Finite Group Databasebeta

← #10823397

Subgroups — #10823397

Order 768.

1188 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5479C211yesmaximal, characteristic
2C3×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C4×#216C211yesmaximal, characteristic, complemented
4C2×C4×#215C211yesmaximal, characteristic, complemented
5#71700C211yesmaximal, characteristic, complemented
6#71699C211yesmaximal, characteristic
7C4×#830C211yesmaximal, characteristic, complemented
8#69689C211yesmaximal, characteristic, complemented
9#69669C211yesmaximal, characteristic, complemented
10#69628C211yesmaximal, characteristic, complemented
11#69606C211yesmaximal, characteristic, complemented
12#69526C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic
14C4×#810C211yesmaximal, characteristic, complemented
15C4×#809C211yesmaximal, characteristic, complemented
16#23572—31nomaximal, Sylow
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×C3×C4×Q8C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#929—21no—
24C2×C4×#67—21no—
25C2×#924C2211yescharacteristic
26#5479—24no—
27#5479—24no—
28C2×#876—21no—
29C2×#875C2211yescharacteristic
30C2×C4×D12C2211yescharacteristic
31C2×#872—21no—
32C2×#870C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C3×#391C2211yescharacteristic
35C3×#389C2211yescharacteristic
36C3×#387—21no—
37C3×#385—21no—
38C3×#380C2211yescharacteristic
39C3×C4×C4⋊C4—21no—
40C3×C4×C4⋊C4C2211yescharacteristic
41C3×C4×C22⋊C4—21no—
42C2×#835C2211yescharacteristic
43C2×#835C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46C4×#216—24no—
47C4×#215—24no—
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#808C2211yescharacteristic
55C2×#807C2211yescharacteristic
56C2×C4×C3⋊C8C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529—31no—
65C2×C4×Q16—31no—
66C2×C4×SD16—31no—
67C4×C22⋊Q8D311yescharacteristic, complemented
68#2059—31no—
69#2042—31no—
70#2035—31no—
71#2033—31no—
72#2026—31no—
73#2015—31no—
74#2001—31no—
75#2000—31no—
76C4×#103—31no—
77C4×#102—31no—
78C4×C22⋊C8—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4D411yescharacteristic
81C23×C3×C4D411yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×D12C2311yescharacteristic
85C22×C4×D3—21no—
86C22×Dic6C2311yescharacteristic
87C3×C22⋊Q8—22no—
88C3×C22⋊Q8—22no—
89C3×C4×Q8—22no—
90C3×C4×Q8—22no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C22⋊C4—21no—
98C2×C3×C22⋊C4—21no—
99C2×C3×C42—22no—
100C2×C3×C42—22no—
101C2×C3×C42—21no—
102C2×C3×C42—21no—
103C2×C3×C42D411yescharacteristic
104C2×C3×C42D411yescharacteristic
105C2×C3×C42C2311yescharacteristic
106C2×C3×C42C2311yescharacteristic
107C2×#217—21no—
108C2×#216—22no—
109C2×#216—22no—
110C2×#216—22no—
111C2×#215—22no—
112C2×#215—22no—
113C2×#215—22no—
114#930—22no—
115#930—22no—
116#929—28no—
117C4×#67—28no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124#924—22no—
125#924—22no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×C4×Dic3—21no—
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135#876—28no—
136#875—22no—
137#875—22no—
138C4×D12—22no—
139C4×D12D414yes—
140#872—28no—
141#870—22no—
142#870—22no—
143C4×Dic6—22no—
144C4×Dic6D414yes—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95—21no—
149C3×#95—21no—
150#835—22no—
151#835—22no—
152#830—22no—
153#830—22no—
154#810—22no—
155#810—22no—
156#810—22no—
157#809—22no—
158#809—22no—
159#809—22no—
160#808—22no—
161#807—22no—
162C4×C3⋊C8—22no—
163C4×C3⋊C8—22no—
164C22×Q16—31no—
165C22×SD16—31no—
166#529—64no—
167#529—64no—
168C2×#126—61no—
169C2×#125—31no—
170C2×#124—31no—
171C2×#123—61no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×#121—31no—
175C2×C4×Q8—31no—
176C2×C4×Q8C2×D311yescharacteristic
177C2×C4×D4—31no—
178C2×C4×D4—61no—
179C2×#117—61no—
180C22×C42C2×D311yescharacteristic
181C4×Q16—64no—
182C4×SD16—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C4×C8—31no—
196C2×C4×C8—31no—
197#391C2×D311yescharacteristic
198#389C2×D311yescharacteristic
199#387—21no—
200#385—21no—
201#380C2×D311yescharacteristic
202C4×C4⋊C4—21no—
203C4×C4⋊C4C2×D311yescharacteristic
204C4×C22⋊C4—21no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#336—31no—
210#336—31no—
211C24×C3C2×D411yescharacteristic
212C23×D3—21no—
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8#4112yes—
219C22×C3×C4—22no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—41no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2411yescharacteristic
241C2×#67—24no—
242C2×#67—42no—
243C2×#67—42no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12C2×D412yes—
253C2×C4×D3—24no—
254C2×C4×D3—42no—
255C2×C4×D3—42no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6C2×D412yes—
262C3×C4⋊C4—24no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—42no—
269C3×C4⋊C4—42no—
270C3×C4⋊C4#4112yes—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—42no—
273C3×C42—22no—
274C3×C42—22no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—42no—
278C3×C42—42no—
279C3×C42C2×D412yes—
280C3×C42C2×D412yes—
281#217—24no—
282#216—28no—
283#215—28no—
284(C2×D3)⋊C4—24no—
285(C2×D3)⋊C4—24no—
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—24no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3C2×D412yes—
291C4⋊Dic3C2×D412yes—
292Dic3⋊C4—24no—
293Dic3⋊C4—24no—
294Dic3⋊C4—24no—
295Dic3⋊C4—24no—
296C4×Dic3—24no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8#4112yes—
308C2×C3⋊C8#4112yes—
309C22×Q8—31no—
310C22×Q8C22×D311yescharacteristic
311C22×D4—31no—
312C22×D4—61no—
313C23×C4—61no—
314C23×C4#6711yescharacteristic
315C23×C4#6711yescharacteristic
316C23×C4C22×D311yescharacteristic
317C2×Q16—62no—
318C2×Q16—62no—
319C2×Q16—62no—
320C2×SD16—62no—
321C2×SD16—62no—
322C2×SD16—62no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8—31no—
326C22×C8—31no—
327#126—68no—
328#125—62no—
329#125—62no—
330#124—62no—
331#124—62no—
332#123—68no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—62no—
336C22⋊Q8—62no—
337#121—62no—
338#121—62no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—34no—
342C4×Q8—62no—
343C4×D4—34no—
344C4×D4—68no—
345C4×D4—62no—
346#117—68no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4C22×D311yescharacteristic
357C2×C4⋊C4C22×D311yescharacteristic
358C2×C4⋊C4C22×D311yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—61no—
362C2×C22⋊C4—61no—
363C2×C22⋊C4—61no—
364C2×C22⋊C4—61no—
365C2×C22⋊C4—61no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—61no—
371C2×C42#6711yescharacteristic
372C2×C42#6711yescharacteristic
373C2×C42C22×D311yescharacteristic
374C2×C42C22×D311yescharacteristic
375#107—62no—
376#106—62no—
377#103—62no—
378#103—62no—
379#103—62no—
380#103—62no—
381#103—62no—
382#102—62no—
383#102—62no—
384#102—62no—
385C22⋊C8—62no—
386C22⋊C8—62no—
387C4×C8—62no—
388C4×C8—62no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3#13512yes—
401C23×C3C22×D411yescharacteristic
402C22×D3—22no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—41no—
408C22×D3—41no—
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—41no—
412C3×Q8—41no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—44no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—44no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4#12012yes—
443C2×C3×C4#12012yes—
444C2×C3×C4#13512yes—
445C2×C3×C4#13712yes—
446C2×C3×C4C22×D411yescharacteristic
447C2×C3×C4C22×D411yescharacteristic
448C2×C3×C4C2×#4111yescharacteristic
449C2×C3×C4C2×#4111yescharacteristic
450C2×C3×C4C2×#4111yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452#67—48no—
453C2×Dic3—22no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462D12—22no—
463D12—22no—
464D12—41no—
465D12—41no—
466C4×D3—48no—
467Dic6—22no—
468Dic6—22no—
469Dic6—41no—
470Dic6—41no—
471C3⋊C8—22no—
472C3⋊C8—22no—
473C3⋊C8—41no—
474C3⋊C8—41no—
475C24—61no—
476C24C2×#6711yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—32no—
483C2×Q8—61no—
484C2×Q8—61no—
485C2×Q8—61no—
486C2×Q8—61no—
487C2×Q8—61no—
488C2×Q8#23512yes—
489C2×D4—32no—
490C2×D4—64no—
491C2×D4—61no—
492C2×D4—61no—
493C2×D4—61no—
494C2×D4—61no—
495C2×D4—61no—
496C2×D4—122no—
497C2×D4—122no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—41no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—64no—
518C22×C4—122no—
519C22×C4—122no—
520C22×C4C2×#6711yescharacteristic
521C22×C4C2×#6711yescharacteristic
522C22×C4C2×#6711yescharacteristic
523C22×C4C2×#6711yescharacteristic
524C22×C4C2×#6711yescharacteristic
525C22×C4C23×D311yescharacteristic
526Q16—68no—
527SD16—68no—
528C2×C8—32no—
529C2×C8—32no—
530C2×C8—61no—
531C2×C8—61no—
532C2×C8—61no—
533C2×C8—61no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C4⋊C4—24no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—32no—
547C4⋊C4—32no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—64no—
551C4⋊C4—64no—
552C4⋊C4—64no—
553C4⋊C4—64no—
554C4⋊C4—61no—
555C4⋊C4—61no—
556C4⋊C4#23512yes—
557C22⋊C4—24no—
558C22⋊C4—42no—
559C22⋊C4—64no—
560C22⋊C4—64no—
561C22⋊C4—64no—
562C22⋊C4—64no—
563C22⋊C4—64no—
564C42—22no—
565C42—22no—
566C42—21no—
567C42—21no—
568C42—42no—
569C42—42no—
570C42—64no—
571C42D3×D412yes—
572C42D3×D412yes—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3C2×#12011yescharacteristic
581C22×C3#52511yescharacteristic
582C22×C3#53211yescharacteristic
583C22×C3C2×#13511yescharacteristic
584C22×C3C2×#13511yescharacteristic
585C22×C3C2×#13711yescharacteristic
586C22×C3#57511yescharacteristic
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—42no—
590C2×D3—81no—
591C2×D3—81no—
592C2×D3—81no—
593C2×D3—81no—
594C3×C4—22no—
595C3×C4—42no—
596C3×C4—41no—
597C3×C4—42no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—81no—
601C3×C4—81no—
602C3×C4#45214yes—
603C3×C4#52511yescharacteristic
604C3×C4#52511yescharacteristic
605C3×C4#53211yescharacteristic
606C3×C4#53211yescharacteristic
607Dic3—42no—
608Dic3—42no—
609Dic3—42no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—62no—
617C23—121no—
618C23—121no—
619C23—121no—
620C23—121no—
621C23—121no—
622C23—121no—
623C23#95012yes—
624C23C22×#6711yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—62no—
630Q8—62no—
631Q8—121no—
632Q8—121no—
633D4—62no—
634D4—62no—
635D4—128no—
636D4—121no—
637D4—121no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—44no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—44no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—62no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—128no—
677C2×C4#93712yes—
678C2×C4#93712yes—
679C2×C4#94212yes—
680C2×C4#95012yes—
681C2×C4C2×#23511yescharacteristic
682C2×C4C2×#23511yescharacteristic
683C2×C4C2×D3×D411yescharacteristic
684C2×C4C2×D3×D411yescharacteristic
685C2×C4D3×#4111yescharacteristic
686C2×C4D3×#4111yescharacteristic
687C8—62no—
688C8—62no—
689C8—121no—
690C8—121no—
691C2×C3—42no—
692C2×C3#238811yescharacteristic
693C2×C3C2×#45211yescharacteristic
694C2×C3#300211yescharacteristic
695C2×C3#310211yescharacteristic
696C2×C3#310811yescharacteristic
697C2×C3#316811yescharacteristic
698C2×C3#317211yescharacteristic
699D3—82no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—122no—
708C22—122no—
709C22—122no—
710C22—241no—
711C22—241no—
712C22—241no—
713C22—241no—
714C22#579111yescharacteristic
715C22C2×#93711yescharacteristic
716C22C2×#94211yescharacteristic
717C22C2×#95011yescharacteristic
718C22C2×#95011yescharacteristic
719C22#582211yescharacteristic
720C22#583211yescharacteristic
721C4—22no—
722C4—41no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—81no—
728C4—81no—
729C4—122no—
730C4—122no—
731C4—122no—
732C4#504714yes—
733C4#554711yescharacteristic
734C4#554711yescharacteristic
735C4#554811yescharacteristic
736C4#554811yescharacteristic
737C3#2357211yescharacteristic, complemented, Sylow
738C2—42no—
739C2—242no—
740C2#8240011yescharacteristic
741C2#8244311yescharacteristic
742C2#8252811yescharacteristic
743C2C2×#504711yescharacteristic
744C2#8292611yescharacteristic
745C2#8313411yescharacteristic
746C2#8334511yescharacteristic
subgroupG/H
centerC22×C4C2×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×C4×C22⋊Q8C2
socleC23×C3C22×D4
prime radicalC2×#930C22
hypercenterC4×C22⋊Q8D3
hypocenterC3#23572
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×C4×C22⋊Q8C2semidirect
3. C2×C4×#216C2semidirect
4. C2×C4×#215C2semidirect
5. #71700C2semidirect
7. C4×#830C2semidirect
8. #69689C2semidirect
9. #69669C2semidirect
10. #69628C2semidirect
11. #69606C2semidirect
12. #69526C2semidirect
14. C4×#810C2semidirect
15. C4×#809C2semidirect
67. C4×C22⋊Q8D3semidirect
737. C3#23572semidirect

Maximal subgroups

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

subgroupindex
C2×#54792
C3×C4×C22⋊Q82
C2×C4×#2162
C2×C4×#2152
#717002
#716992
C4×#8302
#696892
#696692
#696282
#696062
#695262
#695232
C4×#8102
C4×#8092
#235723