Finite Group Databasebeta

← #696090

Subgroups — #696090

Order 512.

3828 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2503C211yesmaximal, characteristic, complemented
2C2×#2487C211yesmaximal, characteristic, complemented
3C2×#2415C211yesmaximal, characteristic, complemented
4C2×#2616C211yesmaximal, characteristic, complemented
5C2×#2388C211yesmaximal, characteristic
6C2×#2311C211yesmaximal, characteristic, complemented
7#16813C212yesmaximal, complemented
8#16809C212yesmaximal, complemented
9#15561C214yesmaximal, complemented
10#15549C214yesmaximal, complemented
11#15223C212yesmaximal, complemented
12#15177C212yesmaximal, complemented
13#15170C212yesmaximal, complemented
14#15065C212yesmaximal, complemented
15#13997C212yesmaximal, complemented
16#13905C212yesmaximal, complemented
17#13801C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26#2616—28no—
27#2503—28no—
28#2487—28no—
29#2415—28no—
30C2×#400C2212yes—
31C2×#400C2212yes—
32C2×#400C2212yes—
33C2×#399C2212yes—
34C2×#397C2212yes—
35#2388—28no—
36C2×#395C2212yes—
37C2×#395C2211yescharacteristic
38C2×#394C2212yes—
39C2×#394C2214yes—
40C2×#394C2211yescharacteristic
41C2×#394C2212yes—
42C2×#394C2212yes—
43C2×#393C2211yescharacteristic
44C2×#392C2211yescharacteristic
45C2×#392C2212yes—
46#2311—28no—
47C2×#391C2212yes—
48C2×#391C2211yescharacteristic
49C2×#391C2212yes—
50C2×#390C2212yes—
51C2×#389C2212yes—
52C2×#389C2211yescharacteristic
53C2×#389C2212yes—
54C2×#388C2212yes—
55C2×#386C2214yes—
56C2×#386C2212yes—
57C2×#385C2212yes—
58C2×#382C2212yes—
59C2×#381C2214yes—
60C2×#380C2212yes—
61C2×#380C2212yes—
62C2×#380C2212yes—
63C2×#380C2211yescharacteristic
64C2×#380C2212yes—
65C2×#380C2211yescharacteristic
66C2×C4×C4⋊C4C2212yes—
67C2×C4×C22⋊C4C2212yes—
68C2×C4×C22⋊C4C2211yescharacteristic
69#1445C2214yes—
70#1445C2214yes—
71#1445C2214yes—
72#1445C2214yes—
73#1444C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1437C2214yes—
83#1437C2214yes—
84#1437C2214yes—
85C4⋊#95C2212yes—
86C4⋊#95C2214yes—
87#1434C2212yes—
88C4×#95C2212yes—
89C22×#41—24no—
90C22×#41—24no—
91C22×#41—24no—
92C22×#41—28no—
93C22×#41—44no—
94C23×Q8C2311yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C23×D4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2311yescharacteristic
103C24×C4C2312yes—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—28no—
108C2×C22⋊Q8—28no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—44no—
111C2×C22⋊Q8—44no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C2×C4×D4—28no—
116C2×C4×D4—28no—
117C2×C4×D4—44no—
118C2×#117—44no—
119C2×#117D418yescomplemented
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2314yes—
156C22×C42C2312yes—
157#400—28no—
158#400—28no—
159#400—28no—
160#399—28no—
161#397—28no—
162#395—28no—
163#395—24no—
164#394—216no—
165#394—28no—
166#394—28no—
167#394—28no—
168#394—24no—
169#393—24no—
170#392—28no—
171#392—24no—
172#391—24no—
173#391—28no—
174#391—28no—
175#390—28no—
176#389—24no—
177#389—28no—
178#389—28no—
179#388—28no—
180#386—216no—
181#386—28no—
182#385—28no—
183#382—28no—
184#381—216no—
185#380—28no—
186#380—28no—
187#380—28no—
188#380—24no—
189#380—28no—
190#380D418yescomplemented
191C4×C4⋊C4—44no—
192C4×C22⋊C4—28no—
193C4×C22⋊C4D418yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2312yes—
215C25C2412yes—
216C25C2411yescharacteristic
217C25C2411yescharacteristic
218C2×#41—232no—
219C2×#41—432no—
220C2×#41—432no—
221C2×#41—416no—
222C2×#41—416no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—24no—
230C22×Q8—24no—
231C22×Q8—24no—
232C22×Q8—42no—
233C22×D4—22no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—22no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—42no—
251C22×D4—42no—
252C22×D4—41no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4—41no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4—42no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2×D414yes—
280C23×C4#4118yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2414yes—
286C23×C4C2414yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C22⋊Q8—432no—
296C22⋊Q8—416no—
297C22⋊Q8—416no—
298C4×D4—432no—
299C4×D4—416no—
300#117—416no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—416no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4C2×D414yes—
336C2×C4⋊C4C2×D414yes—
337C2×C4⋊C4C2×D418yes—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4C2×D418yes—
385C2×C22⋊C4C2×D418yes—
386C2×C22⋊C4C2×D418yes—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—44no—
393C2×C42—44no—
394C2×C42—44no—
395C2×C42—44no—
396C2×C42C2×D418yes—
397C2×C42C2×D418yes—
398#95—24no—
399#95—24no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—24no—
404#95—28no—
405#95—28no—
406#95—28no—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95C2×D414yes—
417#95C2×D414yes—
418#95C2×D418yes—
419C24—22no—
420C24—22no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—22no—
427C24—21no—
428C24—21no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24C22×D412yes—
452C24C22×D412yes—
453C24C22×D412yes—
454C24C2×#4114yes—
455C242−1+412yes—
456C24C2511yescharacteristic
457#41—4128no—
458C2×Q8—28no—
459C2×Q8—48no—
460C2×Q8—48no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—48no—
467C2×Q8—48no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—216no—
471C2×D4—48no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—44no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—44no—
492C2×D4—48no—
493C2×D4—44no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—216no—
499C22×C4—216no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—216no—
539C22×C4—216no—
540C22×C4—216no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—416no—
575C22×C4—48no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4—88no—
584C22×C4#127116yes—
585C22×C4C22×D414yes—
586C22×C4C22×D414yes—
587C22×C4C22×D414yes—
588C22×C4C22×D418yes—
589C22×C4C22×D414yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C2×#4114yes—
597C22×C4C2×#4114yes—
598C22×C4H(5,𝔽2)14yes—
599C22×C42−1+412yes—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—216no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—416no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C4⋊C4—88no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—416no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—44no—
624C22⋊C4—48no—
625C22⋊C4—44no—
626C22⋊C4—88no—
627C22⋊C4—88no—
628C22⋊C4—88no—
629C22⋊C4—88no—
630C42—216no—
631C42—48no—
632C42—44no—
633C42—88no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—41no—
670C23—42no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—41no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23C2×#12714yes—
715C23C23×D411yescharacteristic
716C23C23×D411yescharacteristic
717C23C23×D411yescharacteristic
718C23C22×#4112yes—
719C23C2×H(5,𝔽2)12yes—
720C23C2×2−1+411yescharacteristic
721C23C2×2−1+411yescharacteristic
722C23#58512yes—
723C23#58512yes—
724C23#58511yescharacteristic
725C23#58511yescharacteristic
726Q8—416no—
727Q8—88no—
728D4—416no—
729D4—416no—
730D4—432no—
731D4—432no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—232no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—28no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—28no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—432no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—816no—
813C2×C4—88no—
814C2×C4#52514yes—
815C2×C4C2×#12714yes—
816C2×C4C2×#12714yes—
817C2×C4#53414yes—
818C2×C4#54618yes—
819C2×C4#54618yes—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—42no—
835C22—44no—
836C22—44no—
837C22—42no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—42no—
843C22—81no—
844C22—82no—
845C22—81no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—81no—
854C22—82no—
855C22—81no—
856C22—82no—
857C22C2×#52511yescharacteristic
858C22C22×#12711yescharacteristic
859C22C2×#53411yescharacteristic
860C22#344912yes—
861C22C2×#54612yes—
862C22C2×#54612yes—
863C22#348511yescharacteristic
864C22#348611yescharacteristic
865C22#348911yescharacteristic
866C22#348911yescharacteristic
867C22#348911yescharacteristic
868C22#348911yescharacteristic
869C22#349312yes—
870C22#349512yes—
871C22#350012yes—
872C22#350011yescharacteristic
873C22#350011yescharacteristic
874C22#350712yes—
875C22#351212yes—
876C22#353912yes—
877C22#354112yes—
878C22#354712yes—
879C22#355112yes—
880C4—24no—
881C4—44no—
882C4—48no—
883C4—44no—
884C4—42no—
885C4—44no—
886C4—44no—
887C4—44no—
888C4—81no—
889C4—84no—
890C4—81no—
891C4—82no—
892C4—82no—
893C4#253918yes—
894C2—44no—
895C2—84no—
896C2—82no—
897C2C2×#253911yescharacteristic
898C2#3532911yescharacteristic
899C2#3563411yescharacteristic
900C2#3575911yescharacteristic
901C2#3608011yescharacteristic
902C2#3784712yes—
903C2#3946312yes—
904C2#4290811yescharacteristic
905C2#4299211yescharacteristic
906C2#4509212yes—
907C2#4511412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2388C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2503C2semidirect
2. C2×#2487C2semidirect
3. C2×#2415C2semidirect
4. C2×#2616C2semidirect
6. C2×#2311C2semidirect
7. #16813C2semidirect
8. #16809C2semidirect
9. #15561C2semidirect
10. #15549C2semidirect
11. #15223C2semidirect
12. #15177C2semidirect
13. #15170C2semidirect
14. #15065C2semidirect
15. #13997C2semidirect
16. #13905C2semidirect
17. #13801C2semidirect
119. C2×#117D4semidirect
190. #380D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25032
C2×#24872
C2×#24152
C2×#26162
C2×#23882
C2×#23112
#168132
#168092
#155612
#155492
#152232
#151772
#151702
#150652
#139972
#139052
#138012