Finite Group Databasebeta

← #11884269

Subgroups — #11884269

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic, complemented
2#10595067C211yesmaximal, characteristic, complemented
3#10594887C211yesmaximal, characteristic, complemented
4C2×#63795C211yesmaximal, characteristic, complemented
5#10592813C211yesmaximal, characteristic, complemented
6C3×#5111C211yesmaximal, characteristic, complemented
7#10591173C211yesmaximal, characteristic, complemented
8#10591163C211yesmaximal, characteristic, complemented
9#10590960C211yesmaximal, characteristic, complemented
10#10590942C211yesmaximal, characteristic, complemented
11#10590899C211yesmaximal, characteristic, complemented
12#10590854C211yesmaximal, characteristic, complemented
13#10590771C211yesmaximal, characteristic, complemented
14#10590754C211yesmaximal, characteristic, complemented
15#10590752C211yesmaximal, characteristic, complemented
16#83921—31nomaximal
17#79496—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C22×C32×C8C2211yescharacteristic, complemented
23#64139C2211yescharacteristic
24#64133C2211yescharacteristic, complemented
25C2×#3744C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C2×C3×Dic12C2211yescharacteristic, complemented
28C3×#904—24no—
29C2×C3×D24C2211yescharacteristic
30C2×C3×#204C2211yescharacteristic
31C2×C3×#204C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33#63983—21no—
34#63971—21no—
35#63970—21no—
36#63969—21no—
37D3×(C2×D3)⋊C4—21no—
38#63905—21no—
39Dic3×D12C2211yescharacteristic
40Dic3×D12C2211yescharacteristic, complemented
41D3×Dic3⋊C4—21no—
42#63866C2211yescharacteristic, complemented
43#63864C2211yescharacteristic
44#63856C2211yescharacteristic
45#63856C2211yescharacteristic
46#63850—21no—
47C2×#3719C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3714C2211yescharacteristic
51#63795—24no—
52#63648C2211yescharacteristic
53#63644C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63563C2211yescharacteristic
62#63563C2211yescharacteristic, complemented
63C2×C3×#135—31no—
64#5829—31no—
65#5824—31no—
66C2×#911—31no—
67C2×#908—31no—
68C2×#904D311yescharacteristic, complemented
69#5551—31no—
70#5550—31no—
71C3×#435—31no—
72#5239—31no—
73#5238—31no—
74#5190—31no—
75#5189—31no—
76#5173—31no—
77#5169—31no—
78#5165—31no—
79#5162—31no—
80#5152—31no—
81#5137—31no—
82#5114—31no—
83#5114—31no—
84#5114—61no—
85#5111D311yescharacteristic, complemented
86#4844—31no—
87#4841—31no—
88#4734—31no—
89#4733—31no—
90#4733—31no—
91#4731—31no—
92#4715—31no—
93#4711—31no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C3×#235—22no—
103C3×#235—22no—
104C3×#235—41no—
105C3×#235—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—41no—
120#3795—22no—
121#3795—41no—
122C2×C32×C8—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125#3757—21no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130#3744—22no—
131C3×#217D411yescharacteristic
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×Dic12—22no—
138C3×D24D414yescomplemented
139C3×#204—22no—
140C3×#204—22no—
141C3×ΓL(1,𝔽25)—22no—
142#3724—21no—
143#3724—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3719—41no—
153#3717—41no—
154#3716—22no—
155#3714—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#237—31no—
160C2×D3×D4—31no—
161C2×#235—31no—
162C2×#235C2×D311yescharacteristic
163C2×#235C2×D311yescharacteristic, complemented
164C22×D12—31no—
165C3×#135—64no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C2×C3×M16—31no—
171C22×C3×C8—21no—
172C22×C3×C8C2×D311yescharacteristic, complemented
173C22×C3×C8C2×D311yescharacteristic, complemented
174C3×C4×D4—31no—
175#947—31no—
176#946—31no—
177#946—31no—
178#944—31no—
179C2×#216—31no—
180C2×#215—31no—
181#939—61no—
182#939—61no—
183#938—61no—
184#937—61no—
185#937—61no—
186#935—61no—
187D4×Dic3—31no—
188D4×Dic3—31no—
189C2×#214—31no—
190C2×#213—31no—
191#930—31no—
192#930—31no—
193#930—61no—
194#929—61no—
195#929—61no—
196C4×#67C2×D311yescharacteristic
197C2×(C2×D3)⋊C4—61no—
198#924—31no—
199#924—31no—
200#924—31no—
201#924—31no—
202#924—61no—
203C2×Dic3⋊C4—61no—
204#911—64no—
205#908—64no—
206C2×Dic12—31no—
207C2×Dic12C2×D311yescharacteristic, complemented
208#904—24no—
209C2×D24—31no—
210C2×D24C2×D311yescharacteristic
211C2×#204—31no—
212C2×#204—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—61no—
216C2×#204C2×D311yescharacteristic
217C2×#204C2×D311yescharacteristic, complemented
218C2×ΓL(1,𝔽25)C2×D311yescharacteristic
219#894—61no—
220D3×C4⋊C4—61no—
221#884—61no—
222#883—61no—
223#883—61no—
224D3×C22⋊C4—61no—
225#875—31no—
226C4×D12—31no—
227C4×D12—31no—
228#869—31no—
229C3×C4⋊C8—31no—
230C3×C22⋊C8—31no—
231C3×C22⋊C8—31no—
232C3×#97—31no—
233#835—31no—
234#835—31no—
235#832—31no—
236#832—31no—
237#830C2×D311yescharacteristic, complemented
238#821—31no—
239#821—31no—
240#821—31no—
241#821—31no—
242#821—61no—
243(C2×D3)⋊C8C2×D311yescharacteristic
244#817—31no—
245#817—31no—
246#817—61no—
247#816—31no—
248#816—31no—
249#816—31no—
250#816—31no—
251#816—61no—
252#815C2×D311yescharacteristic, complemented
253Dic3⋊C8C2×D311yescharacteristic, complemented
254C23×C32C2×D411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266#638—81no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272#634—21no—
273#634—21no—
274C3×#67—41no—
275C3×#67—42no—
276C3×#67—42no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12C2×D412yes—
285C3×D12C2×D412yes—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—42no—
289C3×C4×D3—42no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#626—42no—
295#625—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—81no—
299C32×C8—21no—
300C32×C8C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—31no—
305#547—91no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—31no—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—121no—
323C3×#41—121no—
324C2×C3×Q8—31no—
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×C4—61no—
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C2×#67—21no—
338C2×#67—21no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—121no—
345C2×#67D1211yescharacteristic
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349#237—62no—
350#237—121no—
351D3×D4—62no—
352D3×D4—121no—
353#235—22no—
354#235—22no—
355#235—41no—
356#235—41no—
357#235—62no—
358#235—121no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—61no—
362C2×D12—62no—
363C2×D12—61no—
364C2×D12—121no—
365C2×D12C22×D311yescharacteristic
366C2×D12C22×D311yescharacteristic
367C2×C4×D3—21no—
368C2×C4×D3—21no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3C22×D311yescharacteristic
373C2×Dic6—31no—
374C2×Dic6—31no—
375C2×Dic6—61no—
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×Q16—62no—
379C3×SD16—62no—
380C3×SD16—62no—
381C3×D8—34no—
382C3×M16—62no—
383C2×C3×C8—22no—
384C2×C3×C8—22no—
385C2×C3×C8—21no—
386C2×C3×C8—21no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C2×C3×C8—42no—
390C2×C3×C8C22×D311yescharacteristic
391C2×C3×C8C22×D311yescharacteristic
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394C3×C4⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—31no—
397C3×C42—31no—
398#217—61no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—121no—
405#217D1211yescharacteristic
406#216—121no—
407#215—121no—
408#214—62no—
409#213—62no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—121no—
421(C2×D3)⋊C4D1211yescharacteristic
422C4⋊Dic3—31no—
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—31no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—61no—
438Dic3⋊C4—121no—
439Dic3⋊C4D1211yescharacteristic
440C4×Dic3C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442C2×C3⋊C8C22×D311yescharacteristic
443Dic12—22no—
444Dic12—121no—
445D24—62no—
446D24#6714yescomplemented
447#204—22no—
448#204—22no—
449#204—62no—
450#204—62no—
451#204—62no—
452#204—122no—
453#204—121no—
454ΓL(1,𝔽25)—22no—
455C22×C32—21no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—21no—
473C32×C4C22×D411yescharacteristic
474C32×C4H(5,𝔽2)11yescharacteristic
475C3⋊Dic3—41no—
476C3⋊Dic3—41no—
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—21no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—64no—
489C2×Q16—31no—
490C2×Q16—91no—
491C2×SD16—31no—
492C2×SD16—31no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—31no—
499C22×C8D3211yescharacteristic, complemented
500C4⋊Q8—91no—
501#124—91no—
502#123—181no—
503#123—181no—
504#123—181no—
505C22⋊Q8—91no—
506C22⋊Q8—91no—
507C22⋊Q8—91no—
508#121—91no—
509#121—181no—
510#121—181no—
511#120—181no—
512C4×D4—31no—
513C4×D4—91no—
514C4×D4—91no—
515C2×C4⋊C4—181no—
516C2×C22⋊C4—181no—
517#106—91no—
518C4⋊C8—31no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—91no—
523#102—91no—
524#102—91no—
525C22⋊C8—31no—
526C22⋊C8—31no—
527#97—31no—
528C23×C3—21no—
529C23×C3—31no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3C2×D1211yescharacteristic
533C23×C3D3×D411yescharacteristic
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—121no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3C2×D1211yescharacteristic
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×D4—32no—
551C3×D4—32no—
552C3×D4—61no—
553C3×D4—61no—
554C3×D4—121no—
555C3×D4—122no—
556C3×D4—122no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—122no—
573C2×C3×C4—122no—
574C2×C3×C4C2×D1211yescharacteristic
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—41no—
579#67—42no—
580#67—42no—
581#67—122no—
582#67—122no—
583#67—122no—
584#67—241no—
585#67—241no—
586#67—242no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—122no—
599C2×Dic3—122no—
600C2×Dic3—241no—
601C2×Dic3C2×D1211yescharacteristic
602C2×Dic3C2×D1211yescharacteristic
603C2×Dic3C2×D1211yescharacteristic
604D12—21no—
605D12—21no—
606D12—61no—
607D12—61no—
608D12—61no—
609D12—61no—
610D12—121no—
611D12—121no—
612D12—122no—
613D12C2×#6712yes—
614D12C2×#6712yes—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—42no—
618C4×D3—42no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3—241no—
622Dic6—21no—
623Dic6—21no—
624Dic6—21no—
625Dic6—21no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—121no—
631Dic6—121no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—22no—
635C3×C8—41no—
636C3×C8—61no—
637C3×C8—61no—
638C3×C8D3×D412yes—
639C3×C8C2×#6712yes—
640C3⋊C8—21no—
641C3⋊C8—21no—
642C2×C32—41no—
643C2×C32D4211yescharacteristic
644C2×C32#57511yescharacteristic
645C2×C32#57711yescharacteristic
646C3⋊D3—81no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—42no—
650C24—181no—
651#41—62no—
652#41—62no—
653#41—121no—
654#41—121no—
655#41—182no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8—91no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—31no—
663C2×D4—61no—
664C2×D4—61no—
665C2×D4—91no—
666C2×D4—181no—
667C2×D4—182no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—361no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4C2×D3211yescharacteristic
678Q16—62no—
679Q16—361no—
680SD16—62no—
681SD16—62no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685D8—34no—
686D8—182no—
687M16—62no—
688C2×C8—22no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8C2×D3211yescharacteristic
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—91no—
695C4⋊C4—91no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C22⋊C4—31no—
702C22⋊C4—31no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42—31no—
712C22×C3—22no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—62no—
726C22×C3—62no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3C22×D1211yescharacteristic
732C22×C3C2×D3×D411yescharacteristic
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—22no—
736C2×D3—22no—
737C2×D3—21no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—241no—
749C2×D3—241no—
750C2×D3—241no—
751C2×D3—244no—
752C2×D3—244no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—41no—
758C3×C4—61no—
759C3×C4—61no—
760C3×C4—61no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4C2×D3×D411yescharacteristic
764C3×C4#100411yescharacteristic
765C3×C4#100911yescharacteristic
766C3×C4C22×#6711yescharacteristic
767Dic3—21no—
768Dic3—21no—
769Dic3—21no—
770Dic3—41no—
771Dic3—41no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—121no—
778Dic3—241no—
779Dic3—241no—
780Dic3—241no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—31no—
783C23—61no—
784C23—61no—
785C23—181no—
786C23—362no—
787C23—362no—
788C23—721no—
789C23D3×D1211yescharacteristic
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794Q8—181no—
795Q8—181no—
796D4—32no—
797D4—32no—
798D4—61no—
799D4—61no—
800D4—121no—
801D4—122no—
802D4—122no—
803D4—181no—
804D4—181no—
805D4—362no—
806D4—362no—
807D4—721no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—31no—
811C2×C4—31no—
812C2×C4—31no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—122no—
818C2×C4—122no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4—721no—
825C2×C4D3×D1211yescharacteristic
826C2×C4C22×D3211yescharacteristic
827C8—21no—
828C8—61no—
829C8—61no—
830C8D3×#6712yes—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—122no—
838C2×C3—122no—
839C2×C3—121no—
840C2×C3D4×D1211yescharacteristic
841C2×C3#574811yescharacteristic
842C2×C3#575111yescharacteristic
843C2×C3#576811yescharacteristic
844C2×C3#577011yescharacteristic
845C2×C3D4×#6711yescharacteristic
846D3—41no—
847D3—42no—
848D3—42no—
849D3—241no—
850D3—241no—
851D3—481no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—62no—
859C22—62no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22C2×D3×D1211yescharacteristic
869C4—21no—
870C4—61no—
871C4—61no—
872C4—61no—
873C4—121no—
874C4—121no—
875C4—361no—
876C4—361no—
877C4—361no—
878C4#6430711yescharacteristic
879C4C2×D3×#6711yescharacteristic
880C3—21no—
881C3#7949611yescharacteristic, complemented
882C3#8392111yescharacteristic, complemented
883C2—41no—
884C2—121no—
885C2—122no—
886C2—122no—
887C2—721no—
888C2#1059467611yescharacteristic
889C2#1059467911yescharacteristic
890C2D12×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3267
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. C2×C3×#904C2semidirect
2. #10595067C2semidirect
3. #10594887C2semidirect
4. C2×#63795C2semidirect
5. #10592813C2semidirect
6. C3×#5111C2semidirect
7. #10591173C2semidirect
8. #10591163C2semidirect
9. #10590960C2semidirect
10. #10590942C2semidirect
11. #10590899C2semidirect
12. #10590854C2semidirect
13. #10590771C2semidirect
14. #10590754C2semidirect
15. #10590752C2semidirect
19. C2×C3×#235C22semidirect
22. C22×C32×C8C22semidirect
24. #64133C22semidirect
27. C2×C3×Dic12C22semidirect
31. C2×C3×#204C22semidirect
40. Dic3×D12C22semidirect
42. #63866C22semidirect
47. C2×#3719C22semidirect
53. #63644C22semidirect
54. #63643C22semidirect
55. C3×#830C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
62. #63563C22semidirect
68. C2×#904D3semidirect
85. #5111D3semidirect
138. C3×D24D4semidirect
163. C2×#235C2×D3semidirect
172. C22×C3×C8C2×D3semidirect
173. C22×C3×C8C2×D3semidirect
207. C2×Dic12C2×D3semidirect
217. C2×#204C2×D3semidirect
237. #830C2×D3semidirect
252. #815C2×D3semidirect
253. Dic3⋊C8C2×D3semidirect
446. D24#67semidirect
499. C22×C8D32semidirect
781. C32#3267semidirect
881. C3#79496semidirect
882. C3#83921semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
#105950672
#105948872
C2×#637952
#105928132
C3×#51112
#105911732
#105911632
#105909602
#105909422
#105908992
#105908542
#105907712
#105907542
#105907522
#839213
#794963