Finite Group Databasebeta

← #25968253

Subgroups — #25968253

Order 11008.

2108 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148332C211yesmaximal, characteristic, complemented
2#19147924C211yesmaximal, characteristic, complemented
3#19145710C212yesmaximal, complemented
4#19145693C212yesmaximal, complemented
5#19145652C212yesmaximal, complemented
6#19145641C212yesmaximal, complemented
7#19145636C212yesmaximal, complemented
8#19145587C212yesmaximal, complemented
9#19145574C212yesmaximal, complemented
10#19145526C212yesmaximal, complemented
11#19145082C211yesmaximal, characteristic, complemented
12#19145072C211yesmaximal, characteristic, complemented
13#19144964C211yesmaximal, characteristic, complemented
14#19144953C211yesmaximal, characteristic, complemented
15#19144143C211yesmaximal, characteristic, complemented
16#19144132C211yesmaximal, characteristic, complemented
17#19144110C211yesmaximal, characteristic, complemented
18#19144101C211yesmaximal, characteristic, complemented
19#19143847C211yesmaximal, characteristic, complemented
20#19143835C211yesmaximal, characteristic, complemented
21C2×#14583046C211yesmaximal, characteristic, complemented
22#19143249C211yesmaximal, characteristic, complemented
23C43×#3002C211yesmaximal, characteristic, complemented
24C22×#10621898C2211yescharacteristic
25C2×#13063355C2211yescharacteristic, complemented
26C2×#13063350C2211yescharacteristic
27C2×#13063350C2211yescharacteristic
28C2×#13063350C2211yescharacteristic, complemented
29C22×#10621873C2211yescharacteristic, complemented
30C22×D344C2211yescharacteristic, complemented
31#14583614—21no—
32#14583595—21no—
33#14583595—21no—
34#14583572—22no—
35#14583553—21no—
36#14583536—22no—
37#14583527C2211yescharacteristic, complemented
38#14583522C2212yescomplemented
39#14583502C2212yescomplemented
40#14583477—21no—
41#14583477—21no—
42#14583473C2212yescomplemented
43#14583470C2211yescharacteristic
44#14583470C2211yescharacteristic
45#14583466C2212yescomplemented
46#14583463C2211yescharacteristic
47#14583463C2211yescharacteristic
48#14583463C2211yescharacteristic, complemented
49#14583458—22no—
50#14583445C2212yescomplemented
51#14583445C2212yescomplemented
52#14583444C2212yescomplemented
53#14583435C2212yescomplemented
54#14583410—21no—
55#14583410—21no—
56#14583406—22no—
57C2×#13063299C2211yescharacteristic
58#14583382C2211yescharacteristic, complemented
59#14583373C2211yescharacteristic, complemented
60C2×#13063284C2211yescharacteristic
61#14583292C2212yescomplemented
62#14583287C2212yescomplemented
63#14583285C2212yescomplemented
64#14583285C2212yescomplemented
65#14583284C2212yescomplemented
66#14583280C2212yescomplemented
67#14583274C2212yescomplemented
68#14583270C2212yescomplemented
69#14583266C2212yescomplemented
70#14583262C2212yescomplemented
71#14583260C2212yescomplemented
72#14583257C2212yescomplemented
73#14583255C2212yescomplemented
74#14583252C2212yescomplemented
75#14583248C2212yescomplemented
76#14583244C2212yescomplemented
77#14583123C2212yescomplemented
78#14583119C2212yescomplemented
79#14583117C2212yescomplemented
80#14583117C2212yescomplemented
81#14583116C2212yescomplemented
82#14583113C2212yescomplemented
83#14583113C2212yescomplemented
84#14583112C2212yescomplemented
85#14583107C2212yescomplemented
86#14583103C2212yescomplemented
87#14583103C2212yescomplemented
88#14583102C2212yescomplemented
89#14583097C2212yescomplemented
90#14583093C2212yescomplemented
91#14583093C2212yescomplemented
92#14583092C2212yescomplemented
93#14583059C2212yescomplemented
94#14583059C2212yescomplemented
95#14583046C2212yes—
96#14583046C2212yes—
97#14583046C2212yescomplemented
98#14583046C2212yescomplemented
99#14583044C2212yescomplemented
100#14583044C2212yescomplemented
101#14583042C2212yescomplemented
102#14583042C2212yescomplemented
103#14583038C2212yescomplemented
104#14583033C2212yescomplemented
105#14582957C2212yescomplemented
106#14582957C2212yescomplemented
107#14582953C2212yescomplemented
108#14582949C2212yescomplemented
109#14582925C2211yescharacteristic, complemented
110#14582925C2211yescharacteristic, complemented
111#14582907C2211yescharacteristic, complemented
112#14582903C2211yescharacteristic, complemented
113#14582900C2211yescharacteristic
114#14582900C2211yescharacteristic
115C2×#13063250C2211yescharacteristic, complemented
116C2×#13063247C2211yescharacteristic, complemented
117#14582863C2211yescharacteristic
118#14582854C2211yescharacteristic, complemented
119#14582854C2211yescharacteristic, complemented
120C22×#41×C43C2211yescharacteristic
121C2×#135×C43C2211yescharacteristic
122C2×#135×C43C2211yescharacteristic
123C43×#525C2211yescharacteristic
124C43×#452C2211yescharacteristic, complemented
125C43×#452C2211yescharacteristic, complemented
126C43×#451C2211yescharacteristic, complemented
127C43×#450C2211yescharacteristic, complemented
128C43×#449C2211yescharacteristic, complemented
129C43×#449C2211yescharacteristic, complemented
130C43×#448C2211yescharacteristic, complemented
131C43×#447C2211yescharacteristic, complemented
132C43×#416C2211yescharacteristic
133C43×#416C2211yescharacteristic
134C2×C22⋊C8×C43C2211yescharacteristic
135C2×#10621898—21no—
136C2×#10621898—21no—
137C2×#10621898—42no—
138C2×#10621898—42no—
139C2×#10621898C2312yes—
140C2×#10621898C2312yes—
141C2×#10621900—22no—
142C22×Dic86C2311yescharacteristic
143C22×D172C2311yescharacteristic
144C22×D172C2311yescharacteristic
145C22×C22⋊D43—21no—
146C22×C22⋊D43—21no—
147C22×C4×D43—21no—
148#13063355—42no—
149#13063350—42no—
150#13063350—42no—
151#13063350—42no—
152C2×#10621885C2312yes—
153C2×#10621873—42no—
154C2×#10621873C2312yes—
155C2×#10621873C2312yes—
156C2×#10621883C2312yes—
157C2×#10621884C2312yes—
158C2×#10621884C2312yes—
159C2×#10621884C2312yes—
160C2×D344—42no—
161C2×D344C2312yes—
162C2×D344C2312yes—
163C2×#10621882C2312yes—
164C2×#10621882C2312yes—
165C2×#10621882C2312yes—
166C2×#10621877C2311yescharacteristic
167C2×#10621877C2311yescharacteristic
168#13063325—21no—
169#13063324C2312yes—
170#13063323C2312yes—
171#13063323C2312yes—
172#13063321C2312yes—
173#13063321C2312yes—
174#13063321C2312yes—
175#13063320—22no—
176#13063320—22no—
177#13063317—21no—
178#13063316C2312yes—
179#13063314C2312yes—
180#13063314C2312yes—
181#13063314C2312yes—
182#13063312C2312yes—
183#13063312C2312yes—
184#13063311—22no—
185#13063311—22no—
186#13063309—22no—
187#13063309—22no—
188#13063308—22no—
189#13063308—22no—
190#13063307—22no—
191#13063307—22no—
192#13063306—22no—
193#13063306—22no—
194#13063305—22no—
195#13063304—21no—
196#13063304—21no—
197#13063304—21no—
198#13063304—21no—
199#13063302—22no—
200#13063301—22no—
201#13063301—22no—
202#13063299—21no—
203#13063299—21no—
204#13063299—21no—
205#13063299—21no—
206#13063299—21no—
207#13063299—21no—
208#13063299—21no—
209#13063299—21no—
210#13063299C2312yes—
211#13063299C2312yes—
212#13063297—22no—
213#13063297—22no—
214#13063297—22no—
215#13063297—22no—
216#13063297—22no—
217#13063297—22no—
218#13063296—22no—
219#13063296—22no—
220#13063296—22no—
221#13063294—22no—
222#13063294—22no—
223#13063293—22no—
224#13063293—22no—
225#13063293—22no—
226Q8×Dic43C2312yes—
227C4×D172—21no—
228C4×D172—21no—
229D4×Dic43—22no—
230D4×Dic43C2312yes—
231#13063287C2312yes—
232#13063287C2312yes—
233C4×C22⋊D43—22no—
234C4×C22⋊D43—22no—
235C4×C22⋊D43—22no—
236C4×C22⋊D43—22no—
237(C22⋊D43)⋊C4—22no—
238(C22⋊D43)⋊C4—22no—
239#13063284—21no—
240#13063284D412yes—
241#13063284D411yescharacteristic
242#13063284D411yescharacteristic
243#13063284C2311yescharacteristic
244#13063284C2311yescharacteristic
245#13063284C2312yes—
246#13063283—22no—
247C2×C4⋊Dic43—21no—
248C2×C4⋊Dic43D411yescharacteristic
249C2×C4⋊Dic43D411yescharacteristic
250C2×C4⋊Dic43C2311yescharacteristic
251C2×C22⋊Dic43D412yes—
252C2×(C2×D43)⋊C4—21no—
253C22⋊C4×D43—22no—
254C2×C4×Dic43C2312yes—
255Dic43⋊C8C2312yes—
256Dic43⋊C8C2312yes—
257Dic43⋊C8C2312yes—
258Dic43⋊C8C2312yes—
259#13063250C2312yes—
260#13063250C2312yes—
261#13063249C2312yes—
262#13063249C2312yes—
263#13063248C2312yes—
264#13063248C2312yes—
265#13063247C2312yes—
266#13063247C2312yes—
267#13063246C2312yes—
268#13063246C2312yes—
269#13063245C2312yes—
270#13063245C2312yes—
271C22⋊(C43⋊C8)C2312yes—
272C22⋊(C43⋊C8)C2312yes—
273#13063235C2312yes—
274#13063235C2312yes—
275C8×Dic43C2312yes—
276C8×Dic43C2312yes—
277C2×#41×C43—21no—
278C2×#41×C43—21no—
279C2×#41×C43—42no—
280C2×#41×C43—42no—
281C2×#41×C43C2311yescharacteristic
282C2×#41×C43C2311yescharacteristic
283C2×#41×C43C2311yescharacteristic
284C2×#41×C43C2311yescharacteristic
285C2×#41×C43C2311yescharacteristic
286C22×Q8×C43C2311yescharacteristic
287C22×D4×C43—21no—
288C22×D4×C43C2311yescharacteristic
289C23×C4×C43—21no—
290C23×C4×C43C2311yescharacteristic
291#135×C43—42no—
292#135×C43—42no—
293C2×Q16×C43C2311yescharacteristic
294C2×Q16×C43C2311yescharacteristic
295C2×SD16×C43C2311yescharacteristic
296C2×SD16×C43C2311yescharacteristic
297C2×SD16×C43C2311yescharacteristic
298C2×SD16×C43C2311yescharacteristic
299C2×D8×C43C2311yescharacteristic
300C2×D8×C43C2311yescharacteristic
301C22×C8×C43C2311yescharacteristic
302C22×C8×C43C2311yescharacteristic
303#123×C43—21no—
304C22⋊Q8×C43C2311yescharacteristic
305C22⋊Q8×C43C2311yescharacteristic
306#121×C43C2311yescharacteristic
307#121×C43C2311yescharacteristic
308#120×C43—21no—
309C4×D4×C43—21no—
310C4×D4×C43—21no—
311#117×C43C2311yescharacteristic
312#103×C43C2311yescharacteristic
313#103×C43C2311yescharacteristic
314#103×C43C2311yescharacteristic
315#103×C43C2311yescharacteristic
316#102×C43C2311yescharacteristic
317#102×C43C2311yescharacteristic
318#102×C43C2311yescharacteristic
319#102×C43C2311yescharacteristic
320C22⋊C8×C43C2311yescharacteristic
321C22⋊C8×C43C2311yescharacteristic
322C22⋊C8×C43C2311yescharacteristic
323C22⋊C8×C43C2311yescharacteristic
324C24×C43—21no—
325C24×C43C2×D411yescharacteristic
326C23×D43—21no—
327C23×D43—21no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—22no—
331#41×C43—22no—
332#41×C43—22no—
333#41×C43—22no—
334#41×C43—41no—
335#41×C43—41no—
336#41×C43—41no—
337#41×C43—41no—
338#41×C43—44no—
339#41×C43—44no—
340C2×Q8×C43—21no—
341C2×Q8×C43—41no—
342C2×Q8×C43—41no—
343C2×Q8×C43C2411yescharacteristic
344C2×Q8×C43C2411yescharacteristic
345C2×Q8×C43C2411yescharacteristic
346C2×D4×C43—21no—
347C2×D4×C43—21no—
348C2×D4×C43—21no—
349C2×D4×C43—21no—
350C2×D4×C43—21no—
351C2×D4×C43—21no—
352C2×D4×C43—21no—
353C2×D4×C43—21no—
354C2×D4×C43—44no—
355C2×D4×C43—41no—
356C2×D4×C43—41no—
357C2×D4×C43C2411yescharacteristic
358C2×D4×C43C2411yescharacteristic
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×C43—21no—
366C22×C4×C43—21no—
367C22×C4×C43—21no—
368C22×C4×C43—44no—
369C22×C4×C43C2×D411yescharacteristic
370C22×C4×C43C2×D411yescharacteristic
371C22×C4×C43C2×D411yescharacteristic
372C22×C4×C43C2411yescharacteristic
373C22×C4×C43C2411yescharacteristic
374C22×C4×C43C2411yescharacteristic
375C2×C22⋊D43—22no—
376C2×C22⋊D43—22no—
377C2×C22⋊D43—22no—
378C2×C22⋊D43—22no—
379C2×C22⋊D43—22no—
380C2×C22⋊D43—22no—
381C2×C22⋊D43—22no—
382C2×C22⋊D43—22no—
383C2×C22⋊D43—22no—
384C2×C22⋊D43—22no—
385C2×C22⋊D43—44no—
386C2×C22⋊D43—82no—
387C22×Dic43—22no—
388C22×Dic43—21no—
389C22×Dic43—21no—
390C22×Dic43C2×D412yes—
391C22×Dic43C2×D412yes—
392#10621900—84no—
393#10621898—42no—
394#10621898—42no—
395#10621898—42no—
396#10621898—42no—
397#10621898—44no—
398#10621898—44no—
399C2×D172—21no—
400C2×D172—21no—
401C2×D172—22no—
402C2×D172—22no—
403C2×D172—22no—
404C2×D172—22no—
405C2×D172C2412yes—
406C2×D172C2412yes—
407C2×C4×D43—22no—
408C2×C4×D43—22no—
409C2×C4×D43—22no—
410C2×C4×D43—22no—
411C2×C4×D43—44no—
412C2×Dic86—22no—
413C2×Dic86—22no—
414C2×Dic86—21no—
415C2×Dic86—22no—
416C2×Dic86C2412yes—
417Q16×C43—41no—
418Q16×C43—41no—
419SD16×C43—41no—
420SD16×C43—41no—
421SD16×C43—41no—
422SD16×C43—41no—
423D8×C43—41no—
424D8×C43—41no—
425C2×C8×C43—22no—
426C2×C8×C43—22no—
427C2×C8×C43C2411yescharacteristic
428C2×C8×C43C2411yescharacteristic
429C2×C8×C43C2411yescharacteristic
430C2×C8×C43C2411yescharacteristic
431C4⋊C4×C43—21no—
432C4⋊C4×C43—21no—
433C4⋊C4×C43C2411yescharacteristic
434C4⋊C4×C43C2411yescharacteristic
435C22⋊C4×C43—21no—
436C22⋊C4×C43—21no—
437C22⋊C4×C43—21no—
438C22⋊C4×C43—21no—
439C22⋊C4×C43—21no—
440C42×C43—21no—
441C22⋊Dic43—22no—
442C22⋊Dic43—22no—
443C22⋊Dic43—22no—
444C22⋊Dic43—22no—
445C22⋊Dic43—22no—
446C22⋊Dic43C2×D412yes—
447C22⋊Dic43C2×D412yes—
448C22⋊Dic43C2×D412yes—
449C22⋊Dic43C2×D412yes—
450#10621885—42no—
451#10621884—42no—
452#10621884—42no—
453#10621884—42no—
454#10621883—42no—
455#10621882—42no—
456#10621882—42no—
457#10621882—42no—
458(C2×D43)⋊C4—22no—
459(C2×D43)⋊C4—22no—
460(C2×D43)⋊C4—22no—
461(C2×D43)⋊C4—22no—
462(C2×D43)⋊C4—22no—
463(C2×D43)⋊C4—22no—
464(C2×D43)⋊C4—22no—
465(C2×D43)⋊C4—22no—
466(C2×D43)⋊C4—22no—
467(C2×D43)⋊C4—22no—
468C4⋊Dic43—21no—
469C4⋊Dic43—22no—
470C4⋊Dic43—22no—
471C4⋊Dic43C2×D411yescharacteristic
472C4⋊Dic43C2×D411yescharacteristic
473C4⋊Dic43C2×D412yes—
474C4⋊Dic43C2×D412yes—
475C4⋊Dic43C2×D411yescharacteristic
476C4⋊Dic43C2×D411yescharacteristic
477C4⋊Dic43C2412yes—
478Dic43⋊C4—22no—
479Dic43⋊C4—22no—
480Dic43⋊C4—22no—
481Dic43⋊C4—22no—
482Dic43⋊C4—22no—
483Dic43⋊C4—22no—
484C4×Dic43—22no—
485C4×Dic43C2×D412yes—
486C4×Dic43C2×D412yes—
487C4×Dic43C2412yes—
488C4×Dic43C2412yes—
489#10621877—22no—
490#10621877—22no—
491C2×C43⋊C8C2412yes—
492C2×C43⋊C8C2412yes—
493D344—42no—
494D344—42no—
495#10621873—42no—
496#10621873—42no—
497C23×C43—22no—
498C23×C43—21no—
499C23×C43—21no—
500C23×C43—21no—
501C23×C43—41no—
502C23×C43—41no—
503C23×C43—42no—
504C23×C43—81no—
505C23×C43—81no—
506C23×C43C22×D411yescharacteristic
507C23×C43C22×D411yescharacteristic
508C23×C43C22×D411yescharacteristic
509C22×D43—22no—
510C22×D43—22no—
511C22×D43—42no—
512C22×D43—42no—
513C22×D43—81no—
514C22×D43—81no—
515C22×D43—81no—
516C22×D43—81no—
517Q8×C43—21no—
518Q8×C43—21no—
519Q8×C43—21no—
520Q8×C43—21no—
521Q8×C43—21no—
522Q8×C43—21no—
523Q8×C43—42no—
524D4×C43—21no—
525D4×C43—21no—
526D4×C43—21no—
527D4×C43—21no—
528D4×C43—21no—
529D4×C43—21no—
530D4×C43—42no—
531D4×C43—42no—
532D4×C43—42no—
533D4×C43—42no—
534D4×C43—42no—
535D4×C43—42no—
536D4×C43—42no—
537D4×C43—81no—
538C2×C4×C43—22no—
539C2×C4×C43—22no—
540C2×C4×C43—22no—
541C2×C4×C43—21no—
542C2×C4×C43—21no—
543C2×C4×C43—21no—
544C2×C4×C43—21no—
545C2×C4×C43—21no—
546C2×C4×C43—21no—
547C2×C4×C43—21no—
548C2×C4×C43—21no—
549C2×C4×C43—21no—
550C2×C4×C43—42no—
551C2×C4×C43—42no—
552C2×C4×C43—42no—
553C2×C4×C43—42no—
554C2×C4×C43—42no—
555C2×C4×C43—42no—
556C2×C4×C43C22×D411yescharacteristic
557C2×C4×C43C22×D411yescharacteristic
558C2×C4×C43C22×D411yescharacteristic
559C2×C4×C43H(5,𝔽2)12yes—
560C2×C4×C43H(5,𝔽2)12yes—
561C2×C4×C43C2511yescharacteristic
562C22⋊D43—44no—
563C22⋊D43—44no—
564C22⋊D43—44no—
565C22⋊D43—82no—
566C22⋊D43—82no—
567C22⋊D43—82no—
568C22⋊D43—82no—
569C22⋊D43—82no—
570C22⋊D43—82no—
571C22⋊D43—82no—
572C2×Dic43—22no—
573C2×Dic43—22no—
574C2×Dic43—42no—
575C2×Dic43—42no—
576C2×Dic43—42no—
577C2×Dic43—82no—
578C2×Dic43—81no—
579C2×Dic43C22×D412yes—
580C2×Dic43C22×D412yes—
581C2×Dic43C22×D412yes—
582C2×Dic43C22×D412yes—
583D172—22no—
584D172—22no—
585D172—22no—
586D172—22no—
587D172—42no—
588D172—42no—
589C4×D43—44no—
590C4×D43—44no—
591C4×D43—82no—
592C4×D43—82no—
593Dic86—22no—
594Dic86—22no—
595Dic86—42no—
596Dic86—82no—
597C8×C43—21no—
598C8×C43—21no—
599C8×C43—21no—
600C8×C43—21no—
601C43⋊C8—22no—
602C43⋊C8—22no—
603#60815—431nomaximal, Sylow
604C22×C43—21no—
605C22×C43—21no—
606C22×C43—21no—
607C22×C43—21no—
608C22×C43—21no—
609C22×C43—21no—
610C22×C43—21no—
611C22×C43—21no—
612C22×C43—41no—
613C22×C43—41no—
614C22×C43—41no—
615C22×C43—41no—
616C22×C43—41no—
617C22×C43—41no—
618C22×C43—41no—
619C22×C43—41no—
620C22×C43—41no—
621C22×C43—82no—
622C22×C43—84no—
623C22×C43#53512yes—
624C22×C43C23×D411yescharacteristic
625C2×D43—42no—
626C2×D43—42no—
627C2×D43—42no—
628C2×D43—42no—
629C2×D43—42no—
630C2×D43—42no—
631C2×D43—84no—
632C2×D43—162no—
633C4×C43—21no—
634C4×C43—21no—
635C4×C43—41no—
636C4×C43—41no—
637C4×C43—41no—
638C4×C43—41no—
639C4×C43—41no—
640C4×C43#53512yes—
641C4×C43C2×H(5,𝔽2)11yescharacteristic
642C4×C43C2×H(5,𝔽2)11yescharacteristic
643Dic43—22no—
644Dic43—22no—
645Dic43—22no—
646Dic43—22no—
647Dic43—42no—
648Dic43—42no—
649#3494—431no—
650#3449—431no—
651#3225—432no—
652#3224—432no—
653#3221—432no—
654#3220—432no—
655#3219—432no—
656#3214—432no—
657#3212—432no—
658#3207—432no—
659#3155—431no—
660#3154—431no—
661#3137—431no—
662#3136—431no—
663#3046—431no—
664#3045—431no—
665#3042—431no—
666#3041—431no—
667#3006—431no—
668#3005—431no—
669#3002D4311yescharacteristic, complemented
670C2×#449—431no—
671#2924—431no—
672C2×C43—22no—
673C2×C43—41no—
674C2×C43—41no—
675C2×C43—81no—
676C2×C43—81no—
677C2×C43—81no—
678C2×C43C2×#53511yescharacteristic
679C2×C43#358411yescharacteristic
680C2×C43#358511yescharacteristic
681D43—82no—
682D43—82no—
683C22×#41—431no—
684C22×#41C2×D4311yescharacteristic
685C2×#137—431no—
686C2×AGL(1,ℤ/8)—431no—
687C2×AGL(1,ℤ/8)—431no—
688C2×AGL(1,ℤ/8)—431no—
689C2×#135C2×D4311yescharacteristic
690C2×#135C2×D4311yescharacteristic
691C22×SD16—431no—
692C22×D8—431no—
693#555—861no—
694#553—861no—
695#553—861no—
696#551—862no—
697#547—861no—
698#546—862no—
699#544—431no—
700#542—432no—
701#540—432no—
702#537—861no—
703#537—861no—
704#536—431no—
705#536—431no—
706#536—432no—
707#535—431no—
708#535—431no—
709#535—431no—
710#535—432no—
711#534—862no—
712#532—432no—
713#532—432no—
714#532—432no—
715#529—432no—
716#525—861no—
717#525—861no—
718#525—862no—
719#525C2×D4311yescharacteristic
720C2×#121—431no—
721#520—431no—
722#518—431no—
723C2×#117—431no—
724#497—432no—
725#496—432no—
726#496—432no—
727#496—432no—
728#495—432no—
729#495—432no—
730#493—432no—
731#492—432no—
732#491—432no—
733#490—432no—
734#489—432no—
735#489—432no—
736#488—432no—
737#488—432no—
738#487—432no—
739#486—432no—
740#464—432no—
741#464—432no—
742#463—432no—
743#463—432no—
744#463—432no—
745#463—432no—
746#463—432no—
747#463—432no—
748#462—432no—
749#461—432no—
750#461—432no—
751#461—432no—
752#460—432no—
753#459—432no—
754#459—432no—
755#459—432no—
756#452—432no—
757#452—432no—
758#452C2×D4311yescharacteristic, complemented
759#452C2×D4311yescharacteristic, complemented
760#451C2×D4311yescharacteristic, complemented
761#450C2×D4311yescharacteristic, complemented
762#449—432no—
763#449—432no—
764#449—432no—
765#449—432no—
766#449—432no—
767#449—432no—
768#449—432no—
769#449—432no—
770#449C2×D4311yescharacteristic, complemented
771#449C2×D4311yescharacteristic, complemented
772#448—432no—
773#448C2×D4311yescharacteristic, complemented
774#447—432no—
775#447C2×D4311yescharacteristic, complemented
776#433—432no—
777#433—432no—
778#432—432no—
779#431—432no—
780#424—431no—
781#424—431no—
782#419—431no—
783#418—431no—
784#417—431no—
785#417—431no—
786#416C2×D4311yescharacteristic
787#416C2×D4311yescharacteristic
788C2×#103—431no—
789C2×#102—431no—
790#407—431no—
791C2×C22⋊C8C2×D4311yescharacteristic
792#405—431no—
793#405—431no—
794C43#6081511yescharacteristic, complemented, Sylow
795C2×#41—21no—
796C2×#41—21no—
797C2×#41—42no—
798C2×#41—42no—
799C2×#41—432no—
800C2×#41—432no—
801C2×#41—862no—
802C2×#41—861no—
803C2×#41—861no—
804C2×#41—1722no—
805C2×#41—1722no—
806C2×#41C22×D4311yescharacteristic
807C2×#41C22×D4311yescharacteristic
808C2×#41C22×D4311yescharacteristic
809C2×#41C22×D4311yescharacteristic
810C2×#41C22×D4311yescharacteristic
811C22×Q8—431no—
812C22×Q8C22×D4311yescharacteristic
813C22×D4—21no—
814C22×D4—431no—
815C22×D4—431no—
816C22×D4—861no—
817C22×D4—861no—
818C22×D4C22×D4311yescharacteristic
819C23×C4—21no—
820C23×C4—861no—
821C23×C4C22×D4311yescharacteristic
822#137—1722no—
823AGL(1,ℤ/8)—1722no—
824AGL(1,ℤ/8)—1722no—
825AGL(1,ℤ/8)—1722no—
826#135—42no—
827#135—42no—
828C2×Q16—432no—
829C2×Q16C22×D4311yescharacteristic
830C2×Q16C22×D4311yescharacteristic
831C2×SD16—432no—
832C2×SD16—432no—
833C2×SD16—432no—
834C2×SD16—432no—
835C2×SD16—432no—
836C2×SD16—432no—
837C2×SD16—1722no—
838C2×SD16C22×D4311yescharacteristic
839C2×SD16C22×D4311yescharacteristic
840C2×SD16C22×D4311yescharacteristic
841C2×SD16C22×D4311yescharacteristic
842C2×D8—432no—
843C2×D8—432no—
844C2×D8—432no—
845C2×D8—432no—
846C2×D8—432no—
847C2×D8—1722no—
848C2×D8C22×D4311yescharacteristic
849C2×D8C22×D4311yescharacteristic
850C2×M16—431no—
851C2×M16—431no—
852C22×C8C22×D4311yescharacteristic
853C22×C8C22×D4311yescharacteristic
854C4⋊Q8—432no—
855C4⋊Q8—432no—
856C4⋊Q8—432no—
857C4⋊Q8—861no—
858#127—432no—
859#127—432no—
860#127—432no—
861#126—862no—
862#126—862no—
863#125—432no—
864#125—861no—
865#124—432no—
866#124—432no—
867#124—432no—
868#124—432no—
869#124—432no—
870#124—862no—
871#124—862no—
872#123—21no—
873#123—862no—
874#123—862no—
875#123—862no—
876#123—862no—
877#123—862no—
878#123—862no—
879#123—862no—
880#123—862no—
881C22⋊Q8—862no—
882C22⋊Q8—862no—
883C22⋊Q8—861no—
884C22⋊Q8—861no—
885C22⋊Q8—861no—
886C22⋊Q8—861no—
887C22⋊Q8—862no—
888C22⋊Q8—862no—
889C22⋊Q8C22×D4311yescharacteristic
890C22⋊Q8C22×D4311yescharacteristic
891#121—432no—
892#121—432no—
893#121—862no—
894#121—862no—
895#121—861no—
896#121—861no—
897#121—861no—
898#121—861no—
899#121—861no—
900#121—861no—
901#121—862no—
902#121—862no—
903#121—862no—
904#121—862no—
905#121—862no—
906#121—862no—
907#121—862no—
908#121—861no—
909#121—861no—
910#121C22×D4311yescharacteristic
911#121C22×D4311yescharacteristic
912#120—21no—
913#120—862no—
914#120—862no—
915#120—862no—
916#120—862no—
917#120—862no—
918C4×Q8—432no—
919C4×D4—21no—
920C4×D4—21no—
921C4×D4—432no—
922C4×D4—432no—
923C4×D4—432no—
924C4×D4—861no—
925C4×D4—861no—
926C4×D4—862no—
927C4×D4—862no—
928C4×D4—862no—
929C4×D4—862no—
930C4×D4—862no—
931C4×D4—862no—
932C4×D4—862no—
933#117—432no—
934#117—431no—
935#117—431no—
936#117—431no—
937#117—431no—
938#117—432no—
939#117—862no—
940#117—861no—
941#117C22×D4311yescharacteristic
942C2×C4⋊C4—431no—
943C2×C4⋊C4—431no—
944C2×C4⋊C4—431no—
945C2×C4⋊C4—861no—
946C2×C22⋊C4—432no—
947C2×C22⋊C4—862no—
948C2×C22⋊C4—861no—
949C2×C42—432no—
950C4⋊C8—432no—
951C4⋊C8—432no—
952C4⋊C8—432no—
953C4⋊C8—432no—
954#103—432no—
955#103—432no—
956#103—432no—
957#103—432no—
958#103—432no—
959#103—432no—
960#103C22×D4311yescharacteristic
961#103C22×D4311yescharacteristic
962#103C22×D4311yescharacteristic
963#103C22×D4311yescharacteristic
964#102—432no—
965#102—432no—
966#102—432no—
967#102—432no—
968#102—432no—
969#102—432no—
970#102C22×D4311yescharacteristic
971#102C22×D4311yescharacteristic
972#102C22×D4311yescharacteristic
973#102C22×D4311yescharacteristic
974C22⋊C8—432no—
975C22⋊C8—432no—
976C22⋊C8C22×D4311yescharacteristic
977C22⋊C8C22×D4311yescharacteristic
978C22⋊C8C22×D4311yescharacteristic
979C22⋊C8C22×D4311yescharacteristic
980#97—432no—
981#97—432no—
982C4×C8—432no—
983C4×C8—432no—
984C24—21no—
985C24—861no—
986C24—861no—
987C24D4×D4311yescharacteristic
988#41—22no—
989#41—22no—
990#41—22no—
991#41—22no—
992#41—22no—
993#41—22no—
994#41—41no—
995#41—41no—
996#41—41no—
997#41—41no—
998#41—44no—
999#41—44no—
1000#41—3444no—
1001#41—1722no—
1002#41—1722no—
1003#41—1722no—
1004#41—1722no—
1005#41—1724no—
1006#41—1724no—
1007C2×Q8—21no—
1008C2×Q8—41no—
1009C2×Q8—41no—
1010C2×Q8—432no—
1011C2×Q8—862no—
1012C2×Q8—861no—
1013C2×Q8—862no—
1014C2×Q8—862no—
1015C2×Q8C23×D4311yescharacteristic
1016C2×Q8C23×D4311yescharacteristic
1017C2×Q8C23×D4311yescharacteristic
1018C2×D4—21no—
1019C2×D4—21no—
1020C2×D4—21no—
1021C2×D4—21no—
1022C2×D4—21no—
1023C2×D4—21no—
1024C2×D4—21no—
1025C2×D4—21no—
1026C2×D4—41no—
1027C2×D4—41no—
1028C2×D4—44no—
1029C2×D4—432no—
1030C2×D4—432no—
1031C2×D4—862no—
1032C2×D4—862no—
1033C2×D4—862no—
1034C2×D4—862no—
1035C2×D4—862no—
1036C2×D4—862no—
1037C2×D4—862no—
1038C2×D4—862no—
1039C2×D4—862no—
1040C2×D4—862no—
1041C2×D4—861no—
1042C2×D4—861no—
1043C2×D4—862no—
1044C2×D4—862no—
1045C2×D4—862no—
1046C2×D4—862no—
1047C2×D4—3442no—
1048C2×D4—1724no—
1049C2×D4C23×D4311yescharacteristic
1050C2×D4C23×D4311yescharacteristic
1051C2×D4C23×D4311yescharacteristic
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—21no—
1055C22×C4—21no—
1056C22×C4—21no—
1057C22×C4—21no—
1058C22×C4—21no—
1059C22×C4—21no—
1060C22×C4—44no—
1061C22×C4—432no—
1062C22×C4—432no—
1063C22×C4—862no—
1064C22×C4—862no—
1065C22×C4—862no—
1066C22×C4—861no—
1067C22×C4—861no—
1068C22×C4—862no—
1069C22×C4—862no—
1070C22×C4—1724no—
1071C22×C4D4×D4311yescharacteristic
1072C22×C4D4×D4311yescharacteristic
1073C22×C4D4×D4311yescharacteristic
1074C22×C4C23×D4311yescharacteristic
1075C22×C4C23×D4311yescharacteristic
1076C22×C4C23×D4311yescharacteristic
1077Q16—41no—
1078Q16—41no—
1079Q16—1722no—
1080SD16—41no—
1081SD16—41no—
1082SD16—41no—
1083SD16—41no—
1084SD16—1722no—
1085SD16—1722no—
1086SD16—1722no—
1087SD16—1722no—
1088SD16—1722no—
1089SD16—1722no—
1090D8—41no—
1091D8—41no—
1092D8—1722no—
1093D8—1722no—
1094D8—1722no—
1095D8—1722no—
1096D8—1722no—
1097M16—862no—
1098M16—862no—
1099C2×C8—22no—
1100C2×C8—22no—
1101C2×C8—432no—
1102C2×C8—432no—
1103C2×C8C23×D4311yescharacteristic
1104C2×C8C23×D4311yescharacteristic
1105C2×C8C23×D4311yescharacteristic
1106C2×C8C23×D4311yescharacteristic
1107C4⋊C4—21no—
1108C4⋊C4—21no—
1109C4⋊C4—431no—
1110C4⋊C4—431no—
1111C4⋊C4—431no—
1112C4⋊C4—431no—
1113C4⋊C4—432no—
1114C4⋊C4—432no—
1115C4⋊C4—432no—
1116C4⋊C4—862no—
1117C4⋊C4—862no—
1118C4⋊C4—862no—
1119C4⋊C4—862no—
1120C4⋊C4—862no—
1121C4⋊C4—862no—
1122C4⋊C4—862no—
1123C4⋊C4—862no—
1124C4⋊C4—861no—
1125C4⋊C4C23×D4311yescharacteristic
1126C4⋊C4C23×D4311yescharacteristic
1127C22⋊C4—21no—
1128C22⋊C4—21no—
1129C22⋊C4—21no—
1130C22⋊C4—21no—
1131C22⋊C4—21no—
1132C22⋊C4—432no—
1133C22⋊C4—432no—
1134C22⋊C4—432no—
1135C22⋊C4—432no—
1136C22⋊C4—862no—
1137C22⋊C4—862no—
1138C22⋊C4—862no—
1139C22⋊C4—862no—
1140C22⋊C4—862no—
1141C22⋊C4—862no—
1142C22⋊C4—862no—
1143C22⋊C4—862no—
1144C22⋊C4—862no—
1145C22⋊C4—862no—
1146C22⋊C4—862no—
1147C22⋊C4—862no—
1148C22⋊C4—862no—
1149C22⋊C4—862no—
1150C22⋊C4—862no—
1151C42—21no—
1152C42—432no—
1153C42—432no—
1154C42—432no—
1155C42—432no—
1156C42—862no—
1157C23—22no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—41no—
1162C23—41no—
1163C23—42no—
1164C23—81no—
1165C23—81no—
1166C23—862no—
1167C23—862no—
1168C23—3441no—
1169C23—3441no—
1170C23—3441no—
1171C23—3441no—
1172C23—1722no—
1173C23—1722no—
1174C23C2×D4×D4311yescharacteristic
1175C23C2×D4×D4311yescharacteristic
1176C23C2×D4×D4311yescharacteristic
1177Q8—21no—
1178Q8—21no—
1179Q8—21no—
1180Q8—21no—
1181Q8—21no—
1182Q8—21no—
1183Q8—42no—
1184Q8—862no—
1185Q8—862no—
1186Q8—3442no—
1187Q8—1722no—
1188D4—21no—
1189D4—21no—
1190D4—21no—
1191D4—21no—
1192D4—21no—
1193D4—21no—
1194D4—42no—
1195D4—42no—
1196D4—42no—
1197D4—42no—
1198D4—42no—
1199D4—42no—
1200D4—42no—
1201D4—81no—
1202D4—862no—
1203D4—862no—
1204D4—862no—
1205D4—862no—
1206D4—3442no—
1207D4—3442no—
1208D4—3442no—
1209D4—3442no—
1210D4—3442no—
1211D4—3442no—
1212D4—3442no—
1213D4—1724no—
1214D4—1724no—
1215D4—1724no—
1216D4—1722no—
1217D4—1722no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—432no—
1237C2×C4—432no—
1238C2×C4—432no—
1239C2×C4—432no—
1240C2×C4—862no—
1241C2×C4—862no—
1242C2×C4—3442no—
1243C2×C4—3442no—
1244C2×C4—3442no—
1245C2×C4—3441no—
1246C2×C4—1724no—
1247C2×C4—1724no—
1248C2×C4—1722no—
1249C2×C4—1722no—
1250C2×C4—1722no—
1251C2×C4C2×D4×D4311yescharacteristic
1252C2×C4C2×D4×D4311yescharacteristic
1253C2×C4C2×D4×D4311yescharacteristic
1254C2×C4#1306337012yes—
1255C2×C4#1306337012yes—
1256C2×C4C24×D4311yescharacteristic
1257C8—21no—
1258C8—21no—
1259C8—21no—
1260C8—21no—
1261C8—862no—
1262C8—862no—
1263C22—21no—
1264C22—21no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—21no—
1270C22—21no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—82no—
1281C22—84no—
1282C22—3444no—
1283C22—1722no—
1284C22—1722no—
1285C22—1722no—
1286C22—1722no—
1287C22—1722no—
1288C22—1722no—
1289C22—6882no—
1290C22#1458346412yes—
1291C22C22×D4×D4311yescharacteristic
1292C4—21no—
1293C4—21no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—41no—
1299C4—862no—
1300C4—862no—
1301C4—862no—
1302C4—862no—
1303C4—1722no—
1304C4—1722no—
1305C4#1458346412yes—
1306C4C2×#1306337011yescharacteristic
1307C4C2×#1306337011yescharacteristic
1308C2—22no—
1309C2—41no—
1310C2—41no—
1311C2—81no—
1312C2—81no—
1313C2—81no—
1314C2—3442no—
1315C2—3442no—
1316C2C2×#1458346411yescharacteristic
1317C2#1914936411yescharacteristic
1318C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3002C2
socleC22×C43C23×D4
hypercenter#3002D43
hypocenterC43#60815
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. #19148332C2semidirect
2. #19147924C2semidirect
3. #19145710C2semidirect
4. #19145693C2semidirect
5. #19145652C2semidirect
6. #19145641C2semidirect
7. #19145636C2semidirect
8. #19145587C2semidirect
9. #19145574C2semidirect
10. #19145526C2semidirect
11. #19145082C2semidirect
12. #19145072C2semidirect
13. #19144964C2semidirect
14. #19144953C2semidirect
15. #19144143C2semidirect
16. #19144132C2semidirect
17. #19144110C2semidirect
18. #19144101C2semidirect
19. #19143847C2semidirect
20. #19143835C2semidirect
21. C2×#14583046C2semidirect
22. #19143249C2semidirect
23. C43×#3002C2semidirect
25. C2×#13063355C22semidirect
28. C2×#13063350C22semidirect
29. C22×#10621873C22semidirect
30. C22×D344C22semidirect
37. #14583527C22semidirect
38. #14583522C22semidirect
39. #14583502C22semidirect
42. #14583473C22semidirect
45. #14583466C22semidirect
48. #14583463C22semidirect
50. #14583445C22semidirect
51. #14583445C22semidirect
52. #14583444C22semidirect
53. #14583435C22semidirect
58. #14583382C22semidirect
59. #14583373C22semidirect
61. #14583292C22semidirect
62. #14583287C22semidirect
63. #14583285C22semidirect
64. #14583285C22semidirect
65. #14583284C22semidirect
66. #14583280C22semidirect
67. #14583274C22semidirect
68. #14583270C22semidirect
69. #14583266C22semidirect
70. #14583262C22semidirect
71. #14583260C22semidirect
72. #14583257C22semidirect
73. #14583255C22semidirect
74. #14583252C22semidirect
75. #14583248C22semidirect
76. #14583244C22semidirect
77. #14583123C22semidirect
78. #14583119C22semidirect
79. #14583117C22semidirect
80. #14583117C22semidirect
81. #14583116C22semidirect
82. #14583113C22semidirect
83. #14583113C22semidirect
84. #14583112C22semidirect
85. #14583107C22semidirect
86. #14583103C22semidirect
87. #14583103C22semidirect
88. #14583102C22semidirect
89. #14583097C22semidirect
90. #14583093C22semidirect
91. #14583093C22semidirect
92. #14583092C22semidirect
93. #14583059C22semidirect
94. #14583059C22semidirect
97. #14583046C22semidirect
98. #14583046C22semidirect
99. #14583044C22semidirect
100. #14583044C22semidirect
101. #14583042C22semidirect
102. #14583042C22semidirect
103. #14583038C22semidirect
104. #14583033C22semidirect
105. #14582957C22semidirect
106. #14582957C22semidirect
107. #14582953C22semidirect
108. #14582949C22semidirect
109. #14582925C22semidirect
110. #14582925C22semidirect
111. #14582907C22semidirect
112. #14582903C22semidirect
115. C2×#13063250C22semidirect
116. C2×#13063247C22semidirect
118. #14582854C22semidirect
119. #14582854C22semidirect
124. C43×#452C22semidirect
125. C43×#452C22semidirect
126. C43×#451C22semidirect
127. C43×#450C22semidirect
128. C43×#449C22semidirect
129. C43×#449C22semidirect
130. C43×#448C22semidirect
131. C43×#447C22semidirect
669. #3002D43semidirect
758. #452C2×D43semidirect
759. #452C2×D43semidirect
760. #451C2×D43semidirect
761. #450C2×D43semidirect
770. #449C2×D43semidirect
771. #449C2×D43semidirect
773. #448C2×D43semidirect
775. #447C2×D43semidirect
794. C43#60815semidirect

Maximal subgroups

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

subgroupindex
#191483322
#191479242
#191457102
#191456932
#191456522
#191456412
#191456362
#191455872
#191455742
#191455262
#191450822
#191450722
#191449642
#191449532
#191441432
#191441322
#191441102
#191441012
#191438472
#191438352
C2×#145830462
#191432492
C43×#30022
#6081543