Finite Group Databasebeta

← C83×#36820 #35264644

Subgroups — C83×#36820 #35264644

Order 21248.

1768 conjugacy classes of subgroups.

The subgroup lattice has 1498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#2853C211yesmaximal, characteristic, complemented
2C83×#2853C211yesmaximal, characteristic, complemented
3C83×#2797C211yesmaximal, characteristic, complemented
4C83×#2786C211yesmaximal, characteristic, complemented
5C83×#2761C211yesmaximal, characteristic, complemented
6C83×#2758C211yesmaximal, characteristic, complemented
7C83×#2754C211yesmaximal, characteristic, complemented
8C83×#2750C211yesmaximal, characteristic, complemented
9C83×#2749C211yesmaximal, characteristic, complemented
10C83×#2749C211yesmaximal, characteristic, complemented
11C83×#2711C211yesmaximal, characteristic, complemented
12C83×#2708C211yesmaximal, characteristic, complemented
13C83×#2703C211yesmaximal, characteristic, complemented
14C83×#2703C211yesmaximal, characteristic, complemented
15C83×#2703C211yesmaximal, characteristic, complemented
16C83×#2701C211yesmaximal, characteristic, complemented
17C83×#2690C211yesmaximal, characteristic, complemented
18C83×#2687C211yesmaximal, characteristic, complemented
19C83×#2652C211yesmaximal, characteristic, complemented
20C83×#2648C211yesmaximal, characteristic, complemented
21C83×#2602C211yesmaximal, characteristic, complemented
22C83×#2597C211yesmaximal, characteristic, complemented
23C83×#2578C211yesmaximal, characteristic, complemented
24C83×#2569C211yesmaximal, characteristic, complemented
25C83×#2475C211yesmaximal, characteristic, complemented
26C83×#2471C211yesmaximal, 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×#125×C83C2211yescharacteristic
34C2×#123×C83C2211yescharacteristic
35C2×#123×C83C2211yescharacteristic
36C2×#123×C83C2211yescharacteristic
37C2×#123×C83C2211yescharacteristic
38C2×C22⋊Q8×C83C2211yescharacteristic
39C2×#121×C83C2211yescharacteristic
40C2×#121×C83C2211yescharacteristic
41C2×#121×C83C2211yescharacteristic
42C2×C4×D4×C83C2211yescharacteristic
43C2×#117×C83C2211yescharacteristic
44C22×C42×C83C2211yescharacteristic
45#400×C83C2211yescharacteristic
46#400×C83C2211yescharacteristic
47#400×C83C2211yescharacteristic
48#400×C83C2211yescharacteristic
49#400×C83C2211yescharacteristic
50#400×C83C2211yescharacteristic
51#400×C83C2211yescharacteristic
52#400×C83C2211yescharacteristic
53#400×C83C2211yescharacteristic
54#399×C83C2211yescharacteristic
55#398×C83C2211yescharacteristic
56#398×C83C2211yescharacteristic
57#398×C83C2211yescharacteristic
58#398×C83C2211yescharacteristic
59#397×C83C2211yescharacteristic
60#397×C83C2211yescharacteristic
61#397×C83C2211yescharacteristic
62#397×C83C2211yescharacteristic
63#397×C83C2211yescharacteristic
64#397×C83C2211yescharacteristic
65#397×C83C2211yescharacteristic
66#397×C83C2211yescharacteristic
67#397×C83C2211yescharacteristic
68#397×C83C2211yescharacteristic
69#397×C83C2211yescharacteristic
70#397×C83C2211yescharacteristic
71#396×C83C2211yescharacteristic
72#396×C83C2211yescharacteristic
73#396×C83C2211yescharacteristic
74#396×C83C2211yescharacteristic
75#395×C83C2211yescharacteristic
76#394×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#393×C83C2211yescharacteristic
87#392×C83C2211yescharacteristic
88#392×C83C2211yescharacteristic
89#392×C83C2211yescharacteristic
90#392×C83C2211yescharacteristic
91#392×C83C2211yescharacteristic
92#392×C83C2211yescharacteristic
93#391×C83C2211yescharacteristic
94#391×C83C2211yescharacteristic
95#391×C83C2211yescharacteristic
96#390×C83C2211yescharacteristic
97#390×C83C2211yescharacteristic
98#390×C83C2211yescharacteristic
99#390×C83C2211yescharacteristic
100#390×C83C2211yescharacteristic
101#390×C83C2211yescharacteristic
102#390×C83C2211yescharacteristic
103#389×C83C2211yescharacteristic
104#389×C83C2211yescharacteristic
105#388×C83C2211yescharacteristic
106#388×C83C2211yescharacteristic
107#388×C83C2211yescharacteristic
108#388×C83C2211yescharacteristic
109#388×C83C2211yescharacteristic
110#388×C83C2211yescharacteristic
111#388×C83C2211yescharacteristic
112#388×C83C2211yescharacteristic
113#388×C83C2211yescharacteristic
114#388×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#387×C83C2211yescharacteristic
124#387×C83C2211yescharacteristic
125#387×C83C2211yescharacteristic
126#387×C83C2211yescharacteristic
127#387×C83C2211yescharacteristic
128#387×C83C2211yescharacteristic
129#387×C83C2211yescharacteristic
130#387×C83C2211yescharacteristic
131#387×C83C2211yescharacteristic
132#387×C83C2211yescharacteristic
133#387×C83C2211yescharacteristic
134#387×C83C2211yescharacteristic
135#387×C83C2211yescharacteristic
136#387×C83C2211yescharacteristic
137#387×C83C2211yescharacteristic
138#387×C83C2211yescharacteristic
139#386×C83C2211yescharacteristic
140#386×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#383×C83C2211yescharacteristic
170#383×C83C2211yescharacteristic
171#382×C83C2211yescharacteristic
172#381×C83C2211yescharacteristic
173#381×C83C2211yescharacteristic
174#381×C83C2211yescharacteristic
175#380×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×D4×C83C2311yescharacteristic
192C22×D4×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
201C23×C4×C83C2311yescharacteristic
202C23×C4×C83C2311yescharacteristic
203C23×C4×C83C2311yescharacteristic
204C23×C4×C83C2311yescharacteristic
205C23×C4×C83C2311yescharacteristic
206C23×C4×C83C2311yescharacteristic
207C23×C4×C83C2311yescharacteristic
208C23×C4×C83C2311yescharacteristic
209C23×C4×C83C2311yescharacteristic
210#125×C83—42no—
211#123×C83—24no—
212#123×C83—42no—
213#123×C83—42no—
214#123×C83—42no—
215C22⋊Q8×C83—42no—
216#121×C83—42no—
217#121×C83—42no—
218#121×C83—42no—
219C4×D4×C83—24no—
220#117×C83—42no—
221C2×C4⋊C4×C83C2311yescharacteristic
222C2×C4⋊C4×C83C2311yescharacteristic
223C2×C4⋊C4×C83C2311yescharacteristic
224C2×C4⋊C4×C83C2311yescharacteristic
225C2×C4⋊C4×C83C2311yescharacteristic
226C2×C4⋊C4×C83C2311yescharacteristic
227C2×C4⋊C4×C83C2311yescharacteristic
228C2×C4⋊C4×C83C2311yescharacteristic
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×C22⋊C4×C83C2311yescharacteristic
251C2×C22⋊C4×C83C2311yescharacteristic
252C2×C22⋊C4×C83C2311yescharacteristic
253C2×C22⋊C4×C83C2311yescharacteristic
254C2×C22⋊C4×C83C2311yescharacteristic
255C2×C22⋊C4×C83C2311yescharacteristic
256C2×C22⋊C4×C83C2311yescharacteristic
257C2×C22⋊C4×C83C2311yescharacteristic
258C2×C22⋊C4×C83C2311yescharacteristic
259C2×C22⋊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×C42×C83—42no—
297C2×C42×C83C2311yescharacteristic
298C2×C42×C83C2311yescharacteristic
299C2×C42×C83C2311yescharacteristic
300C2×C42×C83C2311yescharacteristic
301C2×C42×C83C2311yescharacteristic
302C2×C42×C83C2311yescharacteristic
303C2×C42×C83C2311yescharacteristic
304C2×C42×C83C2311yescharacteristic
305C2×C42×C83C2311yescharacteristic
306C2×C42×C83C2311yescharacteristic
307#95×C83C2311yescharacteristic
308#95×C83C2311yescharacteristic
309#95×C83C2311yescharacteristic
310#95×C83C2311yescharacteristic
311#95×C83C2311yescharacteristic
312#95×C83C2311yescharacteristic
313#95×C83C2311yescharacteristic
314#95×C83C2311yescharacteristic
315#95×C83C2311yescharacteristic
316#95×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
357C24×C83C2411yescharacteristic
358C24×C83C2411yescharacteristic
359C24×C83C2411yescharacteristic
360C24×C83C2411yescharacteristic
361C24×C83C2411yescharacteristic
362#41×C83—416no—
363C2×Q8×C83—22no—
364C2×Q8×C83—22no—
365C2×Q8×C83—41no—
366C2×D4×C83—22no—
367C2×D4×C83—22no—
368C2×D4×C83—22no—
369C2×D4×C83—22no—
370C2×D4×C83—22no—
371C2×D4×C83—22no—
372C2×D4×C83—22no—
373C2×D4×C83—22no—
374C2×D4×C83—22no—
375C2×D4×C83—22no—
376C2×D4×C83—41no—
377C2×D4×C83—41no—
378C2×D4×C83—41no—
379C2×D4×C83—41no—
380C2×D4×C83—41no—
381C2×D4×C83—41no—
382C2×D4×C83—41no—
383C2×D4×C83—41no—
384C2×D4×C83—41no—
385C2×D4×C83—41no—
386C2×D4×C83—41no—
387C2×D4×C83—41no—
388C2×D4×C83—41no—
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—
396C22×C4×C83—22no—
397C22×C4×C83—22no—
398C22×C4×C83—22no—
399C22×C4×C83—22no—
400C22×C4×C83—22no—
401C22×C4×C83—22no—
402C22×C4×C83—22no—
403C22×C4×C83—41no—
404C22×C4×C83—41no—
405C22×C4×C83—41no—
406C22×C4×C83—41no—
407C22×C4×C83—41no—
408C22×C4×C83—41no—
409C22×C4×C83—41no—
410C22×C4×C83—41no—
411C22×C4×C83—41no—
412C22×C4×C83—41no—
413C22×C4×C83—41no—
414C22×C4×C83—41no—
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#4114yes—
423C22×C4×C83C2411yescharacteristic
424C22×C4×C83C2411yescharacteristic
425C22×C4×C83C2411yescharacteristic
426C22×C4×C83C2411yescharacteristic
427C22×C4×C83C2411yescharacteristic
428C22×C4×C83C2411yescharacteristic
429C22×C4×C83C2411yescharacteristic
430C22×C4×C83C2411yescharacteristic
431C22×C4×C83C2411yescharacteristic
432C22×C4×C83C2411yescharacteristic
433C22×C4×C83C2411yescharacteristic
434C22×C4×C83C2411yescharacteristic
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
449C4⋊C4×C83—22no—
450C4⋊C4×C83—22no—
451C4⋊C4×C83—22no—
452C4⋊C4×C83—22no—
453C4⋊C4×C83—22no—
454C4⋊C4×C83—22no—
455C4⋊C4×C83—22no—
456C4⋊C4×C83—41no—
457C4⋊C4×C83—41no—
458C4⋊C4×C83—41no—
459C4⋊C4×C83—41no—
460C4⋊C4×C83—41no—
461C4⋊C4×C83—41no—
462C4⋊C4×C83—41no—
463C4⋊C4×C83—41no—
464C4⋊C4×C83—41no—
465C4⋊C4×C83—41no—
466C4⋊C4×C83—41no—
467C4⋊C4×C83—41no—
468C4⋊C4×C83—41no—
469C4⋊C4×C83—41no—
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—
478C22⋊C4×C83—22no—
479C22⋊C4×C83—22no—
480C22⋊C4×C83—22no—
481C22⋊C4×C83—22no—
482C22⋊C4×C83—22no—
483C22⋊C4×C83—22no—
484C22⋊C4×C83—22no—
485C22⋊C4×C83—22no—
486C22⋊C4×C83—22no—
487C22⋊C4×C83—41no—
488C22⋊C4×C83—41no—
489C22⋊C4×C83—41no—
490C22⋊C4×C83—41no—
491C22⋊C4×C83—41no—
492C22⋊C4×C83—41no—
493C22⋊C4×C83—41no—
494C22⋊C4×C83—41no—
495C22⋊C4×C83—41no—
496C22⋊C4×C83—41no—
497C22⋊C4×C83—41no—
498C22⋊C4×C83—41no—
499C22⋊C4×C83—41no—
500C22⋊C4×C83—41no—
501C22⋊C4×C83—41no—
502C22⋊C4×C83—41no—
503C22⋊C4×C83—41no—
504C22⋊C4×C83—41no—
505C22⋊C4×C83—41no—
506C22⋊C4×C83—41no—
507C22⋊C4×C83—41no—
508C22⋊C4×C83—41no—
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—
524C42×C83—22no—
525C42×C83—41no—
526C42×C83—41no—
527C42×C83—41no—
528C42×C83—41no—
529C42×C83—41no—
530C42×C83—41no—
531C42×C83—41no—
532C42×C83—41no—
533C42×C83—41no—
534C23×C83—21no—
535C23×C83—21no—
536C23×C83—21no—
537C23×C83—21no—
538C23×C83—21no—
539C23×C83—21no—
540C23×C83—21no—
541C23×C83—21no—
542C23×C83—21no—
543C23×C83—21no—
544C23×C83—21no—
545C23×C83—21no—
546C23×C83—21no—
547C23×C83—21no—
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×C83C2×#4112yes—
568C23×C83H(5,𝔽2)12yes—
569C23×C83C2511yescharacteristic
570Q8×C83—44no—
571D4×C83—44no—
572D4×C83—44no—
573D4×C83—44no—
574D4×C83—44no—
575D4×C83—82no—
576D4×C83—82no—
577D4×C83—82no—
578D4×C83—82no—
579D4×C83—82no—
580D4×C83—82no—
581C2×C4×C83—28no—
582C2×C4×C83—21no—
583C2×C4×C83—21no—
584C2×C4×C83—21no—
585C2×C4×C83—21no—
586C2×C4×C83—21no—
587C2×C4×C83—21no—
588C2×C4×C83—21no—
589C2×C4×C83—21no—
590C2×C4×C83—21no—
591C2×C4×C83—21no—
592C2×C4×C83—21no—
593C2×C4×C83—21no—
594C2×C4×C83—21no—
595C2×C4×C83—21no—
596C2×C4×C83—21no—
597C2×C4×C83—21no—
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—44no—
658C2×C4×C83—44no—
659C2×C4×C83—44no—
660C2×C4×C83—44no—
661C2×C4×C83—82no—
662C2×C4×C83—82no—
663C2×C4×C83—82no—
664C2×C4×C83—82no—
665C2×C4×C83C2×#4112yes—
666C2×C4×C83C2×#4112yes—
667C2×C4×C83H(5,𝔽2)12yes—
668C22×C83—22no—
669C22×C83—22no—
670C22×C83—22no—
671C22×C83—22no—
672C22×C83—22no—
673C22×C83—22no—
674C22×C83—41no—
675C22×C83—41no—
676C22×C83—41no—
677C22×C83—41no—
678C22×C83—41no—
679C22×C83—41no—
680C22×C83—41no—
681C22×C83—41no—
682C22×C83—41no—
683C22×C83—41no—
684C22×C83—41no—
685C22×C83—41no—
686C22×C83—41no—
687C22×C83—41no—
688C22×C83—41no—
689C22×C83—41no—
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×C83C22×#4111yescharacteristic
704C22×C83C2×H(5,𝔽2)11yescharacteristic
705C22×C83C2×H(5,𝔽2)11yescharacteristic
706C22×C83#58511yescharacteristic
707C22×C83#58511yescharacteristic
708C22×C83#58511yescharacteristic
709C22×C83#58511yescharacteristic
710C4×C83—22no—
711C4×C83—22no—
712C4×C83—22no—
713C4×C83—41no—
714C4×C83—41no—
715C4×C83—41no—
716C4×C83—41no—
717C4×C83—41no—
718C4×C83—41no—
719C4×C83—41no—
720C4×C83—41no—
721C4×C83—41no—
722C4×C83—41no—
723C4×C83—41no—
724C4×C83—41no—
725C4×C83—41no—
726C4×C83—41no—
727C4×C83—41no—
728C4×C83—41no—
729C4×C83—41no—
730C4×C83—41no—
731C4×C83—41no—
732C4×C83—41no—
733C4×C83—41no—
734C4×C83—41no—
735C4×C83—41no—
736#36820C8311yesmaximal, characteristic, direct product factor, Sylow
737C2×C83—42no—
738C2×C83—42no—
739C2×C83—81no—
740C2×C83—81no—
741C2×C83—81no—
742C2×C83#345511yescharacteristic
743C2×C83#349011yescharacteristic
744C2×C83#351211yescharacteristic
745C2×C83#353311yescharacteristic
746C2×C83#353311yescharacteristic
747C2×C83#356211yescharacteristic
748C2×C83#356211yescharacteristic
749#2853C2×C8311yescharacteristic, complemented
750#2853C2×C8311yescharacteristic, complemented
751#2797C2×C8311yescharacteristic, complemented
752#2786C2×C8311yescharacteristic, complemented
753#2761C2×C8311yescharacteristic, complemented
754#2758C2×C8311yescharacteristic, complemented
755#2754C2×C8311yescharacteristic, complemented
756#2750C2×C8311yescharacteristic, complemented
757#2749C2×C8311yescharacteristic, complemented
758#2749C2×C8311yescharacteristic, complemented
759#2711C2×C8311yescharacteristic, complemented
760#2708C2×C8311yescharacteristic, complemented
761#2703C2×C8311yescharacteristic, complemented
762#2703C2×C8311yescharacteristic, complemented
763#2703C2×C8311yescharacteristic, complemented
764#2701C2×C8311yescharacteristic, complemented
765#2690C2×C8311yescharacteristic, complemented
766#2687C2×C8311yescharacteristic, complemented
767#2652C2×C8311yescharacteristic, complemented
768#2648C2×C8311yescharacteristic, complemented
769#2602C2×C8311yescharacteristic, complemented
770#2597C2×C8311yescharacteristic, complemented
771#2578C2×C8311yescharacteristic, complemented
772#2569C2×C8311yescharacteristic, complemented
773#2475C2×C8311yescharacteristic, complemented
774#2471C2×C8311yescharacteristic, complemented
775#2430C2×C8311yescharacteristic, complemented
776#2407C2×C8311yescharacteristic, complemented
777#2335C2×C8311yescharacteristic, complemented
778#2318C2×C8311yescharacteristic, complemented
779#2297C2×C8311yescharacteristic, complemented
780C83#3682011yescharacteristic, direct product factor, Sylow
781C22×#41C22×C8311yescharacteristic
782C2×#125C22×C8311yescharacteristic
783C2×#123C22×C8311yescharacteristic
784C2×#123C22×C8311yescharacteristic
785C2×#123C22×C8311yescharacteristic
786C2×#123C22×C8311yescharacteristic
787C2×C22⋊Q8C22×C8311yescharacteristic
788C2×#121C22×C8311yescharacteristic
789C2×#121C22×C8311yescharacteristic
790C2×#121C22×C8311yescharacteristic
791C2×C4×D4C22×C8311yescharacteristic
792C2×#117C22×C8311yescharacteristic
793C22×C42C22×C8311yescharacteristic
794#400C22×C8311yescharacteristic
795#400C22×C8311yescharacteristic
796#400C22×C8311yescharacteristic
797#400C22×C8311yescharacteristic
798#400C22×C8311yescharacteristic
799#400C22×C8311yescharacteristic
800#400C22×C8311yescharacteristic
801#400C22×C8311yescharacteristic
802#400C22×C8311yescharacteristic
803#399C22×C8311yescharacteristic
804#398C22×C8311yescharacteristic
805#398C22×C8311yescharacteristic
806#398C22×C8311yescharacteristic
807#398C22×C8311yescharacteristic
808#397C22×C8311yescharacteristic
809#397C22×C8311yescharacteristic
810#397C22×C8311yescharacteristic
811#397C22×C8311yescharacteristic
812#397C22×C8311yescharacteristic
813#397C22×C8311yescharacteristic
814#397C22×C8311yescharacteristic
815#397C22×C8311yescharacteristic
816#397C22×C8311yescharacteristic
817#397C22×C8311yescharacteristic
818#397C22×C8311yescharacteristic
819#397C22×C8311yescharacteristic
820#396C22×C8311yescharacteristic
821#396C22×C8311yescharacteristic
822#396C22×C8311yescharacteristic
823#396C22×C8311yescharacteristic
824#395C22×C8311yescharacteristic
825#394C22×C8311yescharacteristic
826#394C22×C8311yescharacteristic
827#394C22×C8311yescharacteristic
828#394C22×C8311yescharacteristic
829#394C22×C8311yescharacteristic
830#394C22×C8311yescharacteristic
831#394C22×C8311yescharacteristic
832#394C22×C8311yescharacteristic
833#394C22×C8311yescharacteristic
834#394C22×C8311yescharacteristic
835#393C22×C8311yescharacteristic
836#392C22×C8311yescharacteristic
837#392C22×C8311yescharacteristic
838#392C22×C8311yescharacteristic
839#392C22×C8311yescharacteristic
840#392C22×C8311yescharacteristic
841#392C22×C8311yescharacteristic
842#391C22×C8311yescharacteristic
843#391C22×C8311yescharacteristic
844#391C22×C8311yescharacteristic
845#390C22×C8311yescharacteristic
846#390C22×C8311yescharacteristic
847#390C22×C8311yescharacteristic
848#390C22×C8311yescharacteristic
849#390C22×C8311yescharacteristic
850#390C22×C8311yescharacteristic
851#390C22×C8311yescharacteristic
852#389C22×C8311yescharacteristic
853#389C22×C8311yescharacteristic
854#388C22×C8311yescharacteristic
855#388C22×C8311yescharacteristic
856#388C22×C8311yescharacteristic
857#388C22×C8311yescharacteristic
858#388C22×C8311yescharacteristic
859#388C22×C8311yescharacteristic
860#388C22×C8311yescharacteristic
861#388C22×C8311yescharacteristic
862#388C22×C8311yescharacteristic
863#388C22×C8311yescharacteristic
864#388C22×C8311yescharacteristic
865#388C22×C8311yescharacteristic
866#388C22×C8311yescharacteristic
867#388C22×C8311yescharacteristic
868#388C22×C8311yescharacteristic
869#388C22×C8311yescharacteristic
870#388C22×C8311yescharacteristic
871#388C22×C8311yescharacteristic
872#387C22×C8311yescharacteristic
873#387C22×C8311yescharacteristic
874#387C22×C8311yescharacteristic
875#387C22×C8311yescharacteristic
876#387C22×C8311yescharacteristic
877#387C22×C8311yescharacteristic
878#387C22×C8311yescharacteristic
879#387C22×C8311yescharacteristic
880#387C22×C8311yescharacteristic
881#387C22×C8311yescharacteristic
882#387C22×C8311yescharacteristic
883#387C22×C8311yescharacteristic
884#387C22×C8311yescharacteristic
885#387C22×C8311yescharacteristic
886#387C22×C8311yescharacteristic
887#387C22×C8311yescharacteristic
888#386C22×C8311yescharacteristic
889#386C22×C8311yescharacteristic
890#386C22×C8311yescharacteristic
891#386C22×C8311yescharacteristic
892#386C22×C8311yescharacteristic
893#386C22×C8311yescharacteristic
894#386C22×C8311yescharacteristic
895#386C22×C8311yescharacteristic
896#386C22×C8311yescharacteristic
897#386C22×C8311yescharacteristic
898#386C22×C8311yescharacteristic
899#386C22×C8311yescharacteristic
900#386C22×C8311yescharacteristic
901#386C22×C8311yescharacteristic
902#386C22×C8311yescharacteristic
903#386C22×C8311yescharacteristic
904#386C22×C8311yescharacteristic
905#386C22×C8311yescharacteristic
906#385C22×C8311yescharacteristic
907#385C22×C8311yescharacteristic
908#385C22×C8311yescharacteristic
909#385C22×C8311yescharacteristic
910#385C22×C8311yescharacteristic
911#385C22×C8311yescharacteristic
912#385C22×C8311yescharacteristic
913#385C22×C8311yescharacteristic
914#385C22×C8311yescharacteristic
915#385C22×C8311yescharacteristic
916#385C22×C8311yescharacteristic
917#385C22×C8311yescharacteristic
918#383C22×C8311yescharacteristic
919#383C22×C8311yescharacteristic
920#382C22×C8311yescharacteristic
921#381C22×C8311yescharacteristic
922#381C22×C8311yescharacteristic
923#381C22×C8311yescharacteristic
924#380C22×C8311yescharacteristic
925#380C22×C8311yescharacteristic
926#380C22×C8311yescharacteristic
927#380C22×C8311yescharacteristic
928#380C22×C8311yescharacteristic
929C4×C4⋊C4C22×C8311yescharacteristic
930C4×C22⋊C4C22×C8311yescharacteristic
931C4×C22⋊C4C22×C8311yescharacteristic
932C4×C22⋊C4C22×C8311yescharacteristic
933C4×C22⋊C4C22×C8311yescharacteristic
934C4×C22⋊C4C22×C8311yescharacteristic
935C2×#95C22×C8311yescharacteristic
936C2×#41—24no—
937C2×#41—42no—
938C2×#41—42no—
939C22×Q8C23×C8311yescharacteristic
940C22×D4C23×C8311yescharacteristic
941C22×D4C23×C8311yescharacteristic
942C22×D4C23×C8311yescharacteristic
943C22×D4C23×C8311yescharacteristic
944C22×D4C23×C8311yescharacteristic
945C22×D4C23×C8311yescharacteristic
946C22×D4C23×C8311yescharacteristic
947C22×D4C23×C8311yescharacteristic
948C22×D4C23×C8311yescharacteristic
949C22×D4C23×C8311yescharacteristic
950C23×C4C23×C8311yescharacteristic
951C23×C4C23×C8311yescharacteristic
952C23×C4C23×C8311yescharacteristic
953C23×C4C23×C8311yescharacteristic
954C23×C4C23×C8311yescharacteristic
955C23×C4C23×C8311yescharacteristic
956C23×C4C23×C8311yescharacteristic
957C23×C4C23×C8311yescharacteristic
958C23×C4C23×C8311yescharacteristic
959#125—42no—
960#123—24no—
961#123—42no—
962#123—42no—
963#123—42no—
964C22⋊Q8—42no—
965#121—42no—
966#121—42no—
967#121—42no—
968C4×D4—24no—
969#117—42no—
970C2×C4⋊C4C23×C8311yescharacteristic
971C2×C4⋊C4C23×C8311yescharacteristic
972C2×C4⋊C4C23×C8311yescharacteristic
973C2×C4⋊C4C23×C8311yescharacteristic
974C2×C4⋊C4C23×C8311yescharacteristic
975C2×C4⋊C4C23×C8311yescharacteristic
976C2×C4⋊C4C23×C8311yescharacteristic
977C2×C4⋊C4C23×C8311yescharacteristic
978C2×C4⋊C4C23×C8311yescharacteristic
979C2×C4⋊C4C23×C8311yescharacteristic
980C2×C4⋊C4C23×C8311yescharacteristic
981C2×C4⋊C4C23×C8311yescharacteristic
982C2×C4⋊C4C23×C8311yescharacteristic
983C2×C4⋊C4C23×C8311yescharacteristic
984C2×C4⋊C4C23×C8311yescharacteristic
985C2×C4⋊C4C23×C8311yescharacteristic
986C2×C4⋊C4C23×C8311yescharacteristic
987C2×C4⋊C4C23×C8311yescharacteristic
988C2×C4⋊C4C23×C8311yescharacteristic
989C2×C4⋊C4C23×C8311yescharacteristic
990C2×C4⋊C4C23×C8311yescharacteristic
991C2×C4⋊C4C23×C8311yescharacteristic
992C2×C4⋊C4C23×C8311yescharacteristic
993C2×C4⋊C4C23×C8311yescharacteristic
994C2×C4⋊C4C23×C8311yescharacteristic
995C2×C4⋊C4C23×C8311yescharacteristic
996C2×C4⋊C4C23×C8311yescharacteristic
997C2×C4⋊C4C23×C8311yescharacteristic
998C2×C4⋊C4C23×C8311yescharacteristic
999C2×C22⋊C4C23×C8311yescharacteristic
1000C2×C22⋊C4C23×C8311yescharacteristic
1001C2×C22⋊C4C23×C8311yescharacteristic
1002C2×C22⋊C4C23×C8311yescharacteristic
1003C2×C22⋊C4C23×C8311yescharacteristic
1004C2×C22⋊C4C23×C8311yescharacteristic
1005C2×C22⋊C4C23×C8311yescharacteristic
1006C2×C22⋊C4C23×C8311yescharacteristic
1007C2×C22⋊C4C23×C8311yescharacteristic
1008C2×C22⋊C4C23×C8311yescharacteristic
1009C2×C22⋊C4C23×C8311yescharacteristic
1010C2×C22⋊C4C23×C8311yescharacteristic
1011C2×C22⋊C4C23×C8311yescharacteristic
1012C2×C22⋊C4C23×C8311yescharacteristic
1013C2×C22⋊C4C23×C8311yescharacteristic
1014C2×C22⋊C4C23×C8311yescharacteristic
1015C2×C22⋊C4C23×C8311yescharacteristic
1016C2×C22⋊C4C23×C8311yescharacteristic
1017C2×C22⋊C4C23×C8311yescharacteristic
1018C2×C22⋊C4C23×C8311yescharacteristic
1019C2×C22⋊C4C23×C8311yescharacteristic
1020C2×C22⋊C4C23×C8311yescharacteristic
1021C2×C22⋊C4C23×C8311yescharacteristic
1022C2×C22⋊C4C23×C8311yescharacteristic
1023C2×C22⋊C4C23×C8311yescharacteristic
1024C2×C22⋊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×C42—42no—
1046C2×C42C23×C8311yescharacteristic
1047C2×C42C23×C8311yescharacteristic
1048C2×C42C23×C8311yescharacteristic
1049C2×C42C23×C8311yescharacteristic
1050C2×C42C23×C8311yescharacteristic
1051C2×C42C23×C8311yescharacteristic
1052C2×C42C23×C8311yescharacteristic
1053C2×C42C23×C8311yescharacteristic
1054C2×C42C23×C8311yescharacteristic
1055C2×C42C23×C8311yescharacteristic
1056#95C23×C8311yescharacteristic
1057#95C23×C8311yescharacteristic
1058#95C23×C8311yescharacteristic
1059#95C23×C8311yescharacteristic
1060#95C23×C8311yescharacteristic
1061#95C23×C8311yescharacteristic
1062#95C23×C8311yescharacteristic
1063#95C23×C8311yescharacteristic
1064#95C23×C8311yescharacteristic
1065#95C23×C8311yescharacteristic
1066#95C23×C8311yescharacteristic
1067#95C23×C8311yescharacteristic
1068#95C23×C8311yescharacteristic
1069#95C23×C8311yescharacteristic
1070#95C23×C8311yescharacteristic
1071#95C23×C8311yescharacteristic
1072#95C23×C8311yescharacteristic
1073#95C23×C8311yescharacteristic
1074#95C23×C8311yescharacteristic
1075#95C23×C8311yescharacteristic
1076#95C23×C8311yescharacteristic
1077#95C23×C8311yescharacteristic
1078#95C23×C8311yescharacteristic
1079#95C23×C8311yescharacteristic
1080#95C23×C8311yescharacteristic
1081#95C23×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
1106C24C24×C8311yescharacteristic
1107C24C24×C8311yescharacteristic
1108C24C24×C8311yescharacteristic
1109C24C24×C8311yescharacteristic
1110C24C24×C8311yescharacteristic
1111#41—416no—
1112C2×Q8—22no—
1113C2×Q8—22no—
1114C2×Q8—41no—
1115C2×D4—22no—
1116C2×D4—22no—
1117C2×D4—22no—
1118C2×D4—22no—
1119C2×D4—22no—
1120C2×D4—22no—
1121C2×D4—22no—
1122C2×D4—22no—
1123C2×D4—22no—
1124C2×D4—22no—
1125C2×D4—41no—
1126C2×D4—41no—
1127C2×D4—41no—
1128C2×D4—41no—
1129C2×D4—41no—
1130C2×D4—41no—
1131C2×D4—41no—
1132C2×D4—41no—
1133C2×D4—41no—
1134C2×D4—41no—
1135C2×D4—41no—
1136C2×D4—41no—
1137C2×D4—41no—
1138C2×D4—41no—
1139C2×D4—41no—
1140C2×D4—41no—
1141C2×D4—41no—
1142C2×D4—41no—
1143C2×D4—41no—
1144C2×D4—41no—
1145C22×C4—22no—
1146C22×C4—22no—
1147C22×C4—22no—
1148C22×C4—22no—
1149C22×C4—22no—
1150C22×C4—22no—
1151C22×C4—22no—
1152C22×C4—41no—
1153C22×C4—41no—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4—41no—
1157C22×C4—41no—
1158C22×C4—41no—
1159C22×C4—41no—
1160C22×C4—41no—
1161C22×C4—41no—
1162C22×C4—41no—
1163C22×C4—41no—
1164C22×C4—41no—
1165C22×C4—41no—
1166C22×C4—41no—
1167C22×C4—41no—
1168C22×C4—41no—
1169C22×C4—41no—
1170C22×C4—41no—
1171C22×C4#41×C8314yes—
1172C22×C4C24×C8311yescharacteristic
1173C22×C4C24×C8311yescharacteristic
1174C22×C4C24×C8311yescharacteristic
1175C22×C4C24×C8311yescharacteristic
1176C22×C4C24×C8311yescharacteristic
1177C22×C4C24×C8311yescharacteristic
1178C22×C4C24×C8311yescharacteristic
1179C22×C4C24×C8311yescharacteristic
1180C22×C4C24×C8311yescharacteristic
1181C22×C4C24×C8311yescharacteristic
1182C22×C4C24×C8311yescharacteristic
1183C22×C4C24×C8311yescharacteristic
1184C22×C4C24×C8311yescharacteristic
1185C22×C4C24×C8311yescharacteristic
1186C22×C4C24×C8311yescharacteristic
1187C22×C4C24×C8311yescharacteristic
1188C22×C4C24×C8311yescharacteristic
1189C22×C4C24×C8311yescharacteristic
1190C22×C4C24×C8311yescharacteristic
1191C22×C4C24×C8311yescharacteristic
1192C22×C4C24×C8311yescharacteristic
1193C22×C4C24×C8311yescharacteristic
1194C22×C4C24×C8311yescharacteristic
1195C22×C4C24×C8311yescharacteristic
1196C22×C4C24×C8311yescharacteristic
1197C22×C4C24×C8311yescharacteristic
1198C4⋊C4—22no—
1199C4⋊C4—22no—
1200C4⋊C4—22no—
1201C4⋊C4—22no—
1202C4⋊C4—22no—
1203C4⋊C4—22no—
1204C4⋊C4—22no—
1205C4⋊C4—41no—
1206C4⋊C4—41no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—41no—
1214C4⋊C4—41no—
1215C4⋊C4—41no—
1216C4⋊C4—41no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—41no—
1227C22⋊C4—22no—
1228C22⋊C4—22no—
1229C22⋊C4—22no—
1230C22⋊C4—22no—
1231C22⋊C4—22no—
1232C22⋊C4—22no—
1233C22⋊C4—22no—
1234C22⋊C4—22no—
1235C22⋊C4—22no—
1236C22⋊C4—41no—
1237C22⋊C4—41no—
1238C22⋊C4—41no—
1239C22⋊C4—41no—
1240C22⋊C4—41no—
1241C22⋊C4—41no—
1242C22⋊C4—41no—
1243C22⋊C4—41no—
1244C22⋊C4—41no—
1245C22⋊C4—41no—
1246C22⋊C4—41no—
1247C22⋊C4—41no—
1248C22⋊C4—41no—
1249C22⋊C4—41no—
1250C22⋊C4—41no—
1251C22⋊C4—41no—
1252C22⋊C4—41no—
1253C22⋊C4—41no—
1254C22⋊C4—41no—
1255C22⋊C4—41no—
1256C22⋊C4—41no—
1257C22⋊C4—41no—
1258C22⋊C4—41no—
1259C22⋊C4—41no—
1260C22⋊C4—41no—
1261C22⋊C4—41no—
1262C22⋊C4—41no—
1263C22⋊C4—41no—
1264C22⋊C4—41no—
1265C22⋊C4—41no—
1266C22⋊C4—41no—
1267C22⋊C4—41no—
1268C22⋊C4—41no—
1269C22⋊C4—41no—
1270C22⋊C4—41no—
1271C22⋊C4—41no—
1272C22⋊C4—41no—
1273C42—22no—
1274C42—41no—
1275C42—41no—
1276C42—41no—
1277C42—41no—
1278C42—41no—
1279C42—41no—
1280C42—41no—
1281C42—41no—
1282C42—41no—
1283C23—21no—
1284C23—21no—
1285C23—21no—
1286C23—21no—
1287C23—21no—
1288C23—21no—
1289C23—21no—
1290C23—21no—
1291C23—21no—
1292C23—21no—
1293C23—21no—
1294C23—21no—
1295C23—21no—
1296C23—21no—
1297C23—21no—
1298C23—21no—
1299C23—21no—
1300C23—21no—
1301C23—21no—
1302C23—21no—
1303C23—21no—
1304C23—21no—
1305C23—21no—
1306C23—21no—
1307C23—21no—
1308C23—21no—
1309C23—21no—
1310C23—21no—
1311C23—21no—
1312C23—21no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23C2×#41×C8312yes—
1317C23H(5,𝔽2)×C8312yes—
1318C23C25×C8311yescharacteristic
1319Q8—44no—
1320D4—44no—
1321D4—44no—
1322D4—44no—
1323D4—44no—
1324D4—82no—
1325D4—82no—
1326D4—82no—
1327D4—82no—
1328D4—82no—
1329D4—82no—
1330C2×C4—28no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
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—44no—
1407C2×C4—44no—
1408C2×C4—44no—
1409C2×C4—44no—
1410C2×C4—82no—
1411C2×C4—82no—
1412C2×C4—82no—
1413C2×C4—82no—
1414C2×C4C2×#41×C8312yes—
1415C2×C4C2×#41×C8312yes—
1416C2×C4H(5,𝔽2)×C8312yes—
1417C22—22no—
1418C22—22no—
1419C22—22no—
1420C22—22no—
1421C22—22no—
1422C22—22no—
1423C22—41no—
1424C22—41no—
1425C22—41no—
1426C22—41no—
1427C22—41no—
1428C22—41no—
1429C22—41no—
1430C22—41no—
1431C22—41no—
1432C22—41no—
1433C22—41no—
1434C22—41no—
1435C22—41no—
1436C22—41no—
1437C22—41no—
1438C22—41no—
1439C22—41no—
1440C22—41no—
1441C22—41no—
1442C22—41no—
1443C22—41no—
1444C22—41no—
1445C22—41no—
1446C22—41no—
1447C22—41no—
1448C22—41no—
1449C22—41no—
1450C22—41no—
1451C22—41no—
1452C22C22×#41×C8311yescharacteristic
1453C22C2×H(5,𝔽2)×C8311yescharacteristic
1454C22C2×H(5,𝔽2)×C8311yescharacteristic
1455C22#585×C8311yescharacteristic
1456C22#585×C8311yescharacteristic
1457C22#585×C8311yescharacteristic
1458C22#585×C8311yescharacteristic
1459C4—22no—
1460C4—22no—
1461C4—22no—
1462C4—41no—
1463C4—41no—
1464C4—41no—
1465C4—41no—
1466C4—41no—
1467C4—41no—
1468C4—41no—
1469C4—41no—
1470C4—41no—
1471C4—41no—
1472C4—41no—
1473C4—41no—
1474C4—41no—
1475C4—41no—
1476C4—41no—
1477C4—41no—
1478C4—41no—
1479C4—41no—
1480C4—41no—
1481C4—41no—
1482C4—41no—
1483C4—41no—
1484C4—41no—
1485C2—42no—
1486C2—42no—
1487C2—81no—
1488C2—81no—
1489C2—81no—
1490C2C83×#345511yescharacteristic
1491C2C83×#349011yescharacteristic
1492C2C83×#351211yescharacteristic
1493C2C83×#353311yescharacteristic
1494C2C83×#353311yescharacteristic
1495C2C83×#356211yescharacteristic
1496C2C83×#356211yescharacteristic
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×#2853C2semidirect
2. C83×#2853C2semidirect
3. C83×#2797C2semidirect
4. C83×#2786C2semidirect
5. C83×#2761C2semidirect
6. C83×#2758C2semidirect
7. C83×#2754C2semidirect
8. C83×#2750C2semidirect
9. C83×#2749C2semidirect
10. C83×#2749C2semidirect
11. C83×#2711C2semidirect
12. C83×#2708C2semidirect
13. C83×#2703C2semidirect
14. C83×#2703C2semidirect
15. C83×#2703C2semidirect
16. C83×#2701C2semidirect
17. C83×#2690C2semidirect
18. C83×#2687C2semidirect
19. C83×#2652C2semidirect
20. C83×#2648C2semidirect
21. C83×#2602C2semidirect
22. C83×#2597C2semidirect
23. C83×#2578C2semidirect
24. C83×#2569C2semidirect
25. C83×#2475C2semidirect
26. C83×#2471C2semidirect
27. C83×#2430C2semidirect
28. C83×#2407C2semidirect
29. C83×#2335C2semidirect
30. C83×#2318C2semidirect
31. C83×#2297C2semidirect
736. #36820C83direct (N × H)
749. #2853C2×C83semidirect
750. #2853C2×C83semidirect
751. #2797C2×C83semidirect
752. #2786C2×C83semidirect
753. #2761C2×C83semidirect
754. #2758C2×C83semidirect
755. #2754C2×C83semidirect
756. #2750C2×C83semidirect
757. #2749C2×C83semidirect
758. #2749C2×C83semidirect
759. #2711C2×C83semidirect
760. #2708C2×C83semidirect
761. #2703C2×C83semidirect
762. #2703C2×C83semidirect
763. #2703C2×C83semidirect
764. #2701C2×C83semidirect
765. #2690C2×C83semidirect
766. #2687C2×C83semidirect
767. #2652C2×C83semidirect
768. #2648C2×C83semidirect
769. #2602C2×C83semidirect
770. #2597C2×C83semidirect
771. #2578C2×C83semidirect
772. #2569C2×C83semidirect
773. #2475C2×C83semidirect
774. #2471C2×C83semidirect
775. #2430C2×C83semidirect
776. #2407C2×C83semidirect
777. #2335C2×C83semidirect
778. #2318C2×C83semidirect
779. #2297C2×C83semidirect
780. C83#36820direct (N × H)

Maximal subgroups

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

subgroupindex
C83×#28532
C83×#27972
C83×#27862
C83×#27612
C83×#27582
C83×#27542
C83×#27502
C83×#27492
C83×#27112
C83×#27082
C83×#27032
C83×#27012
C83×#26902
C83×#26872
C83×#26522
C83×#26482
C83×#26022
C83×#25972
C83×#25782
C83×#25692
C83×#24752
C83×#24712
C83×#24302
C83×#24072
C83×#23352
C83×#23182
C83×#22972
#3682083