Finite Group Databasebeta

← #11876896

Subgroups — #11876896

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#10596095C211yesmaximal, characteristic, complemented
2#10594965C211yesmaximal, characteristic, complemented
3C3×#5052C211yesmaximal, characteristic, complemented
4C3×#5049C211yesmaximal, characteristic, complemented
5#10591610C211yesmaximal, characteristic, complemented
6#10591582C211yesmaximal, characteristic, complemented
7#10591572C211yesmaximal, characteristic, complemented
8#10591539C211yesmaximal, characteristic, complemented
9#10591178C211yesmaximal, characteristic, complemented
10#10591165C211yesmaximal, characteristic
11#10591060C211yesmaximal, characteristic, complemented
12#10590539C211yesmaximal, characteristic, complemented
13#10590484C211yesmaximal, characteristic, complemented
14#10590462C211yesmaximal, characteristic, complemented
15#10590417C211yesmaximal, characteristic, complemented
16#80892—31nomaximal
17#80791—31nomaximal
18C32×C22⋊Q8C2211yescharacteristic
19#64156C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64139C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23#64107—21no—
24#64102C2211yescharacteristic
25#64101—21no—
26#64099C2211yescharacteristic
27#64095—21no—
28#64090—21no—
29C2×C3×#216C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C3×#930C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C2×C3×#208C2211yescharacteristic
34C2×C3×#208C2211yescharacteristic
35#67⋊Dic3—21no—
36#63962—21no—
37#63898C2211yescharacteristic
38#63878—21no—
39#63872C2211yescharacteristic
40#63863C2211yescharacteristic
41#63862—21no—
42#63843C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#810C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#807C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63566C2211yescharacteristic
54#63564C2211yescharacteristic
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic
57#63555C2211yescharacteristic
58#63555C2211yescharacteristic
59#63553C2211yescharacteristic
60#63553C2211yescharacteristic
61#5624—31no—
62#5624—31no—
63#5624—31no—
64#5624—61no—
65#5600—31no—
66C3×#470—31no—
67C3×#468—31no—
68#5191—31no—
69#5184—31no—
70#5168—31no—
71#5164—31no—
72#5135—31no—
73#5134—31no—
74Dic3×M16—31no—
75Dic3×M16—31no—
76#5052D311yescharacteristic, complemented
77#5049—31no—
78#5049D311yescharacteristic, complemented
79#5039—31no—
80#4889—31no—
81#4878—31no—
82#4869—31no—
83#4858—31no—
84#4817—31no—
85#4817—31no—
86#4800—31no—
87#4800—31no—
88#4800—31no—
89#4789—31no—
90#4785—31no—
91#4768—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C22×C3⋊Dic3D411yescharacteristic
96C22×C3⋊Dic3D411yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C3×#67—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×D3×Dic3—21no—
103C32×C4⋊C4—21no—
104C32×C4⋊C4C2311yescharacteristic
105C32×C22⋊C4—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752—21no—
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3D411yescharacteristic
116C4×C3⋊Dic3D411yescharacteristic
117C4×C3⋊Dic3C2311yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C3×#217—21no—
120C3×#216—22no—
121C3×#215—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×#208—22no—
127C3×#208—22no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3717—22no—
140#3714—22no—
141#3183—91noSylow
142C2×C3×Q16—31no—
143C2×C3×SD16—31no—
144C2×C3×M16—31no—
145C2×C3×M16—31no—
146C3×C22⋊Q8—21no—
147C3×C22⋊Q8—31no—
148C3×C22⋊Q8C2×D311yescharacteristic
149C3×C22⋊Q8C2×D311yescharacteristic
150C3×#121—31no—
151#947—31no—
152#947—31no—
153#947—31no—
154#947—61no—
155Q8×Dic3—31no—
156Q8×Dic3—31no—
157Q8×Dic3—31no—
158Q8×Dic3—61no—
159C2×#216C2×D311yescharacteristic
160C2×#215—31no—
161C2×#215C2×D311yescharacteristic
162#936—31no—
163#935—61no—
164D4×Dic3—31no—
165D4×Dic3—61no—
166C2×#213—31no—
167#930—31no—
168#930—31no—
169#930—61no—
170#930C2×D311yescharacteristic
171#924C2×D311yescharacteristic
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—61no—
175C2×#208C2×D311yescharacteristic
176C2×#208C2×D311yescharacteristic
177C2×D24—31no—
178C2×#204—31no—
179#898—61no—
180#898—61no—
181#898—61no—
182#898—62no—
183#893—31no—
184#893—31no—
185#893—31no—
186#893—61no—
187#892—61no—
188#892—61no—
189#892—61no—
190#892—62no—
191#890—31no—
192#890—31no—
193#890—31no—
194#890—31no—
195#890—61no—
196#887—31no—
197#886—61no—
198#886—61no—
199#886—62no—
200#886—61no—
201#67⋊C4—61no—
202#67⋊C4—61no—
203#67⋊C4—62no—
204#67⋊C4—61no—
205#879—61no—
206#877—61no—
207C3×#107—31no—
208C3×#106—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#102—31no—
213#835—31no—
214#835C2×D311yescharacteristic
215#835C2×D311yescharacteristic
216#832—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#818—31no—
221#817—31no—
222#816—31no—
223#815—31no—
224#815—31no—
225#815—31no—
226#815—31no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—31no—
231#810C2×D311yescharacteristic
232#809—31no—
233#809—31no—
234#809C2×D311yescharacteristic
235#808—31no—
236#808C2×D311yescharacteristic
237#807—31no—
238#807C2×D311yescharacteristic
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—41no—
253C2×C3⋊Dic3—41no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260C4×C3⋊D3—42no—
261C3×#67—42no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269D3×Dic3—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—31no—
281#469—91no—
282#468—31no—
283#468—91no—
284#442—91no—
285#441—91no—
286#440—91no—
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—
294C2×C3×D4—61no—
295C22×C3×C4—21no—
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C2×#67—21no—
299C2×#67—62no—
300C2×#67—61no—
301C2×#67—61no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—61no—
312C2×D12C22×D311yescharacteristic
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—62no—
317C2×Dic6C22×D311yescharacteristic
318C3×Q16—62no—
319C3×SD16—62no—
320C3×M16—62no—
321C3×M16—62no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C3×C4⋊C4—22no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C22⋊C4—22no—
336C3×C22⋊C4—21no—
337C3×C22⋊C4—21no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340#217—21no—
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—62no—
359(C2×D3)⋊C4—62no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—62no—
375C4⋊Dic3—62no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—62no—
385C4×Dic3—31no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—62no—
402#208—22no—
403#208—22no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—62no—
409#204—62no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32C22×D411yescharacteristic
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—41no—
422C32×C4—41no—
423C32×C4C2×#4111yescharacteristic
424C32×C4C2×#4111yescharacteristic
425C3⋊Dic3—21no—
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—31no—
438C2×M16—31no—
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—31no—
448C22⋊Q8D3211yescharacteristic
449#121—31no—
450#121—91no—
451C4×Q8—91no—
452C4×Q8—91no—
453C4×D4—91no—
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—91no—
473#97—91no—
474C4×C8—91no—
475C4×C8—91no—
476C23×C3—21no—
477C23×C3—61no—
478C23×C3D3×D411yescharacteristic
479C23×C3D3×D411yescharacteristic
480C22×D3—21no—
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—
494C3×D4—122no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—22no—
500C2×C3×C4—22no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—42no—
517#67—124no—
518#67—122no—
519#67—122no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—62no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—122no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—122no—
544C2×Dic3—122no—
545D12—21no—
546D12—21no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—121no—
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#23712yes—
566C3⋊C8#23712yes—
567C2×C32—41no—
568C2×C32#53211yescharacteristic
569C2×C32#57511yescharacteristic
570C2×C32#57511yescharacteristic
571C3⋊D3—81no—
572C3×D3—81no—
573C2×Q8—31no—
574C2×Q8C2×D3211yescharacteristic
575C2×D4—31no—
576C2×D4—61no—
577C2×D4—91no—
578C2×D4—181no—
579C22×C4—91no—
580C22×C4—91no—
581C22×C4—181no—
582C22×C4—181no—
583C22×C4C2×D3211yescharacteristic
584Q16—62no—
585SD16—62no—
586SD16—182no—
587D8—182no—
588M16—62no—
589M16—62no—
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—21no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—91no—
617C42—91no—
618C42—91no—
619C42—91no—
620C42—181no—
621C42—181no—
622C22×C3—22no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C2×D3×D411yescharacteristic
636C22×C3C2×D3×D411yescharacteristic
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
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—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—41no—
654C3×C4—42no—
655C3×C4—42no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—121no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4C2×#23711yescharacteristic
664C3×C4C2×#23711yescharacteristic
665C3×C4D3×#4111yescharacteristic
666C3×C4D3×#4111yescharacteristic
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—62no—
671Dic3—61no—
672Dic3—61no—
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—181no—
688C23#381111yescharacteristic
689Q8—21no—
690Q8—21no—
691Q8—61no—
692Q8—61no—
693D4—61no—
694D4—61no—
695D4—122no—
696D4—181no—
697D4—181no—
698D4—362no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—91no—
707C2×C4—91no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—181no—
711C2×C4—362no—
712C2×C4—362no—
713C2×C4—361no—
714C2×C4—361no—
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—42no—
725C2×C3—41no—
726C2×C3—41no—
727C2×C3—241no—
728C2×C3#559611yescharacteristic
729C2×C3#559611yescharacteristic
730C2×C3#577311yescharacteristic
731C2×C3#577711yescharacteristic
732C2×C3#577711yescharacteristic
733C2×C3#577711yescharacteristic
734D3—81no—
735D3—242no—
736D3—241no—
737D3—241no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—361no—
745C22—361no—
746C22—361no—
747C22C2×#381111yescharacteristic
748C4—21no—
749C4—41no—
750C4—41no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—181no—
755C4—181no—
756C4—181no—
757C4—181no—
758C4—361no—
759C4D3×#23711yescharacteristic
760C4D3×#23711yescharacteristic
761C3—21no—
762C3#8079111yescharacteristic, complemented
763C3#8089211yescharacteristic, complemented
764C2—41no—
765C2—241no—
766C2—721no—
767C2#1059516511yescharacteristic
768C2#1059532311yescharacteristic
769C2#1059547111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10591165C2
hypercenterC22⋊Q8D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596095C2semidirect
2. #10594965C2semidirect
3. C3×#5052C2semidirect
4. C3×#5049C2semidirect
5. #10591610C2semidirect
6. #10591582C2semidirect
7. #10591572C2semidirect
8. #10591539C2semidirect
9. #10591178C2semidirect
11. #10591060C2semidirect
12. #10590539C2semidirect
13. #10590484C2semidirect
14. #10590462C2semidirect
15. #10590417C2semidirect
76. #5052D3semidirect
78. #5049D3semidirect
685. C32#3183semidirect
762. C3#80791semidirect
763. C3#80892semidirect

Maximal subgroups

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

subgroupindex
#105960952
#105949652
C3×#50522
C3×#50492
#105916102
#105915822
#105915722
#105915392
#105911782
#105911652
#105910602
#105905392
#105904842
#105904622
#105904172
#808923
#807913