Finite Group Databasebeta

← #390477

Subgroups — #390477

Order 512.

1231 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23479C211yesmaximal, characteristic
2#21191C211yesmaximal, characteristic
3#21053C211yesmaximal, characteristic, complemented
4C2×#1922C211yesmaximal, characteristic, complemented
5C2×#1896C211yesmaximal, characteristic
6#11329C211yesmaximal, characteristic, complemented
7#11191C211yesmaximal, characteristic, complemented
8#11125C211yesmaximal, characteristic, complemented
9#11097C211yesmaximal, characteristic, complemented
10#11068C211yesmaximal, characteristic, complemented
11#10934C211yesmaximal, characteristic, complemented
12#10909C211yesmaximal, characteristic, complemented
13#10809C211yesmaximal, characteristic, complemented
14#10719C211yesmaximal, characteristic, complemented
15#10712C211yesmaximal, characteristic, complemented
16C2×#525C2211yescharacteristic
17C23×C42C2211yescharacteristic
18C22×#108C2211yescharacteristic
19C2×#427C2211yescharacteristic
20C2×#424C2211yescharacteristic
21C2×#424C2211yescharacteristic
22C22×#104C2211yescharacteristic
23C22×#104C2211yescharacteristic
24C2×#416C2211yescharacteristic
25C2×#416C2211yescharacteristic
26C2×#408C2211yescharacteristic
27C2×#408C2211yescharacteristic
28C2×#407C2211yescharacteristic
29C2×#407C2211yescharacteristic
30C22×C22⋊C8C2211yescharacteristic
31C22×C22⋊C8C2211yescharacteristic
32C2×#405C2211yescharacteristic
33C2×#405C2211yescharacteristic
34#2280C2211yescharacteristic
35#2036C411yescharacteristic, complemented
36#2036C411yescharacteristic, complemented
37#2035C411yescharacteristic, complemented
38#2035C411yescharacteristic, complemented
39#2034C411yescharacteristic, complemented
40#2034C411yescharacteristic, complemented
41#2033C411yescharacteristic, complemented
42#2033C411yescharacteristic, complemented
43#1955—21no—
44#1955—21no—
45#1954—21no—
46#1954—21no—
47#1924—21no—
48#1924—21no—
49#1923—21no—
50#1923—21no—
51#1922—24no—
52#1896—24no—
53C2×#341C2211yescharacteristic
54C2×#341C2211yescharacteristic
55C2×#341C2211yescharacteristic
56#1735C2211yescharacteristic
57C2×#339C2211yescharacteristic
58C2×#339C2211yescharacteristic
59C2×#339C2211yescharacteristic
60C2×#339C2211yescharacteristic
61C2×#339C2211yescharacteristic
62C2×#339C2211yescharacteristic
63#1729C2211yescharacteristic
64#1729C2211yescharacteristic
65C2×#336C2211yescharacteristic
66C2×#336C2211yescharacteristic
67C2×#336C2211yescharacteristic
68C2×#336C2211yescharacteristic
69C22×#41C2311yescharacteristic
70C24×C4—21no—
71C24×C4C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C22×M16C2311yescharacteristic
75C22×M16C2311yescharacteristic
76C23×C8C2311yescharacteristic
77C23×C8C2311yescharacteristic
78C23×C8C2311yescharacteristic
79C23×C8C2311yescharacteristic
80#525—22no—
81#525—22no—
82#525—41no—
83#525—41no—
84C2×#123—21no—
85C2×C22⋊Q8C2×C411yescharacteristic
86C2×C22⋊Q8C2×C411yescharacteristic
87C2×#121C2×C411yescharacteristic
88C2×#121C2×C411yescharacteristic
89C2×#120—21no—
90C2×C4×D4—21no—
91C2×C4×D4—21no—
92C2×#117C2311yescharacteristic
93C2×#117C2311yescharacteristic
94C2×#117C2311yescharacteristic
95C22×C42—22no—
96C22×C42—22no—
97C22×C42—21no—
98C22×C42—41no—
99C22×C42—41no—
100C22×C42—41no—
101C22×C42—41no—
102C22×C42C2311yescharacteristic
103C22×C42C2311yescharacteristic
104C2×#108—41no—
105C2×#108—41no—
106C2×#108—41no—
107#427—22no—
108#427—22no—
109C2×#107C2×C411yescharacteristic, complemented
110C2×#107C2×C411yescharacteristic, complemented
111C2×#106C2×C411yescharacteristic, complemented
112C2×#106C2×C411yescharacteristic, complemented
113#424—22no—
114#424—41no—
115#424—41no—
116#424—41no—
117C2×C4⋊C8—21no—
118C2×C4⋊C8—21no—
119C2×C4⋊C8—21no—
120C2×C4⋊C8—21no—
121C2×#104—22no—
122C2×#104—22no—
123C2×#104—22no—
124C2×#104—41no—
125C2×#104—41no—
126C2×#104—41no—
127#416—41no—
128#416—41no—
129#416—41no—
130#416—41no—
131C2×#103C2×C411yescharacteristic, complemented
132C2×#103C2×C411yescharacteristic, complemented
133C2×#103C2×C411yescharacteristic, complemented
134C2×#103C2×C411yescharacteristic, complemented
135C2×#102C2×C411yescharacteristic, complemented
136C2×#102C2×C411yescharacteristic, complemented
137C2×#102C2×C411yescharacteristic, complemented
138C2×#102C2×C411yescharacteristic, complemented
139#408—22no—
140#408—41no—
141#408—41no—
142#408—41no—
143#407—22no—
144#407—22no—
145#407—41no—
146#407—41no—
147C2×C22⋊C8—21no—
148C2×C22⋊C8—21no—
149C2×C22⋊C8—21no—
150C2×C22⋊C8—21no—
151C2×C22⋊C8—21no—
152C2×C22⋊C8—21no—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—21no—
155C2×C22⋊C8—41no—
156C2×C22⋊C8—41no—
157C2×C22⋊C8—41no—
158C2×C22⋊C8—41no—
159C2×C22⋊C8C2×C411yescharacteristic
160C2×C22⋊C8C2×C411yescharacteristic
161C2×C22⋊C8C2×C411yescharacteristic
162C2×C22⋊C8C2×C411yescharacteristic
163C2×C22⋊C8D411yescharacteristic
164C2×C22⋊C8D411yescharacteristic
165C2×C22⋊C8D411yescharacteristic
166C2×C22⋊C8D411yescharacteristic
167#405—22no—
168#405—22no—
169#405—41no—
170#405—41no—
171C2×#97—21no—
172C2×#97—21no—
173C2×C4×C8—21no—
174C2×C4×C8—21no—
175#381—21no—
176#380C2×C411yescharacteristic
177#380C2×C411yescharacteristic
178#380C2×C411yescharacteristic
179#380C2×C411yescharacteristic
180#379—21no—
181C4×C22⋊C4—21no—
182C4×C22⋊C4—21no—
183#341—22no—
184#341—22no—
185#341—41no—
186#340C2×C411yescharacteristic, complemented
187#340C2×C411yescharacteristic, complemented
188#340C2×C411yescharacteristic, complemented
189#340C2×C411yescharacteristic, complemented
190#339—22no—
191#339—22no—
192#339—41no—
193#339—41no—
194#339—41no—
195#339D414yes—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—22no—
201#336—22no—
202#336—41no—
203#336—41no—
204C25#4111yescharacteristic
205C2×#41—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×#41—21no—
217C22×Q8C22×C411yescharacteristic
218C22×D4—21no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4C22×C411yescharacteristic
222C23×C4—21no—
223C23×C4—21no—
224C23×C4—21no—
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—21no—
228C23×C4—21no—
229C23×C4—21no—
230C23×C4—21no—
231C23×C4—21no—
232C23×C4—21no—
233C23×C4—21no—
234C23×C4—21no—
235C23×C4—21no—
236C23×C4—24no—
237C23×C4—21no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4C22×C411yescharacteristic
245C23×C4C22×C411yescharacteristic
246C23×C4C2×D411yescharacteristic
247C23×C4C2×D411yescharacteristic
248C23×C4#4111yescharacteristic
249C23×C4C2411yescharacteristic
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—21no—
259C2×M16—21no—
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—21no—
263C2×M16—21no—
264C2×M16—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16—21no—
269C2×M16—21no—
270C2×M16—21no—
271C2×M16—21no—
272C2×M16C2×D412yes—
273C2×M16#4112yes—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—21no—
295C22×C8—21no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—21no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—21no—
302C22×C8C22×C411yescharacteristic
303C22×C8C22×C411yescharacteristic
304C22×C8C22×C411yescharacteristic
305C22×C8C22×C411yescharacteristic
306C22×C8C2×D411yescharacteristic
307C22×C8C2×D411yescharacteristic
308C22×C8C2×D411yescharacteristic
309C22×C8C2×D411yescharacteristic
310#123—42no—
311#123—42no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8—41no—
315C22⋊Q8—41no—
316#121—22no—
317#121—22no—
318#121—41no—
319#121—41no—
320#120—42no—
321#120—42no—
322C4×D4—42no—
323C4×D4—42no—
324C4×D4—42no—
325C4×D4—42no—
326#117—21no—
327#117—21no—
328#117—21no—
329#117—21no—
330#117—21no—
331#117—21no—
332#117—21no—
333#117—21no—
334#117—21no—
335#117—21no—
336#117C2×D412yes—
337#117#4112yes—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4C22×C411yescharacteristic
341C2×C4⋊C4C22×C411yescharacteristic
342C2×C4⋊C4C22×C411yescharacteristic
343C2×C4⋊C4C22×C411yescharacteristic
344C2×C4⋊C4C22×C411yescharacteristic
345C2×C4⋊C4C22×C411yescharacteristic
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—21no—
360C2×C42—21no—
361C2×C42—21no—
362C2×C42—21no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—21no—
367C2×C42—21no—
368C2×C42—21no—
369C2×C42—21no—
370C2×C42—44no—
371C2×C42—44no—
372C2×C42—44no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42—44no—
377C2×C42C2×D412yes—
378C2×C42#4112yes—
379#108—44no—
380#107—22no—
381#107—22no—
382#106—22no—
383#106—22no—
384C4⋊C8—42no—
385C4⋊C8—42no—
386C4⋊C8—42no—
387C4⋊C8—42no—
388#104—44no—
389#104—44no—
390#103—41no—
391#103—41no—
392#103—41no—
393#103—41no—
394#102—41no—
395#102—41no—
396#102—41no—
397#102—41no—
398C22⋊C8—41no—
399C22⋊C8—41no—
400C22⋊C8—41no—
401C22⋊C8—41no—
402C22⋊C8—41no—
403C22⋊C8—41no—
404C22⋊C8—41no—
405C22⋊C8—41no—
406C22⋊C8—42no—
407C22⋊C8—42no—
408C22⋊C8—42no—
409C22⋊C8—42no—
410C22⋊C8—42no—
411C22⋊C8—42no—
412C22⋊C8—42no—
413C22⋊C8—42no—
414#97—42no—
415#97—42no—
416C4×C8—42no—
417C4×C8—42no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—41no—
432C24—41no—
433C24C4×D411yescharacteristic
434C24C4×D411yescharacteristic
435C24C2×#4111yescharacteristic
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441#41—41no—
442#41—41no—
443#41—41no—
444#41—41no—
445#41—41no—
446#41—41no—
447#41—41no—
448#41—41no—
449#41—41no—
450#41—41no—
451#41—41no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—81no—
475C2×D4—81no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
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—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—48no—
520C22×C4—48no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—41no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4C4×D411yescharacteristic
557C22×C4C4×D411yescharacteristic
558C22×C4C23×C411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C2×#4111yescharacteristic
562C22×C4C2×#4111yescharacteristic
563C22×C4C2×#4111yescharacteristic
564C22×C4H(5,𝔽2)11yescharacteristic
565C22×C4H(5,𝔽2)11yescharacteristic
566C22×C4H(5,𝔽2)11yescharacteristic
567C22×C4H(5,𝔽2)11yescharacteristic
568C22×C4H(5,𝔽2)11yescharacteristic
569C22×C4H(5,𝔽2)11yescharacteristic
570C22×C42−1+411yescharacteristic
571C22×C42−1+411yescharacteristic
572M16—22no—
573M16—22no—
574M16—22no—
575M16—22no—
576M16—41no—
577M16—41no—
578M16—41no—
579M16—41no—
580M16—41no—
581M16—41no—
582M16—41no—
583M16—41no—
584M16—41no—
585M16—41no—
586M16—41no—
587M16—41no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—22no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—22no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—41no—
617C2×C8—41no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—41no—
626C2×C8—41no—
627C2×C8—41no—
628C2×C8—41no—
629C2×C8—41no—
630C2×C8—41no—
631C2×C8—41no—
632C2×C8—41no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4C4×D412yes—
653C4⋊C4C4×D412yes—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C22⋊C4—41no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C42—22no—
669C42—22no—
670C42—22no—
671C42—22no—
672C42—22no—
673C42—22no—
674C42—48no—
675C42—41no—
676C42—41no—
677C42—41no—
678C42—41no—
679C42—41no—
680C42—41no—
681C42—41no—
682C42—41no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—24no—
688C23—24no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23#44312yes—
723C23#44412yes—
724C23C2×C4×D411yescharacteristic
725C23#53811yescharacteristic
726C23#53911yescharacteristic
727C23#54611yescharacteristic
728C23#55111yescharacteristic
729C23#55111yescharacteristic
730C23#55211yescharacteristic
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—84no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—432no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—81no—
808C2×C4—81no—
809C2×C4—81no—
810C2×C4—81no—
811C2×C4C2×C4×D411yescharacteristic
812C2×C4C4×#4111yescharacteristic
813C2×C4#51811yescharacteristic
814C2×C4#51811yescharacteristic
815C2×C4#52011yescharacteristic
816C2×C4#52011yescharacteristic
817C2×C4#53411yescharacteristic
818C2×C4#53511yescharacteristic
819C2×C4#53611yescharacteristic
820C2×C4#53711yescharacteristic
821C2×C4#53811yescharacteristic
822C2×C4#53911yescharacteristic
823C2×C4#54011yescharacteristic
824C2×C4#54211yescharacteristic
825C2×C4#54211yescharacteristic
826C2×C4#54211yescharacteristic
827C2×C4D4211yescharacteristic
828C2×C4#54611yescharacteristic
829C2×C4#54611yescharacteristic
830C2×C4#54611yescharacteristic
831C2×C4#54711yescharacteristic
832C2×C4#55011yescharacteristic
833C2×C4#55311yescharacteristic
834C2×C4#55511yescharacteristic
835C2×C4#56011yescharacteristic
836C2×C4#56011yescharacteristic
837C2×C4#56211yescharacteristic
838C2×C4#56211yescharacteristic
839C8—41no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—42no—
844C8—41no—
845C8—41no—
846C8—41no—
847C8—41no—
848C8—42no—
849C8—81no—
850C8—81no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22#232511yescharacteristic
889C22#235811yescharacteristic
890C22#235911yescharacteristic
891C22#268511yescharacteristic
892C22#269411yescharacteristic
893C22#273711yescharacteristic
894C22#276111yescharacteristic
895C22C2×#44311yescharacteristic
896C22C2×#44411yescharacteristic
897C22#295611yescharacteristic
898C22#295611yescharacteristic
899C4—44no—
900C4—44no—
901C4—42no—
902C4—42no—
903C4—41no—
904C4—41no—
905C4—81no—
906C4—81no—
907C4—81no—
908C4—81no—
909C4—81no—
910C4#232611yescharacteristic
911C4#233511yescharacteristic
912C4#236311yescharacteristic
913C4#237711yescharacteristic
914C4#267211yescharacteristic
915C4#267311yescharacteristic
916C4#268611yescharacteristic
917C4#269111yescharacteristic
918C2—21no—
919C2—21no—
920C2—21no—
921C2—21no—
922C2—42no—
923C2—42no—
924C2—161no—
925C2#1457311yescharacteristic
926C2#2220411yescharacteristic
927C2#2220711yescharacteristic
928C2#2288611yescharacteristic
929C2#2288811yescharacteristic
930C2#2294811yescharacteristic
931C2#2295011yescharacteristic
subgroupG/H
centerC22×C4C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
socleC23C2×C4×D4
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C22⋊C8 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #21053C2semidirect
4. C2×#1922C2semidirect
6. #11329C2semidirect
7. #11191C2semidirect
8. #11125C2semidirect
9. #11097C2semidirect
10. #11068C2semidirect
11. #10934C2semidirect
12. #10909C2semidirect
13. #10809C2semidirect
14. #10719C2semidirect
15. #10712C2semidirect
35. #2036C4semidirect
36. #2036C4semidirect
37. #2035C4semidirect
38. #2035C4semidirect
39. #2034C4semidirect
40. #2034C4semidirect
41. #2033C4semidirect
42. #2033C4semidirect
109. C2×#107C2×C4semidirect
110. C2×#107C2×C4semidirect
111. C2×#106C2×C4semidirect
112. C2×#106C2×C4semidirect
131. C2×#103C2×C4semidirect
132. C2×#103C2×C4semidirect
133. C2×#103C2×C4semidirect
134. C2×#103C2×C4semidirect
135. C2×#102C2×C4semidirect
136. C2×#102C2×C4semidirect
137. C2×#102C2×C4semidirect
138. C2×#102C2×C4semidirect
186. #340C2×C4semidirect
187. #340C2×C4semidirect
188. #340C2×C4semidirect
189. #340C2×C4semidirect

Maximal subgroups

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

subgroupindex
#234792
#211912
#210532
C2×#19222
C2×#18962
#113292
#111912
#111252
#110972
#110682
#109342
#109092
#108092
#107192
#107122