Finite Group Databasebeta

← #123958

Subgroups — #123958

Order 512.

1670 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2905C211yesmaximal, characteristic
2C22×#344C211yesmaximal, characteristic
3C22×#343C211yesmaximal, characteristic
4C2×#1736C211yesmaximal, characteristic
5C2×#1736C211yesmaximal, characteristic
6C2×#1733C211yesmaximal, characteristic
7C22×#338C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C23×M16C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C22×#117C2211yescharacteristic
13C22×#117C2211yescharacteristic
14C23×C4⋊C4C2211yescharacteristic
15#2905—22no—
16#2905—22no—
17#2905—22no—
18#2905C414yescomplemented
19C2×#424—22no—
20C2×#424—22no—
21C2×#423—22no—
22C2×#344—22no—
23C2×#344—22no—
24C2×#344—22no—
25C2×#343—22no—
26C2×#343—22no—
27C2×#343—22no—
28#1736—22no—
29#1736—22no—
30#1736—22no—
31#1736—22no—
32C2×#340—22no—
33C2×#340C414yescomplemented
34#1733—22no—
35#1733C414yescomplemented
36C2×#339—22no—
37C2×#338—22no—
38C2×#338—22no—
39C2×#338—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×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×M16—21no—
83C22×M16—21no—
84C22×M16—21no—
85C22×M16—21no—
86C22×M16—21no—
87C22×M16—21no—
88C22×M16C2×C412yes—
89C22×M16C2×C412yes—
90C22×M16C2×C412yes—
91C22×M16D412yes—
92C22×M16D412yes—
93C22×M16D412yes—
94C22×M16D412yes—
95C22×M16D412yes—
96C22×M16Q812yes—
97C22×M16Q812yes—
98C23×C8—21no—
99C23×C8—21no—
100C23×C8C2×C412yes—
101C23×C8D412yes—
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×#117C2×C412yes—
120C2×#117D412yes—
121C2×#117D412yes—
122C2×#117D412yes—
123C2×#117D412yes—
124C2×#117Q812yes—
125C2×#117Q812yes—
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⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4C2×C412yes—
139C22×C4⋊C4C2×C412yes—
140C22×C4⋊C4D412yes—
141C22×C4⋊C4Q812yes—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C42—21no—
145C22×C42—21no—
146#424—28no—
147#424—28no—
148#424—28no—
149#424—28no—
150#423—28no—
151#423—28no—
152C2×C4⋊C8—28no—
153#344—28no—
154#343—28no—
155#340—28no—
156#340—28no—
157#339—28no—
158#338—28no—
159C25#4111yescharacteristic
160C23×C4—22no—
161C23×C4—22no—
162C23×C4—22no—
163C23×C4—22no—
164C23×C4—41no—
165C23×C4—41no—
166C23×C4—41no—
167C23×C4—41no—
168C23×C4—41no—
169C23×C4—84no—
170C23×C4C22×C411yescharacteristic
171C23×C4C22×C411yescharacteristic
172C23×C4C22×C411yescharacteristic
173C23×C4C2×D411yescharacteristic
174C23×C4C2×D411yescharacteristic
175C23×C4C2×D411yescharacteristic
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×Q811yescharacteristic
185C23×C4C2×Q811yescharacteristic
186C23×C4C2×Q811yescharacteristic
187C23×C4C2×Q811yescharacteristic
188C23×C4C2×Q811yescharacteristic
189C23×C4#4111yescharacteristic
190C23×C4#4111yescharacteristic
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
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—22no—
251C2×M16—22no—
252C2×M16—22no—
253C2×M16—22no—
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×M16—41no—
299C2×M16—41no—
300C2×M16—41no—
301C2×M16—41no—
302C2×M16—41no—
303C2×M16—41no—
304C2×M16—41no—
305C2×M16—41no—
306C2×M16—41no—
307C2×M16—41no—
308C2×M16—41no—
309C2×M16—41no—
310C2×M16C22⋊C414yes—
311C2×M16C4⋊C414yes—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8—22no—
318C22×C8—22no—
319C22×C8—22no—
320C22×C8—22no—
321C22×C8—22no—
322C22×C8—22no—
323C22×C8—22no—
324C22×C8—22no—
325C22×C8—22no—
326C22×C8—22no—
327C22×C8—22no—
328C22×C8—22no—
329C22×C8—22no—
330C22×C8—41no—
331C22×C8—41no—
332C22×C8—41no—
333C22×C8—41no—
334C22×C8—41no—
335C22×C8—41no—
336C22×C8—41no—
337C22×C8—41no—
338C22×C8C22⋊C414yes—
339C22×C8C4⋊C414yes—
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—22no—
351#117—22no—
352#117—22no—
353#117—22no—
354#117—22no—
355#117—22no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117—22no—
360#117—22no—
361#117—41no—
362#117—41no—
363#117—41no—
364#117—41no—
365#117—41no—
366#117—41no—
367#117C22⋊C414yes—
368#117C22⋊C414yes—
369#117C4⋊C414yes—
370#117C4⋊C414yes—
371#117C4⋊C414yes—
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—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—22no—
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⋊C4—41no—
401C2×C4⋊C4—41no—
402C2×C4⋊C4—41no—
403C2×C4⋊C4—41no—
404C2×C4⋊C4—41no—
405C2×C4⋊C4—41no—
406C2×C4⋊C4—41no—
407C2×C4⋊C4—41no—
408C2×C4⋊C4C4214yes—
409C2×C4⋊C4C22⋊C414yes—
410C2×C4⋊C4C4⋊C414yes—
411C2×C4⋊C4C4⋊C414yes—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—41no—
422C2×C22⋊C4—41no—
423C2×C22⋊C4—41no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—41no—
434C2×C42—41no—
435C2×C42—41no—
436C4⋊C8—232no—
437C24—42no—
438C24—42no—
439C24#11711yescharacteristic
440C24C4×D411yescharacteristic
441C24C4×D411yescharacteristic
442C24#12111yescharacteristic
443C24C22⋊Q811yescharacteristic
444C24C22⋊Q811yescharacteristic
445C24C22⋊Q811yescharacteristic
446C24#12311yescharacteristic
447C24#12311yescharacteristic
448C24#12311yescharacteristic
449C24#12311yescharacteristic
450C24#12511yescharacteristic
451C24#12511yescharacteristic
452C24#12611yescharacteristic
453C24#12611yescharacteristic
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
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—82no—
468C22×C4—82no—
469C22×C4—82no—
470C22×C4—82no—
471C22×C4—84no—
472C22×C4—84no—
473C22×C4—84no—
474C22×C4—84no—
475C22×C4—84no—
476C22×C4—84no—
477C22×C4—84no—
478C22×C4C2×C4211yescharacteristic
479C22×C4C2×C22⋊C411yescharacteristic
480C22×C4C2×C22⋊C411yescharacteristic
481C22×C4C2×C22⋊C411yescharacteristic
482C22×C4C2×C22⋊C411yescharacteristic
483C22×C4C2×C22⋊C411yescharacteristic
484C22×C4C2×C4⋊C411yescharacteristic
485C22×C4C2×C4⋊C411yescharacteristic
486C22×C4C2×C4⋊C411yescharacteristic
487C22×C4C2×C4⋊C411yescharacteristic
488C22×C4C2×C4⋊C411yescharacteristic
489C22×C4C2×C4⋊C411yescharacteristic
490C22×C4C2×C4⋊C411yescharacteristic
491C22×C4#11711yescharacteristic
492C22×C4#11711yescharacteristic
493C22×C4#11711yescharacteristic
494C22×C4#11711yescharacteristic
495C22×C4#11711yescharacteristic
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×D411yescharacteristic
507C22×C4C4×D411yescharacteristic
508C22×C4C4×D411yescharacteristic
509C22×C4C4×D411yescharacteristic
510C22×C4C4×Q811yescharacteristic
511C22×C4C4×Q811yescharacteristic
512C22×C4C4×Q811yescharacteristic
513C22×C4C4×Q811yescharacteristic
514C22×C4C4×Q811yescharacteristic
515C22×C4C4×Q811yescharacteristic
516C22×C4C4×Q811yescharacteristic
517C22×C4C4×Q811yescharacteristic
518C22×C4#12011yescharacteristic
519C22×C4#12011yescharacteristic
520C22×C4#12011yescharacteristic
521C22×C4#12011yescharacteristic
522C22×C4#12011yescharacteristic
523C22×C4#12011yescharacteristic
524C22×C4#12011yescharacteristic
525C22×C4#12011yescharacteristic
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×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×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×C4C22⋊Q811yescharacteristic
563C22×C4C22⋊Q811yescharacteristic
564C22×C4C22⋊Q811yescharacteristic
565C22×C4C22⋊Q811yescharacteristic
566C22×C4C22⋊Q811yescharacteristic
567C22×C4C22⋊Q811yescharacteristic
568C22×C4C22⋊Q811yescharacteristic
569C22×C4C22⋊Q811yescharacteristic
570C22×C4#12311yescharacteristic
571C22×C4#12311yescharacteristic
572C22×C4#12311yescharacteristic
573C22×C4#12311yescharacteristic
574C22×C4#12311yescharacteristic
575C22×C4#12311yescharacteristic
576C22×C4#12311yescharacteristic
577C22×C4#12311yescharacteristic
578C22×C4#12311yescharacteristic
579C22×C4#12311yescharacteristic
580C22×C4#12311yescharacteristic
581C22×C4#12311yescharacteristic
582C22×C4#12411yescharacteristic
583C22×C4#12411yescharacteristic
584C22×C4#12411yescharacteristic
585C22×C4#12411yescharacteristic
586C22×C4#12411yescharacteristic
587C22×C4#12411yescharacteristic
588C22×C4#12411yescharacteristic
589C22×C4#12411yescharacteristic
590C22×C4#12511yescharacteristic
591C22×C4#12511yescharacteristic
592C22×C4#12511yescharacteristic
593C22×C4#12511yescharacteristic
594C22×C4#12511yescharacteristic
595C22×C4#12511yescharacteristic
596C22×C4#12511yescharacteristic
597C22×C4#12511yescharacteristic
598C22×C4#12511yescharacteristic
599C22×C4#12511yescharacteristic
600C22×C4#12611yescharacteristic
601C22×C4#12611yescharacteristic
602C22×C4#12611yescharacteristic
603C22×C4#12611yescharacteristic
604C22×C4#12611yescharacteristic
605C22×C4#12611yescharacteristic
606C22×C4#12711yescharacteristic
607C22×C4#12711yescharacteristic
608C22×C4C4⋊Q811yescharacteristic
609C22×C4C4⋊Q811yescharacteristic
610C22×C4C4⋊Q811yescharacteristic
611C22×C4C4⋊Q811yescharacteristic
612C22×C4C4⋊Q811yescharacteristic
613C22×C4C4⋊Q811yescharacteristic
614C22×C4C4⋊Q811yescharacteristic
615C22×C4C4⋊Q811yescharacteristic
616C22×C4C4⋊Q811yescharacteristic
617C22×C4C4⋊Q811yescharacteristic
618M16—24no—
619M16—24no—
620M16—24no—
621M16—24no—
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—
639M16—42no—
640M16—42no—
641M16—42no—
642M16—42no—
643M16—42no—
644M16—42no—
645M16—42no—
646M16—42no—
647M16—42no—
648M16—42no—
649M16—42no—
650C2×C8—24no—
651C2×C8—24no—
652C2×C8—24no—
653C2×C8—24no—
654C2×C8—24no—
655C2×C8—24no—
656C2×C8—24no—
657C2×C8—24no—
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—
667C2×C8—42no—
668C2×C8—42no—
669C2×C8—42no—
670C2×C8—42no—
671C2×C8—42no—
672C2×C8—42no—
673C2×C8—42no—
674C2×C8—42no—
675C2×C8—42no—
676C2×C8—42no—
677C2×C8—42no—
678C4⋊C4—24no—
679C4⋊C4—24no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4#9518yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C42—24no—
703C42—24no—
704C42—24no—
705C42—24no—
706C42—24no—
707C42—42no—
708C42—42no—
709C42—42no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—41no—
731C23—42no—
732C23C4×C22⋊C411yescharacteristic
733C23#38011yescharacteristic
734C23#38111yescharacteristic
735C23#38511yescharacteristic
736C23#38511yescharacteristic
737C23#38511yescharacteristic
738C23#38511yescharacteristic
739C23#38611yescharacteristic
740C23#38611yescharacteristic
741C23#38711yescharacteristic
742C23#38711yescharacteristic
743C23#38711yescharacteristic
744C23#38711yescharacteristic
745C23#38711yescharacteristic
746C23#38711yescharacteristic
747C23#38811yescharacteristic
748C23#38811yescharacteristic
749C23#38911yescharacteristic
750C23#38911yescharacteristic
751C23#39411yescharacteristic
752C23#39511yescharacteristic
753C23#39611yescharacteristic
754C23#39611yescharacteristic
755C23#39711yescharacteristic
756C23#39711yescharacteristic
757C23#39811yescharacteristic
758C23#39811yescharacteristic
759C23#39811yescharacteristic
760C23#39811yescharacteristic
761C23#39811yescharacteristic
762C23#39911yescharacteristic
763C23#39911yescharacteristic
764C23#40011yescharacteristic
765C23#40011yescharacteristic
766C23#40011yescharacteristic
767C2×C4—28no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—84no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—82no—
776C2×C4—82no—
777C2×C4—84no—
778C2×C4—84no—
779C2×C4—84no—
780C2×C4—84no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4C2×#9511yescharacteristic
786C2×C4C4×C22⋊C411yescharacteristic
787C2×C4C4×C4⋊C411yescharacteristic
788C2×C4C4×C4⋊C411yescharacteristic
789C2×C4C4×C4⋊C411yescharacteristic
790C2×C4C4×C4⋊C411yescharacteristic
791C2×C4#37911yescharacteristic
792C2×C4#38011yescharacteristic
793C2×C4#38011yescharacteristic
794C2×C4#38011yescharacteristic
795C2×C4#38011yescharacteristic
796C2×C4#38011yescharacteristic
797C2×C4#38211yescharacteristic
798C2×C4#38211yescharacteristic
799C2×C4#38411yescharacteristic
800C2×C4#38411yescharacteristic
801C2×C4#38511yescharacteristic
802C2×C4#38511yescharacteristic
803C2×C4#38511yescharacteristic
804C2×C4#38511yescharacteristic
805C2×C4#38511yescharacteristic
806C2×C4#38511yescharacteristic
807C2×C4#38511yescharacteristic
808C2×C4#38511yescharacteristic
809C2×C4#38611yescharacteristic
810C2×C4#38611yescharacteristic
811C2×C4#38611yescharacteristic
812C2×C4#38611yescharacteristic
813C2×C4#38611yescharacteristic
814C2×C4#38611yescharacteristic
815C2×C4#38711yescharacteristic
816C2×C4#38711yescharacteristic
817C2×C4#38711yescharacteristic
818C2×C4#38711yescharacteristic
819C2×C4#38711yescharacteristic
820C2×C4#38711yescharacteristic
821C2×C4#38711yescharacteristic
822C2×C4#38711yescharacteristic
823C2×C4#38711yescharacteristic
824C2×C4#38711yescharacteristic
825C2×C4#38811yescharacteristic
826C2×C4#38811yescharacteristic
827C2×C4#38811yescharacteristic
828C2×C4#38811yescharacteristic
829C2×C4#38811yescharacteristic
830C2×C4#38811yescharacteristic
831C2×C4#38911yescharacteristic
832C2×C4#38911yescharacteristic
833C2×C4#38911yescharacteristic
834C2×C4#38911yescharacteristic
835C2×C4#38911yescharacteristic
836C2×C4#38911yescharacteristic
837C2×C4#38911yescharacteristic
838C2×C4#38911yescharacteristic
839C2×C4#38911yescharacteristic
840C2×C4#38911yescharacteristic
841C2×C4#38911yescharacteristic
842C2×C4#38911yescharacteristic
843C2×C4#38911yescharacteristic
844C2×C4#38911yescharacteristic
845C2×C4#39011yescharacteristic
846C2×C4#39011yescharacteristic
847C2×C4#39011yescharacteristic
848C2×C4#39011yescharacteristic
849C2×C4#39111yescharacteristic
850C2×C4#39111yescharacteristic
851C2×C4#39111yescharacteristic
852C2×C4#39111yescharacteristic
853C2×C4#39111yescharacteristic
854C2×C4#39111yescharacteristic
855C2×C4#39111yescharacteristic
856C2×C4#39111yescharacteristic
857C2×C4#39211yescharacteristic
858C2×C4#39211yescharacteristic
859C2×C4#39211yescharacteristic
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#39411yescharacteristic
871C2×C4#39411yescharacteristic
872C2×C4#39511yescharacteristic
873C2×C4#39511yescharacteristic
874C2×C4#39511yescharacteristic
875C2×C4#39511yescharacteristic
876C2×C4#39511yescharacteristic
877C2×C4#39511yescharacteristic
878C2×C4#39511yescharacteristic
879C2×C4#39611yescharacteristic
880C2×C4#39611yescharacteristic
881C2×C4#39611yescharacteristic
882C2×C4#39611yescharacteristic
883C2×C4#39611yescharacteristic
884C2×C4#39611yescharacteristic
885C2×C4#39711yescharacteristic
886C2×C4#39711yescharacteristic
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
905C8—44no—
906C8—44no—
907C8—44no—
908C8—44no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22C22⋊#9511yescharacteristic
950C22#143611yescharacteristic
951C22#143611yescharacteristic
952C22#143911yescharacteristic
953C22#143911yescharacteristic
954C22#144111yescharacteristic
955C22#144111yescharacteristic
956C22#144111yescharacteristic
957C22#144111yescharacteristic
958C22#144211yescharacteristic
959C22#144211yescharacteristic
960C22#144411yescharacteristic
961C22#144411yescharacteristic
962C22#144511yescharacteristic
963C22#144511yescharacteristic
964C22#190212yes—
965C22#190312yes—
966C4—48no—
967C4—84no—
968C4—84no—
969C4C4⋊#9511yescharacteristic
970C4C4⋊#9511yescharacteristic
971C4#143611yescharacteristic
972C4#143611yescharacteristic
973C4#143811yescharacteristic
974C4#143911yescharacteristic
975C4#143911yescharacteristic
976C4#144111yescharacteristic
977C4#144111yescharacteristic
978C4#144111yescharacteristic
979C4#144111yescharacteristic
980C4#144211yescharacteristic
981C4#144211yescharacteristic
982C4#144411yescharacteristic
983C4#144411yescharacteristic
984C4#144611yescharacteristic
985C2—21no—
986C2—21no—
987C2—21no—
988C2—21no—
989C2—21no—
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—21no—
997C2#755711yescharacteristic
998C2#1078412yes—
999C2#1105811yescharacteristic
1000C2#1105911yescharacteristic
1001C2#1121412yes—
subgroupG/H
center, socleC23#386
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
18. #2905C4semidirect
33. C2×#340C4semidirect
35. #1733C4semidirect

Maximal subgroups

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

subgroupindex
C2×#29052
C22×#3442
C22×#3432
C2×#17362
C2×#17332
C22×#3382