Finite Group Databasebeta

← #123782

Subgroups — #123782

Order 512.

1510 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#344C211yesmaximal, characteristic
2C2×#1742C211yesmaximal, characteristic
3C22×#343C211yesmaximal, characteristic
4C2×#1738C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic
6C2×#1736C211yesmaximal, characteristic
7C2×#1733C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C2×#344—22no—
16C2×#344—22no—
17C2×#344C414yescomplemented
18#1742—22no—
19#1742C414yescomplemented
20C2×#343—22no—
21C2×#343—22no—
22C2×#343—22no—
23C2×#343C414yescomplemented
24#1738—22no—
25#1738—22no—
26C2×#341—22no—
27#1736—22no—
28#1736—22no—
29#1736—22no—
30#1736—22no—
31C2×#340—22no—
32C2×#340—22no—
33#1733—22no—
34#1733—22no—
35C2×#339—22no—
36C24×C4—21no—
37C24×C4C2311yescharacteristic
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×M16—21no—
82C22×M16C2×C412yes—
83C22×M16C2×C412yes—
84C22×M16C2×C412yes—
85C22×M16C2×C412yes—
86C22×M16C2×C412yes—
87C22×M16C2×C412yes—
88C22×M16D412yes—
89C22×M16D412yes—
90C22×M16D412yes—
91C22×M16D412yes—
92C22×M16Q812yes—
93C22×M16Q812yes—
94C23×C8—21no—
95C23×C8—21no—
96C23×C8—21no—
97C23×C8—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×#117C2×C412yes—
118C2×#117C2×C412yes—
119C2×#117D412yes—
120C2×#117D412yes—
121C2×#117D412yes—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—21no—
124C22×C4⋊C4—21no—
125C22×C4⋊C4—21no—
126C22×C4⋊C4—21no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4C2×C412yes—
135C22×C4⋊C4D412yes—
136C22×C4⋊C4D412yes—
137C22×C4⋊C4Q812yes—
138C22×C22⋊C4—21no—
139C22×C22⋊C4—21no—
140C22×C42—21no—
141C22×C42—21no—
142#344—28no—
143#343—28no—
144#343—28no—
145#341—28no—
146#340—28no—
147#340—28no—
148#339—28no—
149C25#4111yescharacteristic
150C23×C4—22no—
151C23×C4—22no—
152C23×C4—22no—
153C23×C4—22no—
154C23×C4—41no—
155C23×C4—41no—
156C23×C4—41no—
157C23×C4—41no—
158C23×C4—41no—
159C23×C4—84no—
160C23×C4C22×C411yescharacteristic
161C23×C4C22×C411yescharacteristic
162C23×C4C22×C411yescharacteristic
163C23×C4C2×D411yescharacteristic
164C23×C4C2×D411yescharacteristic
165C23×C4C2×D411yescharacteristic
166C23×C4C2×D411yescharacteristic
167C23×C4C2×D411yescharacteristic
168C23×C4C2×D411yescharacteristic
169C23×C4C2×D411yescharacteristic
170C23×C4C2×D411yescharacteristic
171C23×C4C2×D411yescharacteristic
172C23×C4C2×Q811yescharacteristic
173C23×C4C2×Q811yescharacteristic
174C23×C4C2×Q811yescharacteristic
175C23×C4#4111yescharacteristic
176C23×C4#4111yescharacteristic
177C23×C4#4111yescharacteristic
178C23×C4#4111yescharacteristic
179C23×C4#4111yescharacteristic
180C23×C4#4111yescharacteristic
181C23×C4#4111yescharacteristic
182C23×C4#4111yescharacteristic
183C23×C4#4111yescharacteristic
184C23×C4#4111yescharacteristic
185C23×C4#4111yescharacteristic
186C23×C4#4111yescharacteristic
187C23×C4#4111yescharacteristic
188C23×C4#4111yescharacteristic
189C23×C4#4111yescharacteristic
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—22no—
244C2×M16—22no—
245C2×M16—22no—
246C2×M16—22no—
247C2×M16—22no—
248C2×M16—22no—
249C2×M16—22no—
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×M16—41no—
292C2×M16—41no—
293C2×M16—41no—
294C2×M16—41no—
295C2×M16—41no—
296C2×M16—41no—
297C2×M16—41no—
298C2×M16C4214yes—
299C2×M16C22⋊C414yes—
300C2×M16C4⋊C414yes—
301C2×M16C4⋊C414yes—
302C22×C8—22no—
303C22×C8—22no—
304C22×C8—22no—
305C22×C8—22no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
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—
323C22×C8—41no—
324C22×C8—41no—
325C22×C8—41no—
326C22×C8—41no—
327C22×C8—41no—
328C22×C8—41no—
329C22×C8—41no—
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—41no—
348#117—41no—
349#117—41no—
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#117C22⋊C414yes—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
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—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—41no—
386C2×C4⋊C4—41no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4—41no—
389C2×C4⋊C4—41no—
390C2×C4⋊C4—41no—
391C2×C4⋊C4—41no—
392C2×C4⋊C4—41no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4—41no—
395C2×C4⋊C4—41no—
396C2×C4⋊C4—41no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4C22⋊C414yes—
401C2×C4⋊C4C4⋊C414yes—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—41no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—41no—
411C2×C22⋊C4—41no—
412C2×C22⋊C4—41no—
413C2×C22⋊C4—41no—
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—
426C24—42no—
427C24—42no—
428C24#11711yescharacteristic
429C24#11711yescharacteristic
430C24#11711yescharacteristic
431C24#12111yescharacteristic
432C24C22⋊Q811yescharacteristic
433C24#12311yescharacteristic
434C24#12311yescharacteristic
435C24#12311yescharacteristic
436C24#12311yescharacteristic
437C24#12411yescharacteristic
438C24#12411yescharacteristic
439C24#12511yescharacteristic
440C24#12511yescharacteristic
441C24#12611yescharacteristic
442C24#12611yescharacteristic
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—82no—
457C22×C4—82no—
458C22×C4—84no—
459C22×C4—84no—
460C22×C4—84no—
461C22×C4—84no—
462C22×C4—82no—
463C22×C4—82no—
464C22×C4—84no—
465C22×C4—84no—
466C22×C4—84no—
467C22×C4C2×C4211yescharacteristic
468C22×C4C2×C22⋊C411yescharacteristic
469C22×C4C2×C22⋊C411yescharacteristic
470C22×C4C2×C22⋊C411yescharacteristic
471C22×C4C2×C4⋊C411yescharacteristic
472C22×C4C2×C4⋊C411yescharacteristic
473C22×C4C2×C4⋊C411yescharacteristic
474C22×C4#11711yescharacteristic
475C22×C4#11711yescharacteristic
476C22×C4#11711yescharacteristic
477C22×C4#11711yescharacteristic
478C22×C4#11711yescharacteristic
479C22×C4#11711yescharacteristic
480C22×C4#11711yescharacteristic
481C22×C4#11711yescharacteristic
482C22×C4#11711yescharacteristic
483C22×C4C4×D411yescharacteristic
484C22×C4C4×D411yescharacteristic
485C22×C4C4×D411yescharacteristic
486C22×C4C4×D411yescharacteristic
487C22×C4C4×D411yescharacteristic
488C22×C4C4×D411yescharacteristic
489C22×C4C4×D411yescharacteristic
490C22×C4C4×D411yescharacteristic
491C22×C4C4×D411yescharacteristic
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×Q811yescharacteristic
502C22×C4C4×Q811yescharacteristic
503C22×C4C4×Q811yescharacteristic
504C22×C4C4×Q811yescharacteristic
505C22×C4C4×Q811yescharacteristic
506C22×C4C4×Q811yescharacteristic
507C22×C4#12011yescharacteristic
508C22×C4#12011yescharacteristic
509C22×C4#12011yescharacteristic
510C22×C4#12011yescharacteristic
511C22×C4#12111yescharacteristic
512C22×C4#12111yescharacteristic
513C22×C4#12111yescharacteristic
514C22×C4#12111yescharacteristic
515C22×C4#12111yescharacteristic
516C22×C4#12111yescharacteristic
517C22×C4#12111yescharacteristic
518C22×C4#12111yescharacteristic
519C22×C4#12111yescharacteristic
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×C4C22⋊Q811yescharacteristic
529C22×C4C22⋊Q811yescharacteristic
530C22×C4C22⋊Q811yescharacteristic
531C22×C4C22⋊Q811yescharacteristic
532C22×C4C22⋊Q811yescharacteristic
533C22×C4C22⋊Q811yescharacteristic
534C22×C4C22⋊Q811yescharacteristic
535C22×C4C22⋊Q811yescharacteristic
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×C4#12311yescharacteristic
546C22×C4#12311yescharacteristic
547C22×C4#12311yescharacteristic
548C22×C4#12311yescharacteristic
549C22×C4#12311yescharacteristic
550C22×C4#12311yescharacteristic
551C22×C4#12311yescharacteristic
552C22×C4#12311yescharacteristic
553C22×C4#12311yescharacteristic
554C22×C4#12311yescharacteristic
555C22×C4#12311yescharacteristic
556C22×C4#12311yescharacteristic
557C22×C4#12311yescharacteristic
558C22×C4#12311yescharacteristic
559C22×C4#12311yescharacteristic
560C22×C4#12311yescharacteristic
561C22×C4#12311yescharacteristic
562C22×C4#12311yescharacteristic
563C22×C4#12311yescharacteristic
564C22×C4#12311yescharacteristic
565C22×C4#12411yescharacteristic
566C22×C4#12411yescharacteristic
567C22×C4#12411yescharacteristic
568C22×C4#12411yescharacteristic
569C22×C4#12411yescharacteristic
570C22×C4#12411yescharacteristic
571C22×C4#12411yescharacteristic
572C22×C4#12411yescharacteristic
573C22×C4#12411yescharacteristic
574C22×C4#12411yescharacteristic
575C22×C4#12511yescharacteristic
576C22×C4#12511yescharacteristic
577C22×C4#12511yescharacteristic
578C22×C4#12511yescharacteristic
579C22×C4#12511yescharacteristic
580C22×C4#12511yescharacteristic
581C22×C4#12511yescharacteristic
582C22×C4#12511yescharacteristic
583C22×C4#12511yescharacteristic
584C22×C4#12511yescharacteristic
585C22×C4#12611yescharacteristic
586C22×C4#12611yescharacteristic
587C22×C4#12611yescharacteristic
588C22×C4#12611yescharacteristic
589C22×C4#12611yescharacteristic
590C22×C4#12611yescharacteristic
591C22×C4#12611yescharacteristic
592C22×C4#12611yescharacteristic
593C22×C4#12611yescharacteristic
594C22×C4#12611yescharacteristic
595C22×C4#12611yescharacteristic
596C22×C4#12611yescharacteristic
597C22×C4#12611yescharacteristic
598C22×C4#12611yescharacteristic
599C22×C4#12611yescharacteristic
600C22×C4#12611yescharacteristic
601C22×C4#12611yescharacteristic
602C22×C4#12611yescharacteristic
603C22×C4#12711yescharacteristic
604C22×C4C4⋊Q811yescharacteristic
605C22×C4C4⋊Q811yescharacteristic
606C22×C4C4⋊Q811yescharacteristic
607M16—24no—
608M16—24no—
609M16—24no—
610M16—24no—
611M16—24no—
612M16—24no—
613M16—24no—
614M16—24no—
615M16—42no—
616M16—42no—
617M16—42no—
618M16—42no—
619M16—42no—
620M16—42no—
621M16—42no—
622M16—42no—
623M16—42no—
624M16—42no—
625M16—42no—
626M16—42no—
627M16—42no—
628M16—42no—
629M16—42no—
630M16—42no—
631M16—42no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16—42no—
636M16—42no—
637M16—42no—
638M16—42no—
639C2×C8—24no—
640C2×C8—24no—
641C2×C8—24no—
642C2×C8—24no—
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—
653C2×C8—42no—
654C2×C8—42no—
655C2×C8—42no—
656C2×C8—42no—
657C2×C8—42no—
658C2×C8—42no—
659C2×C8—42no—
660C2×C8—42no—
661C2×C8—42no—
662C2×C8—42no—
663C2×C8—42no—
664C2×C8—42no—
665C2×C8—42no—
666C2×C8—42no—
667C4⋊C4—24no—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—24no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—42no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C22⋊C4—24no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C42—24no—
692C42—42no—
693C42—42no—
694C42—42no—
695C42—42no—
696C42—42no—
697C42—42no—
698C42—42no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—42no—
710C23—41no—
711C23—42no—
712C23—41no—
713C23—41no—
714C23—42no—
715C23—42no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23#37611yescharacteristic
722C23#38011yescharacteristic
723C23#38111yescharacteristic
724C23#38111yescharacteristic
725C23#38211yescharacteristic
726C23#38211yescharacteristic
727C23#38311yescharacteristic
728C23#38711yescharacteristic
729C23#38711yescharacteristic
730C23#38711yescharacteristic
731C23#38711yescharacteristic
732C23#38711yescharacteristic
733C23#38711yescharacteristic
734C23#38811yescharacteristic
735C23#38811yescharacteristic
736C23#38811yescharacteristic
737C23#38811yescharacteristic
738C23#38811yescharacteristic
739C23#38811yescharacteristic
740C23#39311yescharacteristic
741C23#39411yescharacteristic
742C23#39411yescharacteristic
743C23#39411yescharacteristic
744C23#39711yescharacteristic
745C23#39711yescharacteristic
746C23#39711yescharacteristic
747C23#39711yescharacteristic
748C23#39811yescharacteristic
749C23#39811yescharacteristic
750C23#39811yescharacteristic
751C23#39911yescharacteristic
752C23#40011yescharacteristic
753C23#40011yescharacteristic
754C23#40011yescharacteristic
755C23#40011yescharacteristic
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—84no—
760C2×C4—82no—
761C2×C4—82no—
762C2×C4—84no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4—84no—
766C2×C4—84no—
767C2×C4—84no—
768C2×C4—84no—
769C2×C4—82no—
770C2×C4—84no—
771C2×C4—82no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4C4×C22⋊C411yescharacteristic
775C2×C4C4×C22⋊C411yescharacteristic
776C2×C4C4×C22⋊C411yescharacteristic
777C2×C4C4×C4⋊C411yescharacteristic
778C2×C4C4×C4⋊C411yescharacteristic
779C2×C4C4×C4⋊C411yescharacteristic
780C2×C4#38011yescharacteristic
781C2×C4#38011yescharacteristic
782C2×C4#38111yescharacteristic
783C2×C4#38211yescharacteristic
784C2×C4#38311yescharacteristic
785C2×C4#38311yescharacteristic
786C2×C4#38511yescharacteristic
787C2×C4#38511yescharacteristic
788C2×C4#38511yescharacteristic
789C2×C4#38511yescharacteristic
790C2×C4#38511yescharacteristic
791C2×C4#38511yescharacteristic
792C2×C4#38611yescharacteristic
793C2×C4#38611yescharacteristic
794C2×C4#38611yescharacteristic
795C2×C4#38611yescharacteristic
796C2×C4#38611yescharacteristic
797C2×C4#38611yescharacteristic
798C2×C4#38711yescharacteristic
799C2×C4#38711yescharacteristic
800C2×C4#38711yescharacteristic
801C2×C4#38711yescharacteristic
802C2×C4#38711yescharacteristic
803C2×C4#38711yescharacteristic
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#38811yescharacteristic
817C2×C4#38811yescharacteristic
818C2×C4#38811yescharacteristic
819C2×C4#38811yescharacteristic
820C2×C4#38811yescharacteristic
821C2×C4#38811yescharacteristic
822C2×C4#38811yescharacteristic
823C2×C4#38811yescharacteristic
824C2×C4#38811yescharacteristic
825C2×C4#38811yescharacteristic
826C2×C4#38811yescharacteristic
827C2×C4#38811yescharacteristic
828C2×C4#38811yescharacteristic
829C2×C4#38811yescharacteristic
830C2×C4#38811yescharacteristic
831C2×C4#38811yescharacteristic
832C2×C4#38811yescharacteristic
833C2×C4#38811yescharacteristic
834C2×C4#38911yescharacteristic
835C2×C4#38911yescharacteristic
836C2×C4#38911yescharacteristic
837C2×C4#38911yescharacteristic
838C2×C4#38911yescharacteristic
839C2×C4#38911yescharacteristic
840C2×C4#39011yescharacteristic
841C2×C4#39011yescharacteristic
842C2×C4#39011yescharacteristic
843C2×C4#39111yescharacteristic
844C2×C4#39111yescharacteristic
845C2×C4#39111yescharacteristic
846C2×C4#39211yescharacteristic
847C2×C4#39311yescharacteristic
848C2×C4#39311yescharacteristic
849C2×C4#39411yescharacteristic
850C2×C4#39411yescharacteristic
851C2×C4#39411yescharacteristic
852C2×C4#39411yescharacteristic
853C2×C4#39411yescharacteristic
854C2×C4#39411yescharacteristic
855C2×C4#39511yescharacteristic
856C2×C4#39611yescharacteristic
857C2×C4#39611yescharacteristic
858C2×C4#39611yescharacteristic
859C2×C4#39611yescharacteristic
860C2×C4#39611yescharacteristic
861C2×C4#39611yescharacteristic
862C2×C4#39711yescharacteristic
863C2×C4#39711yescharacteristic
864C2×C4#39711yescharacteristic
865C2×C4#39711yescharacteristic
866C2×C4#39711yescharacteristic
867C2×C4#39711yescharacteristic
868C2×C4#39711yescharacteristic
869C2×C4#39711yescharacteristic
870C2×C4#39711yescharacteristic
871C2×C4#39711yescharacteristic
872C2×C4#39711yescharacteristic
873C2×C4#39811yescharacteristic
874C2×C4#39811yescharacteristic
875C2×C4#39811yescharacteristic
876C2×C4#39811yescharacteristic
877C2×C4#39811yescharacteristic
878C2×C4#39811yescharacteristic
879C2×C4#39911yescharacteristic
880C2×C4#39911yescharacteristic
881C2×C4#40011yescharacteristic
882C2×C4#40011yescharacteristic
883C2×C4#40011yescharacteristic
884C2×C4#40011yescharacteristic
885C2×C4#40011yescharacteristic
886C2×C4#40011yescharacteristic
887C2×C4#40011yescharacteristic
888C2×C4#40011yescharacteristic
889C2×C4#40011yescharacteristic
890C2×C4#40011yescharacteristic
891C2×C4#40011yescharacteristic
892C2×C4#40111yescharacteristic
893C2×C4#40111yescharacteristic
894C8—44no—
895C8—44no—
896C8—44no—
897C8—44no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—21no—
912C22—21no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—22no—
920C22—22no—
921C22—22no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22#143411yescharacteristic
939C22#143411yescharacteristic
940C22#143411yescharacteristic
941C22#143911yescharacteristic
942C22#144011yescharacteristic
943C22#144011yescharacteristic
944C22#144111yescharacteristic
945C22#144211yescharacteristic
946C22#144211yescharacteristic
947C22#144211yescharacteristic
948C22#144211yescharacteristic
949C22#144311yescharacteristic
950C22#144311yescharacteristic
951C22#144511yescharacteristic
952C22#144511yescharacteristic
953C22#204812yes—
954C22#204912yes—
955C4—84no—
956C4—84no—
957C4—84no—
958C4#143611yescharacteristic
959C4#143611yescharacteristic
960C4#143611yescharacteristic
961C4#143711yescharacteristic
962C4#143911yescharacteristic
963C4#143911yescharacteristic
964C4#144011yescharacteristic
965C4#144111yescharacteristic
966C4#144111yescharacteristic
967C4#144211yescharacteristic
968C4#144211yescharacteristic
969C4#144311yescharacteristic
970C4#144311yescharacteristic
971C4#144311yescharacteristic
972C4#144311yescharacteristic
973C4#144511yescharacteristic
974C2—21no—
975C2—21no—
976C2—21no—
977C2—21no—
978C2—21no—
979C2—21no—
980C2—21no—
981C2—21no—
982C2—21no—
983C2—21no—
984C2—21no—
985C2—21no—
986C2#755611yescharacteristic
987C2#1114211yescharacteristic
988C2#1114311yescharacteristic
989C2#1115212yes—
990C2#1127412yes—
subgroupG/H
center, socleC23#394
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
prime radicalC25#41
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
17. C2×#344C4semidirect
19. #1742C4semidirect
23. C2×#343C4semidirect

Maximal subgroups

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

subgroupindex
C22×#3442
C2×#17422
C22×#3432
C2×#17382
C2×#17362
C2×#17332