Finite Group Databasebeta

← #11884108

Subgroups — #11884108

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594915C211yesmaximal, characteristic, complemented
2#10594886C211yesmaximal, characteristic
3C22×#3716C211yesmaximal, characteristic, complemented
4C2×#63800C211yesmaximal, characteristic, complemented
5#10592438C211yesmaximal, characteristic, complemented
6C3×#4731C211yesmaximal, characteristic, complemented
7C3×#4730C211yesmaximal, characteristic, complemented
8#10591187C211yesmaximal, characteristic, complemented
9#10590969C211yesmaximal, characteristic, complemented
10#10590897C211yesmaximal, characteristic, complemented
11#10590861C211yesmaximal, characteristic, complemented
12#10590828C211yesmaximal, characteristic, complemented
13#10590822C211yesmaximal, characteristic, complemented
14#10590752C211yesmaximal, characteristic, complemented
15#10590747C211yesmaximal, characteristic, complemented
16#80169—31nomaximal
17#79495—31nomaximal
18C22×#634C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C2×#3795C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic, complemented
22#64133C2211yescharacteristic
23C2×#3746C2211yescharacteristic, complemented
24C2×#3746C2211yescharacteristic, complemented
25C3×C4×#67C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29C2×C3×#204C2211yescharacteristic
30C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
31#63982—21no—
32#63976—21no—
33#67⋊Dic3—21no—
34D3×#217—21no—
35#63908C2211yescharacteristic
36#63896—21no—
37Dic3×D12C2211yescharacteristic
38#63885—21no—
39#63884—21no—
40#63866C2211yescharacteristic, complemented
41#63860C2211yescharacteristic
42#63857C2211yescharacteristic, complemented
43#63844C2211yescharacteristic, complemented
44#63840—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3716—24no—
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3716C2211yescharacteristic
51#63800—24no—
52C32×C22⋊C8C2211yescharacteristic
53#63643C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic
56C3×#821C2211yescharacteristic
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60#63575C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63566C2211yescharacteristic, complemented
63#5806—31no—
64C22×#214—31no—
65C2×#915—31no—
66C2×#909—31no—
67C22×#204—31no—
68#5632—31no—
69#5550—31no—
70D4×Dic6—31no—
71C3×#450—31no—
72C3×#435—31no—
73#5170—31no—
74#5167—31no—
75#5162—31no—
76#5134—31no—
77#5116—31no—
78#5051—31no—
79#4845—31no—
80#4841—31no—
81#4783—31no—
82#4780—31no—
83#4767—31no—
84#4757—31no—
85#4739—31no—
86#4739—31no—
87#4739—61no—
88#4738—31no—
89#4733—31no—
90#4731D311yescharacteristic, complemented
91#4730D311yescharacteristic, complemented
92#4715—31no—
93#4710—31no—
94C23×C3×D3—21no—
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3—21no—
97C2×#634—22no—
98C2×#634—21no—
99C2×#634—41no—
100C2×#634C2311yescharacteristic
101C2×#634C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67D411yescharacteristic
104C2×C3×D12—22no—
105C2×C3×D12—21no—
106C2×C3×D12—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×#627—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117#3795—22no—
118#3795—41no—
119D3×Dic6—22no—
120D3×Dic6—41no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123#3757—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125#3750—21no—
126#3746—22no—
127#3746—41no—
128C3×#217—21no—
129C3×#217D411yescharacteristic
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8—22no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×#204—22no—
139C3×#204—41no—
140C3×ΓL(1,𝔽25)—22no—
141#3724—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145(C2×D3)⋊Dic3—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#3716—22no—
153#3716—22no—
154#3716—22no—
155#3716D414yescomplemented
156#3266—91noSylow
157C22×C3×D4—31no—
158C2×D3×Q8—31no—
159C2×#237—31no—
160C2×#235—31no—
161C22×D12C2×D311yescharacteristic
162C22×Dic6—31no—
163C22×Dic6—31no—
164C22×Dic6—31no—
165C22×Dic6—61no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×M16—31no—
169C22×C3×C8—31no—
170C3×C22⋊Q8—31no—
171C3×C4×D4—31no—
172#953—61no—
173C2×#217—61no—
174#944—31no—
175C2×#216—31no—
176#939—61no—
177#938—31no—
178#937—61no—
179#936—31no—
180#935—61no—
181D4×Dic3—31no—
182D4×Dic3—61no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—31no—
186C2×#214—31no—
187C2×#214—64no—
188#930—31no—
189C4×#67C2×D311yescharacteristic
190#924—31no—
191#924—31no—
192#924—31no—
193#924—61no—
194#924C2×D311yescharacteristic
195C22×C3⋊C8C2×D311yescharacteristic
196#915—64no—
197#909—64no—
198C2×Dic12—31no—
199C2×Dic12—31no—
200C2×Dic12—31no—
201C2×Dic12—31no—
202C2×Dic12—31no—
203C2×Dic12—61no—
204C2×Dic12—61no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×#204—64no—
210C2×#204C2×D311yescharacteristic
211C2×#204C2×D311yescharacteristic
212C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
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×#102—31no—
231C3×#102—31no—
232C3×C22⋊C8—21no—
233C3×C22⋊C8—31no—
234C3×C22⋊C8C2×D311yescharacteristic
235C3×C22⋊C8C2×D311yescharacteristic
236C3×#97—31no—
237#835—31no—
238#821C2×D311yescharacteristic
239#821C2×D311yescharacteristic
240(C2×D3)⋊C8C2×D311yescharacteristic, complemented
241#818—31no—
242#816—31no—
243#816—31no—
244#816—31no—
245#816—31no—
246#816—31no—
247#816—31no—
248#816—61no—
249#816—61no—
250#815C2×D311yescharacteristic, complemented
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#810—31no—
253#807—31no—
254C23×C32C2×D411yescharacteristic
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3—81no—
260C22×C3×D3C2×D411yescharacteristic
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—42no—
270#634—21no—
271#634—21no—
272#634—21no—
273#634—21no—
274#634—21no—
275#634—42no—
276#634C2×D412yes—
277C3×#67—22no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292#627—42no—
293#625—42no—
294#625—81no—
295D3×Dic3—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—91no—
312#451—91no—
313#450—31no—
314#448—91no—
315#440—91no—
316#435—31no—
317C24×C3—61no—
318C23×D3—21no—
319C2×C3×Q8—31no—
320C2×C3×D4—31no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—62no—
324C2×C3×D4—61no—
325C2×C3×D4—121no—
326C22×C3×C4—21no—
327C22×C3×C4—31no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67D1211yescharacteristic
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—121no—
341D3×Q8—62no—
342D3×Q8—121no—
343#237—62no—
344#237—121no—
345#235—62no—
346#235—121no—
347C2×D12—22no—
348C2×D12—21no—
349C2×D12—41no—
350C2×D12C22×D311yescharacteristic
351C2×D12C22×D311yescharacteristic
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3—61no—
355C2×C4×D3C22×D311yescharacteristic
356C2×Dic6—31no—
357C2×Dic6—31no—
358C2×Dic6—31no—
359C2×Dic6—31no—
360C2×Dic6—31no—
361C2×Dic6—31no—
362C2×Dic6—61no—
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
379C3×SD16—62no—
380C3×SD16—121no—
381C3×M16—62no—
382C2×C3×C8—21no—
383C2×C3×C8—21no—
384C2×C3×C8—31no—
385C2×C3×C8—31no—
386C2×C3×C8—62no—
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C2×C3×C8C22×D311yescharacteristic
390C2×C3×C8C22×D311yescharacteristic
391C3×C4⋊C4—31no—
392C3×C4⋊C4—31no—
393C3×C4⋊C4—61no—
394C3×C22⋊C4—31no—
395C3×C22⋊C4—31no—
396C3×C22⋊C4—61no—
397C3×C42—31no—
398#217—21no—
399#217—61no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—121no—
407#217D1211yescharacteristic
408#216—62no—
409#214—34no—
410#214—62no—
411#214—62no—
412#214—62no—
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)⋊C4D1211yescharacteristic
419C4⋊Dic3—31no—
420C4⋊Dic3—31no—
421C4⋊Dic3—61no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3C22×D311yescharacteristic
426Dic3⋊C4—21no—
427Dic3⋊C4—61no—
428Dic3⋊C4—61no—
429Dic3⋊C4—61no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—121no—
435Dic3⋊C4D1211yescharacteristic
436C4×Dic3—61no—
437C4×Dic3—61no—
438C4×Dic3C22×D311yescharacteristic
439C2×C3⋊C8—22no—
440C2×C3⋊C8C22×D311yescharacteristic
441C2×C3⋊C8C22×D311yescharacteristic
442Dic12—62no—
443Dic12—62no—
444Dic12—62no—
445Dic12—122no—
446Dic12—121no—
447Dic12—121no—
448Dic12—122no—
449#204—22no—
450#204—34no—
451#204—41no—
452#204—62no—
453#204—62no—
454#204—62no—
455ΓL(1,𝔽25)—22no—
456C22×C32—21no—
457C22×C32—21no—
458C22×C32#13712yescomplemented
459C22×C32C22×D411yescharacteristic
460C2×C3×D3—21no—
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3—41no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—84no—
470C32×C4—21no—
471C32×C4C22×D411yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—22no—
474C3⋊Dic3—41no—
475C3⋊Dic3—41no—
476C3⋊Dic3—41no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—91no—
483C22×Q8—91no—
484C22×Q8—91no—
485C22×D4—31no—
486#137—184no—
487C2×Q16—91no—
488C2×Q16—91no—
489C2×Q16—91no—
490C2×SD16—31no—
491C2×SD16—31no—
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—91no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—31no—
524C22⋊C8—31no—
525C22⋊C8D3211yescharacteristic
526#97—31no—
527C23×C3—21no—
528C23×C3—31no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—122no—
532C23×C3—122no—
533C23×C3—241no—
534C23×C3C2×D1211yescharacteristic
535C23×C3D3×D411yescharacteristic
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3—81no—
541C22×D3C2×D1211yescharacteristic
542C3×Q8—61no—
543C3×Q8—61no—
544C3×D4—32no—
545C3×D4—62no—
546C3×D4—61no—
547C3×D4—61no—
548C3×D4—61no—
549C3×D4—122no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—31no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4C2×D1211yescharacteristic
566C2×C3×C4D3×D411yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568C2×C3×C4C23×D311yescharacteristic
569#67—22no—
570#67—122no—
571#67—122no—
572#67—241no—
573#67—241no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—121no—
585C2×Dic3—121no—
586C2×Dic3—121no—
587C2×Dic3—121no—
588C2×Dic3—122no—
589C2×Dic3—122no—
590C2×Dic3—122no—
591C2×Dic3—122no—
592C2×Dic3—124no—
593C2×Dic3—241no—
594C2×Dic3C2×D1211yescharacteristic
595C2×Dic3C2×D1211yescharacteristic
596C2×Dic3C2×D1211yescharacteristic
597D12—21no—
598D12—21no—
599D12—21no—
600D12—42no—
601D12D3×D412yes—
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—122no—
605C4×D3—122no—
606C4×D3—241no—
607Dic6—21no—
608Dic6—21no—
609Dic6—32no—
610Dic6—32no—
611Dic6—62no—
612Dic6—61no—
613Dic6—61no—
614Dic6—62no—
615Dic6—61no—
616Dic6—61no—
617Dic6—61no—
618Dic6—61no—
619Dic6—61no—
620Dic6—61no—
621Dic6—61no—
622Dic6—61no—
623Dic6—121no—
624Dic6—121no—
625Dic6—121no—
626Dic6—121no—
627Dic6—122no—
628Dic6—122no—
629Dic6—122no—
630Dic6—122no—
631Dic6—124no—
632C3×C8—21no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—32no—
637C3×C8—41no—
638C3×C8—41no—
639C3×C8—61no—
640C3⋊C8—21no—
641C3⋊C8D3×D412yes—
642C2×C32—22no—
643C2×C32D4211yescharacteristic
644C2×C32C2×#13711yescharacteristic
645C2×C32#57711yescharacteristic
646C3×D3—41no—
647C3×D3—42no—
648C3×D3—81no—
649C24—61no—
650#41—182no—
651#41—361no—
652C2×Q8—31no—
653C2×Q8—91no—
654C2×Q8—91no—
655C2×Q8—91no—
656C2×Q8—182no—
657C2×Q8—181no—
658C2×Q8—182no—
659C2×Q8—181no—
660C2×Q8—361no—
661C2×Q8—361no—
662C2×D4—31no—
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—62no—
666C2×D4—61no—
667C2×D4—121no—
668C2×D4—181no—
669C2×D4—181no—
670C22×C4—31no—
671C22×C4—181no—
672C22×C4—181no—
673C22×C4—181no—
674C22×C4—181no—
675C22×C4C2×D3211yescharacteristic
676Q16—182no—
677Q16—182no—
678Q16—361no—
679SD16—62no—
680SD16—94no—
681SD16—121no—
682SD16—182no—
683SD16—182no—
684SD16—182no—
685M16—62no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—62no—
689C2×C8C2×D3211yescharacteristic
690C2×C8C2×D3211yescharacteristic
691C4⋊C4—31no—
692C4⋊C4—31no—
693C4⋊C4—61no—
694C4⋊C4—91no—
695C4⋊C4—181no—
696C4⋊C4—181no—
697C4⋊C4—181no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C22⋊C4—31no—
701C22⋊C4—31no—
702C22⋊C4—61no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—181no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—22no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—62no—
722C22×C3—61no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—244no—
729C22×C3#90912yescomplemented
730C22×C3#91512yescomplemented
731C22×C3C22×D1211yescharacteristic
732C22×C3C2×D3×D411yescharacteristic
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—22no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—84no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—41no—
748C3×C4—61no—
749C3×C4—61no—
750C3×C4—61no—
751C3×C4—121no—
752C3×C4—121no—
753C3×C4C2×D3×D411yescharacteristic
754C3×C4C2×D3×D411yescharacteristic
755C3×C4#100411yescharacteristic
756C3×C4#100911yescharacteristic
757Dic3—21no—
758Dic3—21no—
759Dic3—21no—
760Dic3—41no—
761Dic3—41no—
762Dic3—62no—
763Dic3—62no—
764Dic3—122no—
765Dic3—122no—
766Dic3—121no—
767Dic3—121no—
768Dic3—121no—
769Dic3—121no—
770Dic3—121no—
771Dic3—121no—
772Dic3—241no—
773Dic3—241no—
774C32#326611yescharacteristic, complemented, Sylow
775C23—31no—
776C23—61no—
777C23—61no—
778C23—122no—
779C23—122no—
780C23—241no—
781C23D3×D1211yescharacteristic
782Q8—61no—
783Q8—61no—
784Q8—92no—
785Q8—181no—
786Q8—181no—
787Q8—181no—
788Q8—181no—
789Q8—181no—
790Q8—362no—
791Q8—362no—
792D4—32no—
793D4—62no—
794D4—61no—
795D4—61no—
796D4—61no—
797D4—122no—
798D4—362no—
799D4—721no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—31no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—61no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4—181no—
813C2×C4—362no—
814C2×C4—362no—
815C2×C4—362no—
816C2×C4—721no—
817C2×C4D3×D1211yescharacteristic
818C2×C4C22×D3211yescharacteristic
819C8—21no—
820C8—21no—
821C8—32no—
822C8—61no—
823C2×C3—22no—
824C2×C3—22no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—42no—
829C2×C3—121no—
830C2×C3—122no—
831C2×C3—241no—
832C2×C3D4×D1211yescharacteristic
833C2×C3#559011yescharacteristic
834C2×C3C2×#90911yescharacteristic
835C2×C3#575111yescharacteristic
836C2×C3C2×#91511yescharacteristic
837C2×C3#577511yescharacteristic
838D3—42no—
839D3—41no—
840D3—81no—
841C22—21no—
842C22—21no—
843C22—61no—
844C22—61no—
845C22—61no—
846C22—62no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—121no—
851C22—121no—
852C22—244no—
853C22#6380012yescomplemented
854C22C2×D3×D1211yescharacteristic
855C4—21no—
856C4—61no—
857C4—61no—
858C4—61no—
859C4—121no—
860C4—121no—
861C4—182no—
862C4—361no—
863C4—361no—
864C4—361no—
865C4D32×D411yescharacteristic
866C4#6431411yescharacteristic
867C3—21no—
868C3#7949511yescharacteristic, complemented
869C3#8016911yescharacteristic, complemented
870C2—22no—
871C2—121no—
872C2—122no—
873C2—241no—
874C2#1059427711yescharacteristic
875C2C2×#6380011yescharacteristic
876C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594886C2
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
1. #10594915C2semidirect
3. C22×#3716C2semidirect
4. C2×#63800C2semidirect
5. #10592438C2semidirect
6. C3×#4731C2semidirect
7. C3×#4730C2semidirect
8. #10591187C2semidirect
9. #10590969C2semidirect
10. #10590897C2semidirect
11. #10590861C2semidirect
12. #10590828C2semidirect
13. #10590822C2semidirect
14. #10590752C2semidirect
15. #10590747C2semidirect
21. C2×D3×Dic6C22semidirect
23. C2×#3746C22semidirect
24. C2×#3746C22semidirect
30. C2×C3×ΓL(1,𝔽25)C22semidirect
40. #63866C22semidirect
42. #63857C22semidirect
43. #63844C22semidirect
45. C2×#3719C22semidirect
53. #63643C22semidirect
54. #63643C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63575C22semidirect
61. #63567C22semidirect
62. #63566C22semidirect
90. #4731D3semidirect
91. #4730D3semidirect
155. #3716D4semidirect
212. C2×ΓL(1,𝔽25)C2×D3semidirect
240. (C2×D3)⋊C8C2×D3semidirect
250. #815C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
458. C22×C32#137semidirect
729. C22×C3#909semidirect
730. C22×C3#915semidirect
774. C32#3266semidirect
853. C22#63800semidirect
868. C3#79495semidirect
869. C3#80169semidirect

Maximal subgroups

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

subgroupindex
#105949152
#105948862
C22×#37162
C2×#638002
#105924382
C3×#47312
C3×#47302
#105911872
#105909692
#105908972
#105908612
#105908282
#105908222
#105907522
#105907472
#801693
#794953