Finite Group Databasebeta

← #11884419

Subgroups — #11884419

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595078C211yesmaximal, characteristic, complemented
2#10595007C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic, complemented
4C2×#63794C211yesmaximal, characteristic, complemented
5#10592433C211yesmaximal, characteristic, complemented
6C3×#4734C211yesmaximal, characteristic, complemented
7C3×#4730C211yesmaximal, characteristic, complemented
8#10591164C211yesmaximal, characteristic, complemented
9#10590970C211yesmaximal, characteristic, complemented
10#10590944C211yesmaximal, characteristic, complemented
11#10590883C211yesmaximal, characteristic, complemented
12#10590859C211yesmaximal, characteristic, complemented
13#10590828C211yesmaximal, characteristic, complemented
14#10590795C211yesmaximal, characteristic, complemented
15#10590765C211yesmaximal, characteristic, complemented
16#80123—31nomaximal
17#79497—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22#64139C2211yescharacteristic, complemented
23C2×#3745C2211yescharacteristic
24C2×#3744C2211yescharacteristic, complemented
25C3×#930C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic, complemented
28C2×C3×D24C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
31#63983—21no—
32#63979—21no—
33#63958—21no—
34#63958—21no—
35#63921—21no—
36#63911C2211yescharacteristic, complemented
37#63908C2211yescharacteristic
38#63906—21no—
39#63904—21no—
40#63894C2211yescharacteristic
41#63860C2211yescharacteristic
42#63857C2211yescharacteristic
43#63853—21no—
44Dic3×Dic6C2211yescharacteristic, complemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47#63829—24no—
48C2×#3716C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51#63794—24no—
52C32×C22⋊C8C2211yescharacteristic, complemented
53#63648C2211yescharacteristic
54#63643C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#816C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic
63#5834—31no—
64C2×#950—31no—
65C2×#914—31no—
66C2×#908—31no—
67C2×#904—31no—
68#5612—31no—
69#5553—31no—
70#5550—31no—
71C3×#449—31no—
72C3×#435—31no—
73#5166—31no—
74#5156—31no—
75#5154—31no—
76#5134—31no—
77#5115—31no—
78#5038—31no—
79#4845—31no—
80#4843—31no—
81#4817—31no—
82#4808—31no—
83#4786—31no—
84#4780—31no—
85#4734—31no—
86#4734—31no—
87#4734—61no—
88#4734D311yescharacteristic, complemented
89#4733—31no—
90#4732—31no—
91#4730D311yescharacteristic, complemented
92#4712—31no—
93#4710—31no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98#3828—22no—
99#3828—41no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C4×C3⋊D3—21no—
103C2×#634C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67D411yescharacteristic
107C3×#235—22no—
108C3×#235—41no—
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#625—21no—
119C2×#624—21no—
120C2×#624—21no—
121D3×D12—22no—
122D3×D12—41no—
123#3799—22no—
124#3799—41no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127#3752—21no—
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3745—22no—
130#3744—41no—
131C3×#217D411yescharacteristic
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4D411yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8—22no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D24—41no—
141C3×#204—22no—
142C3×ΓL(1,𝔽25)—22no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150Dic32—21no—
151#3719—22no—
152#3717D414yescomplemented
153#3716—22no—
154#3714—22no—
155#3714—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×#239—31no—
159C2×D3×D4—31no—
160C2×#235—31no—
161C2×#235—31no—
162C2×#235—31no—
163C2×#235—61no—
164C2×#235C2×D311yescharacteristic, complemented
165C22×D12—31no—
166C2×C3×SD16—31no—
167C2×C3×D8—31no—
168C2×C3×M16—31no—
169C22×C3×C8—31no—
170C3×#121—31no—
171C3×C4×D4—31no—
172#950—64no—
173Q8×Dic3—31no—
174C2×#216—31no—
175C2×#215—31no—
176#940—31no—
177#940—61no—
178#940—61no—
179#938—31no—
180#938—61no—
181#938—61no—
182#937—61no—
183#937—61no—
184#936—31no—
185C2×#214—31no—
186C2×#213—31no—
187C2×#213—31no—
188#930—31no—
189#930—31no—
190#930—31no—
191#930—61no—
192#930—61no—
193#930C2×D311yescharacteristic
194C4×#67—61no—
195C4×#67C2×D311yescharacteristic
196#924—31no—
197C22×C3⋊C8C2×D311yescharacteristic, complemented
198#914—64no—
199#908—64no—
200C2×Dic12—31no—
201#904—64no—
202C2×D24—31no—
203C2×D24—31no—
204C2×D24—31no—
205C2×D24—31no—
206C2×D24—61no—
207C2×D24C2×D311yescharacteristic
208C2×#204—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204—31no—
212C2×#204—61no—
213C2×#204C2×D311yescharacteristic
214C2×ΓL(1,𝔽25)C2×D311yescharacteristic
215#897—31no—
216#894—61no—
217#893—31no—
218#893—61no—
219#884—61no—
220#884—61no—
221#884—61no—
222#883—61no—
223D3×C22⋊C4—61no—
224D3×C22⋊C4—61no—
225#875—31no—
226#874—31no—
227C4×D12—31no—
228C4×Dic6—31no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#102—31no—
232C3×C22⋊C8—21no—
233C3×C22⋊C8—31no—
234C3×C22⋊C8C2×D311yescharacteristic, complemented
235C3×C22⋊C8C2×D311yescharacteristic, complemented
236C3×#97—31no—
237#832—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243#821C2×D311yescharacteristic, complemented
244(C2×D3)⋊C8C2×D311yescharacteristic
245#818—31no—
246#816—31no—
247#816—31no—
248#816—61no—
249#816C2×D311yescharacteristic, complemented
250#815C2×D311yescharacteristic, complemented
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#809—31no—
253#807—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267#638—42no—
268#638—81no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—42no—
276#634—21no—
277#634—21no—
278C3×#67—41no—
279C3×#67—42no—
280C3×#67—81no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×C4×D3—21no—
291C3×C4×D3—21no—
292C3×C4×D3—42no—
293C3×Dic6—21no—
294C3×Dic6C2×D412yes—
295#626—42no—
296#626—42no—
297#626—42no—
298#626—81no—
299#625—81no—
300#624—42no—
301#624—81no—
302C32×C8—21no—
303C32×C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—91no—
310#496—91no—
311#468—91no—
312#466—91no—
313#464—91no—
314#459—91no—
315#452—91no—
316#449—31no—
317#449—91no—
318#447—91no—
319#440—91no—
320#435—31no—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—121no—
325C2×C3×Q8—31no—
326C2×C3×D4—31no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C22×C3×C4—21no—
332C22×C3×C4—31no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—121no—
349C2×#67—121no—
350C2×#67D1211yescharacteristic
351#239—62no—
352#239—121no—
353D3×D4—62no—
354D3×D4—121no—
355#235—22no—
356#235—41no—
357#235—62no—
358#235—62no—
359#235—62no—
360#235—122no—
361#235—121no—
362#235—121no—
363#235—121no—
364#235—122no—
365C2×D12—31no—
366C2×D12—31no—
367C2×D12—31no—
368C2×D12—31no—
369C2×D12—61no—
370C2×D12—61no—
371C2×D12—62no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—121no—
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×C4×D3—21no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—121no—
387C2×C4×D3C22×D311yescharacteristic
388C2×Dic6—31no—
389C2×Dic6—31no—
390C2×Dic6—61no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—62no—
393C3×D8—121no—
394C3×M16—62no—
395C2×C3×C8—21no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8—62no—
400C2×C3×C8C22×D311yescharacteristic
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C3×C4⋊C4—31no—
405C3×C4⋊C4—31no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—61no—
409C3×C42—31no—
410#217—61no—
411#217—61no—
412#217—61no—
413#217—61no—
414#217D1211yescharacteristic
415#216—62no—
416#215—34no—
417#214—62no—
418#213—62no—
419#213—62no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—121no—
430(C2×D3)⋊C4D1211yescharacteristic
431C4⋊Dic3—31no—
432C4⋊Dic3—31no—
433C4⋊Dic3—61no—
434C4⋊Dic3—61no—
435C4⋊Dic3—61no—
436C4⋊Dic3C22×D311yescharacteristic
437Dic3⋊C4—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4D1211yescharacteristic
440C4×Dic3—61no—
441C4×Dic3—61no—
442C4×Dic3C22×D311yescharacteristic
443C2×C3⋊C8—22no—
444C2×C3⋊C8C22×D311yescharacteristic
445C2×C3⋊C8C22×D311yescharacteristic
446Dic12—62no—
447D24—41no—
448D24—62no—
449D24—62no—
450D24—62no—
451D24—62no—
452D24—122no—
453#204—22no—
454#204—34no—
455#204—62no—
456#204—121no—
457#204—121no—
458#204—122no—
459ΓL(1,𝔽25)—22no—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32—21no—
463C22×C32C22×D411yescharacteristic
464C2×C3⋊D3—22no—
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—21no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479D32—84no—
480C32×C4—21no—
481C32×C4C22×D411yescharacteristic
482C32×C4H(5,𝔽2)11yescharacteristic
483C3⋊Dic3—41no—
484C3⋊Dic3—41no—
485C3×Dic3—21no—
486C3×Dic3—22no—
487C3×Dic3—21no—
488C3×Dic3—21no—
489C3×Dic3—41no—
490C2×#41—31no—
491C2×#41—91no—
492C2×#41—91no—
493C22×D4—91no—
494AGL(1,ℤ/8)—184no—
495#135—184no—
496C2×Q16—91no—
497C2×SD16—31no—
498C2×SD16—91no—
499C2×SD16—91no—
500C2×SD16—91no—
501C2×D8—31no—
502C2×D8—91no—
503C2×D8—91no—
504C2×D8—91no—
505C2×M16—31no—
506C22×C8—31no—
507#127—91no—
508#127—181no—
509#124—91no—
510#123—181no—
511C22⋊Q8—91no—
512#121—31no—
513#121—91no—
514#121—91no—
515#121—181no—
516#121—181no—
517#121—181no—
518#120—181no—
519C4×Q8—91no—
520C4×D4—31no—
521C4×D4—91no—
522C4×D4—181no—
523C2×C22⋊C4—181no—
524#107—91no—
525C4⋊C8—31no—
526#103—31no—
527#103—91no—
528#102—31no—
529#102—91no—
530#102—91no—
531#102—91no—
532C22⋊C8—31no—
533C22⋊C8D3211yescharacteristic, complemented
534#97—31no—
535C23×C3—21no—
536C23×C3—31no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3C2×D1211yescharacteristic
540C23×C3D3×D411yescharacteristic
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—61no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—61no—
547C22×D3—121no—
548C22×D3—121no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—241no—
554C22×D3—241no—
555C22×D3C2×D1211yescharacteristic
556C3×Q8—32no—
557C3×Q8—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—121no—
563C3×D4—122no—
564C3×D4—241no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—41no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—122no—
581C2×C3×C4C2×D1211yescharacteristic
582C2×C3×C4D3×D411yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585#67—41no—
586#67—42no—
587#67—81no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—124no—
594#67—241no—
595#67—241no—
596#67—241no—
597#67—241no—
598#67—241no—
599#67—242no—
600C2×Dic3—21no—
601C2×Dic3—21no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—121no—
607C2×Dic3—121no—
608C2×Dic3C2×D1211yescharacteristic
609C2×Dic3C2×D1211yescharacteristic
610C2×Dic3C2×D1211yescharacteristic
611D12—21no—
612D12—21no—
613D12—21no—
614D12—21no—
615D12—32no—
616D12—32no—
617D12—62no—
618D12—61no—
619D12—61no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—121no—
625D12—121no—
626D12—121no—
627D12—122no—
628D12—122no—
629D12—122no—
630D12—241no—
631C4×D3—21no—
632C4×D3—21no—
633C4×D3—42no—
634C4×D3—122no—
635C4×D3—122no—
636C4×D3—122no—
637C4×D3—122no—
638C4×D3—124no—
639C4×D3—241no—
640C4×D3—241no—
641Dic6—21no—
642Dic6—62no—
643Dic6—61no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—121no—
648Dic6D3×D412yes—
649C3×C8—21no—
650C3×C8—21no—
651C3×C8—21no—
652C3×C8—21no—
653C3×C8—32no—
654C3×C8—41no—
655C3×C8—41no—
656C3×C8—61no—
657C3⋊C8—21no—
658C3⋊C8D3×D412yes—
659C2×C32—41no—
660C2×C32D4211yescharacteristic
661C2×C32#57511yescharacteristic
662C2×C32#57611yescharacteristic
663C3⋊D3—42no—
664C3⋊D3—81no—
665C3×D3—41no—
666C3×D3—81no—
667C3×D3—81no—
668C24—181no—
669#41—62no—
670#41—121no—
671#41—182no—
672#41—182no—
673#41—361no—
674#41—361no—
675C2×Q8—31no—
676C2×Q8—91no—
677C2×D4—31no—
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—91no—
683C2×D4—91no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—182no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—361no—
693C22×C4—31no—
694C22×C4—61no—
695C22×C4—181no—
696C22×C4—181no—
697C22×C4—181no—
698C22×C4C2×D3211yescharacteristic
699Q16—182no—
700SD16—62no—
701SD16—94no—
702SD16—182no—
703SD16—361no—
704D8—121no—
705D8—182no—
706D8—182no—
707D8—182no—
708M16—62no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—62no—
712C2×C8C2×D3211yescharacteristic
713C2×C8C2×D3211yescharacteristic
714C4⋊C4—31no—
715C4⋊C4—31no—
716C4⋊C4—91no—
717C4⋊C4—181no—
718C4⋊C4—181no—
719C22⋊C4—31no—
720C22⋊C4—31no—
721C22⋊C4—61no—
722C22⋊C4—181no—
723C22⋊C4—181no—
724C22⋊C4—181no—
725C22⋊C4—181no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C42—31no—
729C42—181no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3C22×D1211yescharacteristic
750C22×C3C2×D3×D411yescharacteristic
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—122no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—241no—
774C2×D3—241no—
775C2×D3—241no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—244no—
779C2×D3—244no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—41no—
785C3×C4—61no—
786C3×C4—61no—
787C3×C4—62no—
788C3×C4—61no—
789C3×C4—121no—
790C3×C4C2×D3×D411yescharacteristic
791C3×C4C2×D3×D411yescharacteristic
792C3×C4#100411yescharacteristic
793C3×C4#100911yescharacteristic
794Dic3—21no—
795Dic3—21no—
796Dic3—21no—
797Dic3—22no—
798Dic3—41no—
799Dic3—122no—
800Dic3—121no—
801Dic3—121no—
802Dic3—121no—
803Dic3—121no—
804Dic3—241no—
805C32#326811yescharacteristic, complemented, Sylow
806C23—31no—
807C23—61no—
808C23—61no—
809C23—181no—
810C23—181no—
811C23—362no—
812C23—362no—
813C23—721no—
814C23D3×D1211yescharacteristic
815Q8—32no—
816Q8—61no—
817Q8—181no—
818Q8—181no—
819D4—61no—
820D4—61no—
821D4—61no—
822D4—61no—
823D4—92no—
824D4—121no—
825D4—122no—
826D4—181no—
827D4—181no—
828D4—181no—
829D4—241no—
830D4—362no—
831D4—362no—
832D4—362no—
833D4—362no—
834D4—721no—
835D4—721no—
836D4—721no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—31no—
840C2×C4—31no—
841C2×C4—31no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—122no—
847C2×C4—181no—
848C2×C4—181no—
849C2×C4—362no—
850C2×C4—362no—
851C2×C4—721no—
852C2×C4D3×D1211yescharacteristic
853C2×C4C22×D3211yescharacteristic
854C8—21no—
855C8—21no—
856C8—32no—
857C8—61no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—41no—
862C2×C3—41no—
863C2×C3—81no—
864C2×C3—121no—
865C2×C3—241no—
866C2×C3—241no—
867C2×C3D4×D1211yescharacteristic
868C2×C3#559011yescharacteristic
869C2×C3#574811yescharacteristic
870C2×C3#575211yescharacteristic
871C2×C3#576811yescharacteristic
872C2×C3#577411yescharacteristic
873D3—41no—
874D3—81no—
875D3—81no—
876D3—122no—
877D3—122no—
878D3—242no—
879D3—241no—
880D3—241no—
881D3—481no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—61no—
886C22—61no—
887C22—61no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—182no—
895C22—361no—
896C22—361no—
897C22—361no—
898C22—361no—
899C22—361no—
900C22—724no—
901C22C2×D3×D1211yescharacteristic
902C4—21no—
903C4—61no—
904C4—61no—
905C4—61no—
906C4—62no—
907C4—121no—
908C4—361no—
909C4—361no—
910C4D32×D411yescharacteristic
911C4#6431411yescharacteristic
912C3—21no—
913C3#7949711yescharacteristic, complemented
914C3#8012311yescharacteristic, complemented
915C2—41no—
916C2—121no—
917C2—241no—
918C2—241no—
919C2—362no—
920C2—721no—
921C2#1059427711yescharacteristic
922C2#1059467611yescharacteristic
923C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595078C2semidirect
2. #10595007C2semidirect
3. C2×#63829C2semidirect
4. C2×#63794C2semidirect
5. #10592433C2semidirect
6. C3×#4734C2semidirect
7. C3×#4730C2semidirect
8. #10591164C2semidirect
9. #10590970C2semidirect
10. #10590944C2semidirect
11. #10590883C2semidirect
12. #10590859C2semidirect
13. #10590828C2semidirect
14. #10590795C2semidirect
15. #10590765C2semidirect
19. C2×C3×#235C22semidirect
22. #64139C22semidirect
24. C2×#3744C22semidirect
27. C22×C3×C3⋊C8C22semidirect
36. #63911C22semidirect
44. Dic3×Dic6C22semidirect
45. C2×#3719C22semidirect
48. C2×#3716C22semidirect
52. C32×C22⋊C8C22semidirect
54. #63643C22semidirect
55. C3×#821C22semidirect
57. C3×#816C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63575C22semidirect
61. #63564C22semidirect
88. #4734D3semidirect
91. #4730D3semidirect
152. #3717D4semidirect
164. C2×#235C2×D3semidirect
197. C22×C3⋊C8C2×D3semidirect
234. C3×C22⋊C8C2×D3semidirect
235. C3×C22⋊C8C2×D3semidirect
243. #821C2×D3semidirect
249. #816C2×D3semidirect
250. #815C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
533. C22⋊C8D32semidirect
805. C32#3268semidirect
913. C3#79497semidirect
914. C3#80123semidirect

Maximal subgroups

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

subgroupindex
#105950782
#105950072
C2×#638292
C2×#637942
#105924332
C3×#47342
C3×#47302
#105911642
#105909702
#105909442
#105908832
#105908592
#105908282
#105907952
#105907652
#801233
#794973