Finite Group Databasebeta

← #11884255

Subgroups — #11884255

Order 1152.

1066 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5555C211yesmaximal, characteristic, complemented
2C2×#63935C211yesmaximal, characteristic, complemented
3C2×#63925C211yesmaximal, characteristic, complemented
4#10594007C211yesmaximal, characteristic, complemented
5#10592713C211yesmaximal, characteristic, complemented
6C3×#5016C211yesmaximal, characteristic, complemented
7#10591461C211yesmaximal, characteristic, complemented
8#10591450C211yesmaximal, characteristic, complemented
9#10590616C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic, complemented
11#10590520C211yesmaximal, characteristic, complemented
12#10590501C211yesmaximal, characteristic, complemented
13#10590379C211yesmaximal, characteristic, complemented
14#10590376C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#80567—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3799C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic, complemented
23C2×#3753C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic, complemented
26C2×C3×#213C2211yescharacteristic
27C3×#930—21no—
28C2×C3×C4⋊Dic3—21no—
29C3×#897C2211yescharacteristic
30C3×#897C2211yescharacteristic, complemented
31C3×#886—21no—
32C3×#886—21no—
33C3×#875C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×#869C2211yescharacteristic, complemented
36#63935—24no—
37#63925—24no—
38#63922—21no—
39#63921—21no—
40#63912—21no—
41#63908C2211yescharacteristic
42#63856C2211yescharacteristic
43#63854—21no—
44C2×#3718C2211yescharacteristic, complemented
45C2×#3718C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54#63635C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#547—31no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#916—31no—
67C2×#911—31no—
68#5676—31no—
69#5555D311yescharacteristic, complemented
70#5550—31no—
71C3×#463—31no—
72#5239—31no—
73#5238—31no—
74#5173—31no—
75#5158—31no—
76#5086—31no—
77#5083—31no—
78#5060—31no—
79#5052—31no—
80#5048—31no—
81#5047—31no—
82#5046—31no—
83#5016D311yescharacteristic, complemented
84#5014—31no—
85#5014—31no—
86#5014—61no—
87#5011—31no—
88#4841—31no—
89#4836—31no—
90#4816—31no—
91#4808—31no—
92#4778—31no—
93#4776—31no—
94C22×D32—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—22no—
105C3×#237—41no—
106C3×#237—41no—
107C2×C3×D12D411yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×#624—21no—
118D3×D12—22no—
119D3×D12—41no—
120#3799—22no—
121#3799—41no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124C32×C42C2311yescharacteristic
125#3753D414yescomplemented
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C2×C3⋊(C3⋊C8)C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×#214—22no—
131C3×#213—22no—
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×(C2×D3)⋊C4D411yescharacteristic
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3—21no—
142C3×C4⋊Dic3D411yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145#3724—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148#3718—22no—
149#3718—41no—
150#3717—22no—
151#3717—22no—
152#3715—22no—
153#3715—41no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239—31no—
160C2×#237C2×D311yescharacteristic
161C2×#237C2×D311yescharacteristic, complemented
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×SD16—31no—
166C2×C3×D8—31no—
167C3×C4⋊Q8—31no—
168C3×#124—31no—
169C3×#123—61no—
170C3×#123—61no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×#121—61no—
174C3×C4×D4—21no—
175C3×C4×D4—31no—
176C3×C4×D4C2×D311yescharacteristic, complemented
177C3×C4×D4C2×D311yescharacteristic, complemented
178C2×C3×C4⋊C4—61no—
179#950—64no—
180#949—64no—
181#946—31no—
182C2×#216—31no—
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190#938—31no—
191#937—61no—
192C2×#214—31no—
193C2×#214—31no—
194C2×#214C2×D311yescharacteristic, complemented
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—61no—
198C2×#213C2×D311yescharacteristic
199#930—21no—
200#930—31no—
201C2×C4⋊Dic3—21no—
202#924—31no—
203C2×#208—31no—
204C22×C3⋊C8—31no—
205#916—64no—
206#911—64no—
207C2×#204—31no—
208C2×#204—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×D3×C8—31no—
211#897C2×D311yescharacteristic
212#897C2×D311yescharacteristic, complemented
213#894—61no—
214#886—21no—
215#886—21no—
216#884—61no—
217#884—61no—
218#883—61no—
219#882—61no—
220D3×C22⋊C4—61no—
221D3×C22⋊C4—61no—
222#875C2×D311yescharacteristic
223C4×D12—31no—
224C4×D12—31no—
225C4×D12—61no—
226C4×D12C2×D311yescharacteristic
227#869C2×D311yescharacteristic, complemented
228C3×C4⋊C8—31no—
229C3×#103—31no—
230C3×#102—31no—
231#835—31no—
232#835—31no—
233#832—31no—
234#832—31no—
235#832—61no—
236#830—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240#816—31no—
241#816—31no—
242#810C2×D311yescharacteristic, complemented
243#809—31no—
244#809—31no—
245#809—61no—
246#809C2×D311yescharacteristic
247#808—31no—
248#808—31no—
249#808—61no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251#803—31no—
252#803—31no—
253#803—61no—
254C23×C32—21no—
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3C2×D411yescharacteristic
258C22×C3×D3C2×D411yescharacteristic
259C2×D32—42no—
260C2×D32—42no—
261C2×D32—81no—
262C32×D4—21no—
263C32×D4C2×D412yes—
264C2×C32×C4—21no—
265C2×C32×C4—42no—
266C2×C32×C4C2×D411yescharacteristic
267C2×C32×C4C2×D411yescharacteristic
268C2×C32×C4C2411yescharacteristic
269C2×C3⋊Dic3—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)C2×D412yes—
272C4×C3⋊D3—81no—
273C3×#67—42no—
274C3×#67—42no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—42no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—41no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×Dic6—21no—
290C3×Dic6—21no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295#626—42no—
296#626—42no—
297#625—81no—
298#624—42no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)C2×D412yes—
301C3×C3⋊C8—21no—
302C3×C3⋊C8—21no—
303C2×AGL(1,ℤ/8)—91no—
304C2×#135—91no—
305#547—31no—
306#546—91no—
307#497—91no—
308#470—91no—
309#465—91no—
310#463—31no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—91no—
317#435—91no—
318C23×D3—61no—
319C23×D3—61no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—121no—
323C3×#41—121no—
324C2×C3×Q8—31no—
325C2×C3×Q8—31no—
326C2×C3×Q8—31no—
327C2×C3×D4—21no—
328C2×C3×D4—31no—
329C2×C3×D4—31no—
330C2×C3×D4—61no—
331C2×C3×D4—61no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—41no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349#239—62no—
350#239—121no—
351#237—22no—
352#237—22no—
353#237—41no—
354#237—41no—
355D3×D4—62no—
356D3×D4—121no—
357#235—62no—
358#235—121no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—61no—
362C2×D12—62no—
363C2×D12—61no—
364C2×D12—61no—
365C2×D12—121no—
366C2×D12#6711yescharacteristic
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—121no—
373C2×C4×D3C22×D311yescharacteristic
374C2×C4×D3C22×D311yescharacteristic
375C2×Dic6C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×SD16—62no—
379C3×D8—62no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4—61no—
387C3×C4⋊C4—61no—
388C3×C4⋊C4C22×D311yescharacteristic
389C3×C4⋊C4C22×D311yescharacteristic
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—41no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C22⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C42—21no—
400C3×C42C22×D311yescharacteristic
401C3×C42C22×D311yescharacteristic
402#217—61no—
403#217—61no—
404#216—62no—
405#216—62no—
406#216—121no—
407#216—121no—
408#215—62no—
409#215—62no—
410#215—62no—
411#215—121no—
412#214—22no—
413#214—62no—
414#214—121no—
415#213—22no—
416#213—34no—
417#213—34no—
418#213—64no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—21no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—121no—
428(C2×D3)⋊C4#6711yescharacteristic
429(C2×D3)⋊C4#6711yescharacteristic
430C4⋊Dic3—21no—
431C4⋊Dic3—21no—
432C4⋊Dic3—21no—
433C4⋊Dic3—21no—
434C4⋊Dic3—31no—
435C4⋊Dic3—31no—
436C4⋊Dic3—61no—
437C4⋊Dic3#6711yescharacteristic
438Dic3⋊C4—61no—
439Dic3⋊C4—61no—
440#208—62no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—31no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—61no—
447C2×C3⋊C8—62no—
448C2×C3⋊C8C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450#204—62no—
451#204—62no—
452ΓL(1,𝔽25)—62no—
453D3×C8—62no—
454C22×C32—22no—
455C22×C32—41no—
456C22×C32—41no—
457C22×C32C22×D411yescharacteristic
458C2×C3⋊D3—22no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—41no—
468C2×C3×D3—41no—
469C2×C3×D3—41no—
470D32—84no—
471C32×C4—21no—
472C32×C4—21no—
473C32×C4—41no—
474C32×C4C22×D411yescharacteristic
475C32×C4H(5,𝔽2)11yescharacteristic
476C3⋊Dic3—41no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—41no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C2×#41—31no—
483C2×#41—31no—
484C2×#41—91no—
485C22×D4—91no—
486AGL(1,ℤ/8)—184no—
487#135—184no—
488C2×Q16—91no—
489C2×Q16—91no—
490C2×SD16—31no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×D8—31no—
496C2×D8—91no—
497C2×M16—91no—
498C22×C8—91no—
499C4⋊Q8—31no—
500#124—31no—
501#123—61no—
502#123—61no—
503#123—181no—
504C22⋊Q8—31no—
505C22⋊Q8—31no—
506C22⋊Q8—91no—
507#121—61no—
508#121—91no—
509#121—181no—
510#120—181no—
511C4×D4—31no—
512C4×D4—91no—
513C4×D4D3211yescharacteristic, complemented
514C2×C4⋊C4—61no—
515C2×C22⋊C4—181no—
516#106—91no—
517C4⋊C8—31no—
518#103—31no—
519#103—91no—
520#103—91no—
521#102—31no—
522#102—91no—
523#102—91no—
524C22⋊C8—91no—
525C22⋊C8—91no—
526#97—91no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—31no—
530C23×C3—31no—
531C23×C3—41no—
532C23×C3—61no—
533C22×D3—21no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—121no—
537C22×D3—122no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—241no—
542C22×D3—241no—
543C22×D3C2×#6711yescharacteristic
544C22×D3C2×#6711yescharacteristic
545C3×Q8—61no—
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×Q8—61no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—22no—
554C3×D4—41no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—121no—
558C3×D4—122no—
559C3×D4—122no—
560C3×D4D3×D412yes—
561C3×D4D3×D412yes—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—31no—
568C2×C3×C4—31no—
569C2×C3×C4—41no—
570C2×C3×C4—42no—
571C2×C3×C4—42no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—82no—
580C2×C3×C4—122no—
581C2×C3×C4—122no—
582C2×C3×C4D3×D411yescharacteristic
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4C2×#6711yescharacteristic
585C2×C3×C4C2×#6711yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588#67—42no—
589#67—42no—
590#67—122no—
591#67—122no—
592#67—241no—
593#67—241no—
594C2×Dic3—21no—
595C2×Dic3—21no—
596C2×Dic3—21no—
597C2×Dic3—42no—
598C2×Dic3—42no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—121no—
602C2×Dic3C2×#6711yescharacteristic
603C2×Dic3C2×#6711yescharacteristic
604D12—21no—
605D12—21no—
606D12—32no—
607D12—32no—
608D12—41no—
609D12—62no—
610D12—61no—
611D12—61no—
612D12—121no—
613D12—122no—
614D12—122no—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—21no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3—241no—
622C4×D3—241no—
623C4×D3—242no—
624Dic6—21no—
625Dic6—21no—
626Dic6—21no—
627Dic6—21no—
628Dic6—21no—
629Dic6—21no—
630C3×C8—61no—
631C3×C8—61no—
632C3⋊C8—21no—
633C3⋊C8—21no—
634C3⋊C8—32no—
635C3⋊C8—32no—
636C3⋊C8—62no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—121no—
640C2×C32—42no—
641C2×C32D4211yescharacteristic
642C2×C32#57511yescharacteristic
643C2×C32#57711yescharacteristic
644C3⋊D3—42no—
645C3×D3—41no—
646C3×D3—41no—
647C3×D3—81no—
648C24—181no—
649#41—62no—
650#41—62no—
651#41—121no—
652#41—121no—
653#41—182no—
654#41—361no—
655C2×Q8—31no—
656C2×Q8—31no—
657C2×Q8—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—91no—
663C2×D4—181no—
664C2×D4—182no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—361no—
668C2×D4C2×D3211yescharacteristic
669C22×C4—21no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—181no—
675C22×C4—181no—
676Q16—182no—
677Q16—361no—
678SD16—62no—
679SD16—182no—
680SD16—182no—
681SD16—182no—
682SD16—361no—
683D8—62no—
684D8—94no—
685M16—182no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8—91no—
689C2×C8—91no—
690C2×C8—182no—
691C4⋊C4—31no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4—61no—
695C4⋊C4—61no—
696C4⋊C4—91no—
697C4⋊C4—181no—
698C4⋊C4C2×D3211yescharacteristic
699C22⋊C4—21no—
700C22⋊C4—31no—
701C22⋊C4—31no—
702C22⋊C4—61no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42C2×D3211yescharacteristic
710C22×C3—22no—
711C22×C3—22no—
712C22×C3—21no—
713C22×C3—42no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—81no—
725C22×C3—81no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3—121no—
729C22×C3C2×D3×D411yescharacteristic
730C22×C3C22×#6711yescharacteristic
731C2×D3—21no—
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—62no—
741C2×D3—62no—
742C2×D3—122no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—241no—
748C2×D3—241no—
749C2×D3—244no—
750C2×D3—244no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—61no—
762C3×C4—61no—
763C3×C4—81no—
764C3×C4—121no—
765C3×C4—121no—
766C3×C4—121no—
767C3×C4C2×D3×D411yescharacteristic
768C3×C4C2×D3×D411yescharacteristic
769C3×C4#100411yescharacteristic
770C3×C4#100911yescharacteristic
771Dic3—21no—
772Dic3—21no—
773Dic3—41no—
774Dic3—41no—
775Dic3—41no—
776Dic3—121no—
777Dic3—121no—
778Dic3—241no—
779C32#326711yescharacteristic, complemented, Sylow
780C23—21no—
781C23—31no—
782C23—31no—
783C23—61no—
784C23—181no—
785C23—362no—
786C23—362no—
787C23—721no—
788Q8—61no—
789Q8—61no—
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794D4—21no—
795D4—61no—
796D4—61no—
797D4—92no—
798D4—121no—
799D4—122no—
800D4—122no—
801D4—181no—
802D4—362no—
803D4—362no—
804D4—721no—
805D4#380212yes—
806C2×C4—21no—
807C2×C4—31no—
808C2×C4—31no—
809C2×C4—42no—
810C2×C4—61no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—122no—
818C2×C4—122no—
819C2×C4—181no—
820C2×C4—362no—
821C2×C4—721no—
822C2×C4D3×#6711yescharacteristic
823C2×C4D3×#6711yescharacteristic
824C2×C4C22×D3211yescharacteristic
825C8—61no—
826C8—61no—
827C8—92no—
828C8—181no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—42no—
833C2×C3—42no—
834C2×C3—82no—
835C2×C3—121no—
836C2×C3—121no—
837C2×C3—241no—
838C2×C3#560911yescharacteristic
839C2×C3#577011yescharacteristic
840C2×C3#577311yescharacteristic
841C2×C3D4×#6711yescharacteristic
842C2×C3#582211yescharacteristic
843C2×C3#583711yescharacteristic
844D3—41no—
845D3—41no—
846D3—81no—
847D3—122no—
848D3—122no—
849D3—242no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—182no—
863C22—361no—
864C22—361no—
865C22—724no—
866C22C2×D3×#6711yescharacteristic
867C4—21no—
868C4—21no—
869C4—41no—
870C4—61no—
871C4—61no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—361no—
876C4C2×#380211yescharacteristic
877C4#6430711yescharacteristic
878C3—21no—
879C3#8056711yescharacteristic, complemented
880C3#8352211yescharacteristic, complemented
881C2—42no—
882C2—121no—
883C2—121no—
884C2—241no—
885C2—362no—
886C2#1059506911yescharacteristic
887C2#1059509511yescharacteristic
888C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5555C2semidirect
2. C2×#63935C2semidirect
3. C2×#63925C2semidirect
4. #10594007C2semidirect
5. #10592713C2semidirect
6. C3×#5016C2semidirect
7. #10591461C2semidirect
8. #10591450C2semidirect
9. #10590616C2semidirect
10. #10590596C2semidirect
11. #10590520C2semidirect
12. #10590501C2semidirect
13. #10590379C2semidirect
14. #10590376C2semidirect
15. #10590330C2semidirect
19. C2×C3×#237C22semidirect
22. C32×C4×D4C22semidirect
25. C2×C3×#214C22semidirect
30. C3×#897C22semidirect
35. C3×#869C22semidirect
44. C2×#3718C22semidirect
45. C2×#3718C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63659C22semidirect
54. #63635C22semidirect
55. #63630C22semidirect
56. C3×#810C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
69. #5555D3semidirect
83. #5016D3semidirect
125. #3753D4semidirect
161. C2×#237C2×D3semidirect
176. C3×C4×D4C2×D3semidirect
177. C3×C4×D4C2×D3semidirect
194. C2×#214C2×D3semidirect
212. #897C2×D3semidirect
227. #869C2×D3semidirect
242. #810C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
513. C4×D4D32semidirect
779. C32#3267semidirect
879. C3#80567semidirect
880. C3#83522semidirect

Maximal subgroups

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

subgroupindex
C3×#55552
C2×#639352
C2×#639252
#105940072
#105927132
C3×#50162
#105914612
#105914502
#105906162
#105905962
#105905202
#105905012
#105903792
#105903762
#105903302
#835223
#805673