Finite Group Databasebeta

← #11860971

Subgroups — #11860971

Order 1152.

1049 conjugacy classes of subgroups.

The subgroup lattice has 787 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595219C211yesmaximal, characteristic, complemented
2C2×#63936C211yesmaximal, characteristic
3#10594361C211yesmaximal, characteristic, complemented
4#10592470C211yesmaximal, characteristic, complemented
5C3×#4785C211yesmaximal, characteristic, complemented
6C3×#4758C211yesmaximal, characteristic, complemented
7Dic3×#214C211yesmaximal, characteristic, complemented
8#10591430C211yesmaximal, characteristic, complemented
9#10590957C211yesmaximal, characteristic, complemented
10#10590910C211yesmaximal, characteristic, complemented
11#10590794C211yesmaximal, characteristic, complemented
12#10590744C211yesmaximal, characteristic, complemented
13#10590575C211yesmaximal, characteristic, complemented
14#10590480C211yesmaximal, characteristic, complemented
15#10590479C211yesmaximal, characteristic, complemented
16#79868—31nomaximal
17#79650—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C2×#3724—21no—
29#63957—21no—
30#63952—21no—
31#63952—21no—
32#63936C418yescomplemented
33C4×#626—21no—
34#63900C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63881—21no—
37#63877—21no—
38D3×Dic3⋊C4—21no—
39#63874C2211yescharacteristic
40#63844C2211yescharacteristic
41#63844C2211yescharacteristic
42Dic3×Dic6C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44C2×#3716C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63659C2211yescharacteristic
48#63643C2211yescharacteristic
49#63637C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#808C2211yescharacteristic
55C3×#808C2211yescharacteristic
56#63573C2211yescharacteristic
57#63573C2211yescharacteristic
58#63565C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic
61Dic3×C3⋊C8C2211yescharacteristic
62C2×#916—31no—
63C2×#912—31no—
64#5574—31no—
65#5546—31no—
66#5546—31no—
67#5546—31no—
68C3×#442—31no—
69C3×C4×SD16—31no—
70Dic3×SD16—31no—
71#5152—31no—
72#5030—31no—
73C4×#214—31no—
74C4×#214—31no—
75#5014—31no—
76D3×#106—31no—
77D3×#106—31no—
78#4853—31no—
79#4852—31no—
80#4803—31no—
81#4789—31no—
82#4785D311yescharacteristic, complemented
83#4771—31no—
84#4771—31no—
85#4771—31no—
86#4771—61no—
87#4758—31no—
88#4758D311yescharacteristic, complemented
89#4716—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C22×C3⋊Dic3—21no—
96#3830—22no—
97#3830C2×C414yescomplemented
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
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
112C2×C32×C8C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117#3743—22no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#214C2×C414yescomplemented
121C3×#213C2×C414yescomplemented
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133#3724—21no—
134#3724D411yescharacteristic
135#3724D411yescharacteristic
136Dic3⋊Dic3—21no—
137#3722D411yescharacteristic
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143#3719C2×C414yescomplemented
144#3716C2×C414yescomplemented
145#3710C2×C414yescomplemented
146#2952—91noSylow
147C2×#239—31no—
148C2×#237—31no—
149C2×#237—31no—
150C2×#237—31no—
151C2×#237—61no—
152C2×C3×SD16—31no—
153C2×C3×D8—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158Q8×Dic3—31no—
159C2×#216—31no—
160D4×Dic3—31no—
161D4×Dic3C2×D311yescharacteristic
162D4×Dic3C2×D311yescharacteristic
163C2×#214—31no—
164C2×#214C2×D311yescharacteristic
165C2×#213C2×D311yescharacteristic
166C4×#67—61no—
167C4×#67—61no—
168C4×#67—61no—
169C2×Dic3⋊C4—61no—
170C2×Dic3⋊C4—61no—
171C2×Dic3⋊C4—61no—
172#916—38no—
173#912—38no—
174C2×Dic12—31no—
175C2×#204—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×ΓL(1,𝔽25)—31no—
178C2×ΓL(1,𝔽25)—61no—
179C2×D3×C8—31no—
180C2×D3×C8—31no—
181#893—61no—
182#893C2×D311yescharacteristic
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—31no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—61no—
188D3×C4⋊C4—61no—
189#887—31no—
190#887—31no—
191#887C2×D311yescharacteristic
192#67⋊C4—61no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195#877—61no—
196#877—61no—
197#877—61no—
198C4×D12—31no—
199C4×D12—61no—
200#872—31no—
201#872—31no—
202#872—61no—
203C4×Dic6—31no—
204C4×Dic6—31no—
205C4×Dic6—31no—
206C3×#106—31no—
207C3×#106—31no—
208C3×#103—31no—
209C3×#102—21no—
210C3×#102—31no—
211C3×#102C2×D311yescharacteristic
212C3×#102C2×D311yescharacteristic
213C3×#97—31no—
214C3×C4×C8—31no—
215#835—31no—
216#832—31no—
217#832—31no—
218#832—31no—
219#832—61no—
220#821C2×D311yescharacteristic
221#817—31no—
222#817—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#816C2×D311yescharacteristic
227#815—31no—
228#815C2×D311yescharacteristic
229C8×Dic3—31no—
230C8×Dic3C2×D311yescharacteristic
231#810—31no—
232#810—31no—
233#810—31no—
234#810—61no—
235#809—31no—
236#808—31no—
237#808—31no—
238#808C2×D311yescharacteristic
239#808C2×D311yescharacteristic
240#803—31no—
241C4×C3⋊C8—31no—
242C23×C32—21no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3—21no—
245C32×D4—21no—
246C32×D4C22×C412yes—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—24no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—24no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4×C3⋊D3—81no—
255C4×C3⋊D3C22×C412yes—
256C4×C3⋊D3#4112yes—
257#634—21no—
258#634C22×C412yes—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—81no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12C22×C412yes—
270C3×C4×D3—81no—
271C3×Dic6—21no—
272C3×Dic6C22×C412yes—
273#626—24no—
274#624—81no—
275D3×Dic3—24no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8C22×C412yes—
280C3×C3⋊C8C22×C412yes—
281C2×#135—91no—
282#520—91no—
283#520—91no—
284#442—31no—
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—
296C2×C3×Q8—31no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—121no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—121no—
315#239—34no—
316#239—62no—
317#237—34no—
318#237—34no—
319#237—34no—
320#237—64no—
321#237—62no—
322#237—62no—
323#237—62no—
324#237—122no—
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—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—121no—
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C2×Dic6C22×D311yescharacteristic
342C3×SD16—34no—
343C3×D8—34no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—31no—
359C3×C42—31no—
360C3×C42—61no—
361#217—21no—
362#217—21no—
363#217—61no—
364#216—34no—
365#214—34no—
366#214C4×D314yescomplemented
367#213C4×D314yescomplemented
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—61no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—31no—
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—121no—
395C4×Dic3—21no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3C22×D311yescharacteristic
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409Dic12—34no—
410#204—34no—
411ΓL(1,𝔽25)—62no—
412ΓL(1,𝔽25)—62no—
413ΓL(1,𝔽25)—122no—
414D3×C8—34no—
415D3×C8—34no—
416C22×C32—22no—
417C22×C32—41no—
418C22×C32—41no—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—21no—
421C2×C3⋊D3—21no—
422C2×C3⋊D3C4×D412yes—
423C2×C3×D3—22no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C32×C4—41no—
427C32×C4C23×C411yescharacteristic
428C32×C4C2×#4111yescharacteristic
429C3⋊Dic3—22no—
430C3⋊Dic3—41no—
431C3⋊Dic3C4×D412yes—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C2×#41—91no—
441#135—98no—
442C2×Q16—91no—
443C2×SD16—31no—
444C2×SD16—91no—
445C2×D8—31no—
446C2×M16—91no—
447C22×C8—91no—
448C4×Q8—31no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×Q8—91no—
452C4×D4—31no—
453C4×D4—31no—
454C4×D4—31no—
455C4×D4—91no—
456C4×D4—181no—
457C4×D4—181no—
458C4×D4—181no—
459C4×D4—181no—
460#117—91no—
461#117—181no—
462#117—181no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465C2×C4⋊C4—181no—
466C2×C4⋊C4—181no—
467#106—31no—
468#106—31no—
469#106—91no—
470#106—91no—
471#103—31no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—31no—
476#102—91no—
477#102—91no—
478#102D3211yescharacteristic
479#97—31no—
480#97—91no—
481C4×C8—31no—
482C4×C8—91no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—41no—
486C23×C3—61no—
487C22×D3—21no—
488C22×D3—31no—
489C22×D3—31no—
490C22×D3—61no—
491C3×Q8—32no—
492C3×Q8—61no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—22no—
496C3×D4—32no—
497C3×D4—41no—
498C3×D4—61no—
499C3×D4C2×C4×D312yes—
500C3×D4C2×C4×D312yes—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—41no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—241no—
513C2×C3×C4—241no—
514C2×C3×C4—241no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—64no—
518#67—64no—
519#67—64no—
520#67—124no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—61no—
527C2×Dic3—64no—
528C2×Dic3—64no—
529C2×Dic3—64no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—81no—
535C2×Dic3—81no—
536C2×Dic3—124no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—241no—
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544D12—21no—
545D12—64no—
546D12C2×C4×D312yes—
547C4×D3—32no—
548C4×D3—32no—
549C4×D3—32no—
550C4×D3—32no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—64no—
554C4×D3—81no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—242no—
561Dic6—21no—
562Dic6—32no—
563Dic6—32no—
564Dic6—62no—
565Dic6—61no—
566Dic6—61no—
567Dic6—121no—
568Dic6C2×C4×D312yes—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—32no—
572C3×C8—32no—
573C3×C8—41no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C3⋊C8C2×C4×D312yes—
578C3⋊C8C2×C4×D312yes—
579C2×C32—42no—
580C2×C32C2×C4×D411yescharacteristic
581C2×C32#57711yescharacteristic
582C2×C32#57711yescharacteristic
583C3⋊D3—22no—
584C3×D3—42no—
585#41—94no—
586#41—94no—
587#41—182no—
588#41—182no—
589C2×Q8—31no—
590C2×Q8—91no—
591C2×D4—31no—
592C2×D4—181no—
593C2×D4—181no—
594C2×D4C2×D3211yescharacteristic
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—61no—
598C22×C4—91no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604Q16—94no—
605SD16—34no—
606SD16—94no—
607D8—34no—
608M16—182no—
609C2×C8—31no—
610C2×C8—31no—
611C2×C8—94no—
612C2×C8—91no—
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4C2×D3211yescharacteristic
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—61no—
629C22⋊C4—91no—
630C22⋊C4—91no—
631C22⋊C4—181no—
632C42—31no—
633C42—31no—
634C42—61no—
635C42—181no—
636C42—181no—
637C42—181no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—42no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—62no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3C2×D3×D411yescharacteristic
652C22×C3C2×D3×D411yescharacteristic
653C2×D3—22no—
654C2×D3—32no—
655C2×D3—32no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—62no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—121no—
664C2×D3—121no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—61no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—62no—
674C3×C4—81no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4C22×C4×D311yescharacteristic
678C3×C4C22×C4×D311yescharacteristic
679C3×C4D3×#4111yescharacteristic
680C3×C4D3×#4111yescharacteristic
681Dic3—21no—
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—22no—
686Dic3—32no—
687Dic3—32no—
688Dic3—41no—
689Dic3—41no—
690Dic3—62no—
691Dic3—62no—
692Dic3—62no—
693Dic3—122no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697C32#295211yescharacteristic, complemented, Sylow
698C23—21no—
699C23—61no—
700C23—91no—
701Q8—32no—
702Q8—61no—
703Q8—92no—
704Q8—181no—
705D4—21no—
706D4—32no—
707D4—61no—
708D4—184no—
709D4—184no—
710D4C4×D3212yes—
711C2×C4—21no—
712C2×C4—31no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—91no—
720C2×C4—92no—
721C2×C4—92no—
722C2×C4—184no—
723C2×C4—184no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—241no—
727C2×C4—241no—
728C2×C4—241no—
729C2×C4—721no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4C22×D3211yescharacteristic
733C8—21no—
734C8—32no—
735C8—32no—
736C8—181no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—42no—
741C2×C3—42no—
742C2×C3—82no—
743C2×C3—122no—
744C2×C3C4×D3×D411yescharacteristic
745C2×C3C4×D3×D411yescharacteristic
746C2×C3#576211yescharacteristic
747C2×C3#577011yescharacteristic
748C2×C3#577511yescharacteristic
749C2×C3#577511yescharacteristic
750D3—42no—
751D3—62no—
752D3—62no—
753D3—122no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—62no—
758C22—92no—
759C22—121no—
760C22—121no—
761C22—181no—
762C22—181no—
763C22D32×D411yescharacteristic
764C4—41no—
765C4—61no—
766C4—61no—
767C4—61no—
768C4—61no—
769C4—62no—
770C4—92no—
771C4—121no—
772C4—121no—
773C4—182no—
774C4—361no—
775C4C2×C4×D3211yescharacteristic
776C4#6431211yescharacteristic
777C3—21no—
778C3#7965011yescharacteristic, complemented
779C3#7986811yescharacteristic, complemented
780C2—42no—
781C2—122no—
782C2—182no—
783C2#1059425511yescharacteristic
784C2#1059473611yescharacteristic
785C2#1059474911yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#63936C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595219C2semidirect
3. #10594361C2semidirect
4. #10592470C2semidirect
5. C3×#4785C2semidirect
6. C3×#4758C2semidirect
7. Dic3×#214C2semidirect
8. #10591430C2semidirect
9. #10590957C2semidirect
10. #10590910C2semidirect
11. #10590794C2semidirect
12. #10590744C2semidirect
13. #10590575C2semidirect
14. #10590480C2semidirect
15. #10590479C2semidirect
32. #63936C4semidirect
82. #4785D3semidirect
88. #4758D3semidirect
97. #3830C2×C4semidirect
111. #3796C2×C4semidirect
120. C3×#214C2×C4semidirect
121. C3×#213C2×C4semidirect
143. #3719C2×C4semidirect
144. #3716C2×C4semidirect
145. #3710C2×C4semidirect
366. #214C4×D3semidirect
367. #213C4×D3semidirect
697. C32#2952semidirect
778. C3#79650semidirect
779. C3#79868semidirect

Maximal subgroups

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

subgroupindex
#105952192
C2×#639362
#105943612
#105924702
C3×#47852
C3×#47582
Dic3×#2142
#105914302
#105909572
#105909102
#105907942
#105907442
#105905752
#105904802
#105904792
#798683
#796503