Finite Group Databasebeta

← #11872306

Subgroups — #11872306

Order 1152.

858 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595222C211yesmaximal, characteristic, complemented
2#10595217C211yesmaximal, characteristic, complemented
3#10592851C211yesmaximal, characteristic, complemented
4C3×#5158C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6#10591450C211yesmaximal, characteristic, complemented
7#10591445C211yesmaximal, characteristic, complemented
8#10591438C211yesmaximal, characteristic, complemented
9#10591435C211yesmaximal, characteristic, complemented
10#10591413C211yesmaximal, characteristic, complemented
11#10591409C211yesmaximal, characteristic, complemented
12#10590815C211yesmaximal, characteristic, complemented
13#10590743C211yesmaximal, characteristic, complemented
14#10590699C211yesmaximal, characteristic, complemented
15#10590676C211yesmaximal, characteristic, complemented
16#80316—31nomaximal
17#80073—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C3×#940C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27#63980—21no—
28#67⋊Dic3—21no—
29Dic3×#67—21no—
30#63970—21no—
31#63969—21no—
32C2×Dic3⋊Dic3—21no—
33#63962—21no—
34#63955—21no—
35#63908C2211yescharacteristic
36#63898C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38#63869C2211yescharacteristic
39#63855C2211yescharacteristic
40#63843C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45#63644C2211yescharacteristic
46#63642C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53#63576C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63563C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61#5827—31no—
62#5719—31no—
63#5619—31no—
64#5546—31no—
65C3×#459—31no—
66C3×#449—31no—
67#5238—31no—
68#5163—31no—
69Dic3×SD16—31no—
70#5158—31no—
71#5158D311yescharacteristic, complemented
72#5152—31no—
73#5152—31no—
74#5152—61no—
75#5150D311yescharacteristic, complemented
76Dic3×D8—31no—
77#5075—31no—
78#5033—31no—
79#5009—31no—
80#4840—31no—
81#4829—31no—
82#4817—31no—
83#4799—31no—
84#4777—31no—
85#4774—31no—
86#4763—31no—
87#4758—31no—
88#4757—31no—
89#4756—31no—
90#4735—31no—
91#4720—31no—
92C2×C32×D4C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C22×C3⋊Dic3—21no—
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C3×#237—22no—
103C3×#237—22no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C32×D8—22no—
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113#3757—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#214—22no—
121C3×#213—22no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3D411yescharacteristic
138Dic32—21no—
139Dic32—21no—
140#3715—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#237C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×D8—21no—
146C2×C3×D8—31no—
147C2×C3×D8C2×D311yescharacteristic
148C2×C3×D8C2×D311yescharacteristic
149C3×#127—31no—
150C3×#121—31no—
151C3×C4×D4—31no—
152Q8×Dic3—31no—
153Q8×Dic3—31no—
154C2×#215—31no—
155#940C2×D311yescharacteristic
156#939—61no—
157#939—61no—
158#939—61no—
159#938—31no—
160#938—61no—
161#938C2×D311yescharacteristic
162#935—61no—
163#935—61no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—61no—
170D4×Dic3—61no—
171D4×Dic3—61no—
172D4×Dic3—61no—
173D4×Dic3C2×D311yescharacteristic
174C2×#214—31no—
175C2×#214C2×D311yescharacteristic
176C2×#213C2×D311yescharacteristic
177#930—31no—
178C4×#67—61no—
179#926—31no—
180#926—61no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—61no—
183C2×Dic3⋊C4—61no—
184#893—31no—
185D3×C4⋊C4—31no—
186#890—31no—
187#887—31no—
188#886—61no—
189#883—61no—
190#67⋊C4—61no—
191#877—61no—
192#872—31no—
193#870—31no—
194C4×Dic6—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201#835—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—61no—
208#832—61no—
209#832C2×D311yescharacteristic
210#832C2×D311yescharacteristic
211#830—31no—
212#821—31no—
213#821C2×D311yescharacteristic
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8C2×D311yescharacteristic
216#818—31no—
217#817—31no—
218#817—31no—
219#817—31no—
220#817—61no—
221#816—31no—
222#816C2×D311yescharacteristic
223#815—31no—
224#815—31no—
225#815—61no—
226Dic3⋊C8—31no—
227Dic3⋊C8C2×D311yescharacteristic
228C8×Dic3—31no—
229C8×Dic3—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
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—81no—
247C2×C3⋊Dic3—81no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C3×#67—24no—
251C3×#67—81no—
252C3×#67—81no—
253C3×#67—81no—
254C2×C3×Dic3—24no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×Dic6—21no—
267C3×Dic6#4112yes—
268#625—81no—
269D3×Dic3—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—31no—
283#449—31no—
284#449—91no—
285#442—91no—
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—31no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C2×#67—21no—
308C2×#67—21no—
309C2×#67—21no—
310C2×#67—21no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
322C22×Dic3—121no—
323#237—22no—
324#237—22no—
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C3×SD16—62no—
331C3×D8—24no—
332C3×D8—22no—
333C3×D8—22no—
334C3×D8—62no—
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C42—31no—
345#217—21no—
346#217—21no—
347#217—31no—
348#217—31no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—121no—
356#217—121no—
357#215—62no—
358#214—22no—
359#214—62no—
360#213—22no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
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
379Dic3⋊C4—31no—
380Dic3⋊C4—31no—
381Dic3⋊C4—61no—
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
400C22×C32—22no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32C22×D411yescharacteristic
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C32×C4C2×#4111yescharacteristic
414C32×C4C2×#4111yescharacteristic
415C3⋊Dic3—21no—
416C3⋊Dic3—21no—
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C2×#41—31no—
426C2×SD16—31no—
427C2×SD16—91no—
428C2×D8—31no—
429C2×D8D3211yescharacteristic
430#127—31no—
431#125—91no—
432#123—181no—
433#123—181no—
434#121—31no—
435#121—91no—
436#121—181no—
437#121—181no—
438C4×Q8—91no—
439C4×Q8—91no—
440C4×D4—31no—
441C4×D4—91no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—181no—
445C4×D4—181no—
446#117—91no—
447#117—181no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—181no—
450#107—91no—
451#107—91no—
452#106—91no—
453#106—91no—
454C4⋊C8—31no—
455C4⋊C8—91no—
456#103—31no—
457#103—91no—
458#102—31no—
459#102—31no—
460#102—31no—
461#102—91no—
462#102—91no—
463#102—91no—
464C22⋊C8—31no—
465C22⋊C8—91no—
466#97—91no—
467C4×C8—91no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3—61no—
476C22×D3—21no—
477C22×D3D3×D411yescharacteristic
478C3×Q8—32no—
479C3×Q8—61no—
480C3×D4—22no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—21no—
487C3×D4—22no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—64no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—241no—
494C3×D4—241no—
495C3×D4—241no—
496C3×D4#23712yes—
497C3×D4#23712yes—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—64no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—241no—
509C2×C3×C4C23×D311yescharacteristic
510C2×C3×C4C23×D311yescharacteristic
511#67—24no—
512#67—81no—
513#67—81no—
514#67—81no—
515#67—241no—
516#67—241no—
517C2×Dic3—24no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—81no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—241no—
535C2×Dic3—241no—
536C2×Dic3—241no—
537C2×Dic3—241no—
538C2×Dic3—241no—
539C2×Dic3—241no—
540C2×Dic3—242no—
541C2×Dic3—242no—
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545D12—21no—
546D12—21no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—241no—
550C4×D3—241no—
551Dic6—21no—
552Dic6#23712yes—
553C3×C8—22no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C2×C32—42no—
564C2×C32—81no—
565C2×C32#52511yescharacteristic
566C2×C32#57611yescharacteristic
567C2×C32#57711yescharacteristic
568C3×D3—41no—
569C3×D3—81no—
570#41—62no—
571#41—62no—
572C2×Q8—31no—
573C2×D4—31no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—181no—
579C2×D4C2×D3211yescharacteristic
580C2×D4C2×D3211yescharacteristic
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4—181no—
587C22×C4—181no—
588SD16—62no—
589SD16—182no—
590D8—22no—
591D8—62no—
592C2×C8—31no—
593C2×C8—31no—
594C2×C8—91no—
595C2×C8C2×D3211yescharacteristic
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—31no—
616C42—91no—
617C42—181no—
618C42—181no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—81no—
638C22×C3—81no—
639C22×C3—81no—
640C22×C3—81no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—62no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4C2×#23711yescharacteristic
661C3×C4C2×#23711yescharacteristic
662C3×C4C2×#23711yescharacteristic
663C3×C4D3×#4111yescharacteristic
664Dic3—21no—
665Dic3—21no—
666Dic3—22no—
667Dic3—21no—
668Dic3—41no—
669Dic3—41no—
670Dic3—61no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3—241no—
682C32#311911yescharacteristic, complemented, Sylow
683C23—21no—
684C23—21no—
685C23—31no—
686C23—61no—
687Q8—32no—
688Q8—61no—
689D4—21no—
690D4—21no—
691D4—21no—
692D4—64no—
693D4—61no—
694D4—61no—
695D4—241no—
696D4—241no—
697D4—241no—
698D4—721no—
699D4#380512yes—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—64no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—241no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4—721no—
717C2×C4—721no—
718C2×C4C22×D3211yescharacteristic
719C8—21no—
720C8—61no—
721C8—61no—
722C8—181no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—42no—
727C2×C3—42no—
728C2×C3—82no—
729C2×C3—82no—
730C2×C3—81no—
731C2×C3—81no—
732C2×C3—121no—
733C2×C3—241no—
734C2×C3#558611yescharacteristic
735C2×C3#560611yescharacteristic
736C2×C3#575711yescharacteristic
737C2×C3#577011yescharacteristic
738C2×C3#577411yescharacteristic
739C2×C3#577511yescharacteristic
740D3—41no—
741D3—81no—
742C22—22no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—61no—
749C22—61no—
750C22—61no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22D32×D411yescharacteristic
755C4—61no—
756C4—62no—
757C4—61no—
758C4—61no—
759C4—121no—
760C4—121no—
761C4—181no—
762C4—181no—
763C4—361no—
764C4—361no—
765C4D3×#23711yescharacteristic
766C4C2×#380511yescharacteristic
767C3—21no—
768C3#8007311yescharacteristic, complemented
769C3#8031611yescharacteristic, complemented
770C2—42no—
771C2—81no—
772C2—121no—
773C2—241no—
774C2#1059473211yescharacteristic
775C2#1059473611yescharacteristic
776C2#1059513011yescharacteristic
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. #10595217C2semidirect
3. #10592851C2semidirect
4. C3×#5158C2semidirect
5. C3×#5150C2semidirect
6. #10591450C2semidirect
7. #10591445C2semidirect
8. #10591438C2semidirect
9. #10591435C2semidirect
10. #10591413C2semidirect
11. #10591409C2semidirect
12. #10590815C2semidirect
13. #10590743C2semidirect
14. #10590699C2semidirect
15. #10590676C2semidirect
71. #5158D3semidirect
75. #5150D3semidirect
682. C32#3119semidirect
768. C3#80073semidirect
769. C3#80316semidirect

Maximal subgroups

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

subgroupindex
#105952222
#105952172
#105928512
C3×#51582
C3×#51502
#105914502
#105914452
#105914382
#105914352
#105914132
#105914092
#105908152
#105907432
#105906992
#105906762
#803163
#800733