Finite Group Databasebeta

← #11872816

Subgroups — #11872816

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595348C211yesmaximal, characteristic, complemented
2#10595215C211yesmaximal, characteristic
3#10592861C211yesmaximal, characteristic, complemented
4C3×#5169C211yesmaximal, characteristic
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6#10591569C211yesmaximal, characteristic, complemented
7#10591566C211yesmaximal, characteristic, complemented
8#10591559C211yesmaximal, characteristic, complemented
9#10591479C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic
11#10591405C211yesmaximal, characteristic, complemented
12#10590782C211yesmaximal, characteristic, complemented
13#10590744C211yesmaximal, characteristic, complemented
14#10590709C211yesmaximal, characteristic, complemented
15#10590696C211yesmaximal, characteristic, complemented
16#80137—31nomaximal
17#79659—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20#64153C2211yescharacteristic, complemented
21D4×C3⋊Dic3C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27#67⋊Dic3—21no—
28Dic3×#67—21no—
29D3×#217—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63898C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33#63872C2211yescharacteristic, complemented
34#63867—21no—
35#63859—21no—
36#63858—21no—
37#63857C2211yescharacteristic
38#63855C2211yescharacteristic
39#63846—21no—
40#63844C2211yescharacteristic, complemented
41#63841C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43#63662C2211yescharacteristic, complemented
44#63643C2211yescharacteristic, complemented
45#63641C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5798—31no—
62#5625—31no—
63#5583—31no—
64#5545—31no—
65C3×#450—31no—
66C3×C4×SD16—31no—
67#5218—31no—
68#5169D311yescharacteristic
69#5164—31no—
70#5162—31no—
71#5162—31no—
72#5162—31no—
73#5162—61no—
74Dic3×SD16D311yescharacteristic, complemented
75#5045—31no—
76#5026—31no—
77#5018—31no—
78#4871—31no—
79#4868—31no—
80#4818—31no—
81#4815—31no—
82#4776—31no—
83#4766—31no—
84#4763—31no—
85#4763—31no—
86#4758—31no—
87#4757—31no—
88#4723—31no—
89#4720—31no—
90C4×#204—31no—
91#4690—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105C32×SD16—22no—
106C2×C32×C8C2311yescharacteristic
107#3757—21no—
108#3754—22no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111#3750—21no—
112C4×C3⋊Dic3C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#215—22no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×Dic3⋊C4—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3C2311yescharacteristic
124C2×C3×C3⋊C8C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126#3724—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3D411yescharacteristic
138Dic32—21no—
139Dic32—21no—
140#3716—22no—
141#3123—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×SD16—21no—
145C2×C3×SD16—31no—
146C2×C3×SD16C2×D311yescharacteristic
147C2×C3×SD16C2×D311yescharacteristic
148C3×C22⋊Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×D4—31no—
151C2×#217—61no—
152C2×#217—61no—
153#946C2×D311yescharacteristic
154Q8×Dic3C2×D311yescharacteristic, complemented
155#944—31no—
156#944—31no—
157#944—61no—
158C2×#215C2×D311yescharacteristic
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—61no—
164D4×Dic3—61no—
165D4×Dic3—61no—
166D4×Dic3C2×D311yescharacteristic
167C2×#214—31no—
168C2×#214—31no—
169C2×#214—31no—
170C2×#214—61no—
171C4×#67—61no—
172C2×(C2×D3)⋊C4—61no—
173#926—31no—
174#926—31no—
175#924—31no—
176C2×#204—31no—
177#898—61no—
178#897—31no—
179#893—31no—
180#892—31no—
181#890—31no—
182#890—31no—
183#890—61no—
184#889—61no—
185#889—61no—
186#887—31no—
187#67⋊C4—61no—
188D3×C22⋊C4—61no—
189#879—61no—
190#879—61no—
191#876—61no—
192C4×D12—31no—
193#872—31no—
194#870—61no—
195C4×Dic6—31no—
196C3×#106—31no—
197C3×#103—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×C22⋊C8—31no—
202C3×C4×C8—31no—
203#835—31no—
204#835—31no—
205#835—61no—
206#835C2×D311yescharacteristic, complemented
207#832—31no—
208#832C2×D311yescharacteristic
209#832C2×D311yescharacteristic
210#830—31no—
211#821C2×D311yescharacteristic
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8C2×D311yescharacteristic
214#818—31no—
215#817—31no—
216#817C2×D311yescharacteristic, complemented
217#816—31no—
218#816—31no—
219#816—31no—
220#816—61no—
221#815—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#810—31no—
229#809—31no—
230#808—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#803—31no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—81no—
239C22×C3×D3—81no—
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—81no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252#634—21no—
253#634—21no—
254C3×#67—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#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266D3×Dic3—81no—
267D3×Dic3—81no—
268C32×C8—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—91no—
273#518—91no—
274#485—91no—
275#485—91no—
276#478—91no—
277#478—91no—
278#461—91no—
279#461—91no—
280#450—31no—
281#450—91no—
282#440—91no—
283#440—91no—
284C4×SD16—31no—
285C4×SD16—91no—
286#433—91no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×Q8—21no—
290C2×C3×Q8C22×D311yescharacteristic
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×D4—21no—
293C2×C3×D4—31no—
294C2×C3×D4—61no—
295C2×C3×D4—62no—
296C2×C3×D4—62no—
297C2×C3×D4C22×D311yescharacteristic
298C2×C3×D4C22×D311yescharacteristic
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C2×#67—21no—
302C22×Dic3—21no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—121no—
308D3×D4—22no—
309D3×D4—22no—
310C2×D12C22×D311yescharacteristic
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3C22×D311yescharacteristic
314C2×Dic6—31no—
315C2×Dic6—31no—
316C2×Dic6—61no—
317C3×SD16—22no—
318C3×SD16—22no—
319C3×SD16—42no—
320C3×SD16—62no—
321C2×C3×C8—21no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8C22×D311yescharacteristic
325C2×C3×C8C22×D311yescharacteristic
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C22⋊C4—61no—
332C3×C22⋊C4—61no—
333C3×C42—31no—
334C3×C42—61no—
335#217—21no—
336#217—31no—
337#217—31no—
338#217—61no—
339#217—61no—
340#217—61no—
341#217—61no—
342#217—61no—
343#217—61no—
344#217—121no—
345#215—22no—
346#214—62no—
347#214—62no—
348#214—62no—
349#214—122no—
350(C2×D3)⋊C4—21no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—31no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357C4⋊Dic3—21no—
358C4⋊Dic3—31no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—31no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3C22×D311yescharacteristic
367C4⋊Dic3C22×D311yescharacteristic
368C4⋊Dic3C22×D311yescharacteristic
369Dic3⋊C4—21no—
370Dic3⋊C4—31no—
371Dic3⋊C4—31no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—121no—
382Dic3⋊C4—121no—
383C4×Dic3—21no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3C22×D311yescharacteristic
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397#204—62no—
398C22×C32—22no—
399C22×C32—41no—
400C22×C32—41no—
401C22×C32C22×D411yescharacteristic
402C2×C3×D3—21no—
403C2×C3×D3—22no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—84no—
409C32×C4—41no—
410C32×C4C2×#4111yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3⋊Dic3—21no—
413C3⋊Dic3—21no—
414C3⋊Dic3—41no—
415C3⋊Dic3—41no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—41no—
420C3×Dic3—41no—
421C3×Dic3—41no—
422C22×D4—31no—
423C2×SD16—31no—
424C2×SD16—91no—
425C2×SD16—91no—
426C2×SD16D3211yescharacteristic
427C4⋊Q8—91no—
428#126—181no—
429#126—181no—
430#125—91no—
431#125—181no—
432#125—181no—
433C22⋊Q8—31no—
434C22⋊Q8—91no—
435C4×Q8—31no—
436C4×Q8—91no—
437C4×D4—31no—
438C4×D4—91no—
439C4×D4—91no—
440C4×D4—91no—
441C4×D4—181no—
442C4×D4—181no—
443#117—91no—
444#117—91no—
445C2×C22⋊C4—181no—
446C2×C22⋊C4—181no—
447#107—91no—
448#107—91no—
449#106—31no—
450#106—91no—
451C4⋊C8—91no—
452C4⋊C8—91no—
453#103—31no—
454#103—91no—
455#103—91no—
456#103—91no—
457#102—31no—
458#102—31no—
459#102—31no—
460#102—91no—
461C22⋊C8—31no—
462C22⋊C8—91no—
463#97—91no—
464C4×C8—31no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—31no—
468C23×C3—41no—
469C23×C3—64no—
470C23×C3—61no—
471C23×C3—241no—
472C23×C3—241no—
473C22×D3—21no—
474C22×D3—24no—
475C22×D3—81no—
476C22×D3—81no—
477C22×D3D3×D411yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—22no—
487C3×D4—32no—
488C3×D4—41no—
489C3×D4—64no—
490C3×D4—61no—
491C3×D4#23512yes—
492C3×D4#23712yes—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—41no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—241no—
506C2×C3×C4C23×D311yescharacteristic
507C2×C3×C4C23×D311yescharacteristic
508#67—24no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—31no—
513C2×Dic3—31no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—81no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—241no—
526C2×Dic3—241no—
527C2×Dic3—241no—
528C2×Dic3—241no—
529C2×Dic3—242no—
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532C2×Dic3D3×D411yescharacteristic
533D12—21no—
534D12#23712yes—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—241no—
538C4×D3—241no—
539Dic6—61no—
540Dic6—61no—
541Dic6—61no—
542Dic6—61no—
543Dic6—121no—
544Dic6—121no—
545C3×C8—21no—
546C3×C8—21no—
547C3×C8—41no—
548C3×C8—61no—
549C3×C8—61no—
550C3⋊C8—21no—
551C3⋊C8—21no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—121no—
555C2×C32—42no—
556C2×C32#52511yescharacteristic
557C2×C32#57711yescharacteristic
558C2×C32#57711yescharacteristic
559C3×D3—41no—
560C3×D3—42no—
561C24—61no—
562C2×Q8—91no—
563C2×Q8C2×D3211yescharacteristic
564C2×D4—31no—
565C2×D4—61no—
566C2×D4—62no—
567C2×D4—62no—
568C2×D4C2×D3211yescharacteristic
569C22×C4—31no—
570C22×C4—61no—
571C22×C4—181no—
572C22×C4—181no—
573C22×C4—181no—
574SD16—22no—
575SD16—62no—
576SD16—182no—
577SD16—182no—
578C2×C8—31no—
579C2×C8—31no—
580C2×C8—91no—
581C2×C8C2×D3211yescharacteristic
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—31no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—91no—
588C4⋊C4—91no—
589C4⋊C4—91no—
590C4⋊C4—181no—
591C4⋊C4—181no—
592C4⋊C4—181no—
593C4⋊C4—181no—
594C4⋊C4—181no—
595C4⋊C4—181no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—91no—
599C22⋊C4—91no—
600C22⋊C4—181no—
601C22⋊C4—181no—
602C22⋊C4—181no—
603C22⋊C4—181no—
604C22⋊C4—181no—
605C42—31no—
606C42—61no—
607C42—91no—
608C42—181no—
609C42—181no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—42no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—62no—
622C22×C3—81no—
623C22×C3—81no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—244no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—22no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—84no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—81no—
644C3×C4—121no—
645C3×C4—121no—
646C3×C4—121no—
647C3×C4C2×#23511yescharacteristic
648C3×C4C2×#23711yescharacteristic
649C3×C4C2×#23711yescharacteristic
650C3×C4D3×#4111yescharacteristic
651Dic3—21no—
652Dic3—21no—
653Dic3—21no—
654Dic3—41no—
655Dic3—41no—
656Dic3—41no—
657Dic3—62no—
658Dic3—61no—
659Dic3—61no—
660Dic3—61no—
661Dic3—61no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—241no—
668Dic3—241no—
669C32#312311yescharacteristic, complemented, Sylow
670C23—21no—
671C23—31no—
672C23—64no—
673C23—61no—
674C23—241no—
675C23—241no—
676Q8—21no—
677Q8—21no—
678Q8—181no—
679Q8—181no—
680D4—21no—
681D4—32no—
682D4—64no—
683D4—61no—
684D4#380412yes—
685C2×C4—21no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—181no—
697C2×C4—181no—
698C2×C4—241no—
699C2×C4—721no—
700C2×C4—721no—
701C2×C4—721no—
702C2×C4C22×D3211yescharacteristic
703C8—21no—
704C8—61no—
705C8—61no—
706C8—181no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—42no—
711C2×C3—42no—
712C2×C3—82no—
713C2×C3—121no—
714C2×C3—122no—
715C2×C3#554711yescharacteristic
716C2×C3#558611yescharacteristic
717C2×C3#576211yescharacteristic
718C2×C3#576211yescharacteristic
719C2×C3#577011yescharacteristic
720C2×C3#577511yescharacteristic
721D3—41no—
722D3—42no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—61no—
727C22—62no—
728C22—61no—
729C22—61no—
730C22—121no—
731C22—121no—
732C22—244no—
733C22D32×D411yescharacteristic
734C4—41no—
735C4—61no—
736C4—61no—
737C4—61no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4—181no—
742C4—181no—
743C4—361no—
744C4—361no—
745C4D3×#23711yescharacteristic
746C4C2×#380411yescharacteristic
747C3—21no—
748C3#7965911yescharacteristic, complemented
749C3#8013711yescharacteristic, complemented
750C2—42no—
751C2—121no—
752C2—122no—
753C2#1059474911yescharacteristic
754C2#1059475311yescharacteristic
755C2#1059512911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
prime radicalC2×C3×D3×D4C22
hypercenterC2×SD16D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595348C2semidirect
3. #10592861C2semidirect
5. C3×Dic3×SD16C2semidirect
6. #10591569C2semidirect
7. #10591566C2semidirect
8. #10591559C2semidirect
9. #10591479C2semidirect
11. #10591405C2semidirect
12. #10590782C2semidirect
13. #10590744C2semidirect
14. #10590709C2semidirect
15. #10590696C2semidirect
20. #64153C22semidirect
24. C3×Q8×Dic3C22semidirect
33. #63872C22semidirect
40. #63844C22semidirect
43. #63662C22semidirect
44. #63643C22semidirect
45. #63641C22semidirect
46. C3×#835C22semidirect
51. C3×#817C22semidirect
52. C3×C8×Dic3C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63567C22semidirect
60. #63554C22semidirect
74. Dic3×SD16D3semidirect
154. Q8×Dic3C2×D3semidirect
206. #835C2×D3semidirect
216. #817C2×D3semidirect
227. C8×Dic3C2×D3semidirect
669. C32#3123semidirect
748. C3#79659semidirect
749. C3#80137semidirect

Maximal subgroups

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

subgroupindex
#105953482
#105952152
#105928612
C3×#51692
C3×Dic3×SD162
#105915692
#105915662
#105915592
#105914792
#105914592
#105914052
#105907822
#105907442
#105907092
#105906962
#801373
#796593