Finite Group Databasebeta

← #11860781

Subgroups — #11860781

Order 1152.

1045 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595215C211yesmaximal, characteristic
2C2×D3×#214C211yesmaximal, characteristic
3#10594357C211yesmaximal, characteristic, complemented
4#10592457C211yesmaximal, characteristic, complemented
5C3×#4770C211yesmaximal, characteristic
6C3×#4757C211yesmaximal, characteristic, complemented
7#10591446C211yesmaximal, characteristic, complemented
8#10591401C211yesmaximal, characteristic, complemented
9#10590948C211yesmaximal, characteristic, complemented
10#10590909C211yesmaximal, characteristic, complemented
11#10590747C211yesmaximal, characteristic, complemented
12#10590742C211yesmaximal, characteristic, complemented
13#10590571C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#79777—31nomaximal
17#78916—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22#64096C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
26C3×#892C2211yescharacteristic
27C3×#887C2211yescharacteristic, complemented
28#67⋊Dic3—21no—
29Dic3×#67—21no—
30D3×#217—21no—
31C2×(C2×D3)⋊Dic3—21no—
32D3×#214C418yescomplemented
33C4×#627—21no—
34#63898C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63878—21no—
37#63877—21no—
38#63855C2211yescharacteristic
39#63844C2211yescharacteristic, complemented
40#63843C2211yescharacteristic, complemented
41#63841C2211yescharacteristic
42#63837—21no—
43C2×#3716C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46C32×#102C2211yescharacteristic
47#63643C2211yescharacteristic, complemented
48C8×C3⋊Dic3C2211yescharacteristic, complemented
49#63635C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×#816C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55C3×#807C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63574C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62#5798—31no—
63C22×#214—31no—
64C2×D3×SD16—31no—
65#5572—31no—
66#5545—31no—
67#5516—31no—
68C3×#440—31no—
69C3×#418—31no—
70#5164—31no—
71#5122—31no—
72#5120—31no—
73C4×#215—31no—
74C4×#214—31no—
75#4998—31no—
76#4889—31no—
77#4880—31no—
78#4802—31no—
79#4788—31no—
80#4770D311yescharacteristic
81#4758—31no—
82#4758—31no—
83#4758—31no—
84#4758—31no—
85#4758—31no—
86#4758—61no—
87#4757—31no—
88#4757—31no—
89#4757—31no—
90#4757D311yescharacteristic, complemented
91#4710—31no—
92#4708—31no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4C2×C414yes—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×Dic6—22no—
109D3×Dic6C2×C414yescomplemented
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3757—21no—
113#3754C2×C414yescomplemented
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#214C2×C414yescomplemented
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×ΓL(1,𝔽25)—22no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3D411yescharacteristic
134Dic3⋊Dic3D411yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143#3716C2×C414yescomplemented
144#3715C2×C414yescomplemented
145D3×C3⋊C8C2×C414yescomplemented
146#2949—91noSylow
147C22×C3×D4—31no—
148C2×D3×Q8—31no—
149C2×D3×D4C2×D311yescharacteristic
150C22×Dic6—31no—
151C2×C3×SD16—31no—
152C2×C3×M16—31no—
153C3×C4×Q8—31no—
154C3×C4×D4—31no—
155C3×#117—31no—
156C2×#217—61no—
157C2×#217—61no—
158Q8×Dic3—31no—
159C2×#215—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165D4×Dic3—61no—
166D4×Dic3—61no—
167D4×Dic3C2×D311yescharacteristic
168C2×#214—31no—
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—38no—
172C2×#214—31no—
173C2×#214—61no—
174C2×#214C2×D311yescharacteristic
175C4×#67—61no—
176C2×(C2×D3)⋊C4—61no—
177#926—31no—
178#926—31no—
179C22×C3⋊C8—31no—
180D3×SD16—38no—
181C2×#204—31no—
182C2×ΓL(1,𝔽25)C2×D311yescharacteristic
183C2×D3×C8—31no—
184#893—31no—
185#892—31no—
186#892—61no—
187#892C2×D311yescharacteristic
188#887—31no—
189#887—31no—
190#887—31no—
191#887—31no—
192#887—61no—
193#887—61no—
194#887C2×D311yescharacteristic, complemented
195#67⋊C4—61no—
196D3×C22⋊C4—61no—
197#877—61no—
198#877—61no—
199C4×D12—31no—
200#872—31no—
201#872—61no—
202C4×Dic6—31no—
203C4×Dic6—61no—
204C4×Dic6—61no—
205C4×Dic6—61no—
206C3×#107—31no—
207C3×#103—31no—
208C3×#102—21no—
209C3×#102—31no—
210C3×#102—31no—
211C3×#102—31no—
212C3×#102C2×D311yescharacteristic
213C3×#102C2×D311yescharacteristic
214C3×#97—31no—
215#835—31no—
216#832C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218#818—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—61no—
224#816C2×D311yescharacteristic, complemented
225#815—31no—
226#815—31no—
227#815C2×D311yescharacteristic, complemented
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231C8×Dic3—61no—
232#810—31no—
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—31no—
237#808—31no—
238#808—61no—
239#807—31no—
240#807C2×D311yescharacteristic, complemented
241C4×C3⋊C8—31no—
242C23×C32—21no—
243C22×C3×D3—21no—
244C22×C3×D3—24no—
245C22×C3×D3—81no—
246C22×C3×D3—81no—
247C22×C3×D3C2×D411yescharacteristic
248C32×D4—21no—
249C32×D4C22×C412yes—
250C2×C32×C4—21no—
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—81no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257#634—21no—
258#634C22×C412yes—
259C3×#67—24no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—81no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12C22×C412yes—
269C3×C4×D3C22×C412yes—
270C3×C4×D3#4112yes—
271C3×Dic6—21no—
272C3×Dic6C22×C412yes—
273#627—24no—
274D3×Dic3—24no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277C32×C8—21no—
278C3⋊(C3⋊C8)C22×C412yes—
279C3×C3⋊C8—21no—
280C3×C3⋊C8C22×C412yes—
281C22×SD16—91no—
282#519—91no—
283#518—91no—
284#440—31no—
285#440—91no—
286#440—91no—
287#440—91no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×SD16—91no—
291C4×SD16—91no—
292#427—91no—
293#419—91no—
294#418—31no—
295#405—91no—
296C24×C3—61no—
297C23×D3—21no—
298C2×C3×Q8—31no—
299C2×C3×D4—21no—
300C2×C3×D4—34no—
301C2×C3×D4—31no—
302C2×C3×D4—62no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C2×#67—21no—
309C22×Dic3—21no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—121no—
316D3×Q8—34no—
317D3×Q8—62no—
318D3×D4—22no—
319D3×D4C4×D314yes—
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—31no—
326C2×Dic6—31no—
327C2×Dic6—34no—
328C2×Dic6—61no—
329C2×Dic6—62no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—34no—
334C3×M16—62no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—31no—
349C3×C42—61no—
350C3×C42—61no—
351#217—21no—
352#217—31no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360#215—34no—
361#214—34no—
362#214—34no—
363#214—34no—
364#214—34no—
365#214—64no—
366#214C4×D314yescomplemented
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—121no—
390C4×Dic3—21no—
391C4×Dic3—21no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—121no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—34no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204—34no—
412ΓL(1,𝔽25)—22no—
413D3×C8—34no—
414C22×C32—22no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—84no—
424C2×C3×D3C4×D412yes—
425C32×C4—41no—
426C32×C4C23×C411yescharacteristic
427C32×C4C2×#4111yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—22no—
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C4×D412yes—
438C22×Q8—91no—
439C22×D4—31no—
440C2×SD16—31no—
441C2×SD16—91no—
442C2×SD16—98no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×M16—31no—
446C22×C8—91no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×Q8—91no—
450C4×Q8—91no—
451C4×Q8—181no—
452C4×Q8—181no—
453C4×D4—31no—
454C4×D4—91no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—181no—
458C4×D4—181no—
459#117—31no—
460#117—91no—
461#117—91no—
462#117—181no—
463#117—181no—
464C2×C22⋊C4—181no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—91no—
468#106—91no—
469#106—91no—
470#103—31no—
471#103—91no—
472#103—91no—
473#103—91no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102D3211yescharacteristic
478#97—31no—
479#97—91no—
480C4×C8—91no—
481C4×C8—91no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C23×C3—64no—
487C23×C3—61no—
488C23×C3—241no—
489C23×C3—241no—
490C22×D3—21no—
491C22×D3—24no—
492C22×D3—81no—
493C22×D3—81no—
494C22×D3D3×D411yescharacteristic
495C3×Q8—32no—
496C3×Q8—61no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—32no—
501C3×D4—41no—
502C3×D4—64no—
503C3×D4—61no—
504C3×D4C2×C4×D312yes—
505C3×D4C2×C4×D312yes—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—241no—
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—24no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—64no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—81no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—241no—
540C2×Dic3—241no—
541C2×Dic3—241no—
542C2×Dic3—241no—
543C2×Dic3—242no—
544C2×Dic3D3×D411yescharacteristic
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547D12—21no—
548D12C2×C4×D312yes—
549C4×D3—64no—
550C4×D3—241no—
551C4×D3—241no—
552C4×D3C2×C4×D312yes—
553C4×D3#23712yes—
554Dic6—21no—
555Dic6—32no—
556Dic6—32no—
557Dic6—62no—
558Dic6—64no—
559Dic6—61no—
560Dic6—61no—
561Dic6—64no—
562Dic6—121no—
563Dic6C2×C4×D312yes—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—32no—
567C3×C8—41no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—32no—
571C3⋊C8—32no—
572C3⋊C8—62no—
573C3⋊C8C2×C4×D312yes—
574C2×C32—42no—
575C2×C32C2×C4×D411yescharacteristic
576C2×C32#57711yescharacteristic
577C2×C32#57711yescharacteristic
578C3×D3—22no—
579C3×D3—42no—
580C24—61no—
581C2×Q8—31no—
582C2×Q8—94no—
583C2×Q8—91no—
584C2×Q8—181no—
585C2×Q8—182no—
586C2×D4—34no—
587C2×D4—31no—
588C2×D4—62no—
589C2×D4—61no—
590C2×D4C2×D3211yescharacteristic
591C22×C4—31no—
592C22×C4—61no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597SD16—34no—
598SD16—94no—
599SD16—94no—
600SD16—94no—
601M16—62no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—94no—
605C2×C8—91no—
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4C2×D3211yescharacteristic
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—91no—
620C22⋊C4—91no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—61no—
627C42—61no—
628C42—91no—
629C42—181no—
630C42—181no—
631C42—181no—
632C42—181no—
633C22×C3—22no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—32no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—62no—
645C22×C3—81no—
646C22×C3—81no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—244no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—22no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—84no—
658C2×D3#67⋊C412yes—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—32no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—62no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—81no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C22×C4×D311yescharacteristic
671C3×C4C22×C4×D311yescharacteristic
672C3×C4C2×#23711yescharacteristic
673C3×C4D3×#4111yescharacteristic
674Dic3—21no—
675Dic3—21no—
676Dic3—22no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—62no—
681Dic3—61no—
682Dic3—61no—
683Dic3—61no—
684Dic3—61no—
685Dic3—62no—
686Dic3—122no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3#67⋊C412yes—
692C32#294911yescharacteristic, complemented, Sylow
693C23—21no—
694C23—31no—
695C23—64no—
696C23—61no—
697C23—241no—
698C23—241no—
699Q8—32no—
700Q8—61no—
701Q8—92no—
702Q8—184no—
703Q8—181no—
704D4—21no—
705D4—32no—
706D4—64no—
707D4—61no—
708D4C4×D3212yes—
709C2×C4—21no—
710C2×C4—31no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—184no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—241no—
724C2×C4—721no—
725C2×C4—721no—
726C2×C4—721no—
727C2×C4C22×D3211yescharacteristic
728C8—21no—
729C8—32no—
730C8—61no—
731C8—92no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—42no—
736C2×C3—42no—
737C2×C3—62no—
738C2×C3—82no—
739C2×C3—122no—
740C2×C3C2×#67⋊C411yescharacteristic
741C2×C3C4×D3×D411yescharacteristic
742C2×C3#577511yescharacteristic
743C2×C3#577511yescharacteristic
744C2×C3#577511yescharacteristic
745C2×C3#577811yescharacteristic
746D3—22no—
747D3—42no—
748C22—22no—
749C22—32no—
750C22—41no—
751C22—41no—
752C22—61no—
753C22—61no—
754C22—62no—
755C22—121no—
756C22—121no—
757C22—244no—
758C22D32×D411yescharacteristic
759C4—32no—
760C4—41no—
761C4—61no—
762C4—61no—
763C4—62no—
764C4—121no—
765C4—121no—
766C4—181no—
767C4—181no—
768C4—182no—
769C4—361no—
770C4C2×C4×D3211yescharacteristic
771C4D3×#23711yescharacteristic
772C3—21no—
773C3#7891611yescharacteristic, complemented
774C3#7977711yescharacteristic, complemented
775C2—42no—
776C2—62no—
777C2—122no—
778C2D3×#67⋊C411yescharacteristic
779C2#1059473311yescharacteristic
780C2#1059475411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32#2949
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
3. #10594357C2semidirect
4. #10592457C2semidirect
6. C3×#4757C2semidirect
7. #10591446C2semidirect
8. #10591401C2semidirect
9. #10590948C2semidirect
10. #10590909C2semidirect
11. #10590747C2semidirect
12. #10590742C2semidirect
13. #10590571C2semidirect
14. #10590461C2semidirect
15. #10590453C2semidirect
22. #64096C22semidirect
27. C3×#887C22semidirect
32. D3×#214C4semidirect
39. #63844C22semidirect
40. #63843C22semidirect
47. #63643C22semidirect
48. C8×C3⋊Dic3C22semidirect
49. #63635C22semidirect
52. C3×#816C22semidirect
53. C3×#815C22semidirect
55. C3×#807C22semidirect
56. #63575C22semidirect
57. #63574C22semidirect
58. #63567C22semidirect
59. #63566C22semidirect
60. #63555C22semidirect
61. Dic3×C3⋊C8C22semidirect
90. #4757D3semidirect
109. D3×Dic6C2×C4semidirect
113. #3754C2×C4semidirect
120. C3×#214C2×C4semidirect
143. #3716C2×C4semidirect
144. #3715C2×C4semidirect
145. D3×C3⋊C8C2×C4semidirect
194. #887C2×D3semidirect
224. #816C2×D3semidirect
227. #815C2×D3semidirect
240. #807C2×D3semidirect
366. #214C4×D3semidirect
692. C32#2949semidirect
773. C3#78916semidirect
774. C3#79777semidirect

Maximal subgroups

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

subgroupindex
#105952152
C2×D3×#2142
#105943572
#105924572
C3×#47702
C3×#47572
#105914462
#105914012
#105909482
#105909092
#105907472
#105907422
#105905712
#105904612
#105904532
#797773
#789163