Finite Group Databasebeta

← #123995

Subgroups — #123995

Order 512.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#428C211yesmaximal, characteristic
2C22×#344C211yesmaximal, characteristic
3C2×#1740C211yesmaximal, characteristic
4#20347C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic
6C2×#1733C211yesmaximal, characteristic
7#13795C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C22×#117C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15C2×#428—22no—
16C2×#428—22no—
17C2×#428—22no—
18C2×#428—22no—
19C2×#428—22no—
20C2×#428C414yescomplemented
21C22×#107—21no—
22C22×#106—21no—
23C2×#344—22no—
24C2×#344—22no—
25C2×#344C414yescomplemented
26#1740—22no—
27#1740—22no—
28C2×#342—22no—
29#1736—22no—
30#1736—22no—
31#1736—21no—
32#1736—21no—
33#1736—22no—
34#1735—22no—
35C2×#340—22no—
36#1733—22no—
37#1733C414yescomplemented
38C2×#339—22no—
39C4⋊#95—22no—
40C4⋊#95—22no—
41C22⋊#95—22no—
42C24×C4—21no—
43C24×C4C2311yescharacteristic
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×M16C2×C412yes—
64C22×M16C2×C412yes—
65C22×M16C2×C412yes—
66C22×M16C2×C412yes—
67C22×M16D412yes—
68C22×M16D412yes—
69C22×M16D412yes—
70C22×M16Q812yes—
71C22×M16Q812yes—
72C23×C8—21no—
73C23×C8D412yes—
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×#117C2×C412yes—
114C2×#117C2×C412yes—
115C2×#117C2×C412yes—
116C2×#117C2×C412yes—
117C2×#117D412yes—
118C2×#117D412yes—
119C2×#117Q812yes—
120C2×#117Q812yes—
121C2×#117Q812yes—
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⋊C4—21no—
135C22×C4⋊C4C2×C412yes—
136C22×C4⋊C4D411yescharacteristic
137C22×C4⋊C4D411yescharacteristic
138C22×C4⋊C4D412yes—
139C22×C4⋊C4D412yes—
140C22×C4⋊C4D412yes—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4D412yes—
145C22×C42—21no—
146C22×C42—21no—
147C22×C42—21no—
148C22×C42—21no—
149#428—28no—
150#428—28no—
151#428—28no—
152#428—28no—
153C2×#107—24no—
154C2×#107—24no—
155C2×#107—24no—
156C2×#106—24no—
157C2×#106—24no—
158C2×#106—24no—
159C2×#95—28no—
160#344—28no—
161#342—28no—
162#340—28no—
163#340—24no—
164#340—24no—
165#339—28no—
166C25C2×D411yescharacteristic
167C23×C4—22no—
168C23×C4—22no—
169C23×C4—22no—
170C23×C4—22no—
171C23×C4—21no—
172C23×C4—21no—
173C23×C4—22no—
174C23×C4—41no—
175C23×C4—41no—
176C23×C4—41no—
177C23×C4—41no—
178C23×C4—41no—
179C23×C4—84no—
180C23×C4C22×C411yescharacteristic
181C23×C4C22×C411yescharacteristic
182C23×C4C22×C411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×D411yescharacteristic
187C23×C4C2×D411yescharacteristic
188C23×C4C2×D411yescharacteristic
189C23×C4C2×D411yescharacteristic
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2×Q811yescharacteristic
194C23×C4C2×Q811yescharacteristic
195C23×C4C2×Q811yescharacteristic
196C23×C4C2×Q811yescharacteristic
197C23×C4C2×Q811yescharacteristic
198C23×C4#4111yescharacteristic
199C23×C4#4111yescharacteristic
200C23×C4#4111yescharacteristic
201C23×C4#4111yescharacteristic
202C23×C4#4111yescharacteristic
203C23×C4#4111yescharacteristic
204C23×C4#4111yescharacteristic
205C23×C4#4111yescharacteristic
206C23×C4#4111yescharacteristic
207C23×C4#4111yescharacteristic
208C23×C4#4111yescharacteristic
209C23×C4#4111yescharacteristic
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×M16C4214yes—
260C2×M16C22⋊C414yes—
261C2×M16C22⋊C414yes—
262C2×M16C22⋊C414yes—
263C2×M16C4⋊C414yes—
264C2×M16C4⋊C414yes—
265C2×M16C4⋊C414yes—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—22no—
270C22×C8—22no—
271C22×C8—22no—
272C22×C8—22no—
273C22×C8—22no—
274C22×C8—22no—
275C22×C8—22no—
276C22×C8—22no—
277C22×C8—22no—
278C22×C8—22no—
279C22×C8C4⋊C414yes—
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—22no—
310#117—22no—
311#117—22no—
312#117—22no—
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#117C4⋊C414yes—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
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—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
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—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—41no—
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×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⋊C4C22⋊C414yes—
399C2×C4⋊C4C22⋊C412yes—
400C2×C4⋊C4C22⋊C412yes—
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—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—41no—
415C2×C22⋊C4—41no—
416C2×C22⋊C4—41no—
417C2×C22⋊C4—41no—
418C2×C22⋊C4—41no—
419C2×C22⋊C4—41no—
420C2×C22⋊C4—41no—
421C2×C22⋊C4—41no—
422C2×C22⋊C4—41no—
423C2×C22⋊C4—41no—
424C2×C22⋊C4—41no—
425C2×C22⋊C4C4⋊C414yes—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—41no—
436C2×C42—41no—
437C2×C42—41no—
438C2×C42—41no—
439C2×C42—41no—
440C2×C42—41no—
441C2×C42—41no—
442C2×C42—41no—
443C2×C42—41no—
444C2×C42—41no—
445C2×C42—41no—
446C2×C42—41no—
447C2×C42—41no—
448C2×C42—41no—
449C2×C42—41no—
450#107—216no—
451#106—216no—
452#95—88no—
453C24—42no—
454C24—42no—
455C24C2×C4⋊C411yescharacteristic
456C24C4×D411yescharacteristic
457C24C4×D411yescharacteristic
458C24#12011yescharacteristic
459C24#12011yescharacteristic
460C24#12111yescharacteristic
461C24#12111yescharacteristic
462C24#12111yescharacteristic
463C24#12111yescharacteristic
464C24C22⋊Q811yescharacteristic
465C24C22⋊Q811yescharacteristic
466C24#12311yescharacteristic
467C24#12311yescharacteristic
468C24#12711yescharacteristic
469C24C4⋊Q811yescharacteristic
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—44no—
476C22×C4—44no—
477C22×C4—48no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—84no—
498C22×C4—84no—
499C22×C4—82no—
500C22×C4—82no—
501C22×C4—84no—
502C22×C4—84no—
503C22×C4—84no—
504C22×C4—84no—
505C22×C4—82no—
506C22×C4—82no—
507C22×C4C2×C4211yescharacteristic
508C22×C4C2×C22⋊C411yescharacteristic
509C22×C4C2×C22⋊C411yescharacteristic
510C22×C4C2×C22⋊C411yescharacteristic
511C22×C4C2×C22⋊C411yescharacteristic
512C22×C4C2×C22⋊C411yescharacteristic
513C22×C4C2×C4⋊C411yescharacteristic
514C22×C4C2×C4⋊C411yescharacteristic
515C22×C4C2×C4⋊C411yescharacteristic
516C22×C4C2×C4⋊C411yescharacteristic
517C22×C4C2×C4⋊C411yescharacteristic
518C22×C4C2×C4⋊C411yescharacteristic
519C22×C4#11711yescharacteristic
520C22×C4#11711yescharacteristic
521C22×C4#11711yescharacteristic
522C22×C4#11711yescharacteristic
523C22×C4#11711yescharacteristic
524C22×C4#11711yescharacteristic
525C22×C4C4×D411yescharacteristic
526C22×C4C4×D411yescharacteristic
527C22×C4C4×D411yescharacteristic
528C22×C4C4×D411yescharacteristic
529C22×C4C4×D411yescharacteristic
530C22×C4C4×D411yescharacteristic
531C22×C4C4×D411yescharacteristic
532C22×C4C4×D411yescharacteristic
533C22×C4C4×D411yescharacteristic
534C22×C4C4×D411yescharacteristic
535C22×C4C4×D411yescharacteristic
536C22×C4C4×D411yescharacteristic
537C22×C4C4×D411yescharacteristic
538C22×C4C4×D411yescharacteristic
539C22×C4C4×Q811yescharacteristic
540C22×C4C4×Q811yescharacteristic
541C22×C4C4×Q811yescharacteristic
542C22×C4C4×Q811yescharacteristic
543C22×C4C4×Q811yescharacteristic
544C22×C4C4×Q811yescharacteristic
545C22×C4C4×Q811yescharacteristic
546C22×C4C4×Q811yescharacteristic
547C22×C4#12011yescharacteristic
548C22×C4#12011yescharacteristic
549C22×C4#12011yescharacteristic
550C22×C4#12011yescharacteristic
551C22×C4#12011yescharacteristic
552C22×C4#12011yescharacteristic
553C22×C4#12111yescharacteristic
554C22×C4#12111yescharacteristic
555C22×C4#12111yescharacteristic
556C22×C4#12111yescharacteristic
557C22×C4#12111yescharacteristic
558C22×C4#12111yescharacteristic
559C22×C4#12111yescharacteristic
560C22×C4#12111yescharacteristic
561C22×C4#12111yescharacteristic
562C22×C4#12111yescharacteristic
563C22×C4#12111yescharacteristic
564C22×C4#12111yescharacteristic
565C22×C4#12111yescharacteristic
566C22×C4#12111yescharacteristic
567C22×C4#12111yescharacteristic
568C22×C4#12111yescharacteristic
569C22×C4C22⋊Q811yescharacteristic
570C22×C4C22⋊Q811yescharacteristic
571C22×C4C22⋊Q811yescharacteristic
572C22×C4C22⋊Q811yescharacteristic
573C22×C4C22⋊Q811yescharacteristic
574C22×C4C22⋊Q811yescharacteristic
575C22×C4C22⋊Q811yescharacteristic
576C22×C4C22⋊Q811yescharacteristic
577C22×C4C22⋊Q811yescharacteristic
578C22×C4C22⋊Q811yescharacteristic
579C22×C4C22⋊Q811yescharacteristic
580C22×C4C22⋊Q811yescharacteristic
581C22×C4C22⋊Q811yescharacteristic
582C22×C4C22⋊Q811yescharacteristic
583C22×C4C22⋊Q811yescharacteristic
584C22×C4C22⋊Q811yescharacteristic
585C22×C4C22⋊Q811yescharacteristic
586C22×C4C22⋊Q811yescharacteristic
587C22×C4C22⋊Q811yescharacteristic
588C22×C4C22⋊Q811yescharacteristic
589C22×C4C22⋊Q811yescharacteristic
590C22×C4C22⋊Q811yescharacteristic
591C22×C4C22⋊Q811yescharacteristic
592C22×C4C22⋊Q811yescharacteristic
593C22×C4C22⋊Q811yescharacteristic
594C22×C4C22⋊Q811yescharacteristic
595C22×C4#12311yescharacteristic
596C22×C4#12311yescharacteristic
597C22×C4#12311yescharacteristic
598C22×C4#12311yescharacteristic
599C22×C4#12311yescharacteristic
600C22×C4#12311yescharacteristic
601C22×C4#12311yescharacteristic
602C22×C4#12311yescharacteristic
603C22×C4#12311yescharacteristic
604C22×C4#12311yescharacteristic
605C22×C4#12311yescharacteristic
606C22×C4#12311yescharacteristic
607C22×C4#12311yescharacteristic
608C22×C4#12311yescharacteristic
609C22×C4#12411yescharacteristic
610C22×C4#12411yescharacteristic
611C22×C4#12411yescharacteristic
612C22×C4#12411yescharacteristic
613C22×C4#12411yescharacteristic
614C22×C4#12411yescharacteristic
615C22×C4#12411yescharacteristic
616C22×C4#12411yescharacteristic
617C22×C4#12511yescharacteristic
618C22×C4#12511yescharacteristic
619C22×C4#12511yescharacteristic
620C22×C4#12511yescharacteristic
621C22×C4#12511yescharacteristic
622C22×C4#12511yescharacteristic
623C22×C4#12511yescharacteristic
624C22×C4#12511yescharacteristic
625C22×C4#12511yescharacteristic
626C22×C4#12511yescharacteristic
627C22×C4#12511yescharacteristic
628C22×C4#12511yescharacteristic
629C22×C4#12611yescharacteristic
630C22×C4#12611yescharacteristic
631C22×C4#12611yescharacteristic
632C22×C4#12611yescharacteristic
633C22×C4#12611yescharacteristic
634C22×C4#12611yescharacteristic
635C22×C4#12611yescharacteristic
636C22×C4#12611yescharacteristic
637C22×C4#12711yescharacteristic
638C22×C4C4⋊Q811yescharacteristic
639C22×C4C4⋊Q811yescharacteristic
640C22×C4C4⋊Q811yescharacteristic
641C22×C4C4⋊Q811yescharacteristic
642C22×C4C4⋊Q811yescharacteristic
643C22×C4C4⋊Q811yescharacteristic
644C22×C4C4⋊Q811yescharacteristic
645C22×C4C4⋊Q811yescharacteristic
646C22×C4C4⋊Q811yescharacteristic
647M16—24no—
648M16—24no—
649M16—24no—
650M16—24no—
651M16—24no—
652M16—24no—
653M16—24no—
654M16—42no—
655M16—42no—
656M16—42no—
657M16—42no—
658M16—42no—
659M16—42no—
660M16—42no—
661M16—42no—
662M16#9518yescomplemented
663C2×C8—24no—
664C2×C8—24no—
665C2×C8—24no—
666C2×C8—24no—
667C2×C8—24no—
668C2×C8—24no—
669C2×C8—24no—
670C2×C8—24no—
671C2×C8—24no—
672C2×C8—24no—
673C2×C8—42no—
674C2×C8—42no—
675C2×C8—42no—
676C2×C8—42no—
677C4⋊C4—22no—
678C4⋊C4—24no—
679C4⋊C4—22no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—41no—
693C4⋊C4—41no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—42no—
697C4⋊C4—42no—
698C4⋊C4—41no—
699C4⋊C4—41no—
700C4⋊C4—42no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C4⋊C4—42no—
704C4⋊C4—42no—
705C22⋊C4—24no—
706C22⋊C4—24no—
707C22⋊C4—24no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—42no—
721C42—24no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—42no—
727C42—42no—
728C42—42no—
729C42—42no—
730C42—42no—
731C42—42no—
732C42—42no—
733C42—42no—
734C42—42no—
735C42—42no—
736C42—42no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—42no—
748C23—41no—
749C23—42no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23C4×C4⋊C411yescharacteristic
760C23#38011yescharacteristic
761C23#38411yescharacteristic
762C23#38511yescharacteristic
763C23#38511yescharacteristic
764C23#38511yescharacteristic
765C23#38511yescharacteristic
766C23#38611yescharacteristic
767C23#38611yescharacteristic
768C23#38711yescharacteristic
769C23#38711yescharacteristic
770C23#38811yescharacteristic
771C23#38811yescharacteristic
772C23#38911yescharacteristic
773C23#38911yescharacteristic
774C23#38911yescharacteristic
775C23#38911yescharacteristic
776C23#39011yescharacteristic
777C23#39011yescharacteristic
778C23#39211yescharacteristic
779C23#39211yescharacteristic
780C23#39211yescharacteristic
781C23#39411yescharacteristic
782C23#39411yescharacteristic
783C23#39411yescharacteristic
784C23#39511yescharacteristic
785C23#39511yescharacteristic
786C23#39611yescharacteristic
787C23#39611yescharacteristic
788C23#39711yescharacteristic
789C23#39811yescharacteristic
790C23#39811yescharacteristic
791C23#39811yescharacteristic
792C23#39911yescharacteristic
793C23#39911yescharacteristic
794C2×C4—48no—
795C2×C4—48no—
796C2×C4—48no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—84no—
806C2×C4—84no—
807C2×C4—84no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4—82no—
813C2×C4—82no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4—84no—
817C2×C4—84no—
818C2×C4—82no—
819C2×C4—84no—
820C2×C4—82no—
821C2×C4—82no—
822C2×C4—82no—
823C2×C4—82no—
824C2×C4—82no—
825C2×C4C2×#9511yescharacteristic
826C2×C4C4×C22⋊C411yescharacteristic
827C2×C4C4×C22⋊C411yescharacteristic
828C2×C4C4×C4⋊C411yescharacteristic
829C2×C4C4×C4⋊C411yescharacteristic
830C2×C4C4×C4⋊C411yescharacteristic
831C2×C4#37911yescharacteristic
832C2×C4#38011yescharacteristic
833C2×C4#38011yescharacteristic
834C2×C4#38011yescharacteristic
835C2×C4#38011yescharacteristic
836C2×C4#38011yescharacteristic
837C2×C4#38111yescharacteristic
838C2×C4#38211yescharacteristic
839C2×C4#38211yescharacteristic
840C2×C4#38411yescharacteristic
841C2×C4#38511yescharacteristic
842C2×C4#38511yescharacteristic
843C2×C4#38511yescharacteristic
844C2×C4#38511yescharacteristic
845C2×C4#38511yescharacteristic
846C2×C4#38511yescharacteristic
847C2×C4#38511yescharacteristic
848C2×C4#38511yescharacteristic
849C2×C4#38611yescharacteristic
850C2×C4#38611yescharacteristic
851C2×C4#38611yescharacteristic
852C2×C4#38611yescharacteristic
853C2×C4#38611yescharacteristic
854C2×C4#38611yescharacteristic
855C2×C4#38711yescharacteristic
856C2×C4#38711yescharacteristic
857C2×C4#38711yescharacteristic
858C2×C4#38711yescharacteristic
859C2×C4#38711yescharacteristic
860C2×C4#38711yescharacteristic
861C2×C4#38711yescharacteristic
862C2×C4#38711yescharacteristic
863C2×C4#38711yescharacteristic
864C2×C4#38711yescharacteristic
865C2×C4#38711yescharacteristic
866C2×C4#38711yescharacteristic
867C2×C4#38711yescharacteristic
868C2×C4#38711yescharacteristic
869C2×C4#38811yescharacteristic
870C2×C4#38811yescharacteristic
871C2×C4#38811yescharacteristic
872C2×C4#38811yescharacteristic
873C2×C4#38811yescharacteristic
874C2×C4#38811yescharacteristic
875C2×C4#38911yescharacteristic
876C2×C4#38911yescharacteristic
877C2×C4#38911yescharacteristic
878C2×C4#38911yescharacteristic
879C2×C4#38911yescharacteristic
880C2×C4#38911yescharacteristic
881C2×C4#38911yescharacteristic
882C2×C4#38911yescharacteristic
883C2×C4#38911yescharacteristic
884C2×C4#38911yescharacteristic
885C2×C4#38911yescharacteristic
886C2×C4#38911yescharacteristic
887C2×C4#39011yescharacteristic
888C2×C4#39011yescharacteristic
889C2×C4#39111yescharacteristic
890C2×C4#39111yescharacteristic
891C2×C4#39111yescharacteristic
892C2×C4#39111yescharacteristic
893C2×C4#39111yescharacteristic
894C2×C4#39111yescharacteristic
895C2×C4#39111yescharacteristic
896C2×C4#39111yescharacteristic
897C2×C4#39211yescharacteristic
898C2×C4#39311yescharacteristic
899C2×C4#39311yescharacteristic
900C2×C4#39311yescharacteristic
901C2×C4#39311yescharacteristic
902C2×C4#39411yescharacteristic
903C2×C4#39411yescharacteristic
904C2×C4#39411yescharacteristic
905C2×C4#39411yescharacteristic
906C2×C4#39411yescharacteristic
907C2×C4#39511yescharacteristic
908C2×C4#39511yescharacteristic
909C2×C4#39511yescharacteristic
910C2×C4#39511yescharacteristic
911C2×C4#39511yescharacteristic
912C2×C4#39511yescharacteristic
913C2×C4#39611yescharacteristic
914C2×C4#39611yescharacteristic
915C2×C4#39611yescharacteristic
916C2×C4#39611yescharacteristic
917C2×C4#39611yescharacteristic
918C2×C4#39611yescharacteristic
919C2×C4#39711yescharacteristic
920C2×C4#39711yescharacteristic
921C2×C4#39711yescharacteristic
922C2×C4#39811yescharacteristic
923C2×C4#39811yescharacteristic
924C2×C4#39811yescharacteristic
925C2×C4#39811yescharacteristic
926C2×C4#39811yescharacteristic
927C2×C4#39811yescharacteristic
928C2×C4#39811yescharacteristic
929C2×C4#39811yescharacteristic
930C2×C4#39811yescharacteristic
931C2×C4#39811yescharacteristic
932C2×C4#39811yescharacteristic
933C2×C4#39811yescharacteristic
934C2×C4#39811yescharacteristic
935C2×C4#39911yescharacteristic
936C2×C4#39911yescharacteristic
937C2×C4#40011yescharacteristic
938C2×C4#40011yescharacteristic
939C2×C4#40011yescharacteristic
940C2×C4#40011yescharacteristic
941C2×C4#40011yescharacteristic
942C2×C4#40011yescharacteristic
943C2×C4#40011yescharacteristic
944C2×C4#40011yescharacteristic
945C8—28no—
946C8—44no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—22no—
968C22—22no—
969C22—22no—
970C22—22no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—41no—
976C22—41no—
977C22—41no—
978C22—41no—
979C22—41no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—41no—
985C22—41no—
986C22—41no—
987C22C4⋊#9511yescharacteristic
988C22#143611yescharacteristic
989C22#143611yescharacteristic
990C22#143811yescharacteristic
991C22#143911yescharacteristic
992C22#143911yescharacteristic
993C22#143911yescharacteristic
994C22#144111yescharacteristic
995C22#144111yescharacteristic
996C22#144111yescharacteristic
997C22#144211yescharacteristic
998C22#144411yescharacteristic
999C22#144411yescharacteristic
1000C22#144411yescharacteristic
1001C22#144511yescharacteristic
1002C22#200812yes—
1003C22#200912yes—
1004C4—84no—
1005C4—84no—
1006C4—84no—
1007C4—82no—
1008C4—82no—
1009C4—84no—
1010C4C22⋊#9511yescharacteristic
1011C4C4⋊#9511yescharacteristic
1012C4#143611yescharacteristic
1013C4#143611yescharacteristic
1014C4#143911yescharacteristic
1015C4#144111yescharacteristic
1016C4#144111yescharacteristic
1017C4#144111yescharacteristic
1018C4#144111yescharacteristic
1019C4#144111yescharacteristic
1020C4#144211yescharacteristic
1021C4#144211yescharacteristic
1022C4#144211yescharacteristic
1023C4#144411yescharacteristic
1024C4#144511yescharacteristic
1025C4#144611yescharacteristic
1026C2—21no—
1027C2—21no—
1028C2—21no—
1029C2—21no—
1030C2—21no—
1031C2—21no—
1032C2—21no—
1033C2—21no—
1034C2—21no—
1035C2—21no—
1036C2—21no—
1037C2—21no—
1038C2#755711yescharacteristic
1039C2#1103011yescharacteristic
1040C2#1103111yescharacteristic
1041C2#1111712yes—
1042C2#1133312yes—
subgroupG/H
center, socleC23#392
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
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
20. C2×#428C4semidirect
25. C2×#344C4semidirect
37. #1733C4semidirect
662. M16#95semidirect

Maximal subgroups

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

subgroupindex
C22×#4282
C22×#3442
C2×#17402
#203472
C2×#17362
C2×#17332
#137952