Finite Group Databasebeta

← #612864

Subgroups — #612864

Order 512.

7362 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D4C211yesmaximal, characteristic
2C2×#2848C212yesmaximal, complemented
3C2×#2452C212yesmaximal, complemented
4C2×#2440C211yesmaximal, characteristic, complemented
5#14733C214yesmaximal, complemented
6#14726C212yesmaximal, complemented
7#14723C214yesmaximal, complemented
8#14717C212yesmaximal, complemented
9#14697C211yesmaximal, characteristic, complemented
10#14693C212yesmaximal, complemented
11#14018C212yesmaximal, complemented
12#13977C212yesmaximal, complemented
13#13920C212yesmaximal, complemented
14#13907C211yesmaximal, characteristic, complemented
15#13902C211yesmaximal, characteristic
16#13902C211yesmaximal, characteristic
17C4×#385C211yesmaximal, characteristic, complemented
18C24×D4C2211yescharacteristic
19C25×C4C2212yes—
20C22×C4⋊Q8C2211yescharacteristic, complemented
21C22×C22⋊Q8C2212yes—
22C22×C22⋊Q8C2214yescomplemented
23C22×C4×D4—216no—
24C22×C4×D4—28no—
25C22×C4×D4C2214yes—
26C22×C4×D4C2212yes—
27C22×C4×D4C2212yes—
28C23×C4⋊C4C2211yescharacteristic
29C23×C22⋊C4C2212yes—
30C23×C42C2211yescharacteristic
31#2848—216no—
32#2452—216no—
33#2440—28no—
34C2×#398C2212yescomplemented
35C2×#396C2214yescomplemented
36C2×#395C2212yescomplemented
37C2×#393C2214yescomplemented
38C2×#390C2212yes—
39C2×#390C2212yes—
40C2×#390C2212yes—
41C2×#390C2212yes—
42C2×#389C2212yescomplemented
43C2×#389C2211yescharacteristic, complemented
44C2×#389C2212yescomplemented
45C2×#389C2211yescharacteristic, complemented
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2211yescharacteristic
49C2×#385C2211yescharacteristic
50C2×#385C2214yescomplemented
51C2×#385C2214yescomplemented
52C2×#385C2214yescomplemented
53C2×#385C2214yescomplemented
54C2×#384C2211yescharacteristic, complemented
55C2×#380C2212yes—
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2214yescomplemented
59C2×#379C2212yes—
60C2×#379C2212yes—
61C2×#379C2212yes—
62C2×#379C2212yes—
63C2×C4×C4⋊C4C2212yescomplemented
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66#1441C2214yescomplemented
67#1439C2214yescomplemented
68#1439C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1439C2214yescomplemented
72#1439C2214yescomplemented
73#1438C2212yes—
74#1438C2214yes—
75#1438C2212yes—
76#1436C2214yescomplemented
77#1436C2212yescomplemented
78#1436C2212yescomplemented
79C4⋊#95C2212yescomplemented
80C4⋊#95C2212yescomplemented
81C22⋊#95C2212yes—
82C22⋊#95C2211yescharacteristic
83C22⋊#95C2212yes—
84C22⋊#95C2211yescharacteristic
85C22⋊#95C2214yescomplemented
86C22⋊#95C2214yescomplemented
87C4×#95C2212yescomplemented
88C26C2312yes—
89C23×Q8C2312yes—
90C23×D4—28no—
91C23×D4—28no—
92C23×D4—24no—
93C23×D4—24no—
94C23×D4Q818yescomplemented
95C23×D4C2312yes—
96C23×D4C2312yes—
97C24×C4—28no—
98C24×C4—216no—
99C24×C4—28no—
100C24×C4—48no—
101C24×C4—44no—
102C24×C4C2311yescharacteristic
103C24×C4C2314yes—
104C24×C4C2311yescharacteristic
105C24×C4C2312yes—
106C24×C4C2314yes—
107C24×C4C2311yescharacteristic
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—28no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—216no—
112C2×C22⋊Q8—216no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8—44no—
115C2×C22⋊Q8—48no—
116C2×C4×D4—2128no—
117C2×C4×D4—28no—
118C2×C4×D4—216no—
119C2×C4×D4—28no—
120C2×C4×D4—216no—
121C2×C4×D4—28no—
122C2×C4×D4—28no—
123C2×C4×D4—216no—
124C2×C4×D4—28no—
125C2×C4×D4D4116yes—
126C22×C4⋊C4—28no—
127C22×C4⋊C4D418yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C22⋊C4—28no—
144C22×C22⋊C4—216no—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C42—24no—
162C22×C42—28no—
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2312yes—
167C22×C42C2312yes—
168#398—28no—
169#396—216no—
170#395—28no—
171#393—216no—
172#390—28no—
173#390—28no—
174#390—28no—
175#390—28no—
176#389—24no—
177#389—24no—
178#389—28no—
179#389—28no—
180#385—28no—
181#385—28no—
182#385—216no—
183#385—216no—
184#385—24no—
185#385—216no—
186#385—48no—
187#385D418yescomplemented
188#384—24no—
189#380—24no—
190#380—24no—
191#380—28no—
192#380—216no—
193#379—28no—
194#379—28no—
195#379—28no—
196#379—44no—
197C4×C4⋊C4—28no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—24no—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2311yescharacteristic
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C25—28no—
220C25—24no—
221C25—28no—
222C25—24no—
223C25—24no—
224C25—24no—
225C25—24no—
226C25—24no—
227C25—44no—
228C25—44no—
229C25C2×Q818yes—
230C25C2414yes—
231C25C2411yescharacteristic
232C22×Q8—24no—
233C22×Q8—28no—
234C22×Q8—24no—
235C22×Q8—42no—
236C22×Q8—44no—
237C22×D4—232no—
238C22×D4—232no—
239C22×D4—264no—
240C22×D4—28no—
241C22×D4—28no—
242C22×D4—264no—
243C22×D4—232no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4C2×D418yes—
251C22×D4C2×Q818yes—
252C22×D4C2×Q818yes—
253C22×D4#4118yes—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—264no—
261C23×C4—22no—
262C23×C4—28no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—28no—
267C23×C4—28no—
268C23×C4—28no—
269C23×C4—28no—
270C23×C4—28no—
271C23×C4—28no—
272C23×C4—28no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—28no—
276C23×C4—28no—
277C23×C4—44no—
278C23×C4—44no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4—42no—
283C23×C4—432no—
284C23×C4—464no—
285C23×C4—432no—
286C23×C4—464no—
287C23×C4C2×D414yes—
288C23×C4C2×D418yes—
289C23×C4C2×D4116yes—
290C23×C4C2×D414yes—
291C23×C4C2×Q814yes—
292C23×C4#4114yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2414yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C4⋊Q8—416no—
309C22⋊Q8—432no—
310C22⋊Q8—464no—
311C4×D4—2128no—
312C4×D4—264no—
313C4×D4—264no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—232no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2×D418yes—
350C2×C4⋊C4C2×D418yes—
351C2×C4⋊C4C2×D414yes—
352C2×C4⋊C4C2×D418yescomplemented
353C2×C22⋊C4—264no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×D4116yes—
399C2×C22⋊C4C2×D414yes—
400C2×C22⋊C4C2×D414yes—
401C2×C22⋊C4#4114yes—
402C2×C42—232no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—22no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42C2×D418yes—
416#95—22no—
417#95—22no—
418#95—24no—
419#95—24no—
420#95—28no—
421#95—28no—
422#95—24no—
423#95—28no—
424#95—24no—
425#95—24no—
426#95—28no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—44no—
432#95—42no—
433#95—44no—
434#95C2×D418yescomplemented
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—216no—
440C24—216no—
441C24—232no—
442C24—232no—
443C24—216no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24—24no—
453C24—24no—
454C24—24no—
455C24—24no—
456C24—216no—
457C24—216no—
458C24—416no—
459C24—416no—
460C24—416no—
461C24—416no—
462C24—416no—
463C24—416no—
464C24—416no—
465C24—416no—
466C24—416no—
467C24—48no—
468C24—416no—
469C24—48no—
470C24—48no—
471C24—48no—
472C24—48no—
473C24—48no—
474C24C22×D418yes—
475C24C22×D412yes—
476C24C22×D412yes—
477C24C22×Q818yes—
478C24C22×Q812yes—
479C24C2×#4118yes—
480C24C2×#4112yes—
481C24C2×#4112yes—
482C24H(5,𝔽2)12yes—
483C242−1+412yes—
484C24C2511yescharacteristic
485C2×Q8—48no—
486C2×Q8—416no—
487C2×Q8—48no—
488C2×Q8—88no—
489C2×Q8—84no—
490C2×D4—216no—
491C2×D4—216no—
492C2×D4—232no—
493C2×D4—2256no—
494C2×D4—232no—
495C2×D4—216no—
496C2×D4—216no—
497C2×D4—216no—
498C2×D4—216no—
499C2×D4—216no—
500C2×D4—216no—
501C2×D4—216no—
502C2×D4C22⋊Q8132yescomplemented
503C22×C4—28no—
504C22×C4—216no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—28no—
517C22×C4—216no—
518C22×C4—28no—
519C22×C4—216no—
520C22×C4—216no—
521C22×C4—28no—
522C22×C4—232no—
523C22×C4—216no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
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—22no—
542C22×C4—24no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—216no—
557C22×C4—232no—
558C22×C4—232no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—416no—
584C22×C4—48no—
585C22×C4—416no—
586C22×C4—416no—
587C22×C4—416no—
588C22×C4—416no—
589C22×C4—416no—
590C22×C4—416no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—416no—
594C22×C4—416no—
595C22×C4—416no—
596C22×C4—416no—
597C22×C4—4256no—
598C22×C4—416no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—416no—
602C22×C4C22⋊Q8116yescomplemented
603C22×C4C22×D414yes—
604C22×C4C22×D414yes—
605C22×C4C22×D414yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D414yes—
609C22×C4C22×D418yes—
610C22×C4C22×D412yes—
611C22×C4C22×D414yes—
612C22×C4C22×D414yes—
613C22×C4C22×D412yes—
614C22×C4C22×D414yes—
615C22×C4C22×Q812yes—
616C22×C4C22×Q812yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4C2×#4114yes—
621C22×C4C2×#4112yes—
622C22×C4H(5,𝔽2)14yes—
623C4⋊C4—216no—
624C4⋊C4—28no—
625C4⋊C4—216no—
626C4⋊C4—48no—
627C4⋊C4—48no—
628C4⋊C4—416no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—48no—
635C4⋊C4—416no—
636C4⋊C4—84no—
637C4⋊C4#120116yes—
638C22⋊C4—232no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—232no—
643C22⋊C4—416no—
644C22⋊C4—416no—
645C22⋊C4—416no—
646C22⋊C4—416no—
647C22⋊C4—416no—
648C22⋊C4—416no—
649C22⋊C4—48no—
650C22⋊C4—44no—
651C22⋊C4—48no—
652C22⋊C4—88no—
653C22⋊C4—88no—
654C42—216no—
655C42—216no—
656C42—44no—
657C42—44no—
658C42—48no—
659C23—22no—
660C23—24no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—24no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—264no—
676C23—28no—
677C23—28no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—28no—
688C23—28no—
689C23—28no—
690C23—28no—
691C23—28no—
692C23—28no—
693C23—28no—
694C23—464no—
695C23—464no—
696C23—432no—
697C23—432no—
698C23—432no—
699C23—432no—
700C23—464no—
701C23—464no—
702C23—432no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—432no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23C2×C22⋊Q8116yes—
721C23C2×C22⋊Q814yes—
722C23#53214yes—
723C23#54214yes—
724C23D4214yes—
725C23#54814yes—
726C23D4×Q814yes—
727C23#55414yes—
728C23C23×D411yescharacteristic
729C23C23×D412yes—
730C23C23×D411yescharacteristic
731C23C23×Q811yescharacteristic
732C23C22×#4111yescharacteristic
733C23C22×#4112yes—
734C23C22×#4111yescharacteristic
735C23C2×H(5,𝔽2)11yescharacteristic
736C23C2×H(5,𝔽2)12yes—
737C23C2×2−1+411yescharacteristic
738C23#58512yes—
739Q8—816no—
740D4—264no—
741D4—264no—
742C2×C4—232no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—28no—
757C2×C4—232no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—464no—
776C2×C4—432no—
777C2×C4—464no—
778C2×C4—416no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—44no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
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—44no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—42no—
825C2×C4C2×#12018yes—
826C2×C4C2×#12014yes—
827C2×C4C2×C22⋊Q814yes—
828C2×C4C2×C22⋊Q818yes—
829C2×C4C2×C22⋊Q814yes—
830C2×C4#52514yes—
831C2×C4#52518yes—
832C2×C4D4218yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—28no—
838C22—28no—
839C22—28no—
840C22—24no—
841C22—24no—
842C22—28no—
843C22—216no—
844C22—216no—
845C22—216no—
846C22—4128no—
847C22—48no—
848C22—48no—
849C22—48no—
850C22—48no—
851C22—48no—
852C22—48no—
853C22—48no—
854C22—48no—
855C22—48no—
856C22—48no—
857C22—48no—
858C22—48no—
859C22#245218yescomplemented
860C22C22×#12011yescharacteristic
861C22C22×C22⋊Q811yescharacteristic
862C22C22×C22⋊Q812yes—
863C22C2×#52511yescharacteristic
864C22C2×#52512yes—
865C22C2×#53211yescharacteristic
866C22C2×#54211yescharacteristic
867C22#346012yes—
868C22C2×D4211yescharacteristic
869C22C2×D4212yes—
870C22C2×#54811yescharacteristic
871C22C2×D4×Q811yescharacteristic
872C22D4×#4112yes—
873C22D4×#4112yes—
874C22C2×#55411yescharacteristic
875C22#348112yes—
876C22#348411yescharacteristic
877C22#348412yes—
878C22#348711yescharacteristic
879C22#348912yes—
880C22#350112yes—
881C22#351312yes—
882C22#352012yes—
883C4—24no—
884C4—28no—
885C4—28no—
886C4—42no—
887C4—42no—
888C4—44no—
889C4—44no—
890C4—42no—
891C4—44no—
892C4—42no—
893C4—82no—
894C4—84no—
895C4—82no—
896C4—82no—
897C4#284818yescomplemented
898C2—28no—
899C2—416no—
900C2C2×#245211yescharacteristic
901C2#3468112yes—
902C2#3517411yescharacteristic
903C2#3522512yes—
904C2D4×#12011yescharacteristic
905C2D4×C22⋊Q812yes—
906C2#3610211yescharacteristic
907C2#3621512yes—
908C2#3642811yescharacteristic
909C2#3652811yescharacteristic
910C2C2×#284811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2848C2semidirect
3. C2×#2452C2semidirect
4. C2×#2440C2semidirect
5. #14733C2semidirect
6. #14726C2semidirect
7. #14723C2semidirect
8. #14717C2semidirect
9. #14697C2semidirect
10. #14693C2semidirect
11. #14018C2semidirect
12. #13977C2semidirect
13. #13920C2semidirect
14. #13907C2semidirect
17. C4×#385C2semidirect
20. C22×C4⋊Q8C22semidirect
22. C22×C22⋊Q8C22semidirect
34. C2×#398C22semidirect
35. C2×#396C22semidirect
36. C2×#395C22semidirect
37. C2×#393C22semidirect
42. C2×#389C22semidirect
43. C2×#389C22semidirect
44. C2×#389C22semidirect
45. C2×#389C22semidirect
50. C2×#385C22semidirect
51. C2×#385C22semidirect
52. C2×#385C22semidirect
53. C2×#385C22semidirect
54. C2×#384C22semidirect
58. C2×#380C22semidirect
63. C2×C4×C4⋊C4C22semidirect
66. #1441C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
76. #1436C22semidirect
77. #1436C22semidirect
78. #1436C22semidirect
79. C4⋊#95C22semidirect
80. C4⋊#95C22semidirect
85. C22⋊#95C22semidirect
86. C22⋊#95C22semidirect
87. C4×#95C22semidirect
94. C23×D4Q8semidirect
187. #385D4semidirect
352. C2×C4⋊C4C2×D4semidirect
434. #95C2×D4semidirect
502. C2×D4C22⋊Q8semidirect
602. C22×C4C22⋊Q8semidirect
859. C22#2452semidirect
897. C4#2848semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D42
C2×#28482
C2×#24522
C2×#24402
#147332
#147262
#147232
#147172
#146972
#146932
#140182
#139772
#139202
#139072
#139022
C4×#3852