Finite Group Databasebeta

← #25969660

Subgroups — #25969660

Order 11008.

1758 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147983C211yesmaximal, characteristic
2C2×#14583509C211yesmaximal, characteristic, complemented
3#19146046C212yesmaximal, complemented
4#19146044C212yesmaximal, complemented
5#19146037C212yesmaximal, complemented
6#19146035C212yesmaximal, complemented
7#19146024C212yesmaximal, complemented
8#19146022C212yesmaximal, complemented
9#19146016C212yesmaximal, complemented
10#19146014C212yesmaximal, complemented
11#19144416C211yesmaximal, characteristic, complemented
12#19144415C211yesmaximal, characteristic, complemented
13#19144399C211yesmaximal, characteristic, complemented
14#19144397C211yesmaximal, characteristic, complemented
15#19144227C211yesmaximal, characteristic, complemented
16#19144225C211yesmaximal, characteristic, complemented
17#19144221C211yesmaximal, characteristic, complemented
18#19144081C211yesmaximal, characteristic, complemented
19#19144080C211yesmaximal, characteristic, complemented
20#19144066C211yesmaximal, characteristic, complemented
21#19144064C211yesmaximal, characteristic, complemented
22#19143158C211yesmaximal, characteristic, complemented
23C43×#3056C211yesmaximal, characteristic, complemented
24C2×#13063358C2211yescharacteristic
25C2×#13063356C2211yescharacteristic
26C2×#13063355C2211yescharacteristic
27C22×#10621877C2211yescharacteristic
28#14583522C2211yescharacteristic
29#14583522C2211yescharacteristic
30#14583516C2211yescharacteristic
31#14583516C2211yescharacteristic
32#14583509—21no—
33#14583509—21no—
34#14583509—21no—
35#14583509—21no—
36#14583509C2212yes—
37#14583509C2212yes—
38#14583509C2212yes—
39#14583509C2212yes—
40#14583509C2211yescharacteristic
41#14583509C2211yescharacteristic
42#14583502C2211yescharacteristic
43#14583502C2211yescharacteristic
44#14583493—21no—
45#14583493—21no—
46#14583484—21no—
47#14583484—21no—
48#14583452C2211yescharacteristic
49#14583445C2211yescharacteristic
50C2×#13063323C2211yescharacteristic
51#14583431—21no—
52#14583431—21no—
53#14583429—21no—
54#14583429—21no—
55C2×#13063318—21no—
56C2×#13063318—21no—
57C2×#13063316—21no—
58C2×#13063316C2211yescharacteristic
59C2×#13063315—21no—
60#14583410C2211yescharacteristic
61C2×#13063304C2211yescharacteristic
62#41×Dic43C2211yescharacteristic
63#14583367C2211yescharacteristic
64C2×Q8×Dic43C2211yescharacteristic
65C2×#13063290C2211yescharacteristic
66C2×#13063284C2211yescharacteristic
67#14583209C2212yescomplemented
68#14583209C2212yescomplemented
69#14583208C2212yescomplemented
70#14583208C2212yescomplemented
71#14583205C2212yescomplemented
72#14583205C2212yescomplemented
73#14583204C2212yescomplemented
74#14583204C2212yescomplemented
75#14583202C2212yescomplemented
76#14583201C2212yescomplemented
77#14583198C2212yescomplemented
78#14583197C2212yescomplemented
79#14583193C2212yescomplemented
80#14583192C2212yescomplemented
81#14583183C2212yescomplemented
82#14583182C2212yescomplemented
83#14583157C2212yes—
84#14583155C2212yes—
85#14583155C2212yes—
86#14583147C2212yes—
87#14583145C2212yes—
88#14583143C2212yes—
89#14583140C2212yes—
90#14583138C2212yes—
91#14583138C2212yes—
92#14583130C2212yes—
93#14583128C2212yes—
94#14583126C2212yes—
95#14583124C2212yescomplemented
96#14583123C2212yescomplemented
97#14583120C2212yescomplemented
98#14583119C2212yescomplemented
99#14583108C2212yescomplemented
100#14583108C2212yescomplemented
101#14583108C2212yescomplemented
102#14583107C2212yescomplemented
103#14583107C2212yescomplemented
104#14583107C2212yescomplemented
105#14583103C2212yescomplemented
106#14583103C2212yescomplemented
107#14583102C2212yescomplemented
108#14583102C2212yescomplemented
109#14583098C2212yescomplemented
110#14583097C2212yescomplemented
111#14582942C2211yescharacteristic
112#14582941C2211yescharacteristic
113#14582939C2211yescharacteristic
114#14582927C2212yes—
115#14582927C2212yes—
116#14582925C2212yes—
117#14582925C2212yes—
118#14582922C2211yescharacteristic
119#14582922C2211yescharacteristic
120#14582922C2211yescharacteristic
121#14582922C2211yescharacteristic
122#14582909C2211yescharacteristic
123#14582908C2211yescharacteristic
124#14582907C2211yescharacteristic
125#14582901C2211yescharacteristic
126#14582900C2211yescharacteristic
127#14582898C2211yescharacteristic
128C2×#137×C43C2211yescharacteristic
129C22×M16×C43C2211yescharacteristic
130C43×#525C2211yescharacteristic
131C2×C22⋊Q8×C43C2211yescharacteristic
132C43×#470C2212yes—
133C43×#468C2212yes—
134C43×#467C2212yes—
135C43×#465C2212yes—
136C43×#428C2211yescharacteristic
137C43×#419C2211yescharacteristic
138C43×#417C2211yescharacteristic
139C2×#10621898C2311yescharacteristic
140C22×Dic86C2311yescharacteristic
141#13063358—42no—
142#13063356—42no—
143#13063355—42no—
144C2×Dic172C2312yes—
145C2×#10621885C2312yes—
146C2×#10621885C2312yes—
147C2×#10621873C2312yes—
148C2×#10621883C2312yes—
149C2×#10621884C2312yes—
150C2×#10621877—42no—
151C2×#10621877C2311yescharacteristic
152C2×#10621877C2311yescharacteristic
153C2×#10621877C2312yes—
154C22×C43⋊C8C2312yes—
155#13063324C2311yescharacteristic
156#13063324C2311yescharacteristic
157#13063323—21no—
158#13063323—21no—
159#13063323C2312yes—
160#13063323C2312yes—
161#13063323C2311yescharacteristic
162#13063321C2311yescharacteristic
163#13063320—21no—
164#13063320—21no—
165#13063318—22no—
166#13063318—22no—
167#13063318—22no—
168#13063318—22no—
169#13063318—22no—
170#13063318—22no—
171#13063318—22no—
172#13063318—22no—
173#13063318—21no—
174#13063318—21no—
175#13063318—21no—
176#13063318—21no—
177#13063318—21no—
178#13063318—21no—
179#13063316—22no—
180#13063316—22no—
181#13063316—22no—
182#13063316—22no—
183#13063316—21no—
184#13063316—21no—
185#13063316—21no—
186#13063316—21no—
187#13063316C2312yes—
188#13063316C2312yes—
189#13063316C2311yescharacteristic
190#13063316C2311yescharacteristic
191#13063315—22no—
192#13063315—22no—
193#13063315—22no—
194#13063315—22no—
195#13063315—21no—
196#13063315—21no—
197#13063314C2311yescharacteristic
198#13063312—21no—
199#13063312—21no—
200#13063312C2311yescharacteristic
201#13063311—21no—
202#13063311—21no—
203#13063309—21no—
204#13063309—21no—
205#13063308—21no—
206#13063307—21no—
207#13063307—21no—
208#13063307—21no—
209#13063307—21no—
210#13063306—21no—
211#13063306—21no—
212#13063305—21no—
213#13063305—21no—
214#13063304—21no—
215#13063304—21no—
216#13063304C2312yes—
217#13063304C2312yes—
218#13063304C2311yescharacteristic
219#13063304C2311yescharacteristic
220#13063302—21no—
221#13063302—21no—
222#13063302—21no—
223#13063302—21no—
224#13063299C2311yescharacteristic
225#13063299C2311yescharacteristic
226#13063297—21no—
227#13063297—21no—
228#13063297—21no—
229#13063297—21no—
230#13063296—21no—
231#13063296—21no—
232#13063294—21no—
233Q8×Dic43—21no—
234Q8×Dic43—21no—
235Q8×Dic43C2312yes—
236Q8×Dic43C2311yescharacteristic
237Q8×Dic43C2311yescharacteristic
238Q8×Dic43C2312yes—
239C4×Dic86—21no—
240C4×Dic86—21no—
241#13063290—21no—
242#13063290—21no—
243#13063290C2312yes—
244#13063290C2312yes—
245#13063290C2311yescharacteristic
246#13063290C2311yescharacteristic
247D4×Dic43—21no—
248D4×Dic43—21no—
249D4×Dic43C2311yescharacteristic
250D4×Dic43C2311yescharacteristic
251#13063287C2311yescharacteristic
252#13063287C2311yescharacteristic
253C4×C22⋊D43—21no—
254C4×C22⋊D43—21no—
255C4×C22⋊D43—21no—
256C4×C22⋊D43—21no—
257(C22⋊D43)⋊C4—21no—
258(C22⋊D43)⋊C4—21no—
259#13063284—21no—
260#13063284D411yescharacteristic
261#13063284D411yescharacteristic
262#13063284D411yescharacteristic
263#13063284D411yescharacteristic
264#13063284C2311yescharacteristic
265#13063284C2311yescharacteristic
266#13063284C2311yescharacteristic
267#13063284C2311yescharacteristic
268#13063284C2311yescharacteristic
269#13063282—21no—
270C2×C4⋊Dic43—21no—
271C2×C4⋊Dic43—21no—
272C2×C4⋊Dic43D411yescharacteristic
273C2×C4⋊Dic43D411yescharacteristic
274C2×C4⋊Dic43C2311yescharacteristic
275C2×Dic43⋊C4—21no—
276C2×Dic43⋊C4—21no—
277C2×Dic43⋊C4—21no—
278C2×Dic43⋊C4—21no—
279C2×Dic43⋊C4—21no—
280C2×C22⋊Dic43—21no—
281C2×C22⋊Dic43D411yescharacteristic
282C2×C22⋊Dic43D411yescharacteristic
283C2×C4×Dic43—21no—
284C2×C4×Dic43—21no—
285C2×C4×Dic43—21no—
286C2×C4×Dic43C2311yescharacteristic
287C2×C4×Dic43C2311yescharacteristic
288C42×D43—21no—
289#13063259C2312yes—
290#13063258C2312yes—
291#13063258C2312yes—
292#13063257C2312yes—
293#13063256C2312yes—
294#13063256C2312yes—
295Dic43⋊C8C2312yes—
296Dic43⋊C8C2312yes—
297Dic43⋊C8C2312yes—
298Dic43⋊C8C2312yes—
299Dic43⋊C8C2312yes—
300Dic43⋊C8C2312yes—
301Dic43⋊C8C2312yes—
302Dic43⋊C8C2312yes—
303#13063250C2312yes—
304#13063250C2312yes—
305#13063250C2312yes—
306#13063249C2312yes—
307#13063249C2312yes—
308#13063249C2312yes—
309#13063248C2312yes—
310#13063248C2312yes—
311#13063248C2312yes—
312#13063247C2312yes—
313#13063246C2312yes—
314#13063245C2312yes—
315C2×#41×C43C2311yescharacteristic
316C22×Q8×C43C2311yescharacteristic
317C23×C4×C43C2311yescharacteristic
318#137×C43—42no—
319C2×Q16×C43C2312yes—
320C2×SD16×C43C2312yes—
321C2×M16×C43—42no—
322C2×M16×C43C2311yescharacteristic
323C2×M16×C43C2311yescharacteristic
324C2×M16×C43C2312yes—
325C22×C8×C43C2312yes—
326#123×C43—21no—
327C22⋊Q8×C43—21no—
328C22⋊Q8×C43—21no—
329C22⋊Q8×C43C2312yes—
330C22⋊Q8×C43C2312yes—
331C22⋊Q8×C43C2311yescharacteristic
332C22⋊Q8×C43C2311yescharacteristic
333#121×C43C2311yescharacteristic
334#121×C43C2311yescharacteristic
335#120×C43—21no—
336C4×D4×C43—21no—
337C4×D4×C43—21no—
338#117×C43C2311yescharacteristic
339C2×C4⋊C4×C43—21no—
340C2×C4⋊C4×C43C2311yescharacteristic
341C2×C22⋊C4×C43—21no—
342#107×C43C2312yes—
343#106×C43C2312yes—
344#103×C43C2312yes—
345#103×C43C2312yes—
346#103×C43C2312yes—
347#102×C43C2312yes—
348C24×C43C2×D411yescharacteristic
349#41×C43—22no—
350#41×C43—22no—
351C2×Q8×C43—21no—
352C2×Q8×C43—22no—
353C2×Q8×C43—22no—
354C2×Q8×C43C2412yes—
355C2×Q8×C43C2411yescharacteristic
356C2×D4×C43—21no—
357C2×D4×C43—21no—
358C2×D4×C43—21no—
359C2×D4×C43C2411yescharacteristic
360C22×C4×C43—22no—
361C22×C4×C43—22no—
362C22×C4×C43—21no—
363C22×C4×C43—21no—
364C22×C4×C43—21no—
365C22×C4×C43C2×D411yescharacteristic
366C22×C4×C43C2×D411yescharacteristic
367C22×C4×C43C2×D411yescharacteristic
368C22×C4×C43C2411yescharacteristic
369C22×C4×C43C2411yescharacteristic
370C22×C4×C43C2411yescharacteristic
371C2×C22⋊D43—21no—
372C2×C22⋊D43—21no—
373C2×C22⋊D43—21no—
374C2×C22⋊D43—21no—
375C2×C22⋊D43—21no—
376C22×Dic43—21no—
377C22×Dic43—21no—
378C22×Dic43—21no—
379C22×Dic43—21no—
380C22×Dic43C2×D411yescharacteristic
381C22×Dic43C2×D411yescharacteristic
382C22×Dic43C2×D411yescharacteristic
383C22×Dic43C2×D411yescharacteristic
384#10621898—22no—
385#10621898—22no—
386C2×D172C2411yescharacteristic
387C2×C4×D43—21no—
388C2×C4×D43—21no—
389C2×C4×D43—21no—
390C2×Dic86—22no—
391C2×Dic86—22no—
392C2×Dic86—21no—
393C2×Dic86—21no—
394C2×Dic86—21no—
395C2×Dic86C2411yescharacteristic
396C2×Dic86C2412yes—
397Q16×C43—42no—
398SD16×C43—42no—
399M16×C43—22no—
400M16×C43—22no—
401M16×C43—42no—
402C2×C8×C43—42no—
403C2×C8×C43C2412yes—
404C2×C8×C43C2412yes—
405C4⋊C4×C43—22no—
406C4⋊C4×C43—22no—
407C4⋊C4×C43—21no—
408C4⋊C4×C43—21no—
409C4⋊C4×C43—21no—
410C4⋊C4×C43C2412yes—
411C4⋊C4×C43C2411yescharacteristic
412C4⋊C4×C43C2411yescharacteristic
413C22⋊C4×C43—21no—
414C22⋊C4×C43—21no—
415C22⋊C4×C43—22no—
416C22⋊C4×C43—22no—
417C22⋊C4×C43—21no—
418C22⋊C4×C43—21no—
419C22⋊C4×C43—21no—
420C42×C43—21no—
421C22⋊Dic43—21no—
422C22⋊Dic43—21no—
423C22⋊Dic43—21no—
424C22⋊Dic43—21no—
425C22⋊Dic43—22no—
426C22⋊Dic43—22no—
427C22⋊Dic43—21no—
428C22⋊Dic43—21no—
429C22⋊Dic43—21no—
430C22⋊Dic43C2×D411yescharacteristic
431C22⋊Dic43C2×D411yescharacteristic
432C22⋊Dic43C2×D411yescharacteristic
433C22⋊Dic43C2×D411yescharacteristic
434C22⋊Dic43C2×D411yescharacteristic
435C22⋊Dic43C2×D411yescharacteristic
436C22⋊Dic43C2×D411yescharacteristic
437C22⋊Dic43C2×D411yescharacteristic
438#10621885—42no—
439#10621885—42no—
440#10621884—42no—
441#10621883—42no—
442(C2×D43)⋊C4—21no—
443(C2×D43)⋊C4—21no—
444(C2×D43)⋊C4—21no—
445(C2×D43)⋊C4—21no—
446(C2×D43)⋊C4—21no—
447(C2×D43)⋊C4—21no—
448C4⋊Dic43—21no—
449C4⋊Dic43—22no—
450C4⋊Dic43—22no—
451C4⋊Dic43—22no—
452C4⋊Dic43—22no—
453C4⋊Dic43—21no—
454C4⋊Dic43—21no—
455C4⋊Dic43—21no—
456C4⋊Dic43—21no—
457C4⋊Dic43C2×D411yescharacteristic
458C4⋊Dic43C2×D411yescharacteristic
459C4⋊Dic43C2×D411yescharacteristic
460C4⋊Dic43C2×D411yescharacteristic
461C4⋊Dic43C2×D411yescharacteristic
462C4⋊Dic43C2×D411yescharacteristic
463C4⋊Dic43C2×D411yescharacteristic
464C4⋊Dic43C2×D411yescharacteristic
465C4⋊Dic43C2412yes—
466C4⋊Dic43C2411yescharacteristic
467C4⋊Dic43C2411yescharacteristic
468Dic43⋊C4—22no—
469Dic43⋊C4—22no—
470Dic43⋊C4—21no—
471Dic43⋊C4—21no—
472Dic43⋊C4—22no—
473Dic43⋊C4—22no—
474Dic43⋊C4—22no—
475Dic43⋊C4—22no—
476Dic43⋊C4—22no—
477Dic43⋊C4—22no—
478Dic43⋊C4—22no—
479Dic43⋊C4—22no—
480Dic43⋊C4—21no—
481Dic43⋊C4—21no—
482Dic43⋊C4—21no—
483Dic43⋊C4—21no—
484Dic43⋊C4—21no—
485Dic43⋊C4—21no—
486Dic43⋊C4—21no—
487Dic43⋊C4—21no—
488C4×Dic43—21no—
489C4×Dic43—21no—
490C4×Dic43—21no—
491C4×Dic43—21no—
492C4×Dic43—21no—
493C4×Dic43—22no—
494C4×Dic43—22no—
495C4×Dic43—22no—
496C4×Dic43—22no—
497C4×Dic43C2×D411yescharacteristic
498C4×Dic43C2×D411yescharacteristic
499C4×Dic43C2×D411yescharacteristic
500C4×Dic43C2×D411yescharacteristic
501C4×Dic43C2411yescharacteristic
502C4×Dic43C2411yescharacteristic
503C4×Dic43C2411yescharacteristic
504C4×Dic43C2411yescharacteristic
505#10621877—22no—
506#10621877—22no—
507#10621877—42no—
508C2×C43⋊C8—42no—
509C2×C43⋊C8C2412yes—
510C2×C43⋊C8C2412yes—
511Dic172—42no—
512#10621873—42no—
513C23×C43—22no—
514C23×C43—21no—
515C23×C43—41no—
516C23×C43—41no—
517C23×C43C22×D411yescharacteristic
518C23×C43C22×D411yescharacteristic
519C23×C43C22×D411yescharacteristic
520C22×D43—21no—
521Q8×C43—22no—
522Q8×C43—21no—
523Q8×C43—22no—
524Q8×C43—21no—
525Q8×C43—42no—
526D4×C43—21no—
527D4×C43—21no—
528D4×C43—42no—
529D4×C43—81no—
530D4×C43—81no—
531C2×C4×C43—22no—
532C2×C4×C43—22no—
533C2×C4×C43—22no—
534C2×C4×C43—21no—
535C2×C4×C43—21no—
536C2×C4×C43—21no—
537C2×C4×C43—21no—
538C2×C4×C43—22no—
539C2×C4×C43—22no—
540C2×C4×C43—21no—
541C2×C4×C43—21no—
542C2×C4×C43—21no—
543C2×C4×C43—42no—
544C2×C4×C43—42no—
545C2×C4×C43—42no—
546C2×C4×C43C22×D411yescharacteristic
547C2×C4×C43C22×D411yescharacteristic
548C2×C4×C43C22×D411yescharacteristic
549C2×C4×C43H(5,𝔽2)12yes—
550C2×C4×C432−1+412yes—
551C2×C4×C43C2511yescharacteristic
552C22⋊D43—42no—
553C22⋊D43—81no—
554C22⋊D43—81no—
555C22⋊D43—81no—
556C22⋊D43—81no—
557C2×Dic43—22no—
558C2×Dic43—21no—
559C2×Dic43—22no—
560C2×Dic43—21no—
561C2×Dic43—21no—
562C2×Dic43—41no—
563C2×Dic43—41no—
564C2×Dic43—41no—
565C2×Dic43—41no—
566C2×Dic43—42no—
567C2×Dic43—42no—
568C2×Dic43—81no—
569C2×Dic43—81no—
570C2×Dic43C22×D411yescharacteristic
571C2×Dic43C22×D411yescharacteristic
572C2×Dic43C22×D411yescharacteristic
573C2×Dic43C22×D411yescharacteristic
574C2×Dic43C22×D411yescharacteristic
575C2×Dic43C22×D411yescharacteristic
576C2×Dic43C22×D411yescharacteristic
577C2×Dic43C22×D411yescharacteristic
578D172—21no—
579D172—21no—
580C4×D43—42no—
581C4×D43—81no—
582C4×D43—81no—
583Dic86—22no—
584Dic86—21no—
585Dic86—22no—
586Dic86—21no—
587Dic86—42no—
588Dic86—81no—
589Dic86—81no—
590C8×C43—22no—
591C8×C43—22no—
592C43⋊C8—22no—
593C43⋊C8—22no—
594#60921—431nomaximal, Sylow
595C22×C43—21no—
596C22×C43—21no—
597C22×C43—21no—
598C22×C43—21no—
599C22×C43—21no—
600C22×C43—21no—
601C22×C43—21no—
602C22×C43—21no—
603C22×C43—41no—
604C22×C43—41no—
605C22×C43—41no—
606C22×C43—82no—
607C22×C43#53712yes—
608C22×C43C23×D411yescharacteristic
609C2×D43—41no—
610C2×D43—41no—
611C2×D43—41no—
612C4×C43—21no—
613C4×C43—21no—
614C4×C43—41no—
615C4×C43—41no—
616C4×C43—42no—
617C4×C43—41no—
618C4×C43—42no—
619C4×C43#53712yes—
620C4×C43C2×H(5,𝔽2)11yescharacteristic
621C4×C43C2×2−1+411yescharacteristic
622Dic43—21no—
623Dic43—21no—
624Dic43—21no—
625Dic43—21no—
626Dic43—21no—
627Dic43—21no—
628Dic43—21no—
629Dic43—21no—
630Dic43—41no—
631Dic43—41no—
632Dic43—42no—
633Dic43—42no—
634Dic43—41no—
635#3455—431no—
636C2×#541—431no—
637#3261—432no—
638#3261—432no—
639#3260—432no—
640#3260—432no—
641#3258—432no—
642#3258—432no—
643#3258—432no—
644#3258—432no—
645#3080—431no—
646#3080—431no—
647#3078—431no—
648#3078—431no—
649#3056—431no—
650#3056—431no—
651#3056—431no—
652#3056D4311yescharacteristic, complemented
653#3039—431no—
654#3039—431no—
655#3037—431no—
656#3037—431no—
657#2905—431no—
658C2×C43—22no—
659C2×C43—41no—
660C2×C43—41no—
661C2×C43—81no—
662C2×C43C2×#53711yescharacteristic
663C2×C43#358611yescharacteristic
664C2×C43#358611yescharacteristic
665D43—81no—
666C2×#137—431no—
667C2×#137—431no—
668C2×#137—431no—
669C2×#137C2×D4311yescharacteristic
670C22×M16—431no—
671C22×M16C2×D4311yescharacteristic
672#542—431no—
673#542—431no—
674#542—431no—
675#542—431no—
676#541—432no—
677#541—432no—
678#541—432no—
679#541—432no—
680#541—431no—
681#541—431no—
682#541—861no—
683#541—861no—
684#541—861no—
685#541—861no—
686#540—431no—
687#540—431no—
688#539—861no—
689#539—861no—
690#538—861no—
691#538—861no—
692#533—431no—
693#532—431no—
694C2×C4⋊Q8—431no—
695#529—861no—
696#529—861no—
697#529—861no—
698#529—861no—
699C2×#126—861no—
700C2×#126—861no—
701C2×#125—431no—
702C2×#125—861no—
703C2×#125—861no—
704#525—431no—
705#525C2×D4311yescharacteristic
706C2×C22⋊Q8—431no—
707C2×C22⋊Q8C2×D4311yescharacteristic
708C4×#41—431no—
709C4×#41—431no—
710C2×C4×Q8—431no—
711C2×C4×Q8—431no—
712C2×#117—431no—
713#479—432no—
714#479—432no—
715#479—432no—
716#479—432no—
717#479—432no—
718#479—432no—
719#479—432no—
720#479—432no—
721#478—432no—
722#478—432no—
723#478—432no—
724#478—432no—
725#477—432no—
726#477—432no—
727#475—432no—
728#475—432no—
729#470—432no—
730#470—432no—
731#470—432no—
732#470C2×D4312yes—
733#468—432no—
734#468—432no—
735#468—432no—
736#468C2×D4312yes—
737#467—432no—
738#467—432no—
739#467—432no—
740#467C2×D4312yes—
741#465—432no—
742#465—432no—
743#465—432no—
744#465C2×D4312yes—
745#464—432no—
746#464—432no—
747#464—432no—
748#464—432no—
749#462—432no—
750#462—432no—
751#462—432no—
752#462—432no—
753#462—432no—
754#462—432no—
755#461—432no—
756#461—432no—
757#461—432no—
758#461—432no—
759#460—432no—
760#460—432no—
761#428—431no—
762#428—431no—
763#428—431no—
764#428C2×D4311yescharacteristic
765#424—432no—
766#424—432no—
767#424—432no—
768#424—432no—
769#423—431no—
770#423—431no—
771#423—431no—
772#423—431no—
773#419—431no—
774#419—431no—
775#419—431no—
776#419C2×D4311yescharacteristic
777#417—431no—
778#417—431no—
779#417—431no—
780#417C2×D4311yescharacteristic
781C43#6092111yescharacteristic, complemented, Sylow
782C2×#41—431no—
783C2×#41C22×D4311yescharacteristic
784C22×Q8—431no—
785C22×Q8C22×D4311yescharacteristic
786C23×C4C22×D4311yescharacteristic
787#137—42no—
788#137—1722no—
789#137—1722no—
790#137—1722no—
791C2×Q16—432no—
792C2×Q16—432no—
793C2×Q16—432no—
794C2×Q16C22×D4312yes—
795C2×SD16—432no—
796C2×SD16—432no—
797C2×SD16—432no—
798C2×SD16C22×D4312yes—
799C2×M16—42no—
800C2×M16—431no—
801C2×M16—431no—
802C2×M16—432no—
803C2×M16—1722no—
804C2×M16C22×D4311yescharacteristic
805C2×M16C22×D4311yescharacteristic
806C2×M16C22×D4312yes—
807C22×C8—432no—
808C22×C8C22×D4312yes—
809C4⋊Q8—431no—
810C4⋊Q8—431no—
811C4⋊Q8—432no—
812C4⋊Q8—432no—
813C4⋊Q8—431no—
814C4⋊Q8—861no—
815C4⋊Q8—861no—
816#127—431no—
817#126—862no—
818#126—862no—
819#126—862no—
820#126—862no—
821#126—862no—
822#126—862no—
823#126—862no—
824#126—862no—
825#126—861no—
826#126—861no—
827#126—861no—
828#126—861no—
829#126—861no—
830#126—861no—
831#126—861no—
832#126—861no—
833#125—432no—
834#125—432no—
835#125—431no—
836#125—431no—
837#125—861no—
838#125—861no—
839#125—862no—
840#125—862no—
841#125—862no—
842#125—862no—
843#125—862no—
844#125—862no—
845#125—862no—
846#125—862no—
847#125—861no—
848#125—861no—
849#125—861no—
850#125—861no—
851#124—431no—
852#124—431no—
853#124—861no—
854#124—861no—
855#124—861no—
856#124—861no—
857#123—21no—
858#123—861no—
859#123—861no—
860#123—861no—
861#123—861no—
862#123—861no—
863#123—861no—
864#123—861no—
865#123—861no—
866#123—861no—
867C22⋊Q8—21no—
868C22⋊Q8—21no—
869C22⋊Q8—432no—
870C22⋊Q8—432no—
871C22⋊Q8—431no—
872C22⋊Q8—431no—
873C22⋊Q8—861no—
874C22⋊Q8—861no—
875C22⋊Q8—861no—
876C22⋊Q8—861no—
877C22⋊Q8—861no—
878C22⋊Q8—861no—
879C22⋊Q8—861no—
880C22⋊Q8—861no—
881C22⋊Q8C22×D4312yes—
882C22⋊Q8C22×D4312yes—
883C22⋊Q8C22×D4311yescharacteristic
884C22⋊Q8C22×D4311yescharacteristic
885#121—431no—
886#121—431no—
887#121—861no—
888#121—861no—
889#121—861no—
890#121—861no—
891#121—861no—
892#121—861no—
893#121C22×D4311yescharacteristic
894#121C22×D4311yescharacteristic
895#120—21no—
896#120—861no—
897C4×Q8—432no—
898C4×Q8—432no—
899C4×Q8—431no—
900C4×Q8—431no—
901C4×Q8—432no—
902C4×Q8—432no—
903C4×Q8—431no—
904C4×Q8—431no—
905C4×Q8—861no—
906C4×Q8—861no—
907C4×Q8—861no—
908C4×Q8—861no—
909C4×Q8—861no—
910C4×Q8—861no—
911C4×D4—21no—
912C4×D4—21no—
913C4×D4—431no—
914C4×D4—431no—
915C4×D4—431no—
916C4×D4—431no—
917C4×D4—861no—
918C4×D4—861no—
919C4×D4—861no—
920C4×D4—861no—
921C4×D4—861no—
922C4×D4—861no—
923C4×D4—861no—
924C4×D4—861no—
925#117—431no—
926#117—431no—
927#117—431no—
928#117—431no—
929#117—431no—
930#117—431no—
931#117—431no—
932#117—431no—
933#117—431no—
934#117—861no—
935#117—861no—
936#117C22×D4311yescharacteristic
937C2×C4⋊C4—21no—
938C2×C4⋊C4—431no—
939C2×C4⋊C4—431no—
940C2×C4⋊C4—431no—
941C2×C4⋊C4—861no—
942C2×C4⋊C4—861no—
943C2×C4⋊C4—861no—
944C2×C4⋊C4—861no—
945C2×C4⋊C4—861no—
946C2×C4⋊C4—861no—
947C2×C4⋊C4—861no—
948C2×C4⋊C4C22×D4311yescharacteristic
949C2×C22⋊C4—21no—
950C2×C22⋊C4—431no—
951C2×C22⋊C4—431no—
952C2×C22⋊C4—861no—
953C2×C42—431no—
954C2×C42—431no—
955C2×C42—861no—
956C2×C42—861no—
957C2×C42—861no—
958C2×C42—861no—
959#107—432no—
960#107—432no—
961#107—432no—
962#107C22×D4312yes—
963#106—432no—
964#106—432no—
965#106—432no—
966#106C22×D4312yes—
967C4⋊C8—432no—
968C4⋊C8—432no—
969C4⋊C8—432no—
970C4⋊C8—432no—
971C4⋊C8—432no—
972C4⋊C8—432no—
973C4⋊C8—432no—
974C4⋊C8—432no—
975#103—432no—
976#103—432no—
977#103—432no—
978#103—432no—
979#103—432no—
980#103—432no—
981#103—432no—
982#103—432no—
983#103—432no—
984#103C22×D4312yes—
985#103C22×D4312yes—
986#103C22×D4312yes—
987#102—432no—
988#102—432no—
989#102—432no—
990#102C22×D4312yes—
991C24D4×D4311yescharacteristic
992#41—22no—
993#41—22no—
994#41—862no—
995#41—862no—
996C2×Q8—21no—
997C2×Q8—22no—
998C2×Q8—22no—
999C2×Q8—431no—
1000C2×Q8—432no—
1001C2×Q8—861no—
1002C2×Q8—861no—
1003C2×Q8—861no—
1004C2×Q8—862no—
1005C2×Q8—862no—
1006C2×Q8C23×D4311yescharacteristic
1007C2×Q8C23×D4312yes—
1008C2×D4—21no—
1009C2×D4—21no—
1010C2×D4—21no—
1011C2×D4—431no—
1012C2×D4—861no—
1013C2×D4—861no—
1014C2×D4—861no—
1015C2×D4—861no—
1016C2×D4—861no—
1017C2×D4C23×D4311yescharacteristic
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—21no—
1021C22×C4—21no—
1022C22×C4—21no—
1023C22×C4—431no—
1024C22×C4—431no—
1025C22×C4—431no—
1026C22×C4—431no—
1027C22×C4—861no—
1028C22×C4—861no—
1029C22×C4—861no—
1030C22×C4—861no—
1031C22×C4—861no—
1032C22×C4—861no—
1033C22×C4—861no—
1034C22×C4D4×D4311yescharacteristic
1035C22×C4D4×D4311yescharacteristic
1036C22×C4D4×D4311yescharacteristic
1037C22×C4C23×D4311yescharacteristic
1038C22×C4C23×D4311yescharacteristic
1039C22×C4C23×D4311yescharacteristic
1040Q16—42no—
1041Q16—1722no—
1042Q16—1722no—
1043Q16—1722no—
1044SD16—42no—
1045SD16—1722no—
1046SD16—1722no—
1047SD16—1722no—
1048M16—22no—
1049M16—22no—
1050M16—42no—
1051M16—862no—
1052M16—862no—
1053M16—1722no—
1054C2×C8—42no—
1055C2×C8—432no—
1056C2×C8—432no—
1057C2×C8—1722no—
1058C2×C8C23×D4312yes—
1059C2×C8C23×D4312yes—
1060C4⋊C4—22no—
1061C4⋊C4—22no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—431no—
1066C4⋊C4—431no—
1067C4⋊C4—431no—
1068C4⋊C4—431no—
1069C4⋊C4—431no—
1070C4⋊C4—431no—
1071C4⋊C4—431no—
1072C4⋊C4—431no—
1073C4⋊C4—432no—
1074C4⋊C4—431no—
1075C4⋊C4—431no—
1076C4⋊C4—862no—
1077C4⋊C4—862no—
1078C4⋊C4—862no—
1079C4⋊C4—862no—
1080C4⋊C4—862no—
1081C4⋊C4—862no—
1082C4⋊C4—862no—
1083C4⋊C4—862no—
1084C4⋊C4—862no—
1085C4⋊C4—862no—
1086C4⋊C4—862no—
1087C4⋊C4—862no—
1088C4⋊C4—861no—
1089C4⋊C4—861no—
1090C4⋊C4—861no—
1091C4⋊C4—861no—
1092C4⋊C4—861no—
1093C4⋊C4—861no—
1094C4⋊C4—861no—
1095C4⋊C4—861no—
1096C4⋊C4—861no—
1097C4⋊C4—861no—
1098C4⋊C4—861no—
1099C4⋊C4—861no—
1100C4⋊C4—861no—
1101C4⋊C4—862no—
1102C4⋊C4—862no—
1103C4⋊C4—861no—
1104C4⋊C4—861no—
1105C4⋊C4C23×D4312yes—
1106C4⋊C4C23×D4311yescharacteristic
1107C4⋊C4C23×D4311yescharacteristic
1108C22⋊C4—22no—
1109C22⋊C4—22no—
1110C22⋊C4—21no—
1111C22⋊C4—21no—
1112C22⋊C4—21no—
1113C22⋊C4—21no—
1114C22⋊C4—21no—
1115C22⋊C4—431no—
1116C22⋊C4—431no—
1117C22⋊C4—431no—
1118C22⋊C4—431no—
1119C22⋊C4—431no—
1120C22⋊C4—431no—
1121C22⋊C4—431no—
1122C22⋊C4—431no—
1123C22⋊C4—861no—
1124C22⋊C4—861no—
1125C22⋊C4—861no—
1126C22⋊C4—861no—
1127C22⋊C4—861no—
1128C22⋊C4—861no—
1129C22⋊C4—861no—
1130C22⋊C4—861no—
1131C22⋊C4—862no—
1132C22⋊C4—862no—
1133C22⋊C4—861no—
1134C22⋊C4—861no—
1135C22⋊C4—861no—
1136C22⋊C4—861no—
1137C22⋊C4—861no—
1138C42—21no—
1139C42—431no—
1140C42—431no—
1141C42—431no—
1142C42—431no—
1143C42—431no—
1144C42—431no—
1145C42—431no—
1146C42—431no—
1147C42—861no—
1148C42—861no—
1149C42—861no—
1150C42—861no—
1151C42—862no—
1152C42—862no—
1153C42—862no—
1154C42—862no—
1155C42—861no—
1156C23—22no—
1157C23—21no—
1158C23—41no—
1159C23—41no—
1160C23—861no—
1161C23C2×D4×D4311yescharacteristic
1162C23C2×D4×D4311yescharacteristic
1163C23C2×D4×D4311yescharacteristic
1164Q8—22no—
1165Q8—21no—
1166Q8—22no—
1167Q8—21no—
1168Q8—42no—
1169Q8—862no—
1170Q8—861no—
1171Q8—862no—
1172Q8—861no—
1173Q8—3441no—
1174Q8—3441no—
1175Q8—1722no—
1176D4—21no—
1177D4—21no—
1178D4—42no—
1179D4—81no—
1180D4—81no—
1181D4—861no—
1182D4—861no—
1183D4—3441no—
1184D4—3441no—
1185D4—3441no—
1186D4—3441no—
1187D4—1722no—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—431no—
1204C2×C4—431no—
1205C2×C4—431no—
1206C2×C4—431no—
1207C2×C4—431no—
1208C2×C4—431no—
1209C2×C4—431no—
1210C2×C4—431no—
1211C2×C4—861no—
1212C2×C4—861no—
1213C2×C4—861no—
1214C2×C4—862no—
1215C2×C4—862no—
1216C2×C4—3441no—
1217C2×C4—3441no—
1218C2×C4—3441no—
1219C2×C4—3441no—
1220C2×C4—1721no—
1221C2×C4—1721no—
1222C2×C4—1721no—
1223C2×C4—1721no—
1224C2×C4—1722no—
1225C2×C4—1722no—
1226C2×C4—1722no—
1227C2×C4C2×D4×D4311yescharacteristic
1228C2×C4C2×D4×D4311yescharacteristic
1229C2×C4C2×D4×D4311yescharacteristic
1230C2×C4#1306337012yes—
1231C2×C4#1306337212yes—
1232C2×C4C24×D4311yescharacteristic
1233C8—22no—
1234C8—22no—
1235C8—862no—
1236C8—862no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—21no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—82no—
1249C22—1721no—
1250C22—1721no—
1251C22—1721no—
1252C22#1458347612yes—
1253C22C22×D4×D4311yescharacteristic
1254C4—21no—
1255C4—21no—
1256C4—41no—
1257C4—42no—
1258C4—41no—
1259C4—41no—
1260C4—42no—
1261C4—861no—
1262C4—861no—
1263C4—861no—
1264C4—861no—
1265C4—861no—
1266C4—861no—
1267C4—861no—
1268C4—861no—
1269C4—1721no—
1270C4—1722no—
1271C4—1721no—
1272C4—1721no—
1273C4—1722no—
1274C4#1458347612yes—
1275C4C2×#1306337011yescharacteristic
1276C4C2×#1306337211yescharacteristic
1277C2—22no—
1278C2—41no—
1279C2—41no—
1280C2—81no—
1281C2—3441no—
1282C2C2×#1458347611yescharacteristic
1283C2#1914937811yescharacteristic
1284C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3056C2
socleC22×C43C23×D4
prime radical#19147983C2
hypercenter#3056D43
hypocenterC43#60921
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3056

Complements

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

NH ≅ G/Ntype
2. C2×#14583509C2semidirect
3. #19146046C2semidirect
4. #19146044C2semidirect
5. #19146037C2semidirect
6. #19146035C2semidirect
7. #19146024C2semidirect
8. #19146022C2semidirect
9. #19146016C2semidirect
10. #19146014C2semidirect
11. #19144416C2semidirect
12. #19144415C2semidirect
13. #19144399C2semidirect
14. #19144397C2semidirect
15. #19144227C2semidirect
16. #19144225C2semidirect
17. #19144221C2semidirect
18. #19144081C2semidirect
19. #19144080C2semidirect
20. #19144066C2semidirect
21. #19144064C2semidirect
22. #19143158C2semidirect
23. C43×#3056C2semidirect
67. #14583209C22semidirect
68. #14583209C22semidirect
69. #14583208C22semidirect
70. #14583208C22semidirect
71. #14583205C22semidirect
72. #14583205C22semidirect
73. #14583204C22semidirect
74. #14583204C22semidirect
75. #14583202C22semidirect
76. #14583201C22semidirect
77. #14583198C22semidirect
78. #14583197C22semidirect
79. #14583193C22semidirect
80. #14583192C22semidirect
81. #14583183C22semidirect
82. #14583182C22semidirect
95. #14583124C22semidirect
96. #14583123C22semidirect
97. #14583120C22semidirect
98. #14583119C22semidirect
99. #14583108C22semidirect
100. #14583108C22semidirect
101. #14583108C22semidirect
102. #14583107C22semidirect
103. #14583107C22semidirect
104. #14583107C22semidirect
105. #14583103C22semidirect
106. #14583103C22semidirect
107. #14583102C22semidirect
108. #14583102C22semidirect
109. #14583098C22semidirect
110. #14583097C22semidirect
652. #3056D43semidirect
781. C43#60921semidirect

Maximal subgroups

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

subgroupindex
#191479832
C2×#145835092
#191460462
#191460442
#191460372
#191460352
#191460242
#191460222
#191460162
#191460142
#191444162
#191444152
#191443992
#191443972
#191442272
#191442252
#191442212
#191440812
#191440802
#191440662
#191440642
#191431582
C43×#30562
#6092143