Finite Group Databasebeta

← #719973

Subgroups — #719973

Order 512.

2830 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2549C212yesmaximal
2C2×#2440C211yesmaximal, characteristic
3C2×#2659C211yesmaximal, characteristic
4#16827C212yesmaximal, complemented
5#16522C212yesmaximal, complemented
6#15779C212yesmaximal, complemented
7#15766C212yesmaximal, complemented
8#15698C212yesmaximal, complemented
9#15318C212yesmaximal, complemented
10#15137C212yesmaximal, complemented
11#15011C212yesmaximal, complemented
12#14914C212yesmaximal
13#14758C212yesmaximal
14#14004C212yesmaximal
15#13908C211yesmaximal, characteristic
16#13880C211yesmaximal, characteristic
17C2×#1442C211yesmaximal, characteristic
18#13802C211yesmaximal, characteristic
19#13782C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2212yes—
22C22×C22⋊Q8C2212yes—
23C23×C4⋊C4C2211yescharacteristic
24#2659—28no—
25#2549—216no—
26#2440—28no—
27C2×#398C2212yes—
28C2×#398C2212yes—
29C2×#398C2212yes—
30C2×#398C2212yes—
31C2×#398C2212yes—
32C2×#395C2212yes—
33C2×#395C2212yes—
34C2×#395C2212yes—
35C2×#395C2212yes—
36C2×#395C2212yes—
37C2×#395C2212yes—
38C2×#391C2212yes—
39C2×#391C2212yes—
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#389C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2212yes—
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2211yescharacteristic
49C2×#385C2211yescharacteristic
50C2×#384C2211yescharacteristic
51C2×#384C2212yes—
52C2×#380C2212yes—
53C2×#380C2211yescharacteristic
54C2×#380C2212yes—
55C2×#380C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C22×#95C2212yes—
60C22×#95C2211yescharacteristic
61C22×#95C2212yes—
62C22×#95C2211yescharacteristic
63#1446C2212yes—
64#1446C2212yes—
65#1446C2212yes—
66#1444C2212yes—
67#1444C2212yes—
68#1444C2212yes—
69#1444C2212yes—
70#1444C2212yes—
71#1444C2212yes—
72#1444C2211yescharacteristic
73#1444C2211yescharacteristic
74#1444C2212yes—
75#1444C2212yes—
76#1442C2212yes—
77#1442C2212yes—
78#1442C2212yes—
79#1442C2212yes—
80#1442C2211yescharacteristic
81#1442C2211yescharacteristic
82#1442C2212yes—
83#1441C2212yes—
84#1441C2212yes—
85#1441C2212yes—
86#1441C2212yes—
87#1441C2212yes—
88#1441C2212yes—
89#1441C2212yes—
90#1441C2212yes—
91#1441C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100C4⋊#95C2212yes—
101C4⋊#95C2212yes—
102C4⋊#95C2212yes—
103#1434C2212yes—
104#1434C2212yes—
105C22⋊#95C2211yescharacteristic
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2211yescharacteristic
109C4×#95C2212yes—
110C23×Q8C2312yes—
111C23×Q8C2312yes—
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—44no—
119C2×C22⋊Q8—28no—
120C2×C22⋊Q8—28no—
121C2×C22⋊Q8—28no—
122C2×C22⋊Q8—28no—
123C2×C22⋊Q8—44no—
124C2×C22⋊Q8—44no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—44no—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163#398—28no—
164#398—28no—
165#398—28no—
166#398—28no—
167#398—28no—
168#395—28no—
169#395—28no—
170#395—28no—
171#395—28no—
172#395—28no—
173#395—44no—
174#391—28no—
175#391—28no—
176#389—24no—
177#389—24no—
178#389—28no—
179#389—28no—
180#389—44no—
181#385—28no—
182#385—28no—
183#385—44no—
184#385D418yes—
185#385Q818yescomplemented
186#384—24no—
187#384—44no—
188#380—24no—
189#380—28no—
190#380—28no—
191#380D418yes—
192C4×C22⋊C4—24no—
193C4×C22⋊C4—28no—
194C4×C22⋊C4Q818yescomplemented
195C2×#95—24no—
196C2×#95—28no—
197C2×#95—44no—
198C2×#95Q818yescomplemented
199C2×#95C2311yescharacteristic
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2311yescharacteristic
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2311yescharacteristic
239C2×#95C2311yescharacteristic
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C25C2411yescharacteristic
244C22×Q8—24no—
245C22×Q8—24no—
246C22×Q8—24no—
247C22×Q8—24no—
248C22×Q8—24no—
249C22×Q8—42no—
250C22×Q8—42no—
251C22×Q8—42no—
252C22×Q8—42no—
253C22×Q8—42no—
254C22×Q8—42no—
255C22×Q8—42no—
256C22×Q8—42no—
257C22×Q8—42no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×Q818yes—
284C23×C4C2×Q814yes—
285C23×C4C2×Q814yes—
286C23×C4C2×Q814yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C4⋊Q8—416no—
306C22⋊Q8—432no—
307C22⋊Q8—432no—
308C2×C4⋊C4—22no—
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—24no—
316C2×C4⋊C4—24no—
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—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
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—416no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4C2×D414yes—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D418yes—
377C2×C4⋊C4C2×Q818yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4C2×D414yes—
390C2×C22⋊C4C2×D418yes—
391C2×C22⋊C4C2×D414yes—
392C2×C22⋊C4C2×Q814yes—
393C2×C22⋊C4C2×Q814yes—
394C2×C22⋊C4C2×Q814yes—
395C2×C22⋊C4C2×Q814yes—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42C2×Q818yes—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—22no—
416#95—24no—
417#95—24no—
418#95—22no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95C2×D418yes—
447#95C2×D418yes—
448#95C2×Q814yes—
449#95C2×Q814yes—
450#95C2×Q818yes—
451#95C2×Q818yes—
452#95C2×Q818yes—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24C22×D412yes—
458C24C22×D412yes—
459C24C22×Q812yes—
460C24C22×Q812yes—
461C24C22×Q812yes—
462C24H(5,𝔽2)12yes—
463C242−1+412yes—
464C24C2511yescharacteristic
465C2×Q8—48no—
466C2×Q8—48no—
467C2×Q8—48no—
468C2×Q8—48no—
469C2×Q8—48no—
470C2×Q8—84no—
471C2×Q8—84no—
472C2×Q8—84no—
473C2×Q8—84no—
474C2×Q8—84no—
475C2×Q8—84no—
476C2×Q8—84no—
477C2×Q8—84no—
478C2×Q8—84no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
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—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
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—28no—
552C22×C4—28no—
553C22×C4—216no—
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—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—82no—
588C22×C4—84no—
589C22×C4—82no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4C4⋊Q8116yes—
601C22×C4C22×D414yes—
602C22×C4C22×D414yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C22×D414yes—
606C22×C4C22×D412yes—
607C22×C4C22×D414yes—
608C22×C4C22×D412yes—
609C22×C4C22×Q812yes—
610C22×C4C22×Q814yes—
611C22×C4C22×Q814yes—
612C22×C4C22×Q814yes—
613C22×C4C22×Q814yes—
614C22×C4C22×Q812yes—
615C22×C4C22×Q812yes—
616C22×C4C22×Q812yes—
617C22×C4C22×Q812yes—
618C22×C4C22×Q814yes—
619C22×C4C22×Q814yes—
620C22×C4C22×Q812yes—
621C22×C4H(5,𝔽2)14yes—
622C4⋊C4—28no—
623C4⋊C4—44no—
624C4⋊C4—48no—
625C4⋊C4—44no—
626C4⋊C4—48no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—44no—
637C4⋊C4—82no—
638C4⋊C4—82no—
639C4⋊C4—84no—
640C4⋊C4—84no—
641C4⋊C4—84no—
642C4⋊C4—84no—
643C4⋊C4—84no—
644C4⋊C4—84no—
645C4⋊C4—84no—
646C4⋊C4—84no—
647C22⋊C4—28no—
648C22⋊C4—28no—
649C22⋊C4—216no—
650C22⋊C4—28no—
651C22⋊C4—48no—
652C22⋊C4C4⋊Q8116yescomplemented
653C42—48no—
654C42—44no—
655C42—44no—
656C42—84no—
657C42—84no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—22no—
662C23—24no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23C2×C4⋊Q814yes—
675C23C2×C4⋊Q814yes—
676C23#54414yes—
677C23D4214yes—
678C23D4×Q814yes—
679C23D4×Q814yes—
680C23Q8214yes—
681C23C23×D411yescharacteristic
682C23C23×D411yescharacteristic
683C23C23×Q811yescharacteristic
684C23C23×Q811yescharacteristic
685C23C23×Q811yescharacteristic
686C23C2×H(5,𝔽2)11yescharacteristic
687C23C2×H(5,𝔽2)12yes—
688C23C2×2−1+411yescharacteristic
689C23#58512yes—
690C23#58512yes—
691C23#58512yes—
692Q8—816no—
693Q8—816no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
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—416no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
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—42no—
791C2×C4—42no—
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—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—816no—
807C2×C4—88no—
808C2×C4—88no—
809C2×C4—816no—
810C2×C4C2×C4⋊Q818yes—
811C2×C4C2×C4⋊Q814yes—
812C2×C4C2×C4⋊Q814yes—
813C22—24no—
814C22—28no—
815C22—24no—
816C22—28no—
817C22—24no—
818C22—24no—
819C22—28no—
820C22—28no—
821C22—24no—
822C22—24no—
823C22#255118yes—
824C22C22×C4⋊Q811yescharacteristic
825C22C22×C4⋊Q811yescharacteristic
826C22C2×#54411yescharacteristic
827C22#345812yes—
828C22C2×D4211yescharacteristic
829C22C2×D4×Q811yescharacteristic
830C22C2×D4×Q811yescharacteristic
831C22C2×Q8211yescharacteristic
832C22#348411yescharacteristic
833C22#348512yes—
834C22#348511yescharacteristic
835C22#348812yes—
836C22#350011yescharacteristic
837C22#350011yescharacteristic
838C22#350112yes—
839C22#350112yes—
840C22#350112yes—
841C22#350412yes—
842C22#350412yes—
843C22#353412yes—
844C22#356012yes—
845C22#356112yes—
846C22#356412yes—
847C4—24no—
848C4—24no—
849C4—28no—
850C4—44no—
851C4—44no—
852C4—44no—
853C4—44no—
854C4—42no—
855C4—42no—
856C4—44no—
857C4—42no—
858C4—44no—
859C4—44no—
860C4—42no—
861C4—44no—
862C4—82no—
863C4—82no—
864C4—82no—
865C2—28no—
866C2C2×#255111yescharacteristic
867C2#3533011yescharacteristic
868C2#3539111yescharacteristic
869C2#3595012yes—
870C2#3768812yes—
871C2#3962012yes—
872C2#4062012yes—
873C2#4300311yescharacteristic
874C2#4349211yescharacteristic
875C2#4388911yescharacteristic
876C2#4444911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #16827C2semidirect
5. #16522C2semidirect
6. #15779C2semidirect
7. #15766C2semidirect
8. #15698C2semidirect
9. #15318C2semidirect
10. #15137C2semidirect
11. #15011C2semidirect
185. #385Q8semidirect
194. C4×C22⋊C4Q8semidirect
198. C2×#95Q8semidirect
652. C22⋊C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25492
C2×#24402
C2×#26592
#168272
#165222
#157792
#157662
#156982
#153182
#151372
#150112
#149142
#147582
#140042
#139082
#138802
C2×#14422
#138022
#137822