Finite Group Databasebeta

← #10751686

Subgroups — #10751686

Order 768.

2010 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#5231C211yesmaximal, characteristic, complemented
3C2×#5213C211yesmaximal, characteristic
4C2×#4993C211yesmaximal, characteristic, complemented
5#72134C211yesmaximal, characteristic, complemented
6#72127C211yesmaximal, characteristic, complemented
7#71570C212yesmaximal, complemented
8#71569C211yesmaximal, characteristic, complemented
9#71566C212yesmaximal, complemented
10#71550C212yesmaximal
11#71547C212yesmaximal, complemented
12#16600—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C23×#67C2211yescharacteristic
16C2×C3×C22⋊Q8—24no—
17C2×C3×C22⋊Q8—24no—
18C2×C3×C22⋊Q8—24no—
19C22×C3×C4⋊C4C2212yes—
20C22×C3×C4⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yes—
22C22×#217C2212yes—
23C22×#217C2211yescharacteristic
24C22×(C2×D3)⋊C4C2211yescharacteristic
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2211yescharacteristic
27C22×(C2×D3)⋊C4C2212yes—
28C22×Dic3⋊C4C2212yes—
29#5231—24no—
30#5213—24no—
31C2×C3⋊#95C2211yescharacteristic
32C2×C3⋊#95C2211yescharacteristic
33C2×C3⋊#95C2211yescharacteristic
34C2×C3⋊#95C2212yes—
35C2×C3⋊#95C2211yescharacteristic
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41#4993—24no—
42C22×C22⋊Q8D311yescharacteristic, complemented
43C2×#399—31no—
44C2×#393—31no—
45C2×#386—31no—
46#1446—31no—
47#1445—31no—
48#1441—32no—
49#1439—32no—
50#1439—32no—
51#1438—32no—
52C22⋊#95—31no—
53C25×C3C2311yescharacteristic
54C24×D3C2311yescharacteristic
55C22×C3×Q8—22no—
56C22×C3×Q8—22no—
57C22×C3×Q8—42no—
58C22×C3×Q8—42no—
59C22×C3×Q8D414yescomplemented
60C23×C3×C4—22no—
61C23×C3×C4—22no—
62C23×C3×C4—42no—
63C23×C3×C4—42no—
64C23×C3×C4D414yes—
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2312yes—
67C23×C3×C4C2312yes—
68C23×C3×C4C2311yescharacteristic
69C22×#67—22no—
70C22×#67—22no—
71C22×#67—42no—
72C22×#67—42no—
73C22×#67Q814yescomplemented
74C23×Dic3C2312yes—
75C23×Dic3C2311yescharacteristic
76C23×Dic3C2311yescharacteristic
77C23×Dic3C2311yescharacteristic
78C23×Dic3C2312yes—
79C3×C22⋊Q8—232no—
80C2×C3×C4⋊C4—24no—
81C2×C3×C4⋊C4—24no—
82C2×C3×C4⋊C4—24no—
83C2×C3×C4⋊C4—22no—
84C2×C3×C4⋊C4—22no—
85C2×C3×C4⋊C4D414yescomplemented
86C2×C3×C22⋊C4—24no—
87C2×C3×C22⋊C4—24no—
88C2×C3×C22⋊C4—24no—
89C2×#217—22no—
90C2×#217—24no—
91C2×#217—24no—
92C2×#217—42no—
93C2×#217—42no—
94C2×(C2×D3)⋊C4—22no—
95C2×(C2×D3)⋊C4—22no—
96C2×(C2×D3)⋊C4—24no—
97C2×(C2×D3)⋊C4—22no—
98C2×(C2×D3)⋊C4—24no—
99C2×(C2×D3)⋊C4—22no—
100C2×(C2×D3)⋊C4—24no—
101C2×(C2×D3)⋊C4—42no—
102C2×(C2×D3)⋊C4—42no—
103C2×(C2×D3)⋊C4—42no—
104C2×(C2×D3)⋊C4—42no—
105C2×Dic3⋊C4—24no—
106C2×Dic3⋊C4—24no—
107C2×Dic3⋊C4—42no—
108C3⋊#95—22no—
109C3⋊#95—22no—
110C3⋊#95—24no—
111C3⋊#95—22no—
112C3⋊#95—22no—
113C3⋊#95—42no—
114C3⋊#95—42no—
115C3⋊#95—42no—
116C3⋊#95—42no—
117C3⋊#95—42no—
118C23×Q8C2×D311yescharacteristic
119C23×D4—31no—
120C24×C4C2×D311yescharacteristic
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C22×C4⋊C4—32no—
125C22×C4⋊C4C2×D312yes—
126C22×C4⋊C4C2×D311yescharacteristic
127C22×C22⋊C4—31no—
128C22×C22⋊C4—32no—
129C22×C22⋊C4—32no—
130C22×C22⋊C4—31no—
131C22×C22⋊C4—32no—
132C22×C22⋊C4—31no—
133C22×C22⋊C4C2×D312yes—
134#399—64no—
135#393—64no—
136#386—64no—
137C2×#95—31no—
138C2×#95—32no—
139C2×#95—31no—
140C2×#95—31no—
141C2×#95—31no—
142C2×#95—32no—
143C2×#95—32no—
144C2×#95—32no—
145C2×#95—32no—
146C2×#95—32no—
147C24×C3—21no—
148C24×C3—21no—
149C24×C3—22no—
150C24×C3—22no—
151C24×C3—22no—
152C24×C3—22no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3C2×D412yes—
156C24×C3C2×Q812yes—
157C24×C3#4112yes—
158C24×C3C2411yescharacteristic
159C23×D3—21no—
160C23×D3—21no—
161C23×D3—21no—
162C23×D3—22no—
163C23×D3—21no—
164C23×D3—22no—
165C23×D3—22no—
166C23×D3—22no—
167C23×D3—21no—
168C23×D3—21no—
169C23×D3C2×Q812yes—
170C2×C3×Q8—28no—
171C2×C3×Q8—48no—
172C2×C3×Q8—44no—
173C2×C3×Q8—44no—
174C2×C3×Q8—48no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—22no—
178C22×C3×C4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—28no—
194C22×C3×C4—44no—
195C22×C3×C4—44no—
196C22×C3×C4—48no—
197C22×C3×C4—48no—
198C22×C3×C4C2×D414yes—
199C22×C3×C4C2×D412yes—
200C22×C3×C4C2×D414yes—
201C22×C3×C4C2×D412yes—
202C22×C3×C4C2×D412yes—
203C22×C3×C4C2×D412yes—
204C2×#67—28no—
205C2×#67—48no—
206C2×#67—44no—
207C2×#67—44no—
208C2×#67—48no—
209C22×Dic3—21no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—21no—
213C22×Dic3—22no—
214C22×Dic3—22no—
215C22×Dic3—22no—
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—21no—
220C22×Dic3—22no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—21no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—22no—
228C22×Dic3—22no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—22no—
236C22×Dic3C2×Q812yes—
237C22×Dic3#4114yes—
238C3×C4⋊C4—216no—
239C3×C4⋊C4—28no—
240C3×C22⋊C4—216no—
241#217—48no—
242#217—44no—
243(C2×D3)⋊C4—48no—
244(C2×D3)⋊C4—44no—
245(C2×D3)⋊C4—48no—
246(C2×D3)⋊C4—44no—
247Dic3⋊C4—48no—
248C25—31no—
249C25C22×D311yescharacteristic
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—42no—
253C22×Q8—42no—
254C22×Q8#6714yescomplemented
255C22×D4—34no—
256C22×D4—62no—
257C22×D4—62no—
258C22×D4—122no—
259C22×D4—122no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—32no—
263C23×C4—31no—
264C23×C4—31no—
265C23×C4—31no—
266C23×C4—32no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4#6714yes—
270C23×C4C22×D312yes—
271C23×C4C22×D312yes—
272C23×C4C22×D311yescharacteristic
273C23×C4C22×D311yescharacteristic
274C22⋊Q8—232no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—64no—
281C2×C4⋊C4—64no—
282C2×C4⋊C4—122no—
283C2×C4⋊C4#6714yescomplemented
284C2×C22⋊C4—24no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—24no—
287C2×C22⋊C4—64no—
288C2×C22⋊C4—64no—
289C2×C22⋊C4—64no—
290C2×C22⋊C4—62no—
291C2×C22⋊C4—62no—
292C2×C22⋊C4—62no—
293C2×C22⋊C4—64no—
294C2×C22⋊C4—62no—
295C2×C22⋊C4—64no—
296C2×C22⋊C4—62no—
297C2×C22⋊C4—122no—
298C2×C22⋊C4—122no—
299C2×C22⋊C4—122no—
300C2×C22⋊C4—122no—
301C2×C22⋊C4—122no—
302C2×C22⋊C4—122no—
303#95—62no—
304#95—62no—
305#95—64no—
306#95—62no—
307#95—62no—
308#95—122no—
309#95—122no—
310#95—122no—
311#95—122no—
312#95—122no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—22no—
316C23×C3—22no—
317C23×C3—22no—
318C23×C3—22no—
319C23×C3—24no—
320C23×C3—24no—
321C23×C3—22no—
322C23×C3—22no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—24no—
326C23×C3—24no—
327C23×C3—42no—
328C23×C3—42no—
329C23×C3—42no—
330C23×C3—42no—
331C23×C3—42no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3C22⋊Q814yes—
336C23×C3C22×D411yescharacteristic
337C23×C3C22×D411yescharacteristic
338C23×C3C22×D411yescharacteristic
339C23×C3C22×Q811yescharacteristic
340C23×C3C2×#4111yescharacteristic
341C23×C3C2×#4112yes—
342C23×C3H(5,𝔽2)12yes—
343C23×C3H(5,𝔽2)12yes—
344C23×C3H(5,𝔽2)12yes—
345C23×C32−1+411yescharacteristic
346C23×C32−1+411yescharacteristic
347C22×D3—22no—
348C22×D3—24no—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—24no—
352C22×D3—41no—
353C22×D3—41no—
354C22×D3—41no—
355C22×D3—42no—
356C22×D3—41no—
357C22×D3—41no—
358C22×D3—42no—
359C22×D3—41no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—42no—
364C22×D3—41no—
365C22×D3—41no—
366C22×D3—42no—
367C22×D3—42no—
368C22×D3—42no—
369C22×D3—42no—
370C3×Q8—416no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—24no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—24no—
380C2×C3×C4—22no—
381C2×C3×C4—24no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—416no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4#12014yes—
396#67—416no—
397C2×Dic3—22no—
398C2×Dic3—24no—
399C2×Dic3—24no—
400C2×Dic3—24no—
401C2×Dic3—24no—
402C2×Dic3—41no—
403C2×Dic3—42no—
404C2×Dic3—41no—
405C2×Dic3—42no—
406C2×Dic3—42no—
407C2×Dic3—42no—
408C2×Dic3—42no—
409C2×Dic3—41no—
410C2×Dic3—41no—
411C2×Dic3—41no—
412C2×Dic3—42no—
413C2×Dic3—41no—
414C2×Dic3—41no—
415C2×Dic3—41no—
416C2×Dic3—42no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—42no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—21no—
433C24—21no—
434C24—32no—
435C24—62no—
436C24—62no—
437C24—61no—
438C24—61no—
439C24—61no—
440C24—62no—
441C24—62no—
442C24—61no—
443C24—61no—
444C24—61no—
445C24D3×Q812yes—
446C24#23912yes—
447C24C2×#6712yes—
448C24C23×D311yescharacteristic
449C2×Q8—28no—
450C2×Q8—48no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8—48no—
454C2×D4—68no—
455C2×D4—128no—
456C2×D4—128no—
457C2×D4—124no—
458C2×D4—124no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—28no—
478C22×C4—32no—
479C22×C4—34no—
480C22×C4—44no—
481C22×C4—44no—
482C22×C4—48no—
483C22×C4—48no—
484C22×C4—62no—
485C22×C4—62no—
486C22×C4—62no—
487C22×C4—62no—
488C22×C4—61no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—61no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4—62no—
496C22×C4—62no—
497C22×C4—62no—
498C22×C4—62no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4C2×#6714yes—
512C22×C4C2×#6712yes—
513C22×C4C2×#6714yes—
514C22×C4C2×#6712yes—
515C22×C4C2×#6712yes—
516C22×C4C2×#6712yes—
517C4⋊C4—216no—
518C4⋊C4—28no—
519C4⋊C4—128no—
520C22⋊C4—216no—
521C22⋊C4—128no—
522C22⋊C4—124no—
523C22⋊C4—128no—
524C22⋊C4—128no—
525C22⋊C4—124no—
526C22⋊C4—124no—
527C22×C3—24no—
528C22×C3—24no—
529C22×C3—24no—
530C22×C3—42no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—44no—
535C22×C3—44no—
536C22×C3—44no—
537C22×C3—44no—
538C22×C3C2×#12011yescharacteristic
539C22×C3C2×C22⋊Q811yescharacteristic
540C22×C3#53211yescharacteristic
541C22×C3#53411yescharacteristic
542C22×C3#53411yescharacteristic
543C22×C3#53412yes—
544C22×C3#53512yes—
545C22×C3#53511yescharacteristic
546C22×C3#53611yescharacteristic
547C22×C3#53812yes—
548C22×C3#53912yes—
549C22×C3#54212yes—
550C22×C3#54312yes—
551C22×C3#54612yes—
552C22×C3#54811yescharacteristic
553C22×C3#54811yescharacteristic
554C22×C3D4×Q811yescharacteristic
555C22×C3D4×Q811yescharacteristic
556C22×C3#55012yes—
557C22×C3#55112yes—
558C22×C3#55412yes—
559C22×C3#56212yes—
560C22×C3#56212yes—
561C2×D3—42no—
562C2×D3—42no—
563C2×D3—42no—
564C2×D3—44no—
565C2×D3—44no—
566C2×D3—81no—
567C2×D3—81no—
568C2×D3—81no—
569C2×D3—81no—
570C2×D3—82no—
571C2×D3—82no—
572C3×C4—24no—
573C3×C4—42no—
574C3×C4—44no—
575C3×C4—44no—
576Dic3—42no—
577Dic3—44no—
578Dic3—81no—
579Dic3—81no—
580Dic3—82no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—64no—
604C23—64no—
605C23—62no—
606C23—62no—
607C23—62no—
608C23—122no—
609C23—122no—
610C23—122no—
611C23—122no—
612C23—122no—
613C23—122no—
614C23—121no—
615C23—122no—
616C23—121no—
617C23—122no—
618C23—121no—
619C23—121no—
620C23—121no—
621C23—122no—
622C23—121no—
623C23—121no—
624C23—122no—
625C23—121no—
626C23#94614yes—
627C23#100412yes—
628C23#100412yes—
629C23C2×D3×Q811yescharacteristic
630C23C2×#23911yescharacteristic
631C23#100711yescharacteristic
632C23#100711yescharacteristic
633C23D3×#4112yes—
634C23#100912yes—
635C23C22×#6711yescharacteristic
636C23C22×#6711yescharacteristic
637C23C22×#6711yescharacteristic
638Q8—416no—
639D4—1216no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—416no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—64no—
665C2×C4—64no—
666C2×C4—64no—
667C2×C4—62no—
668C2×C4—64no—
669C2×C4—122no—
670C2×C4—122no—
671C2×C4—122no—
672C2×C4—121no—
673C2×C4—122no—
674C2×C4—122no—
675C2×C4—121no—
676C2×C4—122no—
677C2×C4—122no—
678C2×C4—122no—
679C2×C4—122no—
680C2×C4—122no—
681C2×C4—122no—
682C2×C4—122no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4—122no—
686C2×C4—122no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—122no—
691C2×C4—122no—
692C2×C4—121no—
693C2×C4#95314yes—
694C2×C3—44no—
695C2×C3#240911yescharacteristic
696C2×C3#243111yescharacteristic
697C2×C3#256411yescharacteristic
698C2×C3#261311yescharacteristic
699C2×C3#262611yescharacteristic
700C2×C3#266311yescharacteristic
701C2×C3#269212yes—
702C2×C3#269612yes—
703C2×C3#273012yes—
704C2×C3#273212yes—
705C2×C3#281611yescharacteristic
706D3—82no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—42no—
711C22—44no—
712C22—44no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—44no—
717C22—42no—
718C22—122no—
719C22—122no—
720C22—124no—
721C22—122no—
722C22—124no—
723C22—241no—
724C22—242no—
725C22—242no—
726C22—241no—
727C22—241no—
728C22—241no—
729C22#563412yes—
730C22#563612yes—
731C22#563712yes—
732C22#563812yes—
733C22#564012yes—
734C22#564412yes—
735C22#564712yes—
736C22#564712yes—
737C22#580411yescharacteristic
738C22#580412yes—
739C22#580411yescharacteristic
740C22#580512yes—
741C22C2×#94611yescharacteristic
742C22Q8×#6711yescharacteristic
743C22Q8×#6711yescharacteristic
744C22#581611yescharacteristic
745C22#581711yescharacteristic
746C22#581711yescharacteristic
747C22#582912yes—
748C22#583011yescharacteristic
749C22#583211yescharacteristic
750C22#583412yes—
751C22C2×#95311yescharacteristic
752C4—24no—
753C4—42no—
754C4—44no—
755C4—44no—
756C4—124no—
757C4—122no—
758C4—242no—
759C4—241no—
760C4—241no—
761C3#1660011yescharacteristic, complemented, Sylow
762C2—44no—
763C2—242no—
764C2#8278411yescharacteristic
765C2#8279812yes—
766C2#8280612yes—
767C2#8280712yes—
768C2#8282211yescharacteristic
769C2#8282511yescharacteristic
770C2#8283012yes—
771C2#8283311yescharacteristic
772C2#8405411yescharacteristic
773C2#8406811yescharacteristic
774C2#8409211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C22⋊Q8C2
prime radicalC23×#67C22
hypercenterC22×C22⋊Q8D3
hypocenterC3#16600
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C2×#5231C2semidirect
4. C2×#4993C2semidirect
5. #72134C2semidirect
6. #72127C2semidirect
7. #71570C2semidirect
8. #71569C2semidirect
9. #71566C2semidirect
11. #71547C2semidirect
42. C22×C22⋊Q8D3semidirect
59. C22×C3×Q8D4semidirect
73. C22×#67Q8semidirect
85. C2×C3×C4⋊C4D4semidirect
254. C22×Q8#67semidirect
283. C2×C4⋊C4#67semidirect
761. C3#16600semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C2×#52312
C2×#52132
C2×#49932
#721342
#721272
#715702
#715692
#715662
#715502
#715472
#166003