Finite Group Databasebeta

← #649168

Subgroups — #649168

Order 512.

3846 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic
2C2×#2546C211yesmaximal, characteristic, complemented
3C2×#2434C211yesmaximal, characteristic
4C2×#2434C211yesmaximal, characteristic
5C2×#2360C211yesmaximal, characteristic
6C22×#391C211yesmaximal, characteristic
7#15623C214yesmaximal, complemented
8#15360C214yesmaximal, complemented
9#15190C211yesmaximal, characteristic, complemented
10#15188C211yesmaximal, characteristic, complemented
11#15184C211yesmaximal, characteristic, complemented
12#15180C211yesmaximal, characteristic, complemented
13#14736C214yesmaximal
14#14155C211yesmaximal, characteristic, complemented
15#14139C211yesmaximal, characteristic
16#14024C211yesmaximal, characteristic, complemented
17#14004C214yesmaximal
18#14000C211yesmaximal, characteristic, complemented
19C4×#385C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C42C2211yescharacteristic
31#2857—28no—
32#2546—28no—
33#2434—28no—
34#2434—28no—
35C2×#398C2214yes—
36C2×#395C2212yes—
37C2×#395C2214yes—
38C2×#395C2212yes—
39#2360—28no—
40C2×#391—28no—
41C2×#391C2214yes—
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#389C2214yes—
56C2×#389C2214yes—
57C2×#389C2212yes—
58C2×#389C2211yescharacteristic
59C2×#387C2212yes—
60C2×#385C2212yes—
61C2×#385C2212yes—
62C2×#385C2214yes—
63C2×#385C2212yes—
64C2×#385C2212yes—
65C2×#384C2211yescharacteristic
66C2×#380C2214yes—
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2212yes—
72C2×C4×C22⋊C4C2211yescharacteristic
73C22×#95C2214yes—
74#1445C2214yes—
75#1444C2214yes—
76#1444C2214yes—
77#1442C2214yes—
78#1442C2214yes—
79#1442C2214yes—
80#1441C2214yes—
81#1441C2214yes—
82#1441C2214yes—
83#1441C2214yes—
84#1441C2214yes—
85#1441C2214yes—
86#1436C2212yes—
87#1436C2214yes—
88#1436C2212yes—
89#1436C2214yes—
90C4⋊#95C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C22⋊#95C2214yes—
94C22⋊#95C2212yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—24no—
100C23×Q8—24no—
101C23×Q8—24no—
102C23×Q8—42no—
103C23×Q8—42no—
104C23×Q8C2311yescharacteristic
105C23×Q8C2311yescharacteristic
106C23×Q8C2311yescharacteristic
107C23×Q8C2311yescharacteristic
108C23×Q8C2312yes—
109C24×C4C2312yes—
110C24×C4C2312yes—
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—24no—
122C2×C4⋊Q8—24no—
123C2×C4⋊Q8—42no—
124C2×C4⋊Q8—42no—
125C2×C4⋊Q8—42no—
126C2×C4⋊Q8—42no—
127C2×C4⋊Q8—42no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8D418yes—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8—42no—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—24no—
139C22×C4⋊C4—42no—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2314yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2314yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C42—24no—
165C22×C42—24no—
166C22×C42—42no—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2312yes—
171C22×C42C2312yes—
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2312yes—
176#398—216no—
177#395—216no—
178#395—28no—
179#395—28no—
180#391—24no—
181#391—24no—
182#391—24no—
183#391—24no—
184#391—24no—
185#391—24no—
186#391—24no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—24no—
191#391—216no—
192#391—42no—
193#391D418yes—
194#389—216no—
195#389—24no—
196#389—28no—
197#389—216no—
198#387—28no—
199#385—28no—
200#385—216no—
201#385—28no—
202#385—28no—
203#385Q8116yescomplemented
204#384—24no—
205#380—216no—
206C4×C4⋊C4—24no—
207C4×C4⋊C4—24no—
208C4×C4⋊C4—42no—
209C4×C22⋊C4—24no—
210C4×C22⋊C4—28no—
211C4×C22⋊C4D418yes—
212C2×#95—216no—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2312yes—
236C2×#95C2314yes—
237C2×#95C2311yescharacteristic
238C2×#95C2311yescharacteristic
239C2×#95C2314yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C25C2411yescharacteristic
243C22×Q8—232no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—24no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—24no—
256C22×Q8—24no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—24no—
260C22×Q8—24no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—22no—
273C22×Q8—22no—
274C22×Q8—42no—
275C22×Q8—42no—
276C22×Q8—416no—
277C22×Q8—416no—
278C22×Q8—416no—
279C22×Q8—416no—
280C22×Q8—416no—
281C22×Q8—416no—
282C22×Q8C2×D414yes—
283C22×Q8C2×D414yes—
284C22×Q8#4114yes—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—28no—
300C23×C4—24no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—44no—
307C23×C4C2×D414yes—
308C23×C4C2×D414yes—
309C23×C4C2×Q818yes—
310C23×C4#4114yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2411yescharacteristic
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C23×C4C2411yescharacteristic
327C23×C4C2412yes—
328C23×C4C2411yescharacteristic
329C4⋊Q8—416no—
330C4⋊Q8—416no—
331C4⋊Q8—416no—
332C4⋊Q8—416no—
333C4⋊Q8—416no—
334C22⋊Q8—232no—
335C22⋊Q8—416no—
336C4×Q8—416no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—28no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—416no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—42no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4C2×D414yes—
390C2×C4⋊C4C2×D414yes—
391C2×C4⋊C4C2×D418yes—
392C2×C4⋊C4C2×Q818yescomplemented
393C2×C4⋊C4C2×Q818yescomplemented
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4C2×D418yes—
403C2×C22⋊C4C2×D414yes—
404C2×C22⋊C4C2×D414yes—
405C2×C22⋊C4C2×Q818yes—
406C2×C22⋊C4C2×Q818yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—24no—
427C2×C42—416no—
428C2×C42—42no—
429C2×C42—42no—
430C2×C42—44no—
431C2×C42C2×D414yes—
432C2×C42C2×D414yes—
433C2×C42C2×D414yes—
434#95—28no—
435#95—28no—
436#95—28no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—28no—
443#95—28no—
444#95—24no—
445#95—28no—
446#95—28no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—28no—
452#95—24no—
453#95—44no—
454#95—42no—
455#95—44no—
456#95—42no—
457#95—44no—
458#95C2×D4116yes—
459#95C2×D414yes—
460#95C2×D414yes—
461#95C2×Q818yescomplemented
462#95C2×Q818yescomplemented
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24C22×D412yes—
470C24C22×D412yes—
471C24C22×Q814yes—
472C24C2×#4112yes—
473C242−1+414yes—
474C24C2511yescharacteristic
475C2×Q8—216no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—28no—
480C2×Q8—28no—
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—28no—
484C2×Q8—28no—
485C2×Q8—48no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—48no—
490C2×Q8—4128no—
491C2×Q8—48no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—44no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—216no—
532C22×C4—216no—
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—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
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—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—216no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—416no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—84no—
618C22×C4—88no—
619C22×C4#121116yes—
620C22×C4C22×D412yes—
621C22×C4C22×D414yes—
622C22×C4C22×D414yes—
623C22×C4C22×D414yes—
624C22×C4C22×D412yes—
625C22×C4C22×D414yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D414yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×Q814yes—
635C22×C4C22×Q814yes—
636C22×C4C22×Q814yes—
637C22×C4C22×Q814yes—
638C22×C4C22×Q814yes—
639C22×C4C22×Q814yes—
640C22×C4C2×#4114yes—
641C22×C4C2×#4112yes—
642C22×C4C2×#4112yes—
643C22×C4C2×#4112yes—
644C22×C4H(5,𝔽2)12yes—
645C22×C4H(5,𝔽2)12yes—
646C22×C42−1+414yes—
647C4⋊C4—28no—
648C4⋊C4—216no—
649C4⋊C4—28no—
650C4⋊C4—216no—
651C4⋊C4—48no—
652C4⋊C4—416no—
653C4⋊C4—48no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—416no—
657C4⋊C4—48no—
658C4⋊C4—48no—
659C4⋊C4—416no—
660C4⋊C4—48no—
661C4⋊C4—416no—
662C4⋊C4—44no—
663C4⋊C4—48no—
664C4⋊C4—44no—
665C4⋊C4—84no—
666C22⋊C4—216no—
667C22⋊C4—28no—
668C22⋊C4—216no—
669C22⋊C4—48no—
670C22⋊C4C4⋊Q8116yescomplemented
671C42—28no—
672C42—28no—
673C42—28no—
674C42—48no—
675C42—48no—
676C42—44no—
677C42—44no—
678C42—44no—
679C42—84no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—22no—
691C23—22no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23C2×#12114yes—
699C23C2×C4⋊Q814yes—
700C23#53614yes—
701C23D4×Q818yes—
702C23#55718yes—
703C23C23×D411yescharacteristic
704C23C23×D411yescharacteristic
705C23C23×D411yescharacteristic
706C23C23×Q812yes—
707C23C22×#4111yescharacteristic
708C23C22×#4111yescharacteristic
709C23C2×H(5,𝔽2)11yescharacteristic
710C23C2×H(5,𝔽2)11yescharacteristic
711C23C2×2−1+412yes—
712C23C2×2−1+412yes—
713C23#58512yes—
714Q8—432no—
715Q8—416no—
716Q8—416no—
717Q8—416no—
718Q8—88no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—232no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—432no—
769C2×C4—432no—
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—44no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—816no—
822C2×C4C2×#12114yes—
823C2×C4C2×#12114yes—
824C2×C4#52514yes—
825C2×C4C2×C4⋊Q814yes—
826C2×C4C2×C4⋊Q814yes—
827C2×C4#53814yes—
828C2×C4D4214yes—
829C2×C4D4214yes—
830C2×C4#54614yes—
831C2×C4#54614yes—
832C2×C4D4×Q818yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—28no—
838C22—24no—
839C22—28no—
840C22—24no—
841C22—28no—
842C22—28no—
843C22#254618yescomplemented
844C22C22×#12111yescharacteristic
845C22C2×#52511yescharacteristic
846C22C22×C4⋊Q811yescharacteristic
847C22C2×#53611yescharacteristic
848C22C2×#53811yescharacteristic
849C22C2×D4211yescharacteristic
850C22C2×D4211yescharacteristic
851C22C2×#54611yescharacteristic
852C22C2×#54611yescharacteristic
853C22C2×D4×Q812yes—
854C22C2×D4×Q812yes—
855C22C2×#55712yes—
856C22Q8×#4112yes—
857C22#348912yes—
858C22#348912yes—
859C22#349911yescharacteristic
860C22#350011yescharacteristic
861C22#350112yes—
862C22#350312yes—
863C22#350712yes—
864C22#352312yes—
865C22#353812yes—
866C22#356112yes—
867C4—24no—
868C4—24no—
869C4—28no—
870C4—24no—
871C4—44no—
872C4—42no—
873C4—44no—
874C4—44no—
875C4—44no—
876C4—44no—
877C4—44no—
878C4—44no—
879C4—42no—
880C4—44no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4#242418yes—
885C2—28no—
886C2C2×#242411yescharacteristic
887C2C2×#254611yescharacteristic
888C2#3562111yescharacteristic
889C2D4×C4⋊Q811yescharacteristic
890C2#3627611yescharacteristic
891C2#3654512yes—
892C2#3767611yescharacteristic
893C2#3808111yescharacteristic
894C2#3964012yes—
895C2#5899812yes—
896C2#5909612yes—
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
2. C2×#2546C2semidirect
7. #15623C2semidirect
8. #15360C2semidirect
9. #15190C2semidirect
10. #15188C2semidirect
11. #15184C2semidirect
12. #15180C2semidirect
14. #14155C2semidirect
16. #14024C2semidirect
18. #14000C2semidirect
203. #385Q8semidirect
392. C2×C4⋊C4C2×Q8semidirect
393. C2×C4⋊C4C2×Q8semidirect
461. #95C2×Q8semidirect
462. #95C2×Q8semidirect
670. C22⋊C4C4⋊Q8semidirect
843. C22#2546semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25462
C2×#24342
C2×#23602
C22×#3912
#156232
#153602
#151902
#151882
#151842
#151802
#147362
#141552
#141392
#140242
#140042
#140002
C4×#3852