Finite Group Databasebeta

← #11884256

Subgroups — #11884256

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5555C211yesmaximal, characteristic, complemented
2C2×#63933C211yesmaximal, characteristic, complemented
3C2×#63925C211yesmaximal, characteristic, complemented
4#10594003C211yesmaximal, characteristic, complemented
5#10592715C211yesmaximal, characteristic, complemented
6C3×#5014C211yesmaximal, characteristic, complemented
7#10591463C211yesmaximal, characteristic, complemented
8#10591452C211yesmaximal, characteristic, complemented
9#10590614C211yesmaximal, characteristic, complemented
10#10590596C211yesmaximal, characteristic, complemented
11#10590587C211yesmaximal, characteristic, complemented
12#10590577C211yesmaximal, characteristic, complemented
13#10590374C211yesmaximal, characteristic, complemented
14#10590363C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#79879—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic, complemented
24C2×#3753C2211yescharacteristic
25#64084C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27C3×#930—21no—
28C2×C3×C4⋊Dic3—21no—
29C3×#897C2211yescharacteristic
30C3×#897C2211yescharacteristic, complemented
31C3×#886—21no—
32C3×#886—21no—
33C3×C4×D12C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×#869C2211yescharacteristic, complemented
36#63933—24no—
37#63925—24no—
38#63922—21no—
39D3×(C2×D3)⋊C4—21no—
40#63909C2211yescharacteristic
41#63906—21no—
42#63890—21no—
43#63857C2211yescharacteristic
44C2×#3719C2211yescharacteristic, complemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63637C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#808C2211yescharacteristic, complemented
58C3×#803C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#547—31no—
64C2×#950—31no—
65C2×#949—31no—
66C2×#912—31no—
67C2×#911—31no—
68#5555D311yescharacteristic, complemented
69#5554—31no—
70#5550—31no—
71C3×#442—31no—
72#5239—31no—
73#5238—31no—
74#5086—31no—
75#5083—31no—
76#5052—31no—
77#5048—31no—
78#5047—31no—
79#5046—31no—
80#5019—31no—
81#5016—31no—
82#5016—31no—
83#5016—61no—
84#5014D311yescharacteristic, complemented
85#5011—31no—
86#4867—31no—
87#4864—31no—
88#4783—31no—
89#4783—31no—
90#4781—31no—
91#4776—31no—
92#4715—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
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×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—41no—
120#3795—22no—
121#3795—41no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C22⋊C4—21no—
124C32×C42C2311yescharacteristic
125#3754—22no—
126#3753—22no—
127#3752—21no—
128#3752—21no—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C3×#213D414yescomplemented
132C3×(C2×D3)⋊C4—21no—
133C3×(C2×D3)⋊C4—21no—
134C3×(C2×D3)⋊C4—21no—
135C3×(C2×D3)⋊C4D411yescharacteristic
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×C4⋊Dic3—21no—
138C3×C4⋊Dic3—21no—
139C3×C4⋊Dic3—21no—
140C3×C4⋊Dic3—21no—
141C3×C4⋊Dic3D411yescharacteristic
142C3×C4⋊Dic3C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145Dic3⋊Dic3—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148#3719—22no—
149#3719—41no—
150#3717—22no—
151#3717—41no—
152#3715—22no—
153#3715—22no—
154#3711—22no—
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#237—31no—
160C2×#237C2×D311yescharacteristic
161C2×#237C2×D311yescharacteristic, complemented
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×D8—31no—
166C3×C4⋊Q8—31no—
167C3×#123—61no—
168C3×#123—61no—
169C3×C22⋊Q8—31no—
170C3×C22⋊Q8—31no—
171C3×#121—61no—
172C3×C4×D4—21no—
173C3×C4×D4—31no—
174C3×C4×D4—31no—
175C3×C4×D4C2×D311yescharacteristic, complemented
176C3×C4×D4C2×D311yescharacteristic, complemented
177C2×C3×C4⋊C4—61no—
178#950—64no—
179#949—64no—
180C2×#216—31no—
181C2×#216—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186#937—61no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—61no—
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—61no—
195C2×#213C2×D311yescharacteristic
196#930—21no—
197#930—31no—
198#930—61no—
199C2×(C2×D3)⋊C4—61no—
200C2×C4⋊Dic3—21no—
201#924—31no—
202C2×#208—31no—
203C22×C3⋊C8—31no—
204#912—64no—
205#911—64no—
206C2×Dic12—31no—
207C2×Dic12—31no—
208C2×#204—31no—
209C2×#204—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212#897—31no—
213#897C2×D311yescharacteristic
214#897C2×D311yescharacteristic, complemented
215#895—31no—
216#894—61no—
217#886—21no—
218#886—21no—
219#886—61no—
220#884—61no—
221#882—61no—
222D3×C22⋊C4—61no—
223#875—31no—
224#875—31no—
225#875—61no—
226C4×D12C2×D311yescharacteristic
227C4×D12C2×D311yescharacteristic
228#869C2×D311yescharacteristic, complemented
229C3×#106—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×#97—31no—
233#835—31no—
234#835—31no—
235#832C2×D311yescharacteristic, complemented
236#830—31no—
237#830—31no—
238(C2×D3)⋊C8—31no—
239(C2×D3)⋊C8—31no—
240#810—31no—
241#810—31no—
242#810—31no—
243#810—31no—
244#810—61no—
245#809—31no—
246#809—31no—
247#809—61no—
248#809C2×D311yescharacteristic
249#808C2×D311yescharacteristic, complemented
250C4⋊(C3⋊C8)—31no—
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—61no—
253#803C2×D311yescharacteristic, complemented
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)—21no—
272#634—21no—
273#634—21no—
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3—42no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—41no—
285C3×D12C2×D412yes—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—81no—
291C3×Dic6—21no—
292C3×Dic6—21no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295#626—42no—
296#626—81no—
297#625—42no—
298D3×Dic3—42no—
299C3⋊(C3⋊C8)—21no—
300C3⋊(C3⋊C8)—21no—
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yes—
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—91no—
311#461—91no—
312#452—91no—
313#452—91no—
314#450—91no—
315#449—91no—
316#442—31no—
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×D4—21no—
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C2×C3×D4—61no—
330C2×C3×D4—61no—
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C22×C3×C4—21no—
334C22×C3×C4—21no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—41no—
338C22×C3×C4—61no—
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—
349C22×Dic3—61no—
350#237—22no—
351#237—22no—
352#237—41no—
353#237—41no—
354#237—62no—
355#237—121no—
356D3×D4—62no—
357D3×D4—121no—
358#235—62no—
359#235—121no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—61no—
363C2×D12—62no—
364C2×D12—61no—
365C2×D12—61no—
366C2×D12—121no—
367C2×D12#6711yescharacteristic
368C2×D12C22×D311yescharacteristic
369C2×C4×D3—21no—
370C2×C4×D3—61no—
371C2×C4×D3C22×D311yescharacteristic
372C2×C4×D3C22×D311yescharacteristic
373C2×Dic6—31no—
374C2×Dic6—31no—
375C2×Dic6—61no—
376C2×Dic6C22×D311yescharacteristic
377C2×Dic6C22×D311yescharacteristic
378C3×D8—34no—
379C2×C3×C8—31no—
380C2×C3×C8—31no—
381C3×C4⋊C4—21no—
382C3×C4⋊C4—31no—
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×C42—21no—
399C3×C42C22×D311yescharacteristic
400C3×C42C22×D311yescharacteristic
401#217—61no—
402#216—62no—
403#216—121no—
404#215—62no—
405#215—62no—
406#215—62no—
407#215—121no—
408#214—62no—
409#214—62no—
410#214—62no—
411#214—62no—
412#214—122no—
413#213—62no—
414#213—62no—
415#213—122no—
416#213D1214yescomplemented
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
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—121no—
429(C2×D3)⋊C4#6711yescharacteristic
430(C2×D3)⋊C4#6711yescharacteristic
431C4⋊Dic3—21no—
432C4⋊Dic3—21no—
433C4⋊Dic3—21no—
434C4⋊Dic3—21no—
435C4⋊Dic3—61no—
436C4⋊Dic3#6711yescharacteristic
437C4⋊Dic3C22×D311yescharacteristic
438Dic3⋊C4—61no—
439#208—62no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—31no—
442C2×C3⋊C8—31no—
443C2×C3⋊C8—31no—
444C2×C3⋊C8—61no—
445C2×C3⋊C8—61no—
446C2×C3⋊C8—62no—
447C2×C3⋊C8C22×D311yescharacteristic
448C2×C3⋊C8C22×D311yescharacteristic
449Dic12—62no—
450Dic12—121no—
451#204—62no—
452#204—121no—
453ΓL(1,𝔽25)—62no—
454D3×C8—62no—
455C22×C32—22no—
456C22×C32—41no—
457C22×C32—41no—
458C22×C32C22×D411yescharacteristic
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3⋊D3—41no—
462C2×C3×D3—22no—
463C2×C3×D3—21no—
464C2×C3×D3—21no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471D32—84no—
472C32×C4—21no—
473C32×C4—21no—
474C32×C4—41no—
475C32×C4C22×D411yescharacteristic
476C32×C4H(5,𝔽2)11yescharacteristic
477C3⋊Dic3—41no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—41no—
481C3×Dic3—41no—
482C3×Dic3—41no—
483C2×#41—31no—
484C2×#41—31no—
485C2×#41—91no—
486C22×D4—91no—
487AGL(1,ℤ/8)—184no—
488#135—184no—
489C2×Q16—91no—
490C2×Q16—91no—
491C2×SD16—91no—
492C2×SD16—91no—
493C2×SD16—91no—
494C2×SD16—91no—
495C2×SD16—91no—
496C2×D8—31no—
497C2×D8—91no—
498C2×M16—91no—
499C22×C8—91no—
500C4⋊Q8—31no—
501#124—91no—
502#123—61no—
503#123—61no—
504#123—181no—
505C22⋊Q8—31no—
506C22⋊Q8—31no—
507C22⋊Q8—91no—
508#121—61no—
509#121—91no—
510#121—181no—
511#120—181no—
512C4×D4—31no—
513C4×D4—31no—
514C4×D4D3211yescharacteristic, complemented
515C2×C4⋊C4—61no—
516C2×C22⋊C4—181no—
517#106—31no—
518C4⋊C8—91no—
519#103—91no—
520#103—91no—
521#103—91no—
522#102—31no—
523#102—31no—
524#102—91no—
525C22⋊C8—91no—
526C22⋊C8—91no—
527#97—31no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—41no—
533C23×C3—61no—
534C22×D3—21no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—121no—
538C22×D3—122no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3C2×#6711yescharacteristic
545C22×D3C2×#6711yescharacteristic
546C3×Q8—61no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×Q8—61no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—22no—
553C3×D4—32no—
554C3×D4—41no—
555C3×D4—61no—
556C3×D4—121no—
557C3×D4—122no—
558C3×D4—122no—
559C3×D4C2×D1212yes—
560C3×D4D3×D412yes—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—31no—
568C2×C3×C4—41no—
569C2×C3×C4—42no—
570C2×C3×C4—42no—
571C2×C3×C4—61no—
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—82no—
579C2×C3×C4—122no—
580C2×C3×C4—122no—
581C2×C3×C4—241no—
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—122no—
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×Dic3—122no—
603C2×Dic3C2×#6711yescharacteristic
604C2×Dic3C2×#6711yescharacteristic
605D12—21no—
606D12—41no—
607D12—61no—
608D12—61no—
609D12—61no—
610D12—61no—
611D12—121no—
612D12—121no—
613D12—122no—
614D12—241no—
615D12C2×D1212yes—
616C4×D3—21no—
617C4×D3—21no—
618C4×D3—21no—
619C4×D3—21no—
620C4×D3—81no—
621C4×D3—122no—
622Dic6—21no—
623Dic6—21no—
624Dic6—21no—
625Dic6—21no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—61no—
630Dic6—121no—
631Dic6—121no—
632C3×C8—32no—
633C3×C8—61no—
634C3⋊C8—21no—
635C3⋊C8—61no—
636C3⋊C8—61no—
637C3⋊C8—61no—
638C3⋊C8—61no—
639C3⋊C8—121no—
640C3⋊C8—121no—
641C3⋊C8C2×D1212yes—
642C2×C32—42no—
643C2×C32D4211yescharacteristic
644C2×C32#57511yescharacteristic
645C2×C32#57711yescharacteristic
646C3⋊D3—81no—
647C3×D3—41no—
648C3×D3—42no—
649C3×D3—41no—
650C24—181no—
651#41—62no—
652#41—62no—
653#41—121no—
654#41—121no—
655#41—182no—
656#41—361no—
657C2×Q8—31no—
658C2×Q8—31no—
659C2×Q8—91no—
660C2×D4—31no—
661C2×D4—31no—
662C2×D4—61no—
663C2×D4—61no—
664C2×D4—91no—
665C2×D4—181no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—361no—
670C2×D4C2×D3211yescharacteristic
671C22×C4—21no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—61no—
675C22×C4—61no—
676C22×C4—61no—
677C22×C4—181no—
678Q16—182no—
679Q16—361no—
680SD16—182no—
681SD16—182no—
682SD16—182no—
683SD16—182no—
684SD16—361no—
685D8—34no—
686D8—182no—
687M16—182no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—91no—
691C2×C8—91no—
692C2×C8—182no—
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—61no—
697C4⋊C4—61no—
698C4⋊C4—61no—
699C4⋊C4—181no—
700C4⋊C4C2×D3211yescharacteristic
701C22⋊C4—21no—
702C22⋊C4—31no—
703C22⋊C4—31no—
704C22⋊C4—61no—
705C22⋊C4—61no—
706C22⋊C4—61no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C42C2×D3211yescharacteristic
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—42no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—61no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—62no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3C2×D3×D411yescharacteristic
732C22×C3C22×#6711yescharacteristic
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—22no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—41no—
741C2×D3—41no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—241no—
749C2×D3—241no—
750C2×D3—241no—
751C2×D3—244no—
752C2×D3—244no—
753C3×C4—21no—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—21no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—41no—
763C3×C4—61no—
764C3×C4—61no—
765C3×C4—81no—
766C3×C4—121no—
767C3×C4—121no—
768C3×C4—121no—
769C3×C4C22×D1211yescharacteristic
770C3×C4C2×D3×D411yescharacteristic
771C3×C4#100411yescharacteristic
772C3×C4#100911yescharacteristic
773Dic3—21no—
774Dic3—21no—
775Dic3—41no—
776Dic3—41no—
777Dic3—41no—
778Dic3—121no—
779Dic3—121no—
780Dic3—241no—
781C32#326711yescharacteristic, complemented, Sylow
782C23—21no—
783C23—31no—
784C23—31no—
785C23—61no—
786C23—181no—
787C23—362no—
788C23—362no—
789C23—721no—
790Q8—61no—
791Q8—61no—
792Q8—61no—
793Q8—61no—
794Q8—181no—
795Q8—181no—
796D4—21no—
797D4—32no—
798D4—61no—
799D4—121no—
800D4—122no—
801D4—122no—
802D4—181no—
803D4—181no—
804D4—362no—
805D4—362no—
806D4—721no—
807D4D3×D1212yes—
808C2×C4—21no—
809C2×C4—31no—
810C2×C4—31no—
811C2×C4—42no—
812C2×C4—61no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—122no—
820C2×C4—122no—
821C2×C4—181no—
822C2×C4—241no—
823C2×C4—362no—
824C2×C4D3×#6711yescharacteristic
825C2×C4D3×#6711yescharacteristic
826C2×C4C22×D3211yescharacteristic
827C8—32no—
828C8—61no—
829C8—181no—
830C8—181no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—42no—
835C2×C3—42no—
836C2×C3—82no—
837C2×C3—121no—
838C2×C3—121no—
839C2×C3—122no—
840C2×C3D4×D1211yescharacteristic
841C2×C3#577311yescharacteristic
842C2×C3#577511yescharacteristic
843C2×C3D4×#6711yescharacteristic
844C2×C3#582211yescharacteristic
845C2×C3#583711yescharacteristic
846D3—42no—
847D3—41no—
848D3—41no—
849D3—241no—
850D3—241no—
851D3—481no—
852C22—22no—
853C22—41no—
854C22—41no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—62no—
862C22—121no—
863C22—121no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22C2×D3×#6711yescharacteristic
869C4—21no—
870C4—21no—
871C4—41no—
872C4—61no—
873C4—61no—
874C4—121no—
875C4—121no—
876C4—121no—
877C4—361no—
878C4C2×D3×D1211yescharacteristic
879C4#6430711yescharacteristic
880C3—21no—
881C3#7987911yescharacteristic, complemented
882C3#8352211yescharacteristic, complemented
883C2—42no—
884C2—121no—
885C2—121no—
886C2—122no—
887C2—721no—
888C2D12×#6711yescharacteristic
889C2#1059509511yescharacteristic
890C2#1059545511yescharacteristic
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×#63933C2semidirect
3. C2×#63925C2semidirect
4. #10594003C2semidirect
5. #10592715C2semidirect
6. C3×#5014C2semidirect
7. #10591463C2semidirect
8. #10591452C2semidirect
9. #10590614C2semidirect
10. #10590596C2semidirect
11. #10590587C2semidirect
12. #10590577C2semidirect
13. #10590374C2semidirect
14. #10590363C2semidirect
15. #10590326C2semidirect
19. C2×C3×#237C22semidirect
22. C32×C4×D4C22semidirect
23. C2×#3754C22semidirect
30. C3×#897C22semidirect
35. C3×#869C22semidirect
44. C2×#3719C22semidirect
45. C2×#3719C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63637C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
55. C3×#832C22semidirect
57. C3×#808C22semidirect
58. C3×#803C22semidirect
59. #63565C22semidirect
60. #63565C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. #5555D3semidirect
84. #5014D3semidirect
131. C3×#213D4semidirect
161. C2×#237C2×D3semidirect
175. C3×C4×D4C2×D3semidirect
176. C3×C4×D4C2×D3semidirect
214. #897C2×D3semidirect
228. #869C2×D3semidirect
235. #832C2×D3semidirect
249. #808C2×D3semidirect
253. #803C2×D3semidirect
416. #213D12semidirect
514. C4×D4D32semidirect
781. C32#3267semidirect
881. C3#79879semidirect
882. 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×#639332
C2×#639252
#105940032
#105927152
C3×#50142
#105914632
#105914522
#105906142
#105905962
#105905872
#105905772
#105903742
#105903632
#105903262
#835223
#798793