Finite Group Databasebeta

← #11860948

Subgroups — #11860948

Order 1152.

1115 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596045C211yesmaximal, characteristic, complemented
2C2×#63950C211yesmaximal, characteristic
3#10593889C211yesmaximal, characteristic, complemented
4C3×#5030C211yesmaximal, characteristic, complemented
5C3×C4×#215C211yesmaximal, characteristic, complemented
6#10591582C211yesmaximal, characteristic, complemented
7#10591571C211yesmaximal, characteristic, complemented
8#10591554C211yesmaximal, characteristic, complemented
9#10590612C211yesmaximal, characteristic, complemented
10#10590575C211yesmaximal, characteristic, complemented
11#10590483C211yesmaximal, characteristic, complemented
12#10590462C211yesmaximal, characteristic, complemented
13C4×#3717C211yesmaximal, characteristic, complemented
14#10590346C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79832—31nomaximal
17#79650—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22#64102—21no—
23#64102C2211yescharacteristic
24C4⋊C4×C3⋊D3—21no—
25C4⋊C4×C3⋊D3C2211yescharacteristic
26C4×C4⋊(C3⋊D3)—21no—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64081—21no—
29#64081C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63950C418yescomplemented
35#63904—21no—
36#63900C2211yescharacteristic
37#63898C2211yescharacteristic
38#63880—21no—
39#63877—21no—
40D3×Dic3⋊C4—21no—
41#63843C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#803C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56#63566C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63555C2211yescharacteristic
61#63553C2211yescharacteristic
62C2×#919—31no—
63C2×#916—31no—
64#5574—31no—
65#5574—31no—
66#5574—31no—
67#5574—61no—
68#5546—31no—
69C3×#441—31no—
70C3×C4×SD16—31no—
71#5184—31no—
72Dic3×SD16—31no—
73#5030D311yescharacteristic, complemented
74C4×#215—31no—
75C4×#215D311yescharacteristic, complemented
76#5014—31no—
77#4869—31no—
78D3×#106—31no—
79D3×#106—31no—
80#4852—31no—
81#4803—31no—
82#4803—31no—
83#4803—31no—
84#4789—31no—
85#4788—31no—
86#4788—31no—
87#4785—31no—
88#4771—31no—
89#4711—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C2×C32×Q8C2311yescharacteristic
94#3832—22no—
95#3832C2×C414yescomplemented
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3—21no—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796C2×C414yescomplemented
112C32×C4⋊C4—21no—
113C32×C4⋊C4C2311yescharacteristic
114C32×C42—21no—
115C32×C42C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118#3752D411yescharacteristic
119#3752D411yescharacteristic
120C4⋊(C3⋊Dic3)—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122#3750—21no—
123#3750D411yescharacteristic
124#3750D411yescharacteristic
125C4×C3⋊Dic3—21no—
126C4×C3⋊Dic3C2311yescharacteristic
127C3×#216C2×C414yescomplemented
128C3×#215C2×C414yescomplemented
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3724—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3717C2×C414yescomplemented
143#3714C2×C414yescomplemented
144#3712—22no—
145#3710C2×C414yescomplemented
146#2952—91noSylow
147C2×#239—31no—
148C2×#239—31no—
149C2×#239—31no—
150C2×#239—61no—
151C2×#237—31no—
152C2×C3×Q16—31no—
153C2×C3×SD16—31no—
154C3×C4×Q8—21no—
155C3×C4×Q8—31no—
156C3×C4×Q8C2×D311yescharacteristic
157C3×C4×Q8C2×D311yescharacteristic
158C3×C4×D4—31no—
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162Q8×Dic3—61no—
163C2×#216C2×D311yescharacteristic
164C2×#215—31no—
165C2×#215C2×D311yescharacteristic
166D4×Dic3—31no—
167C2×#213—31no—
168C4×#67—61no—
169C2×Dic3⋊C4—61no—
170#919—38no—
171#916—38no—
172C2×D24—31no—
173C2×#204—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)—31no—
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178#893—31no—
179#893—31no—
180#893—31no—
181#893—61no—
182#893—61no—
183#893—61no—
184#893—61no—
185#893—62no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—61no—
191D3×C4⋊C4—61no—
192D3×C4⋊C4—61no—
193D3×C4⋊C4—61no—
194D3×C4⋊C4—62no—
195#887—31no—
196#67⋊C4—61no—
197#877—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—61no—
201C4×D12—61no—
202C4×D12—61no—
203C4×D12—61no—
204C4×D12—62no—
205C4×D12C2×D311yescharacteristic
206#872—31no—
207#872—31no—
208#872—61no—
209#872—61no—
210#872—61no—
211#872—61no—
212#872—62no—
213C4×Dic6C2×D311yescharacteristic
214C3×#106—31no—
215C3×#106—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103—31no—
219C3×#102—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222#835—31no—
223#835C2×D311yescharacteristic
224#835C2×D311yescharacteristic
225#832—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229#817—31no—
230#817—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810C2×D311yescharacteristic
237#809—31no—
238#809—31no—
239#809C2×D311yescharacteristic
240#808—31no—
241#808—31no—
242#808C2×D311yescharacteristic
243#808C2×D311yescharacteristic
244#803C2×D311yescharacteristic
245C4×C3⋊C8C2×D311yescharacteristic
246C22×C3⋊D3—21no—
247C22×C3⋊D3C2×D411yescharacteristic
248C22×C3×D3—21no—
249C32×Q8—21no—
250C32×Q8C22×C412yes—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4⋊(C3⋊D3)—24no—
261C4⋊(C3⋊D3)—21no—
262C4⋊(C3⋊D3)C22×C412yes—
263C4×C3⋊D3—24no—
264C4×C3⋊D3—81no—
265C4×C3⋊D3—81no—
266C4×C3⋊D3—81no—
267C4×C3⋊D3C22×C412yes—
268C4×C3⋊D3#4112yes—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C3×D12—21no—
273C3×D12C22×C412yes—
274C3×C4×D3—81no—
275C3×Dic6—21no—
276C3×Dic6C22×C412yes—
277#626—24no—
278#624—81no—
279D3×Dic3—24no—
280D3×Dic3—81no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8C22×C412yes—
284C3×C3⋊C8C22×C412yes—
285C2×#135—91no—
286#520—91no—
287#520—91no—
288#442—91no—
289#442—91no—
290#441—31no—
291#441—91no—
292C4×SD16—31no—
293C4×SD16—91no—
294C4×SD16—91no—
295C4×SD16—91no—
296C2×#106—91no—
297#417—91no—
298#417—91no—
299#405—91no—
300C2×C3×Q8—21no—
301C2×C3×Q8—31no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C22×C3×C4—61no—
306C2×#67—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309#239—34no—
310#239—34no—
311#239—34no—
312#239—64no—
313#239—62no—
314#239—62no—
315#239—62no—
316#239—64no—
317#237—34no—
318#237—62no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—62no—
325C2×D12—61no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—31no—
329C2×C4×D3—31no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—62no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—62no—
343C2×C4×D3—62no—
344C2×C4×D3—62no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×Dic6C22×D311yescharacteristic
348C3×Q16—34no—
349C3×SD16—34no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C3×C4⋊C4—22no—
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—61no—
364C3×C42—22no—
365C3×C42—21no—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—61no—
369C3×C42C22×D311yescharacteristic
370C3×C42C22×D311yescharacteristic
371#217—61no—
372#216C4×D314yescomplemented
373#215—34no—
374#215C4×D314yescomplemented
375#213—34no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—62no—
387(C2×D3)⋊C4—62no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—62no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—31no—
403Dic3⋊C4—31no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—62no—
412C4×Dic3—21no—
413C4×Dic3—31no—
414C4×Dic3—31no—
415C4×Dic3—61no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—62no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425D24—34no—
426#204—34no—
427ΓL(1,𝔽25)—62no—
428ΓL(1,𝔽25)—62no—
429D3×C8—34no—
430D3×C8—34no—
431C22×C32C22×D411yescharacteristic
432C2×C3⋊D3—22no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—21no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3⋊D3C4×D412yes—
438C2×C3×D3—22no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C32×C4—22no—
442C32×C4—21no—
443C32×C4—21no—
444C32×C4—41no—
445C32×C4C23×C411yescharacteristic
446C32×C4C2×#4111yescharacteristic
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—41no—
450C3⋊Dic3C4×D412yes—
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C2×#41—91no—
455C2×#41—91no—
456#135—98no—
457C2×Q16—31no—
458C2×SD16—31no—
459C2×SD16—91no—
460C2×D8—91no—
461C2×M16—91no—
462C22×C8—91no—
463C4×Q8—31no—
464C4×Q8—91no—
465C4×Q8—91no—
466C4×Q8D3211yescharacteristic
467C4×D4—31no—
468C4×D4—91no—
469C4×D4—91no—
470C4×D4—91no—
471C4×D4—181no—
472C4×D4—181no—
473C4×D4—181no—
474C4×D4—181no—
475#117—91no—
476#117—181no—
477#117—181no—
478C2×C4⋊C4—91no—
479C2×C4⋊C4—91no—
480C2×C4⋊C4—181no—
481C2×C4⋊C4—181no—
482#106—31no—
483#106—31no—
484#106—91no—
485#106—91no—
486#103—31no—
487#103—31no—
488#103—31no—
489#103—91no—
490#102—31no—
491#102—91no—
492#102—91no—
493#102—91no—
494#97—31no—
495#97—91no—
496C4×C8—31no—
497C4×C8—91no—
498C23×C3—61no—
499C22×D3—21no—
500C22×D3—31no—
501C22×D3—31no—
502C22×D3—61no—
503C22×D3—62no—
504C22×D3—61no—
505C22×D3—61no—
506C3×Q8—22no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—22no—
510C3×Q8—32no—
511C3×Q8—61no—
512C3×Q8C2×C4×D312yes—
513C3×Q8C2×C4×D312yes—
514C3×D4—32no—
515C3×D4—61no—
516C2×C3×C4—22no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—22no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—241no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535#67—64no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—64no—
549C2×Dic3—62no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—241no—
553D12—21no—
554D12—32no—
555D12—32no—
556D12—62no—
557D12—64no—
558D12—64no—
559D12—68no—
560D12—62no—
561D12—64no—
562D12—61no—
563D12—61no—
564D12C2×C4×D312yes—
565C4×D3—32no—
566C4×D3—32no—
567C4×D3—32no—
568C4×D3—32no—
569C4×D3—62no—
570C4×D3—62no—
571C4×D3—64no—
572C4×D3—64no—
573C4×D3—64no—
574C4×D3—68no—
575C4×D3—81no—
576C4×D3—241no—
577C4×D3—241no—
578C4×D3—241no—
579C4×D3—241no—
580C4×D3—241no—
581C4×D3—241no—
582C4×D3—241no—
583C4×D3—241no—
584C4×D3—241no—
585C4×D3—242no—
586C4×D3—242no—
587C4×D3—242no—
588Dic6—21no—
589Dic6C2×C4×D312yes—
590C3×C8—32no—
591C3×C8—32no—
592C3×C8—61no—
593C3×C8—61no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8C2×C4×D312yes—
597C3⋊C8C2×C4×D312yes—
598C2×C32C2×C4×D411yescharacteristic
599C2×C32#57711yescharacteristic
600C2×C32#57711yescharacteristic
601C3⋊D3—22no—
602C3⋊D3—42no—
603C3×D3—42no—
604#41—94no—
605#41—94no—
606#41—182no—
607#41—182no—
608C2×Q8—31no—
609C2×Q8C2×D3211yescharacteristic
610C2×D4—31no—
611C2×D4—91no—
612C2×D4—181no—
613C2×D4—181no—
614C22×C4—61no—
615C22×C4—91no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623Q16—34no—
624SD16—34no—
625SD16—94no—
626D8—94no—
627M16—182no—
628C2×C8—31no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—94no—
633C4⋊C4—21no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—91no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4C2×D3211yescharacteristic
645C22⋊C4—61no—
646C22⋊C4—91no—
647C22⋊C4—91no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C42—21no—
652C42—61no—
653C42—91no—
654C42—181no—
655C42—181no—
656C42C2×D3211yescharacteristic
657C22×C3—21no—
658C22×C3—62no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C2×D3×D411yescharacteristic
663C2×D3—22no—
664C2×D3—32no—
665C2×D3—32no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—62no—
669C2×D3—61no—
670C2×D3—61no—
671C2×D3—61no—
672C2×D3—61no—
673C2×D3—64no—
674C2×D3—62no—
675C2×D3—62no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—122no—
679C2×D3—122no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C3×C4—24no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—22no—
690C3×C4—22no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—42no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—62no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4C22×C4×D311yescharacteristic
702C3×C4C22×C4×D311yescharacteristic
703C3×C4D3×#4111yescharacteristic
704C3×C4D3×#4111yescharacteristic
705Dic3—22no—
706Dic3—32no—
707Dic3—32no—
708Dic3—41no—
709Dic3—41no—
710Dic3—62no—
711Dic3—61no—
712Dic3—61no—
713Dic3—61no—
714Dic3—61no—
715Dic3—121no—
716Dic3—121no—
717Dic3—122no—
718Dic3—121no—
719Dic3—121no—
720C32#295211yescharacteristic, complemented, Sylow
721C23—61no—
722C23—91no—
723C23—181no—
724Q8—21no—
725Q8—32no—
726Q8—61no—
727Q8C4×D3212yes—
728D4—32no—
729D4—61no—
730D4—92no—
731D4—184no—
732D4—184no—
733D4—181no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—91no—
740C2×C4—92no—
741C2×C4—92no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—184no—
745C2×C4—184no—
746C2×C4—181no—
747C2×C4—241no—
748C2×C4—721no—
749C2×C4—721no—
750C2×C4—721no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4#381111yescharacteristic
754C2×C4#381111yescharacteristic
755C2×C4C22×D3211yescharacteristic
756C8—32no—
757C8—32no—
758C8—61no—
759C8—61no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—122no—
764C2×C3C4×D3×D411yescharacteristic
765C2×C3C4×D3×D411yescharacteristic
766C2×C3#576211yescharacteristic
767C2×C3#577011yescharacteristic
768C2×C3#577811yescharacteristic
769C2×C3#577811yescharacteristic
770D3—42no—
771D3—62no—
772D3—62no—
773D3—122no—
774D3—124no—
775D3—122no—
776D3—122no—
777C22—62no—
778C22—92no—
779C22—121no—
780C22—121no—
781C22—181no—
782C22—181no—
783C22—182no—
784C22—361no—
785C22—361no—
786C22C2×#381111yescharacteristic
787C4—21no—
788C4—22no—
789C4—21no—
790C4—41no—
791C4—62no—
792C4—92no—
793C4—121no—
794C4—121no—
795C4—181no—
796C4—181no—
797C4—361no—
798C4C2×C4×D3211yescharacteristic
799C4#6430611yescharacteristic
800C3—21no—
801C3#7965011yescharacteristic, complemented
802C3#7983211yescharacteristic, complemented
803C2—122no—
804C2—182no—
805C2—362no—
806C2C4×#381111yescharacteristic
807C2#1059532411yescharacteristic
808C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#63950C2
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. #10596045C2semidirect
3. #10593889C2semidirect
4. C3×#5030C2semidirect
5. C3×C4×#215C2semidirect
6. #10591582C2semidirect
7. #10591571C2semidirect
8. #10591554C2semidirect
9. #10590612C2semidirect
10. #10590575C2semidirect
11. #10590483C2semidirect
12. #10590462C2semidirect
13. C4×#3717C2semidirect
14. #10590346C2semidirect
15. #10590321C2semidirect
34. #63950C4semidirect
73. #5030D3semidirect
75. C4×#215D3semidirect
95. #3832C2×C4semidirect
111. #3796C2×C4semidirect
127. C3×#216C2×C4semidirect
128. C3×#215C2×C4semidirect
142. #3717C2×C4semidirect
143. #3714C2×C4semidirect
145. #3710C2×C4semidirect
372. #216C4×D3semidirect
374. #215C4×D3semidirect
720. C32#2952semidirect
801. C3#79650semidirect
802. C3#79832semidirect

Maximal subgroups

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

subgroupindex
#105960452
C2×#639502
#105938892
C3×#50302
C3×C4×#2152
#105915822
#105915712
#105915542
#105906122
#105905752
#105904832
#105904622
C4×#37172
#105903462
#105903212
#798323
#796503