Finite Group Databasebeta

← #11884414

Subgroups — #11884414

Order 1152.

1087 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5612C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic, complemented
3#10595007C211yesmaximal, characteristic, complemented
4C2×#63822C211yesmaximal, characteristic, complemented
5#10592737C211yesmaximal, characteristic, complemented
6C3×#5037C211yesmaximal, characteristic, complemented
7#10591483C211yesmaximal, characteristic, complemented
8#10591447C211yesmaximal, characteristic, complemented
9#10591442C211yesmaximal, characteristic, complemented
10#10591163C211yesmaximal, characteristic, complemented
11#10591158C211yesmaximal, characteristic, complemented
12#10590616C211yesmaximal, characteristic, complemented
13#10590547C211yesmaximal, characteristic, complemented
14#10590503C211yesmaximal, characteristic, complemented
15#10590478C211yesmaximal, characteristic, complemented
16#83507—31nomaximal
17#80123—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C2×#3799C2211yescharacteristic
22C32×#121C2211yescharacteristic
23C2×#3753C2211yescharacteristic
24#64139C2211yescharacteristic, complemented
25C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×#938—21no—
27C3×#937—21no—
28C3×#936C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C3×#897C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#883—21no—
35C3×D3×C22⋊C4—21no—
36#63979—21no—
37#63958—21no—
38#63934—24no—
39#63911C2211yescharacteristic, complemented
40#63908C2211yescharacteristic
41#63906—21no—
42#63904—21no—
43Dic3×Dic6C2211yescharacteristic, complemented
44C2×#3718C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49#63822—24no—
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63659C2211yescharacteristic
53#63636C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×#546—31no—
64#5834—31no—
65C2×#950—31no—
66C2×#950—31no—
67C2×#932—31no—
68C2×#914—31no—
69#5612D311yescharacteristic, complemented
70#5553—31no—
71C3×#449—31no—
72#5238—31no—
73#5217—31no—
74#5166—31no—
75#5156—31no—
76#5154—31no—
77#5058—31no—
78#5054—31no—
79#5049—31no—
80#5047—31no—
81#5038—31no—
82#5038—31no—
83#5038—61no—
84#5037D311yescharacteristic, complemented
85#5018—31no—
86#5015—31no—
87#5011—31no—
88#4817—31no—
89#4808—31no—
90#4786—31no—
91#4780—31no—
92#4734—31no—
93#4730—31no—
94C23×C3×D3—21no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C3×#235—22no—
107C3×#235—22no—
108C3×#235—41no—
109C3×#235—41no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×C3×Dic6C2311yescharacteristic
118C2×#626—21no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#625—21no—
122C2×#624—21no—
123#3799—22no—
124#3799—41no—
125C32×C4⋊C4C2311yescharacteristic
126C32×C22⋊C4—21no—
127#3753—22no—
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)—22no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#217—21no—
134C3×#217—21no—
135C3×#217D411yescharacteristic
136C3×#214—22no—
137C3×#213—41no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×C4⋊Dic3—21no—
142C3×Dic3⋊C4D411yescharacteristic
143C3×C4×Dic3C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146Dic3⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3718—22no—
150#3717—41no—
151#3715—22no—
152#3715D414yescomplemented
153#3714—22no—
154#3713—22no—
155#3711—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C22×C3×D4—31no—
160C2×#239—31no—
161C2×D3×D4C2×D311yescharacteristic
162C2×#235—31no—
163C2×#235C2×D311yescharacteristic
164C2×#235C2×D311yescharacteristic, complemented
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C3×#124—31no—
168C3×#123—61no—
169C3×C22⋊Q8—31no—
170C3×#121—21no—
171C3×#121—61no—
172C3×#121C2×D311yescharacteristic
173C3×#121C2×D311yescharacteristic
174C3×#120—61no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C2×C3×C22⋊C4—61no—
178#950—64no—
179#950—64no—
180Q8×Dic3—31no—
181C2×#216—31no—
182C2×#216—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186#940—31no—
187#940—61no—
188#940—61no—
189#938—21no—
190#938—31no—
191#938—61no—
192#937—21no—
193#936C2×D311yescharacteristic
194C2×#214—31no—
195C2×#214—31no—
196C2×#214C2×D311yescharacteristic
197#932—64no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—61no—
204C2×#213C2×D311yescharacteristic
205#930—31no—
206#930—31no—
207#930—31no—
208#930—61no—
209#930—61no—
210C4×#67—61no—
211C4×#67C2×D311yescharacteristic
212C2×#208—31no—
213C22×C3⋊C8—31no—
214C22×C3⋊C8—31no—
215C22×C3⋊C8—61no—
216#914—64no—
217C2×D24—31no—
218C2×#204—31no—
219C2×ΓL(1,𝔽25)—31no—
220#897C2×D311yescharacteristic
221#893—61no—
222#893C2×D311yescharacteristic
223#884—61no—
224#884—61no—
225#883—21no—
226D3×C22⋊C4—21no—
227#874—31no—
228C4×Dic6—31no—
229C3×#103—31no—
230C3×#102—31no—
231C3×C22⋊C8—31no—
232#835—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—61no—
237#830—31no—
238#830C2×D311yescharacteristic, complemented
239#821—31no—
240(C2×D3)⋊C8—31no—
241#816—31no—
242#815—31no—
243Dic3⋊C8—31no—
244#810C2×D311yescharacteristic, complemented
245#809—31no—
246#809—31no—
247#809—61no—
248#809C2×D311yescharacteristic, complemented
249#807—31no—
250#807—31no—
251#807—61no—
252C4⋊(C3⋊C8)—31no—
253#803—31no—
254C23×C32—21no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—81no—
262C22×C3×D3C2×D411yescharacteristic
263C32×D4—21no—
264C32×D4—21no—
265C32×D4—81no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271#638—81no—
272C2×C3⋊Dic3—21no—
273C4⋊(C3⋊D3)—21no—
274C4⋊(C3⋊D3)—21no—
275C3×#67—41no—
276C3×#67—42no—
277C3×#67—42no—
278C3×#67—42no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12C2×D412yes—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—42no—
291C3×C4×D3—42no—
292C3×C4×D3—81no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6C2×D412yes—
297#626—42no—
298#626—42no—
299#626—81no—
300#625—81no—
301#624—42no—
302C3⋊(C3⋊C8)—21no—
303C3⋊(C3⋊C8)C2×D412yes—
304C3×C3⋊C8—21no—
305C3×C3⋊C8—21no—
306C2×AGL(1,ℤ/8)—91no—
307C2×#135—91no—
308#550—91no—
309#546—31no—
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—91no—
321C24×C3—61no—
322C23×D3—21no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—121no—
326C3×#41—121no—
327C2×C3×Q8—31no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—21no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—41no—
336C2×C3×D4—61no—
337C2×C3×D4—62no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—121no—
341C2×C3×D4C22×D311yescharacteristic
342C2×C3×D4C22×D311yescharacteristic
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—61no—
346C22×C3×C4—61no—
347C22×C3×C4—61no—
348C22×C3×C4C22×D311yescharacteristic
349C22×C3×C4C22×D311yescharacteristic
350C2×#67—21no—
351C2×#67—21no—
352C2×#67—21no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—121no—
361C2×#67#6711yescharacteristic
362#239—62no—
363#239—121no—
364D3×D4—22no—
365D3×D4—41no—
366#235—22no—
367#235—22no—
368#235—41no—
369#235—41no—
370#235—62no—
371#235—121no—
372C2×D12—31no—
373C2×D12—31no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—21no—
382C2×C4×D3—21no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3C22×D311yescharacteristic
386C2×Dic6C22×D311yescharacteristic
387C2×Dic6C22×D311yescharacteristic
388C3×SD16—62no—
389C3×D8—121no—
390C2×C3×C8—31no—
391C2×C3×C8—31no—
392C3×C4⋊C4—21no—
393C3×C4⋊C4—31no—
394C3×C4⋊C4—61no—
395C3×C4⋊C4C22×D311yescharacteristic
396C3×C4⋊C4C22×D311yescharacteristic
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—31no—
400C3×C22⋊C4—31no—
401C3×C22⋊C4—41no—
402C3×C22⋊C4—61no—
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C42—31no—
407#217—21no—
408#217—21no—
409#217—61no—
410#217#6711yescharacteristic
411#216—62no—
412#216—62no—
413#215—34no—
414#215—62no—
415#215—121no—
416#214—22no—
417#214—34no—
418#214—62no—
419#213—41no—
420#213—62no—
421#213—62no—
422#213—62no—
423#213—62no—
424#213—62no—
425#213—122no—
426(C2×D3)⋊C4—21no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—121no—
432(C2×D3)⋊C4#6711yescharacteristic
433C4⋊Dic3—21no—
434C4⋊Dic3—31no—
435C4⋊Dic3—31no—
436C4⋊Dic3—61no—
437C4⋊Dic3—61no—
438Dic3⋊C4—61no—
439Dic3⋊C4#6711yescharacteristic
440C4×Dic3—61no—
441C4×Dic3—61no—
442C4×Dic3C22×D311yescharacteristic
443#208—62no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—31no—
446C2×C3⋊C8—31no—
447C2×C3⋊C8—31no—
448C2×C3⋊C8—61no—
449C2×C3⋊C8—61no—
450C2×C3⋊C8—62no—
451C2×C3⋊C8—62no—
452C2×C3⋊C8—122no—
453C2×C3⋊C8C22×D311yescharacteristic
454C2×C3⋊C8C22×D311yescharacteristic
455D24—62no—
456#204—121no—
457ΓL(1,𝔽25)—62no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32—41no—
462C22×C32—41no—
463C22×C32—41no—
464C22×C32C22×D411yescharacteristic
465C2×C3⋊D3—41no—
466C2×C3⋊D3—41no—
467C2×C3⋊D3—41no—
468C2×C3×D3—21no—
469C2×C3×D3—22no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—84no—
478C32×C4—21no—
479C32×C4—41no—
480C32×C4C22×D411yescharacteristic
481C32×C4H(5,𝔽2)11yescharacteristic
482C3⋊Dic3—41no—
483C3×Dic3—21no—
484C3×Dic3—22no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—41no—
488C2×#41—31no—
489C2×#41—31no—
490C2×#41—91no—
491C22×D4—31no—
492AGL(1,ℤ/8)—184no—
493#135—184no—
494C2×Q16—91no—
495C2×SD16—31no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×SD16—91no—
499C2×D8—31no—
500C2×D8—91no—
501C2×D8—91no—
502C2×D8—91no—
503C2×M16—91no—
504C22×C8—91no—
505#127—91no—
506#127—181no—
507#124—31no—
508#123—61no—
509C22⋊Q8—31no—
510#121—61no—
511#121—91no—
512#121—91no—
513#121—181no—
514#121—181no—
515#121D3211yescharacteristic
516#120—61no—
517C4×Q8—91no—
518C4×D4—31no—
519C4×D4—31no—
520C4×D4—181no—
521C2×C22⋊C4—61no—
522#107—91no—
523C4⋊C8—91no—
524#103—31no—
525#103—91no—
526#102—31no—
527#102—91no—
528#102—91no—
529#102—91no—
530C22⋊C8—31no—
531C22⋊C8—91no—
532#97—91no—
533C23×C3—21no—
534C23×C3—21no—
535C23×C3—21no—
536C23×C3—31no—
537C23×C3—41no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—122no—
541C23×C3—122no—
542C23×C3—241no—
543C23×C3D3×D411yescharacteristic
544C23×C3C2×#6711yescharacteristic
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—42no—
548C22×D3—42no—
549C22×D3—61no—
550C22×D3—61no—
551C22×D3—81no—
552C22×D3—121no—
553C22×D3C2×#6711yescharacteristic
554C3×Q8—32no—
555C3×Q8—61no—
556C3×Q8—61no—
557C3×Q8—61no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—21no—
561C3×D4—21no—
562C3×D4—32no—
563C3×D4—41no—
564C3×D4—41no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—81no—
569C3×D4—81no—
570C3×D4—82no—
571C3×D4—121no—
572C3×D4—122no—
573C3×D4—122no—
574C3×D4—122no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—31no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—41no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—122no—
594C2×C3×C4—122no—
595C2×C3×C4—241no—
596C2×C3×C4D3×D411yescharacteristic
597C2×C3×C4C2×#6711yescharacteristic
598C2×C3×C4C23×D311yescharacteristic
599C2×C3×C4C23×D311yescharacteristic
600#67—41no—
601#67—42no—
602#67—42no—
603#67—42no—
604#67—122no—
605#67—122no—
606#67—241no—
607#67—241no—
608#67—241no—
609#67—241no—
610#67—241no—
611#67—242no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—121no—
617C2×Dic3C2×#6711yescharacteristic
618C2×Dic3C2×#6711yescharacteristic
619C2×Dic3C2×#6711yescharacteristic
620D12—21no—
621D12—21no—
622D12—21no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—121no—
628D12—121no—
629D12—122no—
630D12—122no—
631D12—241no—
632D12D3×D412yes—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—42no—
636C4×D3—42no—
637C4×D3—81no—
638C4×D3—122no—
639C4×D3—122no—
640Dic6—21no—
641Dic6—21no—
642Dic6—21no—
643Dic6D3×D412yes—
644C3×C8—61no—
645C3×C8—61no—
646C3⋊C8—21no—
647C3⋊C8—21no—
648C3⋊C8—32no—
649C3⋊C8—32no—
650C3⋊C8—62no—
651C3⋊C8—61no—
652C3⋊C8—61no—
653C3⋊C8—121no—
654C2×C32—41no—
655C2×C32—81no—
656C2×C32D4211yescharacteristic
657C2×C32#57511yescharacteristic
658C2×C32#57611yescharacteristic
659C3⋊D3—81no—
660C3×D3—41no—
661C3×D3—42no—
662C3×D3—81no—
663C24—61no—
664#41—62no—
665#41—62no—
666#41—121no—
667#41—121no—
668#41—182no—
669#41—361no—
670C2×Q8—31no—
671C2×Q8—31no—
672C2×D4—21no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—31no—
676C2×D4—61no—
677C2×D4—62no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—91no—
681C2×D4—121no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4C2×D3211yescharacteristic
688C22×C4—31no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—181no—
693C22×C4C2×D3211yescharacteristic
694Q16—182no—
695SD16—62no—
696SD16—94no—
697SD16—182no—
698SD16—361no—
699D8—121no—
700D8—182no—
701D8—182no—
702D8—182no—
703M16—182no—
704C2×C8—31no—
705C2×C8—31no—
706C2×C8—91no—
707C2×C8—91no—
708C2×C8—182no—
709C4⋊C4—31no—
710C4⋊C4—61no—
711C4⋊C4—91no—
712C4⋊C4—181no—
713C4⋊C4C2×D3211yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—31no—
716C22⋊C4—31no—
717C22⋊C4—61no—
718C22⋊C4—61no—
719C22⋊C4—61no—
720C22⋊C4—61no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C42—31no—
724C42—181no—
725C22×C3—22no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—62no—
745C22×C3—81no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—244no—
754C22×C3C2×D3×D411yescharacteristic
755C22×C3C22×#6711yescharacteristic
756C2×D3—21no—
757C2×D3—22no—
758C2×D3—21no—
759C2×D3—21no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—84no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—241no—
773C2×D3—241no—
774C2×D3—241no—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—41no—
780C3×C4—41no—
781C3×C4—41no—
782C3×C4—61no—
783C3×C4—61no—
784C3×C4—62no—
785C3×C4—61no—
786C3×C4—81no—
787C3×C4—121no—
788C3×C4C2×D3×D411yescharacteristic
789C3×C4C2×D3×D411yescharacteristic
790C3×C4#100411yescharacteristic
791C3×C4#100411yescharacteristic
792Dic3—21no—
793Dic3—21no—
794Dic3—21no—
795Dic3—22no—
796Dic3—41no—
797Dic3—121no—
798Dic3—121no—
799Dic3—241no—
800C32#326811yescharacteristic, complemented, Sylow
801C23—21no—
802C23—31no—
803C23—61no—
804C23—61no—
805C23—122no—
806C23—122no—
807C23—181no—
808C23—241no—
809C23D3×#6711yescharacteristic
810Q8—32no—
811Q8—61no—
812Q8—61no—
813Q8—61no—
814D4—21no—
815D4—21no—
816D4—32no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—81no—
821D4—121no—
822D4—122no—
823D4—122no—
824D4—122no—
825D4—181no—
826D4—181no—
827D4—362no—
828D4—362no—
829D4—721no—
830D4—721no—
831D4—721no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—31no—
836C2×C4—31no—
837C2×C4—31no—
838C2×C4—61no—
839C2×C4—61no—
840C2×C4—61no—
841C2×C4—61no—
842C2×C4—122no—
843C2×C4—122no—
844C2×C4—181no—
845C2×C4—241no—
846C2×C4—362no—
847C2×C4D3×#6711yescharacteristic
848C2×C4C22×D3211yescharacteristic
849C8—61no—
850C8—61no—
851C8—92no—
852C8—181no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—42no—
857C2×C3—41no—
858C2×C3—41no—
859C2×C3—81no—
860C2×C3—81no—
861C2×C3—121no—
862C2×C3—122no—
863C2×C3—161no—
864C2×C3—241no—
865C2×C3#559011yescharacteristic
866C2×C3#576811yescharacteristic
867C2×C3#577411yescharacteristic
868C2×C3D4×#6711yescharacteristic
869C2×C3#582211yescharacteristic
870C2×C3#583511yescharacteristic
871D3—41no—
872D3—42no—
873D3—81no—
874D3—241no—
875D3—241no—
876D3—481no—
877C22—21no—
878C22—21no—
879C22—21no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—61no—
884C22—61no—
885C22—61no—
886C22—62no—
887C22—121no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—244no—
893C22—361no—
894C22—361no—
895C22—361no—
896C22C2×D3×#6711yescharacteristic
897C4—21no—
898C4—41no—
899C4—61no—
900C4—61no—
901C4—61no—
902C4—62no—
903C4—121no—
904C4—361no—
905C4D32×D411yescharacteristic
906C4#6431311yescharacteristic
907C3—21no—
908C3#8012311yescharacteristic, complemented
909C3#8350711yescharacteristic, complemented
910C2—41no—
911C2—81no—
912C2—121no—
913C2—122no—
914C2—241no—
915C2—721no—
916C2#1059509711yescharacteristic
917C2#1059528711yescharacteristic
918C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3268
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5612C2semidirect
2. C2×#63934C2semidirect
3. #10595007C2semidirect
4. C2×#63822C2semidirect
5. #10592737C2semidirect
6. C3×#5037C2semidirect
7. #10591483C2semidirect
8. #10591447C2semidirect
9. #10591442C2semidirect
10. #10591163C2semidirect
11. #10591158C2semidirect
12. #10590616C2semidirect
13. #10590547C2semidirect
14. #10590503C2semidirect
15. #10590478C2semidirect
20. C2×C3×#235C22semidirect
24. #64139C22semidirect
25. C22×C3⋊(C3⋊C8)C22semidirect
39. #63911C22semidirect
43. Dic3×Dic6C22semidirect
44. C2×#3718C22semidirect
45. C2×#3717C22semidirect
47. C2×#3715C22semidirect
53. #63636C22semidirect
54. #63634C22semidirect
55. C3×#830C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
62. #63554C22semidirect
69. #5612D3semidirect
84. #5037D3semidirect
152. #3715D4semidirect
164. C2×#235C2×D3semidirect
238. #830C2×D3semidirect
244. #810C2×D3semidirect
248. #809C2×D3semidirect
800. C32#3268semidirect
908. C3#80123semidirect
909. C3#83507semidirect

Maximal subgroups

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

subgroupindex
C3×#56122
C2×#639342
#105950072
C2×#638222
#105927372
C3×#50372
#105914832
#105914472
#105914422
#105911632
#105911582
#105906162
#105905472
#105905032
#105904782
#835073
#801233