Finite Group Databasebeta

← #11872307

Subgroups — #11872307

Order 1152.

862 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595222C211yesmaximal, characteristic, complemented
2#10595125C211yesmaximal, characteristic, complemented
3#10592849C211yesmaximal, characteristic, complemented
4C3×#5158C211yesmaximal, characteristic, complemented
5C3×#5152C211yesmaximal, characteristic, complemented
6#10591479C211yesmaximal, characteristic, complemented
7#10591452C211yesmaximal, characteristic, complemented
8#10591444C211yesmaximal, characteristic, complemented
9Dic3×#214C211yesmaximal, characteristic, complemented
10#10591413C211yesmaximal, characteristic, complemented
11#10591400C211yesmaximal, characteristic, complemented
12#10590820C211yesmaximal, characteristic, complemented
13#10590795C211yesmaximal, characteristic, complemented
14#10590697C211yesmaximal, characteristic, complemented
15#10590677C211yesmaximal, characteristic, complemented
16#80073—31nomaximal
17#79873—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20#64149C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C2×#3753C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27#63978—21no—
28#63975—21no—
29#67⋊Dic3—21no—
30Dic3×#67—21no—
31#63966—21no—
32C2×Dic3⋊Dic3—21no—
33#63958—21no—
34#63955—21no—
35#63909C2211yescharacteristic
36#63894C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38#63872C2211yescharacteristic
39#63855C2211yescharacteristic
40#63843C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43#63659C2211yescharacteristic
44#63648C2211yescharacteristic
45#63641C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53#63576C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5827—31no—
62#5619—31no—
63#5562—31no—
64#5546—31no—
65C3×#449—31no—
66C3×#442—31no—
67#5238—31no—
68#5163—31no—
69Dic3×SD16—31no—
70#5158D311yescharacteristic, complemented
71#5152D311yescharacteristic, complemented
72#5150—31no—
73#5150—31no—
74#5150—61no—
75#5033—31no—
76C4×#214—31no—
77C4×#213—31no—
78#4863—31no—
79#4857—31no—
80#4817—31no—
81#4799—31no—
82#4781—31no—
83#4774—31no—
84#4766—31no—
85#4763—31no—
86#4762—31no—
87#4756—31no—
88#4735—31no—
89#4720—31no—
90#4710—31no—
91#4709—31no—
92C2×C32×D4C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—22no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C32×D8—22no—
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113#3753—22no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#214—22no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136(C2×D3)⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3D411yescharacteristic
138Dic32—21no—
139Dic32—21no—
140#3717—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#237C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×D8—21no—
146C2×C3×D8C2×D311yescharacteristic
147C2×C3×D8C2×D311yescharacteristic
148C3×#121—31no—
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151Q8×Dic3—31no—
152Q8×Dic3—31no—
153C2×#215—31no—
154#940—31no—
155#940—31no—
156#940—61no—
157#939—61no—
158#938—61no—
159#938C2×D311yescharacteristic
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—61no—
163D4×Dic3—61no—
164D4×Dic3—61no—
165D4×Dic3C2×D311yescharacteristic
166D4×Dic3C2×D311yescharacteristic
167C2×#214C2×D311yescharacteristic
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—61no—
171#930—31no—
172#930—61no—
173#929—61no—
174C4×#67—61no—
175#926—31no—
176#926—61no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—61no—
179C2×Dic3⋊C4—61no—
180C2×#204—31no—
181#895—31no—
182#893—31no—
183D3×C4⋊C4—31no—
184#890—31no—
185#890—31no—
186#887—31no—
187#886—61no—
188#884—61no—
189#883—61no—
190#883—61no—
191#67⋊C4—61no—
192#877—61no—
193C4×D12—31no—
194#872—31no—
195C4×Dic6—31no—
196C3×#106—31no—
197C3×#103—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×C22⋊C8—31no—
202C3×#97—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#832—61no—
207#832C2×D311yescharacteristic
208#832C2×D311yescharacteristic
209#832C2×D311yescharacteristic
210#830—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—61no—
215(C2×D3)⋊C8—31no—
216(C2×D3)⋊C8C2×D311yescharacteristic
217#818—31no—
218#817—31no—
219#817C2×D311yescharacteristic
220#816C2×D311yescharacteristic
221#815C2×D311yescharacteristic
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228#810—31no—
229#809—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234C4×C3⋊C8—31no—
235C23×C32—21no—
236C23×C32—21no—
237C22×C3⋊D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×D4—21no—
240C32×D4—21no—
241C32×D4—21no—
242C32×D4#4112yes—
243C2×C32×C4C2411yescharacteristic
244#638—81no—
245#638—81no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—81no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C3×#67—24no—
253C3×#67—81no—
254C2×C3×Dic3—24no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—81no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×Dic6—21no—
267C3×Dic6#4112yes—
268#626—81no—
269#624—81no—
270D3×Dic3—81no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—91no—
276#520—91no—
277#481—91no—
278#480—91no—
279#479—91no—
280#478—91no—
281#460—91no—
282#459—91no—
283#449—31no—
284#449—91no—
285#442—31no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—31no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C2×#67—21no—
306C2×#67—21no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—121no—
313C2×#67—121no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—121no—
321#237—22no—
322#237—22no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C3×SD16—62no—
333C3×D8—22no—
334C3×D8—22no—
335C3×D8—42no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—31no—
348#217—21no—
349#217—21no—
350#217—21no—
351#217—31no—
352#217—31no—
353#217—61no—
354#217—61no—
355#217—121no—
356#215—62no—
357#214—22no—
358#213—62no—
359#213—62no—
360#213—122no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—31no—
381Dic3⋊C4—31no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400#204—62no—
401C22×C32—22no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C32×C4C2×#4111yescharacteristic
415C32×C4C2×#4111yescharacteristic
416C3⋊Dic3—21no—
417C3⋊Dic3—21no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C2×#41—31no—
427C2×SD16—31no—
428C2×SD16—91no—
429C2×D8—91no—
430C2×D8D3211yescharacteristic
431#127—91no—
432#125—91no—
433#123—181no—
434#123—181no—
435#121—31no—
436#121—91no—
437#121—181no—
438#121—181no—
439C4×Q8—91no—
440C4×Q8—91no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—181no—
446C4×D4—181no—
447#117—91no—
448#117—181no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4—181no—
451#107—91no—
452#107—91no—
453#106—31no—
454#106—91no—
455C4⋊C8—91no—
456C4⋊C8—91no—
457#103—31no—
458#103—91no—
459#102—31no—
460#102—31no—
461#102—31no—
462#102—91no—
463#102—91no—
464#102—91no—
465C22⋊C8—31no—
466C22⋊C8—91no—
467#97—31no—
468C4×C8—91no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—41no—
475C23×C3—41no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—121no—
479C22×D3D3×D411yescharacteristic
480C3×Q8—32no—
481C3×Q8—61no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—22no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—64no—
493C3×D4—241no—
494C3×D4#23512yes—
495C3×D4#23712yes—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—64no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—24no—
512#67—81no—
513#67—241no—
514#67—241no—
515#67—241no—
516#67—241no—
517#67—241no—
518#67—242no—
519#67—242no—
520C2×Dic3—24no—
521C2×Dic3—21no—
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—61no—
532C2×Dic3—61no—
533C2×Dic3—81no—
534C2×Dic3—81no—
535C2×Dic3—121no—
536C2×Dic3—241no—
537C2×Dic3—241no—
538C2×Dic3—241no—
539C2×Dic3—242no—
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543D12—61no—
544D12—61no—
545D12—61no—
546D12—61no—
547D12—121no—
548D12—121no—
549D12—241no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—241no—
555Dic6—21no—
556Dic6#23712yes—
557C3×C8—21no—
558C3×C8—21no—
559C3×C8—41no—
560C3×C8—61no—
561C3×C8—61no—
562C3⋊C8—21no—
563C3⋊C8—21no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C3⋊C8—121no—
567C2×C32—42no—
568C2×C32—81no—
569C2×C32#52511yescharacteristic
570C2×C32#57611yescharacteristic
571C2×C32#57711yescharacteristic
572C3⋊D3—81no—
573C3×D3—41no—
574#41—62no—
575#41—62no—
576C2×Q8—31no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4—91no—
580C2×D4—181no—
581C2×D4—181no—
582C2×D4—181no—
583C2×D4C2×D3211yescharacteristic
584C2×D4C2×D3211yescharacteristic
585C22×C4—31no—
586C22×C4—61no—
587C22×C4—61no—
588C22×C4—61no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592SD16—62no—
593SD16—182no—
594D8—22no—
595D8—182no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—91no—
599C2×C8C2×D3211yescharacteristic
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—91no—
615C22⋊C4—91no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C42—31no—
620C42—91no—
621C42—181no—
622C42—181no—
623C22×C3—22no—
624C22×C3—22no—
625C22×C3—21no—
626C22×C3—42no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—81no—
644C22×C3—81no—
645C22×C3C2×D3×D411yescharacteristic
646C22×C3C2×D3×D411yescharacteristic
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—241no—
657C2×D3—241no—
658C2×D3—241no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—62no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4C2×#23511yescharacteristic
669C3×C4C2×#23711yescharacteristic
670C3×C4C2×#23711yescharacteristic
671C3×C4D3×#4111yescharacteristic
672Dic3—21no—
673Dic3—21no—
674Dic3—22no—
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—62no—
680Dic3—61no—
681Dic3—61no—
682Dic3—61no—
683Dic3—61no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—241no—
688C32#311911yescharacteristic, complemented, Sylow
689C23—21no—
690C23—21no—
691C23—31no—
692C23—181no—
693Q8—32no—
694Q8—61no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—64no—
699D4—181no—
700D4—181no—
701D4—241no—
702D4—721no—
703D4—721no—
704D4—721no—
705D4#380412yes—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—64no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—181no—
719C2×C4—241no—
720C2×C4—241no—
721C2×C4—721no—
722C2×C4—721no—
723C2×C4—721no—
724C2×C4C22×D3211yescharacteristic
725C8—21no—
726C8—61no—
727C8—61no—
728C8—181no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—42no—
733C2×C3—42no—
734C2×C3—82no—
735C2×C3—81no—
736C2×C3—81no—
737C2×C3—121no—
738C2×C3—161no—
739C2×C3#554711yescharacteristic
740C2×C3#558611yescharacteristic
741C2×C3#577011yescharacteristic
742C2×C3#577411yescharacteristic
743C2×C3#577411yescharacteristic
744C2×C3#577511yescharacteristic
745D3—41no—
746D3—241no—
747D3—241no—
748D3—481no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—61no—
756C22—61no—
757C22—61no—
758C22—361no—
759C22—361no—
760C22—361no—
761C22D32×D411yescharacteristic
762C4—61no—
763C4—62no—
764C4—61no—
765C4—61no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—181no—
770C4—181no—
771C4—361no—
772C4D3×#23711yescharacteristic
773C4C2×#380411yescharacteristic
774C3—21no—
775C3#7987311yescharacteristic, complemented
776C3#8007311yescharacteristic, complemented
777C2—42no—
778C2—81no—
779C2—121no—
780C2—721no—
781C2#1059473511yescharacteristic
782C2#1059473611yescharacteristic
783C2#1059512911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595222C2semidirect
2. #10595125C2semidirect
3. #10592849C2semidirect
4. C3×#5158C2semidirect
5. C3×#5152C2semidirect
6. #10591479C2semidirect
7. #10591452C2semidirect
8. #10591444C2semidirect
9. Dic3×#214C2semidirect
10. #10591413C2semidirect
11. #10591400C2semidirect
12. #10590820C2semidirect
13. #10590795C2semidirect
14. #10590697C2semidirect
15. #10590677C2semidirect
70. #5158D3semidirect
71. #5152D3semidirect
688. C32#3119semidirect
775. C3#79873semidirect
776. C3#80073semidirect

Maximal subgroups

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

subgroupindex
#105952222
#105951252
#105928492
C3×#51582
C3×#51522
#105914792
#105914522
#105914442
Dic3×#2142
#105914132
#105914002
#105908202
#105907952
#105906972
#105906772
#800733
#798733