Finite Group Databasebeta

← #11884264

Subgroups — #11884264

Order 1152.

1076 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595078C211yesmaximal, characteristic, complemented
2#10594887C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic, complemented
4C2×#63795C211yesmaximal, characteristic, complemented
5#10592432C211yesmaximal, characteristic, complemented
6C3×#4734C211yesmaximal, characteristic, complemented
7C3×#4730C211yesmaximal, characteristic, complemented
8#10591175C211yesmaximal, characteristic, complemented
9#10590969C211yesmaximal, characteristic, complemented
10#10590942C211yesmaximal, characteristic, complemented
11#10590897C211yesmaximal, characteristic, complemented
12#10590849C211yesmaximal, characteristic, complemented
13#10590760C211yesmaximal, characteristic, complemented
14#10590755C211yesmaximal, characteristic, complemented
15#10590746C211yesmaximal, characteristic, complemented
16#80122—31nomaximal
17#79496—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22#64133C2211yescharacteristic, complemented
23C2×#3746C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic
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#63970—21no—
33#63969—21no—
34#63958—21no—
35#63921—21no—
36#63905—21no—
37#63894C2211yescharacteristic
38Dic3×D12C2211yescharacteristic, complemented
39D3×Dic3⋊C4—21no—
40#63866C2211yescharacteristic, complemented
41#63860C2211yescharacteristic
42#63857C2211yescharacteristic
43#63856C2211yescharacteristic
44#63853—21no—
45C2×#3719C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47#63829—24no—
48C2×#3716C2211yescharacteristic
49C2×#3716C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic
51#63795—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#63573C2211yescharacteristic, complemented
61#63567C2211yescharacteristic, complemented
62#63563C2211yescharacteristic
63#5824—31no—
64C2×#950—31no—
65C2×#911—31no—
66C2×#908—31no—
67C2×#904—31no—
68#5612—31no—
69#5551—31no—
70#5550—31no—
71C3×#449—31no—
72C3×#435—31no—
73#5169—31no—
74#5167—31no—
75#5153—31no—
76#5137—31no—
77#5114—31no—
78#5041—31no—
79#4844—31no—
80#4841—31no—
81#4818—31no—
82#4816—31no—
83#4785—31no—
84#4783—31no—
85#4734D311yescharacteristic, complemented
86#4733—31no—
87#4733—31no—
88#4733—31no—
89#4733—61no—
90#4731—31no—
91#4730D311yescharacteristic, complemented
92#4715—31no—
93#4711—31no—
94C22×D32—21no—
95C22×C32×C4C2311yescharacteristic
96C2×#638—21no—
97#3828—22no—
98#3828—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×#634C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C3×#235—22no—
107C3×#235—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#625—21no—
115C2×#624—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—41no—
120#3795—22no—
121#3795—41no—
122C2×C32×C8C2311yescharacteristic
123C2×C32×C8C2311yescharacteristic
124#3757—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3750—21no—
127#3746—41no—
128#3744—22no—
129C3×#217D411yescharacteristic
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8—22no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C3×D24—22no—
139C3×#204—41no—
140C3×ΓL(1,𝔽25)—22no—
141#3724—21no—
142Dic3⋊Dic3—21no—
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—
150(C2×D3)⋊Dic3—21no—
151#3719—22no—
152#3717—22no—
153#3716—22no—
154#3716—22no—
155#3714D414yescomplemented
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×#237—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—
173#946—31no—
174#944—31no—
175C2×#216—31no—
176C2×#215—31no—
177#939—61no—
178#938—61no—
179#938—61no—
180#937—61no—
181#937—61no—
182#936—31no—
183#935—61no—
184D4×Dic3—31no—
185C2×#214—31no—
186C2×#214—31no—
187C2×#213—31no—
188#930C2×D311yescharacteristic
189#929—61no—
190C4×#67C2×D311yescharacteristic
191#924—31no—
192#924—31no—
193#924—31no—
194#924—31no—
195#924—61no—
196C2×Dic3⋊C4—61no—
197C22×C3⋊C8C2×D311yescharacteristic, complemented
198#911—64no—
199#908—64no—
200C2×Dic12—31no—
201C2×Dic12—31no—
202C2×Dic12—31no—
203C2×Dic12—61no—
204#904—64no—
205C2×D24—31no—
206C2×D24C2×D311yescharacteristic
207C2×#204—31no—
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—
218D3×C4⋊C4—61no—
219#884—61no—
220#883—61no—
221#883—61no—
222#883—61no—
223D3×C22⋊C4—61no—
224D3×C22⋊C4—61no—
225#875—31no—
226C4×D12—31no—
227C4×D12—31no—
228#869—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—61no—
242#821C2×D311yescharacteristic, complemented
243(C2×D3)⋊C8C2×D311yescharacteristic
244#817—31no—
245#816—31no—
246#816—31no—
247#816—31no—
248#816—61no—
249#816C2×D311yescharacteristic, complemented
250#815C2×D311yescharacteristic, complemented
251Dic3⋊C8C2×D311yescharacteristic, complemented
252#810—31no—
253#808—31no—
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—42no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)C2×D412yes—
272C4×C3⋊D3—42no—
273#634—21no—
274#634—21no—
275#634—21no—
276#634—21no—
277C3×#67—41no—
278C3×#67—42no—
279C3×#67—81no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12C2×D412yes—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—42no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294#626—42no—
295#625—42no—
296#624—81no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8—21no—
300C32×C8—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
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—31no—
316#442—91no—
317#435—31no—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—62no—
321C3×#41—121no—
322C2×C3×Q8—31no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C22×C3×C4—21no—
329C22×C3×C4—31no—
330C22×C3×C4—61no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C2×#67—21no—
334C2×#67—21no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—121no—
341C2×#67D1211yescharacteristic
342C22×Dic3—61no—
343C22×Dic3—61no—
344#237—62no—
345#237—121no—
346D3×D4—62no—
347D3×D4—121no—
348#235—22no—
349#235—41no—
350#235—62no—
351#235—62no—
352#235—62no—
353#235—122no—
354#235—121no—
355#235—121no—
356#235—121no—
357#235—122no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—61no—
361C2×D12—62no—
362C2×D12—61no—
363C2×D12—121no—
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—121no—
374C2×C4×D3C22×D311yescharacteristic
375C2×Dic6—31no—
376C2×Dic6—31no—
377C2×Dic6—31no—
378C2×Dic6—31no—
379C2×Dic6—61no—
380C2×Dic6—61no—
381C2×Dic6C22×D311yescharacteristic
382C3×SD16—121no—
383C3×D8—62no—
384C3×M16—62no—
385C2×C3×C8—21no—
386C2×C3×C8—21no—
387C2×C3×C8—31no—
388C2×C3×C8—31no—
389C2×C3×C8—62no—
390C2×C3×C8C22×D311yescharacteristic
391C2×C3×C8C22×D311yescharacteristic
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394C3×C4⋊C4—31no—
395C3×C4⋊C4—31no—
396C3×C22⋊C4—31no—
397C3×C22⋊C4—31no—
398C3×C22⋊C4—61no—
399C3×C42—31no—
400#217—61no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—61no—
407#217—121no—
408#217D1211yescharacteristic
409#216—62no—
410#215—62no—
411#214—62no—
412#214—62no—
413#213—34no—
414(C2×D3)⋊C4—21no—
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—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4D1211yescharacteristic
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—121no—
438Dic3⋊C4D1211yescharacteristic
439C4×Dic3C22×D311yescharacteristic
440C2×C3⋊C8—22no—
441C2×C3⋊C8C22×D311yescharacteristic
442C2×C3⋊C8C22×D311yescharacteristic
443Dic12—62no—
444Dic12—121no—
445Dic12—121no—
446Dic12—122no—
447D24—22no—
448D24—34no—
449#204—41no—
450#204—62no—
451#204—62no—
452#204—62no—
453#204—62no—
454#204—62no—
455#204—122no—
456ΓL(1,𝔽25)—22no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32C22×D411yescharacteristic
461C2×C3⋊D3—22no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473D32—84no—
474C32×C4—21no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3⋊Dic3—41no—
478C3⋊Dic3—41no—
479C3⋊Dic3—41no—
480C3×Dic3—21no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—91no—
487C2×#41—91no—
488C22×D4—91no—
489AGL(1,ℤ/8)—184no—
490#135—184no—
491C2×Q16—91no—
492C2×Q16—91no—
493C2×SD16—31no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—31no—
499C2×D8—91no—
500C2×M16—31no—
501C22×C8—31no—
502C4⋊Q8—91no—
503#124—91no—
504#123—181no—
505#123—181no—
506#123—181no—
507C22⋊Q8—91no—
508C22⋊Q8—91no—
509C22⋊Q8—91no—
510#121—31no—
511#121—181no—
512#121—181no—
513#120—181no—
514C4×D4—31no—
515C4×D4—91no—
516C4×D4—91no—
517C2×C4⋊C4—181no—
518C2×C22⋊C4—181no—
519#106—91no—
520C4⋊C8—31no—
521#103—31no—
522#103—91no—
523#103—91no—
524#102—31no—
525#102—91no—
526#102—91no—
527C22⋊C8—31no—
528C22⋊C8D3211yescharacteristic, complemented
529#97—31no—
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—61no—
533C23×C3—61no—
534C23×C3C2×D1211yescharacteristic
535C23×C3D3×D411yescharacteristic
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3C2×D1211yescharacteristic
548C3×Q8—61no—
549C3×Q8—61no—
550C3×D4—32no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—61no—
554C3×D4—121no—
555C3×D4—122no—
556C3×D4—241no—
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×C4C2×D1211yescharacteristic
574C2×C3×C4D3×D411yescharacteristic
575C2×C3×C4C23×D311yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577#67—41no—
578#67—42no—
579#67—81no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—122no—
584#67—122no—
585#67—124no—
586C2×Dic3—21no—
587C2×Dic3—21no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—121no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—122no—
598C2×Dic3—122no—
599C2×Dic3C2×D1211yescharacteristic
600C2×Dic3C2×D1211yescharacteristic
601C2×Dic3C2×D1211yescharacteristic
602D12—21no—
603D12—21no—
604D12—21no—
605D12—32no—
606D12—32no—
607D12—62no—
608D12—61no—
609D12—61no—
610D12—121no—
611D12—122no—
612D12D3×D412yes—
613C4×D3—21no—
614C4×D3—21no—
615C4×D3—42no—
616C4×D3—122no—
617C4×D3—122no—
618C4×D3—124no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3—241no—
622C4×D3—241no—
623Dic6—21no—
624Dic6—21no—
625Dic6—62no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—61no—
631Dic6—61no—
632Dic6—61no—
633Dic6—61no—
634Dic6—121no—
635Dic6—121no—
636Dic6—121no—
637C3×C8—21no—
638C3×C8—21no—
639C3×C8—21no—
640C3×C8—21no—
641C3×C8—32no—
642C3×C8—41no—
643C3×C8—41no—
644C3×C8—61no—
645C3⋊C8—21no—
646C3⋊C8D3×D412yes—
647C2×C32—41no—
648C2×C32D4211yescharacteristic
649C2×C32#57511yescharacteristic
650C2×C32#57711yescharacteristic
651C3⋊D3—42no—
652C3×D3—41no—
653C3×D3—42no—
654C3×D3—81no—
655C24—181no—
656#41—62no—
657#41—121no—
658#41—182no—
659#41—182no—
660#41—361no—
661#41—361no—
662C2×Q8—31no—
663C2×Q8—91no—
664C2×Q8—91no—
665C2×D4—31no—
666C2×D4—31no—
667C2×D4—31no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—91no—
671C2×D4—181no—
672C2×D4—182no—
673C2×D4—181no—
674C2×D4—181no—
675C2×D4—361no—
676C22×C4—31no—
677C22×C4—61no—
678C22×C4—181no—
679C22×C4—181no—
680C22×C4—181no—
681C22×C4—181no—
682C22×C4C2×D3211yescharacteristic
683Q16—182no—
684Q16—361no—
685SD16—121no—
686SD16—182no—
687SD16—182no—
688SD16—182no—
689SD16—182no—
690D8—62no—
691D8—94no—
692M16—62no—
693C2×C8—31no—
694C2×C8—31no—
695C2×C8—62no—
696C2×C8C2×D3211yescharacteristic
697C2×C8C2×D3211yescharacteristic
698C4⋊C4—31no—
699C4⋊C4—31no—
700C4⋊C4—91no—
701C4⋊C4—181no—
702C4⋊C4—181no—
703C4⋊C4—181no—
704C4⋊C4—181no—
705C4⋊C4—181no—
706C22⋊C4—31no—
707C22⋊C4—31no—
708C22⋊C4—61no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C42—31no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—62no—
730C22×C3—61no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3C22×D1211yescharacteristic
737C22×C3C2×D3×D411yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—22no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—122no—
750C2×D3—121no—
751C2×D3—121no—
752C2×D3—121no—
753C2×D3—121no—
754C2×D3—241no—
755C2×D3—241no—
756C2×D3—244no—
757C2×D3—244no—
758C3×C4—21no—
759C3×C4—21no—
760C3×C4—21no—
761C3×C4—21no—
762C3×C4—41no—
763C3×C4—61no—
764C3×C4—61no—
765C3×C4—61no—
766C3×C4—121no—
767C3×C4—121no—
768C3×C4C2×D3×D411yescharacteristic
769C3×C4C2×D3×D411yescharacteristic
770C3×C4#100411yescharacteristic
771C3×C4#100911yescharacteristic
772Dic3—21no—
773Dic3—21no—
774Dic3—21no—
775Dic3—41no—
776Dic3—41no—
777Dic3—122no—
778Dic3—121no—
779Dic3—121no—
780Dic3—121no—
781Dic3—121no—
782Dic3—121no—
783Dic3—121no—
784Dic3—241no—
785Dic3—241no—
786C32#326711yescharacteristic, complemented, Sylow
787C23—31no—
788C23—61no—
789C23—61no—
790C23—181no—
791C23—362no—
792C23—362no—
793C23—721no—
794C23D3×D1211yescharacteristic
795Q8—61no—
796Q8—61no—
797Q8—181no—
798Q8—181no—
799Q8—181no—
800Q8—181no—
801D4—32no—
802D4—61no—
803D4—61no—
804D4—61no—
805D4—92no—
806D4—121no—
807D4—122no—
808D4—181no—
809D4—241no—
810D4—362no—
811D4—362no—
812D4—362no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—31no—
816C2×C4—31no—
817C2×C4—31no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—122no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—181no—
826C2×C4—362no—
827C2×C4—362no—
828C2×C4—362no—
829C2×C4—721no—
830C2×C4D3×D1211yescharacteristic
831C2×C4C22×D3211yescharacteristic
832C8—21no—
833C8—21no—
834C8—32no—
835C8—61no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—41no—
840C2×C3—41no—
841C2×C3—81no—
842C2×C3—122no—
843C2×C3—121no—
844C2×C3—241no—
845C2×C3D4×D1211yescharacteristic
846C2×C3#559011yescharacteristic
847C2×C3#574811yescharacteristic
848C2×C3#575111yescharacteristic
849C2×C3#576811yescharacteristic
850C2×C3#577511yescharacteristic
851D3—41no—
852D3—42no—
853D3—81no—
854D3—122no—
855D3—122no—
856D3—242no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—61no—
861C22—61no—
862C22—61no—
863C22—62no—
864C22—121no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—121no—
869C22—182no—
870C22—361no—
871C22—361no—
872C22—724no—
873C22C2×D3×D1211yescharacteristic
874C4—21no—
875C4—61no—
876C4—61no—
877C4—61no—
878C4—121no—
879C4—121no—
880C4—361no—
881C4—361no—
882C4—361no—
883C4D32×D411yescharacteristic
884C4#6431411yescharacteristic
885C3—21no—
886C3#7949611yescharacteristic, complemented
887C3#8012211yescharacteristic, complemented
888C2—41no—
889C2—121no—
890C2—122no—
891C2—241no—
892C2—362no—
893C2#1059427711yescharacteristic
894C2#1059467611yescharacteristic
895C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊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. #10595078C2semidirect
2. #10594887C2semidirect
3. C2×#63829C2semidirect
4. C2×#63795C2semidirect
5. #10592432C2semidirect
6. C3×#4734C2semidirect
7. C3×#4730C2semidirect
8. #10591175C2semidirect
9. #10590969C2semidirect
10. #10590942C2semidirect
11. #10590897C2semidirect
12. #10590849C2semidirect
13. #10590760C2semidirect
14. #10590755C2semidirect
15. #10590746C2semidirect
19. C2×C3×#235C22semidirect
22. #64133C22semidirect
23. C2×#3746C22semidirect
27. C22×C3×C3⋊C8C22semidirect
38. Dic3×D12C22semidirect
40. #63866C22semidirect
45. C2×#3719C22semidirect
49. C2×#3716C22semidirect
52. C32×C22⋊C8C22semidirect
54. #63643C22semidirect
55. C3×#821C22semidirect
57. C3×#816C22semidirect
58. C3×#815C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. #63573C22semidirect
61. #63567C22semidirect
85. #4734D3semidirect
91. #4730D3semidirect
155. #3714D4semidirect
164. C2×#235C2×D3semidirect
197. C22×C3⋊C8C2×D3semidirect
234. C3×C22⋊C8C2×D3semidirect
235. C3×C22⋊C8C2×D3semidirect
242. #821C2×D3semidirect
249. #816C2×D3semidirect
250. #815C2×D3semidirect
251. Dic3⋊C8C2×D3semidirect
528. C22⋊C8D32semidirect
786. C32#3267semidirect
886. C3#79496semidirect
887. C3#80122semidirect

Maximal subgroups

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

subgroupindex
#105950782
#105948872
C2×#638292
C2×#637952
#105924322
C3×#47342
C3×#47302
#105911752
#105909692
#105909422
#105908972
#105908492
#105907602
#105907552
#105907462
#801223
#794963