Finite Group Databasebeta

← #35566800

Subgroups — #35566800

Order 21248.

2584 conjugacy classes of subgroups.

The subgroup lattice has 1556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128361C211yesmaximal, characteristic
2#24910574C211yesmaximal, characteristic, complemented
3#24910570C211yesmaximal, characteristic, complemented
4#24910548C211yesmaximal, characteristic, complemented
5#24910540C211yesmaximal, characteristic, complemented
6#24910537C211yesmaximal, characteristic, complemented
7#24910509C211yesmaximal, characteristic, complemented
8#24910507C211yesmaximal, characteristic, complemented
9#24910485C211yesmaximal, characteristic, complemented
10#24910476C211yesmaximal, characteristic, complemented
11#24910425C211yesmaximal, characteristic, complemented
12#24910402C211yesmaximal, characteristic, complemented
13#24910400C211yesmaximal, characteristic, complemented
14#24910387C211yesmaximal, characteristic, complemented
15#24910297C211yesmaximal, characteristic, complemented
16#24910287C211yesmaximal, characteristic, complemented
17#24910275C211yesmaximal, characteristic, complemented
18#24910270C211yesmaximal, characteristic, complemented
19#24910214C211yesmaximal, characteristic, complemented
20#24910167C211yesmaximal, characteristic, complemented
21#24910162C211yesmaximal, characteristic, complemented
22#24910004C211yesmaximal, characteristic, complemented
23C4×#14581770C211yesmaximal, characteristic, complemented
24#24909975C211yesmaximal, characteristic, complemented
25#24909949C211yesmaximal, characteristic, complemented
26#24909936C211yesmaximal, characteristic, complemented
27#391×D83C211yesmaximal, characteristic, complemented
28#24909823C211yesmaximal, characteristic, complemented
29#24909822C211yesmaximal, characteristic, complemented
30C4×#14581754C211yesmaximal, characteristic, complemented
31C83×#2332C211yesmaximal, characteristic, complemented
32C22×#13050590C2211yescharacteristic
33C22×Q8×D83C2211yescharacteristic
34#19128361C4116yescomplemented
35C2×#14581781C2211yescharacteristic
36C2×#14581778C2211yescharacteristic
37C2×#14581778C2211yescharacteristic
38C2×#14581770C2211yescharacteristic
39C2×#14581770C2211yescharacteristic
40C2×#14581767C2211yescharacteristic
41C2×#14581765C2211yescharacteristic
42C2×#14581765C2211yescharacteristic
43C2×C4×Dic166C2211yescharacteristic
44C2×#14581757C2211yescharacteristic
45C2×#14581757C2211yescharacteristic
46C2×C4×D332C2211yescharacteristic
47C2×C4×D332C2211yescharacteristic
48C2×#14581754C2211yescharacteristic
49C2×#14581754C2211yescharacteristic
50C2×#14581754C2211yescharacteristic
51C2×#14581754C2211yescharacteristic
52C2×C4×C22⋊D83C2211yescharacteristic
53C2×(C22⋊D83)⋊C4C2211yescharacteristic
54C2×(C22⋊D83)⋊C4C2211yescharacteristic
55C2×(C22⋊D83)⋊C4C2211yescharacteristic
56C2×(C22⋊D83)⋊C4C2211yescharacteristic
57C2×#14581749C2211yescharacteristic
58C2×C4⋊C4×D83C2211yescharacteristic
59C2×C42×D83C2211yescharacteristic
60C2×C42×D83C2211yescharacteristic
61#19127608C2211yescharacteristic
62#19127608C2211yescharacteristic
63#19127607C2211yescharacteristic
64#19127606C2211yescharacteristic
65#19127605C2211yescharacteristic
66#19127605C2211yescharacteristic
67#19127605C2211yescharacteristic
68#19127605C2211yescharacteristic
69#19127605C2211yescharacteristic
70#19127605C2211yescharacteristic
71#19127605C2211yescharacteristic
72#19127605C2211yescharacteristic
73#19127601C2211yescharacteristic
74#19127601C2211yescharacteristic
75#19127598C2211yescharacteristic
76#19127596C2211yescharacteristic
77#19127595C2211yescharacteristic
78#19127595C2211yescharacteristic
79#19127593C2211yescharacteristic
80#19127593C2211yescharacteristic
81#19127593C2211yescharacteristic
82#19127593C2211yescharacteristic
83#19127592C2211yescharacteristic
84#19127592C2211yescharacteristic
85#19127591C2211yescharacteristic
86#19127591C2211yescharacteristic
87#19127591C2211yescharacteristic
88#19127591C2211yescharacteristic
89#19127590C2211yescharacteristic
90#19127590C2211yescharacteristic
91#19127588C2211yescharacteristic
92#19127587C2211yescharacteristic
93#19127587C2211yescharacteristic
94#19127587C2211yescharacteristic
95#19127587C2211yescharacteristic
96#19127585C2211yescharacteristic
97#19127583C2211yescharacteristic
98#19127583C2211yescharacteristic
99#19127583C2211yescharacteristic
100#19127582C2211yescharacteristic
101#19127579C2211yescharacteristic
102#19127579C2211yescharacteristic
103#19127579C2211yescharacteristic
104#19127579C2211yescharacteristic
105#19127579C2211yescharacteristic
106#19127579C2211yescharacteristic
107#19127579C2211yescharacteristic
108#19127579C2211yescharacteristic
109#19127578C2211yescharacteristic
110#19127578C2211yescharacteristic
111#19127577C2211yescharacteristic
112#19127577C2211yescharacteristic
113#19127577C2211yescharacteristic
114#19127577C2211yescharacteristic
115#19127576C2211yescharacteristic
116#19127576C2211yescharacteristic
117#19127575C2211yescharacteristic
118#19127575C2211yescharacteristic
119#19127572C2211yescharacteristic
120#19127572C2211yescharacteristic
121#19127568C2211yescharacteristic
122#19127568C2211yescharacteristic
123#19127565C2211yescharacteristic
124#19127563C2211yescharacteristic
125#19127560C2211yescharacteristic
126#19127560C2211yescharacteristic
127#19127560C2211yescharacteristic
128#19127558C2211yescharacteristic
129C4⋊C4×Dic83C2211yescharacteristic
130C4⋊C4×Dic83C2211yescharacteristic
131C4⋊C4×Dic83C2211yescharacteristic
132C4⋊C4×Dic83C2211yescharacteristic
133C4×Dic83⋊C4C2211yescharacteristic
134C4×Dic83⋊C4C2211yescharacteristic
135C4×Dic83⋊C4C2211yescharacteristic
136#19127552C2211yescharacteristic
137#19127552C2211yescharacteristic
138#19127552C2211yescharacteristic
139C22⋊C4×Dic83C2211yescharacteristic
140C22⋊C4×Dic83C2211yescharacteristic
141C22⋊C4×Dic83C2211yescharacteristic
142C22⋊C4×Dic83C2211yescharacteristic
143C4×(C2×D83)⋊C4C2211yescharacteristic
144C4×(C2×D83)⋊C4C2211yescharacteristic
145C4×(C2×D83)⋊C4C2211yescharacteristic
146C4×(C2×D83)⋊C4C2211yescharacteristic
147C4×(C2×D83)⋊C4C2211yescharacteristic
148C4×(C2×D83)⋊C4C2211yescharacteristic
149C4×(C2×D83)⋊C4C2211yescharacteristic
150C4×(C2×D83)⋊C4C2211yescharacteristic
151C4×(C2×D83)⋊C4C2211yescharacteristic
152C4×C22⋊Dic83C2211yescharacteristic
153#19127548C2211yescharacteristic
154#19127548C2211yescharacteristic
155#19127548C2211yescharacteristic
156#19127548C2211yescharacteristic
157#19127548C2211yescharacteristic
158#19127548C2211yescharacteristic
159#19127548C2211yescharacteristic
160#19127548C2211yescharacteristic
161#19127548C2211yescharacteristic
162#19127547C2211yescharacteristic
163#19127546C2211yescharacteristic
164#19127546C2211yescharacteristic
165#19127546C2211yescharacteristic
166C2×C83⋊#95C2211yescharacteristic
167#95×D83C2211yescharacteristic
168#95×D83C2211yescharacteristic
169#95×D83C2211yescharacteristic
170#95×D83C2211yescharacteristic
171#95×D83C2211yescharacteristic
172C42×Dic83C2211yescharacteristic
173C2×C22⋊Q8×C83C2211yescharacteristic
174#391×C83C2211yescharacteristic
175#391×C83C2211yescharacteristic
176#388×C83C2211yescharacteristic
177#388×C83C2211yescharacteristic
178#388×C83C2211yescharacteristic
179#388×C83C2211yescharacteristic
180#387×C83C2211yescharacteristic
181#387×C83C2211yescharacteristic
182#387×C83C2211yescharacteristic
183#387×C83C2211yescharacteristic
184#381×C83C2211yescharacteristic
185C4×C4⋊C4×C83C2211yescharacteristic
186C4×C4⋊C4×C83C2211yescharacteristic
187C4×C22⋊C4×C83C2211yescharacteristic
188C2×#13050590—42no—
189C2×#13050590—42no—
190C2×#13050590C2×C418yescomplemented
191C22×Dic166C2311yescharacteristic
192C22×Dic166C2311yescharacteristic
193C22×Dic166C2311yescharacteristic
194C2×Q8×D83—42no—
195C2×Q8×D83—42no—
196C2×Q8×D83C2×C418yescomplemented
197C22×D332C2311yescharacteristic
198C22×D332C2311yescharacteristic
199C22×D332C2311yescharacteristic
200C22×C22⋊D83C2311yescharacteristic
201C22×C22⋊D83C2311yescharacteristic
202C22×C22⋊D83C2311yescharacteristic
203C23×Dic83C2311yescharacteristic
204C23×Dic83C2311yescharacteristic
205C22×C4×D83C2311yescharacteristic
206C22×C4×D83C2311yescharacteristic
207C22×C4×D83C2311yescharacteristic
208C22×C4×D83C2311yescharacteristic
209C22×C4×D83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
211C22×C4×D83C2311yescharacteristic
212C22×C4×D83C2311yescharacteristic
213C22×C4×D83C2311yescharacteristic
214C22×C4×D83C2311yescharacteristic
215C22×C4×D83C2311yescharacteristic
216C22×C4×D83C2311yescharacteristic
217C22×C4×D83C2311yescharacteristic
218#14581781C2×C418yescomplemented
219#14581778C2×C418yescomplemented
220#14581778C2×C418yescomplemented
221#14581770C2×C418yescomplemented
222#14581770C2×C418yescomplemented
223#14581767C2×C418yescomplemented
224#14581765C2×C418yescomplemented
225#14581765C2×C418yescomplemented
226C4×Dic166—42no—
227#14581757—42no—
228#14581757C2×C418yescomplemented
229C4×D332—24no—
230C4×D332—24no—
231#14581754—24no—
232#14581754—24no—
233#14581754C2×C418yescomplemented
234#14581754C2×C418yescomplemented
235C4×C22⋊D83C2×C418yescomplemented
236(C22⋊D83)⋊C4—24no—
237(C22⋊D83)⋊C4—24no—
238(C22⋊D83)⋊C4—42no—
239(C22⋊D83)⋊C4—42no—
240#14581749—42no—
241C2×C4⋊Dic83C2311yescharacteristic
242C2×C4⋊Dic83C2311yescharacteristic
243C2×C4⋊Dic83C2311yescharacteristic
244C2×C4⋊Dic83C2311yescharacteristic
245C2×Dic83⋊C4C2311yescharacteristic
246C2×Dic83⋊C4C2311yescharacteristic
247C2×Dic83⋊C4C2311yescharacteristic
248C2×Dic83⋊C4C2311yescharacteristic
249C2×Dic83⋊C4C2311yescharacteristic
250C2×Dic83⋊C4C2311yescharacteristic
251C2×Dic83⋊C4C2311yescharacteristic
252C2×Dic83⋊C4C2311yescharacteristic
253C2×Dic83⋊C4C2311yescharacteristic
254C2×Dic83⋊C4C2311yescharacteristic
255C2×Dic83⋊C4C2311yescharacteristic
256C4⋊C4×D83—42no—
257C2×C22⋊Dic83C2311yescharacteristic
258C2×C22⋊Dic83C2311yescharacteristic
259C2×C22⋊Dic83C2311yescharacteristic
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
282C2×(C2×D83)⋊C4C2311yescharacteristic
283C2×C4×Dic83C2311yescharacteristic
284C2×C4×Dic83C2311yescharacteristic
285C2×C4×Dic83C2311yescharacteristic
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
303C2×C4×Dic83C2311yescharacteristic
304C42×D83—42no—
305C42×D83—42no—
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
334C83⋊#95C2311yescharacteristic
335C83⋊#95C2311yescharacteristic
336C83⋊#95C2311yescharacteristic
337C83⋊#95C2311yescharacteristic
338C83⋊#95C2311yescharacteristic
339C83⋊#95C2311yescharacteristic
340C22×Q8×C83C2311yescharacteristic
341C23×C4×C83C2311yescharacteristic
342C22⋊Q8×C83C2×C418yescomplemented
343C2×C4⋊C4×C83C2311yescharacteristic
344C2×C4⋊C4×C83C2311yescharacteristic
345C2×C4⋊C4×C83C2311yescharacteristic
346C2×C4⋊C4×C83C2311yescharacteristic
347C2×C4⋊C4×C83C2311yescharacteristic
348C2×C4⋊C4×C83C2311yescharacteristic
349C2×C4⋊C4×C83C2311yescharacteristic
350C2×C22⋊C4×C83C2311yescharacteristic
351C2×C22⋊C4×C83C2311yescharacteristic
352C2×C22⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C22⋊C4×C83C2311yescharacteristic
355C2×C22⋊C4×C83C2311yescharacteristic
356C2×C42×C83C2311yescharacteristic
357C2×C42×C83C2311yescharacteristic
358C2×C42×C83C2311yescharacteristic
359C2×C42×C83C2311yescharacteristic
360C2×C42×C83C2311yescharacteristic
361C2×C42×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
370#95×C83C2311yescharacteristic
371#95×C83C2311yescharacteristic
372#95×C83C2311yescharacteristic
373#95×C83C2311yescharacteristic
374#95×C83C2311yescharacteristic
375#95×C83C2311yescharacteristic
376C23×D83C2411yescharacteristic
377C23×D83C2411yescharacteristic
378C23×D83C2411yescharacteristic
379#13050590—416no—
380C2×Dic166—22no—
381C2×Dic166—22no—
382C2×Dic166—22no—
383C2×Dic166—22no—
384C2×Dic166—41no—
385C2×Dic166—41no—
386C2×Dic166C22×C414yes—
387C2×Dic166C22×C414yes—
388C2×Dic166C22×C414yes—
389Q8×D83—416no—
390C2×D332—22no—
391C2×D332—22no—
392C2×D332—22no—
393C2×D332—22no—
394C2×D332—41no—
395C2×D332—41no—
396C2×D332C22×C414yes—
397C2×D332C22×C414yes—
398C2×D332C22×C414yes—
399C2×C22⋊D83—22no—
400C2×C22⋊D83—22no—
401C2×C22⋊D83—22no—
402C2×C22⋊D83—22no—
403C2×C22⋊D83—41no—
404C2×C22⋊D83—41no—
405C2×C22⋊D83C22×C414yes—
406C2×C22⋊D83C22×C414yes—
407C2×C22⋊D83C22×C414yes—
408C22×Dic83—22no—
409C22×Dic83—22no—
410C22×Dic83—41no—
411C22×Dic83—41no—
412C22×Dic83—41no—
413C22×Dic83—41no—
414C22×Dic83C2411yescharacteristic
415C22×Dic83C2411yescharacteristic
416C22×Dic83C2411yescharacteristic
417C22×Dic83C2411yescharacteristic
418C22×Dic83C2411yescharacteristic
419C22×Dic83C2411yescharacteristic
420C22×Dic83C2411yescharacteristic
421C22×Dic83C2411yescharacteristic
422C22×Dic83C2411yescharacteristic
423C22×Dic83C2411yescharacteristic
424C22×Dic83C2411yescharacteristic
425C22×Dic83C2411yescharacteristic
426C22×Dic83C2411yescharacteristic
427C2×C4×D83—22no—
428C2×C4×D83—22no—
429C2×C4×D83—22no—
430C2×C4×D83—22no—
431C2×C4×D83—22no—
432C2×C4×D83—22no—
433C2×C4×D83—22no—
434C2×C4×D83—22no—
435C2×C4×D83—22no—
436C2×C4×D83—22no—
437C2×C4×D83—22no—
438C2×C4×D83—22no—
439C2×C4×D83—22no—
440C2×C4×D83—41no—
441C2×C4×D83—41no—
442C2×C4×D83—41no—
443C2×C4×D83—41no—
444C2×C4×D83—41no—
445C2×C4×D83—41no—
446C2×C4×D83—41no—
447C2×C4×D83—41no—
448C2×C4×D83—41no—
449C2×C4×D83—41no—
450C2×C4×D83—41no—
451C2×C4×D83—41no—
452C2×C4×D83—41no—
453C2×C4×D83—41no—
454C2×C4×D83—41no—
455C2×C4×D83—41no—
456C2×C4×D83—41no—
457C2×C4×D83—41no—
458C2×C4×D83—41no—
459C2×C4×D83—41no—
460C2×C4×D83C22×C414yes—
461C2×C4×D83C22×C414yes—
462C2×C4×D83C22×C414yes—
463C2×C4×D83C22×C414yes—
464C2×C4×D83C22×C414yes—
465C2×C4×D83#4114yescomplemented
466C4⋊Dic83—22no—
467C4⋊Dic83—22no—
468C4⋊Dic83—41no—
469C4⋊Dic83—41no—
470Dic83⋊C4—22no—
471Dic83⋊C4—22no—
472Dic83⋊C4—22no—
473Dic83⋊C4—22no—
474Dic83⋊C4—22no—
475Dic83⋊C4—22no—
476Dic83⋊C4—41no—
477Dic83⋊C4—41no—
478Dic83⋊C4C22×C414yes—
479Dic83⋊C4C22×C414yes—
480Dic83⋊C4C22×C414yes—
481C22⋊Dic83—22no—
482C22⋊Dic83—41no—
483C22⋊Dic83C22×C414yes—
484(C2×D83)⋊C4—22no—
485(C2×D83)⋊C4—22no—
486(C2×D83)⋊C4—22no—
487(C2×D83)⋊C4—22no—
488(C2×D83)⋊C4—22no—
489(C2×D83)⋊C4—22no—
490(C2×D83)⋊C4—22no—
491(C2×D83)⋊C4—22no—
492(C2×D83)⋊C4—41no—
493(C2×D83)⋊C4—41no—
494(C2×D83)⋊C4—41no—
495(C2×D83)⋊C4—41no—
496(C2×D83)⋊C4—41no—
497(C2×D83)⋊C4—41no—
498(C2×D83)⋊C4—41no—
499(C2×D83)⋊C4C22×C414yes—
500(C2×D83)⋊C4C22×C414yes—
501(C2×D83)⋊C4C22×C414yes—
502(C2×D83)⋊C4C22×C414yes—
503(C2×D83)⋊C4C22×C414yes—
504(C2×D83)⋊C4C22×C414yes—
505(C2×D83)⋊C4C22×C414yes—
506(C2×D83)⋊C4#4114yescomplemented
507C4×Dic83—22no—
508C4×Dic83—22no—
509C4×Dic83—22no—
510C4×Dic83—22no—
511C4×Dic83—22no—
512C4×Dic83—22no—
513C4×Dic83—22no—
514C4×Dic83—22no—
515C4×Dic83—22no—
516C4×Dic83—41no—
517C4×Dic83—41no—
518C4×Dic83—41no—
519C4×Dic83—41no—
520C4×Dic83—41no—
521C4×Dic83—41no—
522C4×Dic83—41no—
523C4×Dic83—41no—
524C4×Dic83—41no—
525C4×Dic83C22×C414yes—
526C4×Dic83C22×C414yes—
527C4×Dic83C22×C414yes—
528C24×C83C2411yescharacteristic
529C2×Q8×C83—41no—
530C2×Q8×C83—41no—
531C2×Q8×C83C22×C414yes—
532C22×C4×C83—41no—
533C22×C4×C83—41no—
534C22×C4×C83C22×C414yes—
535C22×C4×C83C2411yescharacteristic
536C22×C4×C83C2411yescharacteristic
537C22×C4×C83C2411yescharacteristic
538C22×C4×C83C2411yescharacteristic
539C22×C4×C83C2411yescharacteristic
540C22×C4×C83C2411yescharacteristic
541C22×C4×C83C2411yescharacteristic
542C22×C4×C83C2411yescharacteristic
543C22×C4×C83C2411yescharacteristic
544C22×C4×C83C2411yescharacteristic
545C22×C4×C83C2411yescharacteristic
546C22×C4×C83C2411yescharacteristic
547C22×C4×C83C2411yescharacteristic
548C22×C4×C83C2411yescharacteristic
549C4⋊C4×C83—22no—
550C4⋊C4×C83—22no—
551C4⋊C4×C83—41no—
552C4⋊C4×C83—41no—
553C4⋊C4×C83C22×C414yes—
554C4⋊C4×C83C22×C414yes—
555C4⋊C4×C83C22×C414yes—
556C22⋊C4×C83—22no—
557C22⋊C4×C83—22no—
558C22⋊C4×C83—41no—
559C22⋊C4×C83—41no—
560C22⋊C4×C83C22×C414yes—
561C22⋊C4×C83C22×C414yes—
562C42×C83—22no—
563C42×C83—22no—
564C42×C83—41no—
565C42×C83—41no—
566C42×C83—41no—
567C42×C83—41no—
568C23×C83—21no—
569C23×C83—21no—
570C23×C83—21no—
571C23×C83—21no—
572C23×C83—21no—
573C23×C83—21no—
574C23×C83C23×C412yes—
575C23×C83C2511yescharacteristic
576C22×D83—21no—
577C22×D83—21no—
578C22×D83—21no—
579C22×D83—21no—
580C22×D83—21no—
581C22×D83—21no—
582C22×D83—21no—
583C22×D83—21no—
584C22×D83—21no—
585C22×D83—21no—
586C22×D83—21no—
587C22×D83—21no—
588C22×D83—21no—
589C22×D83—21no—
590C22×D83—21no—
591C22×D83—21no—
592C22×D83C23×C412yes—
593C22×D83C23×C412yes—
594C22×D83C23×C412yes—
595C22×D83C2×#4112yes—
596C22×D83C2×#4112yes—
597Q8×C83—44no—
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—44no—
633C2×C4×C83C23×C412yes—
634C2×C4×C83C23×C412yes—
635C2×C4×C83C23×C412yes—
636C2×C4×C83C23×C412yes—
637C2×C4×C83C23×C412yes—
638C2×C4×C83C23×C412yes—
639C2×C4×C83C2×#4112yes—
640C2×C4×C83C2×#4112yes—
641C22⋊D83—28no—
642C22⋊D83—28no—
643C22⋊D83—44no—
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—21no—
667C2×Dic83—21no—
668C2×Dic83—21no—
669C2×Dic83—21no—
670C2×Dic83—21no—
671C2×Dic83—21no—
672C2×Dic83—21no—
673C2×Dic83—82no—
674C2×Dic83—82no—
675C2×Dic83C23×C412yes—
676C2×Dic83C23×C412yes—
677C2×Dic83C23×C412yes—
678C2×Dic83C23×C412yes—
679C2×Dic83C23×C412yes—
680C2×Dic83C2×#4112yes—
681C2×Dic83C2×#4112yes—
682C2×Dic83H(5,𝔽2)12yes—
683C2×Dic83H(5,𝔽2)12yes—
684C2×Dic832−1+412yes—
685D332—28no—
686D332—28no—
687D332—44no—
688C4×D83—28no—
689C4×D83—28no—
690C4×D83—44no—
691C4×D83—44no—
692C4×D83—44no—
693C4×D83—44no—
694C4×D83—44no—
695C4×D83—44no—
696C4×D83—44no—
697C4×D83—82no—
698C4×D83—82no—
699C4×D83—82no—
700C4×D83—82no—
701Dic166—28no—
702Dic166—28no—
703Dic166—44no—
704C22×C83—22no—
705C22×C83—22no—
706C22×C83—22no—
707C22×C83—41no—
708C22×C83—41no—
709C22×C83—41no—
710C22×C83—41no—
711C22×C83C24×C411yescharacteristic
712C22×C83C22×#4111yescharacteristic
713C22×C83C22×#4111yescharacteristic
714C22×C83C2×H(5,𝔽2)11yescharacteristic
715C22×C83C2×H(5,𝔽2)11yescharacteristic
716C22×C83C2×2−1+411yescharacteristic
717C22×C83#58511yescharacteristic
718C2×D83—22no—
719C2×D83—22no—
720C2×D83—22no—
721C2×D83—22no—
722C2×D83—22no—
723C2×D83—22no—
724C2×D83—22no—
725C2×D83—22no—
726C2×D83—22no—
727C2×D83—22no—
728C2×D83—22no—
729C2×D83—22no—
730C2×D83—41no—
731C2×D83—41no—
732C2×D83—41no—
733C2×D83—41no—
734C2×D83—41no—
735C2×D83—41no—
736C2×D83—41no—
737C2×D83—41no—
738C2×D83C4×#4114yes—
739C4×C83—22no—
740C4×C83—22no—
741C4×C83—22no—
742C4×C83—22no—
743C4×C83—22no—
744C4×C83—22no—
745C4×C83—22no—
746C4×C83—22no—
747C4×C83—41no—
748C4×C83—41no—
749C4×C83—41no—
750C4×C83—41no—
751C4×C83—41no—
752C4×C83—41no—
753Dic83—22no—
754Dic83—22no—
755Dic83—22no—
756Dic83—22no—
757Dic83—22no—
758Dic83—22no—
759Dic83—22no—
760Dic83—41no—
761Dic83—41no—
762Dic83—41no—
763Dic83—41no—
764Dic83—41no—
765Dic83#51814yes—
766#34327—831nomaximal, Sylow
767C2×C83—42no—
768C2×C83C2×C4×#4111yescharacteristic
769C2×C83C2×#51811yescharacteristic
770C2×C83C4×2−1+411yescharacteristic
771C2×C83#350511yescharacteristic
772C2×C83#351111yescharacteristic
773C2×C83#351411yescharacteristic
774C2×C83#352011yescharacteristic
775D83—24no—
776D83—42no—
777D83—42no—
778C2×#548—831no—
779#2372—831no—
780#2372—831no—
781#2368—831no—
782#2368—831no—
783#2367—831no—
784#2364—831no—
785#2364—831no—
786#2362—831no—
787#2361—831no—
788#2356—831no—
789#2353—831no—
790#2353—831no—
791#2352—831no—
792Q8×C22⋊C4—831no—
793#2339—831no—
794#2337—831no—
795#2337—831no—
796#2332—831no—
797#2332D8311yescharacteristic, complemented
798#2325—831no—
799#2325—831no—
800C4×#124—831no—
801C4×C22⋊Q8—831no—
802C4×#121—831no—
803#2297—831no—
804#2295—831no—
805C2×#391—831no—
806#2275—831no—
807#2275—831no—
808C42×D4—831no—
809C83#3432711yescharacteristic, complemented, Sylow
810C22×#41—831no—
811C23×Q8—831no—
812#548—8316no—
813C2×#124—831no—
814C2×#124—831no—
815C2×#124—831no—
816C2×C22⋊Q8—831no—
817C2×C22⋊Q8—831no—
818C2×C22⋊Q8C2×D8311yescharacteristic
819C2×#121—831no—
820C2×#121—831no—
821C2×#121—831no—
822C2×C4×Q8—831no—
823C2×C4×Q8—831no—
824C2×C4×Q8—831no—
825C2×C4×D4—831no—
826C2×C4×D4—831no—
827C2×C4×D4—831no—
828C2×C4×D4—831no—
829C2×C4×D4—831no—
830C2×C4×D4—831no—
831C2×C4×D4—831no—
832C2×C4×D4—831no—
833C2×C4×D4—831no—
834C2×C4×D4—831no—
835C2×C4×D4—831no—
836C2×#117—831no—
837C22×C4⋊C4—831no—
838C22×C42—831no—
839C22×C42—831no—
840#391—831no—
841#391—831no—
842#391—831no—
843#391—831no—
844#391—831no—
845#391—831no—
846#391—831no—
847#391—831no—
848#391—831no—
849#391—831no—
850#391—831no—
851#391—831no—
852#391C2×D8311yescharacteristic
853#391C2×D8311yescharacteristic
854#390—831no—
855#390—831no—
856#389—831no—
857#389—831no—
858#388—831no—
859#388—831no—
860#388—831no—
861#388—831no—
862#388—831no—
863#388—831no—
864#388—831no—
865#388—831no—
866#388—831no—
867#388—831no—
868#388—831no—
869#388—831no—
870#388—831no—
871#388—831no—
872#388C2×D8311yescharacteristic
873#388C2×D8311yescharacteristic
874#388C2×D8311yescharacteristic
875#388C2×D8311yescharacteristic
876#387—831no—
877#387—831no—
878#387—831no—
879#387—831no—
880#387—831no—
881#387—831no—
882#387—831no—
883#387—831no—
884#387—831no—
885#387—831no—
886#387C2×D8311yescharacteristic
887#387C2×D8311yescharacteristic
888#387C2×D8311yescharacteristic
889#387C2×D8311yescharacteristic
890#386—831no—
891#386—831no—
892#386—831no—
893#386—831no—
894#386—831no—
895#386—831no—
896#386—831no—
897#386—831no—
898#386—831no—
899#386—831no—
900#386—831no—
901#386—831no—
902#386—831no—
903#386—831no—
904#385—831no—
905#385—831no—
906#385—831no—
907#385—831no—
908#385—831no—
909#385—831no—
910#383—831no—
911#383—831no—
912#382—831no—
913#381—831no—
914#381C2×D8311yescharacteristic
915#380—831no—
916#380—831no—
917#380—831no—
918#380—831no—
919C4×C4⋊C4—831no—
920C4×C4⋊C4—831no—
921C4×C4⋊C4—831no—
922C4×C4⋊C4—831no—
923C4×C4⋊C4—831no—
924C4×C4⋊C4—831no—
925C4×C4⋊C4—831no—
926C4×C4⋊C4—831no—
927C4×C4⋊C4—831no—
928C4×C4⋊C4—831no—
929C4×C4⋊C4C2×D8311yescharacteristic
930C4×C4⋊C4C2×D8311yescharacteristic
931C4×C22⋊C4—831no—
932C4×C22⋊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—
944C4×C22⋊C4—831no—
945C4×C22⋊C4—831no—
946C4×C22⋊C4—831no—
947C4×C22⋊C4—831no—
948C4×C22⋊C4—831no—
949C4×C22⋊C4—831no—
950C4×C22⋊C4—831no—
951C4×C22⋊C4—831no—
952C4×C22⋊C4—831no—
953C4×C22⋊C4—831no—
954C4×C22⋊C4C2×D8311yescharacteristic
955#376—831no—
956#376—831no—
957#376—831no—
958#376—831no—
959C2×#95—831no—
960C2×#95—831no—
961C2×#95—831no—
962C2×#95—831no—
963C2×#95—831no—
964C2×#95—831no—
965C43—831no—
966C2×#41—3322no—
967C2×#41—3322no—
968C2×#41—838no—
969C22×Q8—3322no—
970C22×Q8—3322no—
971C22×Q8—838no—
972C22×Q8—831no—
973C22×Q8—831no—
974C22×Q8—831no—
975C22×Q8C22×D8311yescharacteristic
976C22×D4—831no—
977C22×D4—831no—
978C22×D4—831no—
979C22×D4—831no—
980C22×D4—831no—
981C22×D4—831no—
982C23×C4—831no—
983C23×C4—831no—
984C23×C4—831no—
985C23×C4—831no—
986C23×C4—831no—
987C23×C4—831no—
988C23×C4—831no—
989C23×C4—831no—
990C23×C4—831no—
991C23×C4—831no—
992C23×C4—831no—
993C23×C4—831no—
994C23×C4—831no—
995C23×C4—831no—
996C23×C4—831no—
997C23×C4C22×D8311yescharacteristic
998#124—838no—
999#124—838no—
1000#124—838no—
1001C22⋊Q8—838no—
1002C22⋊Q8—838no—
1003C22⋊Q8C4×D8318yescomplemented
1004#121—838no—
1005#121—838no—
1006#121—838no—
1007C4×Q8—3322no—
1008C4×Q8—3322no—
1009C4×Q8—838no—
1010C4×D4—3322no—
1011C4×D4—3322no—
1012C4×D4—838no—
1013C4×D4—838no—
1014C4×D4—838no—
1015C4×D4—1664no—
1016C4×D4—1664no—
1017C4×D4—1664no—
1018C4×D4—1664no—
1019C4×D4—1664no—
1020C4×D4—1664no—
1021#117—3322no—
1022C2×C4⋊C4—3322no—
1023C2×C4⋊C4—831no—
1024C2×C4⋊C4—831no—
1025C2×C4⋊C4—831no—
1026C2×C4⋊C4—831no—
1027C2×C4⋊C4—831no—
1028C2×C4⋊C4—831no—
1029C2×C4⋊C4—831no—
1030C2×C4⋊C4—831no—
1031C2×C4⋊C4—831no—
1032C2×C4⋊C4—831no—
1033C2×C4⋊C4—831no—
1034C2×C4⋊C4—831no—
1035C2×C4⋊C4—831no—
1036C2×C4⋊C4—831no—
1037C2×C4⋊C4—831no—
1038C2×C4⋊C4C22×D8311yescharacteristic
1039C2×C4⋊C4C22×D8311yescharacteristic
1040C2×C4⋊C4C22×D8311yescharacteristic
1041C2×C4⋊C4C22×D8311yescharacteristic
1042C2×C4⋊C4C22×D8311yescharacteristic
1043C2×C4⋊C4C22×D8311yescharacteristic
1044C2×C4⋊C4C22×D8311yescharacteristic
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—831no—
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⋊C4—831no—
1060C2×C22⋊C4—831no—
1061C2×C22⋊C4—831no—
1062C2×C22⋊C4—831no—
1063C2×C22⋊C4—831no—
1064C2×C22⋊C4—831no—
1065C2×C22⋊C4—831no—
1066C2×C22⋊C4—831no—
1067C2×C22⋊C4—831no—
1068C2×C22⋊C4—831no—
1069C2×C22⋊C4—831no—
1070C2×C22⋊C4—831no—
1071C2×C22⋊C4C22×D8311yescharacteristic
1072C2×C22⋊C4C22×D8311yescharacteristic
1073C2×C22⋊C4C22×D8311yescharacteristic
1074C2×C22⋊C4C22×D8311yescharacteristic
1075C2×C22⋊C4C22×D8311yescharacteristic
1076C2×C22⋊C4C22×D8311yescharacteristic
1077C2×C42—3322no—
1078C2×C42—3322no—
1079C2×C42—831no—
1080C2×C42—831no—
1081C2×C42—831no—
1082C2×C42—831no—
1083C2×C42—831no—
1084C2×C42—831no—
1085C2×C42—831no—
1086C2×C42—831no—
1087C2×C42—831no—
1088C2×C42—831no—
1089C2×C42—831no—
1090C2×C42—831no—
1091C2×C42—831no—
1092C2×C42—831no—
1093C2×C42—831no—
1094C2×C42—831no—
1095C2×C42—831no—
1096C2×C42—831no—
1097C2×C42—831no—
1098C2×C42—831no—
1099C2×C42—831no—
1100C2×C42C22×D8311yescharacteristic
1101C2×C42C22×D8311yescharacteristic
1102C2×C42C22×D8311yescharacteristic
1103C2×C42C22×D8311yescharacteristic
1104C2×C42C22×D8311yescharacteristic
1105C2×C42C22×D8311yescharacteristic
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#95—831no—
1118#95—831no—
1119#95—831no—
1120#95—831no—
1121#95—831no—
1122#95—831no—
1123#95—831no—
1124#95—831no—
1125#95—831no—
1126#95—831no—
1127#95—831no—
1128#95—831no—
1129#95—831no—
1130#95—831no—
1131#95—831no—
1132#95—831no—
1133#95—831no—
1134#95—831no—
1135#95—831no—
1136#95—831no—
1137#95—831no—
1138#95—831no—
1139#95—831no—
1140#95C22×D8311yescharacteristic
1141#95C22×D8311yescharacteristic
1142#95C22×D8311yescharacteristic
1143#95C22×D8311yescharacteristic
1144#95C22×D8311yescharacteristic
1145#95C22×D8311yescharacteristic
1146#95C22×D8311yescharacteristic
1147#95C22×D8311yescharacteristic
1148#95C22×D8311yescharacteristic
1149#95C22×D8311yescharacteristic
1150#95C22×D8311yescharacteristic
1151#95C22×D8311yescharacteristic
1152#95C22×D8311yescharacteristic
1153#95C22×D8311yescharacteristic
1154C24—831no—
1155C24—831no—
1156C24—831no—
1157C24C23×D8311yescharacteristic
1158#41—33216no—
1159C2×Q8—41no—
1160C2×Q8—41no—
1161C2×Q8—3321no—
1162C2×Q8—3321no—
1163C2×Q8—33216no—
1164C2×Q8—834no—
1165C2×Q8—834no—
1166C2×Q8—834no—
1167C2×Q8—1662no—
1168C2×Q8—1662no—
1169C2×Q8—1662no—
1170C2×Q8—1662no—
1171C2×Q8C2×C4×D8314yes—
1172C2×D4—3321no—
1173C2×D4—3321no—
1174C2×D4—3321no—
1175C2×D4—3321no—
1176C2×D4—834no—
1177C2×D4—834no—
1178C2×D4—834no—
1179C2×D4—834no—
1180C2×D4—834no—
1181C2×D4—834no—
1182C2×D4—1662no—
1183C2×D4—1662no—
1184C2×D4—1662no—
1185C2×D4—1662no—
1186C2×D4—1662no—
1187C2×D4—1662no—
1188C2×D4—1662no—
1189C2×D4—1662no—
1190C22×C4—41no—
1191C22×C4—41no—
1192C22×C4—3321no—
1193C22×C4—3321no—
1194C22×C4—3321no—
1195C22×C4—3321no—
1196C22×C4—3321no—
1197C22×C4—3321no—
1198C22×C4—3321no—
1199C22×C4—3321no—
1200C22×C4—3321no—
1201C22×C4—3321no—
1202C22×C4—3321no—
1203C22×C4—3321no—
1204C22×C4—3321no—
1205C22×C4—3321no—
1206C22×C4—3321no—
1207C22×C4—3321no—
1208C22×C4—3321no—
1209C22×C4—3321no—
1210C22×C4—3321no—
1211C22×C4—3321no—
1212C22×C4—3321no—
1213C22×C4—3321no—
1214C22×C4—3321no—
1215C22×C4—3321no—
1216C22×C4—834no—
1217C22×C4—834no—
1218C22×C4—834no—
1219C22×C4—834no—
1220C22×C4—831no—
1221C22×C4—831no—
1222C22×C4—831no—
1223C22×C4—831no—
1224C22×C4—831no—
1225C22×C4—831no—
1226C22×C4—831no—
1227C22×C4—831no—
1228C22×C4—834no—
1229C22×C4—834no—
1230C22×C4—831no—
1231C22×C4—831no—
1232C22×C4—831no—
1233C22×C4—831no—
1234C22×C4—831no—
1235C22×C4—1662no—
1236C22×C4—1662no—
1237C22×C4—1662no—
1238C22×C4—1662no—
1239C22×C4—1662no—
1240C22×C4—1662no—
1241C22×C4—1662no—
1242C22×C4—1662no—
1243C22×C4—1662no—
1244C22×C4—1662no—
1245C22×C4—1662no—
1246C22×C4—1662no—
1247C22×C4—1662no—
1248C22×C4—1662no—
1249C22×C4—1662no—
1250C22×C4C2×C4×D8314yes—
1251C22×C4C23×D8311yescharacteristic
1252C22×C4C23×D8311yescharacteristic
1253C22×C4C23×D8311yescharacteristic
1254C22×C4C23×D8311yescharacteristic
1255C22×C4C23×D8311yescharacteristic
1256C22×C4C23×D8311yescharacteristic
1257C22×C4C23×D8311yescharacteristic
1258C22×C4C23×D8311yescharacteristic
1259C22×C4C23×D8311yescharacteristic
1260C22×C4C23×D8311yescharacteristic
1261C22×C4C23×D8311yescharacteristic
1262C22×C4C23×D8311yescharacteristic
1263C22×C4C23×D8311yescharacteristic
1264C22×C4C23×D8311yescharacteristic
1265C4⋊C4—22no—
1266C4⋊C4—22no—
1267C4⋊C4—41no—
1268C4⋊C4—41no—
1269C4⋊C4—3321no—
1270C4⋊C4—3321no—
1271C4⋊C4—3321no—
1272C4⋊C4—3321no—
1273C4⋊C4—834no—
1274C4⋊C4—834no—
1275C4⋊C4—834no—
1276C4⋊C4—1662no—
1277C4⋊C4—1662no—
1278C4⋊C4—1662no—
1279C4⋊C4—1662no—
1280C4⋊C4—1662no—
1281C4⋊C4—1662no—
1282C4⋊C4—1662no—
1283C4⋊C4—1662no—
1284C4⋊C4C2×C4×D8314yes—
1285C4⋊C4C2×C4×D8314yes—
1286C4⋊C4C2×C4×D8314yes—
1287C22⋊C4—22no—
1288C22⋊C4—22no—
1289C22⋊C4—41no—
1290C22⋊C4—41no—
1291C22⋊C4—3321no—
1292C22⋊C4—3321no—
1293C22⋊C4—3321no—
1294C22⋊C4—3321no—
1295C22⋊C4—3321no—
1296C22⋊C4—3321no—
1297C22⋊C4—3321no—
1298C22⋊C4—3321no—
1299C22⋊C4—834no—
1300C22⋊C4—834no—
1301C22⋊C4—834no—
1302C22⋊C4—834no—
1303C22⋊C4—834no—
1304C22⋊C4—834no—
1305C22⋊C4—834no—
1306C22⋊C4—834no—
1307C22⋊C4—834no—
1308C22⋊C4—1662no—
1309C22⋊C4—1662no—
1310C22⋊C4—1662no—
1311C22⋊C4—1662no—
1312C22⋊C4—1662no—
1313C22⋊C4—1662no—
1314C22⋊C4—1662no—
1315C22⋊C4—1662no—
1316C22⋊C4—1662no—
1317C22⋊C4C2×C4×D8314yes—
1318C22⋊C4C2×C4×D8314yes—
1319C42—22no—
1320C42—22no—
1321C42—41no—
1322C42—41no—
1323C42—41no—
1324C42—41no—
1325C42—3321no—
1326C42—3321no—
1327C42—3321no—
1328C42—3321no—
1329C42—3321no—
1330C42—3321no—
1331C42—3321no—
1332C42—3321no—
1333C42—3321no—
1334C42—834no—
1335C42—834no—
1336C42—834no—
1337C42—1662no—
1338C42—1662no—
1339C42—1662no—
1340C42—1662no—
1341C42—1662no—
1342C42—1662no—
1343C42—1662no—
1344C42—1662no—
1345C42—1662no—
1346C23—21no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23—21no—
1351C23—21no—
1352C23—832no—
1353C23—832no—
1354C23—832no—
1355C23—832no—
1356C23—832no—
1357C23—1661no—
1358C23—1661no—
1359C23—1661no—
1360C23—1661no—
1361C23—1661no—
1362C23—1661no—
1363C23—1661no—
1364C23—1661no—
1365C23—1661no—
1366C23—1661no—
1367C23—1661no—
1368C23—1661no—
1369C23—1661no—
1370C23—1661no—
1371C23—1661no—
1372C23—1661no—
1373C23C22×C4×D8312yes—
1374C23C24×D8311yescharacteristic
1375Q8—44no—
1376Q8—3324no—
1377Q8—1668no—
1378Q8—1668no—
1379D4—3324no—
1380D4—3324no—
1381D4—1668no—
1382D4—1668no—
1383D4—1668no—
1384D4—1668no—
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—44no—
1420C2×C4—3324no—
1421C2×C4—3324no—
1422C2×C4—3324no—
1423C2×C4—3324no—
1424C2×C4—3324no—
1425C2×C4—3324no—
1426C2×C4—3324no—
1427C2×C4—832no—
1428C2×C4—832no—
1429C2×C4—832no—
1430C2×C4—832no—
1431C2×C4—832no—
1432C2×C4—832no—
1433C2×C4—832no—
1434C2×C4—832no—
1435C2×C4—832no—
1436C2×C4—832no—
1437C2×C4—6642no—
1438C2×C4—6642no—
1439C2×C4—6642no—
1440C2×C4—6642no—
1441C2×C4—6642no—
1442C2×C4—6642no—
1443C2×C4—1668no—
1444C2×C4—1668no—
1445C2×C4—1661no—
1446C2×C4—1661no—
1447C2×C4—1661no—
1448C2×C4—1661no—
1449C2×C4—1661no—
1450C2×C4—1661no—
1451C2×C4—1661no—
1452C2×C4—1661no—
1453C2×C4—1661no—
1454C2×C4—1661no—
1455C2×C4—1661no—
1456C2×C4—1661no—
1457C2×C4—1661no—
1458C2×C4—1661no—
1459C2×C4—1661no—
1460C2×C4—1661no—
1461C2×C4—1661no—
1462C2×C4—1661no—
1463C2×C4—1661no—
1464C2×C4—1661no—
1465C2×C4—1661no—
1466C2×C4—1661no—
1467C2×C4—1661no—
1468C2×C4—1661no—
1469C2×C4—1661no—
1470C2×C4—1661no—
1471C2×C4—1661no—
1472C2×C4—1661no—
1473C2×C4—1661no—
1474C2×C4C22×C4×D8312yes—
1475C2×C4C22×C4×D8312yes—
1476C2×C4C22×C4×D8312yes—
1477C2×C4C22×C4×D8312yes—
1478C2×C4C22×C4×D8312yes—
1479C2×C4C22×C4×D8312yes—
1480C2×C4#41×D8312yes—
1481C2×C4#41×D8312yes—
1482C22—22no—
1483C22—22no—
1484C22—22no—
1485C22—41no—
1486C22—41no—
1487C22—41no—
1488C22—41no—
1489C22—3321no—
1490C22—3321no—
1491C22—3321no—
1492C22—3321no—
1493C22—3321no—
1494C22—3321no—
1495C22—3321no—
1496C22—3321no—
1497C22—834no—
1498C22—1662no—
1499C22—1662no—
1500C22—1662no—
1501C22—1662no—
1502C22—1662no—
1503C22—1662no—
1504C22—1662no—
1505C22—1662no—
1506C22—1662no—
1507C22—1662no—
1508C22—1662no—
1509C22—1662no—
1510C22C23×C4×D8311yescharacteristic
1511C22C2×#41×D8311yescharacteristic
1512C22C2×#41×D8311yescharacteristic
1513C22H(5,𝔽2)×D8311yescharacteristic
1514C22H(5,𝔽2)×D8311yescharacteristic
1515C222−1+4×D8311yescharacteristic
1516C22#1912853811yescharacteristic
1517C4—22no—
1518C4—22no—
1519C4—22no—
1520C4—22no—
1521C4—22no—
1522C4—22no—
1523C4—22no—
1524C4—22no—
1525C4—41no—
1526C4—41no—
1527C4—41no—
1528C4—41no—
1529C4—41no—
1530C4—41no—
1531C4—3321no—
1532C4—3321no—
1533C4—3321no—
1534C4—3321no—
1535C4—3321no—
1536C4—834no—
1537C4—1662no—
1538C4—1662no—
1539C4—1662no—
1540C4—1662no—
1541C4—1662no—
1542C4—1662no—
1543C4—1662no—
1544C2—42no—
1545C2—3322no—
1546C2—3322no—
1547C2—1664no—
1548C2C4×#41×D8311yescharacteristic
1549C2#518×D8311yescharacteristic
1550C2#2492067211yescharacteristic
1551C2#2492129511yescharacteristic
1552C2#2492136811yescharacteristic
1553C2#2492142211yescharacteristic
1554C2#2492150411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2332C2
socle, cosocleC23×C83C25
prime radicalC2×#19128361C2
hypercenter#2332D83
hypocenterC83#34327
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2332

Complements

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

NH ≅ G/Ntype
2. #24910574C2semidirect
3. #24910570C2semidirect
4. #24910548C2semidirect
5. #24910540C2semidirect
6. #24910537C2semidirect
7. #24910509C2semidirect
8. #24910507C2semidirect
9. #24910485C2semidirect
10. #24910476C2semidirect
11. #24910425C2semidirect
12. #24910402C2semidirect
13. #24910400C2semidirect
14. #24910387C2semidirect
15. #24910297C2semidirect
16. #24910287C2semidirect
17. #24910275C2semidirect
18. #24910270C2semidirect
19. #24910214C2semidirect
20. #24910167C2semidirect
21. #24910162C2semidirect
22. #24910004C2semidirect
23. C4×#14581770C2semidirect
24. #24909975C2semidirect
25. #24909949C2semidirect
26. #24909936C2semidirect
27. #391×D83C2semidirect
28. #24909823C2semidirect
29. #24909822C2semidirect
30. C4×#14581754C2semidirect
31. C83×#2332C2semidirect
34. #19128361C4semidirect
190. C2×#13050590C2×C4semidirect
196. C2×Q8×D83C2×C4semidirect
218. #14581781C2×C4semidirect
219. #14581778C2×C4semidirect
220. #14581778C2×C4semidirect
221. #14581770C2×C4semidirect
222. #14581770C2×C4semidirect
223. #14581767C2×C4semidirect
224. #14581765C2×C4semidirect
225. #14581765C2×C4semidirect
228. #14581757C2×C4semidirect
233. #14581754C2×C4semidirect
234. #14581754C2×C4semidirect
235. C4×C22⋊D83C2×C4semidirect
342. C22⋊Q8×C83C2×C4semidirect
465. C2×C4×D83#41semidirect
506. (C2×D83)⋊C4#41semidirect
797. #2332D83semidirect
809. C83#34327semidirect
1003. C22⋊Q8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191283612
#249105742
#249105702
#249105482
#249105402
#249105372
#249105092
#249105072
#249104852
#249104762
#249104252
#249104022
#249104002
#249103872
#249102972
#249102872
#249102752
#249102702
#249102142
#249101672
#249101622
#249100042
C4×#145817702
#249099752
#249099492
#249099362
#391×D832
#249098232
#249098222
C4×#145817542
C83×#23322
#3432783