Finite Group Databasebeta

← #11860615

Subgroups — #11860615

Order 1152.

1073 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596043C211yesmaximal, characteristic, complemented
2C2×#63951C211yesmaximal, characteristic
3#10593889C211yesmaximal, characteristic
4C3×C4×#216C211yesmaximal, characteristic, complemented
5C3×#5026C211yesmaximal, characteristic, complemented
6#10591582C211yesmaximal, characteristic, complemented
7#10591571C211yesmaximal, characteristic, complemented
8#10591552C211yesmaximal, characteristic, complemented
9#10590611C211yesmaximal, characteristic
10#10590582C211yesmaximal, characteristic, complemented
11#10590482C211yesmaximal, characteristic, complemented
12#10590461C211yesmaximal, characteristic, complemented
13#10590383C211yesmaximal, characteristic, complemented
14C4×#3716C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79776—31nomaximal
17#79719—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22#64101—21no—
23#64101C2211yescharacteristic
24#64096—21no—
25#64096C2211yescharacteristic
26#64081—21no—
27#64081C2211yescharacteristic
28C4×#634—21no—
29C4×#634C2211yescharacteristic
30C2×C3×#216C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63951C418yescomplemented
35#63904—21no—
36#63900C2211yescharacteristic
37#63898C2211yescharacteristic
38#63880—21no—
39#63877—21no—
40D3×Dic3⋊C4—21no—
41#63843C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#807C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#803C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63563C2211yescharacteristic
60#63555C2211yescharacteristic
61#63553C2211yescharacteristic
62C2×#918—31no—
63C2×#915—31no—
64#5574—31no—
65#5572—31no—
66#5572—31no—
67#5572—61no—
68#5546—31no—
69C3×#440—31no—
70C3×C4×Q16—31no—
71#5184—31no—
72Dic3×SD16—31no—
73#5030—31no—
74C4×#216D311yescharacteristic, complemented
75#5026D311yescharacteristic, complemented
76C4×#214—31no—
77#4889—31no—
78#4881—31no—
79#4881—31no—
80#4873—31no—
81#4804—31no—
82D3×#103—31no—
83D3×#103—31no—
84#4790—31no—
85#4789—31no—
86#4788—31no—
87#4772—31no—
88#4757—31no—
89#4716—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C2×C32×Q8C2311yescharacteristic
94Q8×C3⋊D3—22no—
95Q8×C3⋊D3C2×C414yescomplemented
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C2×#634C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107#3796—22no—
108#3796C2×C414yes—
109C32×C4⋊C4—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C42—21no—
112C32×C42C2311yescharacteristic
113#3752—21no—
114#3752D411yescharacteristic
115#3752D411yescharacteristic
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120#3750D411yescharacteristic
121#3750D411yescharacteristic
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3—21no—
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#3719C2×C414yescomplemented
143#3716C2×C414yescomplemented
144#3712C2×C414yescomplemented
145#3710—22no—
146#2947—91noSylow
147C2×#239—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×D3×Q8—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×#216—31no—
164C2×#216C2×D311yescharacteristic
165C2×#215C2×D311yescharacteristic
166D4×Dic3—31no—
167C2×#214—31no—
168C4×#67—61no—
169C2×Dic3⋊C4—61no—
170#918—38no—
171#915—38no—
172C2×Dic12—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—61no—
180#892—31no—
181#892—31no—
182#892—61no—
183#892—61no—
184#892—61no—
185#892—62no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—61no—
189#887—31no—
190#887—31no—
191#887—31no—
192#887—61no—
193#887—61no—
194#887—61no—
195#887—62no—
196#67⋊C4—61no—
197#877—61no—
198C4×D12—61no—
199C4×D12C2×D311yescharacteristic
200#872—31no—
201#872—31no—
202#872—61no—
203#872—61no—
204#872—61no—
205#872—61no—
206#872—62no—
207C4×Dic6—31no—
208C4×Dic6—31no—
209C4×Dic6—61no—
210C4×Dic6—61no—
211C4×Dic6—61no—
212C4×Dic6—62no—
213C4×Dic6C2×D311yescharacteristic
214C3×#107—31no—
215C3×#107—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#817—31no—
228#817—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810—31no—
237#810—31no—
238#810C2×D311yescharacteristic
239#809C2×D311yescharacteristic
240#808—31no—
241#808—31no—
242#807C2×D311yescharacteristic
243#807C2×D311yescharacteristic
244#803C2×D311yescharacteristic
245C4×C3⋊C8C2×D311yescharacteristic
246C22×C3⋊D3C2×D411yescharacteristic
247C22×C3×D3—21no—
248C32×Q8—21no—
249C32×Q8C22×C412yes—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C2×C3⋊Dic3C2×D411yescharacteristic
260C4×C3⋊D3—24no—
261C4×C3⋊D3C22×C412yes—
262C4×C3⋊D3#4112yes—
263#634—21no—
264#634—24no—
265#634C22×C412yes—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C3×D12—21no—
270C3×D12C22×C412yes—
271C3×C4×D3—81no—
272C3×Dic6—21no—
273C3×Dic6C22×C412yes—
274#626—24no—
275#624—81no—
276D3×Dic3—24no—
277D3×Dic3—81no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C3×C3⋊C8C22×C412yes—
282C2×#137—91no—
283#520—91no—
284#519—91no—
285#441—91no—
286#441—91no—
287#440—31no—
288#440—91no—
289C4×Q16—31no—
290C4×Q16—91no—
291C4×SD16—91no—
292C4×SD16—91no—
293#428—91no—
294#416—91no—
295C2×#103—91no—
296#405—91no—
297C2×C3×Q8—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C22×C3×C4—61no—
303C2×#67—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306#239—34no—
307#239—62no—
308D3×Q8—34no—
309D3×Q8—34no—
310D3×Q8—64no—
311D3×Q8—62no—
312D3×Q8—62no—
313D3×Q8—64no—
314#237—34no—
315#237—62no—
316C2×D12—61no—
317C2×D12C22×D311yescharacteristic
318C2×C4×D3—21no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—62no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6—62no—
335C2×Dic6C22×D311yescharacteristic
336C3×Q16—34no—
337C3×SD16—34no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C3×C4⋊C4—22no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—61no—
352C3×C42—22no—
353C3×C42—21no—
354C3×C42—21no—
355C3×C42—21no—
356C3×C42—61no—
357C3×C42C22×D311yescharacteristic
358C3×C42C22×D311yescharacteristic
359#217—61no—
360#216—34no—
361#216C4×D314yescomplemented
362#215C4×D314yescomplemented
363#214—34no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—62no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—62no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—62no—
397Dic3⋊C4—62no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400C4×Dic3—21no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—62no—
413C4×Dic3—62no—
414C4×Dic3—62no—
415C4×Dic3—62no—
416C4×Dic3—61no—
417C4×Dic3—61no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422Dic12—34no—
423#204—34no—
424ΓL(1,𝔽25)—34no—
425ΓL(1,𝔽25)—34no—
426D3×C8—62no—
427D3×C8—62no—
428C22×C32C22×D411yescharacteristic
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3C4×D412yes—
432C2×C3×D3—22no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C32×C4—22no—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—41no—
439C32×C4C23×C411yescharacteristic
440C32×C4C2×#4111yescharacteristic
441C3⋊Dic3—22no—
442C3⋊Dic3—21no—
443C3⋊Dic3—21no—
444C3⋊Dic3—41no—
445C3⋊Dic3C4×D412yes—
446C3×Dic3—22no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C2×#41—91no—
450C22×Q8—91no—
451#137—98no—
452C2×Q16—31no—
453C2×Q16—91no—
454C2×SD16—31no—
455C2×SD16—91no—
456C2×M16—91no—
457C22×C8—91no—
458C4×Q8—31no—
459C4×Q8—91no—
460C4×Q8—91no—
461C4×Q8—91no—
462C4×Q8—91no—
463C4×Q8—181no—
464C4×Q8—181no—
465C4×Q8D3211yescharacteristic
466C4×D4—31no—
467C4×D4—91no—
468C4×D4—181no—
469C4×D4—181no—
470#117—91no—
471#117—91no—
472#117—181no—
473#117—181no—
474#117—181no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—181no—
477#107—31no—
478#107—31no—
479#106—91no—
480#106—91no—
481#103—31no—
482#103—31no—
483#103—31no—
484#103—91no—
485#103—91no—
486#103—91no—
487#102—31no—
488#102—91no—
489#97—31no—
490#97—91no—
491C4×C8—31no—
492C4×C8—91no—
493C23×C3—61no—
494C22×D3—21no—
495C22×D3—31no—
496C22×D3—31no—
497C22×D3—61no—
498C3×Q8—22no—
499C3×Q8—21no—
500C3×Q8—21no—
501C3×Q8—22no—
502C3×Q8—32no—
503C3×Q8—61no—
504C3×Q8C2×C4×D312yes—
505C3×Q8C2×C4×D312yes—
506C3×D4—32no—
507C3×D4—61no—
508C2×C3×C4—22no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—241no—
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—64no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—64no—
541C2×Dic3—62no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—62no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—241no—
548D12—21no—
549D12—64no—
550D12C2×C4×D312yes—
551C4×D3—32no—
552C4×D3—32no—
553C4×D3—32no—
554C4×D3—32no—
555C4×D3—62no—
556C4×D3—62no—
557C4×D3—64no—
558C4×D3—64no—
559C4×D3—64no—
560C4×D3—68no—
561C4×D3—81no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565Dic6—21no—
566Dic6—32no—
567Dic6—32no—
568Dic6—62no—
569Dic6—64no—
570Dic6—64no—
571Dic6—68no—
572Dic6—62no—
573Dic6—61no—
574Dic6—61no—
575Dic6C2×C4×D312yes—
576C3×C8—32no—
577C3×C8—32no—
578C3×C8—61no—
579C3×C8—61no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C3⋊C8C2×C4×D312yes—
583C3⋊C8C2×C4×D312yes—
584C2×C32C2×C4×D411yescharacteristic
585C2×C32#57711yescharacteristic
586C2×C32#57811yescharacteristic
587C3⋊D3—22no—
588C3×D3—42no—
589#41—94no—
590#41—182no—
591C2×Q8—31no—
592C2×Q8—94no—
593C2×Q8—91no—
594C2×Q8—181no—
595C2×Q8—182no—
596C2×Q8C2×D3211yescharacteristic
597C2×D4—31no—
598C2×D4—181no—
599C22×C4—61no—
600C22×C4—91no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4—181no—
605Q16—34no—
606Q16—94no—
607SD16—34no—
608SD16—94no—
609M16—94no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—182no—
615C4⋊C4—21no—
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—91no—
621C4⋊C4—91no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4C2×D3211yescharacteristic
628C22⋊C4—61no—
629C22⋊C4—91no—
630C22⋊C4—91no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C42—21no—
634C42—61no—
635C42—91no—
636C42—181no—
637C42—181no—
638C42—181no—
639C42—181no—
640C42—181no—
641C42C2×D3211yescharacteristic
642C22×C3—21no—
643C22×C3—62no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C2×D3×D411yescharacteristic
648C2×D3—22no—
649C2×D3—32no—
650C2×D3—32no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—62no—
654C2×D3—61no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—121no—
659C2×D3—121no—
660C3×C4—24no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—42no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—62no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4C22×C4×D311yescharacteristic
678C3×C4C22×C4×D311yescharacteristic
679C3×C4D3×#4111yescharacteristic
680C3×C4D3×#4111yescharacteristic
681Dic3—22no—
682Dic3—32no—
683Dic3—32no—
684Dic3—41no—
685Dic3—41no—
686Dic3—62no—
687Dic3—64no—
688Dic3—61no—
689Dic3—61no—
690Dic3—61no—
691Dic3—61no—
692Dic3—62no—
693Dic3—62no—
694Dic3—121no—
695Dic3—121no—
696Dic3—122no—
697Dic3—121no—
698Dic3—121no—
699C32#294711yescharacteristic, complemented, Sylow
700C23—61no—
701C23—91no—
702Q8—21no—
703Q8—32no—
704Q8—61no—
705Q8—92no—
706Q8—184no—
707Q8—181no—
708Q8C4×D3212yes—
709D4—32no—
710D4—61no—
711D4—184no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—91no—
718C2×C4—92no—
719C2×C4—92no—
720C2×C4—91no—
721C2×C4—91no—
722C2×C4—184no—
723C2×C4—184no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—241no—
727C2×C4—721no—
728C2×C4—721no—
729C2×C4#381111yescharacteristic
730C2×C4#381111yescharacteristic
731C2×C4C22×D3211yescharacteristic
732C8—32no—
733C8—32no—
734C8—61no—
735C8—61no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—122no—
740C2×C3C4×D3×D411yescharacteristic
741C2×C3C4×D3×D411yescharacteristic
742C2×C3#576611yescharacteristic
743C2×C3#577011yescharacteristic
744C2×C3#577511yescharacteristic
745C2×C3#577911yescharacteristic
746D3—42no—
747D3—62no—
748D3—62no—
749D3—122no—
750C22—62no—
751C22—92no—
752C22—121no—
753C22—121no—
754C22—181no—
755C22—181no—
756C22C2×#381111yescharacteristic
757C4—21no—
758C4—21no—
759C4—22no—
760C4—41no—
761C4—62no—
762C4—92no—
763C4—121no—
764C4—121no—
765C4—181no—
766C4—181no—
767C4—182no—
768C4—361no—
769C4C2×C4×D3211yescharacteristic
770C4#6430611yescharacteristic
771C3—21no—
772C3#7971911yescharacteristic, complemented
773C3#7977611yescharacteristic, complemented
774C2—122no—
775C2—182no—
776C2C4×#381111yescharacteristic
777C2#1059533711yescharacteristic
778C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3796C22
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32#2947
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. #10596043C2semidirect
4. C3×C4×#216C2semidirect
5. C3×#5026C2semidirect
6. #10591582C2semidirect
7. #10591571C2semidirect
8. #10591552C2semidirect
10. #10590582C2semidirect
11. #10590482C2semidirect
12. #10590461C2semidirect
13. #10590383C2semidirect
14. C4×#3716C2semidirect
15. #10590321C2semidirect
34. #63951C4semidirect
74. C4×#216D3semidirect
75. #5026D3semidirect
95. Q8×C3⋊D3C2×C4semidirect
127. C3×#216C2×C4semidirect
128. C3×#215C2×C4semidirect
142. #3719C2×C4semidirect
143. #3716C2×C4semidirect
144. #3712C2×C4semidirect
361. #216C4×D3semidirect
362. #215C4×D3semidirect
699. C32#2947semidirect
772. C3#79719semidirect
773. C3#79776semidirect

Maximal subgroups

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

subgroupindex
#105960432
C2×#639512
#105938892
C3×C4×#2162
C3×#50262
#105915822
#105915712
#105915522
#105906112
#105905822
#105904822
#105904612
#105903832
C4×#37162
#105903212
#797763
#797193