311yescharacteristic
996C2×C4⋊C4C23×C8311yescharacteristic
997C2×C4⋊C4C23×C8311yescharacteristic
998C2×C4⋊C4C23×C8311yescharacteristic
999C2×C4⋊C4C23×C8311yescharacteristic
1000C2×C4⋊C4C23×C8311yescharacteristic
1001C2×C4⋊C4C23×C8311yescharacteristic
1002C2×C4⋊C4C23×C8311yescharacteristic
1003C2×C4⋊C4C23×C8311yescharacteristic
1004C2×C4⋊C4C23×C8311yescharacteristic
1005C2×C4⋊C4C23×C8311yescharacteristic
1006C2×C4⋊C4C23×C8311yescharacteristic
1007C2×C4⋊C4C23×C8311yescharacteristic
1008C2×C4⋊C4C23×C8311yescharacteristic
1009C2×C4⋊C4C23×C8311yescharacteristic
1010C2×C4⋊C4C23×C8311yescharacteristic
1011C2×C4⋊C4C23×C8311yescharacteristic
1012C2×C4⋊C4C23×C8311yescharacteristic
1013C2×C4⋊C4C23×C8311yescharacteristic
1014C2×C4⋊C4C23×C8311yescharacteristic
1015C2×C4⋊C4C23×C8311yescharacteristic
1016C2×C4⋊C4C23×C8311yescharacteristic
1017C2×C4⋊C4C23×C8311yescharacteristic
1018C2×C4⋊C4C23×C8311yescharacteristic
1019C2×C4⋊C4C23×C8311yescharacteristic
1020C2×C4⋊C4C23×C8311yescharacteristic
1021C2×C4⋊C4C23×C8311yescharacteristic
1022C2×C4⋊C4C23×C8311yescharacteristic
1023C2×C4⋊C4C23×C8311yescharacteristic
1024C2×C4⋊C4C23×C8311yescharacteristic
1025C2×C22⋊C4C23×C8311yescharacteristic
1026C2×C22⋊C4C23×C8311yescharacteristic
1027C2×C22⋊C4C23×C8311yescharacteristic
1028C2×C22⋊C4C23×C8311yescharacteristic
1029C2×C22⋊C4C23×C8311yescharacteristic
1030C2×C22⋊C4C23×C8311yescharacteristic
1031C2×C22⋊C4C23×C8311yescharacteristic
1032C2×C22⋊C4C23×C8311yescharacteristic
1033C2×C22⋊C4C23×C8311yescharacteristic
1034C2×C22⋊C4C23×C8311yescharacteristic
1035C2×C22⋊C4C23×C8311yescharacteristic
1036C2×C22⋊C4C23×C8311yescharacteristic
1037C2×C22⋊C4C23×C8311yescharacteristic
1038C2×C22⋊C4C23×C8311yescharacteristic
1039C2×C22⋊C4C23×C8311yescharacteristic
1040C2×C22⋊C4C23×C8311yescharacteristic
1041C2×C22⋊C4C23×C8311yescharacteristic
1042C2×C22⋊C4C23×C8311yescharacteristic
1043C2×C22⋊C4C23×C8311yescharacteristic
1044C2×C22⋊C4C23×C8311yescharacteristic
1045C2×C22⋊C4C23×C8311yescharacteristic
1046C2×C22⋊C4C23×C8311yescharacteristic
1047C2×C22⋊C4C23×C8311yescharacteristic
1048C2×C22⋊C4C23×C8311yescharacteristic
1049C2×C22⋊C4C23×C8311yescharacteristic
1050C2×C22⋊C4C23×C8311yescharacteristic
1051C2×C22⋊C4C23×C8311yescharacteristic
1052C2×C22⋊C4C23×C8311yescharacteristic
1053C2×C22⋊C4C23×C8311yescharacteristic
1054C2×C22⋊C4C23×C8311yescharacteristic
1055C2×C22⋊C4C23×C8311yescharacteristic
1056C2×C22⋊C4C23×C8311yescharacteristic
1057C2×C22⋊C4C23×C8311yescharacteristic
1058C2×C22⋊C4C23×C8311yescharacteristic
1059C2×C22⋊C4C23×C8311yescharacteristic
1060C2×C22⋊C4C23×C8311yescharacteristic
1061C2×C22⋊C4C23×C8311yescharacteristic
1062C2×C22⋊C4C23×C8311yescharacteristic
1063C2×C22⋊C4C23×C8311yescharacteristic
1064C2×C22⋊C4C23×C8311yescharacteristic
1065C2×C22⋊C4C23×C8311yescharacteristic
1066C2×C22⋊C4C23×C8311yescharacteristic
1067C2×C22⋊C4C23×C8311yescharacteristic
1068C2×C22⋊C4C23×C8311yescharacteristic
1069C2×C22⋊C4C23×C8311yescharacteristic
1070C2×C22⋊C4C23×C8311yescharacteristic
1071C2×C42—42no—
1072C2×C42C23×C8311yescharacteristic
1073C2×C42C23×C8311yescharacteristic
1074C2×C42C23×C8311yescharacteristic
1075C2×C42C23×C8311yescharacteristic
1076C2×C42C23×C8311yescharacteristic
1077C2×C42C23×C8311yescharacteristic
1078C2×C42C23×C8311yescharacteristic
1079C2×C42C23×C8311yescharacteristic
1080C2×C42C23×C8311yescharacteristic
1081C2×C42C23×C8311yescharacteristic
1082#95C23×C8311yescharacteristic
1083#95C23×C8311yescharacteristic
1084#95C23×C8311yescharacteristic
1085#95C23×C8311yescharacteristic
1086#95C23×C8311yescharacteristic
1087#95C23×C8311yescharacteristic
1088#95C23×C8311yescharacteristic
1089#95C23×C8311yescharacteristic
1090#95C23×C8311yescharacteristic
1091#95C23×C8311yescharacteristic
1092#95C23×C8311yescharacteristic
1093#95C23×C8311yescharacteristic
1094#95C23×C8311yescharacteristic
1095#95C23×C8311yescharacteristic
1096#95C23×C8311yescharacteristic
1097#95C23×C8311yescharacteristic
1098#95C23×C8311yescharacteristic
1099#95C23×C8311yescharacteristic
1100#95C23×C8311yescharacteristic
1101#95C23×C8311yescharacteristic
1102#95C23×C8311yescharacteristic
1103#95C23×C8311yescharacteristic
1104#95C23×C8311yescharacteristic
1105#95C23×C8311yescharacteristic
1106#95C23×C8311yescharacteristic
1107#95C23×C8311yescharacteristic
1108#95C23×C8311yescharacteristic
1109#95C23×C8311yescharacteristic
1110#95C23×C8311yescharacteristic
1111#95C23×C8311yescharacteristic
1112#95C23×C8311yescharacteristic
1113#95C23×C8311yescharacteristic
1114#95C23×C8311yescharacteristic
1115#95C23×C8311yescharacteristic
1116#95C23×C8311yescharacteristic
1117#95C23×C8311yescharacteristic
1118#95C23×C8311yescharacteristic
1119#95C23×C8311yescharacteristic
1120#95C23×C8311yescharacteristic
1121#95C23×C8311yescharacteristic
1122#95C23×C8311yescharacteristic
1123#95C23×C8311yescharacteristic
1124#95C23×C8311yescharacteristic
1125#95C23×C8311yescharacteristic
1126#95C23×C8311yescharacteristic
1127#95C23×C8311yescharacteristic
1128C24C24×C8311yescharacteristic
1129C24C24×C8311yescharacteristic
1130C24C24×C8311yescharacteristic
1131C24C24×C8311yescharacteristic
1132C24C24×C8311yescharacteristic
1133#41—416no—
1134C2×Q8—22no—
1135C2×Q8—22no—
1136C2×Q8—22no—
1137C2×Q8—41no—
1138C2×Q8—41no—
1139C2×Q8—41no—
1140C2×Q8—41no—
1141C2×Q8—41no—
1142C2×Q8—41no—
1143C2×D4—22no—
1144C2×D4—22no—
1145C2×D4—22no—
1146C2×D4—22no—
1147C2×D4—22no—
1148C2×D4—22no—
1149C2×D4—22no—
1150C2×D4—22no—
1151C2×D4—22no—
1152C2×D4—22no—
1153C2×D4—22no—
1154C2×D4—41no—
1155C2×D4—41no—
1156C2×D4—41no—
1157C2×D4—41no—
1158C2×D4—41no—
1159C2×D4—41no—
1160C2×D4—41no—
1161C2×D4—41no—
1162C2×D4—41no—
1163C2×D4—41no—
1164C2×D4—41no—
1165C2×D4—41no—
1166C2×D4—41no—
1167C2×D4—41no—
1168C2×D4—41no—
1169C2×D4—41no—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—41no—
1173C22×C4—22no—
1174C22×C4—22no—
1175C22×C4—22no—
1176C22×C4—22no—
1177C22×C4—22no—
1178C22×C4—22no—
1179C22×C4—22no—
1180C22×C4—41no—
1181C22×C4—41no—
1182C22×C4—41no—
1183C22×C4—41no—
1184C22×C4—41no—
1185C22×C4—41no—
1186C22×C4—41no—
1187C22×C4—41no—
1188C22×C4—41no—
1189C22×C4—41no—
1190C22×C4—41no—
1191C22×C4—41no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—41no—
1198C22×C4—41no—
1199C22×C4#41×C8314yes—
1200C22×C4C24×C8311yescharacteristic
1201C22×C4C24×C8311yescharacteristic
1202C22×C4C24×C8311yescharacteristic
1203C22×C4C24×C8311yescharacteristic
1204C22×C4C24×C8311yescharacteristic
1205C22×C4C24×C8311yescharacteristic
1206C22×C4C24×C8311yescharacteristic
1207C22×C4C24×C8311yescharacteristic
1208C22×C4C24×C8311yescharacteristic
1209C22×C4C24×C8311yescharacteristic
1210C22×C4C24×C8311yescharacteristic
1211C22×C4C24×C8311yescharacteristic
1212C22×C4C24×C8311yescharacteristic
1213C22×C4C24×C8311yescharacteristic
1214C22×C4C24×C8311yescharacteristic
1215C22×C4C24×C8311yescharacteristic
1216C22×C4C24×C8311yescharacteristic
1217C22×C4C24×C8311yescharacteristic
1218C22×C4C24×C8311yescharacteristic
1219C22×C4C24×C8311yescharacteristic
1220C22×C4C24×C8311yescharacteristic
1221C22×C4C24×C8311yescharacteristic
1222C22×C4C24×C8311yescharacteristic
1223C22×C4C24×C8311yescharacteristic
1224C22×C4C24×C8311yescharacteristic
1225C22×C4C24×C8311yescharacteristic
1226C4⋊C4—22no—
1227C4⋊C4—22no—
1228C4⋊C4—22no—
1229C4⋊C4—22no—
1230C4⋊C4—22no—
1231C4⋊C4—22no—
1232C4⋊C4—22no—
1233C4⋊C4—22no—
1234C4⋊C4—22no—
1235C4⋊C4—41no—
1236C4⋊C4—41no—
1237C4⋊C4—41no—
1238C4⋊C4—41no—
1239C4⋊C4—41no—
1240C4⋊C4—41no—
1241C4⋊C4—41no—
1242C4⋊C4—41no—
1243C4⋊C4—41no—
1244C4⋊C4—41no—
1245C4⋊C4—41no—
1246C4⋊C4—41no—
1247C4⋊C4—41no—
1248C4⋊C4—41no—
1249C4⋊C4—41no—
1250C4⋊C4—41no—
1251C4⋊C4—41no—
1252C4⋊C4—41no—
1253C4⋊C4—41no—
1254C4⋊C4—41no—
1255C4⋊C4—41no—
1256C4⋊C4—41no—
1257C22⋊C4—22no—
1258C22⋊C4—22no—
1259C22⋊C4—22no—
1260C22⋊C4—22no—
1261C22⋊C4—22no—
1262C22⋊C4—22no—
1263C22⋊C4—22no—
1264C22⋊C4—22no—
1265C22⋊C4—22no—
1266C22⋊C4—22no—
1267C22⋊C4—22no—
1268C22⋊C4—22no—
1269C22⋊C4—22no—
1270C22⋊C4—22no—
1271C22⋊C4—22no—
1272C22⋊C4—22no—
1273C22⋊C4—22no—
1274C22⋊C4—41no—
1275C22⋊C4—41no—
1276C22⋊C4—41no—
1277C22⋊C4—41no—
1278C22⋊C4—41no—
1279C22⋊C4—41no—
1280C22⋊C4—41no—
1281C22⋊C4—41no—
1282C22⋊C4—41no—
1283C22⋊C4—41no—
1284C22⋊C4—41no—
1285C22⋊C4—41no—
1286C22⋊C4—41no—
1287C22⋊C4—41no—
1288C22⋊C4—41no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—41no—
1292C22⋊C4—41no—
1293C22⋊C4—41no—
1294C22⋊C4—41no—
1295C22⋊C4—41no—
1296C22⋊C4—41no—
1297C22⋊C4—41no—
1298C22⋊C4—41no—
1299C22⋊C4—41no—
1300C22⋊C4—41no—
1301C22⋊C4—41no—
1302C22⋊C4—41no—
1303C42—22no—
1304C42—22no—
1305C42—22no—
1306C42—41no—
1307C42—41no—
1308C42—41no—
1309C42—41no—
1310C42—41no—
1311C42—41no—
1312C42—41no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—21no—
1322C23—21no—
1323C23—21no—
1324C23—21no—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—21no—
1330C23—21no—
1331C23—21no—
1332C23—21no—
1333C23—21no—
1334C23—21no—
1335C23—21no—
1336C23—21no—
1337C23—21no—
1338C23—21no—
1339C23—21no—
1340C23—21no—
1341C23—21no—
1342C23—21no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23C2×#41×C8312yes—
1347C23H(5,𝔽2)×C8312yes—
1348C23C25×C8311yescharacteristic
1349Q8—44no—
1350Q8—82no—
1351Q8—82no—
1352D4—44no—
1353D4—44no—
1354D4—44no—
1355D4—44no—
1356D4—82no—
1357D4—82no—
1358D4—82no—
1359D4—82no—
1360D4—82no—
1361D4—82no—
1362C2×C4—28no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—44no—
1437C2×C4—44no—
1438C2×C4—44no—
1439C2×C4—44no—
1440C2×C4—82no—
1441C2×C4—82no—
1442C2×C4—82no—
1443C2×C4—82no—
1444C2×C4C2×#41×C8312yes—
1445C2×C4C2×#41×C8312yes—
1446C2×C4H(5,𝔽2)×C8312yes—
1447C2×C4H(5,𝔽2)×C8312yes—
1448C2×C42−1+4×C8312yes—
1449C22—22no—
1450C22—22no—
1451C22—22no—
1452C22—22no—
1453C22—22no—
1454C22—22no—
1455C22—41no—
1456C22—41no—
1457C22—41no—
1458C22—41no—
1459C22—41no—
1460C22—41no—
1461C22—41no—
1462C22—41no—
1463C22—41no—
1464C22—41no—
1465C22—41no—
1466C22—41no—
1467C22—41no—
1468C22—41no—
1469C22—41no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22—41no—
1474C22—41no—
1475C22—41no—
1476C22—41no—
1477C22—41no—
1478C22—41no—
1479C22—41no—
1480C22—41no—
1481C22—41no—
1482C22—41no—
1483C22—41no—
1484C22C22×#41×C8311yescharacteristic
1485C22C2×H(5,𝔽2)×C8311yescharacteristic
1486C22C2×H(5,𝔽2)×C8311yescharacteristic
1487C22C2×H(5,𝔽2)×C8311yescharacteristic
1488C22C2×2−1+4×C8311yescharacteristic
1489C22#585×C8311yescharacteristic
1490C22#585×C8311yescharacteristic
1491C4—22no—
1492C4—22no—
1493C4—22no—
1494C4—22no—
1495C4—22no—
1496C4—41no—
1497C4—41no—
1498C4—41no—
1499C4—41no—
1500C4—41no—
1501C4—41no—
1502C4—41no—
1503C4—41no—
1504C4—41no—
1505C4—41no—
1506C4—41no—
1507C4—41no—
1508C4—41no—
1509C4—41no—
1510C4—41no—
1511C4—41no—
1512C4—41no—
1513C4—41no—
1514C4—41no—
1515C4—41no—
1516C4—41no—
1517C2—42no—
1518C2—42no—
1519C2—81no—
1520C2—81no—
1521C2—81no—
1522C2C83×#345511yescharacteristic
1523C2C83×#349011yescharacteristic
1524C2C83×#351111yescharacteristic
1525C2C83×#354111yescharacteristic
1526C2C83×#354211yescharacteristic
1527C2C83×#355811yescharacteristic
1528C2C83×#355911yescharacteristic
subgroupG/H
center, socleC23×C83C25
commutator, Frattini, cosocleC23C25×C83
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C83 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C83×#2851C2semidirect
2. C83×#2850C2semidirect
3. C83×#2778C2semidirect
4. C83×#2763C2semidirect
5. C83×#2762C2semidirect
6. C83×#2756C2semidirect
7. C83×#2753C2semidirect
8. C83×#2728C2semidirect
9. C83×#2723C2semidirect
10. C83×#2723C2semidirect
11. C83×#2711C2semidirect
12. C83×#2708C2semidirect
13. C83×#2704C2semidirect
14. C83×#2700C2semidirect
15. C83×#2686C2semidirect
16. C83×#2676C2semidirect
17. C83×#2676C2semidirect
18. C83×#2671C2semidirect
19. C83×#2653C2semidirect
20. C83×#2649C2semidirect
21. C83×#2602C2semidirect
22. C83×#2589C2semidirect
23. C83×#2559C2semidirect
24. C83×#2549C2semidirect
25. C83×#2474C2semidirect
26. C83×#2470C2semidirect
27. C83×#2430C2semidirect
28. C83×#2407C2semidirect
29. C83×#2335C2semidirect
30. C83×#2318C2semidirect
31. C83×#2297C2semidirect
752. #36817C83direct (N × H)
765. #2851C2×C83semidirect
766. #2850C2×C83semidirect
767. #2778C2×C83semidirect
768. #2763C2×C83semidirect
769. #2762C2×C83semidirect
770. #2756C2×C83semidirect
771. #2753C2×C83semidirect
772. #2728C2×C83semidirect
773. #2723C2×C83semidirect
774. #2723C2×C83semidirect
775. #2711C2×C83semidirect
776. #2708C2×C83semidirect
777. #2704C2×C83semidirect
778. #2700C2×C83semidirect
779. #2686C2×C83semidirect
780. #2676C2×C83semidirect
781. #2676C2×C83semidirect
782. #2671C2×C83semidirect
783. #2653C2×C83semidirect
784. #2649C2×C83semidirect
785. #2602C2×C83semidirect
786. #2589C2×C83semidirect
787. #2559C2×C83semidirect
788. #2549C2×C83semidirect
789. #2474C2×C83semidirect
790. #2470C2×C83semidirect
791. #2430C2×C83semidirect
792. #2407C2×C83semidirect
793. #2335C2×C83semidirect
794. #2318C2×C83semidirect
795. #2297C2×C83semidirect
796. C83#36817direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C83×#28512
C83×#28502
C83×#27782
C83×#27632
C83×#27622
C83×#27562
C83×#27532
C83×#27282
C83×#27232
C83×#27112
C83×#27082
C83×#27042
C83×#27002
C83×#26862
C83×#26762
C83×#26712
C83×#26532
C83×#26492
C83×#26022
C83×#25892
C83×#25592
C83×#25492
C83×#24742
C83×#24702
C83×#24302
C83×#24072
C83×#23352
C83×#23182
C83×#22972
#3681783