Finite Group Databasebeta

← #123780

Subgroups — #123780

Order 512.

1434 conjugacy classes of subgroups.

The subgroup lattice has 961 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#344C211yesmaximal, characteristic
2C22×#344C211yesmaximal, characteristic
3C22×#344C211yesmaximal, characteristic
4C2×#1738C211yesmaximal, characteristic
5C2×#1733C211yesmaximal, characteristic
6C2×#1733C211yesmaximal, characteristic
7C2×#1733C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C22×#117C2211yescharacteristic
15C2×#344—22no—
16C2×#344—22no—
17C2×#344—22no—
18C2×#344—22no—
19C2×#344—22no—
20C2×#344—22no—
21C2×#344C414yescomplemented
22C2×#344C414yescomplemented
23C2×#344C414yescomplemented
24#1738—22no—
25#1738—22no—
26C2×#341—22no—
27#1733—22no—
28#1733—22no—
29#1733—22no—
30#1733—22no—
31#1733—22no—
32#1733—22no—
33C2×#339—22no—
34C2×#339—22no—
35C2×#339—22no—
36C24×C4C2311yescharacteristic
37C22×M16—21no—
38C22×M16—21no—
39C22×M16—21no—
40C22×M16—21no—
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×M16—21no—
60C22×M16—21no—
61C22×M16—21no—
62C22×M16—21no—
63C22×M16—21no—
64C22×M16—21no—
65C22×M16—21no—
66C22×M16—21no—
67C22×M16—21no—
68C22×M16—21no—
69C22×M16—21no—
70C22×M16—21no—
71C22×M16—21no—
72C22×M16—21no—
73C22×M16—21no—
74C22×M16—21no—
75C22×M16—21no—
76C22×M16—21no—
77C22×M16—21no—
78C22×M16—21no—
79C22×M16—21no—
80C22×M16—21no—
81C22×M16C2×C412yes—
82C22×M16C2×C412yes—
83C22×M16C2×C412yes—
84C22×M16C2×C412yes—
85C22×M16C2×C412yes—
86C22×M16C2×C412yes—
87C22×M16D412yes—
88C22×M16D412yes—
89C22×M16D412yes—
90C22×M16D412yes—
91C22×M16Q812yes—
92C22×M16Q812yes—
93C23×C8—21no—
94C23×C8—21no—
95C23×C8—21no—
96C23×C8—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×#117—21no—
119C2×#117—21no—
120C2×#117—21no—
121C2×#117—21no—
122C2×#117—21no—
123C2×#117—21no—
124C2×#117C2×C412yes—
125C2×#117C2×C412yes—
126C2×#117C2×C412yes—
127C2×#117D412yes—
128C2×#117D412yes—
129C2×#117D412yes—
130C2×#117D412yes—
131C2×#117D412yes—
132C2×#117Q812yes—
133C22×C4⋊C4—21no—
134C22×C4⋊C4—21no—
135C22×C4⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C22⋊C4—21no—
138C22×C22⋊C4—21no—
139C22×C42—21no—
140C22×C42—21no—
141C22×C42—21no—
142#344—28no—
143#344—28no—
144#344—28no—
145#341—28no—
146#339—28no—
147#339—28no—
148#339—28no—
149C25#4111yescharacteristic
150C23×C4—41no—
151C23×C4—41no—
152C23×C4—41no—
153C23×C4C22×C411yescharacteristic
154C23×C4C22×C411yescharacteristic
155C23×C4C22×C411yescharacteristic
156C23×C4C2×D411yescharacteristic
157C23×C4C2×D411yescharacteristic
158C23×C4C2×D411yescharacteristic
159C23×C4C2×D411yescharacteristic
160C23×C4C2×D411yescharacteristic
161C23×C4C2×D411yescharacteristic
162C23×C4C2×D411yescharacteristic
163C23×C4C2×D411yescharacteristic
164C23×C4C2×D411yescharacteristic
165C23×C4C2×Q811yescharacteristic
166C23×C4C2×Q811yescharacteristic
167C23×C4C2×Q811yescharacteristic
168C23×C4#4111yescharacteristic
169C23×C4#4111yescharacteristic
170C23×C4#4111yescharacteristic
171C23×C4#4111yescharacteristic
172C23×C4#4111yescharacteristic
173C23×C4#4111yescharacteristic
174C23×C4#4111yescharacteristic
175C23×C4#4111yescharacteristic
176C23×C4#4111yescharacteristic
177C23×C4#4111yescharacteristic
178C23×C4#4111yescharacteristic
179C23×C4#4111yescharacteristic
180C23×C4#4111yescharacteristic
181C23×C4#4111yescharacteristic
182C23×C4#4111yescharacteristic
183C2×M16—22no—
184C2×M16—22no—
185C2×M16—22no—
186C2×M16—22no—
187C2×M16—22no—
188C2×M16—22no—
189C2×M16—22no—
190C2×M16—22no—
191C2×M16—22no—
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
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—22no—
233C2×M16—22no—
234C2×M16—22no—
235C2×M16—22no—
236C2×M16—22no—
237C2×M16—22no—
238C2×M16—22no—
239C2×M16—22no—
240C2×M16—22no—
241C2×M16—22no—
242C2×M16—22no—
243C2×M16—41no—
244C2×M16—41no—
245C2×M16—41no—
246C2×M16—41no—
247C2×M16—41no—
248C2×M16—41no—
249C2×M16—41no—
250C2×M16—41no—
251C2×M16—41no—
252C2×M16—41no—
253C2×M16—41no—
254C2×M16—41no—
255C2×M16—41no—
256C2×M16—41no—
257C2×M16—41no—
258C2×M16—41no—
259C2×M16—41no—
260C2×M16—41no—
261C2×M16—41no—
262C2×M16—41no—
263C2×M16—41no—
264C2×M16—41no—
265C2×M16—41no—
266C2×M16—41no—
267C2×M16—41no—
268C2×M16—41no—
269C2×M16—41no—
270C2×M16—41no—
271C2×M16—41no—
272C2×M16—41no—
273C2×M16—41no—
274C2×M16—41no—
275C2×M16—41no—
276C2×M16—41no—
277C2×M16—41no—
278C2×M16—41no—
279C2×M16—41no—
280C2×M16—41no—
281C2×M16—41no—
282C2×M16—41no—
283C2×M16—41no—
284C2×M16—41no—
285C2×M16—41no—
286C2×M16—41no—
287C2×M16—41no—
288C2×M16—41no—
289C2×M16—41no—
290C2×M16—41no—
291C2×M16C4214yes—
292C2×M16C22⋊C414yes—
293C2×M16C4⋊C414yes—
294C2×M16C4⋊C414yes—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8—22no—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—41no—
308C22×C8—41no—
309C22×C8—41no—
310C22×C8—41no—
311C22×C8—41no—
312C22×C8—41no—
313C22×C8—41no—
314C22×C8—41no—
315C22×C8—41no—
316C22×C8—41no—
317C22×C8—41no—
318C22×C8—41no—
319C22×C8—41no—
320C22×C8—41no—
321C22×C8—41no—
322C22×C8—41no—
323#117—22no—
324#117—22no—
325#117—22no—
326#117—22no—
327#117—22no—
328#117—22no—
329#117—22no—
330#117—22no—
331#117—22no—
332#117—22no—
333#117—22no—
334#117—22no—
335#117—22no—
336#117—22no—
337#117—22no—
338#117—22no—
339#117—22no—
340#117—22no—
341#117—22no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—22no—
346#117—22no—
347#117—22no—
348#117—22no—
349#117—22no—
350#117—41no—
351#117—41no—
352#117—41no—
353#117—41no—
354#117—41no—
355#117—41no—
356#117—41no—
357#117—41no—
358#117—41no—
359#117—41no—
360#117—41no—
361#117—41no—
362#117—41no—
363#117—41no—
364#117—41no—
365#117—41no—
366#117—41no—
367#117—41no—
368#117C22⋊C414yes—
369#117C22⋊C414yes—
370#117C4⋊C414yes—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4—41no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4—41no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4—41no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
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⋊C4—41no—
406C2×C22⋊C4—41no—
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—41no—
417C2×C42—41no—
418C2×C42—41no—
419C2×C42—41no—
420C2×C42—41no—
421C2×C42—41no—
422C2×C42—41no—
423C2×C42—41no—
424C2×C42—41no—
425C24—82no—
426C24#11711yescharacteristic
427C24#11711yescharacteristic
428C24#11711yescharacteristic
429C24#12111yescharacteristic
430C24C22⋊Q811yescharacteristic
431C24#12311yescharacteristic
432C24#12311yescharacteristic
433C24#12311yescharacteristic
434C24#12311yescharacteristic
435C24#12411yescharacteristic
436C24#12411yescharacteristic
437C24#12511yescharacteristic
438C24#12511yescharacteristic
439C24#12611yescharacteristic
440C24#12611yescharacteristic
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—84no—
451C22×C4—84no—
452C22×C4—84no—
453C22×C4C2×C4211yescharacteristic
454C22×C4C2×C22⋊C411yescharacteristic
455C22×C4C2×C22⋊C411yescharacteristic
456C22×C4C2×C22⋊C411yescharacteristic
457C22×C4C2×C4⋊C411yescharacteristic
458C22×C4C2×C4⋊C411yescharacteristic
459C22×C4C2×C4⋊C411yescharacteristic
460C22×C4#11711yescharacteristic
461C22×C4#11711yescharacteristic
462C22×C4#11711yescharacteristic
463C22×C4#11711yescharacteristic
464C22×C4#11711yescharacteristic
465C22×C4#11711yescharacteristic
466C22×C4#11711yescharacteristic
467C22×C4#11711yescharacteristic
468C22×C4#11711yescharacteristic
469C22×C4C4×D411yescharacteristic
470C22×C4C4×D411yescharacteristic
471C22×C4C4×D411yescharacteristic
472C22×C4C4×D411yescharacteristic
473C22×C4C4×D411yescharacteristic
474C22×C4C4×D411yescharacteristic
475C22×C4C4×D411yescharacteristic
476C22×C4C4×D411yescharacteristic
477C22×C4C4×D411yescharacteristic
478C22×C4C4×D411yescharacteristic
479C22×C4C4×D411yescharacteristic
480C22×C4C4×D411yescharacteristic
481C22×C4C4×D411yescharacteristic
482C22×C4C4×D411yescharacteristic
483C22×C4C4×D411yescharacteristic
484C22×C4C4×D411yescharacteristic
485C22×C4C4×D411yescharacteristic
486C22×C4C4×D411yescharacteristic
487C22×C4C4×Q811yescharacteristic
488C22×C4C4×Q811yescharacteristic
489C22×C4C4×Q811yescharacteristic
490C22×C4C4×Q811yescharacteristic
491C22×C4C4×Q811yescharacteristic
492C22×C4C4×Q811yescharacteristic
493C22×C4#12011yescharacteristic
494C22×C4#12011yescharacteristic
495C22×C4#12011yescharacteristic
496C22×C4#12011yescharacteristic
497C22×C4#12111yescharacteristic
498C22×C4#12111yescharacteristic
499C22×C4#12111yescharacteristic
500C22×C4#12111yescharacteristic
501C22×C4#12111yescharacteristic
502C22×C4#12111yescharacteristic
503C22×C4#12111yescharacteristic
504C22×C4#12111yescharacteristic
505C22×C4#12111yescharacteristic
506C22×C4#12111yescharacteristic
507C22×C4#12111yescharacteristic
508C22×C4#12111yescharacteristic
509C22×C4#12111yescharacteristic
510C22×C4#12111yescharacteristic
511C22×C4#12111yescharacteristic
512C22×C4#12111yescharacteristic
513C22×C4#12111yescharacteristic
514C22×C4C22⋊Q811yescharacteristic
515C22×C4C22⋊Q811yescharacteristic
516C22×C4C22⋊Q811yescharacteristic
517C22×C4C22⋊Q811yescharacteristic
518C22×C4C22⋊Q811yescharacteristic
519C22×C4C22⋊Q811yescharacteristic
520C22×C4C22⋊Q811yescharacteristic
521C22×C4C22⋊Q811yescharacteristic
522C22×C4C22⋊Q811yescharacteristic
523C22×C4C22⋊Q811yescharacteristic
524C22×C4C22⋊Q811yescharacteristic
525C22×C4C22⋊Q811yescharacteristic
526C22×C4C22⋊Q811yescharacteristic
527C22×C4C22⋊Q811yescharacteristic
528C22×C4C22⋊Q811yescharacteristic
529C22×C4C22⋊Q811yescharacteristic
530C22×C4C22⋊Q811yescharacteristic
531C22×C4#12311yescharacteristic
532C22×C4#12311yescharacteristic
533C22×C4#12311yescharacteristic
534C22×C4#12311yescharacteristic
535C22×C4#12311yescharacteristic
536C22×C4#12311yescharacteristic
537C22×C4#12311yescharacteristic
538C22×C4#12311yescharacteristic
539C22×C4#12311yescharacteristic
540C22×C4#12311yescharacteristic
541C22×C4#12311yescharacteristic
542C22×C4#12311yescharacteristic
543C22×C4#12311yescharacteristic
544C22×C4#12311yescharacteristic
545C22×C4#12311yescharacteristic
546C22×C4#12311yescharacteristic
547C22×C4#12311yescharacteristic
548C22×C4#12311yescharacteristic
549C22×C4#12311yescharacteristic
550C22×C4#12311yescharacteristic
551C22×C4#12411yescharacteristic
552C22×C4#12411yescharacteristic
553C22×C4#12411yescharacteristic
554C22×C4#12411yescharacteristic
555C22×C4#12411yescharacteristic
556C22×C4#12411yescharacteristic
557C22×C4#12411yescharacteristic
558C22×C4#12411yescharacteristic
559C22×C4#12411yescharacteristic
560C22×C4#12411yescharacteristic
561C22×C4#12511yescharacteristic
562C22×C4#12511yescharacteristic
563C22×C4#12511yescharacteristic
564C22×C4#12511yescharacteristic
565C22×C4#12511yescharacteristic
566C22×C4#12511yescharacteristic
567C22×C4#12511yescharacteristic
568C22×C4#12511yescharacteristic
569C22×C4#12511yescharacteristic
570C22×C4#12511yescharacteristic
571C22×C4#12611yescharacteristic
572C22×C4#12611yescharacteristic
573C22×C4#12611yescharacteristic
574C22×C4#12611yescharacteristic
575C22×C4#12611yescharacteristic
576C22×C4#12611yescharacteristic
577C22×C4#12611yescharacteristic
578C22×C4#12611yescharacteristic
579C22×C4#12611yescharacteristic
580C22×C4#12611yescharacteristic
581C22×C4#12611yescharacteristic
582C22×C4#12611yescharacteristic
583C22×C4#12611yescharacteristic
584C22×C4#12611yescharacteristic
585C22×C4#12611yescharacteristic
586C22×C4#12611yescharacteristic
587C22×C4#12611yescharacteristic
588C22×C4#12611yescharacteristic
589C22×C4#12711yescharacteristic
590C22×C4C4⋊Q811yescharacteristic
591C22×C4C4⋊Q811yescharacteristic
592C22×C4C4⋊Q811yescharacteristic
593M16—24no—
594M16—24no—
595M16—24no—
596M16—24no—
597M16—24no—
598M16—24no—
599M16—24no—
600M16—24no—
601M16—42no—
602M16—42no—
603M16—42no—
604M16—42no—
605M16—42no—
606M16—42no—
607M16—42no—
608M16—42no—
609M16—42no—
610M16—42no—
611M16—42no—
612M16—42no—
613M16—42no—
614M16—42no—
615M16—42no—
616M16—42no—
617M16—42no—
618M16—42no—
619M16—42no—
620M16—42no—
621M16—42no—
622M16—42no—
623M16—42no—
624M16—42no—
625C2×C8—24no—
626C2×C8—24no—
627C2×C8—24no—
628C2×C8—24no—
629C2×C8—42no—
630C2×C8—42no—
631C2×C8—42no—
632C2×C8—42no—
633C2×C8—42no—
634C2×C8—42no—
635C2×C8—42no—
636C2×C8—42no—
637C2×C8—42no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8—42no—
641C2×C8—42no—
642C2×C8—42no—
643C2×C8—42no—
644C2×C8—42no—
645C2×C8—42no—
646C2×C8—42no—
647C2×C8—42no—
648C2×C8—42no—
649C2×C8—42no—
650C2×C8—42no—
651C2×C8—42no—
652C2×C8—42no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C42—24no—
678C42—24no—
679C42—24no—
680C42—42no—
681C42—42no—
682C42—42no—
683C42—42no—
684C42—42no—
685C42—42no—
686C42—42no—
687C42—42no—
688C42—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—81no—
697C23—81no—
698C23—81no—
699C23—81no—
700C23—81no—
701C23—81no—
702C23—81no—
703C23—81no—
704C23#37611yescharacteristic
705C23#38011yescharacteristic
706C23#38111yescharacteristic
707C23#38111yescharacteristic
708C23#38211yescharacteristic
709C23#38211yescharacteristic
710C23#38311yescharacteristic
711C23#38711yescharacteristic
712C23#38711yescharacteristic
713C23#38711yescharacteristic
714C23#38711yescharacteristic
715C23#38711yescharacteristic
716C23#38711yescharacteristic
717C23#38811yescharacteristic
718C23#38811yescharacteristic
719C23#38811yescharacteristic
720C23#38811yescharacteristic
721C23#38811yescharacteristic
722C23#38811yescharacteristic
723C23#39311yescharacteristic
724C23#39411yescharacteristic
725C23#39411yescharacteristic
726C23#39411yescharacteristic
727C23#39711yescharacteristic
728C23#39711yescharacteristic
729C23#39711yescharacteristic
730C23#39711yescharacteristic
731C23#39811yescharacteristic
732C23#39811yescharacteristic
733C23#39811yescharacteristic
734C23#39911yescharacteristic
735C23#40011yescharacteristic
736C23#40011yescharacteristic
737C23#40011yescharacteristic
738C23#40011yescharacteristic
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4—84no—
749C2×C4—84no—
750C2×C4—84no—
751C2×C4C4×C22⋊C411yescharacteristic
752C2×C4C4×C22⋊C411yescharacteristic
753C2×C4C4×C22⋊C411yescharacteristic
754C2×C4C4×C4⋊C411yescharacteristic
755C2×C4C4×C4⋊C411yescharacteristic
756C2×C4C4×C4⋊C411yescharacteristic
757C2×C4#38011yescharacteristic
758C2×C4#38011yescharacteristic
759C2×C4#38111yescharacteristic
760C2×C4#38211yescharacteristic
761C2×C4#38311yescharacteristic
762C2×C4#38311yescharacteristic
763C2×C4#38511yescharacteristic
764C2×C4#38511yescharacteristic
765C2×C4#38511yescharacteristic
766C2×C4#38511yescharacteristic
767C2×C4#38511yescharacteristic
768C2×C4#38511yescharacteristic
769C2×C4#38611yescharacteristic
770C2×C4#38611yescharacteristic
771C2×C4#38611yescharacteristic
772C2×C4#38611yescharacteristic
773C2×C4#38611yescharacteristic
774C2×C4#38611yescharacteristic
775C2×C4#38711yescharacteristic
776C2×C4#38711yescharacteristic
777C2×C4#38711yescharacteristic
778C2×C4#38711yescharacteristic
779C2×C4#38711yescharacteristic
780C2×C4#38711yescharacteristic
781C2×C4#38711yescharacteristic
782C2×C4#38711yescharacteristic
783C2×C4#38711yescharacteristic
784C2×C4#38711yescharacteristic
785C2×C4#38711yescharacteristic
786C2×C4#38711yescharacteristic
787C2×C4#38711yescharacteristic
788C2×C4#38711yescharacteristic
789C2×C4#38711yescharacteristic
790C2×C4#38711yescharacteristic
791C2×C4#38711yescharacteristic
792C2×C4#38711yescharacteristic
793C2×C4#38811yescharacteristic
794C2×C4#38811yescharacteristic
795C2×C4#38811yescharacteristic
796C2×C4#38811yescharacteristic
797C2×C4#38811yescharacteristic
798C2×C4#38811yescharacteristic
799C2×C4#38811yescharacteristic
800C2×C4#38811yescharacteristic
801C2×C4#38811yescharacteristic
802C2×C4#38811yescharacteristic
803C2×C4#38811yescharacteristic
804C2×C4#38811yescharacteristic
805C2×C4#38811yescharacteristic
806C2×C4#38811yescharacteristic
807C2×C4#38811yescharacteristic
808C2×C4#38811yescharacteristic
809C2×C4#38811yescharacteristic
810C2×C4#38811yescharacteristic
811C2×C4#38911yescharacteristic
812C2×C4#38911yescharacteristic
813C2×C4#38911yescharacteristic
814C2×C4#38911yescharacteristic
815C2×C4#38911yescharacteristic
816C2×C4#38911yescharacteristic
817C2×C4#39011yescharacteristic
818C2×C4#39011yescharacteristic
819C2×C4#39011yescharacteristic
820C2×C4#39111yescharacteristic
821C2×C4#39111yescharacteristic
822C2×C4#39111yescharacteristic
823C2×C4#39211yescharacteristic
824C2×C4#39311yescharacteristic
825C2×C4#39311yescharacteristic
826C2×C4#39411yescharacteristic
827C2×C4#39411yescharacteristic
828C2×C4#39411yescharacteristic
829C2×C4#39411yescharacteristic
830C2×C4#39411yescharacteristic
831C2×C4#39411yescharacteristic
832C2×C4#39511yescharacteristic
833C2×C4#39611yescharacteristic
834C2×C4#39611yescharacteristic
835C2×C4#39611yescharacteristic
836C2×C4#39611yescharacteristic
837C2×C4#39611yescharacteristic
838C2×C4#39611yescharacteristic
839C2×C4#39711yescharacteristic
840C2×C4#39711yescharacteristic
841C2×C4#39711yescharacteristic
842C2×C4#39711yescharacteristic
843C2×C4#39711yescharacteristic
844C2×C4#39711yescharacteristic
845C2×C4#39711yescharacteristic
846C2×C4#39711yescharacteristic
847C2×C4#39711yescharacteristic
848C2×C4#39711yescharacteristic
849C2×C4#39711yescharacteristic
850C2×C4#39811yescharacteristic
851C2×C4#39811yescharacteristic
852C2×C4#39811yescharacteristic
853C2×C4#39811yescharacteristic
854C2×C4#39811yescharacteristic
855C2×C4#39811yescharacteristic
856C2×C4#39911yescharacteristic
857C2×C4#39911yescharacteristic
858C2×C4#40011yescharacteristic
859C2×C4#40011yescharacteristic
860C2×C4#40011yescharacteristic
861C2×C4#40011yescharacteristic
862C2×C4#40011yescharacteristic
863C2×C4#40011yescharacteristic
864C2×C4#40011yescharacteristic
865C2×C4#40011yescharacteristic
866C2×C4#40011yescharacteristic
867C2×C4#40011yescharacteristic
868C2×C4#40011yescharacteristic
869C2×C4#40111yescharacteristic
870C2×C4#40111yescharacteristic
871C8—44no—
872C8—44no—
873C8—44no—
874C8—44no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—22no—
880C22—22no—
881C22—22no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22#143411yescharacteristic
911C22#143411yescharacteristic
912C22#143411yescharacteristic
913C22#143911yescharacteristic
914C22#144011yescharacteristic
915C22#144011yescharacteristic
916C22#144111yescharacteristic
917C22#144211yescharacteristic
918C22#144211yescharacteristic
919C22#144211yescharacteristic
920C22#144211yescharacteristic
921C22#144311yescharacteristic
922C22#144311yescharacteristic
923C22#144511yescharacteristic
924C22#144511yescharacteristic
925C4—84no—
926C4—84no—
927C4—84no—
928C4#143611yescharacteristic
929C4#143611yescharacteristic
930C4#143611yescharacteristic
931C4#143711yescharacteristic
932C4#143911yescharacteristic
933C4#143911yescharacteristic
934C4#144011yescharacteristic
935C4#144111yescharacteristic
936C4#144111yescharacteristic
937C4#144211yescharacteristic
938C4#144211yescharacteristic
939C4#144311yescharacteristic
940C4#144311yescharacteristic
941C4#144311yescharacteristic
942C4#144311yescharacteristic
943C4#144511yescharacteristic
944C2—21no—
945C2—21no—
946C2—21no—
947C2—21no—
948C2—21no—
949C2—21no—
950C2—21no—
951C2—21no—
952C2—21no—
953C2—21no—
954C2—21no—
955C2—21no—
956C2—21no—
957C2—21no—
958C2#755611yescharacteristic
959C2#1127312yes—
subgroupG/H
centerC2×C4#394
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC22#1442
prime radicalC25#41
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
21. C2×#344C4semidirect
22. C2×#344C4semidirect
23. C2×#344C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3442
C2×#17382
C2×#17332