Finite Group Databasebeta

← #11884307

Subgroups — #11884307

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×#5726C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic, complemented
3C2×#63939C211yesmaximal, characteristic, complemented
4#10594003C211yesmaximal, characteristic, complemented
5#10592785C211yesmaximal, characteristic, complemented
6C3×#5083C211yesmaximal, characteristic, complemented
7#10591655C211yesmaximal, characteristic, complemented
8#10591651C211yesmaximal, characteristic, complemented
9#10591599C211yesmaximal, characteristic, complemented
10#10591598C211yesmaximal, characteristic, complemented
11#10591588C211yesmaximal, characteristic, complemented
12#10591585C211yesmaximal, characteristic, complemented
13#10590366C211yesmaximal, characteristic, complemented
14#10590344C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83522—31nomaximal
17#80445—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×D3×D12C2211yescharacteristic
21C2×#3795C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic, complemented
23C2×#3756C2211yescharacteristic, complemented
24C2×#3756C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic
26C2×#3755C2211yescharacteristic
27#64084C2211yescharacteristic
28C3×#946C2211yescharacteristic
29C3×#946C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×#895—21no—
33C3×#894—21no—
34C3×#894—21no—
35C3×D3×C4⋊C4—21no—
36C3×C4×D12C2211yescharacteristic
37C3×C4×D12C2211yescharacteristic
38C3×C4×D12C2211yescharacteristic, complemented
39#63947—24no—
40#63939—24no—
41#63922—21no—
42D3×(C2×D3)⋊C4—21no—
43#63909C2211yescharacteristic
44#63906—21no—
45#63890—21no—
46#63857C2211yescharacteristic
47C2×#3716C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3713C2211yescharacteristic
50C2×#3711C2211yescharacteristic
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63630C2211yescharacteristic, complemented
53C3×#835C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic, 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×#914—31no—
68#5726D311yescharacteristic, complemented
69#5554—31no—
70#5550—31no—
71C3×#461—31no—
72#5239—31no—
73#5238—31no—
74#5173—31no—
75#5169—31no—
76#5086—31no—
77#5086—31no—
78#5086—61no—
79#5083D311yescharacteristic, complemented
80#5052—31no—
81#5048—31no—
82#5047—31no—
83#5046—31no—
84#5016—31no—
85#5014—31no—
86#5014—31no—
87#5011—31no—
88#4844—31no—
89#4836—31no—
90#4816—31no—
91#4810—31no—
92#4808—31no—
93#4807—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C3×#239—22no—
100C3×#239—22no—
101C3×#239—41no—
102C3×#239—41no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12D411yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
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⋊C4—21no—
123C32×C4⋊C4—21no—
124C32×C42C2311yescharacteristic
125#3756—22no—
126#3756—41no—
127#3755—22no—
128#3755—41no—
129#3752—21no—
130#3752—21no—
131C2×C3⋊(C3⋊C8)C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#215—22no—
134C3×#215—22no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×(C2×D3)⋊C4D411yescharacteristic
141C3×C4⋊Dic3D411yescharacteristic
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×Dic3⋊C4—21no—
145C3×Dic3⋊C4—21no—
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148Dic3⋊Dic3—21no—
149#3722—21no—
150(C2×D3)⋊Dic3—21no—
151#3716—22no—
152#3714—22no—
153#3713D414yescomplemented
154#3711—22no—
155D3×C3⋊C8—22no—
156#3267—91noSylow
157C2×C3×#41—31no—
158C2×C3×#41—31no—
159C2×#239C2×D311yescharacteristic
160C2×#239C2×D311yescharacteristic, complemented
161C2×#237—31no—
162C2×D3×D4—31no—
163C2×#235—31no—
164C22×D12—31no—
165C2×C3×SD16—31no—
166C2×C3×SD16—31no—
167C3×C4⋊Q8—21no—
168C3×C4⋊Q8C2×D311yescharacteristic, complemented
169C3×C4⋊Q8C2×D311yescharacteristic, complemented
170C3×#123—61no—
171C3×#123—61no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—31no—
174C3×#121—61no—
175C3×C4×D4—31no—
176C3×C4×D4—31no—
177C3×C4×D4—31no—
178C2×C3×C4⋊C4—61no—
179#950—64no—
180#949—64no—
181#946C2×D311yescharacteristic
182#946C2×D311yescharacteristic, complemented
183C2×#216—31no—
184C2×#216—31no—
185C2×#216—31no—
186C2×#216—31no—
187C2×#216—61no—
188C2×#216—61no—
189C2×#215—31no—
190C2×#215—31no—
191C2×#215—31no—
192C2×#215—31no—
193C2×#215—61no—
194C2×#215—61no—
195C2×#215C2×D311yescharacteristic
196C2×#215C2×D311yescharacteristic
197#937—61no—
198C2×#214—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202#930—31no—
203#930—61no—
204C2×(C2×D3)⋊C4—61no—
205#924—31no—
206C2×#208—31no—
207C22×C3⋊C8—31no—
208#916—64no—
209#914—64no—
210C2×D24—31no—
211C2×#204—31no—
212C2×ΓL(1,𝔽25)—31no—
213C2×D3×C8—31no—
214#897—31no—
215#895—21no—
216#895—31no—
217#894—21no—
218#894—21no—
219#894—61no—
220D3×C4⋊C4—21no—
221#886—61no—
222#884—61no—
223#882—61no—
224D3×C22⋊C4—61no—
225#875—31no—
226#875—31no—
227#875—61no—
228C4×D12C2×D311yescharacteristic
229C4×D12C2×D311yescharacteristic
230C4×D12C2×D311yescharacteristic, complemented
231C3×C4⋊C8—31no—
232C3×#103—31no—
233C3×#103—31no—
234#835C2×D311yescharacteristic, complemented
235#835C2×D311yescharacteristic, complemented
236#832—31no—
237#832—31no—
238#830—31no—
239#830—31no—
240#821—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243#816—31no—
244#810—31no—
245#809—31no—
246#809—31no—
247#809—31no—
248#808—31no—
249#808—31no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251#803—31no—
252#803—31no—
253#803—61no—
254C22×C3⋊D3—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×Q8—21no—
263C32×Q8—21no—
264C32×Q8—21no—
265C32×Q8—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4C2×D411yescharacteristic
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271C2×C3⋊Dic3—21no—
272C4⋊(C3⋊D3)—21no—
273C4⋊(C3⋊D3)—21no—
274#634—21no—
275#634—21no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—41no—
283C3×D12—42no—
284C3×D12—42no—
285C3×D12C2×D412yes—
286C3×D12C2×D412yes—
287C3×C4×D3—21no—
288C3×C4×D3—21no—
289C3×C4×D3—21no—
290C3×C4×D3—21no—
291C3×C4×D3—42no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294C3×C4×D3—81no—
295#626—42no—
296#626—81no—
297#625—42no—
298D3×Dic3—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—91no—
311#461—31no—
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—21no—
325C2×C3×Q8—21no—
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×Q8C22×D311yescharacteristic
328C2×C3×Q8C22×D311yescharacteristic
329C2×C3×Q8C22×D311yescharacteristic
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—61no—
334C2×C3×D4—61no—
335C22×C3×C4—31no—
336C22×C3×C4—31no—
337C22×C3×C4—61no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C22×Dic3—61no—
346#239—22no—
347#239—22no—
348#239—41no—
349#239—41no—
350#237—62no—
351#237—121no—
352D3×D4—62no—
353D3×D4—121no—
354#235—62no—
355#235—121no—
356C2×D12—21no—
357C2×D12—21no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—61no—
361C2×D12—62no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—121no—
365C2×D12#6711yescharacteristic
366C2×D12C22×D311yescharacteristic
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—21no—
369C2×C4×D3—21no—
370C2×C4×D3—21no—
371C2×C4×D3—21no—
372C2×C4×D3—61no—
373C2×C4×D3C22×D311yescharacteristic
374C2×C4×D3C22×D311yescharacteristic
375C2×Dic6—31no—
376C2×Dic6—31no—
377C2×Dic6—61no—
378C3×SD16—62no—
379C3×SD16—62no—
380C2×C3×C8—31no—
381C2×C3×C8—31no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—31no—
387C3×C4⋊C4—31no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—41no—
390C3×C4⋊C4—41no—
391C3×C4⋊C4—61no—
392C3×C4⋊C4—61no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—31no—
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#216—62no—
404#216—62no—
405#216—122no—
406#216—121no—
407#216—121no—
408#216—122no—
409#215—22no—
410#215—22no—
411#215—62no—
412#215—62no—
413#215—122no—
414#215—121no—
415#215—121no—
416#215—122no—
417#214—62no—
418#213—34no—
419#213—34no—
420#213—62no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
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—121no—
434(C2×D3)⋊C4#6711yescharacteristic
435(C2×D3)⋊C4#6711yescharacteristic
436C4⋊Dic3—61no—
437C4⋊Dic3#6711yescharacteristic
438C4⋊Dic3C22×D311yescharacteristic
439C4⋊Dic3C22×D311yescharacteristic
440Dic3⋊C4—21no—
441Dic3⋊C4—21no—
442Dic3⋊C4—61no—
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⋊C8C22×D311yescharacteristic
452C2×C3⋊C8C22×D311yescharacteristic
453D24—62no—
454#204—62no—
455ΓL(1,𝔽25)—62no—
456D3×C8—62no—
457C22×C32C22×D411yescharacteristic
458C2×C3⋊D3—41no—
459C2×C3⋊D3—41no—
460C2×C3⋊D3—41no—
461C2×C3×D3—22no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—22no—
465C2×C3×D3—21no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—41no—
470C2×C3×D3—41no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473D32—84no—
474C32×C4—21no—
475C32×C4—21no—
476C32×C4—41no—
477C32×C4—41no—
478C32×C4C22×D411yescharacteristic
479C32×C4H(5,𝔽2)11yescharacteristic
480C3⋊Dic3—41no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—41no—
484C3×Dic3—41no—
485C2×#41—31no—
486C2×#41—31no—
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—31no—
495C2×SD16—91no—
496C2×SD16—91no—
497C2×SD16—91no—
498C2×D8—91no—
499C2×D8—91no—
500C2×M16—91no—
501C22×C8—91no—
502C4⋊Q8D3211yescharacteristic, complemented
503#124—91no—
504#123—61no—
505#123—61no—
506#123—181no—
507C22⋊Q8—31no—
508C22⋊Q8—31no—
509C22⋊Q8—91no—
510#121—61no—
511#121—91no—
512#121—181no—
513#120—181no—
514C4×D4—31no—
515C4×D4—31no—
516C4×D4—31no—
517C2×C4⋊C4—61no—
518C2×C22⋊C4—181no—
519#106—91no—
520C4⋊C8—31no—
521#103—31no—
522#103—31no—
523#103—91no—
524#102—91no—
525#102—91no—
526#102—91no—
527C22⋊C8—91no—
528C22⋊C8—91no—
529#97—91no—
530C23×C3—31no—
531C23×C3—31no—
532C23×C3—61no—
533C23×C3—61no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—61no—
537C22×D3—61no—
538C22×D3—121no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3C2×#6711yescharacteristic
546C22×D3C2×#6711yescharacteristic
547C3×Q8—21no—
548C3×Q8—21no—
549C3×Q8—21no—
550C3×Q8—21no—
551C3×Q8—21no—
552C3×Q8—21no—
553C3×Q8—21no—
554C3×Q8—21no—
555C3×Q8—41no—
556C3×Q8—41no—
557C3×Q8—41no—
558C3×Q8—41no—
559C3×D4—32no—
560C3×D4—32no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—121no—
564C3×D4—122no—
565C3×D4—122no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—41no—
576C2×C3×C4—41no—
577C2×C3×C4—61no—
578C2×C3×C4—61no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—61no—
583C2×C3×C4—122no—
584C2×C3×C4—122no—
585C2×C3×C4—122no—
586C2×C3×C4—241no—
587C2×C3×C4D3×D411yescharacteristic
588C2×C3×C4D3×D411yescharacteristic
589C2×C3×C4C2×#6711yescharacteristic
590C2×C3×C4C2×#6711yescharacteristic
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D311yescharacteristic
593#67—122no—
594#67—122no—
595#67—122no—
596#67—241no—
597C2×Dic3—21no—
598C2×Dic3—21no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—121no—
602C2×Dic3—122no—
603C2×Dic3C2×#6711yescharacteristic
604C2×Dic3C2×#6711yescharacteristic
605D12—21no—
606D12—21no—
607D12—41no—
608D12—42no—
609D12—42no—
610D12—61no—
611D12—61no—
612D12—61no—
613D12—61no—
614D12—121no—
615D12—121no—
616D12—122no—
617D12—241no—
618D12D3×D412yes—
619D12D3×D412yes—
620C4×D3—21no—
621C4×D3—21no—
622C4×D3—21no—
623C4×D3—21no—
624C4×D3—42no—
625C4×D3—42no—
626C4×D3—42no—
627C4×D3—81no—
628C4×D3—122no—
629Dic6—61no—
630Dic6—61no—
631Dic6—61no—
632Dic6—61no—
633Dic6—121no—
634Dic6—121no—
635C3×C8—61no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C3⋊C8—32no—
640C3⋊C8—32no—
641C3⋊C8—62no—
642C3⋊C8—62no—
643C3⋊C8—61no—
644C3⋊C8—61no—
645C2×C32D4211yescharacteristic
646C2×C32#57511yescharacteristic
647C2×C32#57711yescharacteristic
648C3⋊D3—81no—
649C3×D3—41no—
650C3×D3—42no—
651C3×D3—41no—
652C3×D3—42no—
653C24—181no—
654#41—62no—
655#41—62no—
656#41—121no—
657#41—121no—
658#41—182no—
659#41—361no—
660C2×Q8—91no—
661C2×Q8C2×D3211yescharacteristic
662C2×Q8C2×D3211yescharacteristic
663C2×D4—31no—
664C2×D4—31no—
665C2×D4—31no—
666C2×D4—61no—
667C2×D4—61no—
668C2×D4—91no—
669C2×D4—181no—
670C2×D4—182no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—361no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—181no—
681Q16—182no—
682Q16—361no—
683SD16—62no—
684SD16—62no—
685SD16—182no—
686SD16—182no—
687SD16—361no—
688D8—94no—
689D8—182no—
690M16—182no—
691C2×C8—31no—
692C2×C8—31no—
693C2×C8—91no—
694C2×C8—91no—
695C2×C8—182no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—31no—
699C4⋊C4—31no—
700C4⋊C4—31no—
701C4⋊C4—61no—
702C4⋊C4—61no—
703C4⋊C4—181no—
704C22⋊C4—31no—
705C22⋊C4—31no—
706C22⋊C4—61no—
707C22⋊C4—61no—
708C22⋊C4—61no—
709C22⋊C4—61no—
710C22⋊C4—181no—
711C22⋊C4—181no—
712C22⋊C4—181no—
713C22⋊C4—181no—
714C42C2×D3211yescharacteristic
715C22×C3—21no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—62no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—62no—
724C22×C3—121no—
725C22×C3—121no—
726C22×C3—121no—
727C22×C3—121no—
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C22×#6711yescharacteristic
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—22no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—22no—
738C2×D3—41no—
739C2×D3—41no—
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—41no—
764C3×C4—41no—
765C3×C4—61no—
766C3×C4—61no—
767C3×C4—81no—
768C3×C4—81no—
769C3×C4—121no—
770C3×C4—121no—
771C3×C4C2×D3×D411yescharacteristic
772C3×C4C2×D3×D411yescharacteristic
773C3×C4#100411yescharacteristic
774C3×C4#100911yescharacteristic
775Dic3—21no—
776Dic3—21no—
777Dic3—41no—
778Dic3—41no—
779Dic3—121no—
780Dic3—121no—
781Dic3—241no—
782C32#326711yescharacteristic, complemented, Sylow
783C23—31no—
784C23—31no—
785C23—61no—
786C23—61no—
787C23—181no—
788C23—362no—
789C23—362no—
790C23—721no—
791Q8—21no—
792Q8—21no—
793Q8—21no—
794Q8—21no—
795Q8—181no—
796Q8—181no—
797D4—32no—
798D4—32no—
799D4—61no—
800D4—61no—
801D4—121no—
802D4—122no—
803D4—122no—
804D4—181no—
805D4—181no—
806D4—362no—
807D4—362no—
808D4—721no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—31no—
812C2×C4—31no—
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—122no—
822C2×C4—181no—
823C2×C4—241no—
824C2×C4—362no—
825C2×C4D3×#6711yescharacteristic
826C2×C4D3×#6711yescharacteristic
827C2×C4C22×D3211yescharacteristic
828C8—61no—
829C8—61no—
830C8—92no—
831C8—181no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—121no—
836C2×C3—121no—
837C2×C3—122no—
838C2×C3—122no—
839C2×C3#560911yescharacteristic
840C2×C3#576211yescharacteristic
841C2×C3#577711yescharacteristic
842C2×C3D4×#6711yescharacteristic
843C2×C3#582211yescharacteristic
844C2×C3#583711yescharacteristic
845D3—42no—
846D3—41no—
847D3—41no—
848D3—42no—
849D3—241no—
850D3—241no—
851D3—481no—
852C22—61no—
853C22—61no—
854C22—62no—
855C22—62no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—61no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22—361no—
865C22—361no—
866C22—361no—
867C22—724no—
868C22C2×D3×#6711yescharacteristic
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—61no—
874C4—61no—
875C4—121no—
876C4—121no—
877C4—361no—
878C4D32×D411yescharacteristic
879C4#6431411yescharacteristic
880C3—21no—
881C3#8044511yescharacteristic, complemented
882C3#8352211yescharacteristic, complemented
883C2—121no—
884C2—121no—
885C2—122no—
886C2—122no—
887C2—721no—
888C2#1059528811yescharacteristic
889C2#1059531711yescharacteristic
890C2#1059531811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3267
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5726C2semidirect
2. C2×#63947C2semidirect
3. C2×#63939C2semidirect
4. #10594003C2semidirect
5. #10592785C2semidirect
6. C3×#5083C2semidirect
7. #10591655C2semidirect
8. #10591651C2semidirect
9. #10591599C2semidirect
10. #10591598C2semidirect
11. #10591588C2semidirect
12. #10591585C2semidirect
13. #10590366C2semidirect
14. #10590344C2semidirect
15. #10590330C2semidirect
19. C2×C3×#239C22semidirect
22. C32×C4⋊Q8C22semidirect
23. C2×#3756C22semidirect
24. C2×#3756C22semidirect
29. C3×#946C22semidirect
38. C3×C4×D12C22semidirect
47. C2×#3716C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63630C22semidirect
53. C3×#835C22semidirect
54. C3×#835C22semidirect
55. C3×C4⋊(C3⋊C8)C22semidirect
56. #63574C22semidirect
57. #63567C22semidirect
60. #63562C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
68. #5726D3semidirect
79. #5083D3semidirect
153. #3713D4semidirect
160. C2×#239C2×D3semidirect
168. C3×C4⋊Q8C2×D3semidirect
169. C3×C4⋊Q8C2×D3semidirect
182. #946C2×D3semidirect
230. C4×D12C2×D3semidirect
234. #835C2×D3semidirect
235. #835C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
502. C4⋊Q8D32semidirect
782. C32#3267semidirect
881. C3#80445semidirect
882. C3#83522semidirect

Maximal subgroups

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

subgroupindex
C3×#57262
C2×#639472
C2×#639392
#105940032
#105927852
C3×#50832
#105916552
#105916512
#105915992
#105915982
#105915882
#105915852
#105903662
#105903442
#105903302
#835223
#804453