Finite Group Databasebeta

← #35577428

Subgroups — #35577428

Order 21248.

2930 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581770C211yesmaximal, characteristic, complemented
2C2×C4×D4×D83C211yesmaximal, characteristic
3#24915798C212yesmaximal, complemented
4#24915749C212yesmaximal, complemented
5#24913281C212yesmaximal, complemented
6#24913273C212yesmaximal, complemented
7#24912812C211yesmaximal, characteristic, complemented
8#24912810C211yesmaximal, characteristic, complemented
9#24912806C211yesmaximal, characteristic, complemented
10#24912648C212yesmaximal, complemented
11#24912642C212yesmaximal, complemented
12#24911779C211yesmaximal, characteristic, complemented
13#24911777C211yesmaximal, characteristic, complemented
14#24910909C212yesmaximal, complemented
15#24910907C212yesmaximal, complemented
16#24910827C211yesmaximal, characteristic, complemented
17#24910825C211yesmaximal, characteristic, complemented
18#24910074C211yesmaximal, characteristic, complemented
19#24910074C211yesmaximal, characteristic, complemented
20#24910037C211yesmaximal, characteristic
21#24910037C211yesmaximal, characteristic
22#380×D83C211yesmaximal, characteristic, complemented
23C83×#2579C211yesmaximal, characteristic, complemented
24C23×Dic166C2211yescharacteristic, complemented
25C22×D4×D83C2211yescharacteristic
26C23×C4×D83C2211yescharacteristic
27C23×C4×D83C2211yescharacteristic
28C2×#14581770—28no—
29C2×#14581770C2212yes—
30C2×#14581770C2212yes—
31C2×#14581770C2212yescomplemented
32C2×#14581770C2212yescomplemented
33C2×#14581770C2212yescomplemented
34C2×#14581769C2212yescomplemented
35C2×C4×D332C2211yescharacteristic
36C2×D4×Dic83C2211yescharacteristic
37C2×#14581754C2211yescharacteristic
38C2×C4×C22⋊D83C2211yescharacteristic
39C2×C4×C22⋊D83C2211yescharacteristic
40C2×(C22⋊D83)⋊C4C2211yescharacteristic
41C2×(C22⋊D83)⋊C4C2211yescharacteristic
42C4×D4×D83—28no—
43C22×Dic83⋊C4C2211yescharacteristic, complemented
44C22×Dic83⋊C4C2211yescharacteristic, complemented
45C2×C4⋊C4×D83C2211yescharacteristic
46C2×C4⋊C4×D83C2212yescomplemented
47C22×(C2×D83)⋊C4C2211yescharacteristic
48C22×(C2×D83)⋊C4C2211yescharacteristic
49C2×C22⋊C4×D83C2211yescharacteristic
50C2×C22⋊C4×D83C2211yescharacteristic
51C2×C22⋊C4×D83C2211yescharacteristic
52C2×C22⋊C4×D83C2211yescharacteristic
53C2×C42×D83C2211yescharacteristic
54#19127643C2212yescomplemented
55#19127642C2212yescomplemented
56#19127637C2212yescomplemented
57#19127636C2212yescomplemented
58#19127634C2212yescomplemented
59#19127634C2212yescomplemented
60#19127631C2212yescomplemented
61#19127624C2212yescomplemented
62#19127623C2212yescomplemented
63#19127623C2212yescomplemented
64#19127622C2212yescomplemented
65#19127621C2212yescomplemented
66#19127614C2212yescomplemented
67#19127613C2212yescomplemented
68#19127605C2212yescomplemented
69#19127605C2212yescomplemented
70#19127598C2212yescomplemented
71#19127596C2212yescomplemented
72#19127586C2212yescomplemented
73#19127585C2212yescomplemented
74#19127582C2212yescomplemented
75#19127581C2211yescharacteristic
76#19127581C2211yescharacteristic
77#19127580C2211yescharacteristic
78#19127580C2211yescharacteristic
79#19127579C2212yes—
80#19127579C2212yes—
81#19127578C2211yescharacteristic
82#19127578C2211yescharacteristic
83#19127577C2212yes—
84#19127577C2212yes—
85#19127576C2211yescharacteristic, complemented
86#19127576C2211yescharacteristic, complemented
87#19127575C2212yes—
88#19127575C2212yes—
89#19127575C2212yescomplemented
90#19127574C2212yescomplemented
91#19127574C2211yescharacteristic, complemented
92#19127574C2211yescharacteristic, complemented
93#19127573C2211yescharacteristic, complemented
94#19127573C2211yescharacteristic, complemented
95#19127572C2212yes—
96#19127572C2212yes—
97#19127572C2212yescomplemented
98#19127563C2212yes—
99#19127563C2212yes—
100#19127561C2211yescharacteristic, complemented
101#19127560C2212yes—
102#19127560C2212yescomplemented
103#19127560C2212yescomplemented
104#19127560C2212yescomplemented
105#19127559C2211yescharacteristic, complemented
106#19127559C2211yescharacteristic, complemented
107#19127559C2212yescomplemented
108#19127558C2212yes—
109#19127558C2212yescomplemented
110#19127558C2212yescomplemented
111#19127556C2212yes—
112#19127556C2212yes—
113#95×D83C2212yescomplemented
114C2×C4×D4×C83C2211yescharacteristic
115C22×C4⋊C4×C83C2211yescharacteristic, complemented
116#398×C83C2212yescomplemented
117#396×C83C2212yescomplemented
118#387×C83C2212yescomplemented
119#386×C83C2211yescharacteristic
120#386×C83C2211yescharacteristic
121#385×C83C2212yescomplemented
122#385×C83C2211yescharacteristic, complemented
123#385×C83C2211yescharacteristic, complemented
124#380×C83C2211yescharacteristic, complemented
125C24×D83C2311yescharacteristic
126C24×D83C2311yescharacteristic
127C22×Dic166—24no—
128C22×Dic166—44no—
129C22×Dic166C2312yes—
130C22×Dic166C2312yes—
131C22×D332C2311yescharacteristic
132C22×C22⋊D83C2311yescharacteristic
133C22×C22⋊D83C2311yescharacteristic
134C2×D4×D83—24no—
135C2×D4×D83—24no—
136C2×D4×D83Q818yescomplemented
137C23×Dic83C2311yescharacteristic
138C23×Dic83C2311yescharacteristic
139C23×Dic83C2311yescharacteristic
140C23×Dic83C2311yescharacteristic
141C22×C4×D83—24no—
142C22×C4×D83—44no—
143C22×C4×D83—44no—
144C22×C4×D83D418yes—
145C22×C4×D83C2311yescharacteristic
146C22×C4×D83C2311yescharacteristic
147C22×C4×D83C2311yescharacteristic
148C22×C4×D83C2311yescharacteristic
149C22×C4×D83C2312yes—
150C22×C4×D83C2312yes—
151C22×C4×D83C2311yescharacteristic
152C22×C4×D83C2311yescharacteristic
153C22×C4×D83C2311yescharacteristic
154C22×C4×D83C2311yescharacteristic
155C22×C4×D83C2311yescharacteristic
156#14581770—28no—
157#14581770—28no—
158#14581770—28no—
159#14581770—28no—
160#14581770—44no—
161#14581769—44no—
162C4×D332—24no—
163D4×Dic83—24no—
164#14581754—24no—
165C4×C22⋊D83—24no—
166C4×C22⋊D83—24no—
167(C22⋊D83)⋊C4—24no—
168(C22⋊D83)⋊C4—24no—
169C2×C4⋊Dic83C2311yescharacteristic
170C2×C4⋊Dic83C2312yes—
171C2×C4⋊Dic83C2312yes—
172C2×C4⋊Dic83C2312yes—
173C2×Dic83⋊C4—24no—
174C2×Dic83⋊C4—24no—
175C2×Dic83⋊C4C2312yes—
176C2×Dic83⋊C4C2312yes—
177C2×Dic83⋊C4C2312yes—
178C2×Dic83⋊C4C2312yes—
179C2×Dic83⋊C4C2311yescharacteristic
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2311yescharacteristic
182C2×Dic83⋊C4C2312yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2312yes—
187C4⋊C4×D83—24no—
188C4⋊C4×D83—44no—
189C2×C22⋊Dic83C2311yescharacteristic
190C2×C22⋊Dic83C2311yescharacteristic
191C2×C22⋊Dic83C2311yescharacteristic
192C2×C22⋊Dic83C2311yescharacteristic
193C2×C22⋊Dic83C2312yes—
194C2×C22⋊Dic83C2312yes—
195C2×(C2×D83)⋊C4—24no—
196C2×(C2×D83)⋊C4—24no—
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2312yes—
199C2×(C2×D83)⋊C4C2312yes—
200C2×(C2×D83)⋊C4C2312yes—
201C2×(C2×D83)⋊C4C2311yescharacteristic
202C2×(C2×D83)⋊C4C2311yescharacteristic
203C2×(C2×D83)⋊C4C2312yes—
204C2×(C2×D83)⋊C4C2312yes—
205C2×(C2×D83)⋊C4C2311yescharacteristic
206C2×(C2×D83)⋊C4C2311yescharacteristic
207C2×(C2×D83)⋊C4C2312yes—
208C2×(C2×D83)⋊C4C2312yes—
209C2×(C2×D83)⋊C4C2312yes—
210C2×(C2×D83)⋊C4C2312yes—
211C22⋊C4×D83—24no—
212C22⋊C4×D83—24no—
213C22⋊C4×D83—24no—
214C22⋊C4×D83—24no—
215C2×C4×Dic83C2311yescharacteristic
216C2×C4×Dic83C2311yescharacteristic
217C2×C4×Dic83C2311yescharacteristic
218C42×D83—24no—
219C83⋊#95C2312yes—
220C83⋊#95C2312yes—
221C83⋊#95C2312yes—
222C83⋊#95C2312yes—
223C83⋊#95C2312yes—
224C83⋊#95C2312yes—
225C83⋊#95C2312yes—
226C83⋊#95C2312yes—
227C83⋊#95C2312yes—
228C83⋊#95C2312yes—
229C83⋊#95C2312yes—
230C83⋊#95C2312yes—
231C83⋊#95C2312yes—
232C83⋊#95C2312yes—
233C83⋊#95C2312yes—
234C22×D4×C83C2311yescharacteristic
235C23×C4×C83C2311yescharacteristic
236C23×C4×C83C2311yescharacteristic
237C23×C4×C83C2311yescharacteristic
238C23×C4×C83C2311yescharacteristic
239C4×D4×C83—24no—
240C2×C4⋊C4×C83—24no—
241C2×C4⋊C4×C83C2312yes—
242C2×C4⋊C4×C83C2312yes—
243C2×C4⋊C4×C83C2311yescharacteristic
244C2×C4⋊C4×C83C2312yes—
245C2×C4⋊C4×C83C2312yes—
246C2×C4⋊C4×C83C2312yes—
247C2×C22⋊C4×C83C2311yescharacteristic
248C2×C22⋊C4×C83C2311yescharacteristic
249C2×C22⋊C4×C83C2311yescharacteristic
250C2×C22⋊C4×C83C2311yescharacteristic
251C2×C22⋊C4×C83C2312yes—
252C2×C22⋊C4×C83C2312yes—
253C2×C42×C83C2311yescharacteristic
254#95×C83C2312yes—
255#95×C83C2312yes—
256#95×C83C2312yes—
257#95×C83C2312yes—
258#95×C83C2312yes—
259C23×D83—22no—
260C23×D83—22no—
261C23×D83—42no—
262C23×D83—42no—
263C23×D83—42no—
264C23×D83—42no—
265C23×D83C2×D414yes—
266C23×D83C2×Q814yes—
267C23×D83C2×Q814yescomplemented
268C23×D83#4114yes—
269C23×D83C2411yescharacteristic
270C23×D83C2411yescharacteristic
271C23×D83C2411yescharacteristic
272C2×Dic166—24no—
273C2×Dic166—24no—
274C2×Dic166—24no—
275C2×Dic166—24no—
276C2×Dic166—42no—
277C2×Dic166—42no—
278C2×Dic166—416no—
279C2×D332—22no—
280C2×D332—22no—
281C2×D332C2×Q814yescomplemented
282C2×C22⋊D83—22no—
283C2×C22⋊D83—22no—
284C2×C22⋊D83—22no—
285C2×C22⋊D83—22no—
286C2×C22⋊D83C2×Q814yes—
287C2×C22⋊D83C2×Q814yescomplemented
288D4×D83—232no—
289C22×Dic83—24no—
290C22×Dic83—22no—
291C22×Dic83—22no—
292C22×Dic83—22no—
293C22×Dic83—24no—
294C22×Dic83—42no—
295C22×Dic83—42no—
296C22×Dic83C2×D414yes—
297C22×Dic83C2411yescharacteristic
298C22×Dic83C2412yes—
299C22×Dic83C2412yes—
300C22×Dic83C2411yescharacteristic
301C22×Dic83C2412yes—
302C22×Dic83C2412yes—
303C22×Dic83C2411yescharacteristic
304C22×Dic83C2411yescharacteristic
305C22×Dic83C2411yescharacteristic
306C2×C4×D83—22no—
307C2×C4×D83—22no—
308C2×C4×D83—24no—
309C2×C4×D83—24no—
310C2×C4×D83—22no—
311C2×C4×D83—22no—
312C2×C4×D83—22no—
313C2×C4×D83—22no—
314C2×C4×D83—24no—
315C2×C4×D83—24no—
316C2×C4×D83—24no—
317C2×C4×D83—416no—
318C2×C4×D83—416no—
319C2×C4×D83—42no—
320C2×C4×D83—42no—
321C2×C4×D83—42no—
322C2×C4×D83—42no—
323C2×C4×D83—42no—
324C2×C4×D83—42no—
325C2×C4×D83—42no—
326C2×C4×D83—42no—
327C2×C4×D83—42no—
328C2×C4×D83C2×D414yes—
329C2×C4×D83C2×D414yes—
330C2×C4×D83C2×D414yes—
331C2×C4×D83C2×D414yes—
332C2×C4×D83C2×Q814yescomplemented
333C4⋊Dic83—22no—
334C4⋊Dic83—42no—
335C4⋊Dic83—42no—
336C4⋊Dic83—42no—
337Dic83⋊C4—24no—
338Dic83⋊C4—24no—
339Dic83⋊C4—22no—
340Dic83⋊C4—24no—
341Dic83⋊C4—24no—
342Dic83⋊C4—22no—
343Dic83⋊C4—24no—
344Dic83⋊C4—24no—
345Dic83⋊C4—42no—
346Dic83⋊C4—42no—
347Dic83⋊C4—42no—
348Dic83⋊C4—42no—
349C22⋊Dic83—22no—
350C22⋊Dic83—22no—
351C22⋊Dic83—22no—
352C22⋊Dic83—22no—
353C22⋊Dic83—42no—
354C22⋊Dic83—42no—
355(C2×D83)⋊C4—24no—
356(C2×D83)⋊C4—24no—
357(C2×D83)⋊C4—24no—
358(C2×D83)⋊C4—24no—
359(C2×D83)⋊C4—22no—
360(C2×D83)⋊C4—22no—
361(C2×D83)⋊C4—24no—
362(C2×D83)⋊C4—24no—
363(C2×D83)⋊C4—22no—
364(C2×D83)⋊C4—22no—
365(C2×D83)⋊C4—42no—
366(C2×D83)⋊C4—42no—
367(C2×D83)⋊C4—42no—
368(C2×D83)⋊C4—42no—
369C4×Dic83—22no—
370C4×Dic83—22no—
371C4×Dic83—22no—
372C24×C83C2411yescharacteristic
373C24×C83C2411yescharacteristic
374C2×D4×C83—22no—
375C2×D4×C83—22no—
376C2×D4×C83C2×Q814yes—
377C22×C4×C83—22no—
378C22×C4×C83—22no—
379C22×C4×C83—22no—
380C22×C4×C83—42no—
381C22×C4×C83—42no—
382C22×C4×C83—42no—
383C22×C4×C83—42no—
384C22×C4×C83C2×D414yes—
385C22×C4×C83C2411yescharacteristic
386C22×C4×C83C2412yes—
387C22×C4×C83C2412yes—
388C22×C4×C83C2411yescharacteristic
389C22×C4×C83C2412yes—
390C22×C4×C83C2412yes—
391C22×C4×C83C2411yescharacteristic
392C22×C4×C83C2411yescharacteristic
393C22×C4×C83C2411yescharacteristic
394C4⋊C4×C83—24no—
395C4⋊C4×C83—24no—
396C4⋊C4×C83—22no—
397C4⋊C4×C83—42no—
398C4⋊C4×C83—42no—
399C4⋊C4×C83—42no—
400C22⋊C4×C83—22no—
401C22⋊C4×C83—22no—
402C22⋊C4×C83—22no—
403C22⋊C4×C83—22no—
404C22⋊C4×C83—42no—
405C22⋊C4×C83—42no—
406C42×C83—22no—
407C23×C83—22no—
408C23×C83—22no—
409C23×C83—21no—
410C23×C83—21no—
411C23×C83—22no—
412C23×C83—22no—
413C23×C83C22×D412yes—
414C23×C83C22×Q812yes—
415C23×C83C22×Q812yes—
416C23×C83C2×#4112yes—
417C23×C83C2511yescharacteristic
418C22×D83—22no—
419C22×D83—22no—
420C22×D83—22no—
421C22×D83—22no—
422C22×D83—21no—
423C22×D83—21no—
424C22×D83—22no—
425C22×D83—22no—
426C22×D83—28no—
427C22×D83—44no—
428C22×D83—44no—
429C22×D83—48no—
430C22×D83—48no—
431C22×D83—48no—
432C22×D83—44no—
433C22×D83—44no—
434C22×D83—48no—
435C22×D83C22⋊Q8116yescomplemented
436C22×D83C22×D412yes—
437C22×D83C22×D412yes—
438C22×D83C22×Q812yes—
439C22×D83C22×Q812yes—
440C22×D83C22×Q812yes—
441C22×D83C2×#4112yes—
442C22×D83C2×#4112yes—
443D4×C83—28no—
444C2×C4×C83—21no—
445C2×C4×C83—21no—
446C2×C4×C83—22no—
447C2×C4×C83—22no—
448C2×C4×C83—21no—
449C2×C4×C83—21no—
450C2×C4×C83—22no—
451C2×C4×C83—22no—
452C2×C4×C83—22no—
453C2×C4×C83—22no—
454C2×C4×C83—22no—
455C2×C4×C83—22no—
456C2×C4×C83—22no—
457C2×C4×C83—22no—
458C2×C4×C83—22no—
459C2×C4×C83—22no—
460C2×C4×C83—22no—
461C2×C4×C83—22no—
462C2×C4×C83—22no—
463C2×C4×C83—22no—
464C2×C4×C83—44no—
465C2×C4×C83—44no—
466C2×C4×C83—44no—
467C2×C4×C83—44no—
468C2×C4×C83C22×D412yes—
469C2×C4×C83C22×D412yes—
470C2×C4×C83C22×Q812yes—
471C22⋊D83—28no—
472C22⋊D83—28no—
473C2×Dic83—21no—
474C2×Dic83—21no—
475C2×Dic83—22no—
476C2×Dic83—28no—
477C2×Dic83—21no—
478C2×Dic83—22no—
479C2×Dic83—22no—
480C2×Dic83—21no—
481C2×Dic83—22no—
482C2×Dic83—22no—
483C2×Dic83—22no—
484C2×Dic83—22no—
485C2×Dic83—22no—
486C2×Dic83—22no—
487C2×Dic83—22no—
488C2×Dic83—22no—
489C2×Dic83—22no—
490C2×Dic83—22no—
491C2×Dic83—22no—
492C2×Dic83—22no—
493C2×Dic83—44no—
494C2×Dic83—44no—
495C2×Dic83—44no—
496C2×Dic83C22×D412yes—
497C2×Dic83C22×D412yes—
498C2×Dic83C22×Q812yes—
499C2×Dic83H(5,𝔽2)14yes—
500D332—28no—
501C4×D83—28no—
502C4×D83—28no—
503C4×D83—28no—
504C4×D83—44no—
505C4×D83—44no—
506C4×D83—44no—
507C4×D83—44no—
508C4×D83—44no—
509C4×D83—44no—
510C4×D83—84no—
511C4×D83—84no—
512Dic166—48no—
513Dic166—48no—
514C22×C83—22no—
515C22×C83—22no—
516C22×C83—24no—
517C22×C83—24no—
518C22×C83—22no—
519C22×C83—24no—
520C22×C83—41no—
521C22×C83—41no—
522C22×C83—42no—
523C22×C83C2×C22⋊Q814yes—
524C22×C83C23×D411yescharacteristic
525C22×C83C23×Q811yescharacteristic
526C22×C83C22×#4111yescharacteristic
527C22×C83C2×H(5,𝔽2)12yes—
528C22×C83#58512yes—
529C2×D83—22no—
530C2×D83—22no—
531C2×D83—22no—
532C2×D83—22no—
533C2×D83—24no—
534C2×D83—24no—
535C2×D83—24no—
536C2×D83—24no—
537C2×D83—22no—
538C2×D83—24no—
539C2×D83—416no—
540C2×D83—416no—
541C2×D83—41no—
542C2×D83—41no—
543C2×D83—42no—
544C2×D83C2×C22⋊Q814yes—
545C2×D83C2×C22⋊Q814yes—
546C4×C83—22no—
547C4×C83—22no—
548C4×C83—22no—
549C4×C83—42no—
550C4×C83—41no—
551C4×C83—41no—
552C4×C83—42no—
553C4×C83—42no—
554C4×C83—42no—
555Dic83—22no—
556Dic83—22no—
557Dic83—42no—
558Dic83—41no—
559Dic83—41no—
560Dic83—42no—
561Dic83—42no—
562Dic83—42no—
563Dic83#53414yes—
564#35010—831nomaximal, Sylow
565C2×C83—24no—
566C2×C83—42no—
567C2×C83C22×C22⋊Q811yescharacteristic
568C2×C83C2×#53411yescharacteristic
569C2×C83#344911yescharacteristic
570C2×C83#350112yes—
571C2×C83#350512yes—
572D83—24no—
573D83—24no—
574D83—42no—
575C22×C22⋊Q8—831no—
576C22×C4×D4—831no—
577#2855—832no—
578#2848—832no—
579#2627—832no—
580#2626—832no—
581#2579—831no—
582#2579—831no—
583#2579—831no—
584#2579D8311yescharacteristic, complemented
585#2564—832no—
586#2564—832no—
587#2487—831no—
588#2487—831no—
589#2417—832no—
590#2417—832no—
591#2409—831no—
592#2409—831no—
593#2315—831no—
594#2315—831no—
595#2308—831no—
596#2308—831no—
597C2×#380—831no—
598C83#3501011yescharacteristic, complemented, Sylow
599C23×Q8—831no—
600C23×D4—831no—
601C24×C4—831no—
602C24×C4—831no—
603C2×C22⋊Q8—832no—
604C2×C22⋊Q8—832no—
605C2×C22⋊Q8—832no—
606C2×C22⋊Q8—832no—
607C2×C22⋊Q8—832no—
608C2×C22⋊Q8—832no—
609C2×C22⋊Q8—1668no—
610C2×C4×D4—831no—
611C2×C4×D4—831no—
612C2×C4×D4—831no—
613C2×C4×D4—831no—
614C2×C4×D4—831no—
615C2×C4×D4—831no—
616C2×C4×D4—831no—
617C2×C4×D4—1668no—
618C2×C4×D4C2×D8311yescharacteristic
619C22×C4⋊C4—832no—
620C22×C4⋊C4—831no—
621C22×C4⋊C4—831no—
622C22×C4⋊C4—831no—
623C22×C4⋊C4C2×D8311yescharacteristic, complemented
624C22×C22⋊C4—831no—
625C22×C22⋊C4—831no—
626C22×C22⋊C4—831no—
627C22×C22⋊C4—831no—
628C22×C22⋊C4—831no—
629C22×C22⋊C4—831no—
630C22×C42—831no—
631#400—832no—
632#400—832no—
633#399—832no—
634#399—832no—
635#398—832no—
636#398—832no—
637#398—832no—
638#398C2×D8312yescomplemented
639#396—832no—
640#396—832no—
641#396—832no—
642#396C2×D8312yescomplemented
643#395—832no—
644#395—832no—
645#393—832no—
646#393—832no—
647#391—832no—
648#391—832no—
649#389—832no—
650#389—832no—
651#387—832no—
652#387—832no—
653#387—832no—
654#387C2×D8312yescomplemented
655#386—831no—
656#386—831no—
657#386—831no—
658#386—831no—
659#386—832no—
660#386—832no—
661#386—831no—
662#386—831no—
663#386—832no—
664#386—832no—
665#386C2×D8311yescharacteristic
666#386C2×D8311yescharacteristic
667#385—832no—
668#385—831no—
669#385—831no—
670#385—832no—
671#385—832no—
672#385—832no—
673#385—831no—
674#385—831no—
675#385—831no—
676#385—831no—
677#385—832no—
678#385—832no—
679#385—832no—
680#385C2×D8312yescomplemented
681#385C2×D8311yescharacteristic, complemented
682#385C2×D8311yescharacteristic, complemented
683#381—832no—
684#381—832no—
685#380—831no—
686#380—832no—
687#380—832no—
688#380—832no—
689#380—832no—
690#380—831no—
691#380—831no—
692#380—832no—
693#380—832no—
694#380—832no—
695#380—832no—
696#380C2×D8311yescharacteristic, complemented
697#379—832no—
698#379—832no—
699C2×#95—832no—
700C25—831no—
701C25—831no—
702C22×Q8—3324no—
703C22×Q8—832no—
704C22×Q8—832no—
705C22×Q8—1664no—
706C22×D4—831no—
707C22×D4—831no—
708C22×D4—838no—
709C22×D4—831no—
710C22×D4—1664no—
711C22×D4—1664no—
712C22×D4C22×D8311yescharacteristic
713C23×C4—3324no—
714C23×C4—3324no—
715C23×C4—838no—
716C23×C4—831no—
717C23×C4—831no—
718C23×C4—831no—
719C23×C4—831no—
720C23×C4—831no—
721C23×C4—831no—
722C23×C4—832no—
723C23×C4—832no—
724C23×C4—831no—
725C23×C4—831no—
726C23×C4—831no—
727C23×C4—831no—
728C23×C4—831no—
729C23×C4—831no—
730C23×C4—831no—
731C23×C4—1664no—
732C23×C4C22×D8311yescharacteristic
733C23×C4C22×D8311yescharacteristic
734C23×C4C22×D8311yescharacteristic
735C23×C4C22×D8311yescharacteristic
736C22⋊Q8—3324no—
737C22⋊Q8—3324no—
738C22⋊Q8—1668no—
739C22⋊Q8—1668no—
740C22⋊Q8—1668no—
741C22⋊Q8—1668no—
742C4×D4—24no—
743C4×D4—1664no—
744C4×D4—1664no—
745C4×D4—1664no—
746C4×D4—1664no—
747C4×D4—1664no—
748C4×D4—1664no—
749C4×D4—1664no—
750C2×C4⋊C4—24no—
751C2×C4⋊C4—3324no—
752C2×C4⋊C4—832no—
753C2×C4⋊C4—832no—
754C2×C4⋊C4—832no—
755C2×C4⋊C4—832no—
756C2×C4⋊C4—832no—
757C2×C4⋊C4—832no—
758C2×C4⋊C4—832no—
759C2×C4⋊C4—831no—
760C2×C4⋊C4—831no—
761C2×C4⋊C4—831no—
762C2×C4⋊C4—832no—
763C2×C4⋊C4—832no—
764C2×C4⋊C4—832no—
765C2×C4⋊C4—832no—
766C2×C4⋊C4—832no—
767C2×C4⋊C4—832no—
768C2×C4⋊C4—1664no—
769C2×C4⋊C4—1664no—
770C2×C4⋊C4—1664no—
771C2×C4⋊C4C22×D8311yescharacteristic
772C2×C4⋊C4C22×D8312yes—
773C2×C4⋊C4C22×D8312yes—
774C2×C4⋊C4C22×D8312yes—
775C2×C4⋊C4C22×D8312yes—
776C2×C4⋊C4C22×D8312yes—
777C2×C22⋊C4—832no—
778C2×C22⋊C4—832no—
779C2×C22⋊C4—832no—
780C2×C22⋊C4—832no—
781C2×C22⋊C4—832no—
782C2×C22⋊C4—832no—
783C2×C22⋊C4—831no—
784C2×C22⋊C4—831no—
785C2×C22⋊C4—831no—
786C2×C22⋊C4—831no—
787C2×C22⋊C4—831no—
788C2×C22⋊C4—831no—
789C2×C22⋊C4—831no—
790C2×C22⋊C4—831no—
791C2×C22⋊C4—832no—
792C2×C22⋊C4—832no—
793C2×C22⋊C4—832no—
794C2×C22⋊C4—832no—
795C2×C22⋊C4—832no—
796C2×C22⋊C4—832no—
797C2×C22⋊C4—1664no—
798C2×C22⋊C4—1664no—
799C2×C22⋊C4—1664no—
800C2×C22⋊C4—1664no—
801C2×C22⋊C4—1664no—
802C2×C22⋊C4—1664no—
803C2×C22⋊C4C22×D8311yescharacteristic
804C2×C22⋊C4C22×D8311yescharacteristic
805C2×C22⋊C4C22×D8311yescharacteristic
806C2×C22⋊C4C22×D8311yescharacteristic
807C2×C22⋊C4C22×D8312yes—
808C2×C22⋊C4C22×D8312yes—
809C2×C42—831no—
810C2×C42—831no—
811C2×C42—831no—
812C2×C42—1664no—
813C2×C42C22×D8311yescharacteristic
814#95—832no—
815#95—832no—
816#95—832no—
817#95—832no—
818#95—832no—
819#95—832no—
820#95—832no—
821#95—832no—
822#95—832no—
823#95—832no—
824#95—832no—
825#95—832no—
826#95—832no—
827#95—832no—
828#95—832no—
829#95C22×D8312yes—
830#95C22×D8312yes—
831#95C22×D8312yes—
832#95C22×D8312yes—
833#95C22×D8312yes—
834C24—3322no—
835C24—3322no—
836C24—3322no—
837C24—3322no—
838C24—834no—
839C24—834no—
840C24—834no—
841C24—834no—
842C24—831no—
843C24—831no—
844C24—831no—
845C24—1662no—
846C24—1662no—
847C24C23×D8311yescharacteristic
848C24C23×D8311yescharacteristic
849C2×Q8—3322no—
850C2×Q8—3322no—
851C2×Q8—33216no—
852C2×Q8—1664no—
853C2×Q8—1664no—
854C2×Q8—1664no—
855C2×Q8—1664no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—834no—
859C2×D4—834no—
860C2×D4—834no—
861C2×D4—1662no—
862C2×D4—1662no—
863C2×D4—16632no—
864C2×D4—1662no—
865C2×D4—1662no—
866C2×D4—1662no—
867C2×D4—1662no—
868C2×D4Q8×D8314yes—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—3322no—
877C22×C4—3322no—
878C22×C4—3322no—
879C22×C4—3322no—
880C22×C4—3322no—
881C22×C4—3322no—
882C22×C4—3322no—
883C22×C4—3322no—
884C22×C4—3322no—
885C22×C4—33216no—
886C22×C4—33216no—
887C22×C4—3322no—
888C22×C4—3322no—
889C22×C4—834no—
890C22×C4—834no—
891C22×C4—831no—
892C22×C4—834no—
893C22×C4—831no—
894C22×C4—831no—
895C22×C4—834no—
896C22×C4—834no—
897C22×C4—834no—
898C22×C4—832no—
899C22×C4—832no—
900C22×C4—831no—
901C22×C4—832no—
902C22×C4—832no—
903C22×C4—831no—
904C22×C4—1662no—
905C22×C4—1664no—
906C22×C4—1662no—
907C22×C4—1662no—
908C22×C4—1664no—
909C22×C4—1664no—
910C22×C4—1664no—
911C22×C4—1664no—
912C22×C4—1662no—
913C22×C4—1662no—
914C22×C4—1662no—
915C22×C4—1664no—
916C22×C4—1662no—
917C22×C4—1662no—
918C22×C4—1662no—
919C22×C4—1664no—
920C22×C4D4×D8314yes—
921C22×C4C23×D8312yes—
922C22×C4C23×D8312yes—
923C22×C4C23×D8311yescharacteristic
924C22×C4C23×D8312yes—
925C22×C4C23×D8312yes—
926C22×C4C23×D8311yescharacteristic
927C22×C4C23×D8311yescharacteristic
928C22×C4C23×D8311yescharacteristic
929C22×C4C23×D8311yescharacteristic
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—22no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—3322no—
937C4⋊C4—3322no—
938C4⋊C4—3322no—
939C4⋊C4—3322no—
940C4⋊C4—3322no—
941C4⋊C4—3322no—
942C4⋊C4—3322no—
943C4⋊C4—1664no—
944C4⋊C4—1664no—
945C4⋊C4—1662no—
946C4⋊C4—1662no—
947C4⋊C4—1664no—
948C4⋊C4—1664no—
949C4⋊C4—1662no—
950C4⋊C4—1664no—
951C4⋊C4—1664no—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—3322no—
959C22⋊C4—3322no—
960C22⋊C4—3322no—
961C22⋊C4—3322no—
962C22⋊C4—3322no—
963C22⋊C4—3322no—
964C22⋊C4—1662no—
965C22⋊C4—1662no—
966C22⋊C4—1662no—
967C22⋊C4—1664no—
968C22⋊C4—1664no—
969C22⋊C4—1664no—
970C22⋊C4—1664no—
971C22⋊C4—1664no—
972C22⋊C4—1664no—
973C22⋊C4—1662no—
974C22⋊C4—1662no—
975C22⋊C4—1662no—
976C22⋊C4—1662no—
977C22⋊C4—1662no—
978C42—22no—
979C42—1662no—
980C42—1662no—
981C42—1662no—
982C23—22no—
983C23—22no—
984C23—21no—
985C23—21no—
986C23—22no—
987C23—22no—
988C23—3324no—
989C23—3328no—
990C23—3328no—
991C23—3324no—
992C23—3328no—
993C23—3324no—
994C23—3328no—
995C23—3324no—
996C23—8316no—
997C23—832no—
998C23—832no—
999C23—832no—
1000C23—832no—
1001C23—832no—
1002C23—832no—
1003C23—832no—
1004C23—1668no—
1005C23—1661no—
1006C23—1661no—
1007C23—1662no—
1008C23—1662no—
1009C23—1662no—
1010C23—1662no—
1011C23—1662no—
1012C23—1662no—
1013C23C2×D4×D8312yes—
1014C23C2×Q8×D8312yes—
1015C23C2×Q8×D8312yes—
1016C23#41×D8312yes—
1017C23C24×D8311yescharacteristic
1018Q8—3328no—
1019Q8—3328no—
1020D4—28no—
1021D4—1668no—
1022D4—1668no—
1023D4—1668no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—44no—
1045C2×C4—44no—
1046C2×C4—44no—
1047C2×C4—44no—
1048C2×C4—3324no—
1049C2×C4—3324no—
1050C2×C4—3324no—
1051C2×C4—3324no—
1052C2×C4—3324no—
1053C2×C4—3324no—
1054C2×C4—3324no—
1055C2×C4—3324no—
1056C2×C4—3324no—
1057C2×C4—832no—
1058C2×C4—834no—
1059C2×C4—832no—
1060C2×C4—832no—
1061C2×C4—6644no—
1062C2×C4—6644no—
1063C2×C4—1668no—
1064C2×C4—1668no—
1065C2×C4—1668no—
1066C2×C4—1661no—
1067C2×C4—1662no—
1068C2×C4—1661no—
1069C2×C4—1662no—
1070C2×C4—1662no—
1071C2×C4—1662no—
1072C2×C4—1662no—
1073C2×C4—1662no—
1074C2×C4—1662no—
1075C2×C4—1662no—
1076C2×C4—1662no—
1077C2×C4—1662no—
1078C2×C4—1662no—
1079C2×C4—1662no—
1080C2×C4—1662no—
1081C2×C4—1662no—
1082C2×C4—1668no—
1083C2×C4—1661no—
1084C2×C4—1661no—
1085C2×C4—1662no—
1086C2×C4C2×D4×D8312yes—
1087C2×C4C2×D4×D8312yes—
1088C2×C4C2×Q8×D8312yes—
1089C22—24no—
1090C22—22no—
1091C22—24no—
1092C22—22no—
1093C22—22no—
1094C22—24no—
1095C22—41no—
1096C22—42no—
1097C22—41no—
1098C22—33216no—
1099C22—33216no—
1100C22—3321no—
1101C22—3322no—
1102C22—3321no—
1103C22—834no—
1104C22—834no—
1105C22—1662no—
1106C22—1664no—
1107C22—1664no—
1108C22—1664no—
1109C22—1662no—
1110C22—1662no—
1111C22—1664no—
1112C22—1664no—
1113C22—1662no—
1114C22—1662no—
1115C22C22⋊Q8×D8314yes—
1116C22C22×D4×D8311yescharacteristic
1117C22C22×Q8×D8311yescharacteristic
1118C22C2×#41×D8311yescharacteristic
1119C22H(5,𝔽2)×D8312yes—
1120C22#1912853712yes—
1121C4—22no—
1122C4—22no—
1123C4—22no—
1124C4—41no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—41no—
1130C4—3321no—
1131C4—3322no—
1132C4—3322no—
1133C4—3322no—
1134C4—3321no—
1135C4—3322no—
1136C4—834no—
1137C4—1662no—
1138C4—1662no—
1139C2—24no—
1140C2—42no—
1141C2—3322no—
1142C2—1664no—
1143C2—1664no—
1144C2C2×C22⋊Q8×D8311yescharacteristic
1145C2#534×D8311yescharacteristic
1146C2#2492079311yescharacteristic
1147C2#2492126212yes—
1148C2#2492129612yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2579C2
prime radicalC22×D4×D83C22
hypercenter#2579D83
hypocenterC83#35010
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2579

Complements

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

NH ≅ G/Ntype
1. C22×#14581770C2semidirect
3. #24915798C2semidirect
4. #24915749C2semidirect
5. #24913281C2semidirect
6. #24913273C2semidirect
7. #24912812C2semidirect
8. #24912810C2semidirect
9. #24912806C2semidirect
10. #24912648C2semidirect
11. #24912642C2semidirect
12. #24911779C2semidirect
13. #24911777C2semidirect
14. #24910909C2semidirect
15. #24910907C2semidirect
16. #24910827C2semidirect
17. #24910825C2semidirect
18. #24910074C2semidirect
19. #24910074C2semidirect
22. #380×D83C2semidirect
23. C83×#2579C2semidirect
24. C23×Dic166C22semidirect
31. C2×#14581770C22semidirect
32. C2×#14581770C22semidirect
33. C2×#14581770C22semidirect
34. C2×#14581769C22semidirect
43. C22×Dic83⋊C4C22semidirect
44. C22×Dic83⋊C4C22semidirect
46. C2×C4⋊C4×D83C22semidirect
54. #19127643C22semidirect
55. #19127642C22semidirect
56. #19127637C22semidirect
57. #19127636C22semidirect
58. #19127634C22semidirect
59. #19127634C22semidirect
60. #19127631C22semidirect
61. #19127624C22semidirect
62. #19127623C22semidirect
63. #19127623C22semidirect
64. #19127622C22semidirect
65. #19127621C22semidirect
66. #19127614C22semidirect
67. #19127613C22semidirect
68. #19127605C22semidirect
69. #19127605C22semidirect
70. #19127598C22semidirect
71. #19127596C22semidirect
72. #19127586C22semidirect
73. #19127585C22semidirect
74. #19127582C22semidirect
85. #19127576C22semidirect
86. #19127576C22semidirect
89. #19127575C22semidirect
90. #19127574C22semidirect
91. #19127574C22semidirect
92. #19127574C22semidirect
93. #19127573C22semidirect
94. #19127573C22semidirect
97. #19127572C22semidirect
100. #19127561C22semidirect
102. #19127560C22semidirect
103. #19127560C22semidirect
104. #19127560C22semidirect
105. #19127559C22semidirect
106. #19127559C22semidirect
107. #19127559C22semidirect
109. #19127558C22semidirect
110. #19127558C22semidirect
113. #95×D83C22semidirect
115. C22×C4⋊C4×C83C22semidirect
116. #398×C83C22semidirect
117. #396×C83C22semidirect
118. #387×C83C22semidirect
121. #385×C83C22semidirect
122. #385×C83C22semidirect
123. #385×C83C22semidirect
124. #380×C83C22semidirect
136. C2×D4×D83Q8semidirect
267. C23×D83C2×Q8semidirect
281. C2×D332C2×Q8semidirect
287. C2×C22⋊D83C2×Q8semidirect
332. C2×C4×D83C2×Q8semidirect
435. C22×D83C22⋊Q8semidirect
584. #2579D83semidirect
598. C83#35010semidirect
623. C22×C4⋊C4C2×D83semidirect
638. #398C2×D83semidirect
642. #396C2×D83semidirect
654. #387C2×D83semidirect
680. #385C2×D83semidirect
681. #385C2×D83semidirect
682. #385C2×D83semidirect
696. #380C2×D83semidirect

Maximal subgroups

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

subgroupindex
C22×#145817702
C2×C4×D4×D832
#249157982
#249157492
#249132812
#249132732
#249128122
#249128102
#249128062
#249126482
#249126422
#249117792
#249117772
#249109092
#249109072
#249108272
#249108252
#249100742
#249100372
#380×D832
C83×#25792
#3501083