Finite Group Databasebeta

← #11889451

Subgroups — #11889451

Order 1152.

806 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
1#10595400C211yesmaximal, characteristic
2#10595380C211yesmaximal, characteristic
3#10592881C211yesmaximal, characteristic, complemented
4C3×#5189C211yesmaximal, characteristic, complemented
5C3×#5186C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic, complemented
7#10591616C211yesmaximal, characteristic, complemented
8#10591596C211yesmaximal, characteristic, complemented
9#10591582C211yesmaximal, characteristic, complemented
10#10591559C211yesmaximal, characteristic, complemented
11D3×#835C211yesmaximal, characteristic, complemented
12#10590948C211yesmaximal, characteristic, complemented
13#10590820C211yesmaximal, characteristic, complemented
14#10590724C211yesmaximal, characteristic
15#10590674C211yesmaximal, characteristic, complemented
16#80915—31nomaximal
17#80195—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21Q8×C3⋊Dic3C2211yescharacteristic
22#64153C2211yescharacteristic
23C2×#3756C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29C4×#625C2211yescharacteristic
30#63891—21no—
31D3×C4⋊Dic3C2211yescharacteristic
32#63887—21no—
33#63879—21no—
34#63878—21no—
35#63872C2211yescharacteristic
36#63862—21no—
37#63857C2211yescharacteristic
38#63851—21no—
39#63845—21no—
40#63843C2211yescharacteristic
41#63841C2211yescharacteristic
42#63839—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63643C2211yescharacteristic
46#63641C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#816C2211yescharacteristic
53#63576C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic
61Q8×#67—31no—
62#5642—31no—
63#5639—31no—
64#5632—31no—
65C3×#470—31no—
66C3×#451—31no—
67C2×#835—31no—
68#5189D311yescharacteristic, complemented
69#5186—31no—
70#5186D311yescharacteristic, complemented
71#5184—31no—
72#5182—31no—
73#5182—31no—
74#5182—61no—
75#5127—31no—
76#5120—31no—
77#5051—31no—
78#5050—31no—
79#5045—31no—
80#4862—31no—
81#4857—31no—
82#4815—31no—
83#4813—31no—
84#4802—31no—
85D3×#103—31no—
86#4799—31no—
87#4797—31no—
88#4797—31no—
89#4789—31no—
90#4730—31no—
91#4721—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#625D411yescharacteristic
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106D3×Dic6—22no—
107D3×Dic6—41no—
108C32×Q16—41no—
109C2×C32×C8C2311yescharacteristic
110#3756—41no—
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114#3750—21no—
115C4×C3⋊Dic3—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#216—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×ΓL(1,𝔽25)—41no—
131#3724D411yescharacteristic
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C22×Dic6—31no—
149C2×C3×Q16—21no—
150C2×C3×Q16—31no—
151C2×C3×Q16C2×D311yescharacteristic
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×M16—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157#946—61no—
158#946C2×D311yescharacteristic
159#946C2×D311yescharacteristic
160#946C2×D311yescharacteristic
161Q8×Dic3—31no—
162Q8×Dic3—31no—
163Q8×Dic3—31no—
164Q8×Dic3—61no—
165#944—31no—
166#944—31no—
167#944—61no—
168#944—61no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—61no—
172C2×#216C2×D311yescharacteristic
173C4×#67—31no—
174C4×#67—31no—
175C4×#67—61no—
176#926—31no—
177C2×C4⋊Dic3—31no—
178#924—31no—
179#924—61no—
180C22×C3⋊C8—31no—
181C2×ΓL(1,𝔽25)C2×D311yescharacteristic
182C2×D3×C8—31no—
183#898—61no—
184#897—31no—
185#896—61no—
186#892—31no—
187#892—61no—
188D3×C4⋊C4—31no—
189#890—31no—
190#890—31no—
191#890—61no—
192#889—61no—
193#888—61no—
194#887—31no—
195#886—61no—
196#883—61no—
197#67⋊C4—61no—
198#879—61no—
199#878—61no—
200#877—61no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#830—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#817—31no—
219#817C2×D311yescharacteristic
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#816C2×D311yescharacteristic
227#815—31no—
228#815—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—61no—
232#810—31no—
233#810—31no—
234#810—31no—
235#808—31no—
236#807—31no—
237#807—31no—
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
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
251#634—21no—
252#634—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—42no—
266C3×Dic6#4112yes—
267#627—42no—
268#625—22no—
269D3×Dic3—42no—
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—31no—
282#467—91no—
283#462—91no—
284#451—31no—
285#451—91no—
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—61no—
294C2×C3×Q8—62no—
295C2×C3×Q8—121no—
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C2×#67—31no—
304C2×#67—31no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307D3×Q8—22no—
308D3×Q8—41no—
309D3×Q8—62no—
310D3×Q8—121no—
311C2×C4×D3—21no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3C22×D311yescharacteristic
315C2×C4×D3C22×D311yescharacteristic
316C2×Dic6—21no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C2×Dic6—62no—
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×Dic6—121no—
324C2×Dic6C22×D311yescharacteristic
325C3×Q16—41no—
326C3×Q16—41no—
327C3×Q16—42no—
328C3×Q16—62no—
329C3×M16—121no—
330C2×C3×C8—21no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8C22×D311yescharacteristic
334C2×C3×C8C22×D311yescharacteristic
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344#217—31no—
345#217—31no—
346#217—61no—
347#217—61no—
348#216—22no—
349#216—121no—
350#216—121no—
351#216—122no—
352(C2×D3)⋊C4—21no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359C4⋊Dic3—31no—
360C4⋊Dic3—31no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—121no—
370C4⋊Dic3C22×D311yescharacteristic
371C4⋊Dic3C22×D311yescharacteristic
372C4⋊Dic3C22×D311yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—31no—
377Dic3⋊C4—31no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—121no—
388Dic3⋊C4—121no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—121no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405ΓL(1,𝔽25)—41no—
406D3×C8—121no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3#13712yes—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4H(5,𝔽2)11yescharacteristic
418C3⋊Dic3—21no—
419C3⋊Dic3—21no—
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3×Dic3—22no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×Q8—31no—
429C22×Q8—91no—
430C2×Q16—31no—
431C2×Q16—91no—
432C2×Q16D3211yescharacteristic
433C2×M16—31no—
434C22×C8—91no—
435C4⋊Q8—91no—
436C4⋊Q8—181no—
437#126—181no—
438#125—91no—
439#125—181no—
440#123—181no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—91no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×D4—91no—
450C4×D4—181no—
451#117—91no—
452#117—181no—
453C2×C4⋊C4—91no—
454#107—91no—
455#106—31no—
456#106—91no—
457C4⋊C8—91no—
458#103—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468C22⋊C8—31no—
469C22⋊C8—91no—
470#97—91no—
471C23×C3—31no—
472C23×C3—31no—
473C22×D3D3×D411yescharacteristic
474C22×D3D3×D411yescharacteristic
475C3×Q8—22no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—32no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—61no—
489C3×Q8—122no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
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—122no—
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—62no—
511#67—62no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—122no—
529C2×Dic3—122no—
530C2×Dic3D3×D411yescharacteristic
531C2×Dic3D3×D411yescharacteristic
532C4×D3—21no—
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—42no—
537C4×D3—122no—
538C4×D3—122no—
539Dic6—21no—
540Dic6—42no—
541Dic6—61no—
542Dic6—61no—
543Dic6—61no—
544Dic6—61no—
545Dic6—121no—
546Dic6—121no—
547Dic6—122no—
548Dic6—122no—
549Dic6#23712yes—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—41no—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—121no—
560C2×C32#54611yescharacteristic
561C2×C32C2×#13711yescharacteristic
562C2×C32#57811yescharacteristic
563C3×D3—22no—
564C3×D3—41no—
565C2×Q8—31no—
566C2×Q8—61no—
567C2×Q8—62no—
568C2×Q8—91no—
569C2×Q8—121no—
570C2×Q8—181no—
571C2×Q8—182no—
572C2×Q8—361no—
573C2×Q8C2×D3211yescharacteristic
574C2×Q8C2×D3211yescharacteristic
575C2×D4—91no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—61no—
579C22×C4—181no—
580C22×C4—181no—
581Q16—41no—
582Q16—62no—
583Q16—361no—
584M16—121no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—91no—
588C2×C8—361no—
589C2×C8C2×D3211yescharacteristic
590C4⋊C4—31no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—61no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—91no—
597C4⋊C4—91no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—91no—
610C22⋊C4—91no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C42—91no—
614C42—181no—
615C42—181no—
616C42—181no—
617C22×C3—21no—
618C22×C3—32no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C2×D3×D411yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—21no—
631C2×D3#91812yes—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—42no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—61no—
640C3×C4—62no—
641C3×C4—61no—
642C3×C4—81no—
643C3×C4—121no—
644C3×C4—121no—
645C3×C4—121no—
646C3×C4C2×#23711yescharacteristic
647C3×C4#100411yescharacteristic
648C3×C4#100411yescharacteristic
649C3×C4D3×#4111yescharacteristic
650Dic3—22no—
651Dic3—21no—
652Dic3—21no—
653Dic3—41no—
654Dic3—41no—
655Dic3—41no—
656Dic3—62no—
657Dic3—61no—
658Dic3—61no—
659Dic3—61no—
660Dic3—61no—
661Dic3—121no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—241no—
667Dic3—241no—
668C32#331211yescharacteristic, complemented, Sylow
669C23—31no—
670C23—31no—
671Q8—21no—
672Q8—21no—
673Q8—21no—
674Q8—21no—
675Q8—32no—
676Q8—61no—
677Q8—122no—
678Q8—181no—
679Q8—181no—
680Q8—362no—
681D4—182no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—91no—
695C2×C4—91no—
696C2×C4—122no—
697C2×C4—181no—
698C2×C4—181no—
699C2×C4—362no—
700C2×C4—362no—
701C2×C4C22×D3211yescharacteristic
702C8—21no—
703C8—61no—
704C8—61no—
705C8—181no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—62no—
710C2×C3—121no—
711C2×C3#559111yescharacteristic
712C2×C3#561011yescharacteristic
713C2×C3C2×#91811yescharacteristic
714C2×C3D3×#13711yescharacteristic
715C2×C3#577911yescharacteristic
716C2×C3#577911yescharacteristic
717D3—22no—
718D3—41no—
719C22—32no—
720C22—61no—
721C22—61no—
722C22—61no—
723C22—61no—
724C22—61no—
725C22D32×D411yescharacteristic
726C4—41no—
727C4—41no—
728C4—61no—
729C4—61no—
730C4—62no—
731C4—121no—
732C4—121no—
733C4—121no—
734C4—181no—
735C4—181no—
736C4—361no—
737C4—361no—
738C4D3×#23711yescharacteristic
739C4#6433011yescharacteristic
740C3—21no—
741C3#8019511yescharacteristic, complemented
742C3#8091511yescharacteristic, complemented
743C2—62no—
744C2—121no—
745C2D3×#91811yescharacteristic
746C2#1059476911yescharacteristic
747C2#1059529011yescharacteristic
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. #10592881C2semidirect
4. C3×#5189C2semidirect
5. C3×#5186C2semidirect
6. #10591653C2semidirect
7. #10591616C2semidirect
8. #10591596C2semidirect
9. #10591582C2semidirect
10. #10591559C2semidirect
11. D3×#835C2semidirect
12. #10590948C2semidirect
13. #10590820C2semidirect
15. #10590674C2semidirect
68. #5189D3semidirect
70. #5186D3semidirect
668. C32#3312semidirect
741. C3#80195semidirect
742. C3#80915semidirect

Maximal subgroups

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

subgroupindex
#105954002
#105953802
#105928812
C3×#51892
C3×#51862
#105916532
#105916162
#105915962
#105915822
#105915592
D3×#8352
#105909482
#105908202
#105907242
#105906742
#809153
#801953