Finite Group Databasebeta

← #760167

Subgroups — #760167

Order 512.

4918 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic, complemented
2C2×#2411C212yesmaximal, complemented
3C22×#388C211yesmaximal, characteristic, complemented
4#16658C214yesmaximal, complemented
5#14933C212yesmaximal, complemented
6#14928C212yesmaximal, complemented
7#14877C212yesmaximal, complemented
8#14806C212yesmaximal, complemented
9#14720C211yesmaximal, characteristic, complemented
10#14719C211yesmaximal, characteristic, complemented
11#14717C211yesmaximal, characteristic, complemented
12#14716C211yesmaximal, characteristic
13#14135C212yesmaximal, complemented
14#14071C214yesmaximal, complemented
15#14016C212yesmaximal, complemented
16#13967C212yesmaximal, complemented
17#13756C211yesmaximal, characteristic, complemented
18C2×#529—28no—
19C2×#529—216no—
20C22×#126C2212yescomplemented
21C22×#125C2211yescharacteristic, complemented
22C22×#124C2211yescharacteristic, complemented
23C22×#123C2212yes—
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#120C2212yes—
27C22×C4×Q8C2211yescharacteristic, complemented
28C22×C4×D4C2212yes—
29C22×C4×D4C2211yescharacteristic, complemented
30C22×#117C2212yes—
31C22×#117C2212yescomplemented
32C23×C4⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C42C2211yescharacteristic
37#2411—216no—
38C2×#396C2214yes—
39C2×#395C2212yescomplemented
40C2×#394C2214yes—
41C2×#394C2212yescomplemented
42C2×#393C2212yes—
43C2×#392C2212yes—
44C2×#390C2214yes—
45C2×#388—28no—
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#388C2212yes—
49C2×#388C2214yes—
50C2×#388C2212yes—
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2214yes—
54C2×#386C2212yes—
55C2×#385C2212yes—
56C2×#379C2212yes—
57C22×#95C2211yescharacteristic
58C22×#95C2211yescharacteristic
59#1444C2214yescomplemented
60#1442C2214yescomplemented
61#1441C2214yescomplemented
62#1441C2212yescomplemented
63#1441C2212yescomplemented
64#1439C2214yes—
65#1439C2214yes—
66#1439C2212yes—
67#1439C2212yes—
68#1439C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1438C2214yes—
72#1438C2214yes—
73#1437C2214yes—
74#1437C2214yescomplemented
75#1436C2214yescomplemented
76#1436C2214yescomplemented
77C4⋊#95C2212yescomplemented
78C4⋊#95C2212yescomplemented
79C22⋊#95C2212yes—
80C22⋊#95C2212yes—
81C22⋊#95C2211yescharacteristic
82C22⋊#95C2211yescharacteristic
83C22⋊#95C2212yes—
84C22⋊#95C2214yescomplemented
85C4×#95C2212yescomplemented
86C4×#95C2212yescomplemented
87C26C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C23×D4C2312yes—
90C23×D4C2311yescharacteristic
91C23×D4C2314yes—
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99#529—2128no—
100C2×#126—28no—
101C2×#126—28no—
102C2×#126—28no—
103C2×#125—28no—
104C2×#125—24no—
105C2×#124—28no—
106C2×#124—24no—
107C2×#123—28no—
108C2×#123—28no—
109C2×#123D4116yescomplemented
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—28no—
112C2×#121—28no—
113C2×#121—24no—
114C2×#120—28no—
115C2×#120—28no—
116C2×#120—44no—
117C2×C4×Q8—28no—
118C2×C4×Q8—24no—
119C2×C4×D4—28no—
120C2×C4×D4—28no—
121C2×C4×D4—28no—
122C2×C4×D4—28no—
123C2×C4×D4—24no—
124C2×#117—28no—
125C2×#117—28no—
126C2×#117—28no—
127C2×#117—28no—
128C2×#117—28no—
129C2×#117—44no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—44no—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2312yes—
142C22×C22⋊C4—24no—
143C22×C22⋊C4—28no—
144C22×C22⋊C4—28no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—24no—
147C22×C22⋊C4—44no—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2312yes—
167C22×C42—28no—
168C22×C42D418yescomplemented
169C22×C42C2312yes—
170C22×C42C2314yes—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175#396—216no—
176#395—44no—
177#394—216no—
178#394—44no—
179#393—44no—
180#392—44no—
181#390—216no—
182#388—216no—
183#388—28no—
184#388—28no—
185#388—28no—
186#388—28no—
187#386—28no—
188#386—216no—
189#386—28no—
190#386—44no—
191#385—28no—
192#379—28no—
193C2×#95—24no—
194C2×#95—24no—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C25—22no—
214C25—24no—
215C25—24no—
216C25—24no—
217C25—22no—
218C25—22no—
219C25—42no—
220C25—42no—
221C25—42no—
222C25C2412yes—
223C25C2412yes—
224C25C2411yescharacteristic
225C22×Q8—24no—
226C22×Q8—22no—
227C22×Q8—24no—
228C22×Q8—42no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—22no—
239C22×D4—28no—
240C22×D4—24no—
241C22×D4—42no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4C2×D418yes—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—28no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—44no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4C2×D418yes—
277C23×C4C2×D414yes—
278C23×C4C2414yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2414yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292#126—264no—
293#125—232no—
294#124—232no—
295#123—264no—
296C22⋊Q8—232no—
297#121—232no—
298#120—432no—
299C4×Q8—232no—
300C4×D4—264no—
301C4×D4—232no—
302#117—264no—
303#117—432no—
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—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—416no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4C2×D418yes—
332C2×C4⋊C4C2×D418yes—
333C2×C22⋊C4—232no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
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—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—416no—
377C2×C22⋊C4—416no—
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⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4C2×D418yes—
387C2×C22⋊C4C2×D418yes—
388C2×C22⋊C4C2×D418yes—
389C2×C22⋊C4#4118yes—
390C2×C22⋊C4#4118yes—
391C2×C42—232no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—28no—
400C2×C42—28no—
401C2×C42—44no—
402C2×C42C2×D414yes—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405C2×C42C2×D414yes—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—28no—
414#95—28no—
415#95—24no—
416#95—24no—
417#95—44no—
418#95—42no—
419#95—42no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—44no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—28no—
429C24—22no—
430C24—24no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—24no—
436C24—24no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—24no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—416no—
450C24—416no—
451C24—48no—
452C24—48no—
453C24—44no—
454C24—44no—
455C24—44no—
456C24—44no—
457C24—44no—
458C24—44no—
459C24—48no—
460C24—48no—
461C24—88no—
462C24—88no—
463C24—84no—
464C24—84no—
465C24C22×D414yes—
466C24C22×D412yes—
467C24C22×D414yes—
468C24C2×#4114yes—
469C24C2×#4114yes—
470C24H(5,𝔽2)12yes—
471C242−1+412yes—
472C24C2511yescharacteristic
473C2×Q8—28no—
474C2×Q8—416no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×D4—28no—
478C2×D4—216no—
479C2×D4—216no—
480C2×D4—216no—
481C2×D4—416no—
482C2×D4—44no—
483C2×D4—416no—
484C2×D4—416no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—416no—
490C2×D4—44no—
491C2×D4—88no—
492C2×D4—88no—
493C2×D4—88no—
494C2×D4—88no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—28no—
510C22×C4—216no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—416no—
567C22×C4—416no—
568C22×C4—416no—
569C22×C4—416no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—48no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—88no—
583C22×C4—88no—
584C22×C4#120116yes—
585C22×C4C22×D414yes—
586C22×C4C22×D412yes—
587C22×C4C22×D414yes—
588C22×C4C22×D414yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D414yes—
593C22×C4C22×D414yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C2×#4114yes—
597C22×C4C2×#4118yes—
598C22×C4C2×#4114yes—
599C22×C4H(5,𝔽2)14yes—
600C4⋊C4—216no—
601C4⋊C4—28no—
602C4⋊C4—216no—
603C4⋊C4—28no—
604C4⋊C4—216no—
605C4⋊C4—216no—
606C4⋊C4—416no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—88no—
610C22⋊C4—216no—
611C22⋊C4—216no—
612C22⋊C4—216no—
613C22⋊C4—216no—
614C22⋊C4—216no—
615C22⋊C4—216no—
616C22⋊C4—216no—
617C22⋊C4—216no—
618C22⋊C4—416no—
619C22⋊C4—416no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—88no—
626C22⋊C4—88no—
627C22⋊C4—88no—
628C22⋊C4—88no—
629C42—216no—
630C42—28no—
631C42—28no—
632C42—28no—
633C42—28no—
634C42—416no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—28no—
640C23—28no—
641C23—28no—
642C23—28no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—28no—
655C23—24no—
656C23—24no—
657C23—416no—
658C23—416no—
659C23—416no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—44no—
673C23—42no—
674C23—42no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—42no—
690C23—44no—
691C23—42no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—832no—
697C23—832no—
698C23—88no—
699C23—88no—
700C23—88no—
701C23—88no—
702C23C2×#12014yes—
703C23#53214yes—
704C23#53714yes—
705C23#54618yes—
706C23#54718yes—
707C23C23×D411yescharacteristic
708C23C23×D412yes—
709C23C22×#4112yes—
710C23C22×#4112yes—
711C23C2×H(5,𝔽2)12yes—
712C23C2×H(5,𝔽2)11yescharacteristic
713C23C2×2−1+411yescharacteristic
714C23#58512yes—
715C23#58512yes—
716Q8—416no—
717D4—416no—
718D4—432no—
719D4—832no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—232no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—28no—
734C2×C4—28no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—28no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—416no—
755C2×C4—416no—
756C2×C4—432no—
757C2×C4—416no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
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—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—88no—
796C2×C4—88no—
797C2×C4C2×#12014yes—
798C2×C4C2×#12014yes—
799C2×C4#52514yes—
800C2×C4#53514yes—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—216no—
808C22—216no—
809C22—44no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—48no—
816C22—48no—
817C22—48no—
818C22—48no—
819C22—832no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—82no—
828C22—84no—
829C22—84no—
830C22—84no—
831C22—84no—
832C22#243018yes—
833C22C22×#12011yescharacteristic
834C22C2×#52511yescharacteristic
835C22C2×#53211yescharacteristic
836C22C2×#53511yescharacteristic
837C22C2×#53711yescharacteristic
838C22#344911yescharacteristic
839C22#344911yescharacteristic
840C22C2×#54612yes—
841C22C2×#54712yes—
842C22D4×#4114yes—
843C22#347514yes—
844C22#348814yes—
845C22#351414yes—
846C22#351912yes—
847C22#352012yes—
848C22#356012yes—
849C22#356412yes—
850C4—24no—
851C4—24no—
852C4—24no—
853C4—24no—
854C4—44no—
855C4—44no—
856C4—42no—
857C4—44no—
858C4—42no—
859C4—44no—
860C4—48no—
861C4—82no—
862C4—82no—
863C4—84no—
864C2—28no—
865C2—84no—
866C2—84no—
867C2C2×#243011yescharacteristic
868C2#3473611yescharacteristic
869C2#3487711yescharacteristic
870C2#3513111yescharacteristic
871C2#3523611yescharacteristic
872C2#3525011yescharacteristic
873C2#3753811yescharacteristic
874C2#5909114yes—
875C2#5910814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14716C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#529C2semidirect
2. C2×#2411C2semidirect
3. C22×#388C2semidirect
4. #16658C2semidirect
5. #14933C2semidirect
6. #14928C2semidirect
7. #14877C2semidirect
8. #14806C2semidirect
9. #14720C2semidirect
10. #14719C2semidirect
11. #14717C2semidirect
13. #14135C2semidirect
14. #14071C2semidirect
15. #14016C2semidirect
16. #13967C2semidirect
17. #13756C2semidirect
20. C22×#126C22semidirect
21. C22×#125C22semidirect
22. C22×#124C22semidirect
27. C22×C4×Q8C22semidirect
29. C22×C4×D4C22semidirect
31. C22×#117C22semidirect
39. C2×#395C22semidirect
41. C2×#394C22semidirect
59. #1444C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
74. #1437C22semidirect
75. #1436C22semidirect
76. #1436C22semidirect
77. C4⋊#95C22semidirect
78. C4⋊#95C22semidirect
84. C22⋊#95C22semidirect
85. C4×#95C22semidirect
86. C4×#95C22semidirect
109. C2×#123D4semidirect
168. C22×C42D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5292
C2×#24112
C22×#3882
#166582
#149332
#149282
#148772
#148062
#147202
#147192
#147172
#147162
#141352
#140712
#140162
#139672
#137562