Finite Group Databasebeta

← #873672

Subgroups — #873672

Order 512.

3486 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2538C211yesmaximal, characteristic
3C2×#2434C211yesmaximal, characteristic, complemented
4C2×#2409C211yesmaximal, characteristic
5#16520C214yesmaximal, complemented
6#15779C214yesmaximal, complemented
7#15421C214yesmaximal, complemented
8#15199C211yesmaximal, characteristic, complemented
9#15195C211yesmaximal, characteristic, complemented
10#15185C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic, complemented
12#15182C211yesmaximal, characteristic, complemented
13#15178C211yesmaximal, characteristic, complemented
14#14702C211yesmaximal, characteristic, complemented
15#14407C214yesmaximal
16#14024C211yesmaximal, characteristic, complemented
17#14024C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2857—28no—
31#2538—28no—
32#2434—28no—
33#2409—28no—
34C2×#396C2212yes—
35C2×#396C2212yes—
36C2×#395C2212yes—
37C2×#395C2214yes—
38C2×#393C2212yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#390C2212yes—
50C2×#389C2214yes—
51C2×#389C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#385C2212yes—
55C2×#385C2214yes—
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#380C2214yes—
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66#1446C2214yes—
67#1445C2214yes—
68#1444C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1437C2212yes—
82#1436C2214yes—
83#1436C2214yes—
84#1436C2214yes—
85#1436C2212yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—42no—
99C23×Q8—42no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×Q8C2312yes—
106C23×D4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2312yes—
110C24×C4C2312yes—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—42no—
114C2×C4⋊Q8—42no—
115C2×C4⋊Q8—42no—
116C2×C4⋊Q8D418yescomplemented
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—42no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×C4×Q8—24no—
130C2×C4×Q8—42no—
131C2×C4×Q8—42no—
132C2×C4×D4—42no—
133C2×C4×D4—42no—
134C2×C4×D4D418yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C42—24no—
165C22×C42—42no—
166C22×C42—42no—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2312yes—
173C22×C42C2312yes—
174#396—28no—
175#396—28no—
176#395—28no—
177#395—216no—
178#393—28no—
179#391—24no—
180#391—24no—
181#391—24no—
182#391—24no—
183#391—24no—
184#391—24no—
185#391—42no—
186#391—42no—
187#391—42no—
188#391—42no—
189#390—28no—
190#389—216no—
191#389—28no—
192#386—28no—
193#386Q8116yescomplemented
194#385—216no—
195#385—28no—
196#384—24no—
197#384—24no—
198#384—42no—
199#380—24no—
200#380—24no—
201#380—24no—
202#380—216no—
203C4×C22⋊C4—24no—
204C4×C22⋊C4—42no—
205C4×C22⋊C4—42no—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C25C2411yescharacteristic
233C25C2411yescharacteristic
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—24no—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—24no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—42no—
256C22×Q8—42no—
257C22×Q8—42no—
258C22×Q8—42no—
259C22×Q8—416no—
260C22×Q8—416no—
261C22×Q8—416no—
262C22×Q8—416no—
263C22×Q8—416no—
264C22×Q8—416no—
265C22×Q8—416no—
266C22×Q8C2×D414yes—
267C22×Q8C2×D414yes—
268C22×Q8#4114yes—
269C22×D4—41no—
270C22×D4—41no—
271C22×D4—42no—
272C22×D4C2×D414yes—
273C22×D4C2×Q818yes—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4C2×D414yes—
300C23×C4C2×D414yes—
301C23×C4C2×Q818yescomplemented
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2411yescharacteristic
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C23×C4C2412yes—
318C23×C4C2411yescharacteristic
319C4⋊Q8—416no—
320C4⋊Q8—416no—
321C22⋊Q8—416no—
322C22⋊Q8—416no—
323C22⋊Q8—416no—
324C22⋊Q8—416no—
325C4×Q8—416no—
326C4×D4—416no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
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—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—41no—
360C2×C4⋊C4—41no—
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—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4C2×D414yes—
375C2×C4⋊C4C2×D4116yes—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4C2×D414yes—
405C2×C22⋊C4C2×D414yes—
406C2×C22⋊C4C2×Q818yes—
407C2×C22⋊C4C2×Q818yes—
408C2×C22⋊C4C2×Q818yescomplemented
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—24no—
414C2×C42—22no—
415C2×C42—24no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—416no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42C2×D414yes—
430C2×C42C2×D414yes—
431#95—24no—
432#95—28no—
433#95—28no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—28no—
440#95—28no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—28no—
445#95—42no—
446#95—44no—
447#95—44no—
448#95—44no—
449#95—42no—
450#95—42no—
451#95—44no—
452#95—44no—
453#95—44no—
454#95—44no—
455#95C2×Q818yescomplemented
456#95C2×Q818yescomplemented
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24C22×D412yes—
476C24C22×D412yes—
477C24C22×Q814yes—
478C24C22×Q814yes—
479C24C2511yescharacteristic
480C2×Q8—28no—
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—28no—
484C2×Q8—28no—
485C2×Q8—28no—
486C2×Q8—28no—
487C2×Q8—28no—
488C2×Q8—28no—
489C2×Q8—48no—
490C2×Q8—48no—
491C2×Q8—48no—
492C2×Q8—48no—
493C2×Q8—48no—
494C2×Q8—48no—
495C2×Q8—4128no—
496C2×Q8—48no—
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×D4—44no—
510C2×D4—44no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4C4⋊Q8116yescomplemented
514C22×C4—21no—
515C22×C4—21no—
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—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
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—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—216no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
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—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
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—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4C22×D412yes—
627C22×C4C22×D414yes—
628C22×C4C22×D412yes—
629C22×C4C22×D414yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D414yes—
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C22×Q814yes—
636C22×C4C22×Q814yes—
637C22×C4C22×Q814yes—
638C22×C4C22×Q814yes—
639C22×C4C22×Q814yes—
640C22×C4C2×#4114yes—
641C22×C4C2×#4112yes—
642C22×C4H(5,𝔽2)12yes—
643C22×C4H(5,𝔽2)12yes—
644C22×C4H(5,𝔽2)12yes—
645C22×C4H(5,𝔽2)12yes—
646C22×C42−1+414yes—
647C4⋊C4—44no—
648C4⋊C4—416no—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—48no—
652C4⋊C4—48no—
653C4⋊C4—416no—
654C4⋊C4—48no—
655C4⋊C4—416no—
656C4⋊C4—48no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—84no—
663C4⋊C4—88no—
664C22⋊C4—216no—
665C22⋊C4—44no—
666C22⋊C4—44no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—84no—
675C22⋊C4—84no—
676C42—28no—
677C42—28no—
678C42—48no—
679C42—48no—
680C42—44no—
681C42—44no—
682C42—44no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—24no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—41no—
718C23—41no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23C2×C4⋊Q814yes—
728C23C2×C4⋊Q814yes—
729C23C23×D411yescharacteristic
730C23C23×D411yescharacteristic
731C23C23×Q812yes—
732C23C22×#4111yescharacteristic
733C23C2×H(5,𝔽2)11yescharacteristic
734C23C2×H(5,𝔽2)11yescharacteristic
735C23C2×H(5,𝔽2)11yescharacteristic
736C23C2×H(5,𝔽2)11yescharacteristic
737C23C2×2−1+412yes—
738C23#58512yes—
739C23#58512yes—
740Q8—432no—
741Q8—416no—
742Q8—416no—
743Q8—416no—
744D4—416no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—432no—
783C2×C4—432no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—416no—
819C2×C4—416no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4C2×C4⋊Q814yes—
846C2×C4#53414yes—
847C2×C4#53414yes—
848C2×C4#53814yes—
849C2×C4D4214yes—
850C2×C4#54614yes—
851C2×C4#54614yes—
852C2×C4D4×Q818yes—
853C2×C4#56014yes—
854C22—24no—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—24no—
859C22—24no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—42no—
873C22—42no—
874C22—44no—
875C22—44no—
876C22C22×C4⋊Q811yescharacteristic
877C22C2×#53411yescharacteristic
878C22C2×#53411yescharacteristic
879C22#344911yescharacteristic
880C22C2×#53811yescharacteristic
881C22C2×D4211yescharacteristic
882C22C2×#54611yescharacteristic
883C22C2×#54611yescharacteristic
884C22C2×D4×Q812yes—
885C22Q8×#4112yes—
886C22#348712yes—
887C22#349911yescharacteristic
888C22#350011yescharacteristic
889C22#350112yes—
890C22#350112yes—
891C22#350112yes—
892C22#350312yes—
893C22#351812yes—
894C22C2×#56011yescharacteristic
895C22#354112yes—
896C22#354112yes—
897C22#354712yes—
898C22#356212yes—
899C4—28no—
900C4—24no—
901C4—42no—
902C4—42no—
903C4—42no—
904C4—44no—
905C4—44no—
906C4—44no—
907C4—44no—
908C4—44no—
909C4—44no—
910C4—82no—
911C4—82no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4#266818yes—
916C2—44no—
917C2—44no—
918C2#3501111yescharacteristic
919C2D4×C4⋊Q811yescharacteristic
920C2#3627611yescharacteristic
921C2#3738811yescharacteristic
922C2#3768311yescharacteristic
923C2#3809111yescharacteristic
924C2#3959512yes—
925C2#3965912yes—
926C2#4549712yes—
927C2C2×#266811yescharacteristic
928C2#5903612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2857C2semidirect
3. C2×#2434C2semidirect
5. #16520C2semidirect
6. #15779C2semidirect
7. #15421C2semidirect
8. #15199C2semidirect
9. #15195C2semidirect
10. #15185C2semidirect
11. #15182C2semidirect
12. #15182C2semidirect
13. #15178C2semidirect
14. #14702C2semidirect
16. #14024C2semidirect
17. #14024C2semidirect
18. #13922C2semidirect
116. C2×C4⋊Q8D4semidirect
193. #386Q8semidirect
301. C23×C4C2×Q8semidirect
408. C2×C22⋊C4C2×Q8semidirect
455. #95C2×Q8semidirect
456. #95C2×Q8semidirect
513. C2×D4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25382
C2×#24342
C2×#24092
#165202
#157792
#154212
#151992
#151952
#151852
#151822
#151782
#147022
#144072
#140242
#139222
C4×#3862