Finite Group Databasebeta

← C2×#14767 #607702

Subgroups — C2×#14767 #607702

Order 512.

6142 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#400C211yesmaximal, characteristic, complemented
2C22×#385C211yesmaximal, characteristic
3C22×#380C211yesmaximal, characteristic
4C23×#95C211yesmaximal, characteristic
5#14767C2116yesmaximal, direct product factor
6C2×#1445C211yesmaximal, characteristic, complemented
7C2×#1443C211yesmaximal, characteristic, complemented
8C2×#1443C211yesmaximal, characteristic, complemented
9C2×#1442C211yesmaximal, characteristic, complemented
10C2×#1442C211yesmaximal, characteristic, complemented
11C2×#1442C211yesmaximal, characteristic, complemented
12C2×#1441C211yesmaximal, characteristic, complemented
13C2×C22⋊#95C211yesmaximal, characteristic
14C2×C22⋊#95C211yesmaximal, characteristic
15C2×C22⋊#95C211yesmaximal, characteristic
16C2×C22⋊#95C211yesmaximal, characteristic
17C25×C4C2211yescharacteristic
18C25×C4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C2×#400—28no—
29C2×#400C2218yescomplemented
30C2×#385—28no—
31C2×#385C2218yes—
32C2×#380—28no—
33C2×#380C2218yes—
34C22×#95—28no—
35C22×#95C2211yescharacteristic
36C22×#95C2211yescharacteristic
37C22×#95C2211yescharacteristic
38C22×#95C2211yescharacteristic
39C22×#95C2211yescharacteristic
40C22×#95C2211yescharacteristic
41C22×#95C2211yescharacteristic
42C22×#95C2211yescharacteristic
43C22×#95C2211yescharacteristic
44C22×#95C2211yescharacteristic
45C22×#95C2211yescharacteristic
46C22×#95C2211yescharacteristic
47C22×#95C2211yescharacteristic
48C22×#95C2211yescharacteristic
49C22×#95C2211yescharacteristic
50C22×#95C2218yes—
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53C22×#95C2211yescharacteristic
54C22×#95C2211yescharacteristic
55C22×#95C2211yescharacteristic
56C22×#95C2211yescharacteristic
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59C22×#95C2211yescharacteristic
60#1445C2218yescomplemented
61#1443C2218yescomplemented
62#1443C2218yescomplemented
63#1442C2218yescomplemented
64#1442C2218yescomplemented
65#1442C2218yescomplemented
66#1441C2218yescomplemented
67C22⋊#95C2218yes—
68C22⋊#95C2218yes—
69C22⋊#95C2218yes—
70C22⋊#95C2218yes—
71C26C2311yescharacteristic
72C24×C4—24no—
73C24×C4—24no—
74C24×C4—24no—
75C24×C4—24no—
76C24×C4—24no—
77C24×C4—24no—
78C24×C4—24no—
79C24×C4—24no—
80C24×C4—24no—
81C24×C4—24no—
82C24×C4—24no—
83C24×C4—24no—
84C24×C4—24no—
85C24×C4—24no—
86C24×C4—42no—
87C24×C4—42no—
88C24×C4—42no—
89C24×C4—42no—
90C24×C4—42no—
91C24×C4—42no—
92C24×C4Q818yes—
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2314yes—
107C24×C4C2314yes—
108C24×C4C2314yes—
109C24×C4C2311yescharacteristic
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—24no—
128C22×C22⋊C4—24no—
129C22×C22⋊C4—24no—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—24no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—24no—
134C22×C22⋊C4—24no—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4D418yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142#400—232no—
143#385—232no—
144#380—232no—
145C2×#95—24no—
146C2×#95—24no—
147C2×#95—24no—
148C2×#95—24no—
149C2×#95—24no—
150C2×#95—24no—
151C2×#95—24no—
152C2×#95—24no—
153C2×#95—24no—
154C2×#95—24no—
155C2×#95—24no—
156C2×#95—24no—
157C2×#95—24no—
158C2×#95—24no—
159C2×#95—24no—
160C2×#95—232no—
161C2×#95—42no—
162C2×#95—42no—
163C2×#95—42no—
164C2×#95—42no—
165C2×#95—42no—
166C2×#95—42no—
167C2×#95—42no—
168C2×#95—42no—
169C2×#95D418yes—
170C2×#95C2314yes—
171C2×#95C2314yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—22no—
200C25—22no—
201C25—22no—
202C25C2×D414yes—
203C25C2×Q814yes—
204C25#4114yes—
205C25#4114yes—
206C25#4114yes—
207C25#4114yes—
208C25#4114yes—
209C25C2412yes—
210C25C2411yescharacteristic
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—232no—
216C23×C4—232no—
217C23×C4—232no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—28no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—28no—
233C23×C4—28no—
234C23×C4—28no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—232no—
265C23×C4—28no—
266C23×C4—28no—
267C23×C4—28no—
268C23×C4—28no—
269C23×C4—28no—
270C23×C4—28no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—28no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—28no—
296C23×C4—28no—
297C23×C4—28no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—416no—
318C23×C4—44no—
319C23×C4—44no—
320C23×C4—44no—
321C23×C4—44no—
322C23×C4—44no—
323C23×C4—44no—
324C23×C4—416no—
325C23×C4—416no—
326C23×C4—416no—
327C23×C4—416no—
328C23×C4—416no—
329C23×C4—416no—
330C23×C4—416no—
331C23×C4—416no—
332C23×C4—416no—
333C23×C4—416no—
334C23×C4—416no—
335C23×C4—416no—
336C23×C4—416no—
337C23×C4—416no—
338C23×C4—416no—
339C23×C4—416no—
340C23×C4C2×D414yes—
341C23×C4C2×D414yes—
342C23×C4C2×D414yes—
343C23×C4C2×D414yes—
344C23×C4C2×D414yes—
345C23×C4C2×Q814yes—
346C23×C4C2×Q8116yes—
347C23×C4C2×Q814yes—
348C23×C4#4114yes—
349C23×C4#4114yes—
350C23×C4#4114yes—
351C23×C4C2412yes—
352C23×C4C2412yes—
353C23×C4C2412yes—
354C23×C4C2412yes—
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2412yes—
358C23×C4C2412yes—
359C23×C4C2412yes—
360C23×C4C2412yes—
361C23×C4C2412yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2412yes—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—28no—
368C2×C4⋊C4—28no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—416no—
378C2×C4⋊C4—416no—
379C2×C4⋊C4—416no—
380C2×C4⋊C4—416no—
381C2×C22⋊C4—232no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—416no—
394C2×C22⋊C4—416no—
395C2×C22⋊C4—416no—
396C2×C22⋊C4C2×D4116yes—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—28no—
405#95—28no—
406#95—28no—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95C2×D4116yes—
421C24—28no—
422C24—28no—
423C24—28no—
424C24—28no—
425C24—28no—
426C24—28no—
427C24—28no—
428C24—28no—
429C24—28no—
430C24—28no—
431C24—28no—
432C24—28no—
433C24—28no—
434C24—28no—
435C24—28no—
436C24—28no—
437C24—28no—
438C24—28no—
439C24—28no—
440C24—28no—
441C24—28no—
442C24—28no—
443C24—28no—
444C24—28no—
445C24—28no—
446C24—28no—
447C24—28no—
448C24—28no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24C22⋊Q8116yes—
458C24#123116yes—
459C24#124116yes—
460C24#125116yes—
461C24#125116yes—
462C24#126116yes—
463C24#126116yes—
464C24C22×D414yes—
465C24C22×D412yes—
466C24C22×D412yes—
467C24C22×Q814yes—
468C24C22×Q812yes—
469C24C2×#4114yes—
470C24C2×#4114yes—
471C24C2×#4114yes—
472C24C2×#4114yes—
473C24C2×#4114yes—
474C24C2×#4112yes—
475C24C2×#4112yes—
476C24C2×#4112yes—
477C24C2×#4112yes—
478C24C2×#4112yes—
479C24C2×#4112yes—
480C24C2×#4112yes—
481C24C2×#4112yes—
482C24H(5,𝔽2)12yes—
483C24H(5,𝔽2)12yes—
484C24H(5,𝔽2)12yes—
485C242−1+412yes—
486C24C2511yescharacteristic
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—232no—
498C22×C4—232no—
499C22×C4—232no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—232no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—416no—
607C22×C4—4128no—
608C22×C4—416no—
609C22×C4—416no—
610C22×C4—416no—
611C22×C4—416no—
612C22×C4—416no—
613C22×C4—416no—
614C22×C4—416no—
615C22×C4—416no—
616C22×C4—416no—
617C22×C4—416no—
618C22×C4—416no—
619C22×C4—416no—
620C22×C4—416no—
621C22×C4—416no—
622C22×C4—4128no—
623C22×C4—4128no—
624C22×C4—44no—
625C22×C4—416no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—416no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—44no—
651C22×C4—44no—
652C22×C4—44no—
653C22×C4—44no—
654C22×C4—44no—
655C22×C4—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4C22⋊Q8116yes—
697C22×C4C22×D414yes—
698C22×C4C22×D414yes—
699C22×C4C22×D414yes—
700C22×C4C22×D414yes—
701C22×C4C22×D414yes—
702C22×C4C22×Q814yes—
703C22×C4C22×Q814yes—
704C22×C4C2×#4114yes—
705C22×C4C2×#4114yes—
706C22×C4C2×#4114yes—
707C4⋊C4—416no—
708C4⋊C4—416no—
709C4⋊C4—416no—
710C4⋊C4—416no—
711C22⋊C4—232no—
712C22⋊C4—416no—
713C22⋊C4—416no—
714C22⋊C4—416no—
715C23—232no—
716C23—232no—
717C23—232no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—232no—
731C23—232no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—232no—
740C23—232no—
741C23—232no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—232no—
752C23—232no—
753C23—232no—
754C23—232no—
755C23—232no—
756C23—232no—
757C23#400164yescomplemented
758C23C2×C22⋊Q818yes—
759C23C2×C22⋊Q814yes—
760C23C2×C22⋊Q814yes—
761C23C2×#12318yes—
762C23C2×#12314yes—
763C23#52514yes—
764C23#52514yes—
765C23C2×#12418yes—
766C23C2×#12414yes—
767C23C2×#12518yes—
768C23C2×#12518yes—
769C23C2×#12514yes—
770C23C2×#12514yes—
771C23C2×#12618yes—
772C23C2×#12618yes—
773C23C2×#12614yes—
774C23C2×#12614yes—
775C23#52914yes—
776C23#52914yes—
777C23#53314yes—
778C23#53814yes—
779C23#53814yes—
780C23#53914yes—
781C23#53914yes—
782C23#54314yes—
783C23#54414yes—
784C23D4214yes—
785C23#54614yes—
786C23#54614yes—
787C23#54614yes—
788C23#54614yes—
789C23#54714yes—
790C23#54814yes—
791C23#55114yes—
792C23#55114yes—
793C23#55114yes—
794C23#55114yes—
795C23#55214yes—
796C23#55214yes—
797C23#55314yes—
798C23#55314yes—
799C23#55314yes—
800C23C23×D411yescharacteristic
801C23C23×D411yescharacteristic
802C23C23×Q811yescharacteristic
803C23C22×#4111yescharacteristic
804C23C22×#4111yescharacteristic
805C23C22×#4111yescharacteristic
806C23C22×#4111yescharacteristic
807C23C22×#4111yescharacteristic
808C23C22×#4111yescharacteristic
809C23C22×#4111yescharacteristic
810C23C22×#4111yescharacteristic
811C23C2×H(5,𝔽2)11yescharacteristic
812C23C2×H(5,𝔽2)11yescharacteristic
813C23C2×H(5,𝔽2)11yescharacteristic
814C23C2×2−1+411yescharacteristic
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—232no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—24no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—24no—
840C2×C4—24no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—464no—
844C2×C4—464no—
845C2×C4—464no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—416no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—416no—
869C2×C4—416no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—416no—
880C2×C4—416no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—88no—
924C2×C4—88no—
925C2×C4—88no—
926C2×C4—88no—
927C2×C4—88no—
928C2×C4—88no—
929C2×C4C2×C22⋊Q818yes—
930C22—28no—
931C22—28no—
932C22—28no—
933C22—28no—
934C22—28no—
935C22—28no—
936C22—28no—
937C22—28no—
938C22—28no—
939C22—28no—
940C22—28no—
941C22—2128no—
942C22—28no—
943C22—28no—
944C22—28no—
945C22C2×#40018yes—
946C22C2×#400116yescomplemented
947C22#243718yes—
948C22#243818yes—
949C22#244218yes—
950C22#244318yes—
951C22#244418yes—
952C22#247218yes—
953C22#248018yes—
954C22#248118yes—
955C22#248818yes—
956C22#249318yes—
957C22#251018yes—
958C22#256918yes—
959C22#264618yes—
960C22#285118yes—
961C22C22×C22⋊Q811yescharacteristic
962C22C22×C22⋊Q811yescharacteristic
963C22C22×#12311yescharacteristic
964C22C2×#52511yescharacteristic
965C22C2×#52511yescharacteristic
966C22C22×#12411yescharacteristic
967C22C22×#12511yescharacteristic
968C22C22×#12511yescharacteristic
969C22C22×#12611yescharacteristic
970C22C22×#12611yescharacteristic
971C22C2×#52911yescharacteristic
972C22C2×#52911yescharacteristic
973C22C2×#53311yescharacteristic
974C22C2×#53811yescharacteristic
975C22C2×#53811yescharacteristic
976C22C2×#53911yescharacteristic
977C22C2×#53911yescharacteristic
978C22C2×#54311yescharacteristic
979C22C2×#54411yescharacteristic
980C22C2×D4211yescharacteristic
981C22C2×#54611yescharacteristic
982C22C2×#54611yescharacteristic
983C22C2×#54611yescharacteristic
984C22C2×#54611yescharacteristic
985C22C2×#54711yescharacteristic
986C22C2×#54811yescharacteristic
987C22C2×#55111yescharacteristic
988C22C2×#55111yescharacteristic
989C22C2×#55111yescharacteristic
990C22C2×#55111yescharacteristic
991C22C2×#55211yescharacteristic
992C22C2×#55211yescharacteristic
993C22C2×#55311yescharacteristic
994C22C2×#55311yescharacteristic
995C22C2×#55311yescharacteristic
996C4—28no—
997C4—44no—
998C4—44no—
999C4—44no—
1000C4—44no—
1001C4—44no—
1002C4—44no—
1003C4—44no—
1004C4—82no—
1005C4—82no—
1006C4—82no—
1007C4—82no—
1008C4—82no—
1009C4—82no—
1010C2—216no—
1011C2#14767116yesdirect product factor
1012C2C22×#40011yescharacteristic
1013C2C2×#264611yescharacteristic
1014C2C2×#243711yescharacteristic
1015C2C2×#244311yescharacteristic
1016C2C2×#247211yescharacteristic
1017C2C2×#248011yescharacteristic
1018C2C2×#248111yescharacteristic
1019C2C2×#244411yescharacteristic
1020C2C2×#244211yescharacteristic
1021C2C2×#243811yescharacteristic
1022C2C2×#248811yescharacteristic
1023C2C2×#249311yescharacteristic
1024C2C2×#251011yescharacteristic
1025C2C2×#256911yescharacteristic
1026C2C2×#285111yescharacteristic
subgroupG/H
center, socleC25C24
commutator, Frattini, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#400C2semidirect
5. #14767C2direct (N × H)
6. C2×#1445C2semidirect
7. C2×#1443C2semidirect
8. C2×#1443C2semidirect
9. C2×#1442C2semidirect
10. C2×#1442C2semidirect
11. C2×#1442C2semidirect
12. C2×#1441C2semidirect
29. C2×#400C22semidirect
60. #1445C22semidirect
61. #1443C22semidirect
62. #1443C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1441C22semidirect
757. C23#400semidirect
946. C22C2×#400semidirect
1011. C2#14767direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4002
C22×#3852
C22×#3802
C23×#952
#147672
C2×#14452
C2×#14432
C2×#14422
C2×#14412
C2×C22⋊#952