Finite Group Databasebeta

← #11860949

Subgroups — #11860949

Order 1152.

1022 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5574C211yesmaximal, characteristic, complemented
2C2×#63947C211yesmaximal, characteristic
3#10593887C211yesmaximal, characteristic, complemented
4#10592729C211yesmaximal, characteristic, complemented
5C3×C4×#215C211yesmaximal, characteristic, complemented
6Dic3×#215C211yesmaximal, characteristic, complemented
7#10591550C211yesmaximal, characteristic, complemented
8#10591541C211yesmaximal, characteristic, complemented
9#10590607C211yesmaximal, characteristic, complemented
10D3×#808C211yesmaximal, characteristic, complemented
11#10590479C211yesmaximal, characteristic, complemented
12#10590455C211yesmaximal, characteristic, complemented
13C4×#3716C211yesmaximal, characteristic, complemented
14#10590344C211yesmaximal, characteristic, complemented
15#10590318C211yesmaximal, characteristic, complemented
16#82558—31nomaximal
17#79650—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#893—21no—
26C3×#893C2211yescharacteristic
27C3×D3×C4⋊C4—21no—
28C3×D3×C4⋊C4C2211yescharacteristic
29C3×C4×D12—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×#872—21no—
33C3×#872C2211yescharacteristic
34#63947C418yescomplemented
35#63902—21no—
36Dic3×D12C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38#63879—21no—
39#63878—21no—
40D3×Dic3⋊C4—21no—
41#63844C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic
47#63637C2211yescharacteristic
48#63635C2211yescharacteristic
49#63630C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56#63567C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C3×#520—31no—
63C2×#950—31no—
64C2×#916—31no—
65#5574D311yescharacteristic, complemented
66#5546—31no—
67#5523—31no—
68C3×C4×SD16—31no—
69#5232—31no—
70Dic3×SD16—31no—
71#5030—31no—
72#5030—31no—
73#5030—31no—
74#5030—61no—
75C4×#215—31no—
76C4×#215D311yescharacteristic, complemented
77C4×#214—31no—
78C4×#214—31no—
79#5014—31no—
80#5014—31no—
81#5014—31no—
82#4997—31no—
83#4966—31no—
84C2×#808—31no—
85D3×#106—31no—
86#4852—31no—
87#4803—31no—
88#4789—31no—
89#4785—31no—
90#4771—31no—
91C4×#204—31no—
92#4689—31no—
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×#239—22no—
96C3×#239C2×C414yescomplemented
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#625—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795C2×C414yescomplemented
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C42—21no—
115C32×C42C2311yescharacteristic
116#3756C2×C414yescomplemented
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#215C2×C414yescomplemented
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3724—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3716C2×C414yescomplemented
143#3713C2×C414yescomplemented
144#3711—22no—
145D3×C3⋊C8C2×C414yescomplemented
146#2952—91noSylow
147C2×C3×#41—31no—
148C2×#239C2×D311yescharacteristic
149C2×#237—31no—
150C2×#235—31no—
151C2×C3×SD16—31no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8C2×D311yescharacteristic
155C3×C4×Q8C2×D311yescharacteristic
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C3×C4×D4—61no—
161C3×#117—31no—
162C3×#117—61no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—61no—
165#950—38no—
166Q8×Dic3C2×D311yescharacteristic
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—61no—
170C2×#215C2×D311yescharacteristic
171D4×Dic3—31no—
172C2×#214—31no—
173C2×#213—31no—
174C2×#213—31no—
175C4×#67—61no—
176C2×C4⋊Dic3—31no—
177C2×Dic3⋊C4—61no—
178C2×#208—31no—
179C22×C3⋊C8—31no—
180#916—38no—
181C2×#204—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×D3×C8—31no—
184#893—21no—
185#893C2×D311yescharacteristic
186#892—61no—
187D3×C4⋊C4—21no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190D3×C4⋊C4C2×D311yescharacteristic
191#887—31no—
192#67⋊C4—61no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195#877—61no—
196C4×D12—21no—
197C4×D12—31no—
198C4×D12C2×D311yescharacteristic
199C4×D12C2×D311yescharacteristic
200#872—21no—
201#872C2×D311yescharacteristic
202C4×Dic6—31no—
203C4×Dic6—31no—
204C4×Dic6—31no—
205C4×Dic6—61no—
206C3×#106—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×C4×C8—31no—
210#835—31no—
211#835—31no—
212#835—61no—
213#835C2×D311yescharacteristic
214#832—31no—
215#832—31no—
216#832—31no—
217#821—31no—
218#817—31no—
219#816—31no—
220#815—31no—
221C8×Dic3—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—61no—
226#809—31no—
227#809—31no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—61no—
235#808C2×D311yescharacteristic
236#803—31no—
237#803—31no—
238#803—31no—
239#803—61no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8C2×D311yescharacteristic
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3C2×D411yescharacteristic
245C32×Q8—21no—
246C32×Q8C22×C412yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254#634—21no—
255#634C22×C412yes—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—24no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12C22×C412yes—
265C3×D12C22×C412yes—
266C3×C4×D3—24no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
271C3×C4×D3C22×C412yes—
272C3×C4×D3#4112yes—
273#625—24no—
274D3×Dic3—24no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282#520—31no—
283#520—91no—
284#442—91no—
285#442—91no—
286#441—91no—
287#441—91no—
288C4×SD16—31no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292C2×#106—91no—
293#417—91no—
294#417—91no—
295#405—91no—
296C3×#41—34no—
297C3×#41—62no—
298C2×C3×Q8—21no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C2×#67—61no—
311C2×#67—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315#239—22no—
316#239C4×D314yescomplemented
317#237—34no—
318#237—62no—
319#235—34no—
320#235—62no—
321C2×D12—21no—
322C2×D12C22×D311yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C3×SD16—34no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—41no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—31no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—21no—
357C3×C42—21no—
358C3×C42—21no—
359C3×C42—31no—
360C3×C42—41no—
361C3×C42—61no—
362C3×C42C22×D311yescharacteristic
363C3×C42C22×D311yescharacteristic
364#217—61no—
365#216—34no—
366#216—34no—
367#216—64no—
368#215C4×D314yescomplemented
369#214—34no—
370#213—34no—
371#213—34no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4#6711yescharacteristic
377(C2×D3)⋊C4#6711yescharacteristic
378C4⋊Dic3—21no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—121no—
392Dic3⋊C4#6711yescharacteristic
393Dic3⋊C4#6711yescharacteristic
394C4×Dic3—21no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—121no—
400C4×Dic3C22×D311yescharacteristic
401#208—62no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—34no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204—34no—
412ΓL(1,𝔽25)—62no—
413D3×C8—34no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3C4×D412yes—
424C32×C4—22no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4—41no—
428C32×C4C23×C411yescharacteristic
429C32×C4C2×#4111yescharacteristic
430C3⋊Dic3—22no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3C4×D412yes—
437C2×#41—31no—
438C2×#41—91no—
439#135—98no—
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×D8—91no—
444C2×M16—91no—
445C22×C8—91no—
446C4×Q8—31no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×Q8D3211yescharacteristic
450C4×D4—31no—
451C4×D4—31no—
452C4×D4—31no—
453C4×D4—61no—
454C4×D4—61no—
455C4×D4—91no—
456C4×D4—181no—
457C4×D4—181no—
458#117—31no—
459#117—61no—
460#117—181no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—61no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—181no—
465#106—31no—
466#106—91no—
467#106—91no—
468#106—91no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#97—91no—
478#97—91no—
479C4×C8—31no—
480C4×C8—91no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—21no—
486C22×D3C2×#6711yescharacteristic
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—22no—
490C3×Q8—41no—
491C3×Q8C2×C4×D312yes—
492C3×Q8C2×C4×D312yes—
493C3×D4—32no—
494C3×D4—32no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4—61no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—32no—
507C2×C3×C4—32no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—64no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—241no—
516C2×C3×C4—241no—
517C2×C3×C4—241no—
518C2×C3×C4—241no—
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C2×#6711yescharacteristic
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525#67—64no—
526#67—64no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—64no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—241no—
537C2×Dic3—241no—
538C2×Dic3C2×#6711yescharacteristic
539C2×Dic3C2×#6711yescharacteristic
540C2×Dic3C2×#6711yescharacteristic
541D12—24no—
542D12—21no—
543D12—21no—
544D12C2×C4×D312yes—
545D12C2×C4×D312yes—
546C4×D3—24no—
547C4×D3—64no—
548C4×D3—81no—
549C4×D3—81no—
550C4×D3—81no—
551C4×D3—81no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3C2×C4×D312yes—
555C4×D3#23512yes—
556Dic6—32no—
557Dic6—32no—
558Dic6—62no—
559Dic6—61no—
560Dic6—61no—
561Dic6—121no—
562C3×C8—32no—
563C3×C8—61no—
564C3⋊C8—21no—
565C3⋊C8—32no—
566C3⋊C8—32no—
567C3⋊C8—62no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C3⋊C8C2×C4×D312yes—
572C2×C32C2×C4×D411yescharacteristic
573C2×C32#57711yescharacteristic
574C2×C32#57711yescharacteristic
575C3×D3—22no—
576C3×D3—42no—
577C3×D3—42no—
578#41—34no—
579#41—62no—
580#41—94no—
581#41—182no—
582C2×Q8—91no—
583C2×Q8C2×D3211yescharacteristic
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—181no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597Q16—94no—
598SD16—34no—
599SD16—94no—
600D8—94no—
601M16—182no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—94no—
605C2×C8—91no—
606C2×C8—91no—
607C4⋊C4—21no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4C2×D3211yescharacteristic
619C22⋊C4—31no—
620C22⋊C4—31no—
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—181no—
625C42—21no—
626C42—31no—
627C42—61no—
628C42—181no—
629C42—181no—
630C42C2×D3211yescharacteristic
631C22×C3—21no—
632C22×C3—32no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—62no—
636C22×C3—62no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C22×#6711yescharacteristic
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—22no—
646C2×D3—22no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3C4×#6712yes—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—22no—
655C3×C4—22no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—32no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—42no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—81no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4C22×C4×D311yescharacteristic
672C3×C4C22×C4×D311yescharacteristic
673C3×C4C2×#23511yescharacteristic
674C3×C4D3×#4111yescharacteristic
675Dic3—21no—
676Dic3—21no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—62no—
681Dic3—122no—
682Dic3—121no—
683Dic3—121no—
684Dic3—241no—
685Dic3C4×#6712yes—
686C32#295211yescharacteristic, complemented, Sylow
687C23—31no—
688C23—61no—
689C23—61no—
690Q8—21no—
691Q8—92no—
692Q8—181no—
693Q8C4×D3212yes—
694D4—32no—
695D4—32no—
696D4—64no—
697D4—61no—
698D4—61no—
699D4—184no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—32no—
704C2×C4—32no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—64no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—184no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—241no—
714C2×C4—241no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4D3×#6711yescharacteristic
720C2×C4D3×#6711yescharacteristic
721C2×C4C22×D3211yescharacteristic
722C8—32no—
723C8—61no—
724C8—92no—
725C8—181no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—62no—
730C2×C3—122no—
731C2×C3—122no—
732C2×C3C4×D3×D411yescharacteristic
733C2×C3#576211yescharacteristic
734C2×C3#577011yescharacteristic
735C2×C3C2×C4×#6711yescharacteristic
736C2×C3#583611yescharacteristic
737C2×C3#583711yescharacteristic
738D3—22no—
739D3—42no—
740D3—42no—
741C22—32no—
742C22—61no—
743C22—61no—
744C22—62no—
745C22—62no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22C2×D3×#6711yescharacteristic
751C4—21no—
752C4—22no—
753C4—21no—
754C4—32no—
755C4—41no—
756C4—61no—
757C4—61no—
758C4—121no—
759C4—121no—
760C4—182no—
761C4—361no—
762C4C2×C4×D3211yescharacteristic
763C4D3×#23511yescharacteristic
764C3—21no—
765C3#7965011yescharacteristic, complemented
766C3#8255811yescharacteristic, complemented
767C2—62no—
768C2—122no—
769C2—122no—
770C2C4×D3×#6711yescharacteristic
771C2#1059531811yescharacteristic
772C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#63947C2
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32#2952
LCSG ▷ 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×#5574C2semidirect
3. #10593887C2semidirect
4. #10592729C2semidirect
5. C3×C4×#215C2semidirect
6. Dic3×#215C2semidirect
7. #10591550C2semidirect
8. #10591541C2semidirect
9. #10590607C2semidirect
10. D3×#808C2semidirect
11. #10590479C2semidirect
12. #10590455C2semidirect
13. C4×#3716C2semidirect
14. #10590344C2semidirect
15. #10590318C2semidirect
34. #63947C4semidirect
65. #5574D3semidirect
76. C4×#215D3semidirect
96. C3×#239C2×C4semidirect
111. #3795C2×C4semidirect
116. #3756C2×C4semidirect
122. C3×#215C2×C4semidirect
142. #3716C2×C4semidirect
143. #3713C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
316. #239C4×D3semidirect
368. #215C4×D3semidirect
686. C32#2952semidirect
765. C3#79650semidirect
766. C3#82558semidirect

Maximal subgroups

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

subgroupindex
C3×#55742
C2×#639472
#105938872
#105927292
C3×C4×#2152
Dic3×#2152
#105915502
#105915412
#105906072
D3×#8082
#105904792
#105904552
C4×#37162
#105903442
#105903182
#825583
#796503