Finite Group Databasebeta

← #11872810

Subgroups — #11872810

Order 1152.

836 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5625C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic
3#10592744C211yesmaximal, characteristic, complemented
4C3×#5046C211yesmaximal, characteristic
5#10591566C211yesmaximal, characteristic, complemented
6#10591564C211yesmaximal, characteristic, complemented
7#10591564C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#10591169C211yesmaximal, characteristic
10#10591127C211yesmaximal, characteristic, complemented
11#10591056C211yesmaximal, characteristic, complemented
12#10590469C211yesmaximal, characteristic, complemented
13#10590467C211yesmaximal, characteristic, complemented
14#10590454C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#83447—31nomaximal
17#80137—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20#64135C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic, complemented
22C3×#944C2211yescharacteristic, complemented
23C2×C3×#215C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#890—21no—
28C3×#890C2211yescharacteristic, complemented
29C3×#889—21no—
30C3×#887C2211yescharacteristic, complemented
31C3×#879—21no—
32C3×#879—21no—
33D3×#217—21no—
34D3×#217—21no—
35#63898—21no—
36#63898—21no—
37Dic3×D12C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40Dic3×D12C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63662C2211yescharacteristic, complemented
44#63662C2211yescharacteristic, complemented
45#63657C2211yescharacteristic
46#63635C2211yescharacteristic, complemented
47#63634C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#541—31no—
62#5798—31no—
63#5625D311yescharacteristic, complemented
64#5521—31no—
65C3×#450—31no—
66#5218—31no—
67#5164—31no—
68#5162—31no—
69#5162—31no—
70Dic3×SD16—31no—
71#5083—31no—
72#5083—31no—
73#5066—31no—
74#5066—31no—
75#5046—31no—
76#5046D311yescharacteristic
77#5045—31no—
78#5045—31no—
79#5045—31no—
80#5045—61no—
81#5026—31no—
82#5026—31no—
83C4×#215—31no—
84C4×#215—31no—
85#5000—31no—
86#4766—31no—
87#4763—31no—
88#4758—31no—
89#4757—31no—
90#4723—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×Q8C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×C3×D12—21no—
96C2×C3×D12—22no—
97C2×C3×D12—22no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×D3×Dic3—21no—
102C2×D3×Dic3—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C22⋊C4—21no—
108#3757—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4×C3⋊Dic3—21no—
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#217D411yescharacteristic
116C3×#217D411yescharacteristic
117C3×#215—22no—
118C3×#215—22no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3715—22no—
140#3715—22no—
141#3123—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C3×C4⋊Q8—31no—
147C3×#126—61no—
148C3×#126—61no—
149C3×#125—31no—
150C3×#125—61no—
151C3×#125—61no—
152C3×C22⋊Q8—21no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8C2×D311yescharacteristic
155C3×C22⋊Q8C2×D311yescharacteristic
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×#117—31no—
159C2×#217—61no—
160C2×#217—61no—
161Q8×Dic3C2×D311yescharacteristic, complemented
162#944C2×D311yescharacteristic, complemented
163C2×#215—31no—
164C2×#215—31no—
165C2×#215C2×D311yescharacteristic
166C2×#215C2×D311yescharacteristic
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—31no—
171D4×Dic3—61no—
172D4×Dic3—61no—
173C2×#214—31no—
174C2×#214—31no—
175#926—31no—
176#926—31no—
177#926—61no—
178#926C2×D311yescharacteristic
179#924C2×D311yescharacteristic
180#893—61no—
181#893—61no—
182#890—21no—
183#890C2×D311yescharacteristic, complemented
184#889—21no—
185#887C2×D311yescharacteristic, complemented
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#879—21no—
189#879—21no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—31no—
194C3×#102—31no—
195C3×#102—31no—
196C3×C22⋊C8—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—61no—
204#835—61no—
205#832—31no—
206#832—31no—
207#830—31no—
208#830—31no—
209#830—61no—
210#830C2×D311yescharacteristic
211#818—31no—
212#817—31no—
213#816—31no—
214#816—31no—
215#815—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218C8×Dic3—31no—
219#809—31no—
220#809—31no—
221#809C2×D311yescharacteristic
222#809C2×D311yescharacteristic
223#808—31no—
224#808—31no—
225#808—31no—
226#808—61no—
227#807—31no—
228#807—31no—
229#807—31no—
230#807—61no—
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—81no—
240C22×C3×D3—81no—
241C32×Q8—21no—
242C32×Q8—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×D12—24no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12#4112yes—
261C3×D12#4112yes—
262C3×Dic6—21no—
263C3×Dic6—21no—
264D3×Dic3—81no—
265D3×Dic3—81no—
266D3×Dic3—81no—
267D3×Dic3—81no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#541—31no—
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—91no—
285C4×SD16—91no—
286#433—91no—
287C24×C3—61no—
288C23×D3—21no—
289C2×C3×Q8—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—62no—
296C2×C3×D4—62no—
297C2×C3×D4—61no—
298C22×C3×C4—21no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C2×D12—21no—
306C2×D12—22no—
307C2×D12—22no—
308C2×D12C22×D311yescharacteristic
309C2×D12C22×D311yescharacteristic
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×Dic6C22×D311yescharacteristic
315C3×SD16—62no—
316C3×SD16—62no—
317C2×C3×C8—31no—
318C2×C3×C8—31no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—41no—
326C3×C4⋊C4—61no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C22⋊C4—21no—
336C3×C22⋊C4—21no—
337C3×C22⋊C4—31no—
338C3×C22⋊C4—31no—
339C3×C22⋊C4—41no—
340C3×C22⋊C4—61no—
341C3×C42—31no—
342C3×C42—31no—
343C3×C42—61no—
344C3×C42—61no—
345#217—21no—
346#217—61no—
347#217—61no—
348#217—61no—
349#217—61no—
350#217—61no—
351#217—61no—
352#217—121no—
353#217#6711yescharacteristic
354#217#6711yescharacteristic
355#215—22no—
356#215—22no—
357#215—62no—
358#215—62no—
359#214—62no—
360#214—62no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365C4⋊Dic3—21no—
366C4⋊Dic3—21no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3#6711yescharacteristic
374C4⋊Dic3#6711yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381C4×Dic3—21no—
382C4×Dic3—21no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—121no—
386C4×Dic3C22×D311yescharacteristic
387C4×Dic3C22×D311yescharacteristic
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32C22×D411yescharacteristic
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—84no—
407C32×C4—21no—
408C32×C4—41no—
409C32×C4—41no—
410C32×C4C2×#4111yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3⋊Dic3—41no—
413C3⋊Dic3—41no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C22×D4—31no—
421C2×SD16—31no—
422C2×SD16—31no—
423C2×SD16—91no—
424C2×SD16—91no—
425C4⋊Q8—31no—
426#126—61no—
427#126—61no—
428#125—31no—
429#125—61no—
430#125—61no—
431C22⋊Q8—31no—
432C22⋊Q8D3211yescharacteristic
433C4×Q8—31no—
434C4×Q8—31no—
435C4×D4—91no—
436C4×D4—91no—
437C4×D4—91no—
438C4×D4—91no—
439C4×D4—181no—
440C4×D4—181no—
441#117—31no—
442#117—91no—
443C2×C22⋊C4—181no—
444C2×C22⋊C4—181no—
445#107—91no—
446#107—91no—
447#106—91no—
448#106—91no—
449C4⋊C8—91no—
450C4⋊C8—91no—
451#103—91no—
452#103—91no—
453#103—91no—
454#103—91no—
455#102—31no—
456#102—31no—
457#102—91no—
458#102—91no—
459C22⋊C8—31no—
460C22⋊C8—91no—
461#97—91no—
462C4×C8—91no—
463C23×C3—21no—
464C23×C3—64no—
465C23×C3—61no—
466C23×C3—61no—
467C23×C3—241no—
468C23×C3—241no—
469C23×C3D3×D411yescharacteristic
470C23×C3C2×#6711yescharacteristic
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—24no—
474C22×D3—81no—
475C22×D3—81no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—41no—
481C3×Q8—41no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×D4—32no—
485C3×D4—32no—
486C3×D4—64no—
487C3×D4—61no—
488C3×D4—61no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4C2×#6711yescharacteristic
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—241no—
522C2×Dic3—241no—
523C2×Dic3—241no—
524C2×Dic3—241no—
525C2×Dic3C2×#6711yescharacteristic
526C2×Dic3C2×#6711yescharacteristic
527C2×Dic3C2×#6711yescharacteristic
528C2×Dic3C2×#6711yescharacteristic
529D12—24no—
530D12—21no—
531D12—21no—
532D12#23712yes—
533D12#23712yes—
534C4×D3—241no—
535C4×D3—241no—
536C4×D3—241no—
537C4×D3—241no—
538Dic6—21no—
539Dic6—21no—
540C3×C8—61no—
541C3×C8—61no—
542C3⋊C8—21no—
543C3⋊C8—21no—
544C3⋊C8—61no—
545C3⋊C8—61no—
546C3⋊C8—61no—
547C3⋊C8—61no—
548C3⋊C8—121no—
549C3⋊C8—121no—
550C2×C32—41no—
551C2×C32#52511yescharacteristic
552C2×C32#57711yescharacteristic
553C2×C32#57711yescharacteristic
554C3×D3—42no—
555C3×D3—42no—
556C24—61no—
557C2×Q8—31no—
558C2×Q8C2×D3211yescharacteristic
559C2×D4—31no—
560C2×D4—31no—
561C2×D4—62no—
562C2×D4—62no—
563C2×D4—61no—
564C22×C4—181no—
565C22×C4—181no—
566C22×C4—181no—
567C22×C4—181no—
568C22×C4C2×D3211yescharacteristic
569SD16—62no—
570SD16—62no—
571SD16—182no—
572SD16—182no—
573C2×C8—31no—
574C2×C8—31no—
575C2×C8—91no—
576C2×C8—91no—
577C4⋊C4—21no—
578C4⋊C4—31no—
579C4⋊C4—31no—
580C4⋊C4—31no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—91no—
589C4⋊C4—91no—
590C4⋊C4C2×D3211yescharacteristic
591C22⋊C4—21no—
592C22⋊C4—31no—
593C22⋊C4—31no—
594C22⋊C4—61no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C22⋊C4—181no—
599C22⋊C4—181no—
600C42—31no—
601C42—31no—
602C42—61no—
603C42—61no—
604C42—181no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—62no—
616C22×C3—62no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3—244no—
622C22×C3C2×D3×D411yescharacteristic
623C22×C3C22×#6711yescharacteristic
624C2×D3—22no—
625C2×D3—22no—
626C2×D3—41no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—41no—
630C2×D3—84no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—81no—
645C3×C4—81no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4C2×#23711yescharacteristic
649C3×C4C2×#23711yescharacteristic
650C3×C4D3×#4111yescharacteristic
651C3×C4D3×#4111yescharacteristic
652Dic3—21no—
653Dic3—21no—
654Dic3—21no—
655Dic3—21no—
656Dic3—41no—
657Dic3—41no—
658Dic3—121no—
659Dic3—121no—
660Dic3—121no—
661Dic3—121no—
662Dic3—241no—
663Dic3—241no—
664C32#312311yescharacteristic, complemented, Sylow
665C23—64no—
666C23—61no—
667C23—61no—
668C23—241no—
669C23—241no—
670C23D3×#6711yescharacteristic
671Q8—21no—
672Q8—21no—
673Q8—61no—
674Q8—61no—
675D4—32no—
676D4—32no—
677D4—64no—
678D4—61no—
679D4—61no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—721no—
693C2×C4—721no—
694C2×C4—721no—
695C2×C4—721no—
696C2×C4D3×#6711yescharacteristic
697C2×C4C22×D3211yescharacteristic
698C8—61no—
699C8—61no—
700C8—181no—
701C8—181no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—41no—
706C2×C3—41no—
707C2×C3—81no—
708C2×C3—122no—
709C2×C3—122no—
710C2×C3#558611yescharacteristic
711C2×C3#576211yescharacteristic
712C2×C3#577511yescharacteristic
713C2×C3#582811yescharacteristic
714C2×C3#583711yescharacteristic
715C2×C3#583711yescharacteristic
716D3—42no—
717D3—42no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—62no—
722C22—62no—
723C22—121no—
724C22—121no—
725C22—121no—
726C22—121no—
727C22—244no—
728C22C2×D3×#6711yescharacteristic
729C4—21no—
730C4—41no—
731C4—41no—
732C4—61no—
733C4—61no—
734C4—61no—
735C4—61no—
736C4—121no—
737C4—121no—
738C4—361no—
739C4—361no—
740C4D3×#23711yescharacteristic
741C4D3×#23711yescharacteristic
742C3—21no—
743C3#8013711yescharacteristic, complemented
744C3#8344711yescharacteristic, complemented
745C2—41no—
746C2—122no—
747C2—122no—
748C2#1059515411yescharacteristic
749C2#1059531811yescharacteristic
750C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC22⋊Q8D32
hypocenterC32#3123
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. C3×#5625C2semidirect
3. #10592744C2semidirect
5. #10591566C2semidirect
6. #10591564C2semidirect
7. #10591564C2semidirect
8. Dic3×#215C2semidirect
10. #10591127C2semidirect
11. #10591056C2semidirect
12. #10590469C2semidirect
13. #10590467C2semidirect
14. #10590454C2semidirect
15. #10590453C2semidirect
21. C3×Q8×Dic3C22semidirect
22. C3×#944C22semidirect
28. C3×#890C22semidirect
30. C3×#887C22semidirect
43. #63662C22semidirect
44. #63662C22semidirect
46. #63635C22semidirect
47. #63634C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5625D3semidirect
161. Q8×Dic3C2×D3semidirect
162. #944C2×D3semidirect
183. #890C2×D3semidirect
185. #887C2×D3semidirect
664. C32#3123semidirect
743. C3#80137semidirect
744. C3#83447semidirect

Maximal subgroups

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

subgroupindex
C3×#56252
#105949822
#105927442
C3×#50462
#105915662
#105915642
Dic3×#2152
#105911692
#105911272
#105910562
#105904692
#105904672
#105904542
#105904532
#834473
#801373