Finite Group Databasebeta

← #722655

Subgroups — #722655

Order 512.

4650 conjugacy classes of subgroups.

The subgroup lattice has 881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic
2C2×#2434C211yesmaximal, characteristic, complemented
3C2×#2409C211yesmaximal, characteristic
4C22×#395C211yesmaximal, characteristic, complemented
5#16608C212yesmaximal, complemented
6#16254C212yesmaximal, complemented
7#15849C212yesmaximal, complemented
8#15762C212yesmaximal, complemented
9#15671C212yesmaximal, complemented
10#15265C212yesmaximal, complemented
11#14914C212yesmaximal, complemented
12#14881C212yesmaximal, complemented
13#14720C212yesmaximal, complemented
14#14720C212yesmaximal, complemented
15#14281C211yesmaximal, characteristic, complemented
16#14016C212yesmaximal
17#14015C212yesmaximal
18#13923C211yesmaximal, characteristic, complemented
19#13784C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C2×#554—28no—
22C2×#554—28no—
23C2×#554—28no—
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2212yes—
26C22×#125C2211yescharacteristic
27C22×#125C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C22×C22⋊Q8C2212yes—
35C22×C4×Q8C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37C22×C4×D4C2211yescharacteristic
38C22×C4×D4C2211yescharacteristic
39C23×C4⋊C4C2211yescharacteristic
40C23×C4⋊C4C2211yescharacteristic
41C23×C4⋊C4C2212yes—
42#2434—28no—
43#2409—28no—
44C2×#395—28no—
45C2×#395C2212yes—
46C2×#395C2212yes—
47C2×#395C2212yes—
48C2×#395C2212yes—
49C2×#395C2212yes—
50C2×#395C2212yes—
51C2×#395C2212yes—
52C2×#395C2214yes—
53C2×#393C2212yes—
54C2×#391C2212yes—
55C2×#391C2212yes—
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#385C2212yes—
59C2×#385C2212yes—
60C2×#385C2212yes—
61C2×#385C2214yes—
62C2×#380C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C22×#95C2212yes—
65C22×#95C2211yescharacteristic
66#1446C2214yes—
67#1446C2212yes—
68#1445C2212yes—
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1442C2214yes—
74#1441C2212yes—
75#1441C2212yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2212yes—
80#1441C2212yes—
81#1439C2214yes—
82#1439C2214yes—
83#1437C2212yes—
84#1436C2214yes—
85#1436C2214yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1434C2212yes—
90C22⋊#95C2214yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C22⋊#95C2212yes—
94C22⋊#95C2212yes—
95C22⋊#95C2212yes—
96C22⋊#95C2212yes—
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—24no—
100C23×Q8—48no—
101C23×Q8C2312yes—
102C23×Q8C2312yes—
103C23×Q8C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×Q8C2311yescharacteristic
106C23×D4C2311yescharacteristic
107C24×C4C2312yes—
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2312yes—
114C24×C4C2311yescharacteristic
115#554—2128no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—28no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—48no—
121C2×#125—24no—
122C2×#125—24no—
123C2×#125—24no—
124C2×#125—24no—
125C2×#125—24no—
126C2×#125—24no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—28no—
134C2×C22⋊Q8—24no—
135C2×C22⋊Q8—24no—
136C2×C22⋊Q8—24no—
137C2×C22⋊Q8—24no—
138C2×C22⋊Q8—24no—
139C2×C22⋊Q8—24no—
140C2×C22⋊Q8—24no—
141C2×C22⋊Q8—24no—
142C2×C22⋊Q8—24no—
143C2×C22⋊Q8—24no—
144C2×C22⋊Q8—24no—
145C2×C22⋊Q8—48no—
146C2×C22⋊Q8D418yes—
147C2×C4×Q8—24no—
148C2×C4×Q8—24no—
149C2×C4×Q8—24no—
150C2×C4×D4—24no—
151C2×C4×D4—24no—
152C2×C4×D4—24no—
153C2×C4×D4—24no—
154C2×C4×D4—24no—
155C2×C4×D4—24no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4D418yes—
159C22×C4⋊C4—24no—
160C22×C4⋊C4—24no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—24no—
163C22×C4⋊C4—24no—
164C22×C4⋊C4—28no—
165C22×C4⋊C4—48no—
166C22×C4⋊C4D418yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2314yes—
176C22×C4⋊C4C2314yes—
177C22×C4⋊C4C2314yes—
178C22×C4⋊C4C2314yes—
179C22×C4⋊C4C2314yes—
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2314yes—
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2314yes—
199C22×C42C2311yescharacteristic
200C22×C42C2311yescharacteristic
201C22×C42C2311yescharacteristic
202C22×C42C2312yes—
203#395—28no—
204#395—28no—
205#395—28no—
206#395—28no—
207#395—28no—
208#395—28no—
209#395—28no—
210#395—48no—
211#393—28no—
212#391—28no—
213#391—28no—
214#386—28no—
215#386Q8116yescomplemented
216#385—28no—
217#385—28no—
218#385—28no—
219#385—48no—
220#380—24no—
221C4×C22⋊C4—24no—
222C2×#95—28no—
223C2×#95—24no—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2312yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2314yes—
241C2×#95C2314yes—
242C2×#95C2314yes—
243C2×#95C2314yes—
244C2×#95C2314yes—
245C25C2411yescharacteristic
246C25C2411yescharacteristic
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—24no—
251C22×Q8—24no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—24no—
258C22×Q8—24no—
259C22×Q8—24no—
260C22×Q8—24no—
261C22×Q8—28no—
262C22×Q8—28no—
263C22×Q8—24no—
264C22×Q8—44no—
265C22×Q8—44no—
266C22×Q8—42no—
267C22×Q8—44no—
268C22×Q8—44no—
269C22×Q8—432no—
270C22×Q8—432no—
271C22×Q8—432no—
272C22×Q8—416no—
273C22×Q8C2×D414yes—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—24no—
277C22×D4C2×D414yes—
278C22×D4C2×Q818yes—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—28no—
291C23×C4—24no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—44no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—44no—
303C23×C4—44no—
304C23×C4—44no—
305C23×C4—44no—
306C23×C4—44no—
307C23×C4—44no—
308C23×C4C2×D414yes—
309C23×C4C2×D414yes—
310C23×C4C2×D414yes—
311C23×C4C2×D414yes—
312C23×C4C2×D414yes—
313C23×C4C2×D414yes—
314C23×C4C2×Q818yes—
315C23×C4C2414yes—
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2414yes—
326C23×C4C2414yes—
327C23×C4C2414yes—
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C4⋊Q8—232no—
333C4⋊Q8—432no—
334#125—232no—
335#125—232no—
336C22⋊Q8—232no—
337C22⋊Q8—232no—
338C22⋊Q8—232no—
339C22⋊Q8—232no—
340C22⋊Q8—232no—
341C22⋊Q8—232no—
342C22⋊Q8—432no—
343C4×Q8—232no—
344C4×D4—232no—
345C4×D4—232no—
346C4×D4—232no—
347C2×C4⋊C4—232no—
348C2×C4⋊C4—232no—
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—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—28no—
390C2×C4⋊C4—28no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—28no—
393C2×C4⋊C4—28no—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—28no—
396C2×C4⋊C4—28no—
397C2×C4⋊C4—28no—
398C2×C4⋊C4—28no—
399C2×C4⋊C4—28no—
400C2×C4⋊C4—44no—
401C2×C4⋊C4—44no—
402C2×C4⋊C4—44no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4—44no—
405C2×C4⋊C4—44no—
406C2×C4⋊C4—432no—
407C2×C4⋊C4C2×D414yes—
408C2×C4⋊C4C2×D414yes—
409C2×C4⋊C4C2×D414yes—
410C2×C4⋊C4C2×D414yes—
411C2×C4⋊C4C2×D414yes—
412C2×C4⋊C4C2×D414yes—
413C2×C4⋊C4C2×D414yes—
414C2×C4⋊C4C2×D414yes—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—28no—
436C2×C22⋊C4—44no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—44no—
439C2×C22⋊C4C2×D414yes—
440C2×C22⋊C4C2×D414yes—
441C2×C22⋊C4C2×D414yes—
442C2×C22⋊C4C2×D414yes—
443C2×C22⋊C4C2×Q818yes—
444C2×C22⋊C4C2×Q8116yescomplemented
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—22no—
451C2×C42—22no—
452C2×C42—22no—
453C2×C42—24no—
454C2×C42—44no—
455C2×C42C2×D414yes—
456#95—24no—
457#95—24no—
458#95—28no—
459#95—28no—
460#95—24no—
461#95—24no—
462#95—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—28no—
467#95—44no—
468#95—44no—
469#95—44no—
470#95—44no—
471#95—44no—
472#95—44no—
473#95—44no—
474#95—44no—
475#95—44no—
476#95C2×Q8116yescomplemented
477C24—24no—
478C24—22no—
479C24—22no—
480C24—21no—
481C24—21no—
482C24—24no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24C22×D412yes—
487C24C22×D412yes—
488C24C22×D412yes—
489C24C22×D412yes—
490C24C22×Q814yes—
491C24C22×Q814yes—
492C242−1+414yes—
493C24C2511yescharacteristic
494C2×Q8—28no—
495C2×Q8—216no—
496C2×Q8—216no—
497C2×Q8—28no—
498C2×Q8—28no—
499C2×Q8—48no—
500C2×Q8—48no—
501C2×Q8—48no—
502C2×Q8—416no—
503C2×Q8—416no—
504C2×Q8—416no—
505C2×Q8—416no—
506C2×Q8—44no—
507C2×Q8—48no—
508C2×Q8—48no—
509C2×Q8—4128no—
510C2×Q8—48no—
511C2×Q8—48no—
512C2×Q8—44no—
513C2×Q8—84no—
514C2×Q8—84no—
515C2×Q8—84no—
516C2×Q8—84no—
517C2×Q8—84no—
518C2×D4—28no—
519C2×D4—28no—
520C2×D4—216no—
521C2×D4—216no—
522C2×D4C4⋊Q8116yescomplemented
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—216no—
533C22×C4—28no—
534C22×C4—216no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—416no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—416no—
607C22×C4—416no—
608C22×C4—44no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—416no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4—84no—
616C22×C4—84no—
617C22×C4—84no—
618C22×C4—84no—
619C22×C4—84no—
620C22×C4—84no—
621C22×C4—84no—
622C22×C4#120116yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C22×D412yes—
636C22×C4C22×D412yes—
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C22×Q818yes—
641C22×C4C22×Q818yes—
642C22×C4C22×Q814yes—
643C22×C4H(5,𝔽2)18yes—
644C22×C42−1+414yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—28no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—28no—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—28no—
655C4⋊C4—28no—
656C4⋊C4—28no—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—416no—
662C4⋊C4—416no—
663C4⋊C4—416no—
664C4⋊C4—416no—
665C4⋊C4—416no—
666C4⋊C4—48no—
667C22⋊C4—28no—
668C22⋊C4—28no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—216no—
673C22⋊C4—28no—
674C22⋊C4—416no—
675C22⋊C4—416no—
676C22⋊C4—48no—
677C42—28no—
678C42—28no—
679C42—28no—
680C42—48no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—28no—
689C23—28no—
690C23—28no—
691C23—28no—
692C23—22no—
693C23—22no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—28no—
699C23—28no—
700C23—41no—
701C23—41no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—44no—
706C23—44no—
707C23C2×#12014yes—
708C23C2×C4⋊Q814yes—
709C23C2×C4⋊Q814yes—
710C23#53614yes—
711C23D4×Q818yes—
712C23D4×Q818yes—
713C23C23×D411yescharacteristic
714C23C23×D411yescharacteristic
715C23C23×D411yescharacteristic
716C23C23×Q812yes—
717C23C2×H(5,𝔽2)14yes—
718C23C2×2−1+412yes—
719C23C2×2−1+412yes—
720C23#58512yes—
721Q8—416no—
722Q8—432no—
723Q8—432no—
724Q8—88no—
725Q8—88no—
726D4—232no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
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—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—28no—
753C2×C4—28no—
754C2×C4—28no—
755C2×C4—28no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—28no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—416no—
770C2×C4—416no—
771C2×C4—416no—
772C2×C4—432no—
773C2×C4—432no—
774C2×C4—44no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—44no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
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—44no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—88no—
815C2×C4—88no—
816C2×C4—88no—
817C2×C4C2×#12014yes—
818C2×C4C2×#12014yes—
819C2×C4C2×C4⋊Q814yes—
820C2×C4#53614yes—
821C22—24no—
822C22—28no—
823C22—216no—
824C22—28no—
825C22—28no—
826C22—28no—
827C22—24no—
828C22—28no—
829C22—24no—
830C22—42no—
831C22—48no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—42no—
836C22#243418yes—
837C22C22×#12011yescharacteristic
838C22C22×C4⋊Q811yescharacteristic
839C22C2×#53611yescharacteristic
840C22C2×#53611yescharacteristic
841C22#344911yescharacteristic
842C22C2×D4×Q812yes—
843C22C2×D4×Q812yes—
844C22#348412yes—
845C22#348412yes—
846C22#348412yes—
847C22#348912yes—
848C22#348912yes—
849C22#350114yes—
850C22#350314yes—
851C22#354114yes—
852C22#355214yes—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—24no—
857C4—48no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—48no—
864C4—48no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—84no—
870C2—28no—
871C2—44no—
872C2C2×#243411yescharacteristic
873C2#3530511yescharacteristic
874C2#3534611yescharacteristic
875C2#3592812yes—
876C2#3958812yes—
877C2#3959212yes—
878C2#4058912yes—
879C2#4310014yes—
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
2. C2×#2434C2semidirect
4. C22×#395C2semidirect
5. #16608C2semidirect
6. #16254C2semidirect
7. #15849C2semidirect
8. #15762C2semidirect
9. #15671C2semidirect
10. #15265C2semidirect
11. #14914C2semidirect
12. #14881C2semidirect
13. #14720C2semidirect
14. #14720C2semidirect
15. #14281C2semidirect
18. #13923C2semidirect
215. #386Q8semidirect
444. C2×C22⋊C4C2×Q8semidirect
476. #95C2×Q8semidirect
522. C2×D4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#24342
C2×#24092
C22×#3952
#166082
#162542
#158492
#157622
#156712
#152652
#149142
#148812
#147202
#142812
#140162
#140152
#139232
#137842