Finite Group Databasebeta

← #123987

Subgroups — #123987

Order 512.

1806 conjugacy classes of subgroups.

The subgroup lattice has 998 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×#1733C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6C22×#339C211yesmaximal, characteristic
7#13756C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C22×#117C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C42C2211yescharacteristic
15#2911—22no—
16#2911—22no—
17#2911—22no—
18#2911—22no—
19C2×#428—22no—
20C2×#428C414yescomplemented
21C2×#427—22no—
22C2×#344—22no—
23C2×#344—22no—
24C2×#344C414yescomplemented
25#1740—22no—
26#1740—22no—
27C2×#342—22no—
28#1733—22no—
29#1733—22no—
30C2×#339—22no—
31C2×#339—22no—
32C2×#339—22no—
33C2×#339—22no—
34C2×#339—22no—
35C2×#339—22no—
36C2×#339C414yescomplemented
37C4⋊#95—22no—
38C22⋊#95—22no—
39C4×#95—22no—
40C24×C4—21no—
41C24×C4C2311yescharacteristic
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×M16C2×C412yes—
61C22×M16C2×C412yes—
62C22×M16C2×C412yes—
63C22×M16C2×C412yes—
64C22×M16D412yes—
65C22×M16D412yes—
66C22×M16D412yes—
67C22×M16D412yes—
68C22×M16Q812yes—
69C22×M16Q812yes—
70C23×C8—21no—
71C23×C8—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×#117C2×C412yes—
112C2×#117C2×C412yes—
113C2×#117C2×C412yes—
114C2×#117D412yes—
115C2×#117D412yes—
116C2×#117D412yes—
117C2×#117D412yes—
118C2×#117Q812yes—
119C2×#117Q812yes—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4C2×C412yes—
123C22×C4⋊C4D412yes—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4D412yes—
128C22×C42—21no—
129C22×C42—21no—
130C22×C42—21no—
131C22×C42—21no—
132C22×C42—21no—
133C22×C42—21no—
134C22×C42—21no—
135C22×C42—21no—
136C22×C42—21no—
137C22×C42—21no—
138C22×C42—21no—
139C22×C42—21no—
140C22×C42—21no—
141C22×C42—21no—
142C22×C42—21no—
143C22×C42C2×C412yes—
144C22×C42D412yes—
145C22×C42Q812yes—
146#428—28no—
147#428—28no—
148#428—28no—
149#428—28no—
150#427—28no—
151#427—28no—
152C2×#107—24no—
153C2×#106—24no—
154C2×#95—28no—
155#344—28no—
156#342—28no—
157#339—28no—
158#339—28no—
159#339—28no—
160C25C2×D411yescharacteristic
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—22no—
165C23×C4—22no—
166C23×C4—22no—
167C23×C4—48no—
168C23×C4—41no—
169C23×C4—41no—
170C23×C4—41no—
171C23×C4—41no—
172C23×C4—41no—
173C23×C4C22×C411yescharacteristic
174C23×C4C22×C411yescharacteristic
175C23×C4C22×C411yescharacteristic
176C23×C4C2×D411yescharacteristic
177C23×C4C2×D411yescharacteristic
178C23×C4C2×D411yescharacteristic
179C23×C4C2×D411yescharacteristic
180C23×C4C2×D411yescharacteristic
181C23×C4C2×D411yescharacteristic
182C23×C4C2×D411yescharacteristic
183C23×C4C2×D411yescharacteristic
184C23×C4C2×D411yescharacteristic
185C23×C4C2×D411yescharacteristic
186C23×C4C2×Q811yescharacteristic
187C23×C4C2×Q811yescharacteristic
188C23×C4C2×Q811yescharacteristic
189C23×C4C2×Q811yescharacteristic
190C23×C4C2×Q811yescharacteristic
191C23×C4#4111yescharacteristic
192C23×C4#4111yescharacteristic
193C23×C4#4111yescharacteristic
194C23×C4#4111yescharacteristic
195C23×C4#4111yescharacteristic
196C23×C4#4111yescharacteristic
197C23×C4#4111yescharacteristic
198C23×C4#4111yescharacteristic
199C23×C4#4111yescharacteristic
200C23×C4#4111yescharacteristic
201C23×C4#4111yescharacteristic
202C23×C4#4111yescharacteristic
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—41no—
240C2×M16—41no—
241C2×M16—41no—
242C2×M16—41no—
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×M16C4214yes—
252C2×M16C22⋊C414yes—
253C2×M16C22⋊C414yes—
254C2×M16C22⋊C414yes—
255C2×M16C4⋊C414yes—
256C2×M16C4⋊C414yes—
257C2×M16C4⋊C414yes—
258C2×M16C4⋊C414yes—
259C22×C8—22no—
260C22×C8—22no—
261C22×C8—22no—
262C22×C8—22no—
263C22×C8—22no—
264C22×C8—22no—
265C22×C8—22no—
266C22×C8—22no—
267C22×C8—22no—
268C22×C8—22no—
269C22×C8—41no—
270C22×C8—41no—
271C22×C8—41no—
272C22×C8—41no—
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—41no—
307#117—41no—
308#117—41no—
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#117C4⋊C414yes—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
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—41no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—41no—
355C2×C4⋊C4—41no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—41no—
359C2×C4⋊C4C22⋊C414yes—
360C2×C4⋊C4C22⋊C414yes—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—41no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—41no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4C4⋊C414yes—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—41no—
410C2×C42—41no—
411C2×C42—41no—
412C2×C42—41no—
413C2×C42—41no—
414C2×C42—41no—
415C2×C42—41no—
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—
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—
436C2×C42C4⋊C414yes—
437#107—216no—
438#106—216no—
439#95—416no—
440C24—44no—
441C24C2×C4⋊C411yescharacteristic
442C24C4×D411yescharacteristic
443C24C4×D411yescharacteristic
444C24#12011yescharacteristic
445C24#12011yescharacteristic
446C24#12111yescharacteristic
447C24#12111yescharacteristic
448C24#12111yescharacteristic
449C24#12111yescharacteristic
450C24C22⋊Q811yescharacteristic
451C24C22⋊Q811yescharacteristic
452C24#12311yescharacteristic
453C24#12311yescharacteristic
454C24#12711yescharacteristic
455C24C4⋊Q811yescharacteristic
456C22×C4—28no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—48no—
462C22×C4—48no—
463C22×C4—44no—
464C22×C4—48no—
465C22×C4—48no—
466C22×C4—48no—
467C22×C4—48no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—48no—
475C22×C4—48no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—84no—
486C22×C4—84no—
487C22×C4C2×C4211yescharacteristic
488C22×C4C2×C22⋊C411yescharacteristic
489C22×C4C2×C22⋊C411yescharacteristic
490C22×C4C2×C22⋊C411yescharacteristic
491C22×C4C2×C22⋊C411yescharacteristic
492C22×C4C2×C22⋊C411yescharacteristic
493C22×C4C2×C4⋊C411yescharacteristic
494C22×C4C2×C4⋊C411yescharacteristic
495C22×C4C2×C4⋊C411yescharacteristic
496C22×C4C2×C4⋊C411yescharacteristic
497C22×C4C2×C4⋊C411yescharacteristic
498C22×C4C2×C4⋊C411yescharacteristic
499C22×C4#11711yescharacteristic
500C22×C4#11711yescharacteristic
501C22×C4#11711yescharacteristic
502C22×C4#11711yescharacteristic
503C22×C4#11711yescharacteristic
504C22×C4#11711yescharacteristic
505C22×C4C4×D411yescharacteristic
506C22×C4C4×D411yescharacteristic
507C22×C4C4×D411yescharacteristic
508C22×C4C4×D411yescharacteristic
509C22×C4C4×D411yescharacteristic
510C22×C4C4×D411yescharacteristic
511C22×C4C4×D411yescharacteristic
512C22×C4C4×D411yescharacteristic
513C22×C4C4×D411yescharacteristic
514C22×C4C4×D411yescharacteristic
515C22×C4C4×D411yescharacteristic
516C22×C4C4×D411yescharacteristic
517C22×C4C4×D411yescharacteristic
518C22×C4C4×D411yescharacteristic
519C22×C4C4×Q811yescharacteristic
520C22×C4C4×Q811yescharacteristic
521C22×C4C4×Q811yescharacteristic
522C22×C4C4×Q811yescharacteristic
523C22×C4C4×Q811yescharacteristic
524C22×C4C4×Q811yescharacteristic
525C22×C4C4×Q811yescharacteristic
526C22×C4C4×Q811yescharacteristic
527C22×C4#12011yescharacteristic
528C22×C4#12011yescharacteristic
529C22×C4#12011yescharacteristic
530C22×C4#12011yescharacteristic
531C22×C4#12011yescharacteristic
532C22×C4#12011yescharacteristic
533C22×C4#12111yescharacteristic
534C22×C4#12111yescharacteristic
535C22×C4#12111yescharacteristic
536C22×C4#12111yescharacteristic
537C22×C4#12111yescharacteristic
538C22×C4#12111yescharacteristic
539C22×C4#12111yescharacteristic
540C22×C4#12111yescharacteristic
541C22×C4#12111yescharacteristic
542C22×C4#12111yescharacteristic
543C22×C4#12111yescharacteristic
544C22×C4#12111yescharacteristic
545C22×C4#12111yescharacteristic
546C22×C4#12111yescharacteristic
547C22×C4#12111yescharacteristic
548C22×C4#12111yescharacteristic
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×C4C22⋊Q811yescharacteristic
563C22×C4C22⋊Q811yescharacteristic
564C22×C4C22⋊Q811yescharacteristic
565C22×C4C22⋊Q811yescharacteristic
566C22×C4C22⋊Q811yescharacteristic
567C22×C4C22⋊Q811yescharacteristic
568C22×C4C22⋊Q811yescharacteristic
569C22×C4C22⋊Q811yescharacteristic
570C22×C4C22⋊Q811yescharacteristic
571C22×C4C22⋊Q811yescharacteristic
572C22×C4C22⋊Q811yescharacteristic
573C22×C4C22⋊Q811yescharacteristic
574C22×C4C22⋊Q811yescharacteristic
575C22×C4#12311yescharacteristic
576C22×C4#12311yescharacteristic
577C22×C4#12311yescharacteristic
578C22×C4#12311yescharacteristic
579C22×C4#12311yescharacteristic
580C22×C4#12311yescharacteristic
581C22×C4#12311yescharacteristic
582C22×C4#12311yescharacteristic
583C22×C4#12311yescharacteristic
584C22×C4#12311yescharacteristic
585C22×C4#12311yescharacteristic
586C22×C4#12311yescharacteristic
587C22×C4#12311yescharacteristic
588C22×C4#12311yescharacteristic
589C22×C4#12411yescharacteristic
590C22×C4#12411yescharacteristic
591C22×C4#12411yescharacteristic
592C22×C4#12411yescharacteristic
593C22×C4#12411yescharacteristic
594C22×C4#12411yescharacteristic
595C22×C4#12411yescharacteristic
596C22×C4#12411yescharacteristic
597C22×C4#12511yescharacteristic
598C22×C4#12511yescharacteristic
599C22×C4#12511yescharacteristic
600C22×C4#12511yescharacteristic
601C22×C4#12511yescharacteristic
602C22×C4#12511yescharacteristic
603C22×C4#12511yescharacteristic
604C22×C4#12511yescharacteristic
605C22×C4#12511yescharacteristic
606C22×C4#12511yescharacteristic
607C22×C4#12511yescharacteristic
608C22×C4#12511yescharacteristic
609C22×C4#12611yescharacteristic
610C22×C4#12611yescharacteristic
611C22×C4#12611yescharacteristic
612C22×C4#12611yescharacteristic
613C22×C4#12611yescharacteristic
614C22×C4#12611yescharacteristic
615C22×C4#12611yescharacteristic
616C22×C4#12611yescharacteristic
617C22×C4#12711yescharacteristic
618C22×C4C4⋊Q811yescharacteristic
619C22×C4C4⋊Q811yescharacteristic
620C22×C4C4⋊Q811yescharacteristic
621C22×C4C4⋊Q811yescharacteristic
622C22×C4C4⋊Q811yescharacteristic
623C22×C4C4⋊Q811yescharacteristic
624C22×C4C4⋊Q811yescharacteristic
625C22×C4C4⋊Q811yescharacteristic
626C22×C4C4⋊Q811yescharacteristic
627M16—24no—
628M16—24no—
629M16—24no—
630M16—24no—
631M16—24no—
632M16—24no—
633M16—24no—
634M16—24no—
635M16—24no—
636M16—42no—
637M16—42no—
638M16—42no—
639M16—42no—
640M16—42no—
641M16—42no—
642M16#9518yescomplemented
643C2×C8—24no—
644C2×C8—24no—
645C2×C8—24no—
646C2×C8—24no—
647C2×C8—24no—
648C2×C8—24no—
649C2×C8—24no—
650C2×C8—24no—
651C2×C8—42no—
652C2×C8—42no—
653C2×C8—42no—
654C2×C8—42no—
655C2×C8—42no—
656C2×C8—42no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C42—24no—
690C42—24no—
691C42—24no—
692C42—42no—
693C42—42no—
694C42—42no—
695C42—42no—
696C42—42no—
697C42—42no—
698C42—42no—
699C42—42no—
700C42—42no—
701C42—42no—
702C42—42no—
703C42—42no—
704C42—42no—
705C42—42no—
706C42—42no—
707C42—42no—
708C42—42no—
709C42—42no—
710C42—42no—
711C42—42no—
712C42—42no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23C4×C4⋊C411yescharacteristic
729C23#38011yescharacteristic
730C23#38411yescharacteristic
731C23#38511yescharacteristic
732C23#38511yescharacteristic
733C23#38511yescharacteristic
734C23#38511yescharacteristic
735C23#38611yescharacteristic
736C23#38611yescharacteristic
737C23#38711yescharacteristic
738C23#38711yescharacteristic
739C23#38811yescharacteristic
740C23#38811yescharacteristic
741C23#38911yescharacteristic
742C23#38911yescharacteristic
743C23#38911yescharacteristic
744C23#38911yescharacteristic
745C23#39011yescharacteristic
746C23#39011yescharacteristic
747C23#39211yescharacteristic
748C23#39211yescharacteristic
749C23#39211yescharacteristic
750C23#39411yescharacteristic
751C23#39411yescharacteristic
752C23#39411yescharacteristic
753C23#39511yescharacteristic
754C23#39511yescharacteristic
755C23#39611yescharacteristic
756C23#39611yescharacteristic
757C23#39711yescharacteristic
758C23#39811yescharacteristic
759C23#39811yescharacteristic
760C23#39811yescharacteristic
761C23#39911yescharacteristic
762C23#39911yescharacteristic
763C2×C4—28no—
764C2×C4—48no—
765C2×C4—44no—
766C2×C4—48no—
767C2×C4—48no—
768C2×C4—48no—
769C2×C4—48no—
770C2×C4—48no—
771C2×C4—44no—
772C2×C4—48no—
773C2×C4—48no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—84no—
779C2×C4—84no—
780C2×C4—84no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4—84no—
787C2×C4—84no—
788C2×C4C2×#9511yescharacteristic
789C2×C4C4×C22⋊C411yescharacteristic
790C2×C4C4×C22⋊C411yescharacteristic
791C2×C4C4×C4⋊C411yescharacteristic
792C2×C4C4×C4⋊C411yescharacteristic
793C2×C4C4×C4⋊C411yescharacteristic
794C2×C4#37911yescharacteristic
795C2×C4#38011yescharacteristic
796C2×C4#38011yescharacteristic
797C2×C4#38011yescharacteristic
798C2×C4#38011yescharacteristic
799C2×C4#38011yescharacteristic
800C2×C4#38111yescharacteristic
801C2×C4#38211yescharacteristic
802C2×C4#38211yescharacteristic
803C2×C4#38411yescharacteristic
804C2×C4#38511yescharacteristic
805C2×C4#38511yescharacteristic
806C2×C4#38511yescharacteristic
807C2×C4#38511yescharacteristic
808C2×C4#38511yescharacteristic
809C2×C4#38511yescharacteristic
810C2×C4#38511yescharacteristic
811C2×C4#38511yescharacteristic
812C2×C4#38611yescharacteristic
813C2×C4#38611yescharacteristic
814C2×C4#38611yescharacteristic
815C2×C4#38611yescharacteristic
816C2×C4#38611yescharacteristic
817C2×C4#38611yescharacteristic
818C2×C4#38711yescharacteristic
819C2×C4#38711yescharacteristic
820C2×C4#38711yescharacteristic
821C2×C4#38711yescharacteristic
822C2×C4#38711yescharacteristic
823C2×C4#38711yescharacteristic
824C2×C4#38711yescharacteristic
825C2×C4#38711yescharacteristic
826C2×C4#38711yescharacteristic
827C2×C4#38711yescharacteristic
828C2×C4#38711yescharacteristic
829C2×C4#38711yescharacteristic
830C2×C4#38711yescharacteristic
831C2×C4#38711yescharacteristic
832C2×C4#38811yescharacteristic
833C2×C4#38811yescharacteristic
834C2×C4#38811yescharacteristic
835C2×C4#38811yescharacteristic
836C2×C4#38811yescharacteristic
837C2×C4#38811yescharacteristic
838C2×C4#38911yescharacteristic
839C2×C4#38911yescharacteristic
840C2×C4#38911yescharacteristic
841C2×C4#38911yescharacteristic
842C2×C4#38911yescharacteristic
843C2×C4#38911yescharacteristic
844C2×C4#38911yescharacteristic
845C2×C4#38911yescharacteristic
846C2×C4#38911yescharacteristic
847C2×C4#38911yescharacteristic
848C2×C4#38911yescharacteristic
849C2×C4#38911yescharacteristic
850C2×C4#39011yescharacteristic
851C2×C4#39011yescharacteristic
852C2×C4#39111yescharacteristic
853C2×C4#39111yescharacteristic
854C2×C4#39111yescharacteristic
855C2×C4#39111yescharacteristic
856C2×C4#39111yescharacteristic
857C2×C4#39111yescharacteristic
858C2×C4#39111yescharacteristic
859C2×C4#39111yescharacteristic
860C2×C4#39211yescharacteristic
861C2×C4#39311yescharacteristic
862C2×C4#39311yescharacteristic
863C2×C4#39311yescharacteristic
864C2×C4#39311yescharacteristic
865C2×C4#39411yescharacteristic
866C2×C4#39411yescharacteristic
867C2×C4#39411yescharacteristic
868C2×C4#39411yescharacteristic
869C2×C4#39411yescharacteristic
870C2×C4#39511yescharacteristic
871C2×C4#39511yescharacteristic
872C2×C4#39511yescharacteristic
873C2×C4#39511yescharacteristic
874C2×C4#39511yescharacteristic
875C2×C4#39511yescharacteristic
876C2×C4#39611yescharacteristic
877C2×C4#39611yescharacteristic
878C2×C4#39611yescharacteristic
879C2×C4#39611yescharacteristic
880C2×C4#39611yescharacteristic
881C2×C4#39611yescharacteristic
882C2×C4#39711yescharacteristic
883C2×C4#39711yescharacteristic
884C2×C4#39711yescharacteristic
885C2×C4#39811yescharacteristic
886C2×C4#39811yescharacteristic
887C2×C4#39811yescharacteristic
888C2×C4#39811yescharacteristic
889C2×C4#39811yescharacteristic
890C2×C4#39811yescharacteristic
891C2×C4#39811yescharacteristic
892C2×C4#39811yescharacteristic
893C2×C4#39811yescharacteristic
894C2×C4#39811yescharacteristic
895C2×C4#39811yescharacteristic
896C2×C4#39811yescharacteristic
897C2×C4#39811yescharacteristic
898C2×C4#39911yescharacteristic
899C2×C4#39911yescharacteristic
900C2×C4#40011yescharacteristic
901C2×C4#40011yescharacteristic
902C2×C4#40011yescharacteristic
903C2×C4#40011yescharacteristic
904C2×C4#40011yescharacteristic
905C2×C4#40011yescharacteristic
906C2×C4#40011yescharacteristic
907C2×C4#40011yescharacteristic
908C8—28no—
909C8—44no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—22no—
916C22—22no—
917C22—22no—
918C22—22no—
919C22—22no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22C4⋊#9511yescharacteristic
945C22#143611yescharacteristic
946C22#143611yescharacteristic
947C22#143811yescharacteristic
948C22#143911yescharacteristic
949C22#143911yescharacteristic
950C22#143911yescharacteristic
951C22#144111yescharacteristic
952C22#144111yescharacteristic
953C22#144111yescharacteristic
954C22#144211yescharacteristic
955C22#144411yescharacteristic
956C22#144411yescharacteristic
957C22#144411yescharacteristic
958C22#144511yescharacteristic
959C22#190614yes—
960C4—48no—
961C4—84no—
962C4—84no—
963C4—84no—
964C4—84no—
965C4C22⋊#9511yescharacteristic
966C4C4⋊#9511yescharacteristic
967C4#143611yescharacteristic
968C4#143611yescharacteristic
969C4#143911yescharacteristic
970C4#144111yescharacteristic
971C4#144111yescharacteristic
972C4#144111yescharacteristic
973C4#144111yescharacteristic
974C4#144111yescharacteristic
975C4#144211yescharacteristic
976C4#144211yescharacteristic
977C4#144211yescharacteristic
978C4#144411yescharacteristic
979C4#144511yescharacteristic
980C4#144611yescharacteristic
981C2—21no—
982C2—21no—
983C2—21no—
984C2—21no—
985C2—21no—
986C2—21no—
987C2—21no—
988C2—21no—
989C2—21no—
990C2—21no—
991C2—21no—
992C2—21no—
993C2#755711yescharacteristic
994C2#1089512yes—
995C2#1101912yes—
996C2#1121512yes—
subgroupG/H
centerC22×C4#121
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
socleC23#386
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ 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
24. C2×#344C4semidirect
36. C2×#339C4semidirect
642. M16#95semidirect

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
C22×#3392
#137562