Finite Group Databasebeta

← #11889388

Subgroups — #11889388

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#625C211yesmaximal, characteristic
2#10595380C211yesmaximal, characteristic
3#10592883C211yesmaximal, characteristic, complemented
4C3×#5186C211yesmaximal, characteristic, complemented
5C3×#5186C211yesmaximal, characteristic, complemented
6#10591638C211yesmaximal, characteristic, complemented
7#10591635C211yesmaximal, characteristic, complemented
8#10591633C211yesmaximal, characteristic, complemented
9#10591615C211yesmaximal, characteristic, complemented
10#10591557C211yesmaximal, characteristic, complemented
11D3×#835C211yesmaximal, characteristic, complemented
12#10590904C211yesmaximal, characteristic, complemented
13#10590725C211yesmaximal, characteristic
14#10590711C211yesmaximal, characteristic, complemented
15#10590675C211yesmaximal, characteristic, complemented
16#80196—31nomaximal
17#80195—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C4×#625—21no—
28C4×#625C2211yescharacteristic
29#63891—21no—
30D3×C4⋊Dic3C2211yescharacteristic
31#63878—21no—
32#63873—21no—
33#63873C2211yescharacteristic
34#63872C2211yescharacteristic
35#63862—21no—
36#63856—21no—
37#63856—21no—
38#63856C2211yescharacteristic
39#63856C2211yescharacteristic
40#63845—21no—
41#63841C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63644C2211yescharacteristic
47#63642C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54#63575C2211yescharacteristic
55#63573C2211yescharacteristic
56#63572C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61Q8×#67—31no—
62Q8×#67—31no—
63#5642—31no—
64#5639—31no—
65C3×#451—31no—
66C3×#451—31no—
67#5225—31no—
68C2×#835—31no—
69#5189—31no—
70#5188—31no—
71#5186D311yescharacteristic, complemented
72#5186D311yescharacteristic, complemented
73#5184—31no—
74#5184—31no—
75#5184—61no—
76#5182—31no—
77#5182—31no—
78#5052—31no—
79#5051—31no—
80#4815—31no—
81#4805—31no—
82#4802—31no—
83D3×#103—31no—
84#4799—31no—
85#4797—31no—
86#4797—31no—
87#4796—31no—
88#4730—31no—
89#4728—31no—
90#4723—31no—
91#4721—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C3×D3×Q8—22no—
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C3×D3×Q8—41no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#625D411yescharacteristic
107C2×D3×Dic3—21no—
108C32×Q16—22no—
109C2×C32×C8C2311yescharacteristic
110C4⋊(C3⋊Dic3)—21no—
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#216—41no—
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128#3724—21no—
129#3724—21no—
130#3724—21no—
131#3724—21no—
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C2×D3×Q8C2×D311yescharacteristic
149C2×C3×Q16—21no—
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×Q16C2×D311yescharacteristic
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156#946—31no—
157#946—31no—
158#946—61no—
159#946—61no—
160#946C2×D311yescharacteristic
161#946C2×D311yescharacteristic
162Q8×Dic3—31no—
163Q8×Dic3—31no—
164Q8×Dic3—31no—
165Q8×Dic3—31no—
166Q8×Dic3—61no—
167Q8×Dic3—61no—
168#944—31no—
169#944—31no—
170#944—61no—
171#944—61no—
172C2×#216C2×D311yescharacteristic
173C2×#216C2×D311yescharacteristic
174C4×#67—31no—
175C4×#67—31no—
176C4×#67—61no—
177C4×#67—61no—
178#926—31no—
179C2×C4⋊Dic3—31no—
180#924—31no—
181#924—31no—
182#924—61no—
183#924—61no—
184C2×#208—31no—
185C22×C3⋊C8—31no—
186C2×ΓL(1,𝔽25)—31no—
187C2×D3×C8—31no—
188#898—61no—
189#892—31no—
190#892—61no—
191D3×C4⋊C4—31no—
192#890—31no—
193#890—31no—
194#890—61no—
195#889—61no—
196#886—61no—
197#883—61no—
198#879—61no—
199#877—61no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—61no—
215#835—61no—
216#835C2×D311yescharacteristic
217#835C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic
219(C2×D3)⋊C8C2×D311yescharacteristic
220#818—31no—
221#817—31no—
222#817—31no—
223#817—31no—
224#817—61no—
225#816—31no—
226#816—31no—
227#816C2×D311yescharacteristic
228#816C2×D311yescharacteristic
229#815—31no—
230#815—31no—
231#815—61no—
232Dic3⋊C8—31no—
233Dic3⋊C8—31no—
234#810—31no—
235#810—31no—
236#808—31no—
237#807—31no—
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—42no—
262C3×C4×D3—42no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6—42no—
269#625—22no—
270D3×Dic3—42no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—91no—
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—31no—
285#451—31no—
286#441—91no—
287#435—91no—
288#419—91no—
289C2×#103—91no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—62no—
298C2×C3×Q8—121no—
299C2×C3×Q8—121no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—31no—
309C2×#67—31no—
310C22×Dic3—61no—
311D3×Q8—22no—
312D3×Q8—22no—
313D3×Q8—41no—
314D3×Q8—41no—
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—61no—
318C2×C4×D3C22×D311yescharacteristic
319C2×C4×D3C22×D311yescharacteristic
320C2×Dic6—21no—
321C2×Dic6—21no—
322C2×Dic6C22×D311yescharacteristic
323C2×Dic6C22×D311yescharacteristic
324C3×Q16—24no—
325C3×Q16—22no—
326C3×Q16—22no—
327C3×Q16—121no—
328C3×Q16—121no—
329C2×C3×C8—21no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340#217—31no—
341#217—31no—
342#217—61no—
343#217—61no—
344#217—61no—
345#216—41no—
346#216—41no—
347(C2×D3)⋊C4—21no—
348(C2×D3)⋊C4—21no—
349(C2×D3)⋊C4—31no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354C4⋊Dic3—31no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—121no—
368C4⋊Dic3—121no—
369C4⋊Dic3C22×D311yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386C4×Dic3—31no—
387C4×Dic3—31no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—121no—
396C4×Dic3—121no—
397#208—121no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404ΓL(1,𝔽25)—121no—
405D3×C8—121no—
406C22×C32C22×D411yescharacteristic
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3#13712yes—
413C32×C4—22no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4H(5,𝔽2)11yescharacteristic
417C3⋊Dic3—21no—
418C3⋊Dic3—21no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C22×Q8—31no—
428C22×Q8—31no—
429C2×Q16—31no—
430C2×Q16—31no—
431C2×Q16D3211yescharacteristic
432C2×M16—91no—
433C22×C8—91no—
434C4⋊Q8—91no—
435C4⋊Q8—181no—
436#126—181no—
437#125—91no—
438#125—181no—
439#123—181no—
440C22⋊Q8—31no—
441C22⋊Q8—31no—
442C22⋊Q8—91no—
443C22⋊Q8—91no—
444C22⋊Q8—181no—
445C22⋊Q8—181no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×D4—91no—
449C4×D4—181no—
450#117—91no—
451#117—181no—
452C2×C4⋊C4—91no—
453#107—91no—
454#106—91no—
455#106—91no—
456C4⋊C8—91no—
457#103—31no—
458#103—31no—
459#103—31no—
460#103—31no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467C22⋊C8—31no—
468C22⋊C8—31no—
469#97—91no—
470C23×C3—31no—
471C23×C3—31no—
472C22×D3D3×D411yescharacteristic
473C22×D3D3×D411yescharacteristic
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—22no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—22no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×Q8—122no—
489C3×Q8—122no—
490C3×Q8#23712yes—
491C3×Q8#23712yes—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
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—61no—
508C2×C3×C4—61no—
509C2×C3×C4—122no—
510C2×C3×C4—122no—
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513#67—62no—
514#67—62no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—122no—
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—21no—
538C4×D3—42no—
539C4×D3—42no—
540C4×D3—122no—
541Dic6—21no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—42no—
546Dic6—42no—
547C3×C8—22no—
548C3×C8—21no—
549C3×C8—21no—
550C3×C8—61no—
551C3×C8—61no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—121no—
557C2×C32#54611yescharacteristic
558C2×C32C2×#13711yescharacteristic
559C2×C32#57811yescharacteristic
560C3×D3—22no—
561C3×D3—41no—
562C2×Q8—31no—
563C2×Q8—31no—
564C2×Q8—61no—
565C2×Q8—61no—
566C2×Q8—62no—
567C2×Q8—62no—
568C2×Q8—121no—
569C2×Q8—121no—
570C2×Q8C2×D3211yescharacteristic
571C2×Q8C2×D3211yescharacteristic
572C2×D4—91no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—61no—
576C22×C4—61no—
577C22×C4—181no—
578Q16—22no—
579Q16—121no—
580Q16—121no—
581M16—361no—
582C2×C8—31no—
583C2×C8—31no—
584C2×C8—91no—
585C2×C8—361no—
586C2×C8C2×D3211yescharacteristic
587C4⋊C4—31no—
588C4⋊C4—31no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—91no—
592C4⋊C4—91no—
593C4⋊C4—91no—
594C4⋊C4—181no—
595C4⋊C4—181no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C22⋊C4—61no—
604C22⋊C4—61no—
605C22⋊C4—91no—
606C22⋊C4—91no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—91no—
611C42—181no—
612C42—181no—
613C42—181no—
614C22×C3—21no—
615C22×C3—32no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—61no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3C2×D3×D411yescharacteristic
622C22×C3C2×D3×D411yescharacteristic
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—21no—
628C2×D3#91812yes—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—42no—
634C3×C4—42no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—61no—
638C3×C4—61no—
639C3×C4—121no—
640C3×C4—121no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4C2×#23711yescharacteristic
644C3×C4C2×#23711yescharacteristic
645C3×C4#100411yescharacteristic
646C3×C4#100411yescharacteristic
647Dic3—21no—
648Dic3—21no—
649Dic3—41no—
650Dic3—41no—
651Dic3—41no—
652Dic3—41no—
653Dic3—61no—
654Dic3—61no—
655Dic3—61no—
656Dic3—61no—
657Dic3—121no—
658Dic3—121no—
659Dic3—121no—
660Dic3—121no—
661Dic3—121no—
662Dic3—121no—
663Dic3—241no—
664Dic3—241no—
665C32#331211yescharacteristic, complemented, Sylow
666C23—31no—
667C23—31no—
668Q8—21no—
669Q8—21no—
670Q8—21no—
671Q8—61no—
672Q8—61no—
673Q8—61no—
674Q8—61no—
675Q8—122no—
676Q8—122no—
677Q8#380512yes—
678D4—182no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—181no—
696C2×C4—181no—
697C2×C4—362no—
698C2×C4C22×D3211yescharacteristic
699C8—21no—
700C8—61no—
701C8—61no—
702C8—181no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—62no—
707C2×C3—121no—
708C2×C3#559111yescharacteristic
709C2×C3#559111yescharacteristic
710C2×C3C2×#91811yescharacteristic
711C2×C3#576611yescharacteristic
712C2×C3D3×#13711yescharacteristic
713C2×C3#577911yescharacteristic
714D3—22no—
715D3—41no—
716C22—32no—
717C22—61no—
718C22—61no—
719C22—61no—
720C22—61no—
721C22—61no—
722C22D32×D411yescharacteristic
723C4—22no—
724C4—41no—
725C4—61no—
726C4—61no—
727C4—121no—
728C4—121no—
729C4—121no—
730C4—121no—
731C4—181no—
732C4—181no—
733C4—361no—
734C4—361no—
735C4#6431311yescharacteristic
736C4C2×#380511yescharacteristic
737C3—21no—
738C3#8019511yescharacteristic, complemented
739C3#8019611yescharacteristic, complemented
740C2—62no—
741C2—121no—
742C2D3×#91811yescharacteristic
743C2#1059476611yescharacteristic
744C2#1059522511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×#625D4
hypercenterC2×Q16D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
3. #10592883C2semidirect
4. C3×#5186C2semidirect
5. C3×#5186C2semidirect
6. #10591638C2semidirect
7. #10591635C2semidirect
8. #10591633C2semidirect
9. #10591615C2semidirect
10. #10591557C2semidirect
11. D3×#835C2semidirect
12. #10590904C2semidirect
14. #10590711C2semidirect
15. #10590675C2semidirect
71. #5186D3semidirect
72. #5186D3semidirect
665. C32#3312semidirect
738. C3#80195semidirect
739. C3#80196semidirect

Maximal subgroups

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

subgroupindex
Q8×#6252
#105953802
#105928832
C3×#51862
#105916382
#105916352
#105916332
#105916152
#105915572
D3×#8352
#105909042
#105907252
#105907112
#105906752
#801963
#801953