Finite Group Databasebeta

← #11882325

Subgroups — #11882325

Order 1152.

858 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594949C211yesmaximal, characteristic, complemented
2#10594910C211yesmaximal, characteristic, complemented
3#10592813C211yesmaximal, characteristic, complemented
4C3×#5115C211yesmaximal, characteristic, complemented
5C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
6#10591175C211yesmaximal, characteristic, complemented
7#10591164C211yesmaximal, characteristic, complemented
8#10590879C211yesmaximal, characteristic, complemented
9#10590860C211yesmaximal, characteristic, complemented
10#10590805C211yesmaximal, characteristic, complemented
11#10590774C211yesmaximal, characteristic, complemented
12#10590772C211yesmaximal, characteristic, complemented
13#10590757C211yesmaximal, characteristic, complemented
14#10590755C211yesmaximal, characteristic, complemented
15#10590753C211yesmaximal, characteristic, complemented
16#80703—31nomaximal
17#79028—31nomaximal
18C2×#3804—21no—
19C22×C32×C8C2211yescharacteristic
20#64139C2211yescharacteristic
21#64133C2211yescharacteristic
22C2×#3744C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C3×#930C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×C3×D24C2211yescharacteristic
28#63978—21no—
29Dic3×#67—21no—
30#63961—21no—
31#63918C2211yescharacteristic
32#63911C2211yescharacteristic
33#63894C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36#63880—21no—
37#63877—21no—
38#63869C2211yescharacteristic
39#63860C2211yescharacteristic
40#63859—21no—
41#63852—21no—
42#63844C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45#63648C2211yescharacteristic
46#63644C2211yescharacteristic
47#63643C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×Dic3⋊C8C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5600—31no—
62#5596—31no—
63#5479—31no—
64#5477—31no—
65C3×#466—31no—
66C2×C3×C4⋊C8—31no—
67#5153—31no—
68#5150—31no—
69#5115—31no—
70#5115D311yescharacteristic, complemented
71#5114—31no—
72#5114—31no—
73#5114—31no—
74#5114—61no—
75C2×Dic3⋊C8D311yescharacteristic, complemented
76#5041—31no—
77#5038—31no—
78#4891—31no—
79#4875—31no—
80#4850—31no—
81#4848—31no—
82#4847—31no—
83#4847—31no—
84#4844—31no—
85#4844—31no—
86#4843—31no—
87#4842—31no—
88#4787—31no—
89#4763—31no—
90#4762—31no—
91#4761—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3D411yescharacteristic
99C22×C3×Dic3D411yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×#627—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#624—21no—
106#3804—44no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×C32×C8—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3744—41no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4×Dic3D411yescharacteristic
123C3×C4×Dic3D411yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8—41no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D24—41no—
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3716—41no—
141#3714—41no—
142#3247—91noSylow
143C2×#237—61no—
144C2×#235—61no—
145C2×C3×D8—31no—
146C22×C3×C8—21no—
147C22×C3×C8—31no—
148C22×C3×C8C2×D311yescharacteristic
149C22×C3×C8C2×D311yescharacteristic
150C3×#121—31no—
151C3×#121—31no—
152C2×C3×C42—31no—
153#940—31no—
154#939—61no—
155#936—31no—
156#935—61no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—61no—
160C2×#214—31no—
161C2×#213—31no—
162#930—31no—
163#930—31no—
164#930—61no—
165#930—61no—
166#930C2×D311yescharacteristic
167#930C2×D311yescharacteristic
168#929—61no—
169C4×#67—61no—
170#924—31no—
171#924—31no—
172#924—61no—
173C2×C4×Dic3C2×D311yescharacteristic
174C22×C3⋊C8C2×D311yescharacteristic
175C2×D24—31no—
176C2×D24C2×D311yescharacteristic
177C2×#204—31no—
178C2×#204—31no—
179C2×#204—31no—
180C2×#204—61no—
181#893—31no—
182#890—31no—
183#888—31no—
184#887—31no—
185#885—61no—
186#67⋊C4—61no—
187#879—61no—
188#877—61no—
189#876—61no—
190#875—31no—
191#875—61no—
192#874—31no—
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—31no—
196C4×D12—61no—
197#872—61no—
198#870—31no—
199#869—31no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×C4⋊C8—31no—
203C3×C4⋊C8—31no—
204C3×C4⋊C8—31no—
205C3×C4⋊C8—31no—
206C3×#102—31no—
207C3×#102—31no—
208#832—31no—
209#832—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218#818—31no—
219#818C2×D311yescharacteristic
220#817—31no—
221#817—31no—
222#817—31no—
223#817—61no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—61no—
228Dic3⋊C8C2×D311yescharacteristic
229Dic3⋊C8C2×D311yescharacteristic
230Dic3⋊C8C2×D311yescharacteristic
231Dic3⋊C8C2×D311yescharacteristic
232#810—31no—
233#809—31no—
234#808—31no—
235#807—31no—
236C23×C32C2×D411yescharacteristic
237C22×C3⋊D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244#638—42no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250#634—21no—
251#634—21no—
252C3×#67—42no—
253C3×#67—42no—
254C2×C3×Dic3—22no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266#627—42no—
267#626—42no—
268#626—42no—
269#624—42no—
270D3×Dic3—42no—
271D3×Dic3—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#532—91no—
277#529—91no—
278#478—91no—
279#478—91no—
280#477—91no—
281#476—91no—
282#466—31no—
283#466—91no—
284#465—91no—
285#465—91no—
286#463—91no—
287#463—91no—
288#460—91no—
289#459—91no—
290C2×C4⋊C8—31no—
291C2×C3×D4—31no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C2×C3×D4—61no—
295C22×C3×C4—21no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C2×#67—21no—
301C2×#67—21no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—121no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3D1211yescharacteristic
310C22×Dic3D1211yescharacteristic
311#237—124no—
312#235—124no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12C22×D311yescharacteristic
319C2×D12C22×D311yescharacteristic
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×Dic6—31no—
325C2×Dic6—31no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C3×D8—121no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C2×C3×C8—41no—
335C2×C3×C8—41no—
336C2×C3×C8—42no—
337C2×C3×C8—121no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C42—31no—
347C3×C42—31no—
348C3×C42—31no—
349C3×C42—31no—
350#217—61no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—121no—
357#214—121no—
358#213—121no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—121no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3D1211yescharacteristic
392C4×Dic3D1211yescharacteristic
393C4×Dic3C22×D311yescharacteristic
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—41no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D24—41no—
399D24—121no—
400#204—121no—
401#204—121no—
402#204—122no—
403#204—121no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32AGL(1,ℤ/8)12yes—
407C22×C32C22×D411yescharacteristic
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C32×C4—21no—
418C32×C4H(5,𝔽2)11yescharacteristic
419C32×C42−1+411yescharacteristic
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3⋊Dic3—41no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3#13512yes—
429C2×#41—181no—
430C2×SD16—91no—
431C2×SD16—91no—
432C2×D8—31no—
433C2×D8—91no—
434C22×C8—31no—
435C22×C8D3211yescharacteristic
436C4⋊Q8—91no—
437#127—91no—
438#126—181no—
439#125—91no—
440#124—91no—
441#124—181no—
442#123—181no—
443C22⋊Q8—91no—
444#121—31no—
445#121—31no—
446#121—91no—
447#121—181no—
448C4×Q8—91no—
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—91no—
452C4×D4—181no—
453C4×D4—181no—
454#117—181no—
455C2×C42—31no—
456#107—31no—
457#107—91no—
458#106—91no—
459#106—91no—
460C4⋊C8—31no—
461C4⋊C8—31no—
462C4⋊C8—31no—
463C4⋊C8—31no—
464#103—91no—
465#103—91no—
466#102—31no—
467#102—31no—
468#102—91no—
469#102—91no—
470#102—91no—
471#102—91no—
472C23×C3—21no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3C2×D1211yescharacteristic
476C23×C3D3×D411yescharacteristic
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—121no—
482C3×D4—61no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—61no—
486C3×D4—122no—
487C3×D4—122no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—62no—
501C2×C3×C4—62no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4C2×D1211yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508#67—42no—
509#67—42no—
510#67—122no—
511#67—122no—
512#67—122no—
513#67—122no—
514#67—242no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—122no—
529C2×Dic3—122no—
530C2×Dic3C2×D1211yescharacteristic
531C2×Dic3C2×D1211yescharacteristic
532C2×Dic3C2×D1211yescharacteristic
533C2×Dic3C2×D1211yescharacteristic
534D12—21no—
535D12—21no—
536D12—21no—
537D12—21no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—61no—
542D12—121no—
543D12—121no—
544D12—122no—
545D12—122no—
546C4×D3—122no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—122no—
550Dic6—61no—
551Dic6—61no—
552Dic6—61no—
553Dic6—61no—
554Dic6—121no—
555Dic6—121no—
556Dic6—122no—
557Dic6—122no—
558C3×C8—22no—
559C3×C8—21no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—41no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C2×C32—22no—
569C2×C32#53711yescharacteristic
570C2×C32C2×#13511yescharacteristic
571C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
572C3⋊D3—81no—
573C3×D3—81no—
574C3×D3—81no—
575#41—364no—
576C2×Q8—91no—
577C2×Q8—181no—
578C2×D4—31no—
579C2×D4—31no—
580C2×D4—61no—
581C2×D4—61no—
582C2×D4—91no—
583C2×D4—181no—
584C2×D4—181no—
585C2×D4—181no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4C2×D3211yescharacteristic
592SD16—361no—
593SD16—361no—
594D8—121no—
595D8—361no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—41no—
599C2×C8—121no—
600C2×C8C2×D3211yescharacteristic
601C2×C8C2×D3211yescharacteristic
602C4⋊C4—31no—
603C4⋊C4—31no—
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—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—31no—
621C42—31no—
622C42—31no—
623C42—31no—
624C42—181no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—22no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3#90812yes—
640C22×C3#91112yes—
641C22×C3C22×D1211yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—241no—
656C2×D3—241no—
657C2×D3—241no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—32no—
663C3×C4—41no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4#100411yescharacteristic
670C3×C4#100411yescharacteristic
671C3×C4#100711yescharacteristic
672C3×C4#101011yescharacteristic
673Dic3—21no—
674Dic3—21no—
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—241no—
685Dic3—241no—
686Dic3—241no—
687Dic3#90412yes—
688C32#324711yescharacteristic, complemented, Sylow
689C23—61no—
690C23—61no—
691C23—181no—
692C23D3×D1211yescharacteristic
693Q8—181no—
694Q8—181no—
695Q8—362no—
696D4—61no—
697D4—61no—
698D4—61no—
699D4—61no—
700D4—122no—
701D4—122no—
702D4—181no—
703D4—181no—
704D4—362no—
705D4—362no—
706D4—362no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—31no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—362no—
721C2×C4—362no—
722C2×C4—362no—
723C2×C4D3×D1211yescharacteristic
724C2×C4C22×D3211yescharacteristic
725C8—21no—
726C8—21no—
727C8—61no—
728C8—61no—
729C2×C3—22no—
730C2×C3—22no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—42no—
735C2×C3—241no—
736C2×C3—241no—
737C2×C3#551011yescharacteristic
738C2×C3#559711yescharacteristic
739C2×C3C2×#90411yescharacteristic
740C2×C3C2×#90811yescharacteristic
741C2×C3C2×#91111yescharacteristic
742C2×C3D3×#13511yescharacteristic
743D3—81no—
744D3—81no—
745D3—241no—
746D3—241no—
747D3—481no—
748C22—21no—
749C22—21no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—121no—
756C22—361no—
757C22—361no—
758C22—361no—
759C22#6379512yes—
760C22C2×D3×D1211yescharacteristic
761C4—21no—
762C4—32no—
763C4—61no—
764C4—61no—
765C4—61no—
766C4—121no—
767C4—121no—
768C4—361no—
769C4—361no—
770C4—361no—
771C4#6429711yescharacteristic
772C4#6433011yescharacteristic
773C3—21no—
774C3#7902811yescharacteristic, complemented
775C3#8070311yescharacteristic, complemented
776C2—22no—
777C2—241no—
778C2—241no—
779C2—721no—
780C2C2×#6379511yescharacteristic
781C2D3×#90411yescharacteristic
782C2#1059491111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3247
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #10594949C2semidirect
2. #10594910C2semidirect
3. #10592813C2semidirect
4. C3×#5115C2semidirect
5. C2×C3×Dic3⋊C8C2semidirect
6. #10591175C2semidirect
7. #10591164C2semidirect
8. #10590879C2semidirect
9. #10590860C2semidirect
10. #10590805C2semidirect
11. #10590774C2semidirect
12. #10590772C2semidirect
13. #10590757C2semidirect
14. #10590755C2semidirect
15. #10590753C2semidirect
70. #5115D3semidirect
75. C2×Dic3⋊C8D3semidirect
688. C32#3247semidirect
774. C3#79028semidirect
775. C3#80703semidirect

Maximal subgroups

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

subgroupindex
#105949492
#105949102
#105928132
C3×#51152
C2×C3×Dic3⋊C82
#105911752
#105911642
#105908792
#105908602
#105908052
#105907742
#105907722
#105907572
#105907552
#105907532
#807033
#790283