Finite Group Databasebeta

← #11884099

Subgroups — #11884099

Order 1152.

1128 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×#63951C211yesmaximal, characteristic, complemented
3C2×#63940C211yesmaximal, characteristic, complemented
4#10594005C211yesmaximal, characteristic
5C3×#5028C211yesmaximal, characteristic, complemented
6C3×#5026C211yesmaximal, characteristic, complemented
7#10591603C211yesmaximal, characteristic, complemented
8#10591592C211yesmaximal, characteristic, complemented
9#10590618C211yesmaximal, characteristic, complemented
10#10590597C211yesmaximal, characteristic, complemented
11#10590525C211yesmaximal, characteristic, complemented
12#10590506C211yesmaximal, characteristic, complemented
13#10590372C211yesmaximal, characteristic, complemented
14#10590365C211yesmaximal, characteristic, complemented
15#10590328C211yesmaximal, characteristic, complemented
16#80627—31nomaximal
17#79795—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C2×#3802C2211yescharacteristic
21C2×#3796C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic, complemented
23#64106—21no—
24#64106—21no—
25#64106C2211yescharacteristic
26#64106C2211yescharacteristic, complemented
27C4×C4⋊(C3⋊D3)—21no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29#64078—21no—
30#64078C2211yescharacteristic, complemented
31C2×C3×#216C2211yescharacteristic, complemented
32C2×C3×#215C2211yescharacteristic
33C2×C3×#215C2211yescharacteristic
34C3×#875C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic
36#63951—24no—
37#63940—24no—
38#63923—21no—
39D3×(C2×D3)⋊C4—21no—
40#63916C2211yescharacteristic
41#63906—21no—
42#63891—21no—
43#63871C2211yescharacteristic
44C2×#3719C2211yescharacteristic, complemented
45C2×#3719C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3716C2211yescharacteristic
49C2×#3716C2211yescharacteristic
50C2×#3712C2211yescharacteristic, complemented
51C2×#3710C2211yescharacteristic
52C3×#835C2211yescharacteristic, complemented
53C3×#810C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#807C2211yescharacteristic, complemented
57C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
58C3×#803C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63567C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62#63557C2211yescharacteristic, complemented
63C2×#918—31no—
64C2×#915—31no—
65C2×D3×SD16—31no—
66C2×D3×SD16—31no—
67#5676—31no—
68Q8×D12—31no—
69Q8×D12—31no—
70Q8×D12—61no—
71#5554—31no—
72C3×#464—31no—
73C3×#440—31no—
74#5186—31no—
75#5170—31no—
76#5060—31no—
77#5028D311yescharacteristic, complemented
78#5026D311yescharacteristic, complemented
79#5019—31no—
80#4887—31no—
81#4886—31no—
82#4841—31no—
83#4836—31no—
84#4813—31no—
85#4809—31no—
86#4808—31no—
87#4806—31no—
88#4783—31no—
89#4780—31no—
90#4776—31no—
91#4776—31no—
92#4715—31no—
93#4706—31no—
94C22×D32—21no—
95C2×C32×Q8C2311yescharacteristic
96Q8×C3⋊D3—22no—
97Q8×C3⋊D3—22no—
98Q8×C3⋊D3—41no—
99Q8×C3⋊D3—41no—
100C2×C4⋊(C3⋊D3)D411yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×C4×C3⋊D3C2311yescharacteristic
105C2×#634—21no—
106C2×#634—21no—
107C2×#634C2311yescharacteristic
108C2×#634C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×Dic6C2311yescharacteristic
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116C2×D3×Dic3—21no—
117#3802—22no—
118#3802—41no—
119#3796—22no—
120#3796—41no—
121C32×C4⋊C4—21no—
122C32×C4⋊C4C2311yescharacteristic
123C32×C42—21no—
124C32×C42C2311yescharacteristic
125#3752—21no—
126#3752—21no—
127#3752D411yescharacteristic
128#3752D411yescharacteristic
129C4⋊(C3⋊Dic3)—21no—
130C4⋊(C3⋊Dic3)—21no—
131C4⋊(C3⋊Dic3)—21no—
132C4⋊(C3⋊Dic3)—21no—
133C4⋊(C3⋊Dic3)D411yescharacteristic
134C3×#216—22no—
135C3×#215—22no—
136C3×#215D414yescomplemented
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
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#3716—22no—
151#3716—22no—
152#3716—22no—
153#3716—41no—
154#3712—22no—
155#3710—22no—
156#3266—91noSylow
157C2×#239—31no—
158C2×D3×Q8—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×D3×Q8—31no—
162C2×D3×Q8—61no—
163C2×D3×Q8—61no—
164C2×#237—31no—
165C2×D3×D4—31no—
166C2×D3×D4—31no—
167C2×C3×Q16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C3×#124—31no—
171C3×C4×Q8—21no—
172C3×C4×Q8C2×D311yescharacteristic, complemented
173C3×C4×Q8C2×D311yescharacteristic, complemented
174C3×C4×D4—31no—
175#946—31no—
176C2×#216—31no—
177C2×#216—31no—
178C2×#216C2×D311yescharacteristic, complemented
179C2×#215C2×D311yescharacteristic
180C2×#215C2×D311yescharacteristic
181#938—31no—
182C2×#214—31no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—31no—
186#930—61no—
187C2×(C2×D3)⋊C4—61no—
188#918—64no—
189#915—64no—
190D3×SD16—64no—
191D3×SD16—64no—
192C2×Dic12—31no—
193C2×Dic12—31no—
194C2×#204—31no—
195C2×#204—31no—
196C2×#204—31no—
197C2×#204—31no—
198C2×ΓL(1,𝔽25)—31no—
199C2×ΓL(1,𝔽25)—31no—
200C2×D3×C8—31no—
201C2×D3×C8—31no—
202#897—31no—
203#897—31no—
204#897—31no—
205#897—31no—
206#897—31no—
207#897—61no—
208#897—61no—
209#897—61no—
210#897—61no—
211#897—61no—
212#897—61no—
213#897—62no—
214#897—62no—
215#895—31no—
216#886—61no—
217#884—61no—
218#883—61no—
219#882—61no—
220#882—61no—
221D3×C22⋊C4—61no—
222#875C2×D311yescharacteristic
223C4×D12—31no—
224C4×D12—31no—
225C4×D12—61no—
226C4×D12—61no—
227C4×D12—61no—
228C4×D12—62no—
229C4×D12C2×D311yescharacteristic
230#869—31no—
231#869—31no—
232#869—61no—
233#869—61no—
234#869—61no—
235#869—62no—
236C3×#107—31no—
237C3×C4⋊C8—31no—
238C3×#103—31no—
239C3×#103—31no—
240C3×#102—31no—
241C3×#102—31no—
242C3×#97—31no—
243#835C2×D311yescharacteristic, complemented
244(C2×D3)⋊C8—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8—31no—
248#816—31no—
249#816—31no—
250#810—31no—
251#810—31no—
252#810C2×D311yescharacteristic, complemented
253#809C2×D311yescharacteristic
254#809C2×D311yescharacteristic
255#807C2×D311yescharacteristic, complemented
256C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
257#803C2×D311yescharacteristic, complemented
258C22×C3⋊D3C2×D411yescharacteristic
259C22×C3⋊D3C2×D411yescharacteristic
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—81no—
265C32×Q8—21no—
266C32×Q8C2×D412yes—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3C2×D411yescharacteristic
275C2×C3⋊Dic3C2×D411yescharacteristic
276C4⋊(C3⋊D3)—22no—
277C4×C3⋊D3—21no—
278C4×C3⋊D3—21no—
279C4×C3⋊D3—21no—
280C4×C3⋊D3—21no—
281C4×C3⋊D3—42no—
282C4×C3⋊D3—42no—
283#634—21no—
284#634—21no—
285#634—21no—
286#634—21no—
287#634—42no—
288#634—42no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C3×D12—21no—
292C3×D12—21no—
293C3×D12—21no—
294C3×D12C2×D412yes—
295C3×C4×D3—81no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298#626—42no—
299#626—81no—
300#625—42no—
301D3×Dic3—42no—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#137—91no—
307C22×SD16—91no—
308D4×Q8—91no—
309#546—91no—
310#497—91no—
311#468—91no—
312#467—91no—
313#464—31no—
314#461—91no—
315#452—91no—
316#451—91no—
317#450—91no—
318#448—91no—
319#440—31no—
320#435—91no—
321C23×D3—61no—
322C23×D3—61no—
323C2×C3×Q8—21no—
324C2×C3×Q8—31no—
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×Q8C22×D311yescharacteristic
327C2×C3×D4—31no—
328C2×C3×D4—31no—
329C22×C3×C4—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C22×Dic3—61no—
335#239—62no—
336#239—121no—
337D3×Q8—62no—
338D3×Q8—62no—
339D3×Q8—62no—
340D3×Q8—62no—
341D3×Q8—122no—
342D3×Q8—122no—
343D3×Q8—121no—
344D3×Q8—121no—
345D3×Q8—121no—
346D3×Q8—121no—
347D3×Q8—122no—
348D3×Q8—122no—
349#237—62no—
350#237—121no—
351D3×D4—62no—
352D3×D4—62no—
353D3×D4—121no—
354D3×D4—121no—
355C2×D12—31no—
356C2×D12—31no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12C22×D311yescharacteristic
361C2×D12C22×D311yescharacteristic
362C2×C4×D3—21no—
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3—31no—
366C2×C4×D3—31no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×Dic6—31no—
377C2×Dic6—31no—
378C2×Dic6—31no—
379C2×Dic6—31no—
380C2×Dic6—61no—
381C2×Dic6—61no—
382C2×Dic6—61no—
383C2×Dic6—61no—
384C2×Dic6—61no—
385C2×Dic6—61no—
386C2×Dic6—62no—
387C2×Dic6—62no—
388C2×Dic6C22×D311yescharacteristic
389C3×Q16—62no—
390C3×SD16—34no—
391C3×SD16—62no—
392C2×C3×C8—31no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C3×C4⋊C4—22no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—21no—
399C3×C4⋊C4—21no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4C22×D311yescharacteristic
402C3×C4⋊C4C22×D311yescharacteristic
403C3×C22⋊C4—61no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C42—22no—
407C3×C42—21no—
408C3×C42—21no—
409C3×C42—21no—
410C3×C42C22×D311yescharacteristic
411C3×C42C22×D311yescharacteristic
412#217—61no—
413#216—22no—
414#216—62no—
415#216—121no—
416#215—22no—
417#215D1214yescomplemented
418#214—62no—
419#214—62no—
420#214—62no—
421#214—121no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—31no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—62no—
439(C2×D3)⋊C4—62no—
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442C4⋊Dic3—61no—
443C4⋊Dic3—61no—
444C4⋊Dic3—61no—
445C4⋊Dic3—61no—
446C4⋊Dic3—61no—
447C4⋊Dic3—61no—
448C4⋊Dic3—62no—
449C4⋊Dic3—62no—
450C4⋊Dic3—62no—
451C4⋊Dic3—62no—
452C4⋊Dic3—61no—
453C4⋊Dic3—61no—
454C4⋊Dic3—61no—
455C4⋊Dic3—61no—
456C4⋊Dic3C22×D311yescharacteristic
457Dic3⋊C4—61no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460C2×C3⋊C8C22×D311yescharacteristic
461C2×C3⋊C8C22×D311yescharacteristic
462Dic12—62no—
463Dic12—121no—
464#204—62no—
465#204—62no—
466#204—62no—
467#204—121no—
468ΓL(1,𝔽25)—62no—
469ΓL(1,𝔽25)—62no—
470D3×C8—62no—
471D3×C8—62no—
472C22×C32C22×D411yescharacteristic
473C2×C3⋊D3—21no—
474C2×C3⋊D3—21no—
475C2×C3⋊D3—21no—
476C2×C3⋊D3—21no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3#13712yescomplemented
479C2×C3×D3—22no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485D32—84no—
486C32×C4—22no—
487C32×C4—21no—
488C32×C4—21no—
489C32×C4—41no—
490C32×C4C22×D411yescharacteristic
491C32×C4H(5,𝔽2)11yescharacteristic
492C3⋊Dic3—21no—
493C3⋊Dic3—21no—
494C3⋊Dic3—41no—
495C3⋊Dic3—41no—
496C3×Dic3—41no—
497C3×Dic3—41no—
498C2×#41—91no—
499C22×Q8—91no—
500C22×Q8—91no—
501C22×D4—91no—
502#137—184no—
503C2×Q16—31no—
504C2×Q16—91no—
505C2×Q16—91no—
506C2×SD16—31no—
507C2×SD16—31no—
508C2×SD16—91no—
509C2×SD16—91no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—184no—
513C2×M16—91no—
514C22×C8—91no—
515C4⋊Q8—91no—
516C4⋊Q8—181no—
517#124—31no—
518#123—181no—
519C22⋊Q8—91no—
520C22⋊Q8—91no—
521C22⋊Q8—91no—
522C22⋊Q8—181no—
523C22⋊Q8—181no—
524#121—91no—
525#121—181no—
526#120—181no—
527C4×Q8D3211yescharacteristic, complemented
528C4×D4—31no—
529C4×D4—91no—
530C4×D4—181no—
531C2×C22⋊C4—181no—
532#107—31no—
533C4⋊C8—31no—
534#103—31no—
535#103—31no—
536#103—91no—
537#103—91no—
538#102—31no—
539#102—31no—
540C22⋊C8—91no—
541C22⋊C8—91no—
542#97—31no—
543C23×C3—61no—
544C23×C3—61no—
545C22×D3—21no—
546C22×D3—21no—
547C22×D3—31no—
548C22×D3—31no—
549C22×D3—31no—
550C22×D3—31no—
551C22×D3—61no—
552C22×D3—61no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—241no—
558C22×D3—241no—
559C3×Q8—22no—
560C3×Q8—21no—
561C3×Q8—21no—
562C3×Q8—22no—
563C3×Q8—61no—
564C3×Q8—61no—
565C3×Q8C2×D1212yes—
566C3×Q8D3×D412yes—
567C3×D4—32no—
568C3×D4—61no—
569C3×D4—61no—
570C3×D4—61no—
571C2×C3×C4—22no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—22no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4—241no—
583C2×C3×C4D3×D411yescharacteristic
584C2×C3×C4D3×D411yescharacteristic
585C2×C3×C4D3×D411yescharacteristic
586C2×C3×C4D3×D411yescharacteristic
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589#67—122no—
590#67—122no—
591#67—122no—
592#67—241no—
593C2×Dic3—21no—
594C2×Dic3—21no—
595C2×Dic3—31no—
596C2×Dic3—31no—
597C2×Dic3—31no—
598C2×Dic3—31no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—122no—
608D12—21no—
609D12—21no—
610D12—21no—
611D12—62no—
612D12—62no—
613D12—64no—
614D12—122no—
615D12—241no—
616D12C2×D1212yes—
617C4×D3—61no—
618C4×D3—61no—
619C4×D3—61no—
620C4×D3—61no—
621C4×D3—61no—
622C4×D3—61no—
623C4×D3—61no—
624C4×D3—61no—
625C4×D3—81no—
626C4×D3—121no—
627C4×D3—121no—
628C4×D3—121no—
629C4×D3—121no—
630C4×D3—122no—
631C4×D3—122no—
632C4×D3—122no—
633C4×D3—122no—
634C4×D3—122no—
635C4×D3—124no—
636C4×D3—124no—
637Dic6—21no—
638Dic6—21no—
639Dic6—61no—
640Dic6—61no—
641Dic6—61no—
642Dic6—61no—
643Dic6—61no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—121no—
648Dic6—121no—
649Dic6—121no—
650Dic6—121no—
651Dic6—122no—
652Dic6—122no—
653Dic6—122no—
654Dic6—122no—
655Dic6—124no—
656Dic6—124no—
657C3×C8—32no—
658C3×C8—61no—
659C3×C8—61no—
660C3×C8—61no—
661C3⋊C8—21no—
662C3⋊C8—21no—
663C3⋊C8—21no—
664C3⋊C8C2×D1212yes—
665C2×C32D4211yescharacteristic
666C2×C32C2×#13711yescharacteristic
667C2×C32#57711yescharacteristic
668C3⋊D3—22no—
669C3⋊D3—41no—
670C3×D3—42no—
671C3×D3—81no—
672C24—181no—
673#41—182no—
674#41—361no—
675C2×Q8—31no—
676C2×Q8—91no—
677C2×Q8—91no—
678C2×Q8—181no—
679C2×Q8—181no—
680C2×Q8—182no—
681C2×Q8—182no—
682C2×Q8—361no—
683C2×Q8—361no—
684C2×Q8C2×D3211yescharacteristic
685C2×D4—31no—
686C2×D4—31no—
687C2×D4—91no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—181no—
691C2×D4—182no—
692C2×D4—361no—
693C22×C4—61no—
694C22×C4—91no—
695C22×C4—91no—
696C22×C4—181no—
697C22×C4—181no—
698C22×C4—181no—
699Q16—62no—
700Q16—182no—
701Q16—361no—
702SD16—34no—
703SD16—62no—
704SD16—182no—
705SD16—182no—
706SD16—182no—
707SD16—361no—
708M16—182no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—182no—
714C4⋊C4—21no—
715C4⋊C4—31no—
716C4⋊C4—91no—
717C4⋊C4—181no—
718C4⋊C4—181no—
719C4⋊C4—181no—
720C4⋊C4—181no—
721C4⋊C4—181no—
722C4⋊C4C2×D3211yescharacteristic
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—91no—
727C22⋊C4—91no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C42—21no—
733C42C2×D3211yescharacteristic
734C22×C3—21no—
735C22×C3—62no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3C2×D3×D411yescharacteristic
742C22×C3C2×D3×D411yescharacteristic
743C2×D3—22no—
744C2×D3—32no—
745C2×D3—32no—
746C2×D3—41no—
747C2×D3—41no—
748C2×D3—41no—
749C2×D3—41no—
750C2×D3—41no—
751C2×D3—62no—
752C2×D3—61no—
753C2×D3—61no—
754C2×D3—61no—
755C2×D3—61no—
756C2×D3—62no—
757C2×D3—61no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—244no—
768C2×D3—244no—
769C3×C4—24no—
770C3×C4—22no—
771C3×C4—21no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—21no—
775C3×C4—22no—
776C3×C4—22no—
777C3×C4—21no—
778C3×C4—21no—
779C3×C4—41no—
780C3×C4—42no—
781C3×C4—41no—
782C3×C4—41no—
783C3×C4—121no—
784C3×C4—121no—
785C3×C4C22×D1211yescharacteristic
786C3×C4C2×D3×D411yescharacteristic
787C3×C4#100911yescharacteristic
788C3×C4#100911yescharacteristic
789Dic3—41no—
790Dic3—41no—
791Dic3—61no—
792Dic3—61no—
793Dic3—61no—
794Dic3—61no—
795Dic3—121no—
796Dic3—121no—
797Dic3—122no—
798Dic3—122no—
799Dic3—121no—
800Dic3—121no—
801Dic3—121no—
802Dic3—121no—
803C32#326611yescharacteristic, complemented, Sylow
804C23—61no—
805C23—61no—
806C23—91no—
807C23—91no—
808C23—362no—
809C23—362no—
810C23—721no—
811Q8—21no—
812Q8—61no—
813Q8—61no—
814Q8—181no—
815Q8—181no—
816Q8—181no—
817Q8—181no—
818Q8—362no—
819Q8—362no—
820Q8D3×D1212yes—
821D4—32no—
822D4—61no—
823D4—61no—
824D4—61no—
825D4—182no—
826D4—362no—
827D4—362no—
828D4—721no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—61no—
832C2×C4—61no—
833C2×C4—91no—
834C2×C4—91no—
835C2×C4—181no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—181no—
841C2×C4—241no—
842C2×C4—362no—
843C2×C4—362no—
844C2×C4—362no—
845C2×C4#381111yescharacteristic
846C2×C4#381111yescharacteristic
847C2×C4C22×D3211yescharacteristic
848C8—32no—
849C8—61no—
850C8—61no—
851C8—61no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—21no—
855C2×C3—122no—
856C2×C3—241no—
857C2×C3D4×D1211yescharacteristic
858C2×C3#560911yescharacteristic
859C2×C3#577011yescharacteristic
860C2×C3#577511yescharacteristic
861C2×C3D3×#13711yescharacteristic
862C2×C3D3×#13711yescharacteristic
863D3—42no—
864D3—62no—
865D3—62no—
866D3—81no—
867D3—122no—
868D3—122no—
869D3—121no—
870D3—121no—
871C22—62no—
872C22—92no—
873C22—121no—
874C22—121no—
875C22—121no—
876C22—121no—
877C22—121no—
878C22—181no—
879C22—181no—
880C22—181no—
881C22—181no—
882C22—181no—
883C22—724no—
884C22C2×#381111yescharacteristic
885C4—22no—
886C4—21no—
887C4—21no—
888C4—41no—
889C4—121no—
890C4—121no—
891C4—181no—
892C4—181no—
893C4—361no—
894C4—361no—
895C4C2×D3×D1211yescharacteristic
896C4#6430811yescharacteristic
897C3—21no—
898C3#7979511yescharacteristic, complemented
899C3#8062711yescharacteristic, complemented
900C2—122no—
901C2—182no—
902C2—241no—
903C2—361no—
904C2#1059507411yescharacteristic
905C2#1059532211yescharacteristic
906C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10594005C2
hypercenterC4×Q8D32
hypocenterC32#3266
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. Q8×C4⋊(C3⋊D3)C2semidirect
2. C2×#63951C2semidirect
3. C2×#63940C2semidirect
5. C3×#5028C2semidirect
6. C3×#5026C2semidirect
7. #10591603C2semidirect
8. #10591592C2semidirect
9. #10590618C2semidirect
10. #10590597C2semidirect
11. #10590525C2semidirect
12. #10590506C2semidirect
13. #10590372C2semidirect
14. #10590365C2semidirect
15. #10590328C2semidirect
19. C2×Q8×C3⋊D3C22semidirect
22. C32×C4×Q8C22semidirect
26. #64106C22semidirect
30. #64078C22semidirect
31. C2×C3×#216C22semidirect
44. C2×#3719C22semidirect
45. C2×#3719C22semidirect
50. C2×#3712C22semidirect
52. C3×#835C22semidirect
53. C3×#810C22semidirect
56. C3×#807C22semidirect
57. C3×C4⋊(C3⋊C8)C22semidirect
58. C3×#803C22semidirect
59. #63567C22semidirect
60. #63567C22semidirect
62. #63557C22semidirect
77. #5028D3semidirect
78. #5026D3semidirect
136. C3×#215D4semidirect
172. C3×C4×Q8C2×D3semidirect
173. C3×C4×Q8C2×D3semidirect
178. C2×#216C2×D3semidirect
243. #835C2×D3semidirect
252. #810C2×D3semidirect
255. #807C2×D3semidirect
256. C4⋊(C3⋊C8)C2×D3semidirect
257. #803C2×D3semidirect
417. #215D12semidirect
478. C2×C3⋊D3#137semidirect
527. C4×Q8D32semidirect
803. C32#3266semidirect
898. C3#79795semidirect
899. C3#80627semidirect

Maximal subgroups

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

subgroupindex
Q8×C4⋊(C3⋊D3)2
C2×#639512
C2×#639402
#105940052
C3×#50282
C3×#50262
#105916032
#105915922
#105906182
#105905972
#105905252
#105905062
#105903722
#105903652
#105903282
#806273
#797953