Finite Group Databasebeta

← #10826959

Subgroups — #10826959

Order 768.

1928 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#5791C211yesmaximal, characteristic
3C2×#5228C211yesmaximal, characteristic, complemented
4C2×#5227C211yesmaximal, characteristic, complemented
5C2×#5047C212yesmaximal, complemented
6#72126C211yesmaximal, characteristic, complemented
7#71700C212yesmaximal, complemented
8#71699C212yesmaximal, complemented
9#71693C212yesmaximal, complemented
10#71560C211yesmaximal, characteristic, complemented
11#71559C211yesmaximal, characteristic, complemented
12#23922—31nomaximal, Sylow
13C23×C3×Q8C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C22×#235C2211yescharacteristic
16C2×C3×C22⋊Q8—21no—
17C2×C3×C22⋊Q8—21no—
18C2×C3×C22⋊Q8—28no—
19C2×C3×C22⋊Q8C2212yes—
20C2×C3×C22⋊Q8C2212yes—
21C22×C3×C4⋊C4—21no—
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4—21no—
24C2×#953—21no—
25C22×#216C2212yescomplemented
26C22×#215C2212yescomplemented
27#5791—24no—
28#5791—24no—
29C2×#930C2211yescharacteristic
30C2×#930C2211yescharacteristic
31C2×#929—21no—
32C2×C4×#67—21no—
33C2×C4×#67—21no—
34C2×#926C2211yescharacteristic
35C2×#924C2211yescharacteristic
36C2×#924C2211yescharacteristic
37#5228—24no—
38#5227—24no—
39C2×#835C2212yescomplemented
40C2×#835C2212yescomplemented
41C2×#830C2212yes—
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic
44C2×#830C2212yes—
45#5047—28no—
46C2×#810C2212yescomplemented
47C2×#809C2212yescomplemented
48#4529C2212yescomplemented
49#4529C2212yescomplemented
50C2×#525—31no—
51C22×C22⋊Q8D311yescharacteristic, complemented
52C2×#452—32no—
53C2×#451—31no—
54C2×#448—31no—
55#2001—32no—
56#2000—32no—
57#1874—31no—
58#1873—32no—
59#1872—31no—
60#1779—31no—
61C25×C3D411yescharacteristic
62C22×C3×Q8—24no—
63C22×C3×Q8—21no—
64C22×C3×Q8—22no—
65C22×C3×Q8—22no—
66C22×C3×Q8—42no—
67C22×C3×Q8C2312yes—
68C23×C3×C4—21no—
69C23×C3×C4—21no—
70C23×C3×C4—22no—
71C23×C3×C4—22no—
72C23×C3×C4—24no—
73C23×C3×C4—42no—
74C23×C3×C4D411yescharacteristic
75C23×C3×C4D411yescharacteristic
76C23×C3×C4D411yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C22×#67—21no—
81C22×#67—21no—
82C22×#67—21no—
83C2×#235—22no—
84C2×#235—24no—
85C2×#235—22no—
86C2×#235—42no—
87C22×D12C2311yescharacteristic
88C22×C4×D3—21no—
89C22×Dic6C2311yescharacteristic
90C3×C22⋊Q8—28no—
91C3×C22⋊Q8—28no—
92C3×C22⋊Q8—24no—
93C3×C22⋊Q8—24no—
94C3×C22⋊Q8—24no—
95C3×C22⋊Q8D418yescomplemented
96C2×C3×C4⋊C4—28no—
97C2×C3×C4⋊C4—22no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—24no—
101C2×C3×C4⋊C4C2312yes—
102C2×C3×C22⋊C4—28no—
103C2×C3×C22⋊C4—22no—
104C2×C3×C22⋊C4—22no—
105#953—28no—
106C2×#217—21no—
107C2×#217—21no—
108C2×#217—21no—
109C2×#216—24no—
110C2×#216—24no—
111C2×#216—42no—
112C2×#215—24no—
113C2×#215—24no—
114C2×#215—42no—
115#930—22no—
116#930—22no—
117#930—22no—
118#930D414yes—
119#929—28no—
120C4×#67—28no—
121C4×#67—28no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4—21no—
124#926—22no—
125#926—22no—
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4⋊Dic3C2311yescharacteristic
128#924—22no—
129#924—22no—
130#924—22no—
131#924D414yes—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—21no—
135C22×C3⋊C8C2312yes—
136C22×C3⋊C8C2312yes—
137#835—24no—
138#835—24no—
139#830—22no—
140#830—22no—
141#830—24no—
142#830—42no—
143#810—24no—
144#809—24no—
145C22×#41—31no—
146C23×Q8C2×D311yescharacteristic
147C24×C4C2×D311yescharacteristic
148C22×Q16—32no—
149C22×SD16—32no—
150#525—64no—
151#525—64no—
152C2×#123—61no—
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—28no—
156C2×C22⋊Q8—31no—
157C2×C22⋊Q8—31no—
158C2×C22⋊Q8C2×D312yes—
159C2×C22⋊Q8C2×D312yes—
160C2×#121—31no—
161C2×#121—31no—
162C2×#120—61no—
163C2×C4×D4—61no—
164C2×C4×D4—61no—
165C2×#117—31no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4C2×D311yescharacteristic
168C22×C22⋊C4—21no—
169#452—68no—
170#451—64no—
171#448—64no—
172C2×#103—32no—
173C2×#103—32no—
174C2×#103—32no—
175C2×#102—32no—
176C2×C22⋊C8—31no—
177C2×C22⋊C8—32no—
178C2×C22⋊C8—31no—
179C2×C22⋊C8—32no—
180#340—32no—
181#340—32no—
182C24×C3—22no—
183C24×C3—22no—
184C24×C3—22no—
185C24×C3—22no—
186C24×C3—22no—
187C24×C3—41no—
188C24×C3—41no—
189C24×C3C2×D411yescharacteristic
190C24×C3C2×D411yescharacteristic
191C24×C3C2×D411yescharacteristic
192C23×D3—21no—
193C2×C3×Q8—24no—
194C2×C3×Q8—22no—
195C2×C3×Q8—22no—
196C2×C3×Q8—22no—
197C2×C3×Q8—22no—
198C2×C3×Q8—22no—
199C2×C3×Q8—48no—
200C2×C3×Q8—48no—
201C2×C3×Q8—42no—
202C2×C3×Q8—42no—
203C2×C3×Q8C2×D414yes—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—24no—
210C22×C3×C4—24no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—41no—
224C22×C3×C4—41no—
225C22×C3×C4—41no—
226C22×C3×C4—48no—
227C22×C3×C4—48no—
228C22×C3×C4—42no—
229C22×C3×C4—42no—
230C22×C3×C4—42no—
231C22×C3×C4—42no—
232C22×C3×C4C2×D412yes—
233C22×C3×C4C2×D412yes—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D414yes—
238C22×C3×C4C2411yescharacteristic
239C2×#67—24no—
240C2×#67—24no—
241C2×#67—24no—
242C2×#67—42no—
243C2×#67—42no—
244C2×#67—42no—
245C2×#67—42no—
246C2×#67—42no—
247C2×#67—42no—
248C22×Dic3—21no—
249C22×Dic3—21no—
250C22×Dic3—21no—
251#235—48no—
252#235—48no—
253C2×D12—22no—
254C2×D12—22no—
255C2×D12—21no—
256C2×D12C2×D412yes—
257C2×C4×D3—24no—
258C2×C4×D3—42no—
259C2×C4×D3—42no—
260C2×Dic6—22no—
261C2×Dic6—22no—
262C2×Dic6—21no—
263C2×Dic6C2×D412yes—
264C3×C4⋊C4—24no—
265C3×C4⋊C4—28no—
266C3×C4⋊C4—28no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4C2×D414yes—
269C3×C22⋊C4—28no—
270C3×C22⋊C4—28no—
271#217—24no—
272#217—24no—
273#217—24no—
274#216—48no—
275#215—48no—
276(C2×D3)⋊C4—24no—
277(C2×D3)⋊C4—24no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3C2×D412yes—
281C4⋊Dic3C2×D412yes—
282Dic3⋊C4—24no—
283Dic3⋊C4—24no—
284C4×Dic3—24no—
285C2×C3⋊C8—22no—
286C2×C3⋊C8—22no—
287C2×C3⋊C8—22no—
288C2×C3⋊C8—22no—
289C2×C3⋊C8—22no—
290C2×C3⋊C8—22no—
291C25#6711yescharacteristic
292C2×#41—62no—
293C2×#41—62no—
294C2×#41—64no—
295C2×#41—122no—
296C22×Q8—24no—
297C22×Q8—21no—
298C22×Q8—22no—
299C22×Q8—22no—
300C22×Q8—31no—
301C22×Q8—42no—
302C22×Q8C22×D312yes—
303C22×D4—31no—
304C22×D4—61no—
305C22×D4—61no—
306C22×D4—61no—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—24no—
312C23×C4—42no—
313C23×C4—61no—
314C23×C4#6711yescharacteristic
315C23×C4#6711yescharacteristic
316C23×C4#6711yescharacteristic
317C23×C4C22×D311yescharacteristic
318C23×C4C22×D311yescharacteristic
319C23×C4C22×D311yescharacteristic
320C2×Q16—64no—
321C2×Q16—64no—
322C2×Q16—122no—
323C2×SD16—64no—
324C2×SD16—64no—
325C2×SD16—122no—
326C22×C8—32no—
327C22×C8—32no—
328#123—68no—
329C22⋊Q8—28no—
330C22⋊Q8—28no—
331C22⋊Q8—24no—
332C22⋊Q8—24no—
333C22⋊Q8—24no—
334C22⋊Q8—34no—
335C22⋊Q8—62no—
336C22⋊Q8—62no—
337C22⋊Q8—62no—
338C22⋊Q8#6718yescomplemented
339#121—34no—
340#121—62no—
341#121—62no—
342#121—62no—
343#120—68no—
344C4×D4—68no—
345C4×D4—68no—
346#117—62no—
347#117—62no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4C22×D312yes—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—61no—
362C2×C22⋊C4—61no—
363C2×C22⋊C4—61no—
364C2×C22⋊C4—61no—
365C2×C22⋊C4—61no—
366C2×C42—61no—
367#103—64no—
368#103—64no—
369#103—64no—
370#102—64no—
371C22⋊C8—62no—
372C22⋊C8—62no—
373C22⋊C8—64no—
374C22⋊C8—122no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—28no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—44no—
393C23×C3—44no—
394C23×C3—44no—
395C23×C3—44no—
396C23×C3—44no—
397C23×C3—44no—
398C23×C3#12012yes—
399C23×C3#12012yes—
400C23×C3#13512yes—
401C23×C3#13712yes—
402C23×C3#13712yes—
403C23×C3C22×D411yescharacteristic
404C22×D3—22no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—41no—
408C22×D3—41no—
409C22×D3—41no—
410C22×D3—41no—
411C3×Q8—24no—
412C3×Q8—24no—
413C3×Q8—48no—
414C3×Q8—42no—
415C3×Q8—42no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—21no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—44no—
430C2×C3×C4—44no—
431C2×C3×C4—44no—
432C2×C3×C4—48no—
433C2×C3×C4—48no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4#12012yes—
441C2×C3×C4#12012yes—
442C2×C3×C4C22×D411yescharacteristic
443C2×C3×C4C22×D411yescharacteristic
444C2×C3×C4C22×D412yes—
445C2×C3×C4H(5,𝔽2)12yes—
446#67—48no—
447#67—48no—
448#67—48no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458D12—24no—
459D12—42no—
460C4×D3—48no—
461Dic6—24no—
462Dic6—42no—
463C3⋊C8—42no—
464C3⋊C8—42no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—41no—
471C24—41no—
472C24—61no—
473C24C2×#6711yescharacteristic
474C24C2×#6711yescharacteristic
475C24C2×#6711yescharacteristic
476#41—128no—
477#41—128no—
478C2×Q8—24no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—32no—
485C2×Q8—48no—
486C2×Q8—48no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—61no—
490C2×Q8—62no—
491C2×Q8—62no—
492C2×Q8C2×#6714yes—
493C2×D4—32no—
494C2×D4—64no—
495C2×D4—64no—
496C2×D4—64no—
497C2×D4—61no—
498C2×D4—62no—
499C2×D4—62no—
500C2×D4—122no—
501C2×D4—122no—
502C2×D4—122no—
503C2×D4—122no—
504C2×D4—122no—
505C2×D4—122no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—64no—
535C22×C4—61no—
536C22×C4—61no—
537C22×C4—61no—
538C22×C4—122no—
539C22×C4—122no—
540C22×C4D3×D412yes—
541C22×C4D3×D412yes—
542C22×C4C2×#6711yescharacteristic
543C22×C4C2×#6711yescharacteristic
544C22×C4C2×#6711yescharacteristic
545C22×C4C2×#6714yes—
546C22×C4C23×D311yescharacteristic
547Q16—128no—
548SD16—128no—
549C2×C8—62no—
550C2×C8—62no—
551C2×C8—62no—
552C2×C8—62no—
553C2×C8—62no—
554C2×C8—62no—
555C4⋊C4—24no—
556C4⋊C4—28no—
557C4⋊C4—28no—
558C4⋊C4—22no—
559C4⋊C4—32no—
560C4⋊C4—32no—
561C4⋊C4—64no—
562C4⋊C4—64no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4C2×#6714yes—
566C22⋊C4—28no—
567C22⋊C4—28no—
568C22⋊C4—64no—
569C22⋊C4—64no—
570C22⋊C4—64no—
571C22⋊C4—64no—
572C22⋊C4—64no—
573C42—64no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—416no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3#45214yescomplemented
596C22×C3C2×#12011yescharacteristic
597C22×C3C2×#12011yescharacteristic
598C22×C3#53411yescharacteristic
599C22×C3C2×#13511yescharacteristic
600C22×C3C2×#13711yescharacteristic
601C22×C3C2×#13711yescharacteristic
602C22×C3#57511yescharacteristic
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—81no—
607C2×D3—81no—
608C2×D3—81no—
609C2×D3—81no—
610C3×C4—22no—
611C3×C4—22no—
612C3×C4—41no—
613C3×C4—44no—
614C3×C4—44no—
615C3×C4D4212yes—
616C3×C4D4212yes—
617Dic3—42no—
618Dic3—42no—
619Dic3—42no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—28no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—62no—
644C23—121no—
645C23—121no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23#93712yes—
651C23#94212yes—
652C23#94212yes—
653C23#95012yes—
654C23#95312yes—
655C23C22×#6711yescharacteristic
656Q8—24no—
657Q8—24no—
658Q8—48no—
659Q8—42no—
660Q8—42no—
661Q8—64no—
662Q8—122no—
663D4—64no—
664D4—128no—
665D4—128no—
666D4—128no—
667D4—122no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—21no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—44no—
684C2×C4—48no—
685C2×C4—48no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—128no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4#93712yes—
703C2×C4#95312yes—
704C2×C4C2×D3×D411yescharacteristic
705C2×C4C2×D3×D411yescharacteristic
706C2×C4#100412yes—
707C2×C4C22×#6712yes—
708C8—122no—
709C8—122no—
710C2×C3—24no—
711C2×C3—42no—
712C2×C3—42no—
713C2×C3#240311yescharacteristic
714C2×C3C2×#45211yescharacteristic
715C2×C3#300211yescharacteristic
716C2×C3#300411yescharacteristic
717C2×C3#300711yescharacteristic
718C2×C3#319011yescharacteristic
719C2×C3#319611yescharacteristic
720D3—82no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—416no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—122no—
743C22—122no—
744C22—122no—
745C22—241no—
746C22—241no—
747C22—241no—
748C22—241no—
749C22#504714yescomplemented
750C22C2×#93711yescharacteristic
751C22#580411yescharacteristic
752C22C2×#94211yescharacteristic
753C22C2×#94211yescharacteristic
754C22C2×#95011yescharacteristic
755C22#582211yescharacteristic
756C22C2×#95311yescharacteristic
757C4—22no—
758C4—22no—
759C4—41no—
760C4—44no—
761C4—44no—
762C4—122no—
763C4—122no—
764C4—122no—
765C4D4×#6712yes—
766C4D4×#6712yes—
767C3#2392211yescharacteristic, complemented, Sylow
768C2—24no—
769C2—42no—
770C2—42no—
771C2—242no—
772C2C2×#504711yescharacteristic
773C2#8273511yescharacteristic
774C2#8273711yescharacteristic
775C2#8273911yescharacteristic
776C2#8405211yescharacteristic
777C2#8405911yescharacteristic
778C2#8408011yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC22×C3×C22⋊Q8C2
socleC23×C3C22×D4
prime radicalC2×#5791C2
hypercenterC22×C22⋊Q8D3
hypocenterC3#23922
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
3. C2×#5228C2semidirect
4. C2×#5227C2semidirect
5. C2×#5047C2semidirect
6. #72126C2semidirect
7. #71700C2semidirect
8. #71699C2semidirect
9. #71693C2semidirect
10. #71560C2semidirect
11. #71559C2semidirect
25. C22×#216C22semidirect
26. C22×#215C22semidirect
39. C2×#835C22semidirect
40. C2×#835C22semidirect
46. C2×#810C22semidirect
47. C2×#809C22semidirect
48. #4529C22semidirect
49. #4529C22semidirect
51. C22×C22⋊Q8D3semidirect
95. C3×C22⋊Q8D4semidirect
338. C22⋊Q8#67semidirect
595. C22×C3#452semidirect
749. C22#5047semidirect
767. C3#23922semidirect

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×#57912
C2×#52282
C2×#52272
C2×#50472
#721262
#717002
#716992
#716932
#715602
#715592
#239223