Finite Group Databasebeta

← #35569504

Subgroups — #35569504

Order 21248.

2292 conjugacy classes of subgroups.

The subgroup lattice has 1522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128378C211yesmaximal, characteristic
2#24910653C211yesmaximal, characteristic, complemented
3#24910635C211yesmaximal, characteristic, complemented
4#24910609C211yesmaximal, characteristic, complemented
5#24910589C211yesmaximal, characteristic, complemented
6#24910542C211yesmaximal, characteristic, complemented
7#24910450C211yesmaximal, characteristic, complemented
8#24910448C211yesmaximal, characteristic, complemented
9#24910441C211yesmaximal, characteristic
10#24910407C211yesmaximal, characteristic, complemented
11#24910372C211yesmaximal, characteristic, complemented
12#24910345C211yesmaximal, characteristic, complemented
13#24910318C211yesmaximal, characteristic, complemented
14#24910307C211yesmaximal, characteristic, complemented
15#24910305C211yesmaximal, characteristic, complemented
16#24910252C211yesmaximal, characteristic, complemented
17#24910246C211yesmaximal, characteristic, complemented
18#24910241C211yesmaximal, characteristic, complemented
19#24910231C211yesmaximal, characteristic, complemented
20#24910177C211yesmaximal, characteristic, complemented
21#24910147C211yesmaximal, characteristic, complemented
22#24910136C211yesmaximal, characteristic, complemented
23#24910116C211yesmaximal, characteristic
24#24910092C211yesmaximal, characteristic, complemented
25#24910085C211yesmaximal, characteristic, complemented
26#24910076C211yesmaximal, characteristic, complemented
27#24910067C211yesmaximal, characteristic, complemented
28#24910001C211yesmaximal, characteristic, complemented
29#24909901C211yesmaximal, characteristic, complemented
30#388×D83C211yesmaximal, characteristic, complemented
31C83×#2378C211yesmaximal, characteristic, complemented
32#19128378C4116yescomplemented
33C2×#14581787C2211yescharacteristic
34C2×#14581787C2211yescharacteristic
35C2×#14581781C2211yescharacteristic
36C2×#14581777C2211yescharacteristic
37C2×#14581777C2211yescharacteristic
38C2×#14581776C2211yescharacteristic
39C2×#14581768C2211yescharacteristic
40C2×#14581762C2211yescharacteristic
41C2×Q8×Dic83C2211yescharacteristic, complemented
42C2×C4×D332C2211yescharacteristic
43C2×#14581754C2211yescharacteristic
44C2×#14581754C2211yescharacteristic
45C2×#14581754C2211yescharacteristic
46C2×C4×C22⋊D83C2211yescharacteristic
47C2×#14581751C2211yescharacteristic
48C2×#14581750C2211yescharacteristic
49C2×#14581750C2211yescharacteristic, complemented
50C2×#14581749C2211yescharacteristic
51C2×#14581748C2211yescharacteristic
52C2×C4⋊C4×D83C2211yescharacteristic
53C22×(C2×D83)⋊C4C2211yescharacteristic
54C2×C22⋊C4×D83C2211yescharacteristic
55C2×C22⋊C4×D83C2211yescharacteristic
56C2×C22⋊C4×D83C2211yescharacteristic
57C2×C22⋊C4×D83C2211yescharacteristic
58C2×C42×D83C2211yescharacteristic
59#19127608C2211yescharacteristic, complemented
60#19127603C2211yescharacteristic
61#19127601C2211yescharacteristic
62#19127601C2211yescharacteristic
63#19127600C2211yescharacteristic, complemented
64#19127600C2211yescharacteristic, complemented
65#19127600C2211yescharacteristic, complemented
66#19127599C2211yescharacteristic, complemented
67#19127599C2211yescharacteristic, complemented
68#19127598C2211yescharacteristic, complemented
69#19127597C2211yescharacteristic, complemented
70#19127596C2211yescharacteristic, complemented
71#19127595C2211yescharacteristic
72#19127595C2211yescharacteristic
73#19127594C2211yescharacteristic
74#19127594C2211yescharacteristic
75#19127594C2211yescharacteristic
76#19127594C2211yescharacteristic
77#19127593C2211yescharacteristic
78#19127593C2211yescharacteristic
79#19127593C2211yescharacteristic
80#19127593C2211yescharacteristic, complemented
81#19127592C2211yescharacteristic
82#19127592C2211yescharacteristic, complemented
83#19127591C2211yescharacteristic
84#19127591C2211yescharacteristic
85#19127590C2211yescharacteristic
86#19127590C2211yescharacteristic
87#19127590C2211yescharacteristic
88#19127590C2211yescharacteristic
89#19127590C2211yescharacteristic, complemented
90#19127590C2211yescharacteristic, complemented
91#19127590C2211yescharacteristic, complemented
92#19127590C2211yescharacteristic, complemented
93#19127589C2211yescharacteristic
94#19127589C2211yescharacteristic
95#19127588C2211yescharacteristic, complemented
96#19127588C2211yescharacteristic, complemented
97#19127588C2211yescharacteristic, complemented
98#19127587C2211yescharacteristic, complemented
99#19127587C2211yescharacteristic, complemented
100#19127586C2211yescharacteristic, complemented
101#19127586C2211yescharacteristic, complemented
102#19127585C2211yescharacteristic, complemented
103#19127584C2211yescharacteristic, complemented
104#19127584C2211yescharacteristic, complemented
105#19127583C2211yescharacteristic, complemented
106#19127582C2211yescharacteristic, complemented
107#19127579C2211yescharacteristic
108#19127579C2211yescharacteristic
109#19127579C2211yescharacteristic
110#19127579C2211yescharacteristic
111#19127577C2211yescharacteristic
112#19127577C2211yescharacteristic
113#19127575C2211yescharacteristic
114#19127575C2211yescharacteristic
115#19127575C2211yescharacteristic
116#19127575C2211yescharacteristic
117#19127575C2211yescharacteristic
118#19127575C2211yescharacteristic
119#19127575C2211yescharacteristic
120#19127575C2211yescharacteristic
121#19127575C2211yescharacteristic
122#19127575C2211yescharacteristic, complemented
123#19127575C2211yescharacteristic, complemented
124#19127575C2211yescharacteristic, complemented
125#19127572C2211yescharacteristic
126#19127572C2211yescharacteristic
127#19127572C2211yescharacteristic
128#19127572C2211yescharacteristic
129#19127572C2211yescharacteristic
130#19127572C2211yescharacteristic
131#19127572C2211yescharacteristic, complemented
132#19127572C2211yescharacteristic, complemented
133#19127570C2211yescharacteristic, complemented
134#19127570C2211yescharacteristic, complemented
135#19127568C2211yescharacteristic, complemented
136#19127566C2211yescharacteristic, complemented
137#19127565C2211yescharacteristic, complemented
138#19127565C2211yescharacteristic, complemented
139#19127565C2211yescharacteristic, complemented
140#19127563C2211yescharacteristic
141#19127561C2211yescharacteristic
142#19127559C2211yescharacteristic
143#19127559C2211yescharacteristic
144#19127559C2211yescharacteristic
145#19127558C2211yescharacteristic
146#19127558C2211yescharacteristic, complemented
147#19127556C2211yescharacteristic
148C4⋊C4×Dic83C2211yescharacteristic, complemented
149C4⋊C4×Dic83C2211yescharacteristic, complemented
150C4⋊C4×Dic83C2211yescharacteristic, complemented
151C4×Dic83⋊C4C2211yescharacteristic, complemented
152C4×Dic83⋊C4C2211yescharacteristic, complemented
153#19127552C2211yescharacteristic, complemented
154#19127552C2211yescharacteristic, complemented
155#19127552C2211yescharacteristic, complemented
156#19127552C2211yescharacteristic, complemented
157C22⋊C4×Dic83C2211yescharacteristic
158C4×(C2×D83)⋊C4C2211yescharacteristic
159C4×(C2×D83)⋊C4C2211yescharacteristic
160C4×(C2×D83)⋊C4C2211yescharacteristic
161C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
162#19127548C2211yescharacteristic
163#19127548C2211yescharacteristic
164#19127548C2211yescharacteristic
165#19127548C2211yescharacteristic
166#19127548C2211yescharacteristic
167#19127548C2211yescharacteristic, complemented
168#19127547C2211yescharacteristic, complemented
169#19127546C2211yescharacteristic, complemented
170#95×D83C2211yescharacteristic
171#95×D83C2211yescharacteristic
172#95×D83C2211yescharacteristic, complemented
173C2×C22⋊Q8×C83C2211yescharacteristic
174#391×C83C2211yescharacteristic, complemented
175#391×C83C2211yescharacteristic, complemented
176#389×C83C2211yescharacteristic, complemented
177#389×C83C2211yescharacteristic, complemented
178#388×C83C2211yescharacteristic
179#388×C83C2211yescharacteristic
180#388×C83C2211yescharacteristic
181#388×C83C2211yescharacteristic
182#387×C83C2211yescharacteristic, complemented
183#387×C83C2211yescharacteristic, complemented
184#387×C83C2211yescharacteristic, complemented
185#387×C83C2211yescharacteristic, complemented
186#381×C83C2211yescharacteristic
187#380×C83C2211yescharacteristic
188C24×D83C2311yescharacteristic
189C22×D332C2311yescharacteristic
190C22×D332C2311yescharacteristic
191C22×C22⋊D83C2311yescharacteristic
192C23×Dic83C2311yescharacteristic
193C22×C4×D83C2311yescharacteristic
194C22×C4×D83C2311yescharacteristic
195C22×C4×D83C2311yescharacteristic
196C22×C4×D83C2311yescharacteristic
197C22×C4×D83C2311yescharacteristic
198C22×C4×D83C2311yescharacteristic
199C22×C4×D83C2311yescharacteristic
200C22×C4×D83C2311yescharacteristic
201C22×C4×D83C2311yescharacteristic
202C22×C4×D83C2311yescharacteristic
203C22×C4×D83C2311yescharacteristic
204#14581787C2×C418yescomplemented
205#14581787C2×C418yescomplemented
206#14581781C2×C418yescomplemented
207#14581777C2×C418yescomplemented
208#14581777C2×C418yescomplemented
209#14581776C2×C418yescomplemented
210#14581768C2×C418yescomplemented
211#14581762C2×C418yes—
212Q8×Dic83—42no—
213C4×D332—42no—
214#14581754—42no—
215#14581754—42no—
216#14581754C2×C418yescomplemented
217C4×C22⋊D83C2×C418yescomplemented
218#14581751—42no—
219#14581750—42no—
220#14581750C2×C418yescomplemented
221#14581749—42no—
222#14581748C2×C418yescomplemented
223C2×C4⋊Dic83C2311yescharacteristic
224C2×C4⋊Dic83C2311yescharacteristic
225C2×C4⋊Dic83C2311yescharacteristic
226C2×C4⋊Dic83C2311yescharacteristic
227C2×C4⋊Dic83C2311yescharacteristic
228C2×C4⋊Dic83C2311yescharacteristic
229C2×C4⋊Dic83C2311yescharacteristic
230C2×C4⋊Dic83C2311yescharacteristic
231C2×C4⋊Dic83C2311yescharacteristic
232C2×C4⋊Dic83C2311yescharacteristic
233C2×Dic83⋊C4C2311yescharacteristic
234C2×Dic83⋊C4C2311yescharacteristic
235C2×Dic83⋊C4C2311yescharacteristic
236C2×Dic83⋊C4C2311yescharacteristic
237C2×Dic83⋊C4C2311yescharacteristic
238C2×Dic83⋊C4C2311yescharacteristic
239C2×Dic83⋊C4C2311yescharacteristic
240C2×Dic83⋊C4C2311yescharacteristic
241C2×Dic83⋊C4C2311yescharacteristic
242C2×Dic83⋊C4C2311yescharacteristic
243C2×Dic83⋊C4C2311yescharacteristic
244C2×Dic83⋊C4C2311yescharacteristic
245C2×Dic83⋊C4C2311yescharacteristic
246C2×Dic83⋊C4C2311yescharacteristic
247C2×Dic83⋊C4C2311yescharacteristic
248C4⋊C4×D83—42no—
249C2×C22⋊Dic83C2311yescharacteristic
250C2×C22⋊Dic83C2311yescharacteristic
251C2×C22⋊Dic83C2311yescharacteristic
252C2×C22⋊Dic83C2311yescharacteristic
253C2×C22⋊Dic83C2311yescharacteristic
254C2×(C2×D83)⋊C4C2×C418yescomplemented
255C2×(C2×D83)⋊C4C2311yescharacteristic
256C2×(C2×D83)⋊C4C2311yescharacteristic
257C2×(C2×D83)⋊C4C2311yescharacteristic
258C2×(C2×D83)⋊C4C2311yescharacteristic
259C2×(C2×D83)⋊C4C2311yescharacteristic
260C2×(C2×D83)⋊C4C2311yescharacteristic
261C2×(C2×D83)⋊C4C2311yescharacteristic
262C2×(C2×D83)⋊C4C2311yescharacteristic
263C2×(C2×D83)⋊C4C2311yescharacteristic
264C2×(C2×D83)⋊C4C2311yescharacteristic
265C2×(C2×D83)⋊C4C2311yescharacteristic
266C2×(C2×D83)⋊C4C2311yescharacteristic
267C2×(C2×D83)⋊C4C2311yescharacteristic
268C2×(C2×D83)⋊C4C2311yescharacteristic
269C2×(C2×D83)⋊C4C2311yescharacteristic
270C2×(C2×D83)⋊C4C2311yescharacteristic
271C2×(C2×D83)⋊C4C2311yescharacteristic
272C2×(C2×D83)⋊C4C2311yescharacteristic
273C2×(C2×D83)⋊C4C2311yescharacteristic
274C2×(C2×D83)⋊C4C2311yescharacteristic
275C2×(C2×D83)⋊C4C2311yescharacteristic
276C2×(C2×D83)⋊C4C2311yescharacteristic
277C2×(C2×D83)⋊C4C2311yescharacteristic
278C2×(C2×D83)⋊C4C2311yescharacteristic
279C2×(C2×D83)⋊C4C2311yescharacteristic
280C2×(C2×D83)⋊C4C2311yescharacteristic
281C2×(C2×D83)⋊C4C2311yescharacteristic
282C22⋊C4×D83—42no—
283C22⋊C4×D83—42no—
284C22⋊C4×D83—42no—
285C22⋊C4×D83C2×C418yescomplemented
286C2×C4×Dic83C2311yescharacteristic
287C2×C4×Dic83C2311yescharacteristic
288C2×C4×Dic83C2311yescharacteristic
289C2×C4×Dic83C2311yescharacteristic
290C2×C4×Dic83C2311yescharacteristic
291C2×C4×Dic83C2311yescharacteristic
292C2×C4×Dic83C2311yescharacteristic
293C2×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C2×C4×Dic83C2311yescharacteristic
296C2×C4×Dic83C2311yescharacteristic
297C2×C4×Dic83C2311yescharacteristic
298C2×C4×Dic83C2311yescharacteristic
299C2×C4×Dic83C2311yescharacteristic
300C2×C4×Dic83C2311yescharacteristic
301C2×C4×Dic83C2311yescharacteristic
302C2×C4×Dic83C2311yescharacteristic
303C42×D83—42no—
304C83⋊#95C2311yescharacteristic
305C83⋊#95C2311yescharacteristic
306C83⋊#95C2311yescharacteristic
307C83⋊#95C2311yescharacteristic
308C83⋊#95C2311yescharacteristic
309C83⋊#95C2311yescharacteristic
310C83⋊#95C2311yescharacteristic
311C83⋊#95C2311yescharacteristic
312C83⋊#95C2311yescharacteristic
313C83⋊#95C2311yescharacteristic
314C83⋊#95C2311yescharacteristic
315C83⋊#95C2311yescharacteristic
316C83⋊#95C2311yescharacteristic
317C83⋊#95C2311yescharacteristic
318C83⋊#95C2311yescharacteristic
319C83⋊#95C2311yescharacteristic
320C83⋊#95C2311yescharacteristic
321C83⋊#95C2311yescharacteristic
322C83⋊#95C2311yescharacteristic
323C83⋊#95C2311yescharacteristic
324C83⋊#95C2311yescharacteristic
325C83⋊#95C2311yescharacteristic
326C83⋊#95C2311yescharacteristic
327C83⋊#95C2311yescharacteristic
328C83⋊#95C2311yescharacteristic
329C83⋊#95C2311yescharacteristic
330C83⋊#95C2311yescharacteristic
331C83⋊#95C2311yescharacteristic
332C83⋊#95C2311yescharacteristic
333C83⋊#95C2311yescharacteristic
334C22×Q8×C83C2311yescharacteristic
335C23×C4×C83C2311yescharacteristic
336C22⋊Q8×C83C2×C418yescomplemented
337C2×C4⋊C4×C83C2311yescharacteristic
338C2×C4⋊C4×C83C2311yescharacteristic
339C2×C4⋊C4×C83C2311yescharacteristic
340C2×C4⋊C4×C83C2311yescharacteristic
341C2×C4⋊C4×C83C2311yescharacteristic
342C2×C4⋊C4×C83C2311yescharacteristic
343C2×C4⋊C4×C83C2311yescharacteristic
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C4⋊C4×C83C2311yescharacteristic
346C2×C22⋊C4×C83C2311yescharacteristic
347C2×C22⋊C4×C83C2311yescharacteristic
348C2×C22⋊C4×C83C2311yescharacteristic
349C2×C22⋊C4×C83C2311yescharacteristic
350C2×C22⋊C4×C83C2311yescharacteristic
351C2×C22⋊C4×C83C2311yescharacteristic
352C2×C42×C83C2311yescharacteristic
353C2×C42×C83C2311yescharacteristic
354C2×C42×C83C2311yescharacteristic
355C2×C42×C83C2311yescharacteristic
356#95×C83C2311yescharacteristic
357#95×C83C2311yescharacteristic
358#95×C83C2311yescharacteristic
359#95×C83C2311yescharacteristic
360#95×C83C2311yescharacteristic
361#95×C83C2311yescharacteristic
362#95×C83C2311yescharacteristic
363#95×C83C2311yescharacteristic
364#95×C83C2311yescharacteristic
365#95×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369#95×C83C2311yescharacteristic
370C23×D83—22no—
371C23×D83—22no—
372C23×D83—41no—
373C23×D83—41no—
374C23×D83—41no—
375C23×D83—41no—
376C23×D83C22×C414yes—
377C23×D83C2411yescharacteristic
378C23×D83C2411yescharacteristic
379C23×D83C2411yescharacteristic
380C2×D332—22no—
381C2×D332—22no—
382C2×D332—41no—
383C2×D332—41no—
384C2×D332C22×C414yes—
385C2×D332C22×C414yes—
386C2×C22⋊D83—41no—
387C2×C22⋊D83—41no—
388C2×C22⋊D83C22×C414yes—
389C22×Dic83—41no—
390C22×Dic83—41no—
391C22×Dic83C22×C414yes—
392C22×Dic83C2411yescharacteristic
393C22×Dic83C2411yescharacteristic
394C22×Dic83C2411yescharacteristic
395C22×Dic83C2411yescharacteristic
396C22×Dic83C2411yescharacteristic
397C22×Dic83C2411yescharacteristic
398C22×Dic83C2411yescharacteristic
399C22×Dic83C2411yescharacteristic
400C22×Dic83C2411yescharacteristic
401C22×Dic83C2411yescharacteristic
402C22×Dic83C2411yescharacteristic
403C22×Dic83C2411yescharacteristic
404C22×Dic83C2411yescharacteristic
405C2×C4×D83—22no—
406C2×C4×D83—22no—
407C2×C4×D83—22no—
408C2×C4×D83—22no—
409C2×C4×D83—22no—
410C2×C4×D83—22no—
411C2×C4×D83—22no—
412C2×C4×D83—41no—
413C2×C4×D83—41no—
414C2×C4×D83—41no—
415C2×C4×D83—41no—
416C2×C4×D83—41no—
417C2×C4×D83—41no—
418C2×C4×D83—41no—
419C2×C4×D83—41no—
420C2×C4×D83—41no—
421C2×C4×D83—41no—
422C2×C4×D83—41no—
423C2×C4×D83—41no—
424C2×C4×D83—41no—
425C2×C4×D83—41no—
426C2×C4×D83—41no—
427C2×C4×D83—41no—
428C2×C4×D83—41no—
429C2×C4×D83—41no—
430C2×C4×D83—41no—
431C2×C4×D83—41no—
432C2×C4×D83—41no—
433C2×C4×D83—41no—
434C2×C4×D83—41no—
435C2×C4×D83C22×C414yes—
436C2×C4×D83C22×C414yes—
437C2×C4×D83C22×C414yes—
438C4⋊Dic83—22no—
439C4⋊Dic83—41no—
440C4⋊Dic83—41no—
441C4⋊Dic83—41no—
442C4⋊Dic83—41no—
443C4⋊Dic83—41no—
444C4⋊Dic83—41no—
445C4⋊Dic83—41no—
446C4⋊Dic83C22×C414yes—
447C4⋊Dic83C22×C414yes—
448Dic83⋊C4—41no—
449Dic83⋊C4—41no—
450Dic83⋊C4—41no—
451Dic83⋊C4—41no—
452Dic83⋊C4—41no—
453Dic83⋊C4—41no—
454Dic83⋊C4—41no—
455Dic83⋊C4—41no—
456Dic83⋊C4—41no—
457Dic83⋊C4—41no—
458Dic83⋊C4—41no—
459Dic83⋊C4—41no—
460Dic83⋊C4C22×C414yes—
461Dic83⋊C4C22×C414yes—
462Dic83⋊C4C22×C414yes—
463C22⋊Dic83—22no—
464C22⋊Dic83—41no—
465C22⋊Dic83—41no—
466C22⋊Dic83—41no—
467C22⋊Dic83C22×C414yes—
468(C2×D83)⋊C4—22no—
469(C2×D83)⋊C4—22no—
470(C2×D83)⋊C4—22no—
471(C2×D83)⋊C4—22no—
472(C2×D83)⋊C4—22no—
473(C2×D83)⋊C4—22no—
474(C2×D83)⋊C4—41no—
475(C2×D83)⋊C4—41no—
476(C2×D83)⋊C4—41no—
477(C2×D83)⋊C4—41no—
478(C2×D83)⋊C4—41no—
479(C2×D83)⋊C4—41no—
480(C2×D83)⋊C4—41no—
481(C2×D83)⋊C4—41no—
482(C2×D83)⋊C4—41no—
483(C2×D83)⋊C4—41no—
484(C2×D83)⋊C4C22×C414yes—
485(C2×D83)⋊C4C22×C414yes—
486(C2×D83)⋊C4C22×C414yes—
487(C2×D83)⋊C4C22×C414yes—
488(C2×D83)⋊C4C22×C414yes—
489(C2×D83)⋊C4C22×C414yes—
490(C2×D83)⋊C4C22×C414yes—
491(C2×D83)⋊C4C22×C414yes—
492(C2×D83)⋊C4C22×C414yes—
493(C2×D83)⋊C4C22×C414yes—
494(C2×D83)⋊C4C22×C414yes—
495C4×Dic83—22no—
496C4×Dic83—22no—
497C4×Dic83—22no—
498C4×Dic83—22no—
499C4×Dic83—41no—
500C4×Dic83—41no—
501C4×Dic83—41no—
502C4×Dic83—41no—
503C4×Dic83—41no—
504C4×Dic83—41no—
505C4×Dic83—41no—
506C4×Dic83—41no—
507C4×Dic83—41no—
508C4×Dic83—41no—
509C4×Dic83C22×C414yes—
510C4×Dic83C22×C414yes—
511C4×Dic83C22×C414yes—
512C24×C83C2411yescharacteristic
513C2×Q8×C83—41no—
514C2×Q8×C83—41no—
515C2×Q8×C83C22×C414yes—
516C22×C4×C83—41no—
517C22×C4×C83—41no—
518C22×C4×C83C22×C414yes—
519C22×C4×C83C2411yescharacteristic
520C22×C4×C83C2411yescharacteristic
521C22×C4×C83C2411yescharacteristic
522C22×C4×C83C2411yescharacteristic
523C22×C4×C83C2411yescharacteristic
524C22×C4×C83C2411yescharacteristic
525C22×C4×C83C2411yescharacteristic
526C22×C4×C83C2411yescharacteristic
527C22×C4×C83C2411yescharacteristic
528C22×C4×C83C2411yescharacteristic
529C22×C4×C83C2411yescharacteristic
530C22×C4×C83C2411yescharacteristic
531C22×C4×C83C2411yescharacteristic
532C22×C4×C83C2411yescharacteristic
533C4⋊C4×C83—41no—
534C4⋊C4×C83—41no—
535C4⋊C4×C83—41no—
536C4⋊C4×C83—41no—
537C4⋊C4×C83—41no—
538C4⋊C4×C83—41no—
539C4⋊C4×C83C22×C414yes—
540C4⋊C4×C83C22×C414yes—
541C4⋊C4×C83C22×C414yes—
542C22⋊C4×C83—41no—
543C22⋊C4×C83—41no—
544C22⋊C4×C83—41no—
545C22⋊C4×C83—41no—
546C22⋊C4×C83C22×C414yes—
547C22⋊C4×C83C22×C414yes—
548C42×C83—41no—
549C42×C83—41no—
550C42×C83—41no—
551C42×C83—41no—
552C23×C83—21no—
553C23×C83—21no—
554C23×C83—21no—
555C23×C83—21no—
556C23×C83—21no—
557C23×C83—21no—
558C23×C83C23×C412yes—
559C23×C83C2511yescharacteristic
560C22×D83—21no—
561C22×D83—21no—
562C22×D83—21no—
563C22×D83—21no—
564C22×D83—21no—
565C22×D83—21no—
566C22×D83—21no—
567C22×D83—21no—
568C22×D83—21no—
569C22×D83—21no—
570C22×D83—21no—
571C22×D83—21no—
572C22×D83—21no—
573C22×D83—21no—
574C22×D83—21no—
575C22×D83—21no—
576C22×D83—28no—
577C22×D83—44no—
578C22×D83—44no—
579C22×D83—82no—
580C22×D83—82no—
581C22×D83—82no—
582C22×D83—82no—
583C22×D83C23×C412yes—
584C22×D83C23×C412yes—
585C22×D83C23×C412yes—
586C22×D83H(5,𝔽2)12yes—
587C22×D832−1+412yes—
588Q8×C83—44no—
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—44no—
626C2×C4×C83C23×C412yes—
627C2×C4×C83C23×C412yes—
628C2×C4×C83C23×C412yes—
629C2×C4×C83C23×C412yes—
630C2×C4×C83C23×C412yes—
631C2×C4×C83C23×C412yes—
632C22⋊D83—44no—
633C2×Dic83—21no—
634C2×Dic83—21no—
635C2×Dic83—21no—
636C2×Dic83—21no—
637C2×Dic83—21no—
638C2×Dic83—21no—
639C2×Dic83—21no—
640C2×Dic83—21no—
641C2×Dic83—21no—
642C2×Dic83—21no—
643C2×Dic83—21no—
644C2×Dic83—21no—
645C2×Dic83—21no—
646C2×Dic83—21no—
647C2×Dic83—21no—
648C2×Dic83—21no—
649C2×Dic83—21no—
650C2×Dic83—21no—
651C2×Dic83—21no—
652C2×Dic83—21no—
653C2×Dic83—21no—
654C2×Dic83—21no—
655C2×Dic83—21no—
656C2×Dic83—21no—
657C2×Dic83—21no—
658C2×Dic83—21no—
659C2×Dic83—21no—
660C2×Dic83—21no—
661C2×Dic83—21no—
662C2×Dic83—21no—
663C2×Dic83—21no—
664C2×Dic83—21no—
665C2×Dic83—21no—
666C2×Dic83—44no—
667C2×Dic83C23×C412yes—
668C2×Dic83C23×C412yes—
669C2×Dic83C23×C412yes—
670C2×Dic83C23×C412yes—
671C2×Dic83C23×C412yes—
672C2×Dic83H(5,𝔽2)12yes—
673D332—28no—
674D332—44no—
675C4×D83—28no—
676C4×D83—44no—
677C4×D83—44no—
678C4×D83—44no—
679C4×D83—44no—
680C4×D83—82no—
681C4×D83—82no—
682C4×D83—82no—
683C4×D83—82no—
684C4×D83—82no—
685C4×D83—82no—
686C22×C83—22no—
687C22×C83—22no—
688C22×C83—22no—
689C22×C83—41no—
690C22×C83—41no—
691C22×C83—41no—
692C22×C83—41no—
693C22×C83C24×C411yescharacteristic
694C22×C83C2×H(5,𝔽2)11yescharacteristic
695C22×C83C2×H(5,𝔽2)11yescharacteristic
696C22×C83C2×2−1+411yescharacteristic
697C22×C83#58511yescharacteristic
698C22×C83#58511yescharacteristic
699C22×C83#58511yescharacteristic
700C2×D83—22no—
701C2×D83—22no—
702C2×D83—22no—
703C2×D83—22no—
704C2×D83—22no—
705C2×D83—22no—
706C2×D83—22no—
707C2×D83—22no—
708C2×D83—22no—
709C2×D83—22no—
710C2×D83—22no—
711C2×D83—22no—
712C2×D83—41no—
713C2×D83—41no—
714C2×D83—41no—
715C2×D83—41no—
716C2×D83—41no—
717C2×D83—41no—
718C2×D83—41no—
719C2×D83—41no—
720C2×D83—88no—
721C2×D83#52014yes—
722C4×C83—22no—
723C4×C83—22no—
724C4×C83—22no—
725C4×C83—22no—
726C4×C83—22no—
727C4×C83—22no—
728C4×C83—41no—
729C4×C83—41no—
730C4×C83—41no—
731C4×C83—41no—
732C4×C83—41no—
733C4×C83—41no—
734C4×C83—41no—
735C4×C83—41no—
736Dic83—22no—
737Dic83—22no—
738Dic83—22no—
739Dic83—22no—
740Dic83—22no—
741Dic83—22no—
742Dic83—41no—
743Dic83—41no—
744Dic83—41no—
745Dic83—41no—
746Dic83—41no—
747Dic83—41no—
748Dic83—41no—
749#34479—831nomaximal, Sylow
750C2×C83—42no—
751C2×C83C2×#52011yescharacteristic
752C2×C83#342811yescharacteristic
753C2×C83C4×H(5,𝔽2)11yescharacteristic
754C2×C83#353511yescharacteristic
755C2×C83#354211yescharacteristic
756C2×C83#354511yescharacteristic
757C2×C83#356411yescharacteristic
758D83—24no—
759D83—42no—
760D83—42no—
761C2×#551—831no—
762#2383—831no—
763#2379—831no—
764#2378D8311yescharacteristic, complemented
765#2376—831no—
766#2373—831no—
767#2368—831no—
768#2359—831no—
769#2359—831no—
770#2358—831no—
771#2354—831no—
772#2349—831no—
773#2346—831no—
774#2343—831no—
775#2342—831no—
776#2342—831no—
777#2335—831no—
778#2335—831no—
779#2334—831no—
780#2334—831no—
781#2326—831no—
782#2323—831no—
783#2322—831no—
784#2321—831no—
785#2318—831no—
786#2317—831no—
787#2315—831no—
788#2314—831no—
789C4×C22⋊Q8—831no—
790#2290—831no—
791C2×#388—831no—
792C83#3447911yescharacteristic, complemented, Sylow
793#551—8316no—
794C2×#126—831no—
795C2×#126—831no—
796C2×#124—831no—
797C2×#123—831no—
798C2×#123—831no—
799C2×#123—831no—
800C2×C22⋊Q8—831no—
801C2×C22⋊Q8C2×D8311yescharacteristic
802C2×#120—831no—
803C2×C4×Q8—831no—
804C2×C4×D4—831no—
805C2×C4×D4—831no—
806C2×C4×D4—831no—
807C2×C4×D4—831no—
808C2×C4×D4—831no—
809C2×#117—831no—
810C2×#117—831no—
811C2×#117—831no—
812C2×#117—831no—
813C2×#117—831no—
814C22×C4⋊C4—831no—
815C22×C22⋊C4—831no—
816C22×C22⋊C4—831no—
817C22×C22⋊C4—831no—
818C22×C22⋊C4—831no—
819C22×C22⋊C4—831no—
820C22×C42—831no—
821#391—831no—
822#391C2×D8311yescharacteristic, complemented
823#391C2×D8311yescharacteristic, complemented
824#390—831no—
825#390—831no—
826#390—831no—
827#389—831no—
828#389—831no—
829#389—831no—
830#389—831no—
831#389—831no—
832#389—831no—
833#389—831no—
834#389—831no—
835#389C2×D8311yescharacteristic, complemented
836#389C2×D8311yescharacteristic, complemented
837#388—831no—
838#388—831no—
839#388—831no—
840#388—831no—
841#388—831no—
842#388—831no—
843#388—831no—
844#388—831no—
845#388—831no—
846#388—831no—
847#388—831no—
848#388—831no—
849#388—831no—
850#388—831no—
851#388—831no—
852#388—831no—
853#388—831no—
854#388—831no—
855#388—831no—
856#388—831no—
857#388—831no—
858#388—831no—
859#388—831no—
860#388—831no—
861#388C2×D8311yescharacteristic
862#388C2×D8311yescharacteristic
863#388C2×D8311yescharacteristic
864#388C2×D8311yescharacteristic
865#387—831no—
866#387—831no—
867#387—831no—
868#387—831no—
869#387—831no—
870#387—831no—
871#387—831no—
872#387—831no—
873#387—831no—
874#387—831no—
875#387—831no—
876#387—831no—
877#387C2×D8311yescharacteristic, complemented
878#387C2×D8311yescharacteristic, complemented
879#387C2×D8311yescharacteristic, complemented
880#387C2×D8311yescharacteristic, complemented
881#386—831no—
882#386—831no—
883#386—831no—
884#386—831no—
885#386—831no—
886#386—831no—
887#385—831no—
888#385—831no—
889#385—831no—
890#385—831no—
891#385—831no—
892#385—831no—
893#385—831no—
894#385—831no—
895#385—831no—
896#385—831no—
897#385—831no—
898#385—831no—
899#385—831no—
900#385—831no—
901#385—831no—
902#385—831no—
903#385—831no—
904#385—831no—
905#385—831no—
906#385—831no—
907#384—831no—
908#384—831no—
909#383—831no—
910#382—831no—
911#382—831no—
912#382—831no—
913#382—831no—
914#381—831no—
915#381C2×D8311yescharacteristic
916#380—831no—
917#380—831no—
918#380—831no—
919#380—831no—
920#380—831no—
921#380—831no—
922#380C2×D8311yescharacteristic
923#379—831no—
924C4×C4⋊C4—831no—
925C4×C4⋊C4—831no—
926C4×C4⋊C4—831no—
927C4×C4⋊C4—831no—
928C4×C4⋊C4—831no—
929C4×C4⋊C4—831no—
930C4×C4⋊C4—831no—
931C4×C4⋊C4—831no—
932C4×C4⋊C4—831no—
933C4×C22⋊C4—831no—
934C4×C22⋊C4—831no—
935C4×C22⋊C4—831no—
936C4×C22⋊C4—831no—
937C4×C22⋊C4—831no—
938C4×C22⋊C4—831no—
939C4×C22⋊C4—831no—
940C4×C22⋊C4—831no—
941C4×C22⋊C4—831no—
942C4×C22⋊C4—831no—
943C4×C22⋊C4—831no—
944#376—831no—
945#376—831no—
946C2×#95—831no—
947C2×#95—831no—
948C2×#95—831no—
949C25—831no—
950C22×Q8C22×D8311yescharacteristic
951C22×D4—831no—
952C22×D4—831no—
953C22×D4—831no—
954C23×C4—831no—
955C23×C4—831no—
956C23×C4—831no—
957C23×C4—831no—
958C23×C4—831no—
959C23×C4—831no—
960C23×C4—831no—
961C23×C4—831no—
962C23×C4—831no—
963C23×C4—831no—
964C23×C4—831no—
965C23×C4—831no—
966C23×C4C22×D8311yescharacteristic
967#126—838no—
968#126—838no—
969#124—838no—
970#123—838no—
971#123—838no—
972#123—838no—
973C22⋊Q8—838no—
974C22⋊Q8C4×D8318yescomplemented
975#120—838no—
976C4×Q8—3322no—
977C4×D4—3322no—
978C4×D4—3322no—
979C4×D4—3322no—
980C4×D4—838no—
981C4×D4—838no—
982#117—3322no—
983#117—3322no—
984#117—3322no—
985#117—838no—
986#117—838no—
987C2×C4⋊C4—3322no—
988C2×C4⋊C4—831no—
989C2×C4⋊C4—831no—
990C2×C4⋊C4—831no—
991C2×C4⋊C4—831no—
992C2×C4⋊C4—831no—
993C2×C4⋊C4—831no—
994C2×C4⋊C4—831no—
995C2×C4⋊C4—831no—
996C2×C4⋊C4—831no—
997C2×C4⋊C4—831no—
998C2×C4⋊C4—831no—
999C2×C4⋊C4—831no—
1000C2×C4⋊C4—831no—
1001C2×C4⋊C4—831no—
1002C2×C4⋊C4—831no—
1003C2×C4⋊C4—831no—
1004C2×C4⋊C4—831no—
1005C2×C4⋊C4—831no—
1006C2×C4⋊C4—831no—
1007C2×C4⋊C4—831no—
1008C2×C4⋊C4—831no—
1009C2×C4⋊C4—831no—
1010C2×C4⋊C4—831no—
1011C2×C4⋊C4—831no—
1012C2×C4⋊C4—831no—
1013C2×C4⋊C4C22×D8311yescharacteristic
1014C2×C4⋊C4C22×D8311yescharacteristic
1015C2×C4⋊C4C22×D8311yescharacteristic
1016C2×C4⋊C4C22×D8311yescharacteristic
1017C2×C4⋊C4C22×D8311yescharacteristic
1018C2×C4⋊C4C22×D8311yescharacteristic
1019C2×C4⋊C4C22×D8311yescharacteristic
1020C2×C4⋊C4C22×D8311yescharacteristic
1021C2×C4⋊C4C22×D8311yescharacteristic
1022C2×C22⋊C4—3322no—
1023C2×C22⋊C4—3322no—
1024C2×C22⋊C4—3322no—
1025C2×C22⋊C4—831no—
1026C2×C22⋊C4—831no—
1027C2×C22⋊C4—831no—
1028C2×C22⋊C4—831no—
1029C2×C22⋊C4—831no—
1030C2×C22⋊C4—831no—
1031C2×C22⋊C4—831no—
1032C2×C22⋊C4—831no—
1033C2×C22⋊C4—831no—
1034C2×C22⋊C4—831no—
1035C2×C22⋊C4—831no—
1036C2×C22⋊C4—831no—
1037C2×C22⋊C4—831no—
1038C2×C22⋊C4—831no—
1039C2×C22⋊C4—838no—
1040C2×C22⋊C4—831no—
1041C2×C22⋊C4—831no—
1042C2×C22⋊C4—831no—
1043C2×C22⋊C4—831no—
1044C2×C22⋊C4—831no—
1045C2×C22⋊C4—831no—
1046C2×C22⋊C4—831no—
1047C2×C22⋊C4—831no—
1048C2×C22⋊C4—831no—
1049C2×C22⋊C4—831no—
1050C2×C22⋊C4—831no—
1051C2×C22⋊C4—838no—
1052C2×C22⋊C4—831no—
1053C2×C22⋊C4—831no—
1054C2×C22⋊C4—831no—
1055C2×C22⋊C4—831no—
1056C2×C22⋊C4—831no—
1057C2×C22⋊C4—831no—
1058C2×C22⋊C4—831no—
1059C2×C22⋊C4C22×D8311yescharacteristic
1060C2×C22⋊C4C22×D8311yescharacteristic
1061C2×C22⋊C4C22×D8311yescharacteristic
1062C2×C22⋊C4C22×D8311yescharacteristic
1063C2×C22⋊C4C22×D8311yescharacteristic
1064C2×C22⋊C4C22×D8311yescharacteristic
1065C2×C42—3322no—
1066C2×C42—831no—
1067C2×C42—831no—
1068C2×C42—831no—
1069C2×C42—831no—
1070C2×C42—831no—
1071C2×C42—831no—
1072C2×C42—831no—
1073C2×C42—831no—
1074C2×C42—831no—
1075C2×C42—831no—
1076C2×C42—831no—
1077C2×C42—831no—
1078C2×C42—831no—
1079C2×C42—831no—
1080C2×C42—831no—
1081C2×C42—831no—
1082C2×C42—831no—
1083C2×C42C22×D8311yescharacteristic
1084C2×C42C22×D8311yescharacteristic
1085C2×C42C22×D8311yescharacteristic
1086C2×C42C22×D8311yescharacteristic
1087#95—831no—
1088#95—831no—
1089#95—831no—
1090#95—831no—
1091#95—831no—
1092#95—831no—
1093#95—831no—
1094#95—831no—
1095#95—831no—
1096#95—831no—
1097#95—831no—
1098#95—831no—
1099#95—831no—
1100#95—831no—
1101#95—831no—
1102#95—831no—
1103#95—831no—
1104#95—831no—
1105#95—831no—
1106#95—831no—
1107#95—831no—
1108#95—831no—
1109#95—831no—
1110#95—831no—
1111#95—831no—
1112#95—831no—
1113#95—831no—
1114#95—831no—
1115#95—831no—
1116#95—831no—
1117#95C22×D8311yescharacteristic
1118#95C22×D8311yescharacteristic
1119#95C22×D8311yescharacteristic
1120#95C22×D8311yescharacteristic
1121#95C22×D8311yescharacteristic
1122#95C22×D8311yescharacteristic
1123#95C22×D8311yescharacteristic
1124#95C22×D8311yescharacteristic
1125#95C22×D8311yescharacteristic
1126#95C22×D8311yescharacteristic
1127#95C22×D8311yescharacteristic
1128#95C22×D8311yescharacteristic
1129#95C22×D8311yescharacteristic
1130#95C22×D8311yescharacteristic
1131C24—3321no—
1132C24—3321no—
1133C24—3321no—
1134C24—3321no—
1135C24—834no—
1136C24—831no—
1137C24—831no—
1138C24—831no—
1139C24—1662no—
1140C24—1662no—
1141C24C23×D8311yescharacteristic
1142C2×Q8—41no—
1143C2×Q8—41no—
1144C2×Q8C2×C4×D8314yes—
1145C2×D4—3321no—
1146C2×D4—3321no—
1147C2×D4—3321no—
1148C2×D4—3321no—
1149C2×D4—834no—
1150C2×D4—834no—
1151C2×D4—834no—
1152C2×D4—1662no—
1153C2×D4—1662no—
1154C22×C4—41no—
1155C22×C4—41no—
1156C22×C4—3321no—
1157C22×C4—3321no—
1158C22×C4—3321no—
1159C22×C4—3321no—
1160C22×C4—3321no—
1161C22×C4—3321no—
1162C22×C4—3321no—
1163C22×C4—3321no—
1164C22×C4—3321no—
1165C22×C4—3321no—
1166C22×C4—3321no—
1167C22×C4—3321no—
1168C22×C4—3321no—
1169C22×C4—3321no—
1170C22×C4—3321no—
1171C22×C4—3321no—
1172C22×C4—3321no—
1173C22×C4—3321no—
1174C22×C4—3321no—
1175C22×C4—3321no—
1176C22×C4—3321no—
1177C22×C4—3321no—
1178C22×C4—3321no—
1179C22×C4—3321no—
1180C22×C4—3321no—
1181C22×C4—834no—
1182C22×C4—834no—
1183C22×C4—834no—
1184C22×C4—831no—
1185C22×C4—831no—
1186C22×C4—831no—
1187C22×C4—831no—
1188C22×C4—831no—
1189C22×C4—831no—
1190C22×C4—834no—
1191C22×C4—831no—
1192C22×C4—831no—
1193C22×C4—831no—
1194C22×C4—831no—
1195C22×C4—831no—
1196C22×C4—831no—
1197C22×C4—831no—
1198C22×C4—1662no—
1199C22×C4—1662no—
1200C22×C4—1662no—
1201C22×C4—1662no—
1202C22×C4—1662no—
1203C22×C4—1662no—
1204C22×C4—1662no—
1205C22×C4C2×C4×D8314yes—
1206C22×C4C23×D8311yescharacteristic
1207C22×C4C23×D8311yescharacteristic
1208C22×C4C23×D8311yescharacteristic
1209C22×C4C23×D8311yescharacteristic
1210C22×C4C23×D8311yescharacteristic
1211C22×C4C23×D8311yescharacteristic
1212C22×C4C23×D8311yescharacteristic
1213C22×C4C23×D8311yescharacteristic
1214C22×C4C23×D8311yescharacteristic
1215C22×C4C23×D8311yescharacteristic
1216C22×C4C23×D8311yescharacteristic
1217C22×C4C23×D8311yescharacteristic
1218C22×C4C23×D8311yescharacteristic
1219C22×C4C23×D8311yescharacteristic
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—41no—
1226C4⋊C4—3321no—
1227C4⋊C4—3321no—
1228C4⋊C4—3321no—
1229C4⋊C4—3321no—
1230C4⋊C4—3321no—
1231C4⋊C4—3321no—
1232C4⋊C4—3321no—
1233C4⋊C4—3321no—
1234C4⋊C4—3321no—
1235C4⋊C4—3321no—
1236C4⋊C4—3321no—
1237C4⋊C4—3321no—
1238C4⋊C4—3321no—
1239C4⋊C4—3321no—
1240C4⋊C4—3321no—
1241C4⋊C4—3321no—
1242C4⋊C4—3321no—
1243C4⋊C4—3321no—
1244C4⋊C4—3321no—
1245C4⋊C4—834no—
1246C4⋊C4—834no—
1247C4⋊C4—834no—
1248C4⋊C4—834no—
1249C4⋊C4—834no—
1250C4⋊C4—1662no—
1251C4⋊C4C2×C4×D8314yes—
1252C4⋊C4C2×C4×D8314yes—
1253C4⋊C4C2×C4×D8314yes—
1254C22⋊C4—41no—
1255C22⋊C4—41no—
1256C22⋊C4—41no—
1257C22⋊C4—41no—
1258C22⋊C4—3321no—
1259C22⋊C4—3321no—
1260C22⋊C4—3321no—
1261C22⋊C4—3321no—
1262C22⋊C4—3321no—
1263C22⋊C4—3321no—
1264C22⋊C4—3321no—
1265C22⋊C4—3321no—
1266C22⋊C4—3321no—
1267C22⋊C4—3321no—
1268C22⋊C4—3321no—
1269C22⋊C4—3321no—
1270C22⋊C4—3321no—
1271C22⋊C4—834no—
1272C22⋊C4—834no—
1273C22⋊C4—834no—
1274C22⋊C4—834no—
1275C22⋊C4—834no—
1276C22⋊C4—834no—
1277C22⋊C4—834no—
1278C22⋊C4—834no—
1279C22⋊C4—834no—
1280C22⋊C4—834no—
1281C22⋊C4—834no—
1282C22⋊C4—834no—
1283C22⋊C4—1662no—
1284C22⋊C4—1662no—
1285C22⋊C4—1662no—
1286C22⋊C4—1662no—
1287C22⋊C4—1662no—
1288C22⋊C4—1662no—
1289C22⋊C4—1662no—
1290C22⋊C4C2×C4×D8314yes—
1291C22⋊C4C2×C4×D8314yes—
1292C42—41no—
1293C42—41no—
1294C42—41no—
1295C42—41no—
1296C42—3321no—
1297C42—3321no—
1298C42—3321no—
1299C42—3321no—
1300C42—3321no—
1301C42—3321no—
1302C42—3321no—
1303C42—3321no—
1304C42—3321no—
1305C42—3321no—
1306C42—834no—
1307C42—834no—
1308C42—834no—
1309C42—1662no—
1310C42—1662no—
1311C42—1662no—
1312C42—1662no—
1313C23—21no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—21no—
1319C23—3324no—
1320C23—3324no—
1321C23—832no—
1322C23—832no—
1323C23—832no—
1324C23—832no—
1325C23—832no—
1326C23—6642no—
1327C23—6642no—
1328C23—6642no—
1329C23—6642no—
1330C23—1668no—
1331C23—1661no—
1332C23—1661no—
1333C23—1661no—
1334C23—1661no—
1335C23—1661no—
1336C23—1661no—
1337C23—1661no—
1338C23—1661no—
1339C23—1661no—
1340C23—1661no—
1341C23—1661no—
1342C23—1661no—
1343C23—1661no—
1344C23—1661no—
1345C23—1661no—
1346C23—1661no—
1347C23C22×C4×D8312yes—
1348C23C24×D8311yescharacteristic
1349Q8—44no—
1350D4—3324no—
1351D4—3324no—
1352D4—1668no—
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—44no—
1390C2×C4—3324no—
1391C2×C4—3324no—
1392C2×C4—3324no—
1393C2×C4—3324no—
1394C2×C4—3324no—
1395C2×C4—832no—
1396C2×C4—832no—
1397C2×C4—832no—
1398C2×C4—832no—
1399C2×C4—832no—
1400C2×C4—832no—
1401C2×C4—6642no—
1402C2×C4—6642no—
1403C2×C4—6642no—
1404C2×C4—6642no—
1405C2×C4—6642no—
1406C2×C4—6642no—
1407C2×C4—1668no—
1408C2×C4—1661no—
1409C2×C4—1661no—
1410C2×C4—1661no—
1411C2×C4—1661no—
1412C2×C4—1661no—
1413C2×C4—1661no—
1414C2×C4—1661no—
1415C2×C4—1661no—
1416C2×C4—1661no—
1417C2×C4—1661no—
1418C2×C4—1661no—
1419C2×C4—1661no—
1420C2×C4—1661no—
1421C2×C4—1661no—
1422C2×C4—1661no—
1423C2×C4—1661no—
1424C2×C4—1661no—
1425C2×C4—1661no—
1426C2×C4—1661no—
1427C2×C4—1661no—
1428C2×C4—1661no—
1429C2×C4—1661no—
1430C2×C4—1661no—
1431C2×C4—1661no—
1432C2×C4—1661no—
1433C2×C4—1661no—
1434C2×C4—1661no—
1435C2×C4—1661no—
1436C2×C4—1661no—
1437C2×C4—1661no—
1438C2×C4—1661no—
1439C2×C4—1661no—
1440C2×C4—1661no—
1441C2×C4C22×C4×D8312yes—
1442C2×C4C22×C4×D8312yes—
1443C2×C4C22×C4×D8312yes—
1444C2×C4C22×C4×D8312yes—
1445C2×C4C22×C4×D8312yes—
1446C2×C4C22×C4×D8312yes—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—41no—
1451C22—41no—
1452C22—41no—
1453C22—41no—
1454C22—3321no—
1455C22—3321no—
1456C22—3321no—
1457C22—3321no—
1458C22—3321no—
1459C22—3321no—
1460C22—3321no—
1461C22—3321no—
1462C22—834no—
1463C22—6648no—
1464C22—1662no—
1465C22—1662no—
1466C22—1662no—
1467C22—1662no—
1468C22—1662no—
1469C22—1662no—
1470C22—1662no—
1471C22—1662no—
1472C22—1662no—
1473C22—1662no—
1474C22—1662no—
1475C22—1662no—
1476C22C23×C4×D8311yescharacteristic
1477C22H(5,𝔽2)×D8311yescharacteristic
1478C22H(5,𝔽2)×D8311yescharacteristic
1479C222−1+4×D8311yescharacteristic
1480C22#1912853611yescharacteristic
1481C22#1912853811yescharacteristic
1482C22#1912853811yescharacteristic
1483C4—22no—
1484C4—22no—
1485C4—22no—
1486C4—22no—
1487C4—22no—
1488C4—22no—
1489C4—41no—
1490C4—41no—
1491C4—41no—
1492C4—41no—
1493C4—41no—
1494C4—41no—
1495C4—41no—
1496C4—41no—
1497C4—3321no—
1498C4—3321no—
1499C4—3321no—
1500C4—3321no—
1501C4—3321no—
1502C4—3321no—
1503C4—3321no—
1504C4—1662no—
1505C4—1662no—
1506C4—1662no—
1507C4—1662no—
1508C4—1662no—
1509C4—1662no—
1510C2—42no—
1511C2—3322no—
1512C2—3322no—
1513C2—1664no—
1514C2#520×D8311yescharacteristic
1515C2#2492066511yescharacteristic
1516C2#2492066711yescharacteristic
1517C2#2492167411yescharacteristic
1518C2#2492177611yescharacteristic
1519C2#2492181311yescharacteristic
1520C2#2492208511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2378C2
socle, cosocleC23×C83C25
prime radicalC2×#14581762C22
hypercenter#2378D83
hypocenterC83#34479
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2378

Complements

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

NH ≅ G/Ntype
2. #24910653C2semidirect
3. #24910635C2semidirect
4. #24910609C2semidirect
5. #24910589C2semidirect
6. #24910542C2semidirect
7. #24910450C2semidirect
8. #24910448C2semidirect
10. #24910407C2semidirect
11. #24910372C2semidirect
12. #24910345C2semidirect
13. #24910318C2semidirect
14. #24910307C2semidirect
15. #24910305C2semidirect
16. #24910252C2semidirect
17. #24910246C2semidirect
18. #24910241C2semidirect
19. #24910231C2semidirect
20. #24910177C2semidirect
21. #24910147C2semidirect
22. #24910136C2semidirect
24. #24910092C2semidirect
25. #24910085C2semidirect
26. #24910076C2semidirect
27. #24910067C2semidirect
28. #24910001C2semidirect
29. #24909901C2semidirect
30. #388×D83C2semidirect
31. C83×#2378C2semidirect
32. #19128378C4semidirect
41. C2×Q8×Dic83C22semidirect
49. C2×#14581750C22semidirect
59. #19127608C22semidirect
63. #19127600C22semidirect
64. #19127600C22semidirect
65. #19127600C22semidirect
66. #19127599C22semidirect
67. #19127599C22semidirect
68. #19127598C22semidirect
69. #19127597C22semidirect
70. #19127596C22semidirect
80. #19127593C22semidirect
82. #19127592C22semidirect
89. #19127590C22semidirect
90. #19127590C22semidirect
91. #19127590C22semidirect
92. #19127590C22semidirect
95. #19127588C22semidirect
96. #19127588C22semidirect
97. #19127588C22semidirect
98. #19127587C22semidirect
99. #19127587C22semidirect
100. #19127586C22semidirect
101. #19127586C22semidirect
102. #19127585C22semidirect
103. #19127584C22semidirect
104. #19127584C22semidirect
105. #19127583C22semidirect
106. #19127582C22semidirect
122. #19127575C22semidirect
123. #19127575C22semidirect
124. #19127575C22semidirect
131. #19127572C22semidirect
132. #19127572C22semidirect
133. #19127570C22semidirect
134. #19127570C22semidirect
135. #19127568C22semidirect
136. #19127566C22semidirect
137. #19127565C22semidirect
138. #19127565C22semidirect
139. #19127565C22semidirect
146. #19127558C22semidirect
148. C4⋊C4×Dic83C22semidirect
149. C4⋊C4×Dic83C22semidirect
150. C4⋊C4×Dic83C22semidirect
151. C4×Dic83⋊C4C22semidirect
152. C4×Dic83⋊C4C22semidirect
153. #19127552C22semidirect
154. #19127552C22semidirect
155. #19127552C22semidirect
156. #19127552C22semidirect
161. C4×(C2×D83)⋊C4C22semidirect
167. #19127548C22semidirect
168. #19127547C22semidirect
169. #19127546C22semidirect
172. #95×D83C22semidirect
174. #391×C83C22semidirect
175. #391×C83C22semidirect
176. #389×C83C22semidirect
177. #389×C83C22semidirect
182. #387×C83C22semidirect
183. #387×C83C22semidirect
184. #387×C83C22semidirect
185. #387×C83C22semidirect
204. #14581787C2×C4semidirect
205. #14581787C2×C4semidirect
206. #14581781C2×C4semidirect
207. #14581777C2×C4semidirect
208. #14581777C2×C4semidirect
209. #14581776C2×C4semidirect
210. #14581768C2×C4semidirect
216. #14581754C2×C4semidirect
217. C4×C22⋊D83C2×C4semidirect
220. #14581750C2×C4semidirect
222. #14581748C2×C4semidirect
254. C2×(C2×D83)⋊C4C2×C4semidirect
285. C22⋊C4×D83C2×C4semidirect
336. C22⋊Q8×C83C2×C4semidirect
764. #2378D83semidirect
792. C83#34479semidirect
822. #391C2×D83semidirect
823. #391C2×D83semidirect
835. #389C2×D83semidirect
836. #389C2×D83semidirect
877. #387C2×D83semidirect
878. #387C2×D83semidirect
879. #387C2×D83semidirect
880. #387C2×D83semidirect
974. C22⋊Q8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283782
#249106532
#249106352
#249106092
#249105892
#249105422
#249104502
#249104482
#249104412
#249104072
#249103722
#249103452
#249103182
#249103072
#249103052
#249102522
#249102462
#249102412
#249102312
#249101772
#249101472
#249101362
#249101162
#249100922
#249100852
#249100762
#249100672
#249100012
#249099012
#388×D832
C83×#23782
#3447983