Finite Group Databasebeta

← #356292

Subgroups — #356292

Order 512.

1422 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34121C211yesmaximal, characteristic
2C2×#1806C211yesmaximal, characteristic
3C4⋊C4×M16C211yesmaximal, characteristic, complemented
4C2×#1759C211yesmaximal, characteristic
5#13759C211yesmaximal, characteristic, complemented
6#10933C211yesmaximal, characteristic
7#10933C211yesmaximal, characteristic
8#10924C211yesmaximal, characteristic
9#10923C211yesmaximal, characteristic
10#10851C211yesmaximal, characteristic, complemented
11#10840C211yesmaximal, characteristic, complemented
12#10808C211yesmaximal, characteristic, complemented
13#10808C211yesmaximal, characteristic, complemented
14#10701C211yesmaximal, characteristic, complemented
15C4×#339C211yesmaximal, characteristic, complemented
16C2×C4×#41C2211yescharacteristic
17C2×#423C2211yescharacteristic
18C22×#104C2211yescharacteristic
19C22×#104C2211yescharacteristic
20C22×#104C2211yescharacteristic
21C22×#104C2211yescharacteristic
22C2×C4×M16C2211yescharacteristic
23C2×C4×M16C2211yescharacteristic
24C2×C4×M16C2211yescharacteristic
25#2357C412yescomplemented
26#2356C412yescomplemented
27#2355C412yescomplemented
28#2354C412yescomplemented
29#2353—22no—
30#2352—22no—
31#2298—21no—
32#2298—21no—
33#2297C2211yescharacteristic
34#2297C2211yescharacteristic
35#2285C2211yescharacteristic
36#2283—21no—
37C4×#117—21no—
38C4×#117C2211yescharacteristic
39C4×#117C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×#376C2211yescharacteristic
43C2×#376C2211yescharacteristic
44C2×C43C2211yescharacteristic
45#1806C418yescomplemented
46#1771—21no—
47#1771—21no—
48#1770—21no—
49C8×C4⋊C4—21no—
50#1759C418yescomplemented
51C2×#339C2211yescharacteristic
52C2×#339C2211yescharacteristic
53C2×#339C2211yescharacteristic
54C2×#339C2211yescharacteristic
55C2×#339C2211yescharacteristic
56C2×#339C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63#1728C2211yescharacteristic
64#1728C2211yescharacteristic
65#1436—22no—
66#1436—22no—
67C4×#95C2211yescharacteristic
68C4×#95C2211yescharacteristic
69C22×#41C2311yescharacteristic
70C22×M16C2311yescharacteristic
71C22×M16C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C4×#41—22no—
75C4×#41—22no—
76C4×#41C2×C414yes—
77C4×#41C2×C414yes—
78C2×C4×Q8C2×C411yescharacteristic
79C2×C4×Q8C2×C411yescharacteristic
80C2×C4×D4—21no—
81C2×C4×D4—21no—
82C2×C4×D4C2×C411yescharacteristic
83C2×C4×D4C2×C411yescharacteristic
84C2×#117—22no—
85C2×#117—21no—
86C2×#117C2311yescharacteristic
87C2×#117C2311yescharacteristic
88C2×#117C2311yescharacteristic
89C22×C4⋊C4—21no—
90C22×C4⋊C4D412yes—
91C22×C42—21no—
92C22×C42—22no—
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100#423—22no—
101#423C2×C414yes—
102C2×C4⋊C8—21no—
103C2×C4⋊C8—21no—
104C2×#104—22no—
105C2×#104—22no—
106C2×#104—22no—
107C2×#104—22no—
108C2×#104—41no—
109C2×#104—41no—
110C2×#104—41no—
111C2×#104—41no—
112C2×#104C2×C414yes—
113C2×#104C2×C414yes—
114C2×#104C2×C414yes—
115C2×#104C2×C414yes—
116C4×M16—22no—
117C4×M16—22no—
118C4×M16—22no—
119C4×M16—41no—
120C4×M16—41no—
121C4×M16C2×C414yes—
122C2×#97—21no—
123C2×#97—21no—
124C2×#97—21no—
125C2×C4×C8—21no—
126C2×C4×C8—21no—
127C2×C4×C8—21no—
128#391C2×C412yes—
129#391C2×C412yes—
130#390C2×C412yes—
131#390C2×C412yes—
132#388—22no—
133#388—22no—
134#388—22no—
135#388—22no—
136#387—22no—
137#387—22no—
138#387—22no—
139#387—22no—
140#386—22no—
141#386—22no—
142#384C2×C412yes—
143#383—22no—
144#382—22no—
145#382C2×C412yes—
146#381—22no—
147#380—21no—
148#380—21no—
149#380—22no—
150C4×C4⋊C4—22no—
151C4×C4⋊C4—21no—
152C4×C4⋊C4—21no—
153C4×C4⋊C4—22no—
154C4×C4⋊C4C2×C412yes—
155C4×C4⋊C4C2×C412yes—
156C4×C4⋊C4C2×C412yes—
157C4×C4⋊C4C2×C412yes—
158C4×C4⋊C4C2×C414yes—
159C4×C4⋊C4C2×C412yes—
160C4×C4⋊C4C2×C412yes—
161C4×C4⋊C4D411yescharacteristic
162C4×C4⋊C4D411yescharacteristic
163C4×C4⋊C4D411yescharacteristic
164C4×C4⋊C4D411yescharacteristic
165C4×C22⋊C4—22no—
166C4×C22⋊C4—22no—
167C4×C22⋊C4—21no—
168C4×C22⋊C4—21no—
169C4×C22⋊C4—21no—
170C4×C22⋊C4—21no—
171C4×C22⋊C4—22no—
172#376—21no—
173#376—21no—
174#376—22no—
175#376—22no—
176#376—22no—
177#376—41no—
178#376C2×C414yes—
179C2×#95—21no—
180C2×#95—21no—
181C2×#95—21no—
182C2×#95—22no—
183C2×#95—22no—
184C2×#95—22no—
185C2×#95D412yes—
186C43—21no—
187C43—21no—
188C43—22no—
189C43—41no—
190#339—22no—
191#339—22no—
192#339—22no—
193#339—22no—
194#339—41no—
195#339—41no—
196#339—41no—
197#339—41no—
198#339C2×C414yes—
199#339C2×C414yes—
200#339C2×C414yes—
201#339C2×C414yes—
202#336—21no—
203#336—21no—
204#336—21no—
205#336—21no—
206C2×#41—21no—
207C2×#41—21no—
208C2×#41—21no—
209C2×#41—21no—
210C2×#41—21no—
211C2×#41—21no—
212C2×#41—21no—
213C2×#41—21no—
214C2×#41—21no—
215C2×#41—21no—
216C2×#41C22×C412yes—
217C2×#41C22×C412yes—
218C22×Q8C22×C411yescharacteristic
219C22×D4—21no—
220C22×D4C22×C411yescharacteristic
221C23×C4—21no—
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4C2×D412yes—
229C23×C4C2×D412yes—
230C23×C4C2×D411yescharacteristic
231C23×C4C2×D411yescharacteristic
232C23×C4C2411yescharacteristic
233C2×M16—21no—
234C2×M16—21no—
235C2×M16—21no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16C22×C412yes—
252C2×M16C22×C412yes—
253C2×M16C22×C412yes—
254C2×M16C22×C412yes—
255C2×M16#4112yes—
256C2×M16#4112yes—
257C22×C8—21no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C4×Q8—22no—
262C4×Q8—22no—
263C4×Q8C4214yescomplemented
264C4×Q8C4214yescomplemented
265C4×D4—24no—
266C4×D4—24no—
267C4×D4—24no—
268C4×D4—24no—
269C4×D4—22no—
270C4×D4—22no—
271C4×D4C4214yescomplemented
272C4×D4C4214yescomplemented
273#117—21no—
274#117—21no—
275#117—24no—
276#117—24no—
277#117—21no—
278#117—21no—
279#117—21no—
280#117—21no—
281#117—21no—
282#117—21no—
283#117—21no—
284#117—21no—
285#117—48no—
286#117C22×C412yes—
287#117C22×C412yes—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4C22⋊C412yes—
296C2×C4⋊C4C22⋊C412yes—
297C2×C4⋊C4C22⋊C412yes—
298C2×C4⋊C4C22⋊C412yes—
299C2×C4⋊C4C22×C412yes—
300C2×C4⋊C4C22×C412yes—
301C2×C4⋊C4C22×C411yescharacteristic
302C2×C4⋊C4C22×C411yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—24no—
327C2×C42—24no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—21no—
343C2×C42—21no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—21no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—44no—
350C2×C42—44no—
351C2×C42—44no—
352C2×C42C22×C412yes—
353C2×C42C22×C412yes—
354C2×C42C22×C412yes—
355C2×C42C22×C412yes—
356C2×C42C22×C412yes—
357C2×C42C22×C412yes—
358C2×C42C22×C411yescharacteristic
359C2×C42C22×C411yescharacteristic
360C2×C42C22×C412yes—
361C2×C42C22×C412yes—
362C2×C42C2×D411yescharacteristic
363C2×C42C2×D411yescharacteristic
364C2×C42C2×D411yescharacteristic
365C2×C42C2×D411yescharacteristic
366C2×C42C2×D411yescharacteristic
367C2×C42C2×D411yescharacteristic
368C2×C42#4112yes—
369C2×C42#4112yes—
370C2×C42#4112yes—
371C2×C42#4112yes—
372C4⋊C8—24no—
373C4⋊C8—24no—
374#104—28no—
375#104—28no—
376#104—44no—
377#104—44no—
378#97—24no—
379#97—42no—
380#97—42no—
381C4×C8—24no—
382C4×C8—42no—
383C4×C8—42no—
384#95—22no—
385#95—22no—
386#95—22no—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95—22no—
393#95—22no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95C22⋊C412yes—
401#95C22⋊C412yes—
402#95C22⋊C412yes—
403#95C22⋊C412yes—
404C24—21no—
405C24C22×D411yescharacteristic
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—22no—
412#41—22no—
413#41—22no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419#41—41no—
420#41—41no—
421#41—41no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C2×C4212yes—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—41no—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4C2×C4212yes—
440C22×C4—24no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—44no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—82no—
485C22×C4C2×C22⋊C412yes—
486C22×C4C2×C22⋊C412yes—
487C22×C4C2×C22⋊C412yes—
488C22×C4C2×C22⋊C411yescharacteristic
489C22×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C412yes—
493C22×C4C4×D412yes—
494C22×C4C4×D412yes—
495C22×C4C4×D412yes—
496C22×C4C4×D412yes—
497C22×C4C23×C411yescharacteristic
498C22×C4C23×C411yescharacteristic
499C22×C4C23×C411yescharacteristic
500C22×C4C22×D411yescharacteristic
501C22×C4C2×#4111yescharacteristic
502C22×C4C2×#4111yescharacteristic
503C22×C4C2×#4111yescharacteristic
504C22×C4C2×#4111yescharacteristic
505C22×C4C2×#4111yescharacteristic
506C22×C4C2×#4111yescharacteristic
507C22×C4H(5,𝔽2)11yescharacteristic
508C22×C4H(5,𝔽2)11yescharacteristic
509C22×C42−1+411yescharacteristic
510C22×C42−1+411yescharacteristic
511M16—22no—
512M16—22no—
513M16—22no—
514M16—22no—
515M16—22no—
516M16—22no—
517M16—22no—
518M16—22no—
519M16—22no—
520M16—41no—
521M16—41no—
522M16—41no—
523M16—41no—
524M16—41no—
525M16—41no—
526M16#11714yescomplemented
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—24no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—22no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—48no—
552C4⋊C4—44no—
553C4⋊C4—82no—
554C4⋊C4C2×C4212yes—
555C4⋊C4C2×C4212yes—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—44no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—44no—
566C22⋊C4—82no—
567C22⋊C4—82no—
568C42—22no—
569C42—22no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—22no—
574C42—22no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—22no—
584C42—22no—
585C42—24no—
586C42—24no—
587C42—22no—
588C42—22no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—44no—
594C42—416no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—41no—
605C42—44no—
606C42—82no—
607C42—82no—
608C42C2×C4212yes—
609C42C2×C4212yes—
610C42#11712yes—
611C42#11712yes—
612C42#11714yescomplemented
613C42C4×D412yes—
614C42C4×D412yes—
615C42C4×D412yes—
616C42C4×D412yes—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—41no—
621C23—41no—
622C23—42no—
623C23—42no—
624C23C22×C22⋊C411yescharacteristic
625C23C2×C4×D411yescharacteristic
626C23C2×C4×D411yescharacteristic
627C23#54611yescharacteristic
628C23#54711yescharacteristic
629C23#54811yescharacteristic
630C23#55011yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—41no—
634Q8—41no—
635D4—22no—
636D4—22no—
637D4—42no—
638D4—42no—
639D4—42no—
640D4—42no—
641D4—41no—
642D4—41no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—48no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—84no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4C4×C22⋊C412yes—
706C2×C4C4×C22⋊C412yes—
707C2×C4C4×C22⋊C412yes—
708C2×C4C4×C22⋊C412yes—
709C2×C4#42114yes—
710C2×C4C22×C4211yescharacteristic
711C2×C4C2×#11711yescharacteristic
712C2×C4C2×#11711yescharacteristic
713C2×C4C2×#11711yescharacteristic
714C2×C4C2×C4×D411yescharacteristic
715C2×C4C2×C4×D411yescharacteristic
716C2×C4C4×#4111yescharacteristic
717C2×C4C4×#4111yescharacteristic
718C2×C4C4×#4111yescharacteristic
719C2×C4C4×#4111yescharacteristic
720C2×C4#51811yescharacteristic
721C2×C4#51911yescharacteristic
722C2×C4#52011yescharacteristic
723C2×C4#52011yescharacteristic
724C2×C4#52011yescharacteristic
725C2×C4#52011yescharacteristic
726C2×C4#54611yescharacteristic
727C2×C4#54711yescharacteristic
728C2×C4#54811yescharacteristic
729C2×C4#55011yescharacteristic
730C2×C4#55211yescharacteristic
731C2×C4#55211yescharacteristic
732C2×C4#55311yescharacteristic
733C2×C4#55311yescharacteristic
734C2×C4#55511yescharacteristic
735C2×C4#55511yescharacteristic
736C2×C4#55611yescharacteristic
737C2×C4#55611yescharacteristic
738C8—24no—
739C8—42no—
740C8—42no—
741C8—42no—
742C22—22no—
743C22—22no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—22no—
749C22—22no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—82no—
754C22—82no—
755C22C2×C4×C22⋊C411yescharacteristic
756C22#233911yescharacteristic
757C22#234111yescharacteristic
758C22#235211yescharacteristic
759C22#235411yescharacteristic
760C22#236211yescharacteristic
761C22#236311yescharacteristic
762C22C2×#42112yes—
763C22#290112yes—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—24no—
769C4—44no—
770C4—44no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4—82no—
781C4C4×#11711yescharacteristic
782C4#227411yescharacteristic
783C4#234611yescharacteristic
784C4#234711yescharacteristic
785C4#235211yescharacteristic
786C4#235411yescharacteristic
787C4#236211yescharacteristic
788C4#236311yescharacteristic
789C2—21no—
790C2—21no—
791C2—21no—
792C2—21no—
793C2—82no—
794C2#1380111yescharacteristic
795C2C4×#42111yescharacteristic
796C2#2040511yescharacteristic
797C2#2250612yes—
798C2#2255112yes—
subgroupG/H
centerC22×C4C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
socleC23C22×C22⋊C4
prime radicalC22×#41C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×M16C2semidirect
5. #13759C2semidirect
10. #10851C2semidirect
11. #10840C2semidirect
12. #10808C2semidirect
13. #10808C2semidirect
14. #10701C2semidirect
15. C4×#339C2semidirect
25. #2357C4semidirect
26. #2356C4semidirect
27. #2355C4semidirect
28. #2354C4semidirect
45. #1806C4semidirect
50. #1759C4semidirect
263. C4×Q8C42semidirect
264. C4×Q8C42semidirect
271. C4×D4C42semidirect
272. C4×D4C42semidirect
526. M16#117semidirect
612. C42#117semidirect

Maximal subgroups

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

subgroupindex
#341212
C2×#18062
C4⋊C4×M162
C2×#17592
#137592
#109332
#109242
#109232
#108512
#108402
#108082
#107012
C4×#3392