Finite Group Databasebeta

← #353372

Subgroups — #353372

Order 512.

4458 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#520C211yesmaximal, characteristic
2C22×#417C211yesmaximal, characteristic
3C22×#416C211yesmaximal, characteristic
4C2×#1736C211yesmaximal, characteristic, complemented
5C22×#340C211yesmaximal, characteristic, complemented
6C2×#1729C211yesmaximal, characteristic, complemented
7#13795C211yesmaximal, characteristic, complemented
8#10789C214yesmaximal, complemented
9#10788C214yesmaximal, complemented
10C23×#41C2211yescharacteristic
11C23×M16C2211yescharacteristic
12C24×C8C2211yescharacteristic
13C2×#520—24no—
14C2×#520—24no—
15C2×#520—24no—
16C2×#520—24no—
17C2×#520—24no—
18C2×#520C418yescomplemented
19C22×C4×Q8C2212yes—
20C22×C4×D4—22no—
21C22×C4×D4C2212yes—
22C22×#117—21no—
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C4⋊C4—21no—
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C2×#417—24no—
29C2×#417—24no—
30C2×#417C418yescomplemented
31C2×#416—24no—
32C2×#416—24no—
33C2×#416C418yescomplemented
34C22×#103C2212yes—
35C22×#103C2212yes—
36C22×#102C2212yes—
37C22×#102C2212yes—
38#1736—24no—
39C2×#340—24no—
40C2×#340C2214yes—
41C2×#340C2214yes—
42#1729—24no—
43C2×#336C2214yes—
44C4⋊#95—21no—
45C4⋊#95—21no—
46C4⋊#95C2214yes—
47C22⋊#95—22no—
48C22×#41—22no—
49C22×#41—22no—
50C22×#41—22no—
51C22×#41—22no—
52C22×#41—22no—
53C22×#41—22no—
54C22×#41—22no—
55C22×#41C2×C414yes—
56C22×#41C2×C414yes—
57C22×#41C2×C414yes—
58C22×#41D414yes—
59C22×#41D414yes—
60C22×#41D414yes—
61C22×#41Q814yes—
62C23×Q8C2311yescharacteristic
63C23×D4—21no—
64C23×D4C2311yescharacteristic
65C24×C4—21no—
66C24×C4—21no—
67C24×C4—22no—
68C24×C4—21no—
69C24×C4C2311yescharacteristic
70C22×M16—22no—
71C22×M16—22no—
72C22×M16—22no—
73C22×M16—22no—
74C22×M16—22no—
75C22×M16—22no—
76C22×M16C2×C414yescomplemented
77C23×C8—22no—
78C23×C8—22no—
79C23×C8—22no—
80C23×C8—22no—
81C23×C8—22no—
82C23×C8—22no—
83C23×C8C2×C414yescomplemented
84C23×C8C2312yes—
85C23×C8C2312yes—
86#520—232no—
87#520—232no—
88#520—232no—
89#520—232no—
90C2×C4×Q8—24no—
91C2×C4×Q8—24no—
92C2×C4×Q8—24no—
93C2×C4×Q8—24no—
94C2×C4×Q8—24no—
95C2×C4×Q8C2×C418yescomplemented
96C2×C4×D4—216no—
97C2×C4×D4—216no—
98C2×C4×D4—24no—
99C2×C4×D4—24no—
100C2×C4×D4—24no—
101C2×C4×D4—24no—
102C2×C4×D4—216no—
103C2×C4×D4—24no—
104C2×C4×D4C2×C418yescomplemented
105C2×#117—28no—
106C2×#117—28no—
107C2×#117—22no—
108C2×#117—22no—
109C2×#117—22no—
110C2×#117—22no—
111C2×#117—22no—
112C2×#117—28no—
113C2×#117—22no—
114C2×#117—22no—
115C2×#117—22no—
116C2×#117—22no—
117C2×#117C2×C414yes—
118C2×#117C2×C414yescomplemented
119C2×#117D414yes—
120C22×C4⋊C4—28no—
121C22×C4⋊C4—28no—
122C22×C4⋊C4—21no—
123C22×C4⋊C4—22no—
124C22×C4⋊C4—22no—
125C22×C4⋊C4—22no—
126C22×C4⋊C4—22no—
127C22×C4⋊C4—28no—
128C22×C4⋊C4—22no—
129C22×C4⋊C4—22no—
130C22×C4⋊C4—22no—
131C22×C4⋊C4—22no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—22no—
134C22×C4⋊C4C2×C414yes—
135C22×C4⋊C4C2×C414yescomplemented
136C22×C4⋊C4D411yescharacteristic
137C22×C4⋊C4D411yescharacteristic
138C22×C4⋊C4D414yes—
139C22×C4⋊C4D414yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C22⋊C4—22no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4D412yes—
146C22×C42—22no—
147C22×C42—21no—
148C22×C42C2312yes—
149#417—232no—
150#416—232no—
151C2×#103—24no—
152C2×#103—24no—
153C2×#103—24no—
154C2×#103—24no—
155C2×#103C2×C418yescomplemented
156C2×#103C2×C418yescomplemented
157C2×#102—24no—
158C2×#102—24no—
159C2×#102—24no—
160C2×#102—24no—
161C2×#102C2×C418yescomplemented
162C2×#102C2×C418yescomplemented
163C2×#95—24no—
164C2×#95—24no—
165#340—28no—
166#340—28no—
167#336—28no—
168C25—21no—
169C25C2×D411yescharacteristic
170C2×#41—28no—
171C2×#41—28no—
172C2×#41—28no—
173C2×#41—28no—
174C2×#41—28no—
175C2×#41—28no—
176C2×#41—28no—
177C2×#41—28no—
178C2×#41—28no—
179C2×#41—28no—
180C2×#41—28no—
181C2×#41—28no—
182C2×#41—28no—
183C2×#41—28no—
184C2×#41—28no—
185C2×#41—28no—
186C2×#41—28no—
187C2×#41—28no—
188C2×#41—28no—
189C2×#41—28no—
190C2×#41—28no—
191C2×#41C42116yes—
192C2×#41C22⋊C4116yes—
193C2×#41C22⋊C4116yes—
194C2×#41C22⋊C4116yes—
195C2×#41C4⋊C4116yes—
196C2×#41C4⋊C4116yes—
197C2×#41C4⋊C4116yes—
198C22×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8—21no—
203C22×Q8—21no—
204C22×Q8—21no—
205C22×Q8C22×C412yes—
206C22×Q8C22×C412yes—
207C22×Q8C22×C412yes—
208C22×Q8C2×D412yes—
209C22×Q8C2×D412yes—
210C22×Q8C2×D412yes—
211C22×Q8C2×Q812yes—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4—21no—
222C22×D4—21no—
223C22×D4—21no—
224C22×D4—21no—
225C22×D4—21no—
226C22×D4C22×C412yes—
227C22×D4C22×C412yes—
228C22×D4C22×C412yes—
229C22×D4C2×D412yes—
230C22×D4C2×D412yes—
231C22×D4C2×D412yes—
232C22×D4C2×Q812yes—
233C23×C4—21no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—22no—
242C23×C4—28no—
243C23×C4—28no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—28no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—84no—
254C23×C4—84no—
255C23×C4—82no—
256C23×C4—82no—
257C23×C4—82no—
258C23×C4—82no—
259C23×C4C22×C412yes—
260C23×C4C22×C412yes—
261C23×C4C22×C412yes—
262C23×C4C2×D412yes—
263C23×C4C2×D412yes—
264C23×C4C2×D412yes—
265C23×C4C2×D412yes—
266C23×C4C2×D412yes—
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D412yes—
269C23×C4C2×D412yes—
270C23×C4C2×D412yes—
271C23×C4C2×Q812yes—
272C23×C4#4112yes—
273C23×C4#4112yes—
274C23×C4#4112yes—
275C23×C4#4112yes—
276C23×C4C2411yescharacteristic
277C2×M16—28no—
278C2×M16—28no—
279C2×M16—28no—
280C2×M16—44no—
281C2×M16—44no—
282C2×M16—44no—
283C2×M16—44no—
284C22×C8—28no—
285C22×C8—28no—
286C22×C8—28no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—44no—
300C22×C8—44no—
301C22×C8—44no—
302C22×C8—44no—
303C22×C8C22×C414yes—
304C22×C8C22×C414yes—
305C4×Q8—216no—
306C4×Q8—216no—
307C4×Q8—216no—
308C4×Q8—216no—
309C4×D4—2128no—
310C4×D4—216no—
311C4×D4—216no—
312C4×D4—216no—
313C4×D4—216no—
314#117—264no—
315#117—28no—
316#117—28no—
317#117—28no—
318#117—28no—
319#117—28no—
320#117—28no—
321#117—44no—
322#117—44no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—264no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
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—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4C22⋊C414yes—
358C2×C4⋊C4C22⋊C414yes—
359C2×C4⋊C4C22⋊C4116yes—
360C2×C4⋊C4C22×C414yes—
361C2×C4⋊C4C22×C414yes—
362C2×C4⋊C4C22×C414yes—
363C2×C4⋊C4C2×D414yes—
364C2×C4⋊C4C2×D414yes—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4C22⋊C418yes—
374C2×C42—28no—
375C2×C42—28no—
376C2×C42—28no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42C22×C414yes—
385C2×C42C2×D414yes—
386#103—216no—
387#103—216no—
388#102—216no—
389#102—216no—
390#95—84no—
391#95—84no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24C2×C22⋊C412yes—
408C24C4×D412yes—
409C24C4×D412yes—
410C24#12012yes—
411C24#12012yes—
412C24#12112yes—
413C24C22⋊Q812yes—
414C24C22×D411yescharacteristic
415#41—232no—
416#41—232no—
417#41—232no—
418#41—232no—
419#41—232no—
420#41—232no—
421#41—232no—
422#41#95164yescomplemented
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—22no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—22no—
443C2×Q8—22no—
444C2×Q8C2×C4214yes—
445C2×Q8C2×C22⋊C414yes—
446C2×Q8C2×C22⋊C414yes—
447C2×Q8C2×C22⋊C414yes—
448C2×Q8C2×C4⋊C414yes—
449C2×Q8C2×C4⋊C414yes—
450C2×Q8C2×C4⋊C414yes—
451C2×D4—216no—
452C2×D4—216no—
453C2×D4—216no—
454C2×D4—216no—
455C2×D4—216no—
456C2×D4—216no—
457C2×D4—216no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4C2×C4214yes—
480C2×D4C2×C22⋊C414yes—
481C2×D4C2×C22⋊C414yes—
482C2×D4C2×C22⋊C414yes—
483C2×D4C2×C4⋊C414yes—
484C2×D4C2×C4⋊C414yes—
485C2×D4C2×C4⋊C414yes—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—216no—
494C22×C4—216no—
495C22×C4—216no—
496C22×C4—216no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—216no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—232no—
512C22×C4—216no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—44no—
523C22×C4—42no—
524C22×C4—44no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—48no—
528C22×C4—816no—
529C22×C4—88no—
530C22×C4—84no—
531C22×C4—84no—
532C22×C4—88no—
533C22×C4—88no—
534C22×C4—88no—
535C22×C4—88no—
536C22×C4—816no—
537C22×C4—84no—
538C22×C4—84no—
539C22×C4—88no—
540C22×C4C2×C4214yes—
541C22×C4C2×C22⋊C414yes—
542C22×C4C2×C22⋊C414yes—
543C22×C4C2×C22⋊C414yes—
544C22×C4C2×C22⋊C414yes—
545C22×C4C2×C22⋊C414yes—
546C22×C4C2×C22⋊C414yes—
547C22×C4C2×C22⋊C412yes—
548C22×C4C2×C4⋊C414yes—
549C22×C4C2×C4⋊C414yes—
550C22×C4C2×C4⋊C414yes—
551C22×C4#11714yes—
552C22×C4#11714yes—
553C22×C4C4×D414yes—
554C22×C4C4×D414yes—
555C22×C4C4×D414yes—
556C22×C4C4×D414yes—
557C22×C4C4×D414yes—
558C22×C4C4×D414yes—
559C22×C4C4×D412yes—
560C22×C4C4×D412yes—
561C22×C4#12014yes—
562C22×C4#12014yes—
563C22×C4#12012yes—
564C22×C4#12012yes—
565C22×C4#12114yes—
566C22×C4#12114yes—
567C22×C4#12114yes—
568C22×C4#12112yes—
569C22×C4C22⋊Q814yes—
570C22×C4C22⋊Q814yes—
571C22×C4C22⋊Q814yes—
572C22×C4C22⋊Q812yes—
573C22×C4#12314yes—
574C22×C4#12314yes—
575C22×C4#12314yes—
576C22×C4#12314yes—
577C22×C4C23×C411yescharacteristic
578C22×C4C23×C411yescharacteristic
579C22×C4C23×C411yescharacteristic
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×Q811yescharacteristic
587C22×C4C2×#4111yescharacteristic
588C22×C4C2×#4111yescharacteristic
589C22×C4C2×#4111yescharacteristic
590C22×C4C2×#4111yescharacteristic
591M16—416no—
592C2×C8—24no—
593C2×C8—24no—
594C2×C8—24no—
595C2×C8—24no—
596C2×C8—24no—
597C2×C8—24no—
598C2×C8—42no—
599C2×C8—42no—
600C2×C8—42no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8—42no—
604C2×C8—42no—
605C2×C8—42no—
606C2×C8—416no—
607C4⋊C4—232no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4—24no—
611C4⋊C4—28no—
612C4⋊C4—216no—
613C4⋊C4—28no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—48no—
623C4⋊C4C2×C22⋊C418yes—
624C22⋊C4—232no—
625C22⋊C4—216no—
626C22⋊C4—48no—
627C42—232no—
628C42—24no—
629C42—24no—
630C42—24no—
631C42—24no—
632C42—48no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23C4×C22⋊C414yes—
673C23#37914yes—
674C23#38014yes—
675C23#38514yes—
676C23#38514yes—
677C23#38614yes—
678C23#38614yes—
679C23C22×C22⋊C411yescharacteristic
680C23C2×C4×D411yescharacteristic
681C23C2×C4×D411yescharacteristic
682C23C2×#12011yescharacteristic
683C23C2×#12011yescharacteristic
684C23C2×#12111yescharacteristic
685C23C2×C22⋊Q811yescharacteristic
686C23#57612yes—
687C23#57712yes—
688C23#57712yes—
689C23#57812yes—
690Q8—24no—
691Q8—24no—
692Q8—24no—
693Q8—24no—
694Q8—24no—
695Q8—24no—
696Q8—24no—
697Q8C2×#9518yes—
698D4—264no—
699D4—24no—
700D4—24no—
701D4—24no—
702D4—24no—
703D4—24no—
704D4—24no—
705D4—24no—
706D4C2×#9518yes—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—264no—
715C2×C4—28no—
716C2×C4—28no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—28no—
720C2×C4—48no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—48no—
729C2×C4—44no—
730C2×C4—48no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—816no—
736C2×C4—832no—
737C2×C4—816no—
738C2×C4—82no—
739C2×C4—82no—
740C2×C4—82no—
741C2×C4—82no—
742C2×C4—82no—
743C2×C4—84no—
744C2×C4—82no—
745C2×C4C2×#9518yes—
746C2×C4C4×C22⋊C414yes—
747C2×C4C4×C22⋊C418yes—
748C2×C4#37914yes—
749C2×C4#38014yes—
750C2×C4#38018yes—
751C2×C4#38118yes—
752C2×C4#38514yes—
753C2×C4#38514yes—
754C2×C4#38518yes—
755C2×C4#38518yes—
756C2×C4#38614yes—
757C2×C4#38614yes—
758C2×C4#38618yes—
759C2×C4#38618yes—
760C2×C4C22×C4211yescharacteristic
761C2×C4C22×C22⋊C411yescharacteristic
762C2×C4C22×C22⋊C411yescharacteristic
763C2×C4C22×C22⋊C411yescharacteristic
764C2×C4C22×C22⋊C411yescharacteristic
765C2×C4C22×C4⋊C411yescharacteristic
766C2×C4C22×C4⋊C411yescharacteristic
767C2×C4C22×C4⋊C411yescharacteristic
768C2×C4C2×#11711yescharacteristic
769C2×C4C2×#11711yescharacteristic
770C2×C4C2×C4×D411yescharacteristic
771C2×C4C2×C4×D411yescharacteristic
772C2×C4C2×C4×D411yescharacteristic
773C2×C4C2×C4×D411yescharacteristic
774C2×C4C2×C4×D411yescharacteristic
775C2×C4C2×C4×D411yescharacteristic
776C2×C4C2×#12011yescharacteristic
777C2×C4C2×#12011yescharacteristic
778C2×C4C2×#12111yescharacteristic
779C2×C4C2×#12111yescharacteristic
780C2×C4C2×#12111yescharacteristic
781C2×C4C2×C22⋊Q811yescharacteristic
782C2×C4C2×C22⋊Q811yescharacteristic
783C2×C4C2×C22⋊Q811yescharacteristic
784C2×C4C2×#12311yescharacteristic
785C2×C4C2×#12311yescharacteristic
786C2×C4C2×#12311yescharacteristic
787C2×C4C2×#12311yescharacteristic
788C8—44no—
789C8—44no—
790C22—24no—
791C22—24no—
792C22—28no—
793C22—24no—
794C22—24no—
795C22—28no—
796C22—28no—
797C22—24no—
798C22—24no—
799C22—28no—
800C22—28no—
801C22—44no—
802C22—44no—
803C22—48no—
804C22—44no—
805C22—44no—
806C22—48no—
807C22—48no—
808C22—44no—
809C22—44no—
810C22—48no—
811C22C22⋊#9518yes—
812C22C2×C4×C22⋊C411yescharacteristic
813C22C2×#37911yescharacteristic
814C22C2×#38011yescharacteristic
815C22C2×#38511yescharacteristic
816C22C2×#38511yescharacteristic
817C22C2×#38611yescharacteristic
818C22C2×#38611yescharacteristic
819C22#289712yes—
820C22#289812yes—
821C22#294612yes—
822C22#294712yes—
823C22#295112yes—
824C22#295212yes—
825C22#300811yescharacteristic
826C22#300911yescharacteristic
827C22#301011yescharacteristic
828C22#301111yescharacteristic
829C22#301212yes—
830C22#301312yes—
831C22#304512yes—
832C22#304612yes—
833C22#308312yes—
834C22#308412yes—
835C4—28no—
836C4—44no—
837C4—48no—
838C4—44no—
839C4—84no—
840C4—84no—
841C4C22⋊#9518yes—
842C4C22×#9511yescharacteristic
843C4C2×C4×C22⋊C411yescharacteristic
844C4C2×#38011yescharacteristic
845C4C2×#38111yescharacteristic
846C4C2×#38511yescharacteristic
847C4C2×#38511yescharacteristic
848C4C2×#38611yescharacteristic
849C4C2×#38611yescharacteristic
850C2—28no—
851C2—48no—
852C2C2×C22⋊#9511yescharacteristic
853C2#2041512yes—
854C2#2060211yescharacteristic
855C2#2060311yescharacteristic
856C2#2065212yes—
857C2#2087812yes—
858C2#2088111yescharacteristic
859C2#2088211yescharacteristic
860C2#2093111yescharacteristic
861C2#2093211yescharacteristic
862C2#2093712yes—
subgroupG/H
center, socleC24C22×D4
commutatorC2×C4C22×C42
Frattini, cosocleC23×C4C24
prime radicalC23×#41C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×#117 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#1736C2semidirect
5. C22×#340C2semidirect
6. C2×#1729C2semidirect
7. #13795C2semidirect
8. #10789C2semidirect
9. #10788C2semidirect
18. C2×#520C4semidirect
30. C2×#417C4semidirect
33. C2×#416C4semidirect
76. C22×M16C2×C4semidirect
83. C23×C8C2×C4semidirect
95. C2×C4×Q8C2×C4semidirect
104. C2×C4×D4C2×C4semidirect
118. C2×#117C2×C4semidirect
135. C22×C4⋊C4C2×C4semidirect
155. C2×#103C2×C4semidirect
156. C2×#103C2×C4semidirect
161. C2×#102C2×C4semidirect
162. C2×#102C2×C4semidirect
422. #41#95semidirect

Maximal subgroups

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

subgroupindex
C22×#5202
C22×#4172
C22×#4162
C2×#17362
C22×#3402
C2×#17292
#137952
#107892
#107882