Finite Group Databasebeta

← #2655671

Subgroups — #2655671

Order 512.

2406 conjugacy classes of subgroups.

The subgroup lattice has 951 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16952C212yesmaximal, complemented
2#16823C211yesmaximal, characteristic, complemented
3#16738C212yesmaximal, complemented
4#16666C211yesmaximal, characteristic, complemented
5#16614C212yesmaximal, complemented
6#16375C212yesmaximal, complemented
7#16299C212yesmaximal, complemented
8#16297C212yesmaximal
9#15993C212yesmaximal, complemented
10#15985C212yesmaximal, complemented
11#15770C212yesmaximal, complemented
12#15586C212yesmaximal, complemented
13#15246C212yesmaximal, complemented
14#14717C211yesmaximal, characteristic
15#14674C211yesmaximal, characteristic, complemented
16#14338C211yesmaximal, characteristic
17#14213C211yesmaximal, characteristic, complemented
18#13873C212yesmaximal
19#13869C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23C2×#395C2212yescomplemented
24C2×#393C2211yescharacteristic
25C2×#393C2211yescharacteristic
26C2×#393C2212yes—
27C2×#393C2212yes—
28C2×#393C2212yes—
29C2×#391C2212yescomplemented
30C2×#388C2212yes—
31C2×#388C2212yes—
32C2×#387C2212yescomplemented
33C2×#381C2211yescharacteristic
34C2×#381C2211yescharacteristic
35C2×#380C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2212yes—
38C2×#379C2212yes—
39C2×#379C2211yescharacteristic
40C2×#379C2212yes—
41C2×C4×C22⋊C4C2212yes—
42#1446C2212yescomplemented
43#1446C2212yescomplemented
44#1446C2212yescomplemented
45#1446C2212yescomplemented
46#1445C2212yescomplemented
47#1445C2212yescomplemented
48#1445C2212yescomplemented
49#1444C2212yescomplemented
50#1444C2212yescomplemented
51#1443C2212yescomplemented
52#1443C2212yescomplemented
53#1443C2212yescomplemented
54#1442C2212yescomplemented
55#1442C2212yescomplemented
56#1442C2212yescomplemented
57#1442C2212yescomplemented
58#1442C2212yescomplemented
59#1442C2212yescomplemented
60#1442C2212yescomplemented
61#1441C2212yescomplemented
62#1441C2212yescomplemented
63#1441C2212yescomplemented
64#1441C2212yescomplemented
65#1440C2212yes—
66#1440C2212yes—
67#1440C2212yes—
68#1440C2212yes—
69#1439C2211yescharacteristic
70#1439C2211yescharacteristic
71#1439C2211yescharacteristic
72#1439C2212yes—
73#1439C2212yes—
74#1439C2211yescharacteristic
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2211yescharacteristic
82#1439C2212yes—
83#1439C2211yescharacteristic
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1437C2212yes—
91#1437C2212yes—
92#1436C2212yescomplemented
93#1436C2212yescomplemented
94#1436C2212yescomplemented
95#1436C2212yescomplemented
96#1434C2212yescomplemented
97#1434C2212yescomplemented
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2211yescharacteristic
103C22⋊#95C2211yescharacteristic
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2211yescharacteristic
107C26C2311yescharacteristic
108C23×Q8C2311yescharacteristic
109C23×Q8C2312yes—
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8—44no—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C22⋊C4—24no—
127C22×C22⋊C4—42no—
128C22×C22⋊C4—42no—
129C22×C22⋊C4—42no—
130C22×C22⋊C4—42no—
131C22×C22⋊C4Q818yescomplemented
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2312yes—
156#395—44no—
157#393—24no—
158#393—44no—
159#393—42no—
160#393—44no—
161#393—44no—
162#391—44no—
163#388—44no—
164#388—44no—
165#387—44no—
166#381—24no—
167#381—42no—
168#380—44no—
169#380—42no—
170#380—42no—
171#379—44no—
172#379—44no—
173#379—42no—
174C4×C22⋊C4—44no—
175C2×#95C2312yes—
176C2×#95C2311yescharacteristic
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2311yescharacteristic
221C25—22no—
222C25—22no—
223C25—22no—
224C25—22no—
225C25—41no—
226C25—41no—
227C25—42no—
228C25—42no—
229C25—42no—
230C25—42no—
231C25C2×Q814yes—
232C25C2411yescharacteristic
233C25C2411yescharacteristic
234C25C2411yescharacteristic
235C22×Q8—22no—
236C22×Q8—24no—
237C22×Q8—41no—
238C22×Q8—42no—
239C22×Q8—42no—
240C22×Q8—42no—
241C22×Q8—42no—
242C22×Q8—41no—
243C22×Q8—42no—
244C22×Q8—42no—
245C22×Q8—42no—
246C22×Q8—42no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—41no—
255C23×C4—41no—
256C23×C4—41no—
257C23×C4—41no—
258C23×C4—41no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—41no—
262C23×C4—42no—
263C23×C4—41no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4C2×Q814yes—
268C23×C4C2×Q814yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C22⋊Q8—416no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—41no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—416no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—416no—
348C2×C22⋊C4—42no—
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—41no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4C2×Q818yes—
379C2×C22⋊C4C2×Q818yes—
380C2×C22⋊C4#4114yes—
381C2×C42—24no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—22no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—41no—
411#95—41no—
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—41no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433C24—21no—
434C24—21no—
435C24—22no—
436C24—22no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—21no—
441C24—22no—
442C24—22no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24—21no—
447C24—22no—
448C24—22no—
449C24—21no—
450C24—21no—
451C24—22no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24—21no—
458C24—22no—
459C24—28no—
460C24—28no—
461C24—48no—
462C24—44no—
463C24—48no—
464C24—44no—
465C24—44no—
466C24—44no—
467C24—44no—
468C24—48no—
469C24—44no—
470C24—44no—
471C24—84no—
472C24—84no—
473C24—82no—
474C24—84no—
475C24—84no—
476C24—82no—
477C24—84no—
478C24—84no—
479C24—84no—
480C24—84no—
481C24—84no—
482C24C22×Q812yes—
483C24C22×Q812yes—
484C24C22×Q812yes—
485C24C2×#4112yes—
486C24H(5,𝔽2)12yes—
487C24H(5,𝔽2)12yes—
488C24H(5,𝔽2)12yes—
489C24C2511yescharacteristic
490C2×Q8—44no—
491C2×Q8—48no—
492C2×Q8—82no—
493C2×Q8—84no—
494C2×Q8—82no—
495C2×Q8—84no—
496C2×Q8—84no—
497C2×Q8—84no—
498C2×Q8—84no—
499C2×Q8—84no—
500C2×Q8—84no—
501C2×Q8—84no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
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—28no—
533C22×C4—28no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
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—21no—
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—21no—
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—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—48no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4—84no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—82no—
620C22×C4—84no—
621C22×C4—84no—
622C22×C4C22×Q814yes—
623C22×C4C22×Q814yes—
624C22×C4C2×#4112yes—
625C22×C4C2×#4112yes—
626C22×C4H(5,𝔽2)12yes—
627C22×C4H(5,𝔽2)14yes—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—44no—
631C4⋊C4—84no—
632C4⋊C4—82no—
633C4⋊C4—84no—
634C4⋊C4—84no—
635C4⋊C4—82no—
636C4⋊C4—84no—
637C4⋊C4—84no—
638C22⋊C4—216no—
639C22⋊C4—48no—
640C22⋊C4—44no—
641C22⋊C4—44no—
642C22⋊C4—48no—
643C22⋊C4—44no—
644C22⋊C4—48no—
645C22⋊C4—44no—
646C22⋊C4—48no—
647C22⋊C4—84no—
648C22⋊C4—82no—
649C22⋊C4—84no—
650C22⋊C4—84no—
651C22⋊C4—84no—
652C22⋊C4—82no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C22⋊C4—84no—
658C22⋊C4—84no—
659C22⋊C4—84no—
660C42—84no—
661C42—84no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—24no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—22no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—22no—
687C23—24no—
688C23—22no—
689C23—24no—
690C23—22no—
691C23—24no—
692C23—22no—
693C23—416no—
694C23—416no—
695C23—42no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—41no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—41no—
714C23—41no—
715C23—42no—
716C23—42no—
717C23—41no—
718C23—41no—
719C23—42no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—41no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—816no—
732C23—88no—
733C23—816no—
734C23—88no—
735C23—816no—
736C23—88no—
737C23—88no—
738C23—816no—
739C23—88no—
740C23#54314yes—
741C23#55414yes—
742C23C23×Q811yescharacteristic
743C23C22×#4111yescharacteristic
744C23C2×H(5,𝔽2)11yescharacteristic
745C23C2×H(5,𝔽2)11yescharacteristic
746C23C2×H(5,𝔽2)11yescharacteristic
747C23C2×H(5,𝔽2)11yescharacteristic
748C23C2×H(5,𝔽2)12yes—
749C23#58512yes—
750C23#58512yes—
751C23#58511yescharacteristic
752C23#58512yes—
753Q8—88no—
754Q8—816no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—41no—
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—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
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—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
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—42no—
859C2×C4—88no—
860C2×C4—88no—
861C2×C4—88no—
862C2×C4—88no—
863C22—28no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—42no—
869C22—42no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—42no—
884C22—42no—
885C22—44no—
886C22—42no—
887C22—42no—
888C22—44no—
889C22—42no—
890C22—832no—
891C22—81no—
892C22—82no—
893C22—81no—
894C22—81no—
895C22—82no—
896C22—81no—
897C22C2×#54311yescharacteristic
898C22#345812yes—
899C22C2×#55411yescharacteristic
900C22#349011yescharacteristic
901C22#349411yescharacteristic
902C22#350112yes—
903C22#350111yescharacteristic
904C22#351312yes—
905C22#352112yes—
906C22#353211yescharacteristic
907C22#353311yescharacteristic
908C22#353312yes—
909C22#353311yescharacteristic
910C22#353411yescharacteristic
911C22#353711yescharacteristic
912C22#354012yes—
913C22#354212yes—
914C22#354512yes—
915C22#354512yes—
916C22#354511yescharacteristic
917C22#355812yes—
918C22#355812yes—
919C22#356812yes—
920C4—42no—
921C4—44no—
922C4—42no—
923C4—42no—
924C4—44no—
925C4—44no—
926C4—81no—
927C4—82no—
928C4—82no—
929C4—82no—
930C4—82no—
931C4—82no—
932C4—82no—
933C4—82no—
934C4—82no—
935C4—82no—
936C2—44no—
937C2—44no—
938C2—82no—
939C2#3747911yescharacteristic
940C2#3787211yescharacteristic
941C2#3895912yes—
942C2#4060811yescharacteristic
943C2#4062712yes—
944C2#4807012yes—
945C2#4899711yescharacteristic
946C2#5199311yescharacteristic
947C2#5627011yescharacteristic
948C2#5666011yescharacteristic
949C2#5764312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #16952C2semidirect
2. #16823C2semidirect
3. #16738C2semidirect
4. #16666C2semidirect
5. #16614C2semidirect
6. #16375C2semidirect
7. #16299C2semidirect
9. #15993C2semidirect
10. #15985C2semidirect
11. #15770C2semidirect
12. #15586C2semidirect
13. #15246C2semidirect
15. #14674C2semidirect
17. #14213C2semidirect
23. C2×#395C22semidirect
29. C2×#391C22semidirect
32. C2×#387C22semidirect
42. #1446C22semidirect
43. #1446C22semidirect
44. #1446C22semidirect
45. #1446C22semidirect
46. #1445C22semidirect
47. #1445C22semidirect
48. #1445C22semidirect
49. #1444C22semidirect
50. #1444C22semidirect
51. #1443C22semidirect
52. #1443C22semidirect
53. #1443C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
92. #1436C22semidirect
93. #1436C22semidirect
94. #1436C22semidirect
95. #1436C22semidirect
96. #1434C22semidirect
97. #1434C22semidirect
131. C22×C22⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
#169522
#168232
#167382
#166662
#166142
#163752
#162992
#162972
#159932
#159852
#157702
#155862
#152462
#147172
#146742
#143382
#142132
#138732
#138692