Finite Group Databasebeta

← #11884191

Subgroups — #11884191

Order 1152.

1067 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595067C211yesmaximal, characteristic
2#10594915C211yesmaximal, characteristic, complemented
3C2×#63831C211yesmaximal, characteristic, complemented
4C2×D3×#204C211yesmaximal, characteristic, complemented
5#10592437C211yesmaximal, characteristic, complemented
6C3×#4733C211yesmaximal, characteristic, complemented
7C3×#4728C211yesmaximal, characteristic, complemented
8#10591178C211yesmaximal, characteristic, complemented
9#10590949C211yesmaximal, characteristic, complemented
10#10590946C211yesmaximal, characteristic, complemented
11#10590899C211yesmaximal, characteristic, complemented
12#10590848C211yesmaximal, characteristic, complemented
13#10590813C211yesmaximal, characteristic, complemented
14#10590752C211yesmaximal, characteristic, complemented
15#10590747C211yesmaximal, characteristic, complemented
16#80241—31nomaximal
17#79495—31nomaximal
18C22×#634C2211yescharacteristic, complemented
19C2×C3×#235C2211yescharacteristic
20C2×D3×D12C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22#64139C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24C2×#3744C2211yescharacteristic
25C3×C4×#67C2211yescharacteristic
26C3×#924C2211yescharacteristic, complemented
27C2×C3×#208C2211yescharacteristic, complemented
28C2×C3×Dic12C2211yescharacteristic, complemented
29C2×C3×#204C2211yescharacteristic
30C2×C3×D3×C8C2211yescharacteristic
31#63983—21no—
32#63982—21no—
33#67⋊Dic3—21no—
34#63971—21no—
35D3×(C2×D3)⋊C4—21no—
36#63896—21no—
37Dic3×D12C2211yescharacteristic
38#63866C2211yescharacteristic, complemented
39#63864C2211yescharacteristic
40#63857C2211yescharacteristic
41#63856C2211yescharacteristic
42#63850—21no—
43#63844C2211yescharacteristic, complemented
44#63840—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3719C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic
48#63831—24no—
49C2×#3716C2211yescharacteristic
50C2×#3716C2211yescharacteristic
51D3×#204—24no—
52C32×C22⋊C8C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×(C2×D3)⋊C8C2211yescharacteristic
57C3×#816C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63564C2211yescharacteristic
63#5829—31no—
64C2×#951—31no—
65C2×D3×SD16—31no—
66C2×#909—31no—
67C22×#204—31no—
68#5632—31no—
69#5550—31no—
70D4×Dic6—31no—
71C3×#452—31no—
72C3×#435—31no—
73#5190—31no—
74#5186—31no—
75#5162—31no—
76#5134—31no—
77#5116—31no—
78#5049—31no—
79#4845—31no—
80#4841—31no—
81#4813—31no—
82#4798—31no—
83#4776—31no—
84#4757—31no—
85#4739—31no—
86#4738—31no—
87#4738—31no—
88#4738—61no—
89#4733D311yescharacteristic, complemented
90#4731—31no—
91#4728D311yescharacteristic, complemented
92#4715—31no—
93#4710—31no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97C22×C3⋊Dic3—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634—22no—
100C2×#634—21no—
101C2×#634—41no—
102C2×#634C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C3×#235—22no—
107C3×#235—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#627—21no—
114C2×#626—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117D3×D12—22no—
118D3×D12—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3744—22no—
126#3744—41no—
127C3×#217—21no—
128C3×#217D411yescharacteristic
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C3×#208—22no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×Dic12—41no—
138C3×#204—22no—
139C3×D3×C8—22no—
140#3724—21no—
141#3724—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145#3722—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150Dic32—21no—
151#3719—22no—
152#3719—22no—
153#3717—22no—
154#3716—22no—
155#3716D414yescomplemented
156#3266—91noSylow
157C2×C3×#41—31no—
158C2×D3×Q8—31no—
159C2×D3×D4—31no—
160C2×#235C2×D311yescharacteristic
161C22×D12—31no—
162C22×Dic6—31no—
163C22×Dic6—31no—
164C22×Dic6—31no—
165C22×Dic6—61no—
166C2×C3×Q16—31no—
167C2×C3×SD16—31no—
168C2×C3×M16—31no—
169C22×C3×C8—31no—
170C3×C22⋊Q8—31no—
171C3×C4×D4—31no—
172#951—64no—
173#947—31no—
174#946—31no—
175#944—31no—
176C2×#216—31no—
177C2×#216—31no—
178C2×#215—31no—
179#939—61no—
180#937—61no—
181#937—61no—
182D4×Dic3—31no—
183D4×Dic3—61no—
184C2×#214—31no—
185C2×#214—31no—
186#930—31no—
187#930—31no—
188#930—61no—
189#929—61no—
190C4×#67C2×D311yescharacteristic
191C2×(C2×D3)⋊C4—61no—
192#924—31no—
193#924—31no—
194#924C2×D311yescharacteristic, complemented
195C2×#208C2×D311yescharacteristic, complemented
196D3×SD16—64no—
197#909—64no—
198C2×Dic12—31no—
199C2×Dic12—31no—
200C2×Dic12C2×D311yescharacteristic, complemented
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—61no—
209C2×#204—61no—
210C2×#204—64no—
211C2×#204C2×D311yescharacteristic
212C2×D3×C8C2×D311yescharacteristic
213#897—31no—
214#896—61no—
215#894—61no—
216#888—61no—
217#888—61no—
218#887—31no—
219#884—61no—
220#67⋊C4—61no—
221D3×C22⋊C4—61no—
222#878—61no—
223#878—61no—
224#878—61no—
225#875—31no—
226C4×D12—31no—
227#869—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#835—31no—
238#821—31no—
239#821C2×D311yescharacteristic
240(C2×D3)⋊C8C2×D311yescharacteristic
241#818—31no—
242#816—31no—
243#816—31no—
244#816—31no—
245#816—31no—
246#816—31no—
247#816—61no—
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×D3C2×D411yescharacteristic
258C2×D32—42no—
259C2×D32—42no—
260C2×D32—81no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265#638—81no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—42no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272#634—21no—
273#634—21no—
274#634—21no—
275#634—42no—
276#634C2×D412yes—
277C3×#67—22no—
278C3×#67—42no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—42no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#627—42no—
295#626—42no—
296D3×Dic3—42no—
297D3×Dic3—81no—
298C32×C8—21no—
299C32×C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8C2×D412yes—
302C2×#137—91no—
303C22×SD16—91no—
304D4×Q8—91no—
305#546—91no—
306#497—91no—
307#468—91no—
308#467—91no—
309#464—91no—
310#461—91no—
311#452—31no—
312#451—91no—
313#450—91no—
314#448—91no—
315#440—91no—
316#435—31no—
317C23×D3—61no—
318C23×D3—61no—
319C3×#41—62no—
320C3×#41—121no—
321C2×C3×Q8—31no—
322C2×C3×Q8—31no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—61no—
326C22×C3×C4—21no—
327C22×C3×C4—31no—
328C22×C3×C4—61no—
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C2×#67—21no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—121no—
336C2×#67D1211yescharacteristic
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—61no—
341C22×Dic3—121no—
342D3×Q8—62no—
343D3×Q8—121no—
344D3×D4—62no—
345D3×D4—121no—
346#235—22no—
347#235—41no—
348C2×D12—31no—
349C2×D12—31no—
350C2×D12—61no—
351C2×D12—62no—
352C2×D12—61no—
353C2×D12—121no—
354C2×D12C22×D311yescharacteristic
355C2×C4×D3—21no—
356C2×C4×D3—61no—
357C2×C4×D3—61no—
358C2×C4×D3C22×D311yescharacteristic
359C2×Dic6—31no—
360C2×Dic6—31no—
361C2×Dic6—31no—
362C2×Dic6—31no—
363C2×Dic6—61no—
364C2×Dic6—61no—
365C2×Dic6—62no—
366C2×Dic6—62no—
367C2×Dic6—62no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6—61no—
372C2×Dic6—122no—
373C2×Dic6—121no—
374C2×Dic6—121no—
375C2×Dic6—121no—
376C2×Dic6—121no—
377C2×Dic6—122no—
378C2×Dic6C22×D311yescharacteristic
379C2×Dic6C22×D311yescharacteristic
380C3×Q16—121no—
381C3×SD16—62no—
382C3×M16—62no—
383C2×C3×C8—21no—
384C2×C3×C8—21no—
385C2×C3×C8—31no—
386C2×C3×C8—31no—
387C2×C3×C8—62no—
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C2×C3×C8C22×D311yescharacteristic
391C2×C3×C8C22×D311yescharacteristic
392C3×C4⋊C4—31no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—61no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—31no—
397C3×C22⋊C4—61no—
398C3×C42—31no—
399#217—21no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217D1211yescharacteristic
404#216—62no—
405#216—62no—
406#215—62no—
407#214—34no—
408#214—62no—
409(C2×D3)⋊C4—61no—
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—121no—
419(C2×D3)⋊C4D1211yescharacteristic
420C4⋊Dic3—31no—
421C4⋊Dic3—31no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3C22×D311yescharacteristic
427Dic3⋊C4—21no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4D1211yescharacteristic
436C4×Dic3—61no—
437C4×Dic3—61no—
438C4×Dic3C22×D311yescharacteristic
439#208—22no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442Dic12—41no—
443Dic12—62no—
444Dic12—62no—
445#204—22no—
446#204—34no—
447#204—62no—
448#204—62no—
449#204—62no—
450#204—62no—
451#204—122no—
452#204—121no—
453#204—121no—
454#204—122no—
455D3×C8—22no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32C22×D411yescharacteristic
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—22no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3#13712yescomplemented
469D32—84no—
470C32×C4—21no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—22no—
474C3⋊Dic3—41no—
475C3⋊Dic3—41no—
476C3×Dic3—21no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—31no—
483C22×Q8—91no—
484C22×Q8—91no—
485C22×D4—91no—
486#137—184no—
487C2×Q16—31no—
488C2×Q16—91no—
489C2×Q16—91no—
490C2×SD16—31no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—184no—
497C2×M16—31no—
498C22×C8—31no—
499C4⋊Q8—91no—
500C4⋊Q8—181no—
501#124—91no—
502#123—181no—
503C22⋊Q8—31no—
504C22⋊Q8—91no—
505C22⋊Q8—91no—
506C22⋊Q8—181no—
507C22⋊Q8—181no—
508#121—91no—
509#121—181no—
510#120—181no—
511C4×Q8—91no—
512C4×D4—31no—
513C4×D4—91no—
514C4×D4—181no—
515C2×C22⋊C4—181no—
516#107—91no—
517C4⋊C8—31no—
518#103—31no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—91no—
524C22⋊C8—31no—
525C22⋊C8D3211yescharacteristic, complemented
526#97—31no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—61no—
530C23×C3C2×D1211yescharacteristic
531C23×C3D3×D411yescharacteristic
532C22×D3—21no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—121no—
536C22×D3—122no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—241no—
541C22×D3—241no—
542C22×D3C2×D1211yescharacteristic
543C3×Q8—61no—
544C3×Q8—61no—
545C3×Q8—61no—
546C3×Q8—61no—
547C3×D4—32no—
548C3×D4—62no—
549C3×D4—61no—
550C3×D4—122no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—41no—
561C2×C3×C4—41no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—122no—
568C2×C3×C4C2×D1211yescharacteristic
569C2×C3×C4D3×D411yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571C2×C3×C4C23×D311yescharacteristic
572#67—22no—
573#67—42no—
574#67—122no—
575#67—241no—
576#67—241no—
577#67—242no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—121no—
588C2×Dic3—121no—
589C2×Dic3—121no—
590C2×Dic3—122no—
591C2×Dic3—122no—
592C2×Dic3—122no—
593C2×Dic3—124no—
594C2×Dic3—241no—
595C2×Dic3C2×D1211yescharacteristic
596C2×Dic3C2×D1211yescharacteristic
597C2×Dic3C2×D1211yescharacteristic
598D12—21no—
599D12—61no—
600D12—61no—
601D12—61no—
602D12—61no—
603D12—121no—
604D12—121no—
605D12—122no—
606D12D3×D412yes—
607C4×D3—21no—
608C4×D3—21no—
609C4×D3—42no—
610C4×D3—122no—
611C4×D3—241no—
612Dic6—21no—
613Dic6—21no—
614Dic6—21no—
615Dic6—21no—
616Dic6—32no—
617Dic6—32no—
618Dic6—62no—
619Dic6—61no—
620Dic6—61no—
621Dic6—62no—
622Dic6—61no—
623Dic6—61no—
624Dic6—61no—
625Dic6—61no—
626Dic6—121no—
627Dic6—121no—
628Dic6—122no—
629Dic6—122no—
630Dic6—122no—
631Dic6—122no—
632Dic6—124no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—21no—
637C3×C8—32no—
638C3×C8—41no—
639C3×C8—41no—
640C3×C8—61no—
641C3⋊C8—21no—
642C3⋊C8D3×D412yes—
643C2×C32—41no—
644C2×C32D4211yescharacteristic
645C2×C32C2×#13711yescharacteristic
646C2×C32#57711yescharacteristic
647C3⋊D3—81no—
648C3×D3—22no—
649C3×D3—42no—
650C24—181no—
651#41—62no—
652#41—121no—
653C2×Q8—31no—
654C2×Q8—31no—
655C2×Q8—91no—
656C2×Q8—91no—
657C2×Q8—182no—
658C2×Q8—181no—
659C2×Q8—182no—
660C2×Q8—181no—
661C2×Q8—361no—
662C2×Q8—361no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—61no—
666C2×D4—91no—
667C2×D4—181no—
668C2×D4—182no—
669C2×D4—181no—
670C2×D4—361no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4—181no—
676C22×C4C2×D3211yescharacteristic
677Q16—121no—
678Q16—182no—
679Q16—182no—
680SD16—62no—
681SD16—94no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685SD16—361no—
686M16—62no—
687C2×C8—31no—
688C2×C8—31no—
689C2×C8—62no—
690C2×C8C2×D3211yescharacteristic
691C2×C8C2×D3211yescharacteristic
692C4⋊C4—31no—
693C4⋊C4—31no—
694C4⋊C4—61no—
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—61no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C42—31no—
711C42—181no—
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—32no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—62no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3C22×D1211yescharacteristic
729C22×C3C2×D3×D411yescharacteristic
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—22no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—241no—
742C2×D3—241no—
743C2×D3—241no—
744C2×D3—244no—
745C2×D3—244no—
746C2×D3#90912yescomplemented
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—41no—
752C3×C4—61no—
753C3×C4—61no—
754C3×C4—61no—
755C3×C4—121no—
756C3×C4—121no—
757C3×C4—121no—
758C3×C4C2×D3×D411yescharacteristic
759C3×C4C2×D3×D411yescharacteristic
760C3×C4#100411yescharacteristic
761C3×C4#100911yescharacteristic
762Dic3—21no—
763Dic3—21no—
764Dic3—21no—
765Dic3—41no—
766Dic3—41no—
767Dic3—41no—
768Dic3—62no—
769Dic3—62no—
770Dic3—122no—
771Dic3—122no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—241no—
777C32#326611yescharacteristic, complemented, Sylow
778C23—31no—
779C23—61no—
780C23—181no—
781C23—362no—
782C23—362no—
783C23—721no—
784C23D3×D1211yescharacteristic
785Q8—61no—
786Q8—61no—
787Q8—61no—
788Q8—61no—
789Q8—92no—
790Q8—181no—
791Q8—181no—
792Q8—181no—
793Q8—362no—
794Q8—362no—
795D4—32no—
796D4—62no—
797D4—61no—
798D4—122no—
799D4—181no—
800D4—181no—
801D4—362no—
802D4—721no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—31no—
806C2×C4—31no—
807C2×C4—31no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—122no—
814C2×C4—181no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—362no—
818C2×C4—362no—
819C2×C4—721no—
820C2×C4D3×D1211yescharacteristic
821C2×C4C22×D3211yescharacteristic
822C8—21no—
823C8—21no—
824C8—32no—
825C8—61no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—42no—
830C2×C3—41no—
831C2×C3—41no—
832C2×C3—62no—
833C2×C3—122no—
834C2×C3D4×D1211yescharacteristic
835C2×C3#559011yescharacteristic
836C2×C3C2×#90911yescharacteristic
837C2×C3#575111yescharacteristic
838C2×C3#577011yescharacteristic
839C2×C3D3×#13711yescharacteristic
840D3—22no—
841D3—42no—
842D3—241no—
843D3—241no—
844D3—481no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—32no—
849C22—61no—
850C22—61no—
851C22—62no—
852C22—121no—
853C22—121no—
854C22—361no—
855C22—361no—
856C22—361no—
857C22—724no—
858C22C2×D3×D1211yescharacteristic
859C4—21no—
860C4—61no—
861C4—61no—
862C4—61no—
863C4—121no—
864C4—121no—
865C4—121no—
866C4—182no—
867C4—361no—
868C4—361no—
869C4D32×D411yescharacteristic
870C4#6431411yescharacteristic
871C3—21no—
872C3#7949511yescharacteristic, complemented
873C3#8024111yescharacteristic, complemented
874C2—41no—
875C2—62no—
876C2—122no—
877C2—721no—
878C2#1059427711yescharacteristic
879C2#1059467911yescharacteristic
880C2D3×#90911yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595067C2
hypercenterC22⋊C8D32
hypocenterC32#3266
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
2. #10594915C2semidirect
3. C2×#63831C2semidirect
4. C2×D3×#204C2semidirect
5. #10592437C2semidirect
6. C3×#4733C2semidirect
7. C3×#4728C2semidirect
8. #10591178C2semidirect
9. #10590949C2semidirect
10. #10590946C2semidirect
11. #10590899C2semidirect
12. #10590848C2semidirect
13. #10590813C2semidirect
14. #10590752C2semidirect
15. #10590747C2semidirect
18. C22×#634C22semidirect
26. C3×#924C22semidirect
27. C2×C3×#208C22semidirect
28. C2×C3×Dic12C22semidirect
38. #63866C22semidirect
43. #63844C22semidirect
45. C2×#3719C22semidirect
46. C2×#3719C22semidirect
52. C32×C22⋊C8C22semidirect
53. #63643C22semidirect
54. #63643C22semidirect
57. C3×#816C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63575C22semidirect
61. #63566C22semidirect
89. #4733D3semidirect
91. #4728D3semidirect
155. #3716D4semidirect
194. #924C2×D3semidirect
195. C2×#208C2×D3semidirect
200. C2×Dic12C2×D3semidirect
234. C3×C22⋊C8C2×D3semidirect
235. C3×C22⋊C8C2×D3semidirect
249. #816C2×D3semidirect
250. #815C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
468. C2×C3×D3#137semidirect
525. C22⋊C8D32semidirect
746. C2×D3#909semidirect
777. C32#3266semidirect
872. C3#79495semidirect
873. C3#80241semidirect

Maximal subgroups

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

subgroupindex
#105950672
#105949152
C2×#638312
C2×D3×#2042
#105924372
C3×#47332
C3×#47282
#105911782
#105909492
#105909462
#105908992
#105908482
#105908132
#105907522
#105907472
#802413
#794953