Finite Group Databasebeta

← #11889400

Subgroups — #11889400

Order 1152.

804 conjugacy classes of subgroups.

The subgroup lattice has 749 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5513C211yesmaximal, characteristic
2Dic6×#67C211yesmaximal, characteristic
3#10592670C211yesmaximal, characteristic, complemented
4C2×C3×#810C211yesmaximal, characteristic, complemented
5#10591187C211yesmaximal, characteristic, complemented
6#10591185C211yesmaximal, characteristic, complemented
7#10591155C211yesmaximal, characteristic
8#10590604C211yesmaximal, characteristic, complemented
9#10590600C211yesmaximal, characteristic, complemented
10#10590562C211yesmaximal, characteristic, complemented
11#10590561C211yesmaximal, characteristic, complemented
12#10590520C211yesmaximal, characteristic, complemented
13#10590519C211yesmaximal, characteristic, complemented
14#10590491C211yesmaximal, characteristic, complemented
15#10590477C211yesmaximal, characteristic, complemented
16#83603—31nomaximal
17#78810—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×#929—21no—
23C3×C4×#67C2211yescharacteristic
24C3×#926—21no—
25C3×#924C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C3×#898—21no—
28C3×#897C2211yescharacteristic
29C3×#892C2211yescharacteristic
30C3×#890C2211yescharacteristic
31C3×#889—21no—
32C3×#887C2211yescharacteristic
33Dic3×#67—21no—
34#63964—21no—
35#63887—21no—
36#63866C2211yescharacteristic
37#63856C2211yescharacteristic
38Dic3×Dic6C2211yescharacteristic
39#63839—21no—
40C2×#3719C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44#63657C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47#63635C2211yescharacteristic
48#63635C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53#63575C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×#552—31no—
62Q8×#67—31no—
63D4×Dic6—31no—
64#5513D311yescharacteristic
65C2×C3×#103—31no—
66#5228—31no—
67#5116—31no—
68#5111—31no—
69#5069—31no—
70#5063—31no—
71#5052—31no—
72#5051—31no—
73#5050—31no—
74#5050—31no—
75#5031—31no—
76#5030—31no—
77#5011—31no—
78#5004—31no—
79#4996—31no—
80#4971—31no—
81#4971—31no—
82#4971—61no—
83C2×#810D311yescharacteristic, complemented
84#4816—31no—
85#4814—31no—
86#4809—31no—
87#4802—31no—
88#4797—31no—
89#4796—31no—
90#4795—31no—
91#4789—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6—22no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6—41no—
101C2×C3×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×D3×Dic3—21no—
106D3×Dic6—22no—
107D3×Dic6—41no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C4⋊C4C2311yescharacteristic
111#3757—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217D411yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3719—41no—
141#3718—22no—
142#3718—41no—
143#3711—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C22×Dic6—31no—
148C22×Dic6C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C3×#117—31no—
159C3×#117—61no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4C2×D311yescharacteristic
162C2×C3×C4⋊C4C2×D311yescharacteristic
163#946—31no—
164#946—61no—
165Q8×Dic3—31no—
166#944—31no—
167#944—61no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—31no—
172C2×#216—31no—
173D4×Dic3—61no—
174#929—21no—
175C4×#67—61no—
176C4×#67C2×D311yescharacteristic
177#926—21no—
178#924—31no—
179#924—31no—
180#924—31no—
181#924—61no—
182#924—61no—
183#924C2×D311yescharacteristic
184C2×#208—31no—
185C22×C3⋊C8C2×D311yescharacteristic
186C2×Dic12—31no—
187C2×ΓL(1,𝔽25)—31no—
188#898—21no—
189#897C2×D311yescharacteristic
190#892C2×D311yescharacteristic
191#890C2×D311yescharacteristic
192#889—21no—
193#888—61no—
194#887C2×D311yescharacteristic
195#878—61no—
196#878—61no—
197#869—31no—
198C4×Dic6—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#830—31no—
207#830—31no—
208#830—31no—
209#830—61no—
210(C2×D3)⋊C8—31no—
211#818—31no—
212#816—31no—
213#816—31no—
214#815—31no—
215Dic3⋊C8—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—61no—
224#810—61no—
225#810C2×D311yescharacteristic
226#810C2×D311yescharacteristic
227#810C2×D311yescharacteristic
228#810C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—61no—
234#808—61no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—42no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249#634—21no—
250#634—21no—
251C3×#67—22no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—42no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6#4112yes—
269#627—42no—
270D3×Dic3—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—31no—
276D4×Q8—91no—
277#491—91no—
278#485—91no—
279#483—91no—
280#479—91no—
281#470—91no—
282#467—91no—
283#462—91no—
284#451—91no—
285#451—91no—
286#441—91no—
287#435—91no—
288#419—91no—
289C2×#103—31no—
290C2×C3×Q8—31no—
291C2×C3×Q8—31no—
292C2×C3×Q8—31no—
293C2×C3×Q8—62no—
294C2×C3×Q8—61no—
295C2×C3×Q8—121no—
296C2×C3×D4—31no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—41no—
302C22×C3×C4—61no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C2×#67#6711yescharacteristic
306C22×Dic3—21no—
307C22×Dic3—61no—
308D3×Q8—62no—
309D3×Q8—121no—
310C2×C4×D3—61no—
311C2×C4×D3C22×D311yescharacteristic
312C2×Dic6—22no—
313C2×Dic6—21no—
314C2×Dic6—31no—
315C2×Dic6—31no—
316C2×Dic6—41no—
317C2×Dic6—61no—
318C2×Dic6—62no—
319C2×Dic6—61no—
320C2×Dic6—61no—
321C2×Dic6—121no—
322C2×Dic6C22×D311yescharacteristic
323C2×Dic6C22×D311yescharacteristic
324C2×Dic6C22×D311yescharacteristic
325C2×C3×C8—31no—
326C2×C3×C8—31no—
327C2×C3×C8—121no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—41no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—31no—
350C3×C42—61no—
351C3×C42—61no—
352#217—21no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—121no—
357#217#6711yescharacteristic
358#216—62no—
359#216—62no—
360#216—121no—
361#216—121no—
362#216—121no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4#6711yescharacteristic
367C4⋊Dic3—21no—
368C4⋊Dic3—21no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—121no—
387Dic3⋊C4#6711yescharacteristic
388C4×Dic3—21no—
389C4×Dic3—21no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3C22×D311yescharacteristic
393#208—121no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—41no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—121no—
404ΓL(1,𝔽25)—121no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32#13712yes—
408C22×C32C22×D411yescharacteristic
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C32×C4—21no—
413C32×C4—41no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4H(5,𝔽2)11yescharacteristic
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×Q8—31no—
427C22×Q8—91no—
428C2×Q16—91no—
429C2×Q16—91no—
430C2×Q16—91no—
431C2×M16—91no—
432C22×C8—31no—
433C4⋊Q8—91no—
434C4⋊Q8—181no—
435#126—61no—
436#125—31no—
437#125—61no—
438#123—61no—
439C22⋊Q8—31no—
440C22⋊Q8—31no—
441C22⋊Q8—91no—
442C22⋊Q8—91no—
443C22⋊Q8—181no—
444C22⋊Q8—181no—
445C4×Q8—31no—
446C4×Q8—91no—
447C4×D4—31no—
448C4×D4—181no—
449#117—31no—
450#117—61no—
451C2×C4⋊C4D3211yescharacteristic
452#107—91no—
453#106—91no—
454#106—91no—
455C4⋊C8—91no—
456#103—31no—
457#103—31no—
458#103—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468#97—91no—
469C23×C3—21no—
470C23×C3—31no—
471C23×C3D3×D411yescharacteristic
472C23×C3C2×#6711yescharacteristic
473C22×D3C2×#6711yescharacteristic
474C3×Q8—32no—
475C3×Q8—61no—
476C3×Q8—61no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8—122no—
481C3×D4—62no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—42no—
500C2×C3×C4—42no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—82no—
508C2×C3×C4—122no—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4C2×#6711yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513#67—22no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—42no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—122no—
526C2×Dic3C2×#6711yescharacteristic
527C2×Dic3C2×#6711yescharacteristic
528C2×Dic3C2×#6711yescharacteristic
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—122no—
532Dic6—21no—
533Dic6—21no—
534Dic6—21no—
535Dic6—21no—
536Dic6—21no—
537Dic6—42no—
538Dic6—61no—
539Dic6—61no—
540Dic6—61no—
541Dic6—61no—
542Dic6—121no—
543Dic6—121no—
544Dic6—122no—
545Dic6—122no—
546Dic6#23512yes—
547C3×C8—61no—
548C3×C8—61no—
549C3⋊C8—21no—
550C3⋊C8—21no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—121no—
556C3⋊C8—121no—
557C2×C32—22no—
558C2×C32#54611yescharacteristic
559C2×C32C2×#13711yescharacteristic
560C2×C32#57811yescharacteristic
561C3×D3—41no—
562C2×Q8—31no—
563C2×Q8—31no—
564C2×Q8—31no—
565C2×Q8—62no—
566C2×Q8—61no—
567C2×Q8—91no—
568C2×Q8—121no—
569C2×Q8—181no—
570C2×Q8—182no—
571C2×Q8—361no—
572C2×D4—31no—
573C22×C4—21no—
574C22×C4—31no—
575C22×C4—61no—
576C22×C4—181no—
577C22×C4C2×D3211yescharacteristic
578Q16—182no—
579Q16—361no—
580Q16—361no—
581M16—361no—
582C2×C8—31no—
583C2×C8—31no—
584C2×C8—91no—
585C2×C8—91no—
586C2×C8—121no—
587C4⋊C4—21no—
588C4⋊C4—31no—
589C4⋊C4—31no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—91no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4C2×D3211yescharacteristic
602C4⋊C4C2×D3211yescharacteristic
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—31no—
611C42—61no—
612C42—61no—
613C42—181no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—22no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3#91512yes—
626C22×C3#95112yes—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C22×#6711yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—62no—
645C3×C4—81no—
646C3×C4—81no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4C2×#23511yescharacteristic
651C3×C4#100411yescharacteristic
652C3×C4D3×#4111yescharacteristic
653C3×C4#100911yescharacteristic
654Dic3—22no—
655Dic3—21no—
656Dic3—21no—
657Dic3—21no—
658Dic3—41no—
659Dic3—41no—
660Dic3—41no—
661Dic3—121no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—241no—
666Dic3—241no—
667C32#331211yescharacteristic, complemented, Sylow
668C23—31no—
669C23D3×#6711yescharacteristic
670Q8—32no—
671Q8—61no—
672Q8—61no—
673Q8—61no—
674Q8—61no—
675Q8—61no—
676Q8—122no—
677Q8—181no—
678Q8—181no—
679Q8—362no—
680D4—62no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—42no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—122no—
696C2×C4—181no—
697C2×C4—181no—
698C2×C4—362no—
699C2×C4D3×#6711yescharacteristic
700C2×C4C22×D3211yescharacteristic
701C8—61no—
702C8—61no—
703C8—181no—
704C8—181no—
705C2×C3—22no—
706C2×C3—22no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—42no—
711C2×C3—121no—
712C2×C3#549011yescharacteristic
713C2×C3C2×#91511yescharacteristic
714C2×C3#576611yescharacteristic
715C2×C3C2×#95111yescharacteristic
716C2×C3#582911yescharacteristic
717C2×C3#583811yescharacteristic
718D3—41no—
719C22—21no—
720C22—21no—
721C22—61no—
722C22—61no—
723C22—61no—
724C22#6392912yes—
725C22C2×D3×#6711yescharacteristic
726C4—21no—
727C4—41no—
728C4—41no—
729C4—61no—
730C4—61no—
731C4—62no—
732C4—61no—
733C4—121no—
734C4—121no—
735C4—121no—
736C4—361no—
737C4—361no—
738C4D3×#23511yescharacteristic
739C4#6430711yescharacteristic
740C3—21no—
741C3#7881011yescharacteristic, complemented
742C3#8360311yescharacteristic, complemented
743C2—22no—
744C2—121no—
745C2#1059506511yescharacteristic
746C2C2×#6392911yescharacteristic
747C2#1059532711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC2×C4⋊C4D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10592670C2semidirect
4. C2×C3×#810C2semidirect
5. #10591187C2semidirect
6. #10591185C2semidirect
8. #10590604C2semidirect
9. #10590600C2semidirect
10. #10590562C2semidirect
11. #10590561C2semidirect
12. #10590520C2semidirect
13. #10590519C2semidirect
14. #10590491C2semidirect
15. #10590477C2semidirect
83. C2×#810D3semidirect
667. C32#3312semidirect
741. C3#78810semidirect
742. C3#83603semidirect

Maximal subgroups

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

subgroupindex
C3×#55132
Dic6×#672
#105926702
C2×C3×#8102
#105911872
#105911852
#105911552
#105906042
#105906002
#105905622
#105905612
#105905202
#105905192
#105904912
#105904772
#836033
#788103