Finite Group Databasebeta

← #11876916

Subgroups — #11876916

Order 1152.

857 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596051C211yesmaximal, characteristic, complemented
2#10593875C211yesmaximal, characteristic, complemented
3C3×#5030C211yesmaximal, characteristic, complemented
4C3×#5026C211yesmaximal, characteristic, complemented
5#10591610C211yesmaximal, characteristic, complemented
6#10591600C211yesmaximal, characteristic, complemented
7#10591590C211yesmaximal, characteristic, complemented
8#10591539C211yesmaximal, characteristic, complemented
9#10590539C211yesmaximal, characteristic, complemented
10#10590522C211yesmaximal, characteristic, complemented
11#10590508C211yesmaximal, characteristic
12#10590417C211yesmaximal, characteristic, complemented
13#10590362C211yesmaximal, characteristic, complemented
14#10590346C211yesmaximal, characteristic, complemented
15#10590247C211yesmaximal, characteristic, complemented
16#79826—31nomaximal
17#79793—31nomaximal
18C32×C4×Q8C2211yescharacteristic
19#64156C2211yescharacteristic
20#64155C2211yescharacteristic
21#64107—21no—
22#64104C2211yescharacteristic
23#64103—21no—
24#64099C2211yescharacteristic
25C4×C4⋊(C3⋊D3)—21no—
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27#64081—21no—
28C42×C3⋊D3C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63916C2211yescharacteristic
34C4×#626—21no—
35#63872C2211yescharacteristic
36#63871C2211yescharacteristic
37#63863C2211yescharacteristic
38#63862—21no—
39#63855—21no—
40#63853—21no—
41C2×#3717C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×#3712C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#807C2211yescharacteristic
51C3×#803C2211yescharacteristic
52C3×#803C2211yescharacteristic
53#63575C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59#63553C2211yescharacteristic
60#63553C2211yescharacteristic
61#5580—31no—
62#5580—31no—
63#5580—31no—
64#5580—61no—
65#5557—31no—
66C3×#441—31no—
67C3×#440—31no—
68#5191—31no—
69#5189—31no—
70#5174—31no—
71#5168—31no—
72#5030D311yescharacteristic, complemented
73#5026—31no—
74#5026D311yescharacteristic, complemented
75#5014—31no—
76#4886—31no—
77#4878—31no—
78#4865—31no—
79#4858—31no—
80#4816—31no—
81#4812—31no—
82#4812—31no—
83#4800—31no—
84#4800—31no—
85#4800—31no—
86#4782—31no—
87#4768—31no—
88#4711—31no—
89#4710—31no—
90#4707—31no—
91#4707—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3D411yescharacteristic
97C2×C4×C3⋊D3D411yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C32×C4⋊C4—21no—
104C32×C4⋊C4C2311yescharacteristic
105C32×C42—21no—
106C32×C42C2311yescharacteristic
107#3752—21no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116C4×C3⋊Dic3D411yescharacteristic
117C4×C3⋊Dic3D411yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C3×#216—22no—
120C3×#215—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137#3717—22no—
138#3714—22no—
139#3712—22no—
140#3712—22no—
141#3183—91noSylow
142C2×C3×Q16—31no—
143C2×C3×SD16—31no—
144C3×C4×Q8—21no—
145C3×C4×Q8—31no—
146C3×C4×Q8C2×D311yescharacteristic
147C3×C4×Q8C2×D311yescharacteristic
148C3×C4×D4—31no—
149#947—31no—
150#947—31no—
151#947—31no—
152#947—61no—
153#946—31no—
154#946—31no—
155#946—31no—
156#946—61no—
157C2×#216C2×D311yescharacteristic
158C2×#215—31no—
159C2×#215C2×D311yescharacteristic
160#938—31no—
161#936—31no—
162C2×#213—31no—
163C4×#67—61no—
164#926—61no—
165C2×D24—31no—
166C2×#204—31no—
167C2×ΓL(1,𝔽25)—31no—
168C2×ΓL(1,𝔽25)—31no—
169C2×ΓL(1,𝔽25)—31no—
170C2×ΓL(1,𝔽25)—31no—
171#898—61no—
172#898—61no—
173#898—61no—
174#898—62no—
175#897—31no—
176#895—31no—
177#895—31no—
178#895—31no—
179#895—61no—
180#894—61no—
181#894—61no—
182#894—61no—
183#894—62no—
184#890—31no—
185#890—31no—
186#890—31no—
187#890—31no—
188#890—61no—
189#883—61no—
190#879—61no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—61no—
194C4×D12—61no—
195C4×D12—61no—
196C4×D12—62no—
197C4×D12—61no—
198C4×D12C2×D311yescharacteristic
199#872—61no—
200#872—61no—
201#872—61no—
202#872—62no—
203C42×D3—31no—
204C42×D3—31no—
205C42×D3—61no—
206C4×Dic6C2×D311yescharacteristic
207C3×#107—31no—
208C3×#106—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#102—31no—
213C3×#97—31no—
214C3×#97—31no—
215#835—31no—
216#835C2×D311yescharacteristic
217#835C2×D311yescharacteristic
218#832—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#818—31no—
223#817—31no—
224#816—31no—
225C8×Dic3—31no—
226C8×Dic3—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229#810C2×D311yescharacteristic
230#809—31no—
231#809—31no—
232#809C2×D311yescharacteristic
233#808—31no—
234#808C2×D311yescharacteristic
235#807—31no—
236#807C2×D311yescharacteristic
237#803C2×D311yescharacteristic
238#803C2×D311yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—42no—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—41no—
259C4×C3⋊D3—41no—
260C4×C3⋊D3—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269#626—42no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272C3×C3⋊C8#4112yes—
273C3×C3⋊C8#4112yes—
274#529—91no—
275#529—91no—
276#499—91no—
277#495—91no—
278#488—91no—
279#488—91no—
280#470—91no—
281#469—91no—
282#468—91no—
283#468—91no—
284#442—91no—
285#441—31no—
286#440—31no—
287#440—91no—
288C4×M16—91no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×D4—31no—
294C22×C3×C4—61no—
295C2×#67—61no—
296C2×D12—31no—
297C2×D12—31no—
298C2×D12—61no—
299C2×D12—61no—
300C2×D12—61no—
301C2×D12—62no—
302C2×D12—61no—
303C2×D12C22×D311yescharacteristic
304C2×C4×D3—21no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—31no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—31no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—62no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×Dic6C22×D311yescharacteristic
318C3×Q16—62no—
319C3×SD16—62no—
320C2×C3×C8—31no—
321C2×C3×C8—31no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C3×C4⋊C4—22no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4C22×D311yescharacteristic
332C3×C4⋊C4C22×D311yescharacteristic
333C3×C22⋊C4—61no—
334C3×C42—22no—
335C3×C42—21no—
336C3×C42—21no—
337C3×C42—21no—
338C3×C42—61no—
339C3×C42C22×D311yescharacteristic
340C3×C42C22×D311yescharacteristic
341#217—61no—
342#217—61no—
343#217—61no—
344#216—22no—
345#215—22no—
346#215—62no—
347#213—62no—
348(C2×D3)⋊C4—21no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—62no—
365(C2×D3)⋊C4—62no—
366(C2×D3)⋊C4—62no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
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⋊Dic3—62no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—62no—
389Dic3⋊C4—62no—
390C4×Dic3—21no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—31no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404D24—62no—
405#204—62no—
406ΓL(1,𝔽25)—62no—
407ΓL(1,𝔽25)—62no—
408ΓL(1,𝔽25)—62no—
409ΓL(1,𝔽25)—62no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3⋊D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C32×C4—21no—
421C32×C4—21no—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4C2×#4111yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3⋊Dic3—21no—
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C2×Q16—31no—
434C2×SD16—31no—
435C2×SD16—91no—
436C2×D8—91no—
437C2×M16—91no—
438C2×M16—91no—
439#126—181no—
440#126—181no—
441#125—91no—
442#125—91no—
443#124—91no—
444#124—91no—
445#123—181no—
446#123—181no—
447C22⋊Q8—91no—
448C22⋊Q8—91no—
449#121—91no—
450#121—91no—
451C4×Q8—31no—
452C4×Q8D3211yescharacteristic
453C4×D4—31no—
454C4×D4—91no—
455C4×D4—181no—
456C4×D4—181no—
457#117—181no—
458#117—181no—
459C2×C42—91no—
460#107—31no—
461#107—91no—
462#106—31no—
463#106—91no—
464#103—31no—
465#103—31no—
466#103—31no—
467#103—91no—
468#102—31no—
469#102—91no—
470#102—91no—
471#102—91no—
472#97—31no—
473#97—31no—
474C4×C8—91no—
475C4×C8—91no—
476C23×C3—61no—
477C22×D3—21no—
478C22×D3—31no—
479C22×D3—31no—
480C22×D3—61no—
481C22×D3—62no—
482C22×D3—61no—
483C22×D3—61no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×D4—61no—
493C3×D4—61no—
494C2×C3×C4—22no—
495C2×C3×C4—22no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—122no—
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4D3×D411yescharacteristic
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513#67—122no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—62no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529D12—21no—
530D12—21no—
531D12—61no—
532D12—61no—
533D12—61no—
534D12—61no—
535D12—121no—
536D12—121no—
537D12—124no—
538D12—122no—
539D12—122no—
540D12—122no—
541C4×D3—42no—
542C4×D3—61no—
543C4×D3—61no—
544C4×D3—61no—
545C4×D3—61no—
546C4×D3—121no—
547C4×D3—121no—
548C4×D3—121no—
549C4×D3—121no—
550C4×D3—121no—
551C4×D3—121no—
552C4×D3—122no—
553C4×D3—124no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557Dic6—21no—
558Dic6—21no—
559C3×C8—32no—
560C3×C8—32no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C3⋊C8#23512yes—
566C3⋊C8#23512yes—
567C2×C32#53211yescharacteristic
568C2×C32#57511yescharacteristic
569C2×C32#57511yescharacteristic
570C3⋊D3—41no—
571C3⋊D3—81no—
572C3×D3—81no—
573C2×Q8—31no—
574C2×Q8C2×D3211yescharacteristic
575C2×D4—31no—
576C2×D4—91no—
577C2×D4—181no—
578C2×D4—181no—
579C22×C4—61no—
580C22×C4—91no—
581C22×C4—91no—
582C22×C4—91no—
583C22×C4—181no—
584Q16—62no—
585SD16—62no—
586SD16—182no—
587D8—182no—
588M16—182no—
589M16—182no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—31no—
594C4⋊C4—21no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—61no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—21no—
617C42—61no—
618C42—91no—
619C42—91no—
620C42—91no—
621C42C2×D3211yescharacteristic
622C22×C3—21no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3C2×D3×D411yescharacteristic
627C22×C3C2×D3×D411yescharacteristic
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—62no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—122no—
641C2×D3—122no—
642C2×D3—122no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C3×C4—22no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—41no—
657C3×C4—42no—
658C3×C4—42no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4C2×#23511yescharacteristic
667C3×C4C2×#23511yescharacteristic
668C3×C4D3×#4111yescharacteristic
669C3×C4D3×#4111yescharacteristic
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—61no—
678Dic3—61no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—122no—
683Dic3—121no—
684Dic3—121no—
685C32#318311yescharacteristic, complemented, Sylow
686C23—61no—
687C23—91no—
688C23—181no—
689Q8—21no—
690Q8—21no—
691Q8—61no—
692Q8—61no—
693D4—61no—
694D4—61no—
695D4—181no—
696D4—181no—
697D4—362no—
698D4—362no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—91no—
705C2×C4—91no—
706C2×C4—91no—
707C2×C4—122no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—361no—
712C2×C4—361no—
713C2×C4—362no—
714C2×C4#381111yescharacteristic
715C2×C4#381111yescharacteristic
716C2×C4C22×D3211yescharacteristic
717C8—32no—
718C8—32no—
719C8—61no—
720C8—61no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—241no—
725C2×C3#554811yescharacteristic
726C2×C3#554811yescharacteristic
727C2×C3#577311yescharacteristic
728C2×C3#577711yescharacteristic
729C2×C3#577711yescharacteristic
730C2×C3#577711yescharacteristic
731D3—81no—
732D3—122no—
733D3—121no—
734D3—121no—
735D3—242no—
736D3—241no—
737D3—241no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—181no—
742C22—181no—
743C22—181no—
744C22—361no—
745C22—361no—
746C22—361no—
747C22C2×#381111yescharacteristic
748C4—21no—
749C4—21no—
750C4—41no—
751C4—41no—
752C4—121no—
753C4—121no—
754C4—121no—
755C4—181no—
756C4—181no—
757C4—181no—
758C4—361no—
759C4D3×#23511yescharacteristic
760C4D3×#23511yescharacteristic
761C3—21no—
762C3#7979311yescharacteristic, complemented
763C3#7982611yescharacteristic, complemented
764C2—241no—
765C2—361no—
766C2—721no—
767C2#1059501711yescharacteristic
768C2#1059532311yescharacteristic
769C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10590508C2
hypercenterC4×Q8D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596051C2semidirect
2. #10593875C2semidirect
3. C3×#5030C2semidirect
4. C3×#5026C2semidirect
5. #10591610C2semidirect
6. #10591600C2semidirect
7. #10591590C2semidirect
8. #10591539C2semidirect
9. #10590539C2semidirect
10. #10590522C2semidirect
12. #10590417C2semidirect
13. #10590362C2semidirect
14. #10590346C2semidirect
15. #10590247C2semidirect
72. #5030D3semidirect
74. #5026D3semidirect
685. C32#3183semidirect
762. C3#79793semidirect
763. C3#79826semidirect

Maximal subgroups

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

subgroupindex
#105960512
#105938752
C3×#50302
C3×#50262
#105916102
#105916002
#105915902
#105915392
#105905392
#105905222
#105905082
#105904172
#105903622
#105903462
#105902472
#798263
#797933