Finite Group Databasebeta

← #525004

Subgroups — #525004

Order 512.

5196 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#547C211yesmaximal, characteristic
2C2×#2341C211yesmaximal, characteristic, complemented
3C2×#2297C211yesmaximal, characteristic, complemented
4#14702C211yesmaximal, characteristic, complemented
5#14505C214yesmaximal, complemented
6#14363C214yesmaximal, complemented
7#14287C212yesmaximal, complemented
8#14167C212yesmaximal, complemented
9#14138C211yesmaximal, characteristic, complemented
10#14024C212yesmaximal, complemented
11#13969C212yesmaximal, complemented
12#13937C212yesmaximal, complemented
13#13923C212yesmaximal, complemented
14#13916C212yesmaximal, complemented
15#13871C211yesmaximal, characteristic, complemented
16#13776C212yesmaximal, complemented
17C4×#386C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C23×#41C2211yescharacteristic
20C2×#547—28no—
21C2×#547—28no—
22C2×#547C4116yescomplemented
23C22×C4⋊Q8C2211yescharacteristic
24C22×#123C2212yes—
25C22×#123C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×#121C2212yes—
29C22×C4×Q8C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C23×C4⋊C4C2212yes—
34C23×C42C2211yescharacteristic
35#2341—28no—
36#2297—28no—
37C2×#391C2212yes—
38C2×#391C2212yes—
39C2×#391C2212yes—
40C2×#390C2214yes—
41C2×#390C2212yes—
42C2×#390C2212yes—
43C2×#386C2212yes—
44C2×#386C2214yes—
45C2×#381C2214yes—
46C2×#380C2211yescharacteristic
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×C4×C22⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2212yes—
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53C2×C4×C22⋊C4C2212yes—
54#1441C2214yes—
55#1441C2214yes—
56#1441C2214yes—
57#1440C2214yes—
58#1440C2212yes—
59#1440C2214yes—
60#1440C2214yes—
61#1439C2214yes—
62#1438C2212yes—
63#1438C2214yes—
64#1438C2214yes—
65#1437C2214yes—
66#1437C2212yes—
67#1437C2211yescharacteristic
68#1437C2211yescharacteristic
69#1436C2214yes—
70#1436C2212yes—
71#1436C2212yes—
72#1436C2212yes—
73#1436C2212yes—
74#1436C2214yes—
75#1436C2211yescharacteristic
76#1436C2212yes—
77#1436C2214yes—
78#1436C2211yescharacteristic
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C22⋊#95C2214yes—
83C22⋊#95C2214yes—
84C22⋊#95C2214yes—
85C22⋊#95C2214yes—
86C22⋊#95C2212yes—
87C4×#95C2212yes—
88C22×#41—24no—
89C22×#41—24no—
90C22×#41—44no—
91C22×#41—44no—
92C22×#41—44no—
93C22×#41—44no—
94C22×#41C2×C418yes—
95C22×#41C2×C418yescomplemented
96C22×#41D418yes—
97C22×#41D418yes—
98C23×Q8C2311yescharacteristic
99C23×Q8C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C23×D4C2311yescharacteristic
102C23×D4C2312yes—
103C23×D4C2312yes—
104C24×C4C2311yescharacteristic
105C24×C4C2312yes—
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108C24×C4C2312yes—
109C24×C4C2312yes—
110#547—2128no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8C2×C418yescomplemented
114C2×#123—28no—
115C2×#123—28no—
116C2×#123—28no—
117C2×#123—28no—
118C2×#123C2×C4116yes—
119C2×#123C2×C4116yescomplemented
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8C2×C418yes—
125C2×C22⋊Q8C2×C418yescomplemented
126C2×#121—28no—
127C2×#121—28no—
128C2×#121C2×C4116yes—
129C2×C4×Q8—28no—
130C2×C4×Q8—44no—
131C2×C4×Q8—44no—
132C2×C4×D4—24no—
133C2×C4×D4—24no—
134C2×C4×D4—24no—
135C2×C4×D4—24no—
136C2×C4×D4C2×C418yes—
137C2×C4×D4C2×C418yescomplemented
138C2×#117—24no—
139C2×#117—44no—
140C22×C4⋊C4—28no—
141C22×C4⋊C4—28no—
142C22×C4⋊C4C2×C4116yescomplemented
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2314yes—
167C22×C42—24no—
168C22×C42—44no—
169C22×C42C2312yes—
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2312yes—
175C22×C42C2314yes—
176#391—28no—
177#391—44no—
178#391—44no—
179#390—28no—
180#390—216no—
181#390—28no—
182#386—216no—
183#386—28no—
184#381—216no—
185#380—24no—
186#380—28no—
187#380—44no—
188C4×C22⋊C4—24no—
189C4×C22⋊C4—28no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4—28no—
192C4×C22⋊C4—44no—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C25C2411yescharacteristic
216C25C2412yes—
217C25C2411yescharacteristic
218C2×#41—232no—
219C2×#41—432no—
220C2×#41—432no—
221C2×#41—416no—
222C2×#41—416no—
223C2×#41—432no—
224C2×#41—416no—
225C2×#41—432no—
226C2×#41—416no—
227C2×#41C22⋊C4164yescomplemented
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—24no—
231C22×Q8—24no—
232C22×Q8—24no—
233C22×Q8—24no—
234C22×Q8C22×C414yes—
235C22×Q8C22×C414yes—
236C22×Q8C2×D414yes—
237C22×Q8C2×D414yes—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—42no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4C22×C414yes—
251C22×D4C22×C414yes—
252C22×D4C22×C418yes—
253C22×D4C22×C418yes—
254C22×D4C2×D414yes—
255C22×D4C2×D414yes—
256C22×D4C2×D418yes—
257C22×D4C2×D418yes—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—28no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—44no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4—44no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4C22×C414yes—
282C23×C4C22×C418yes—
283C23×C4C22×C414yes—
284C23×C4C22×C418yes—
285C23×C4C22×C418yes—
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4C2×D418yes—
289C23×C4C2×D418yes—
290C23×C4C2414yes—
291C23×C4C2412yes—
292C23×C4C2414yes—
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C4⋊Q8—232no—
305#123—264no—
306#123—264no—
307C22⋊Q8—232no—
308C22⋊Q8—232no—
309#121—264no—
310C4×Q8—432no—
311C4×D4—232no—
312C4×D4—232no—
313#117—416no—
314C2×C4⋊C4—264no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4C22×C414yes—
337C2×C4⋊C4C22×C418yes—
338C2×C4⋊C4C22×C418yes—
339C2×C4⋊C4C22×C418yes—
340C2×C4⋊C4C22×C414yes—
341C2×C4⋊C4C22×C418yes—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
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⋊C4C22×C414yes—
381C2×C22⋊C4C22×C414yes—
382C2×C22⋊C4C22×C418yes—
383C2×C22⋊C4C22×C418yes—
384C2×C22⋊C4C22×C418yes—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—28no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—44no—
398C2×C42—44no—
399C2×C42—44no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—416no—
403C2×C42C22×C414yes—
404#95—22no—
405#95—24no—
406#95—22no—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—28no—
411#95—28no—
412#95—24no—
413#95—24no—
414#95—42no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—42no—
419#95—42no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95#4118yescomplemented
426C24—24no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—22no—
434C24—24no—
435C24—24no—
436C24—22no—
437C24—22no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24C23×C412yes—
447C24C23×C412yes—
448C24C23×C414yes—
449C24C22×D412yes—
450C24C22×D412yes—
451C24C22×D414yes—
452C24C22×D414yes—
453C24C2511yescharacteristic
454#41—4128no—
455#41—4128no—
456C2×Q8—28no—
457C2×Q8—216no—
458C2×Q8—216no—
459C2×Q8—216no—
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—44no—
463C2×Q8—48no—
464C2×Q8—44no—
465C2×Q8C2×C22⋊C4116yes—
466C2×D4—28no—
467C2×D4—216no—
468C2×D4—28no—
469C2×D4—216no—
470C2×D4—28no—
471C2×D4—216no—
472C2×D4—28no—
473C2×D4—44no—
474C2×D4—416no—
475C2×D4—416no—
476C2×D4—416no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—416no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4C2×C22⋊C4116yes—
485C2×D4C2×C22⋊C4132yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—216no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—216no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—28no—
534C22×C4—216no—
535C22×C4—216no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—48no—
558C22×C4—416no—
559C22×C4—416no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—416no—
563C22×C4—48no—
564C22×C4—416no—
565C22×C4—416no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—416no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—44no—
578C22×C4C2×C22⋊C4116yes—
579C22×C4C2×C22⋊C4132yes—
580C22×C4C23×C412yes—
581C22×C4C23×C414yes—
582C22×C4C23×C412yes—
583C22×C4C23×C414yes—
584C22×C4C23×C412yes—
585C22×C4C23×C414yes—
586C22×C4C23×C412yes—
587C22×C4C23×C412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D414yes—
590C22×C4C22×D412yes—
591C22×C4C22×D414yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C2×#4114yes—
595C22×C4C2×#4114yes—
596C22×C4C2×#4114yes—
597C22×C4H(5,𝔽2)14yes—
598C22×C4H(5,𝔽2)14yes—
599C22×C42−1+414yes—
600C4⋊C4—28no—
601C4⋊C4—216no—
602C4⋊C4—216no—
603C4⋊C4—216no—
604C4⋊C4—28no—
605C4⋊C4—216no—
606C4⋊C4—416no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C22⋊C4—216no—
610C22⋊C4—28no—
611C22⋊C4—216no—
612C22⋊C4—28no—
613C22⋊C4—216no—
614C22⋊C4—48no—
615C22⋊C4—416no—
616C22⋊C4—48no—
617C22⋊C4—416no—
618C22⋊C4—416no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—88no—
622C22⋊C4—84no—
623C22⋊C4—88no—
624C42—28no—
625C42—44no—
626C42—44no—
627C42—48no—
628C42—416no—
629C42—48no—
630C42—48no—
631C23—24no—
632C23—22no—
633C23—24no—
634C23—28no—
635C23—24no—
636C23—22no—
637C23—28no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—28no—
643C23—24no—
644C23—24no—
645C23—28no—
646C23—28no—
647C23—24no—
648C23—24no—
649C23—28no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—24no—
660C23—42no—
661C23—44no—
662C23—44no—
663C23—42no—
664C23—44no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—42no—
669C23—44no—
670C23—42no—
671C23—44no—
672C23—42no—
673C23—44no—
674C23—42no—
675C23—44no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23C22×C22⋊C414yes—
693C23C22×C22⋊C418yes—
694C23C24×C411yescharacteristic
695C23C23×D411yescharacteristic
696C23C23×D411yescharacteristic
697C23C22×#4112yes—
698C23C2×H(5,𝔽2)12yes—
699C23C2×H(5,𝔽2)12yes—
700C23C2×2−1+412yes—
701C23#58512yes—
702C23#58512yes—
703Q8—232no—
704Q8—416no—
705D4—232no—
706D4—432no—
707D4—416no—
708D4—432no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—28no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—28no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—232no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—28no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—432no—
741C2×C4—432no—
742C2×C4—432no—
743C2×C4—432no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—416no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4C22×C22⋊C414yes—
790C2×C4C22×C22⋊C418yes—
791C2×C4C22×C22⋊C414yes—
792C2×C4C4×#4114yes—
793C2×C4#51818yes—
794C2×C4#53414yes—
795C2×C4#53418yes—
796C2×C4#53414yes—
797C22—28no—
798C22—24no—
799C22—28no—
800C22—24no—
801C22—24no—
802C22—28no—
803C22—48no—
804C22—44no—
805C22—44no—
806C22—48no—
807C22—44no—
808C22—48no—
809C22—44no—
810C22—48no—
811C22—44no—
812C22—48no—
813C22—44no—
814C22—48no—
815C22—44no—
816C22—42no—
817C22—44no—
818C22—42no—
819C22—42no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22C23×C22⋊C411yescharacteristic
825C22C2×C4×#4111yescharacteristic
826C22C2×#51812yes—
827C22#342811yescharacteristic
828C22C4×2−1+412yes—
829C22C2×#53412yes—
830C22C2×#53411yescharacteristic
831C22C2×#53411yescharacteristic
832C22D4×#4112yes—
833C22D4×#4112yes—
834C22#348912yes—
835C22#349911yescharacteristic
836C22#350011yescharacteristic
837C22#350612yes—
838C22#351112yes—
839C22#351712yes—
840C22#352012yes—
841C22#353912yes—
842C22#354112yes—
843C22#355412yes—
844C22#356212yes—
845C4—24no—
846C4—24no—
847C4—28no—
848C4—44no—
849C4—44no—
850C4—44no—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—44no—
855C4—82no—
856C4—84no—
857C4—84no—
858C4#230818yes—
859C2—48no—
860C2—44no—
861C2—82no—
862C2C2×#230811yescharacteristic
863C2C22⋊C4×#4111yescharacteristic
864C2#3425911yescharacteristic
865C2#3431612yes—
866C2#3447312yes—
867C2#3988412yes—
868C2#3988912yes—
869C2#3995612yes—
870C2#3996112yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#547C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2341C2semidirect
3. C2×#2297C2semidirect
4. #14702C2semidirect
5. #14505C2semidirect
6. #14363C2semidirect
7. #14287C2semidirect
8. #14167C2semidirect
9. #14138C2semidirect
10. #14024C2semidirect
11. #13969C2semidirect
12. #13937C2semidirect
13. #13923C2semidirect
14. #13916C2semidirect
15. #13871C2semidirect
16. #13776C2semidirect
17. C4×#386C2semidirect
22. C2×#547C4semidirect
95. C22×#41C2×C4semidirect
113. C2×C4⋊Q8C2×C4semidirect
119. C2×#123C2×C4semidirect
125. C2×C22⋊Q8C2×C4semidirect
137. C2×C4×D4C2×C4semidirect
142. C22×C4⋊C4C2×C4semidirect
227. C2×#41C22⋊C4semidirect
425. #95#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5472
C2×#23412
C2×#22972
#147022
#145052
#143632
#142872
#141672
#141382
#140242
#139692
#139372
#139232
#139162
#138712
#137762
C4×#3862