Finite Group Databasebeta

← #123951

Subgroups — #123951

Order 512.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1131 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2317C211yesmaximal, characteristic
2C22×#343C211yesmaximal, characteristic
3C2×#1736C211yesmaximal, characteristic
4C2×#1736C211yesmaximal, characteristic
5C22×#339C211yesmaximal, characteristic
6C22×#339C211yesmaximal, characteristic
7C2×C4⋊#95C211yesmaximal, characteristic
8C23×M16C2211yescharacteristic
9C23×M16C2211yescharacteristic
10C22×#117C2211yescharacteristic
11C22×#117C2211yescharacteristic
12C23×C4⋊C4C2211yescharacteristic
13C23×C4⋊C4C2211yescharacteristic
14C23×C42C2211yescharacteristic
15#2317—22no—
16#2317—22no—
17#2317—22no—
18#2317C414yescomplemented
19C2×#389—22no—
20C2×#385—22no—
21C2×#384—21no—
22C2×#382—21no—
23C22×#95—22no—
24C2×#343—22no—
25C2×#343—22no—
26C2×#343—22no—
27#1736—22no—
28#1736—22no—
29#1736—22no—
30#1736C414yescomplemented
31C2×#340—21no—
32C2×#340—21no—
33C2×#340—22no—
34C2×#339—22no—
35C2×#339—22no—
36C2×#339—22no—
37C2×#339—22no—
38C2×#339—22no—
39C2×#339C414yescomplemented
40C4⋊#95—22no—
41C4⋊#95—22no—
42C24×C4—21no—
43C24×C4—21no—
44C24×C4D412yes—
45C24×C4C2311yescharacteristic
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×M16C2×C412yes—
69C22×M16C2×C412yes—
70C22×M16D412yes—
71C22×M16D412yes—
72C22×M16Q812yes—
73C22×M16Q812yes—
74C23×C8—21no—
75C23×C8—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×#117C2×C412yes—
93C2×#117C2×C412yes—
94C2×#117C2×C412yes—
95C2×#117C2×C412yes—
96C2×#117D412yes—
97C2×#117D412yes—
98C2×#117D412yes—
99C2×#117Q812yes—
100C22×C4⋊C4—21no—
101C22×C4⋊C4—21no—
102C22×C4⋊C4—21no—
103C22×C4⋊C4—21no—
104C22×C4⋊C4—21no—
105C22×C4⋊C4—21no—
106C22×C4⋊C4—21no—
107C22×C4⋊C4—21no—
108C22×C4⋊C4—21no—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4—21no—
114C22×C4⋊C4—21no—
115C22×C4⋊C4—21no—
116C22×C4⋊C4—21no—
117C22×C4⋊C4—21no—
118C22×C4⋊C4—21no—
119C22×C4⋊C4—21no—
120C22×C4⋊C4—21no—
121C22×C4⋊C4—21no—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4C2×C412yes—
125C22×C4⋊C4C2×C412yes—
126C22×C4⋊C4D412yes—
127C22×C4⋊C4D411yescharacteristic
128C22×C4⋊C4D411yescharacteristic
129C22×C4⋊C4D412yes—
130C22×C4⋊C4D412yes—
131C22×C4⋊C4Q812yes—
132C22×C22⋊C4—21no—
133C22×C22⋊C4—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×C42—21no—
144C22×C42—21no—
145C22×C42—21no—
146C22×C42—21no—
147C22×C42C2×C412yes—
148C22×C42D412yes—
149C22×C42Q812yes—
150#389—28no—
151#389—28no—
152#385—28no—
153#385—28no—
154#384—24no—
155#384—24no—
156#382—24no—
157#382—24no—
158C2×#95—24no—
159C2×#95—28no—
160C2×#95—48no—
161#343—28no—
162#340—24no—
163#340—24no—
164#340—28no—
165#339—28no—
166#339—28no—
167C25C2×D411yescharacteristic
168C23×C4—24no—
169C23×C4—24no—
170C23×C4—22no—
171C23×C4—22no—
172C23×C4—22no—
173C23×C4—22no—
174C23×C4—22no—
175C23×C4—22no—
176C23×C4—22no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—42no—
186C23×C4—42no—
187C23×C4—41no—
188C23×C4—41no—
189C23×C4—41no—
190C23×C4—41no—
191C23×C4—44no—
192C23×C4—44no—
193C23×C4—44no—
194C23×C4—44no—
195C23×C4—41no—
196C23×C4—41no—
197C23×C4—41no—
198C23×C4—41no—
199C23×C4C22⋊C414yes—
200C23×C4C22×C411yescharacteristic
201C23×C4C22×C411yescharacteristic
202C23×C4C22×C411yescharacteristic
203C23×C4C2×D411yescharacteristic
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×Q811yescharacteristic
214C23×C4C2×Q811yescharacteristic
215C23×C4C2×Q811yescharacteristic
216C23×C4C2×Q811yescharacteristic
217C23×C4C2×Q811yescharacteristic
218C23×C4#4111yescharacteristic
219C23×C4#4111yescharacteristic
220C23×C4#4111yescharacteristic
221C23×C4#4111yescharacteristic
222C23×C4#4111yescharacteristic
223C23×C4#4111yescharacteristic
224C23×C4#4111yescharacteristic
225C23×C4#4111yescharacteristic
226C23×C4#4111yescharacteristic
227C23×C4#4111yescharacteristic
228C23×C4#4111yescharacteristic
229C23×C4#4111yescharacteristic
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—22no—
255C2×M16—22no—
256C2×M16—22no—
257C2×M16—22no—
258C2×M16—22no—
259C2×M16—22no—
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×M16C4⋊C414yescomplemented
285C2×M16C4⋊C414yescomplemented
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—41no—
293C22×C8—41no—
294C22×C8—41no—
295C22×C8—41no—
296C22×C8—41no—
297C22×C8—41no—
298C22×C8—41no—
299C22×C8—41no—
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—22no—
314#117—22no—
315#117—22no—
316#117—22no—
317#117—22no—
318#117—22no—
319#117—22no—
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#117C4214yes—
329#117C22⋊C414yes—
330#117C4⋊C414yes—
331#117C4⋊C414yes—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—216no—
373C2×C4⋊C4—41no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4—41no—
376C2×C4⋊C4—41no—
377C2×C4⋊C4—41no—
378C2×C4⋊C4—41no—
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⋊C4—41no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—84no—
402C2×C4⋊C4—84no—
403C2×C4⋊C4C22⋊C412yes—
404C2×C4⋊C4C22⋊C412yes—
405C2×C4⋊C4C22⋊C414yes—
406C2×C4⋊C4C22⋊C414yes—
407C2×C4⋊C4C4⋊C414yes—
408C2×C4⋊C4C4⋊C414yescomplemented
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—41no—
418C2×C22⋊C4—41no—
419C2×C22⋊C4—41no—
420C2×C22⋊C4—41no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
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—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—41no—
445C2×C42—41no—
446C2×C42—41no—
447C2×C42—41no—
448C2×C42—41no—
449C2×C42—41no—
450C2×C42—41no—
451C2×C42—41no—
452C2×C42—41no—
453C2×C42—41no—
454C2×C42—41no—
455C2×C42—41no—
456C2×C42—41no—
457C2×C42—41no—
458C2×C42—41no—
459C2×C42—41no—
460C2×C42C4⋊C414yescomplemented
461#95—216no—
462#95—416no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24C2×C22⋊C411yescharacteristic
468C24C4×D411yescharacteristic
469C24C4×D411yescharacteristic
470C24#12011yescharacteristic
471C24#12011yescharacteristic
472C24#12011yescharacteristic
473C24#12111yescharacteristic
474C24#12111yescharacteristic
475C24#12111yescharacteristic
476C24C22⋊Q811yescharacteristic
477C24C22⋊Q811yescharacteristic
478C24C22⋊Q811yescharacteristic
479C24#12311yescharacteristic
480C24#12411yescharacteristic
481C24C4⋊Q811yescharacteristic
482C22×C4—24no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—48no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—48no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—44no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—44no—
545C22×C4—42no—
546C22×C4—84no—
547C22×C4—84no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—84no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4—82no—
554C22×C4—82no—
555C22×C4—84no—
556C22×C4C2×C4211yescharacteristic
557C22×C4C2×C22⋊C411yescharacteristic
558C22×C4C2×C22⋊C411yescharacteristic
559C22×C4C2×C22⋊C411yescharacteristic
560C22×C4C2×C22⋊C411yescharacteristic
561C22×C4C2×C4⋊C411yescharacteristic
562C22×C4C2×C4⋊C411yescharacteristic
563C22×C4C2×C4⋊C411yescharacteristic
564C22×C4C2×C4⋊C411yescharacteristic
565C22×C4C2×C4⋊C411yescharacteristic
566C22×C4C2×C4⋊C411yescharacteristic
567C22×C4C2×C4⋊C411yescharacteristic
568C22×C4#11711yescharacteristic
569C22×C4#11711yescharacteristic
570C22×C4#11711yescharacteristic
571C22×C4#11711yescharacteristic
572C22×C4#11711yescharacteristic
573C22×C4#11711yescharacteristic
574C22×C4C4×D411yescharacteristic
575C22×C4C4×D411yescharacteristic
576C22×C4C4×D411yescharacteristic
577C22×C4C4×D411yescharacteristic
578C22×C4C4×D411yescharacteristic
579C22×C4C4×D411yescharacteristic
580C22×C4C4×D411yescharacteristic
581C22×C4C4×D411yescharacteristic
582C22×C4C4×D411yescharacteristic
583C22×C4C4×D411yescharacteristic
584C22×C4C4×D411yescharacteristic
585C22×C4C4×D411yescharacteristic
586C22×C4C4×D411yescharacteristic
587C22×C4C4×D411yescharacteristic
588C22×C4C4×Q811yescharacteristic
589C22×C4C4×Q811yescharacteristic
590C22×C4C4×Q811yescharacteristic
591C22×C4C4×Q811yescharacteristic
592C22×C4C4×Q811yescharacteristic
593C22×C4C4×Q811yescharacteristic
594C22×C4C4×Q811yescharacteristic
595C22×C4C4×Q811yescharacteristic
596C22×C4#12011yescharacteristic
597C22×C4#12011yescharacteristic
598C22×C4#12011yescharacteristic
599C22×C4#12011yescharacteristic
600C22×C4#12011yescharacteristic
601C22×C4#12111yescharacteristic
602C22×C4#12111yescharacteristic
603C22×C4#12111yescharacteristic
604C22×C4#12111yescharacteristic
605C22×C4#12111yescharacteristic
606C22×C4#12111yescharacteristic
607C22×C4#12111yescharacteristic
608C22×C4#12111yescharacteristic
609C22×C4#12111yescharacteristic
610C22×C4#12111yescharacteristic
611C22×C4#12111yescharacteristic
612C22×C4#12111yescharacteristic
613C22×C4#12111yescharacteristic
614C22×C4#12111yescharacteristic
615C22×C4#12111yescharacteristic
616C22×C4#12111yescharacteristic
617C22×C4#12111yescharacteristic
618C22×C4C22⋊Q811yescharacteristic
619C22×C4C22⋊Q811yescharacteristic
620C22×C4C22⋊Q811yescharacteristic
621C22×C4C22⋊Q811yescharacteristic
622C22×C4C22⋊Q811yescharacteristic
623C22×C4C22⋊Q811yescharacteristic
624C22×C4C22⋊Q811yescharacteristic
625C22×C4C22⋊Q811yescharacteristic
626C22×C4C22⋊Q811yescharacteristic
627C22×C4C22⋊Q811yescharacteristic
628C22×C4C22⋊Q811yescharacteristic
629C22×C4C22⋊Q811yescharacteristic
630C22×C4C22⋊Q811yescharacteristic
631C22×C4C22⋊Q811yescharacteristic
632C22×C4C22⋊Q811yescharacteristic
633C22×C4C22⋊Q811yescharacteristic
634C22×C4C22⋊Q811yescharacteristic
635C22×C4C22⋊Q811yescharacteristic
636C22×C4C22⋊Q811yescharacteristic
637C22×C4C22⋊Q811yescharacteristic
638C22×C4C22⋊Q811yescharacteristic
639C22×C4C22⋊Q811yescharacteristic
640C22×C4C22⋊Q811yescharacteristic
641C22×C4C22⋊Q811yescharacteristic
642C22×C4C22⋊Q811yescharacteristic
643C22×C4#12311yescharacteristic
644C22×C4#12311yescharacteristic
645C22×C4#12311yescharacteristic
646C22×C4#12311yescharacteristic
647C22×C4#12311yescharacteristic
648C22×C4#12311yescharacteristic
649C22×C4#12311yescharacteristic
650C22×C4#12311yescharacteristic
651C22×C4#12311yescharacteristic
652C22×C4#12311yescharacteristic
653C22×C4#12311yescharacteristic
654C22×C4#12311yescharacteristic
655C22×C4#12311yescharacteristic
656C22×C4#12311yescharacteristic
657C22×C4#12311yescharacteristic
658C22×C4#12411yescharacteristic
659C22×C4#12411yescharacteristic
660C22×C4#12411yescharacteristic
661C22×C4#12411yescharacteristic
662C22×C4#12411yescharacteristic
663C22×C4#12411yescharacteristic
664C22×C4#12411yescharacteristic
665C22×C4#12511yescharacteristic
666C22×C4#12511yescharacteristic
667C22×C4#12511yescharacteristic
668C22×C4#12511yescharacteristic
669C22×C4#12511yescharacteristic
670C22×C4#12511yescharacteristic
671C22×C4#12511yescharacteristic
672C22×C4#12511yescharacteristic
673C22×C4#12511yescharacteristic
674C22×C4#12511yescharacteristic
675C22×C4#12511yescharacteristic
676C22×C4#12511yescharacteristic
677C22×C4#12611yescharacteristic
678C22×C4#12611yescharacteristic
679C22×C4#12611yescharacteristic
680C22×C4#12611yescharacteristic
681C22×C4#12611yescharacteristic
682C22×C4#12611yescharacteristic
683C22×C4#12611yescharacteristic
684C22×C4#12611yescharacteristic
685C22×C4#12711yescharacteristic
686C22×C4#12711yescharacteristic
687C22×C4C4⋊Q811yescharacteristic
688C22×C4C4⋊Q811yescharacteristic
689C22×C4C4⋊Q811yescharacteristic
690C22×C4C4⋊Q811yescharacteristic
691C22×C4C4⋊Q811yescharacteristic
692C22×C4C4⋊Q811yescharacteristic
693C22×C4C4⋊Q811yescharacteristic
694C22×C4C4⋊Q811yescharacteristic
695C22×C4C4⋊Q811yescharacteristic
696M16—24no—
697M16—24no—
698M16—24no—
699M16—24no—
700M16—42no—
701M16—42no—
702M16—42no—
703M16—42no—
704M16—42no—
705M16—42no—
706M16—42no—
707M16—42no—
708M16—42no—
709M16—42no—
710M16—42no—
711M16—42no—
712C2×C8—24no—
713C2×C8—24no—
714C2×C8—42no—
715C2×C8—42no—
716C2×C8—42no—
717C2×C8—42no—
718C2×C8—42no—
719C2×C8—42no—
720C2×C8—42no—
721C2×C8—42no—
722C2×C8—42no—
723C2×C8—42no—
724C2×C8—42no—
725C2×C8—42no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—22no—
735C4⋊C4—42no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—41no—
744C4⋊C4—41no—
745C4⋊C4—42no—
746C4⋊C4—42no—
747C4⋊C4—42no—
748C4⋊C4—41no—
749C4⋊C4—41no—
750C4⋊C4—42no—
751C4⋊C4—42no—
752C4⋊C4—42no—
753C4⋊C4—816no—
754C4⋊C4#9518yescomplemented
755C22⋊C4—24no—
756C22⋊C4—24no—
757C22⋊C4—24no—
758C22⋊C4—24no—
759C22⋊C4—42no—
760C22⋊C4—42no—
761C22⋊C4—42no—
762C22⋊C4—42no—
763C42—24no—
764C42—24no—
765C42—24no—
766C42—24no—
767C42—24no—
768C42—24no—
769C42—42no—
770C42—42no—
771C42—42no—
772C42—42no—
773C42—42no—
774C42—42no—
775C42—42no—
776C42—42no—
777C42—42no—
778C42—42no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23C4×C22⋊C411yescharacteristic
812C23#37911yescharacteristic
813C23#38011yescharacteristic
814C23#38511yescharacteristic
815C23#38511yescharacteristic
816C23#38511yescharacteristic
817C23#38511yescharacteristic
818C23#38611yescharacteristic
819C23#38611yescharacteristic
820C23#38611yescharacteristic
821C23#38611yescharacteristic
822C23#38711yescharacteristic
823C23#38711yescharacteristic
824C23#38811yescharacteristic
825C23#38811yescharacteristic
826C23#38911yescharacteristic
827C23#38911yescharacteristic
828C23#39111yescharacteristic
829C23#39111yescharacteristic
830C23#39211yescharacteristic
831C23#39211yescharacteristic
832C23#39311yescharacteristic
833C23#39311yescharacteristic
834C23#39411yescharacteristic
835C23#39411yescharacteristic
836C23#39411yescharacteristic
837C23#39511yescharacteristic
838C23#39511yescharacteristic
839C23#39511yescharacteristic
840C23#39611yescharacteristic
841C23#39611yescharacteristic
842C23#39811yescharacteristic
843C23#39811yescharacteristic
844C23#39811yescharacteristic
845C23#40011yescharacteristic
846C23#45312yes—
847C23#45412yes—
848C23#45512yes—
849C23#45612yes—
850C2×C4—28no—
851C2×C4—28no—
852C2×C4—48no—
853C2×C4—48no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—48no—
858C2×C4—48no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—48no—
869C2×C4—48no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—44no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—84no—
878C2×C4—84no—
879C2×C4—84no—
880C2×C4—84no—
881C2×C4—84no—
882C2×C4—84no—
883C2×C4—81no—
884C2×C4—82no—
885C2×C4—82no—
886C2×C4—81no—
887C2×C4—82no—
888C2×C4—81no—
889C2×C4—82no—
890C2×C4—81no—
891C2×C4—84no—
892C2×C4—82no—
893C2×C4—84no—
894C2×C4—82no—
895C2×C4—84no—
896C2×C4C2×#9511yescharacteristic
897C2×C4C4×C22⋊C411yescharacteristic
898C2×C4C4×C4⋊C411yescharacteristic
899C2×C4C4×C4⋊C411yescharacteristic
900C2×C4C4×C4⋊C411yescharacteristic
901C2×C4C4×C4⋊C411yescharacteristic
902C2×C4#38011yescharacteristic
903C2×C4#38011yescharacteristic
904C2×C4#38011yescharacteristic
905C2×C4#38011yescharacteristic
906C2×C4#38011yescharacteristic
907C2×C4#38111yescharacteristic
908C2×C4#38211yescharacteristic
909C2×C4#38211yescharacteristic
910C2×C4#38411yescharacteristic
911C2×C4#38411yescharacteristic
912C2×C4#38511yescharacteristic
913C2×C4#38511yescharacteristic
914C2×C4#38511yescharacteristic
915C2×C4#38511yescharacteristic
916C2×C4#38511yescharacteristic
917C2×C4#38511yescharacteristic
918C2×C4#38511yescharacteristic
919C2×C4#38511yescharacteristic
920C2×C4#38611yescharacteristic
921C2×C4#38611yescharacteristic
922C2×C4#38611yescharacteristic
923C2×C4#38611yescharacteristic
924C2×C4#38711yescharacteristic
925C2×C4#38711yescharacteristic
926C2×C4#38711yescharacteristic
927C2×C4#38711yescharacteristic
928C2×C4#38711yescharacteristic
929C2×C4#38711yescharacteristic
930C2×C4#38711yescharacteristic
931C2×C4#38711yescharacteristic
932C2×C4#38711yescharacteristic
933C2×C4#38711yescharacteristic
934C2×C4#38711yescharacteristic
935C2×C4#38711yescharacteristic
936C2×C4#38711yescharacteristic
937C2×C4#38711yescharacteristic
938C2×C4#38811yescharacteristic
939C2×C4#38811yescharacteristic
940C2×C4#38811yescharacteristic
941C2×C4#38811yescharacteristic
942C2×C4#38811yescharacteristic
943C2×C4#38811yescharacteristic
944C2×C4#38911yescharacteristic
945C2×C4#38911yescharacteristic
946C2×C4#38911yescharacteristic
947C2×C4#38911yescharacteristic
948C2×C4#38911yescharacteristic
949C2×C4#38911yescharacteristic
950C2×C4#38911yescharacteristic
951C2×C4#38911yescharacteristic
952C2×C4#38911yescharacteristic
953C2×C4#38911yescharacteristic
954C2×C4#38911yescharacteristic
955C2×C4#38911yescharacteristic
956C2×C4#38911yescharacteristic
957C2×C4#38911yescharacteristic
958C2×C4#39011yescharacteristic
959C2×C4#39011yescharacteristic
960C2×C4#39011yescharacteristic
961C2×C4#39011yescharacteristic
962C2×C4#39111yescharacteristic
963C2×C4#39111yescharacteristic
964C2×C4#39111yescharacteristic
965C2×C4#39111yescharacteristic
966C2×C4#39111yescharacteristic
967C2×C4#39111yescharacteristic
968C2×C4#39211yescharacteristic
969C2×C4#39211yescharacteristic
970C2×C4#39311yescharacteristic
971C2×C4#39311yescharacteristic
972C2×C4#39411yescharacteristic
973C2×C4#39411yescharacteristic
974C2×C4#39411yescharacteristic
975C2×C4#39411yescharacteristic
976C2×C4#39411yescharacteristic
977C2×C4#39511yescharacteristic
978C2×C4#39511yescharacteristic
979C2×C4#39511yescharacteristic
980C2×C4#39511yescharacteristic
981C2×C4#39511yescharacteristic
982C2×C4#39611yescharacteristic
983C2×C4#39611yescharacteristic
984C2×C4#39611yescharacteristic
985C2×C4#39611yescharacteristic
986C2×C4#39611yescharacteristic
987C2×C4#39611yescharacteristic
988C2×C4#39711yescharacteristic
989C2×C4#39711yescharacteristic
990C2×C4#39711yescharacteristic
991C2×C4#39711yescharacteristic
992C2×C4#39811yescharacteristic
993C2×C4#39811yescharacteristic
994C2×C4#39811yescharacteristic
995C2×C4#39811yescharacteristic
996C2×C4#39811yescharacteristic
997C2×C4#39811yescharacteristic
998C2×C4#39811yescharacteristic
999C2×C4#39811yescharacteristic
1000C2×C4#39811yescharacteristic
1001C2×C4#39811yescharacteristic
1002C2×C4#39811yescharacteristic
1003C2×C4#39811yescharacteristic
1004C2×C4#39811yescharacteristic
1005C2×C4#39911yescharacteristic
1006C2×C4#39911yescharacteristic
1007C2×C4#39911yescharacteristic
1008C2×C4#39911yescharacteristic
1009C2×C4#40011yescharacteristic
1010C2×C4#40011yescharacteristic
1011C2×C4#40011yescharacteristic
1012C2×C4#40011yescharacteristic
1013C2×C4#40011yescharacteristic
1014C2×C4#40011yescharacteristic
1015C2×C4#40011yescharacteristic
1016C8—44no—
1017C8—44no—
1018C22—22no—
1019C22—22no—
1020C22—22no—
1021C22—22no—
1022C22—22no—
1023C22—22no—
1024C22—22no—
1025C22—22no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—21no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—22no—
1050C22—21no—
1051C22—21no—
1052C22—21no—
1053C22—21no—
1054C22—21no—
1055C22—21no—
1056C22—21no—
1057C22—21no—
1058C22C22⋊#9511yescharacteristic
1059C22#143611yescharacteristic
1060C22#143611yescharacteristic
1061C22#143811yescharacteristic
1062C22#143911yescharacteristic
1063C22#143911yescharacteristic
1064C22#144111yescharacteristic
1065C22#144111yescharacteristic
1066C22#144111yescharacteristic
1067C22#144111yescharacteristic
1068C22#144211yescharacteristic
1069C22#144211yescharacteristic
1070C22#144411yescharacteristic
1071C22#144411yescharacteristic
1072C22#144611yescharacteristic
1073C22#179212yes—
1074C22#179312yes—
1075C22#185912yes—
1076C22#186012yes—
1077C22#188212yes—
1078C22#188312yes—
1079C22#200211yescharacteristic
1080C22#200311yescharacteristic
1081C22#200411yescharacteristic
1082C22#200511yescharacteristic
1083C22#202712yes—
1084C22#202812yes—
1085C22#203712yes—
1086C22#203812yes—
1087C22#206012yes—
1088C22#206112yes—
1089C4—48no—
1090C4—48no—
1091C4—84no—
1092C4—84no—
1093C4—82no—
1094C4—82no—
1095C4C4⋊#9511yescharacteristic
1096C4C4⋊#9511yescharacteristic
1097C4#143611yescharacteristic
1098C4#143611yescharacteristic
1099C4#143911yescharacteristic
1100C4#143911yescharacteristic
1101C4#144111yescharacteristic
1102C4#144111yescharacteristic
1103C4#144111yescharacteristic
1104C4#144111yescharacteristic
1105C4#144211yescharacteristic
1106C4#144211yescharacteristic
1107C4#144411yescharacteristic
1108C4#144411yescharacteristic
1109C4#144511yescharacteristic
1110C4#144511yescharacteristic
1111C2—21no—
1112C2—21no—
1113C2—21no—
1114C2—21no—
1115C2—21no—
1116C2—21no—
1117C2—21no—
1118C2—21no—
1119C2#755711yescharacteristic
1120C2#1078112yes—
1121C2#1099711yescharacteristic
1122C2#1099811yescharacteristic
1123C2#1106311yescharacteristic
1124C2#1106411yescharacteristic
1125C2#1121712yes—
1126C2#1127612yes—
1127C2#1133911yescharacteristic
1128C2#1134011yescharacteristic
1129C2#1139212yes—
subgroupG/H
center, socleC24#120
commutatorC22×C4C2×C42
Frattini, cosocleC24×C4C23
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
18. #2317C4semidirect
30. #1736C4semidirect
39. C2×#339C4semidirect
284. C2×M16C4⋊C4semidirect
285. C2×M16C4⋊C4semidirect
408. C2×C4⋊C4C4⋊C4semidirect
460. C2×C42C4⋊C4semidirect
754. C4⋊C4#95semidirect

Maximal subgroups

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

subgroupindex
C2×#23172
C22×#3432
C2×#17362
C22×#3392
C2×C4⋊#952