Finite Group Databasebeta

← #641724

Subgroups — #641724

Order 512.

4334 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic
2C2×#2627C211yesmaximal, characteristic, complemented
3C22×#385C211yesmaximal, characteristic
4C22×#380C211yesmaximal, characteristic
5#16561C214yesmaximal, complemented
6#16400C212yesmaximal, complemented
7#16264C212yesmaximal, complemented
8#14935C212yesmaximal, complemented
9#14826C212yesmaximal, complemented
10#14821C214yesmaximal, complemented
11#14758C212yesmaximal, complemented
12#14728C212yesmaximal, complemented
13#14339C211yesmaximal, characteristic, complemented
14#14281C211yesmaximal, characteristic, complemented
15#14275C211yesmaximal, characteristic, complemented
16#13877C212yesmaximal
17#13869C212yesmaximal
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2212yes—
25C23×C22⋊C4C2212yes—
26C23×C22⋊C4C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28#2848—28no—
29#2627—28no—
30C2×#400C2212yescomplemented
31C2×#398C2214yescomplemented
32C2×#398C2214yescomplemented
33C2×#395C2212yescomplemented
34C2×#385—28no—
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#381C2212yes—
45C2×#381C2212yes—
46C2×#380—28no—
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2214yes—
55C2×#380C2211yescharacteristic
56C2×#379C2212yes—
57C22×#95C2211yescharacteristic
58C22×#95C2212yes—
59C22×#95C2211yescharacteristic
60#1446C2212yescomplemented
61#1445C2212yescomplemented
62#1444C2212yescomplemented
63#1444C2214yescomplemented
64#1443C2214yescomplemented
65#1442C2214yescomplemented
66#1442C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2212yescomplemented
69#1441C2214yescomplemented
70#1441C2214yescomplemented
71#1441C2214yescomplemented
72#1441C2214yescomplemented
73#1441C2214yescomplemented
74#1441C2214yescomplemented
75#1441C2214yescomplemented
76#1440C2214yes—
77#1440C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80C22⋊#95C2212yes—
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2214yes—
84C22⋊#95C2214yes—
85C22⋊#95C2212yes—
86C22⋊#95C2214yes—
87C26C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—44no—
92C24×C4—44no—
93C24×C4D418yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2314yes—
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—44no—
111C2×C22⋊Q8—44no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—28no—
117C22×C4⋊C4—44no—
118C22×C4⋊C4—44no—
119C22×C4⋊C4—44no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2312yes—
135C22×C22⋊C4—24no—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—24no—
138C22×C22⋊C4—28no—
139C22×C22⋊C4—28no—
140C22×C22⋊C4—44no—
141C22×C22⋊C4—44no—
142C22×C22⋊C4Q818yescomplemented
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156#400—28no—
157#398—216no—
158#398—48no—
159#395—28no—
160#385—28no—
161#385—28no—
162#385—28no—
163#385—28no—
164#385—28no—
165#385—28no—
166#385—28no—
167#385—28no—
168#385—44no—
169#381—28no—
170#381—44no—
171#380—24no—
172#380—24no—
173#380—24no—
174#380—24no—
175#380—28no—
176#380—28no—
177#380—28no—
178#380—48no—
179#380D418yes—
180#379—28no—
181C2×#95—24no—
182C2×#95—24no—
183C2×#95—28no—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—24no—
212C25—24no—
213C25—22no—
214C25—42no—
215C25—42no—
216C25C2×D414yes—
217C25C2×Q814yes—
218C25#4114yes—
219C25C2411yescharacteristic
220C25C2411yescharacteristic
221C25C2411yescharacteristic
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—42no—
226C22×Q8—42no—
227C23×C4—24no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—24no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—232no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—28no—
254C23×C4—28no—
255C23×C4—28no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—28no—
261C23×C4—416no—
262C23×C4—42no—
263C23×C4—416no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—44no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—44no—
276C23×C4—42no—
277C23×C4—44no—
278C23×C4—42no—
279C23×C4—432no—
280C23×C4—432no—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4C2×Q814yes—
289C23×C4C2×Q814yes—
290C23×C4#4114yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2414yes—
298C23×C4C2414yes—
299C23×C4C2411yescharacteristic
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C22⋊Q8—416no—
306C22⋊Q8—416no—
307C22⋊Q8—416no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—432no—
342C2×C4⋊C4—416no—
343C2×C4⋊C4—416no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4C2×D418yes—
350C2×C22⋊C4—232no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—432no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—416no—
383C2×C22⋊C4C2×D418yes—
384C2×C22⋊C4C2×Q818yes—
385C2×C22⋊C4C2×Q818yes—
386#95—28no—
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—28no—
396#95—28no—
397#95—28no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95C2×D418yes—
410C24—21no—
411C24—21no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—21no—
416C24—22no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—28no—
421C24—28no—
422C24—28no—
423C24—28no—
424C24—216no—
425C24—216no—
426C24—28no—
427C24—28no—
428C24—28no—
429C24—28no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—22no—
438C24—44no—
439C24—44no—
440C24—48no—
441C24—48no—
442C24—48no—
443C24—48no—
444C24—48no—
445C24—48no—
446C24—48no—
447C24—48no—
448C24—48no—
449C24—48no—
450C24C22⋊Q8116yes—
451C24C22×D412yes—
452C24C22×D412yes—
453C24C22×D412yes—
454C24C22×D412yes—
455C24C22×Q812yes—
456C24C22×Q812yes—
457C24C22×Q812yes—
458C24C2×#4112yes—
459C24C2×#4112yes—
460C24C2×#4112yes—
461C24C2×#4112yes—
462C24H(5,𝔽2)14yes—
463C24H(5,𝔽2)12yes—
464C242−1+414yes—
465C242−1+412yes—
466C24C2511yescharacteristic
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—84no—
471C2×Q8—84no—
472C22×C4—216no—
473C22×C4—216no—
474C22×C4—28no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—28no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—4128no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—416no—
572C22×C4—416no—
573C22×C4—416no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—48no—
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—416no—
588C22×C4—88no—
589C22×C4—88no—
590C22×C4—88no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4#121116yes—
596C22×C4C22×D418yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×Q814yes—
604C22×C4C22×Q814yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4H(5,𝔽2)14yes—
608C4⋊C4—48no—
609C4⋊C4—416no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—44no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—88no—
622C4⋊C4—88no—
623C22⋊C4—216no—
624C22⋊C4—216no—
625C22⋊C4—216no—
626C22⋊C4—416no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—232no—
671C23—22no—
672C23—232no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—416no—
687C23—416no—
688C23—432no—
689C23—432no—
690C23—416no—
691C23—416no—
692C23—416no—
693C23—432no—
694C23—432no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23C2×#12114yes—
704C23C2×C22⋊Q814yes—
705C23C2×C22⋊Q814yes—
706C23C2×C22⋊Q814yes—
707C23#53414yes—
708C23#53614yes—
709C23#53714yes—
710C23#53918yes—
711C23#54418yes—
712C23#54614yes—
713C23D4×Q814yes—
714C23#55214yes—
715C23#55414yes—
716C23C23×D411yescharacteristic
717C23C23×D411yescharacteristic
718C23C23×Q811yescharacteristic
719C23C22×#4111yescharacteristic
720C23C22×#4111yescharacteristic
721C23C2×H(5,𝔽2)12yes—
722C23C2×H(5,𝔽2)12yes—
723C23C2×H(5,𝔽2)11yescharacteristic
724C23C2×2−1+412yes—
725C23C2×2−1+411yescharacteristic
726C23#58512yes—
727Q8—88no—
728C2×C4—232no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—28no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—416no—
753C2×C4—416no—
754C2×C4—416no—
755C2×C4—416no—
756C2×C4—416no—
757C2×C4—416no—
758C2×C4—42no—
759C2×C4—416no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
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—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—832no—
810C2×C4—88no—
811C2×C4—88no—
812C2×C4C2×#12114yes—
813C2×C4C2×#12114yes—
814C2×C4#53414yes—
815C22—28no—
816C22—28no—
817C22—28no—
818C22—28no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—28no—
831C22—28no—
832C22—28no—
833C22—28no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—464no—
839C22—44no—
840C22—44no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—44no—
846C22—44no—
847C22#241718yes—
848C22#262718yescomplemented
849C22C22×#12111yescharacteristic
850C22C22×C22⋊Q811yescharacteristic
851C22C2×#53411yescharacteristic
852C22C2×#53411yescharacteristic
853C22C2×#53611yescharacteristic
854C22C2×#53711yescharacteristic
855C22#344911yescharacteristic
856C22C2×#53912yes—
857C22C2×#54412yes—
858C22C2×#54611yescharacteristic
859C22C2×D4×Q811yescharacteristic
860C22C2×#55211yescharacteristic
861C22C2×#55411yescharacteristic
862C22#348412yes—
863C22#348912yes—
864C22#349012yes—
865C22#349512yes—
866C22#350112yes—
867C22#350512yes—
868C22#353412yes—
869C22#353512yes—
870C22#353612yes—
871C22#353812yes—
872C4—24no—
873C4—24no—
874C4—24no—
875C4—48no—
876C4—44no—
877C4—42no—
878C4—44no—
879C4—84no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4—82no—
886C2—28no—
887C2—28no—
888C2—44no—
889C2C2×#262711yescharacteristic
890C2C2×#241711yescharacteristic
891C2#3498111yescharacteristic
892C2#3501011yescharacteristic
893C2#3530611yescharacteristic
894C2#3744211yescharacteristic
895C2#3745211yescharacteristic
896C2#3768512yes—
897C2#3769212yes—
898C2#3787312yes—
899C2#3788012yes—
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
2. C2×#2627C2semidirect
5. #16561C2semidirect
6. #16400C2semidirect
7. #16264C2semidirect
8. #14935C2semidirect
9. #14826C2semidirect
10. #14821C2semidirect
11. #14758C2semidirect
12. #14728C2semidirect
13. #14339C2semidirect
14. #14281C2semidirect
15. #14275C2semidirect
30. C2×#400C22semidirect
31. C2×#398C22semidirect
32. C2×#398C22semidirect
33. C2×#395C22semidirect
60. #1446C22semidirect
61. #1445C22semidirect
62. #1444C22semidirect
63. #1444C22semidirect
64. #1443C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
74. #1441C22semidirect
75. #1441C22semidirect
142. C22×C22⋊C4Q8semidirect
848. C22#2627semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#26272
C22×#3852
C22×#3802
#165612
#164002
#162642
#149352
#148262
#148212
#147582
#147282
#143392
#142812
#142752
#138772
#138692