Finite Group Databasebeta

← #11860612

Subgroups — #11860612

Order 1152.

1087 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596045C211yesmaximal, characteristic
2C2×#63945C211yesmaximal, characteristic
3#10593848C211yesmaximal, characteristic, complemented
4C3×#5030C211yesmaximal, characteristic, complemented
5C3×C4×#216C211yesmaximal, characteristic, complemented
6#10591582C211yesmaximal, characteristic, complemented
7#10591581C211yesmaximal, characteristic, complemented
8#10591560C211yesmaximal, characteristic
9#10590601C211yesmaximal, characteristic, complemented
10#10590583C211yesmaximal, characteristic, complemented
11#10590484C211yesmaximal, characteristic, complemented
12#10590483C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14C4×#3717C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79830—31nomaximal
17#79719—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×#3797C2211yescharacteristic
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×#216C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63945C418yescomplemented
35#63849C2211yescharacteristic
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38#63837—21no—
39#63837—21no—
40#63836—21no—
41#63836—21no—
42C2×#3717C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#807C2211yescharacteristic
52C3×#803C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63555C2211yescharacteristic
61#63553C2211yescharacteristic
62C2×#918—31no—
63C2×#918—31no—
64#5574—31no—
65#5574—31no—
66#5574—61no—
67#5572—31no—
68#5572—31no—
69C3×#441—31no—
70C3×C4×Q16—31no—
71#5184—31no—
72Dic3×Q16—31no—
73#5030D311yescharacteristic, complemented
74C4×#216D311yescharacteristic, complemented
75#5026—31no—
76C4×#215—31no—
77#4889—31no—
78#4881—31no—
79#4861—31no—
80#4852—31no—
81#4817—31no—
82#4804—31no—
83#4804—31no—
84D3×#103—31no—
85D3×#103—31no—
86#4790—31no—
87#4789—31no—
88#4788—31no—
89#4710—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C2×C32×Q8C2311yescharacteristic
94#3832—22no—
95#3832C2×C414yes—
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×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#624—21no—
107#3797—22no—
108#3797C2×C414yescomplemented
109C32×C4⋊C4—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C42—21no—
112C32×C42C2311yescharacteristic
113#3752—21no—
114#3752—21no—
115#3752D411yescharacteristic
116#3752D411yescharacteristic
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3750D411yescharacteristic
121#3750D411yescharacteristic
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C3×#216C2×C414yescomplemented
125C3×#216C2×C414yescomplemented
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139Dic32—21no—
140Dic32—21no—
141Dic32—21no—
142#3717C2×C414yescomplemented
143#3717C2×C414yescomplemented
144#3712C2×C414yescomplemented
145#3710—22no—
146#2947—91noSylow
147C2×#239—31no—
148C2×#239—31no—
149C2×#239—61no—
150C2×D3×Q8—31no—
151C2×D3×Q8—31no—
152C2×C3×Q16—31no—
153C2×C3×Q16—31no—
154C3×C4×Q8—21no—
155C3×C4×Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8C2×D311yescharacteristic
158C3×C4×Q8C2×D311yescharacteristic
159Q8×Dic3—31no—
160Q8×Dic3—31no—
161Q8×Dic3—31no—
162Q8×Dic3—31no—
163Q8×Dic3—61no—
164C2×#216C2×D311yescharacteristic
165C2×#216C2×D311yescharacteristic
166C2×#215—31no—
167C2×#215—31no—
168#918—38no—
169#918—38no—
170C2×#204—31no—
171C2×#204—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176#893—31no—
177#893—31no—
178#893—61no—
179#893—61no—
180#893—61no—
181#893—62no—
182#892—31no—
183#892—31no—
184#892—61no—
185#892—61no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—61no—
189D3×C4⋊C4—61no—
190D3×C4⋊C4—61no—
191D3×C4⋊C4—62no—
192#887—31no—
193#887—31no—
194#887—61no—
195#887—61no—
196C4×D12—31no—
197C4×D12—31no—
198C4×D12—61no—
199C4×D12—61no—
200C4×D12—61no—
201C4×D12—62no—
202#872—31no—
203#872—31no—
204#872—61no—
205#872—61no—
206#872—61no—
207#872—61no—
208#872—61no—
209#872—62no—
210C4×Dic6—61no—
211C4×Dic6—61no—
212C4×Dic6C2×D311yescharacteristic
213C4×Dic6C2×D311yescharacteristic
214C3×#107—31no—
215C3×#106—31no—
216C3×#103—31no—
217C3×#103—31no—
218C3×#103—31no—
219C3×#103—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222#835—31no—
223#835—31no—
224#835C2×D311yescharacteristic
225#835C2×D311yescharacteristic
226#821—31no—
227#821—31no—
228#818—31no—
229#817—31no—
230#816—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810C2×D311yescharacteristic
237#810C2×D311yescharacteristic
238#809—31no—
239#809—31no—
240#808—31no—
241#808C2×D311yescharacteristic
242#807—31no—
243#807C2×D311yescharacteristic
244#803C2×D311yescharacteristic
245C4×C3⋊C8C2×D311yescharacteristic
246C22×C3⋊D3—21no—
247C22×C3⋊D3C2×D411yescharacteristic
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⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C2×C3⋊Dic3C2×D411yescharacteristic
259C4⋊(C3⋊D3)—24no—
260C4⋊(C3⋊D3)—21no—
261C4⋊(C3⋊D3)C22×C412yes—
262C4×C3⋊D3—24no—
263C4×C3⋊D3—81no—
264C4×C3⋊D3—81no—
265C4×C3⋊D3—81no—
266C4×C3⋊D3C22×C412yes—
267C4×C3⋊D3#4112yes—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6C22×C412yes—
275C3×Dic6C22×C412yes—
276#627—24no—
277#624—24no—
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—31no—
286#441—91no—
287#440—91no—
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×Q8—31no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302#239—34no—
303#239—34no—
304#239—64no—
305#239—62no—
306#239—62no—
307#239—64no—
308D3×Q8—34no—
309D3×Q8—34no—
310D3×Q8—62no—
311D3×Q8—62no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—62no—
318C2×C4×D3—31no—
319C2×C4×D3—31no—
320C2×C4×D3—61no—
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×C4×D3—61no—
330C2×C4×D3—62no—
331C2×C4×D3—62no—
332C2×C4×D3—62no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6C22×D311yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C3×Q16—34no—
340C3×Q16—34no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C3×C4⋊C4—22no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C42—22no—
356C3×C42—21no—
357C3×C42—21no—
358C3×C42—21no—
359C3×C42—61no—
360C3×C42—61no—
361C3×C42C22×D311yescharacteristic
362C3×C42C22×D311yescharacteristic
363#216C4×D314yescomplemented
364#216C4×D314yescomplemented
365#215—34no—
366#215—34no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—62no—
378(C2×D3)⋊C4—62no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—62no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—31no—
396Dic3⋊C4—31no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—62no—
404C4×Dic3—21no—
405C4×Dic3—21no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3—61no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416C4×Dic3—61no—
417C4×Dic3—62no—
418C2×C3⋊C8C22×D311yescharacteristic
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421C2×C3⋊C8C22×D311yescharacteristic
422#204—34no—
423#204—34no—
424ΓL(1,𝔽25)—34no—
425ΓL(1,𝔽25)—34no—
426D3×C8—62no—
427D3×C8—62no—
428C22×C32C22×D411yescharacteristic
429C2×C3⋊D3—22no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3—41no—
433C2×C3⋊D3—41no—
434C2×C3⋊D3C4×D412yes—
435C32×C4—22no—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—41no—
439C32×C4C23×C411yescharacteristic
440C32×C4C2×#4111yescharacteristic
441C3⋊Dic3—21no—
442C3⋊Dic3—21no—
443C3⋊Dic3—41no—
444C3⋊Dic3C4×D412yes—
445C3×Dic3—22no—
446C3×Dic3—22no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C2×#41—91no—
450C22×Q8—91no—
451#137—98no—
452C2×Q16—31no—
453C2×Q16—31no—
454C2×SD16—91no—
455C2×SD16—91no—
456C2×M16—91no—
457C22×C8—91no—
458C4×Q8—31no—
459C4×Q8—31no—
460C4×Q8—91no—
461C4×Q8—91no—
462C4×Q8—91no—
463C4×Q8—181no—
464C4×Q8—181no—
465C4×Q8D3211yescharacteristic
466C4×D4—91no—
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—91no—
479#106—31no—
480#106—91no—
481#103—31no—
482#103—31no—
483#103—31no—
484#103—31no—
485#103—91no—
486#103—91no—
487#102—91no—
488#102—91no—
489#97—31no—
490#97—91no—
491C4×C8—31no—
492C4×C8—91no—
493C22×D3—31no—
494C22×D3—31no—
495C22×D3—61no—
496C22×D3—62no—
497C22×D3—61no—
498C22×D3—61no—
499C3×Q8—22no—
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—22no—
503C3×Q8—32no—
504C3×Q8—32no—
505C3×Q8—61no—
506C3×Q8—61no—
507C3×Q8C2×C4×D312yes—
508C3×Q8C2×C4×D312yes—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—22no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—62no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544D12—32no—
545D12—32no—
546D12—62no—
547D12—64no—
548D12—64no—
549D12—68no—
550D12—62no—
551D12—61no—
552D12—61no—
553C4×D3—32no—
554C4×D3—32no—
555C4×D3—32no—
556C4×D3—32no—
557C4×D3—62no—
558C4×D3—62no—
559C4×D3—64no—
560C4×D3—64no—
561C4×D3—64no—
562C4×D3—64no—
563C4×D3—68no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—242no—
571C4×D3—242no—
572C4×D3—242no—
573Dic6—21no—
574Dic6—21no—
575Dic6—64no—
576Dic6—64no—
577Dic6C2×C4×D312yes—
578Dic6C2×C4×D312yes—
579C3×C8—32no—
580C3×C8—32no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8C2×C4×D312yes—
586C3⋊C8C2×C4×D312yes—
587C2×C32C2×C4×D411yescharacteristic
588C2×C32#57711yescharacteristic
589C2×C32#57811yescharacteristic
590C3⋊D3—22no—
591C3⋊D3—42no—
592#41—94no—
593#41—182no—
594C2×Q8—31no—
595C2×Q8—31no—
596C2×Q8—94no—
597C2×Q8—181no—
598C2×Q8—182no—
599C2×Q8C2×D3211yescharacteristic
600C2×D4—91no—
601C2×D4—181no—
602C22×C4—91no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608Q16—34no—
609Q16—34no—
610SD16—94no—
611SD16—94no—
612M16—94no—
613C2×C8—31no—
614C2×C8—31no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—182no—
618C4⋊C4—21no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—91no—
624C4⋊C4—91no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—91no—
632C22⋊C4—91no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C42—21no—
637C42—61no—
638C42—61no—
639C42—91no—
640C42—181no—
641C42—181no—
642C42—181no—
643C42—181no—
644C42C2×D3211yescharacteristic
645C22×C3—21no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C2×D3×D411yescharacteristic
648C2×D3—32no—
649C2×D3—32no—
650C2×D3—62no—
651C2×D3—61no—
652C2×D3—61no—
653C2×D3—61no—
654C2×D3—61no—
655C2×D3—64no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—122no—
661C2×D3—122no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C3×C4—24no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—22no—
672C3×C4—22no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—42no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—62no—
681C3×C4—62no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4C22×C4×D311yescharacteristic
685C3×C4C22×C4×D311yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4D3×#4111yescharacteristic
688Dic3—22no—
689Dic3—22no—
690Dic3—32no—
691Dic3—32no—
692Dic3—41no—
693Dic3—41no—
694Dic3—62no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—121no—
700Dic3—121no—
701Dic3—122no—
702Dic3—121no—
703Dic3—121no—
704C32#294711yescharacteristic, complemented, Sylow
705C23—91no—
706C23—181no—
707Q8—21no—
708Q8—32no—
709Q8—32no—
710Q8—61no—
711Q8—61no—
712Q8—184no—
713Q8C4×D3212yes—
714D4—92no—
715D4—184no—
716D4—181no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—91no—
724C2×C4—92no—
725C2×C4—92no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—184no—
729C2×C4—184no—
730C2×C4—181no—
731C2×C4—721no—
732C2×C4—721no—
733C2×C4—721no—
734C2×C4#381111yescharacteristic
735C2×C4#381111yescharacteristic
736C2×C4C22×D3211yescharacteristic
737C8—32no—
738C8—32no—
739C8—61no—
740C8—61no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3C4×D3×D411yescharacteristic
745C2×C3C4×D3×D411yescharacteristic
746C2×C3#576611yescharacteristic
747C2×C3#577011yescharacteristic
748C2×C3#577811yescharacteristic
749C2×C3#577911yescharacteristic
750D3—62no—
751D3—62no—
752D3—122no—
753D3—124no—
754D3—122no—
755D3—122no—
756C22—92no—
757C22—181no—
758C22—181no—
759C22—182no—
760C22—361no—
761C22—361no—
762C22C2×#381111yescharacteristic
763C4—21no—
764C4—21no—
765C4—22no—
766C4—41no—
767C4—62no—
768C4—62no—
769C4—92no—
770C4—121no—
771C4—121no—
772C4—181no—
773C4—181no—
774C4—361no—
775C4C2×C4×D3211yescharacteristic
776C4#6430611yescharacteristic
777C3—21no—
778C3#7971911yescharacteristic, complemented
779C3#7983011yescharacteristic, complemented
780C2—182no—
781C2—362no—
782C2C4×#381111yescharacteristic
783C2#1059533711yescharacteristic
784C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3832C22
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
3. #10593848C2semidirect
4. C3×#5030C2semidirect
5. C3×C4×#216C2semidirect
6. #10591582C2semidirect
7. #10591581C2semidirect
9. #10590601C2semidirect
10. #10590583C2semidirect
11. #10590484C2semidirect
12. #10590483C2semidirect
13. #10590362C2semidirect
14. C4×#3717C2semidirect
15. #10590321C2semidirect
34. #63945C4semidirect
73. #5030D3semidirect
74. C4×#216D3semidirect
108. #3797C2×C4semidirect
124. C3×#216C2×C4semidirect
125. C3×#216C2×C4semidirect
142. #3717C2×C4semidirect
143. #3717C2×C4semidirect
144. #3712C2×C4semidirect
363. #216C4×D3semidirect
364. #216C4×D3semidirect
704. C32#2947semidirect
778. C3#79719semidirect
779. C3#79830semidirect

Maximal subgroups

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

subgroupindex
#105960452
C2×#639452
#105938482
C3×#50302
C3×C4×#2162
#105915822
#105915812
#105915602
#105906012
#105905832
#105904842
#105904832
#105903622
C4×#37172
#105903212
#798303
#797193