Finite Group Databasebeta

← #11884429

Subgroups — #11884429

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×#5599C211yesmaximal, characteristic, complemented
2C2×#63925C211yesmaximal, characteristic, complemented
3#10595067C211yesmaximal, characteristic, complemented
4C2×#63822C211yesmaximal, characteristic, complemented
5#10592737C211yesmaximal, characteristic, complemented
6C3×#5037C211yesmaximal, characteristic, complemented
7#10591472C211yesmaximal, characteristic, complemented
8#10591461C211yesmaximal, characteristic, complemented
9#10591428C211yesmaximal, characteristic, complemented
10#10591163C211yesmaximal, characteristic, complemented
11#10591158C211yesmaximal, characteristic, complemented
12#10590595C211yesmaximal, characteristic, complemented
13#10590536C211yesmaximal, characteristic, complemented
14#10590515C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#83577—31nomaximal
17#80128—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic, complemented
21C2×D3×D12C2211yescharacteristic
22C32×#121C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24#64139C2211yescharacteristic
25C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×#940—21no—
27C3×#940C2211yescharacteristic, complemented
28C3×#939—21no—
29C2×C3×#214C2211yescharacteristic, complemented
30C2×C3×#213C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C3×#895C2211yescharacteristic
33C3×#887C2211yescharacteristic, complemented
34C3×#884—21no—
35C3×#67⋊C4—21no—
36#63983—21no—
37#63971—21no—
38#63925—24no—
39D3×(C2×D3)⋊C4—21no—
40Dic3×D12C2211yescharacteristic
41#63864C2211yescharacteristic
42#63856C2211yescharacteristic
43#63850—21no—
44C2×#3718C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic
46C2×#3715C2211yescharacteristic
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49#63822—24no—
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52#63659C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54#63634C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62#63554C2211yescharacteristic, complemented
63C3×#550—31no—
64#5829—31no—
65C2×#950—31no—
66C2×#950—31no—
67C2×#949—31no—
68C2×#911—31no—
69#5599D311yescharacteristic, complemented
70#5550—31no—
71C3×#449—31no—
72#5239—31no—
73#5238—31no—
74#5176—31no—
75#5173—31no—
76#5150—31no—
77#5074—31no—
78#5072—31no—
79#5042—31no—
80#5038—31no—
81#5038—31no—
82#5038—61no—
83#5037D311yescharacteristic, complemented
84#5036—31no—
85#5028—31no—
86#5026—31no—
87#5011—31no—
88#4812—31no—
89#4798—31no—
90#4773—31no—
91#4757—31no—
92#4734—31no—
93#4730—31no—
94C22×D32—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×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67D411yescharacteristic
106C22×C3×Dic3—21no—
107C3×#237—22no—
108C3×#237—41no—
109C3×#235—22no—
110C3×#235—22no—
111C3×#235—41no—
112C3×#235—41no—
113C2×C3×D12—21no—
114C2×C3×D12C2311yescharacteristic
115C2×C3×D12C2311yescharacteristic
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C2×#626—21no—
122C2×D3×Dic3—21no—
123D3×D12—22no—
124D3×D12—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×#217D411yescharacteristic
134C3×#214—41no—
135C3×#213—22no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4D411yescharacteristic
140C3×C4×Dic3—21no—
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144#3724—21no—
145#3722—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3718—22no—
150#3717—22no—
151#3715—22no—
152#3715D414yescomplemented
153#3714—41no—
154#3713—22no—
155#3711—22no—
156#3268—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×C3×#41—31no—
160C2×#237C2×D311yescharacteristic
161C2×D3×D4—31no—
162C2×#235C2×D311yescharacteristic
163C2×#235C2×D311yescharacteristic, complemented
164C22×D12—31no—
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C3×#127—31no—
168C3×#127—61no—
169C3×#121—21no—
170C3×#121—31no—
171C3×#121—61no—
172C3×#121—61no—
173C3×#121C2×D311yescharacteristic, complemented
174C3×#121C2×D311yescharacteristic, complemented
175C3×C4×Q8—31no—
176C3×C4×D4—31no—
177C3×C4×D4—61no—
178#950—64no—
179#950—64no—
180#949—64no—
181#947—31no—
182#946—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188#940—21no—
189#940C2×D311yescharacteristic, complemented
190#939—21no—
191#939—61no—
192#937—61no—
193#937—61no—
194D4×Dic3—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214C2×D311yescharacteristic, complemented
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—61no—
208#929—61no—
209C4×#67C2×D311yescharacteristic
210C2×(C2×D3)⋊C4—61no—
211#924—31no—
212C2×#208—31no—
213C22×C3⋊C8—31no—
214C22×C3⋊C8—31no—
215C22×C3⋊C8—61no—
216#911—64no—
217C2×D24—31no—
218C2×#204—31no—
219C2×ΓL(1,𝔽25)—31no—
220#895C2×D311yescharacteristic
221#894—61no—
222#887C2×D311yescharacteristic, complemented
223#884—21no—
224#884—61no—
225#67⋊C4—21no—
226D3×C22⋊C4—61no—
227#875—31no—
228C4×D12—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
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×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—81no—
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—
279C3×#67—42no—
280C3×#67—81no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—42no—
284C2×C3×Dic3C2×D411yescharacteristic
285C2×C3×Dic3C2×D411yescharacteristic
286C2×C3×Dic3C2×D411yescharacteristic
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—81no—
291C3×D12C2×D412yes—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×C4×D3—42no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—21no—
299C3×Dic6C2×D412yes—
300#626—42no—
301D3×Dic3—81no—
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—31no—
309#546—91no—
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—
321C23×D3—61no—
322C23×D3—61no—
323C3×#41—62no—
324C3×#41—62no—
325C3×#41—62no—
326C3×#41—121no—
327C3×#41—121no—
328C3×#41—121no—
329C2×C3×Q8—31no—
330C2×C3×Q8—31no—
331C2×C3×D4—21no—
332C2×C3×D4—21no—
333C2×C3×D4—21no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—31no—
337C2×C3×D4—41no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—31no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C2×#67—21no—
354C2×#67—21no—
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—21no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—121no—
362C2×#67#6711yescharacteristic
363C22×Dic3—21no—
364C22×Dic3—61no—
365#237—22no—
366#237—41no—
367D3×D4—62no—
368D3×D4—121no—
369#235—22no—
370#235—22no—
371#235—41no—
372#235—41no—
373C2×D12—21no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—61no—
377C2×D12—62no—
378C2×D12—61no—
379C2×D12—121no—
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D311yescharacteristic
382C2×C4×D3—21no—
383C2×C4×D3—21no—
384C2×C4×D3—61no—
385C2×C4×D3C22×D311yescharacteristic
386C2×Dic6C22×D311yescharacteristic
387C2×Dic6C22×D311yescharacteristic
388C3×SD16—121no—
389C3×D8—62no—
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×C42—31no—
404C3×C42—61no—
405#217—61no—
406#217—61no—
407#217#6711yescharacteristic
408#216—62no—
409#216—62no—
410#215—34no—
411#215—62no—
412#215—62no—
413#214—34no—
414#214—41no—
415#214—62no—
416#213—22no—
417#213—62no—
418#213—62no—
419#213—62no—
420#213—62no—
421#213—122no—
422#213—121no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—121no—
433(C2×D3)⋊C4#6711yescharacteristic
434C4⋊Dic3—31no—
435C4⋊Dic3—31no—
436C4⋊Dic3—61no—
437Dic3⋊C4—21no—
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440Dic3⋊C4#6711yescharacteristic
441C4×Dic3—21no—
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—121no—
456#204—62no—
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—22no—
469C2×C3×D3—21no—
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—
477D32—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—31no—
491C22×D4—91no—
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—31no—
506#127—61no—
507#124—91no—
508#123—181no—
509C22⋊Q8—91no—
510#121—31no—
511#121—61no—
512#121—61no—
513#121—91no—
514#121—181no—
515#121D3211yescharacteristic, complemented
516#120—181no—
517C4×Q8—31no—
518C4×D4—31no—
519C4×D4—61no—
520C4×D4—91no—
521C2×C22⋊C4—181no—
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×C3D3×D411yescharacteristic
541C23×C3C2×#6711yescharacteristic
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—61no—
545C22×D3—61no—
546C22×D3—121no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—241no—
552C22×D3—241no—
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—
575C3×D4—122no—
576C3×D4—241no—
577C3×D4—241no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—31no—
587C2×C3×C4—31no—
588C2×C3×C4—31no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—122no—
597C2×C3×C4—122no—
598C2×C3×C4—122no—
599C2×C3×C4D3×D411yescharacteristic
600C2×C3×C4C2×#6711yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C23×D311yescharacteristic
603#67—41no—
604#67—42no—
605#67—42no—
606#67—42no—
607#67—42no—
608#67—81no—
609#67—122no—
610#67—241no—
611#67—241no—
612#67—242no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—42no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—121no—
619C2×Dic3—241no—
620C2×Dic3C2×#6711yescharacteristic
621C2×Dic3C2×#6711yescharacteristic
622C2×Dic3C2×#6711yescharacteristic
623D12—21no—
624D12—21no—
625D12—21no—
626D12—61no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—81no—
631D12—121no—
632D12—121no—
633D12—122no—
634D12D3×D412yes—
635C4×D3—21no—
636C4×D3—21no—
637C4×D3—42no—
638C4×D3—42no—
639C4×D3—241no—
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—181no—
664#41—62no—
665#41—62no—
666#41—62no—
667#41—121no—
668#41—121no—
669#41—121no—
670C2×Q8—31no—
671C2×Q8—31no—
672C2×D4—21no—
673C2×D4—31no—
674C2×D4—31no—
675C2×D4—31no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—61no—
680C2×D4—61no—
681C2×D4—61no—
682C2×D4—91no—
683C2×D4—181no—
684C2×D4—182no—
685C2×D4—181no—
686C2×D4—361no—
687C2×D4C2×D3211yescharacteristic
688C22×C4—31no—
689C22×C4—61no—
690C22×C4—61no—
691C22×C4—61no—
692C22×C4—181no—
693C22×C4C2×D3211yescharacteristic
694Q16—182no—
695SD16—94no—
696SD16—121no—
697SD16—182no—
698SD16—182no—
699D8—62no—
700D8—182no—
701D8—182no—
702D8—361no—
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—181no—
719C22⋊C4—181no—
720C22⋊C4—181no—
721C22⋊C4—181no—
722C22⋊C4—181no—
723C42—31no—
724C42—61no—
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—62no—
744C22×C3—61no—
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×C3C2×D3×D411yescharacteristic
754C22×C3C22×#6711yescharacteristic
755C2×D3—21no—
756C2×D3—21no—
757C2×D3—21no—
758C2×D3—22no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—241no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—244no—
774C2×D3—244no—
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—61no—
785C3×C4—62no—
786C3×C4—81no—
787C3×C4—121no—
788C3×C4C2×D3×D411yescharacteristic
789C3×C4C2×D3×D411yescharacteristic
790C3×C4#100411yescharacteristic
791C3×C4#100411yescharacteristic
792Dic3—22no—
793Dic3—21no—
794Dic3—21no—
795Dic3—21no—
796Dic3—41no—
797Dic3—121no—
798Dic3—121no—
799Dic3—241no—
800C32#326811yescharacteristic, complemented, Sylow
801C23—21no—
802C23—31no—
803C23—61no—
804C23—61no—
805C23—181no—
806C23—362no—
807C23—362no—
808C23—721no—
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—122no—
826D4—181no—
827D4—181no—
828D4—241no—
829D4—241no—
830D4—362no—
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—122no—
845C2×C4—181no—
846C2×C4—721no—
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—42no—
872D3—41no—
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—361no—
893C22—361no—
894C22—361no—
895C22—724no—
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#8012811yescharacteristic, complemented
909C3#8357711yescharacteristic, 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×#5599C2semidirect
2. C2×#63925C2semidirect
3. #10595067C2semidirect
4. C2×#63822C2semidirect
5. #10592737C2semidirect
6. C3×#5037C2semidirect
7. #10591472C2semidirect
8. #10591461C2semidirect
9. #10591428C2semidirect
10. #10591163C2semidirect
11. #10591158C2semidirect
12. #10590595C2semidirect
13. #10590536C2semidirect
14. #10590515C2semidirect
15. #10590454C2semidirect
20. C2×C3×#235C22semidirect
22. C32×#121C22semidirect
25. C22×C3⋊(C3⋊C8)C22semidirect
27. C3×#940C22semidirect
29. C2×C3×#214C22semidirect
33. C3×#887C22semidirect
44. C2×#3718C22semidirect
47. C2×#3715C22semidirect
52. #63659C22semidirect
54. #63634C22semidirect
55. C3×#830C22semidirect
56. C3×#810C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
62. #63554C22semidirect
69. #5599D3semidirect
83. #5037D3semidirect
152. #3715D4semidirect
163. C2×#235C2×D3semidirect
173. C3×#121C2×D3semidirect
174. C3×#121C2×D3semidirect
189. #940C2×D3semidirect
197. C2×#214C2×D3semidirect
222. #887C2×D3semidirect
238. #830C2×D3semidirect
244. #810C2×D3semidirect
515. #121D32semidirect
800. C32#3268semidirect
908. C3#80128semidirect
909. C3#83577semidirect

Maximal subgroups

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

subgroupindex
C3×#55992
C2×#639252
#105950672
C2×#638222
#105927372
C3×#50372
#105914722
#105914612
#105914282
#105911632
#105911582
#105905952
#105905362
#105905152
#105904542
#835773
#801283