Finite Group Databasebeta

← #123983

Subgroups — #123983

Order 512.

1626 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2911C211yesmaximal, characteristic
2C22×#344C211yesmaximal, characteristic
3C2×#1740C211yesmaximal, characteristic
4C2×#1740C211yesmaximal, characteristic
5C2×#1733C211yesmaximal, characteristic
6C2×#1733C211yesmaximal, characteristic
7C2×#1733C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C22×#117C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15#2911—22no—
16#2911—22no—
17#2911—22no—
18#2911C414yescomplemented
19C2×#428—22no—
20C2×#428—22no—
21C2×#427—22no—
22C2×#344—22no—
23C2×#344—22no—
24C2×#344C414yescomplemented
25#1740—22no—
26#1740—22no—
27#1740—22no—
28#1740—22no—
29C2×#342—22no—
30C2×#342—22no—
31#1733—22no—
32#1733—22no—
33#1733—22no—
34#1733—22no—
35#1733—22no—
36#1733C414yescomplemented
37C2×#339—22no—
38C2×#339—22no—
39C2×#339—22no—
40C24×C4C2311yescharacteristic
41C22×M16—21no—
42C22×M16—21no—
43C22×M16—21no—
44C22×M16—21no—
45C22×M16—21no—
46C22×M16—21no—
47C22×M16—21no—
48C22×M16—21no—
49C22×M16—21no—
50C22×M16—21no—
51C22×M16—21no—
52C22×M16—21no—
53C22×M16—21no—
54C22×M16—21no—
55C22×M16—21no—
56C22×M16—21no—
57C22×M16—21no—
58C22×M16—21no—
59C22×M16C2×C412yes—
60C22×M16C2×C412yes—
61C22×M16C2×C412yes—
62C22×M16C2×C412yes—
63C22×M16D412yes—
64C22×M16D412yes—
65C22×M16D412yes—
66C22×M16D412yes—
67C22×M16Q812yes—
68C22×M16Q812yes—
69C23×C8—21no—
70C23×C8—21no—
71C2×#117—21no—
72C2×#117—21no—
73C2×#117—21no—
74C2×#117—21no—
75C2×#117—21no—
76C2×#117—21no—
77C2×#117—21no—
78C2×#117—21no—
79C2×#117—21no—
80C2×#117—21no—
81C2×#117—21no—
82C2×#117—21no—
83C2×#117—21no—
84C2×#117—21no—
85C2×#117—21no—
86C2×#117—21no—
87C2×#117—21no—
88C2×#117—21no—
89C2×#117—21no—
90C2×#117—21no—
91C2×#117—21no—
92C2×#117—21no—
93C2×#117—21no—
94C2×#117—21no—
95C2×#117—21no—
96C2×#117—21no—
97C2×#117—21no—
98C2×#117—21no—
99C2×#117—21no—
100C2×#117—21no—
101C2×#117—21no—
102C2×#117—21no—
103C2×#117—21no—
104C2×#117—21no—
105C2×#117—21no—
106C2×#117—21no—
107C2×#117—21no—
108C2×#117—21no—
109C2×#117—21no—
110C2×#117—21no—
111C2×#117—21no—
112C2×#117—21no—
113C2×#117—21no—
114C2×#117—21no—
115C2×#117—21no—
116C2×#117—21no—
117C2×#117—21no—
118C2×#117C2×C412yes—
119C2×#117C2×C412yes—
120C2×#117C2×C412yes—
121C2×#117C2×C412yes—
122C2×#117C2×C412yes—
123C2×#117D412yes—
124C2×#117D412yes—
125C2×#117D412yes—
126C2×#117D412yes—
127C2×#117D412yes—
128C2×#117D412yes—
129C2×#117Q812yes—
130C2×#117Q812yes—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4Q812yes—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C22⋊C4D412yes—
141C22×C42—21no—
142C22×C42—21no—
143C22×C42—21no—
144C22×C42—21no—
145C22×C42—21no—
146#428—28no—
147#428—28no—
148#428—28no—
149#428—28no—
150#427—28no—
151#427—28no—
152C2×#107—24no—
153C2×#106—24no—
154#344—28no—
155#342—28no—
156#342—28no—
157#339—28no—
158#339—28no—
159#339—28no—
160C25C2×D411yescharacteristic
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—41no—
164C23×C4—41no—
165C23×C4—41no—
166C23×C4C22×C411yescharacteristic
167C23×C4C22×C411yescharacteristic
168C23×C4C22×C411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D411yescharacteristic
171C23×C4C2×D411yescharacteristic
172C23×C4C2×D411yescharacteristic
173C23×C4C2×D411yescharacteristic
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×Q811yescharacteristic
180C23×C4C2×Q811yescharacteristic
181C23×C4C2×Q811yescharacteristic
182C23×C4C2×Q811yescharacteristic
183C23×C4C2×Q811yescharacteristic
184C23×C4#4111yescharacteristic
185C23×C4#4111yescharacteristic
186C23×C4#4111yescharacteristic
187C23×C4#4111yescharacteristic
188C23×C4#4111yescharacteristic
189C23×C4#4111yescharacteristic
190C23×C4#4111yescharacteristic
191C23×C4#4111yescharacteristic
192C23×C4#4111yescharacteristic
193C23×C4#4111yescharacteristic
194C23×C4#4111yescharacteristic
195C23×C4#4111yescharacteristic
196C2×M16—22no—
197C2×M16—22no—
198C2×M16—22no—
199C2×M16—22no—
200C2×M16—22no—
201C2×M16—22no—
202C2×M16—22no—
203C2×M16—22no—
204C2×M16—22no—
205C2×M16—22no—
206C2×M16—22no—
207C2×M16—22no—
208C2×M16—22no—
209C2×M16—22no—
210C2×M16—22no—
211C2×M16—22no—
212C2×M16—22no—
213C2×M16—22no—
214C2×M16—22no—
215C2×M16—22no—
216C2×M16—22no—
217C2×M16—22no—
218C2×M16—22no—
219C2×M16—22no—
220C2×M16—22no—
221C2×M16—22no—
222C2×M16—22no—
223C2×M16—22no—
224C2×M16—22no—
225C2×M16—22no—
226C2×M16—22no—
227C2×M16—22no—
228C2×M16—22no—
229C2×M16—22no—
230C2×M16—22no—
231C2×M16—22no—
232C2×M16—41no—
233C2×M16—41no—
234C2×M16—41no—
235C2×M16—41no—
236C2×M16—41no—
237C2×M16—41no—
238C2×M16—41no—
239C2×M16—41no—
240C2×M16—41no—
241C2×M16—41no—
242C2×M16—41no—
243C2×M16—41no—
244C2×M16C4214yes—
245C2×M16C22⋊C414yes—
246C2×M16C22⋊C414yes—
247C2×M16C22⋊C414yes—
248C2×M16C4⋊C414yes—
249C2×M16C4⋊C414yes—
250C2×M16C4⋊C414yes—
251C2×M16C4⋊C414yes—
252C22×C8—22no—
253C22×C8—22no—
254C22×C8—22no—
255C22×C8—22no—
256C22×C8—22no—
257C22×C8—22no—
258C22×C8—22no—
259C22×C8—22no—
260C22×C8—22no—
261C22×C8—22no—
262C22×C8—41no—
263C22×C8—41no—
264C22×C8—41no—
265C22×C8—41no—
266#117—22no—
267#117—22no—
268#117—22no—
269#117—22no—
270#117—22no—
271#117—22no—
272#117—22no—
273#117—22no—
274#117—22no—
275#117—22no—
276#117—22no—
277#117—22no—
278#117—22no—
279#117—22no—
280#117—22no—
281#117—22no—
282#117—22no—
283#117—22no—
284#117—22no—
285#117—22no—
286#117—22no—
287#117—22no—
288#117—22no—
289#117—22no—
290#117—22no—
291#117—22no—
292#117—22no—
293#117—22no—
294#117—22no—
295#117—22no—
296#117—22no—
297#117—22no—
298#117—22no—
299#117—22no—
300#117—22no—
301#117—22no—
302#117—22no—
303#117—22no—
304#117—22no—
305#117—22no—
306#117—22no—
307#117—22no—
308#117—22no—
309#117—41no—
310#117—41no—
311#117—41no—
312#117—41no—
313#117—41no—
314#117—41no—
315#117—41no—
316#117—41no—
317#117—41no—
318#117—41no—
319#117—41no—
320#117—41no—
321#117—41no—
322#117—41no—
323#117—41no—
324#117—41no—
325#117—41no—
326#117—41no—
327#117—41no—
328#117—41no—
329#117—41no—
330#117—41no—
331#117—41no—
332#117—41no—
333#117—41no—
334#117—41no—
335#117—41no—
336#117—41no—
337#117—41no—
338#117—41no—
339#117—41no—
340#117—41no—
341#117—41no—
342#117—41no—
343#117C22⋊C414yes—
344#117C22⋊C414yes—
345#117C4⋊C414yes—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—41no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4—41no—
365C2×C4⋊C4—41no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4—41no—
371C2×C4⋊C4—41no—
372C2×C4⋊C4—41no—
373C2×C4⋊C4—41no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4C4⋊C414yes—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—41no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—41no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—41no—
404C2×C22⋊C4—41no—
405C2×C22⋊C4C4⋊C414yes—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—41no—
420C2×C42—41no—
421C2×C42—41no—
422C2×C42—41no—
423C2×C42—41no—
424C2×C42—41no—
425C2×C42—41no—
426C2×C42—41no—
427C2×C42—41no—
428C2×C42—41no—
429C2×C42—41no—
430C2×C42—41no—
431C2×C42—41no—
432C2×C42—41no—
433C2×C42—41no—
434C2×C42—41no—
435C2×C42—41no—
436#107—216no—
437#106—216no—
438C24—82no—
439C24C2×C4⋊C411yescharacteristic
440C24C4×D411yescharacteristic
441C24C4×D411yescharacteristic
442C24#12011yescharacteristic
443C24#12011yescharacteristic
444C24#12111yescharacteristic
445C24#12111yescharacteristic
446C24#12111yescharacteristic
447C24#12111yescharacteristic
448C24C22⋊Q811yescharacteristic
449C24C22⋊Q811yescharacteristic
450C24#12311yescharacteristic
451C24#12311yescharacteristic
452C24#12711yescharacteristic
453C24C4⋊Q811yescharacteristic
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—84no—
470C22×C4—84no—
471C22×C4—84no—
472C22×C4—84no—
473C22×C4—84no—
474C22×C4C2×C4211yescharacteristic
475C22×C4C2×C22⋊C411yescharacteristic
476C22×C4C2×C22⋊C411yescharacteristic
477C22×C4C2×C22⋊C411yescharacteristic
478C22×C4C2×C22⋊C411yescharacteristic
479C22×C4C2×C22⋊C411yescharacteristic
480C22×C4C2×C4⋊C411yescharacteristic
481C22×C4C2×C4⋊C411yescharacteristic
482C22×C4C2×C4⋊C411yescharacteristic
483C22×C4C2×C4⋊C411yescharacteristic
484C22×C4C2×C4⋊C411yescharacteristic
485C22×C4C2×C4⋊C411yescharacteristic
486C22×C4#11711yescharacteristic
487C22×C4#11711yescharacteristic
488C22×C4#11711yescharacteristic
489C22×C4#11711yescharacteristic
490C22×C4#11711yescharacteristic
491C22×C4#11711yescharacteristic
492C22×C4C4×D411yescharacteristic
493C22×C4C4×D411yescharacteristic
494C22×C4C4×D411yescharacteristic
495C22×C4C4×D411yescharacteristic
496C22×C4C4×D411yescharacteristic
497C22×C4C4×D411yescharacteristic
498C22×C4C4×D411yescharacteristic
499C22×C4C4×D411yescharacteristic
500C22×C4C4×D411yescharacteristic
501C22×C4C4×D411yescharacteristic
502C22×C4C4×D411yescharacteristic
503C22×C4C4×D411yescharacteristic
504C22×C4C4×D411yescharacteristic
505C22×C4C4×D411yescharacteristic
506C22×C4C4×Q811yescharacteristic
507C22×C4C4×Q811yescharacteristic
508C22×C4C4×Q811yescharacteristic
509C22×C4C4×Q811yescharacteristic
510C22×C4C4×Q811yescharacteristic
511C22×C4C4×Q811yescharacteristic
512C22×C4C4×Q811yescharacteristic
513C22×C4C4×Q811yescharacteristic
514C22×C4#12011yescharacteristic
515C22×C4#12011yescharacteristic
516C22×C4#12011yescharacteristic
517C22×C4#12011yescharacteristic
518C22×C4#12011yescharacteristic
519C22×C4#12011yescharacteristic
520C22×C4#12111yescharacteristic
521C22×C4#12111yescharacteristic
522C22×C4#12111yescharacteristic
523C22×C4#12111yescharacteristic
524C22×C4#12111yescharacteristic
525C22×C4#12111yescharacteristic
526C22×C4#12111yescharacteristic
527C22×C4#12111yescharacteristic
528C22×C4#12111yescharacteristic
529C22×C4#12111yescharacteristic
530C22×C4#12111yescharacteristic
531C22×C4#12111yescharacteristic
532C22×C4#12111yescharacteristic
533C22×C4#12111yescharacteristic
534C22×C4#12111yescharacteristic
535C22×C4#12111yescharacteristic
536C22×C4C22⋊Q811yescharacteristic
537C22×C4C22⋊Q811yescharacteristic
538C22×C4C22⋊Q811yescharacteristic
539C22×C4C22⋊Q811yescharacteristic
540C22×C4C22⋊Q811yescharacteristic
541C22×C4C22⋊Q811yescharacteristic
542C22×C4C22⋊Q811yescharacteristic
543C22×C4C22⋊Q811yescharacteristic
544C22×C4C22⋊Q811yescharacteristic
545C22×C4C22⋊Q811yescharacteristic
546C22×C4C22⋊Q811yescharacteristic
547C22×C4C22⋊Q811yescharacteristic
548C22×C4C22⋊Q811yescharacteristic
549C22×C4C22⋊Q811yescharacteristic
550C22×C4C22⋊Q811yescharacteristic
551C22×C4C22⋊Q811yescharacteristic
552C22×C4C22⋊Q811yescharacteristic
553C22×C4C22⋊Q811yescharacteristic
554C22×C4C22⋊Q811yescharacteristic
555C22×C4C22⋊Q811yescharacteristic
556C22×C4C22⋊Q811yescharacteristic
557C22×C4C22⋊Q811yescharacteristic
558C22×C4C22⋊Q811yescharacteristic
559C22×C4C22⋊Q811yescharacteristic
560C22×C4C22⋊Q811yescharacteristic
561C22×C4C22⋊Q811yescharacteristic
562C22×C4#12311yescharacteristic
563C22×C4#12311yescharacteristic
564C22×C4#12311yescharacteristic
565C22×C4#12311yescharacteristic
566C22×C4#12311yescharacteristic
567C22×C4#12311yescharacteristic
568C22×C4#12311yescharacteristic
569C22×C4#12311yescharacteristic
570C22×C4#12311yescharacteristic
571C22×C4#12311yescharacteristic
572C22×C4#12311yescharacteristic
573C22×C4#12311yescharacteristic
574C22×C4#12311yescharacteristic
575C22×C4#12311yescharacteristic
576C22×C4#12411yescharacteristic
577C22×C4#12411yescharacteristic
578C22×C4#12411yescharacteristic
579C22×C4#12411yescharacteristic
580C22×C4#12411yescharacteristic
581C22×C4#12411yescharacteristic
582C22×C4#12411yescharacteristic
583C22×C4#12411yescharacteristic
584C22×C4#12511yescharacteristic
585C22×C4#12511yescharacteristic
586C22×C4#12511yescharacteristic
587C22×C4#12511yescharacteristic
588C22×C4#12511yescharacteristic
589C22×C4#12511yescharacteristic
590C22×C4#12511yescharacteristic
591C22×C4#12511yescharacteristic
592C22×C4#12511yescharacteristic
593C22×C4#12511yescharacteristic
594C22×C4#12511yescharacteristic
595C22×C4#12511yescharacteristic
596C22×C4#12611yescharacteristic
597C22×C4#12611yescharacteristic
598C22×C4#12611yescharacteristic
599C22×C4#12611yescharacteristic
600C22×C4#12611yescharacteristic
601C22×C4#12611yescharacteristic
602C22×C4#12611yescharacteristic
603C22×C4#12611yescharacteristic
604C22×C4#12711yescharacteristic
605C22×C4C4⋊Q811yescharacteristic
606C22×C4C4⋊Q811yescharacteristic
607C22×C4C4⋊Q811yescharacteristic
608C22×C4C4⋊Q811yescharacteristic
609C22×C4C4⋊Q811yescharacteristic
610C22×C4C4⋊Q811yescharacteristic
611C22×C4C4⋊Q811yescharacteristic
612C22×C4C4⋊Q811yescharacteristic
613C22×C4C4⋊Q811yescharacteristic
614M16—24no—
615M16—24no—
616M16—24no—
617M16—24no—
618M16—24no—
619M16—24no—
620M16—24no—
621M16—24no—
622M16—24no—
623M16—42no—
624M16—42no—
625M16—42no—
626M16—42no—
627M16—42no—
628M16—42no—
629M16#9518yes—
630C2×C8—24no—
631C2×C8—24no—
632C2×C8—24no—
633C2×C8—24no—
634C2×C8—24no—
635C2×C8—24no—
636C2×C8—24no—
637C2×C8—24no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8—42no—
641C2×C8—42no—
642C2×C8—42no—
643C2×C8—42no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—42no—
650C4⋊C4—42no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C42—24no—
685C42—24no—
686C42—24no—
687C42—42no—
688C42—42no—
689C42—42no—
690C42—42no—
691C42—42no—
692C42—42no—
693C42—42no—
694C42—42no—
695C42—42no—
696C42—42no—
697C42—42no—
698C42—42no—
699C42—42no—
700C42—42no—
701C42—42no—
702C42—42no—
703C42—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23C4×C4⋊C411yescharacteristic
720C23#38011yescharacteristic
721C23#38411yescharacteristic
722C23#38511yescharacteristic
723C23#38511yescharacteristic
724C23#38511yescharacteristic
725C23#38511yescharacteristic
726C23#38611yescharacteristic
727C23#38611yescharacteristic
728C23#38711yescharacteristic
729C23#38711yescharacteristic
730C23#38811yescharacteristic
731C23#38811yescharacteristic
732C23#38911yescharacteristic
733C23#38911yescharacteristic
734C23#38911yescharacteristic
735C23#38911yescharacteristic
736C23#39011yescharacteristic
737C23#39011yescharacteristic
738C23#39211yescharacteristic
739C23#39211yescharacteristic
740C23#39211yescharacteristic
741C23#39411yescharacteristic
742C23#39411yescharacteristic
743C23#39411yescharacteristic
744C23#39511yescharacteristic
745C23#39511yescharacteristic
746C23#39611yescharacteristic
747C23#39611yescharacteristic
748C23#39711yescharacteristic
749C23#39811yescharacteristic
750C23#39811yescharacteristic
751C23#39811yescharacteristic
752C23#39911yescharacteristic
753C23#39911yescharacteristic
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—84no—
760C2×C4—84no—
761C2×C4—84no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4—84no—
767C2×C4—84no—
768C2×C4—84no—
769C2×C4—84no—
770C2×C4—84no—
771C2×C4—84no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4C2×#9511yescharacteristic
775C2×C4C4×C22⋊C411yescharacteristic
776C2×C4C4×C22⋊C411yescharacteristic
777C2×C4C4×C4⋊C411yescharacteristic
778C2×C4C4×C4⋊C411yescharacteristic
779C2×C4C4×C4⋊C411yescharacteristic
780C2×C4#37911yescharacteristic
781C2×C4#38011yescharacteristic
782C2×C4#38011yescharacteristic
783C2×C4#38011yescharacteristic
784C2×C4#38011yescharacteristic
785C2×C4#38011yescharacteristic
786C2×C4#38111yescharacteristic
787C2×C4#38211yescharacteristic
788C2×C4#38211yescharacteristic
789C2×C4#38411yescharacteristic
790C2×C4#38511yescharacteristic
791C2×C4#38511yescharacteristic
792C2×C4#38511yescharacteristic
793C2×C4#38511yescharacteristic
794C2×C4#38511yescharacteristic
795C2×C4#38511yescharacteristic
796C2×C4#38511yescharacteristic
797C2×C4#38511yescharacteristic
798C2×C4#38611yescharacteristic
799C2×C4#38611yescharacteristic
800C2×C4#38611yescharacteristic
801C2×C4#38611yescharacteristic
802C2×C4#38611yescharacteristic
803C2×C4#38611yescharacteristic
804C2×C4#38711yescharacteristic
805C2×C4#38711yescharacteristic
806C2×C4#38711yescharacteristic
807C2×C4#38711yescharacteristic
808C2×C4#38711yescharacteristic
809C2×C4#38711yescharacteristic
810C2×C4#38711yescharacteristic
811C2×C4#38711yescharacteristic
812C2×C4#38711yescharacteristic
813C2×C4#38711yescharacteristic
814C2×C4#38711yescharacteristic
815C2×C4#38711yescharacteristic
816C2×C4#38711yescharacteristic
817C2×C4#38711yescharacteristic
818C2×C4#38811yescharacteristic
819C2×C4#38811yescharacteristic
820C2×C4#38811yescharacteristic
821C2×C4#38811yescharacteristic
822C2×C4#38811yescharacteristic
823C2×C4#38811yescharacteristic
824C2×C4#38911yescharacteristic
825C2×C4#38911yescharacteristic
826C2×C4#38911yescharacteristic
827C2×C4#38911yescharacteristic
828C2×C4#38911yescharacteristic
829C2×C4#38911yescharacteristic
830C2×C4#38911yescharacteristic
831C2×C4#38911yescharacteristic
832C2×C4#38911yescharacteristic
833C2×C4#38911yescharacteristic
834C2×C4#38911yescharacteristic
835C2×C4#38911yescharacteristic
836C2×C4#39011yescharacteristic
837C2×C4#39011yescharacteristic
838C2×C4#39111yescharacteristic
839C2×C4#39111yescharacteristic
840C2×C4#39111yescharacteristic
841C2×C4#39111yescharacteristic
842C2×C4#39111yescharacteristic
843C2×C4#39111yescharacteristic
844C2×C4#39111yescharacteristic
845C2×C4#39111yescharacteristic
846C2×C4#39211yescharacteristic
847C2×C4#39311yescharacteristic
848C2×C4#39311yescharacteristic
849C2×C4#39311yescharacteristic
850C2×C4#39311yescharacteristic
851C2×C4#39411yescharacteristic
852C2×C4#39411yescharacteristic
853C2×C4#39411yescharacteristic
854C2×C4#39411yescharacteristic
855C2×C4#39411yescharacteristic
856C2×C4#39511yescharacteristic
857C2×C4#39511yescharacteristic
858C2×C4#39511yescharacteristic
859C2×C4#39511yescharacteristic
860C2×C4#39511yescharacteristic
861C2×C4#39511yescharacteristic
862C2×C4#39611yescharacteristic
863C2×C4#39611yescharacteristic
864C2×C4#39611yescharacteristic
865C2×C4#39611yescharacteristic
866C2×C4#39611yescharacteristic
867C2×C4#39611yescharacteristic
868C2×C4#39711yescharacteristic
869C2×C4#39711yescharacteristic
870C2×C4#39711yescharacteristic
871C2×C4#39811yescharacteristic
872C2×C4#39811yescharacteristic
873C2×C4#39811yescharacteristic
874C2×C4#39811yescharacteristic
875C2×C4#39811yescharacteristic
876C2×C4#39811yescharacteristic
877C2×C4#39811yescharacteristic
878C2×C4#39811yescharacteristic
879C2×C4#39811yescharacteristic
880C2×C4#39811yescharacteristic
881C2×C4#39811yescharacteristic
882C2×C4#39811yescharacteristic
883C2×C4#39811yescharacteristic
884C2×C4#39911yescharacteristic
885C2×C4#39911yescharacteristic
886C2×C4#40011yescharacteristic
887C2×C4#40011yescharacteristic
888C2×C4#40011yescharacteristic
889C2×C4#40011yescharacteristic
890C2×C4#40011yescharacteristic
891C2×C4#40011yescharacteristic
892C2×C4#40011yescharacteristic
893C2×C4#40011yescharacteristic
894C8—28no—
895C8—44no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22C4⋊#9511yescharacteristic
932C22#143611yescharacteristic
933C22#143611yescharacteristic
934C22#143811yescharacteristic
935C22#143911yescharacteristic
936C22#143911yescharacteristic
937C22#143911yescharacteristic
938C22#144111yescharacteristic
939C22#144111yescharacteristic
940C22#144111yescharacteristic
941C22#144211yescharacteristic
942C22#144411yescharacteristic
943C22#144411yescharacteristic
944C22#144411yescharacteristic
945C22#144511yescharacteristic
946C4—84no—
947C4—84no—
948C4—84no—
949C4—84no—
950C4—84no—
951C4C22⋊#9511yescharacteristic
952C4C4⋊#9511yescharacteristic
953C4#143611yescharacteristic
954C4#143611yescharacteristic
955C4#143911yescharacteristic
956C4#144111yescharacteristic
957C4#144111yescharacteristic
958C4#144111yescharacteristic
959C4#144111yescharacteristic
960C4#144111yescharacteristic
961C4#144211yescharacteristic
962C4#144211yescharacteristic
963C4#144211yescharacteristic
964C4#144411yescharacteristic
965C4#144511yescharacteristic
966C4#144611yescharacteristic
967C2—21no—
968C2—21no—
969C2—21no—
970C2—21no—
971C2—21no—
972C2—21no—
973C2—21no—
974C2—21no—
975C2—21no—
976C2—21no—
977C2—21no—
978C2—21no—
979C2—21no—
980C2—21no—
981C2#755711yescharacteristic
982C2#1111912yes—
subgroupG/H
centerC2×C4#394
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC22#1439
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
18. #2911C4semidirect
24. C2×#344C4semidirect
36. #1733C4semidirect

Maximal subgroups

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

subgroupindex
C2×#29112
C22×#3442
C2×#17402
C2×#17332