Finite Group Databasebeta

← #879000

Subgroups — #879000

Order 512.

2194 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17078C211yesmaximal, characteristic, complemented
2#17072C211yesmaximal, characteristic, complemented
3#16937C212yesmaximal, complemented
4#15993C212yesmaximal
5#15770C212yesmaximal
6#15426C212yesmaximal
7#15354C212yesmaximal
8#15058C212yesmaximal, complemented
9#15011C212yesmaximal, complemented
10#14887C212yesmaximal
11#14702C211yesmaximal, characteristic
12#14697C211yesmaximal, characteristic
13#14554C212yesmaximal, complemented
14#14471C211yesmaximal, characteristic, complemented
15#14446C211yesmaximal, characteristic, complemented
16#14236C212yesmaximal, complemented
17#14094C212yesmaximal, complemented
18#13943C212yesmaximal
19#13756C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C42C2211yescharacteristic
24C2×#395C2212yes—
25C2×#395C2212yes—
26C2×#395C2212yes—
27C2×#395C2212yes—
28C2×#393C2212yes—
29C2×#391C2211yescharacteristic
30C2×#391C2212yes—
31C2×#391C2212yes—
32C2×#391C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2212yes—
36C2×#388C2212yes—
37C2×#388C2212yes—
38C2×#387C2212yes—
39C2×#385C2212yes—
40C2×#380C2211yescharacteristic
41C2×#380C2211yescharacteristic
42C2×#380C2211yescharacteristic
43#1446C2212yes—
44#1446C2212yes—
45#1445C2212yes—
46#1445C2212yes—
47#1445C2212yes—
48#1445C2212yes—
49#1444C2212yes—
50#1444C2212yes—
51#1443C2212yes—
52#1443C2212yes—
53#1443C2212yes—
54#1442C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1442C2212yes—
59#1442C2212yes—
60#1441C2212yes—
61#1441C2212yes—
62#1441C2212yes—
63#1441C2212yes—
64#1441C2212yes—
65#1441C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1440C2212yes—
70#1440C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1436C2212yes—
75#1436C2212yes—
76#1436C2212yes—
77#1436C2212yes—
78#1436C2212yes—
79#1436C2212yes—
80#1436C2212yes—
81#1436C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2212yes—
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95#1434C2212yes—
96#1434C2212yes—
97#1434C2212yes—
98#1434C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C4×#95C2212yes—
105C4×#95C2212yes—
106C4×#95C2212yes—
107C23×Q8C2311yescharacteristic
108C23×Q8C2312yes—
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C2×#117—24no—
116C2×#117—42no—
117C2×#117—42no—
118C2×#117—42no—
119C2×#117—42no—
120C2×#117Q818yescomplemented
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C42—24no—
147C22×C42—42no—
148C22×C42—42no—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157#395—28no—
158#395—28no—
159#395—44no—
160#395—44no—
161#393—44no—
162#391—24no—
163#391—44no—
164#391—42no—
165#391—44no—
166#389—24no—
167#389—42no—
168#389—44no—
169#388—44no—
170#388—44no—
171#387—28no—
172#385—44no—
173#380—24no—
174#380—42no—
175#380—42no—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C25C2411yescharacteristic
226C22×Q8—22no—
227C22×Q8—24no—
228C22×Q8—22no—
229C22×Q8—24no—
230C22×Q8—22no—
231C22×Q8—41no—
232C22×Q8—41no—
233C22×Q8—41no—
234C22×Q8—42no—
235C22×Q8—41no—
236C22×Q8—42no—
237C22×Q8—42no—
238C22×Q8—42no—
239C22×Q8—42no—
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—41no—
257C23×C4—41no—
258C23×C4—41no—
259C23×C4—41no—
260C23×C4C2×Q814yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C22⋊Q8—416no—
280#117—416no—
281#117—416no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4C2×Q814yes—
335C2×C4⋊C4C2×Q814yes—
336C2×C4⋊C4#4114yes—
337C2×C4⋊C4#4114yes—
338C2×C4⋊C4#4114yes—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4C2×Q818yes—
357C2×C42—24no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—24no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42—41no—
369C2×C42—41no—
370C2×C42—41no—
371C2×C42—41no—
372C2×C42—41no—
373C2×C42—41no—
374C2×C42—416no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42C2×Q818yes—
381C2×C42#4114yes—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24C22×Q812yes—
444C24H(5,𝔽2)12yes—
445C24H(5,𝔽2)12yes—
446C24C2511yescharacteristic
447C2×Q8—48no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—48no—
451C2×Q8—44no—
452C2×Q8—82no—
453C2×Q8—82no—
454C2×Q8—82no—
455C2×Q8—82no—
456C2×Q8—84no—
457C2×Q8—84no—
458C2×Q8—84no—
459C2×Q8—84no—
460C2×Q8—84no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
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—22no—
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—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4C22×Q814yes—
590C22×C4C22×Q814yes—
591C22×C4C22×Q812yes—
592C22×C4C22×Q812yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#4114yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4H(5,𝔽2)12yes—
603C22×C4H(5,𝔽2)12yes—
604C22×C4H(5,𝔽2)12yes—
605C22×C42−1+412yes—
606C22×C42−1+412yes—
607C22×C42−1+412yes—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—48no—
617C4⋊C4—44no—
618C4⋊C4—82no—
619C4⋊C4—82no—
620C4⋊C4—82no—
621C4⋊C4—82no—
622C4⋊C4—84no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C4⋊C4—84no—
627C22⋊C4—216no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C42—44no—
634C42—48no—
635C42—44no—
636C42—44no—
637C42—48no—
638C42—44no—
639C42—84no—
640C42—84no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23#54314yes—
676C23C23×Q811yescharacteristic
677C23C22×#4111yescharacteristic
678C23C22×#4111yescharacteristic
679C23C22×#4111yescharacteristic
680C23C22×#4111yescharacteristic
681C23C2×H(5,𝔽2)11yescharacteristic
682C23C2×H(5,𝔽2)11yescharacteristic
683C23C2×H(5,𝔽2)11yescharacteristic
684C23C2×H(5,𝔽2)11yescharacteristic
685C23C2×H(5,𝔽2)11yescharacteristic
686C23C2×2−1+411yescharacteristic
687C23C2×2−1+411yescharacteristic
688C23C2×2−1+411yescharacteristic
689C23#58511yescharacteristic
690C23#58511yescharacteristic
691Q8—88no—
692Q8—816no—
693C2×C4—232no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—416no—
740C2×C4—416no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4#53314yes—
819C2×C4#54414yes—
820C2×C4#55514yes—
821C2×C4#55614yes—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22C2×#53311yescharacteristic
838C22C2×#54311yescharacteristic
839C22C2×#54411yescharacteristic
840C22#345911yescharacteristic
841C22#346011yescharacteristic
842C22C2×#55511yescharacteristic
843C22C2×#55611yescharacteristic
844C22Q8×#4111yescharacteristic
845C22Q8×#4111yescharacteristic
846C22#348111yescharacteristic
847C22#348211yescharacteristic
848C22#348211yescharacteristic
849C22#349011yescharacteristic
850C22#349011yescharacteristic
851C22#349011yescharacteristic
852C22#349211yescharacteristic
853C22#349211yescharacteristic
854C22#349211yescharacteristic
855C22#349411yescharacteristic
856C22#349511yescharacteristic
857C22#350311yescharacteristic
858C22#350311yescharacteristic
859C22#351411yescharacteristic
860C22#351811yescharacteristic
861C22#351911yescharacteristic
862C22#352211yescharacteristic
863C22#353111yescharacteristic
864C22#353411yescharacteristic
865C22#353511yescharacteristic
866C22#353711yescharacteristic
867C22#353811yescharacteristic
868C22#355011yescharacteristic
869C22#355011yescharacteristic
870C22#355811yescharacteristic
871C22#355911yescharacteristic
872C4—24no—
873C4—24no—
874C4—24no—
875C4—24no—
876C4—44no—
877C4—44no—
878C4—42no—
879C4—42no—
880C4—44no—
881C4—44no—
882C4—44no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C2—44no—
891C2#3505211yescharacteristic
892C2#3628811yescharacteristic
893C2#3648011yescharacteristic
894C2#3730811yescharacteristic
895C2#3794911yescharacteristic
896C2#3795611yescharacteristic
897C2#3844411yescharacteristic
898C2#3844511yescharacteristic
899C2#3876011yescharacteristic
900C2#3878211yescharacteristic
901C2#4623011yescharacteristic
902C2#4629011yescharacteristic
903C2#5229011yescharacteristic
904C2#5923411yescharacteristic
905C2#6004611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17078C2semidirect
2. #17072C2semidirect
3. #16937C2semidirect
8. #15058C2semidirect
9. #15011C2semidirect
13. #14554C2semidirect
14. #14471C2semidirect
15. #14446C2semidirect
16. #14236C2semidirect
17. #14094C2semidirect
120. C2×#117Q8semidirect

Maximal subgroups

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

subgroupindex
#170782
#170722
#169372
#159932
#157702
#154262
#153542
#150582
#150112
#148872
#147022
#146972
#145542
#144712
#144462
#142362
#140942
#139432
#137562