Finite Group Databasebeta

← #4382004

Subgroups — #4382004

Order 512.

4396 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#539C211yesmaximal, characteristic
2C2×#2434C211yesmaximal, characteristic, complemented
3C2×#2409C211yesmaximal, characteristic, complemented
4C2×#2614C211yesmaximal, characteristic, complemented
5#16656C212yesmaximal, complemented
6#16608C212yesmaximal, complemented
7#16024C212yesmaximal, complemented
8#15982C212yesmaximal, complemented
9#15950C212yesmaximal
10#15949C212yesmaximal, complemented
11#15849C212yesmaximal, complemented
12#15668C212yesmaximal, complemented
13#15265C212yesmaximal, complemented
14#15265C212yesmaximal, complemented
15#14723C212yesmaximal, complemented
16#14720C212yesmaximal, complemented
17#14660C211yesmaximal, characteristic, complemented
18#14287C211yesmaximal, characteristic, complemented
19#13940C211yesmaximal, characteristic, complemented
20C24×Q8C2211yescharacteristic
21C2×#539—28no—
22C2×#539—28no—
23C2×#539—28no—
24C22×C4⋊Q8C2212yes—
25C22×#126C2211yescharacteristic
26C22×#126C2211yescharacteristic
27C22×#125C2211yescharacteristic
28C22×#125C2211yescharacteristic
29C22×#123C2211yescharacteristic
30C22×#123C2211yescharacteristic
31C22×#123C2211yescharacteristic
32C22×#123C2211yescharacteristic
33C22×#123C2212yes—
34C22×C22⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic
36C22×C22⋊Q8C2211yescharacteristic
37C22×C22⋊Q8C2212yes—
38C22×#121C2211yescharacteristic
39C22×C4×D4C2211yescharacteristic
40C22×C4×D4C2211yescharacteristic
41C23×C4⋊C4C2211yescharacteristic
42#2614—28no—
43#2434—28no—
44#2409—28no—
45C2×#395C2212yes—
46C2×#395C2212yes—
47C2×#395C2212yes—
48C2×#395C2212yes—
49C2×#395C2212yes—
50C2×#393C2212yes—
51C2×#393C2212yes—
52C2×#393C2212yes—
53C2×#391C2212yes—
54C2×#391C2212yes—
55C2×#386C2212yes—
56C2×#385C2212yes—
57C2×#385C2212yes—
58C2×#385C2212yes—
59C2×#385C2214yes—
60C2×#385C2214yes—
61C2×#381C2211yescharacteristic
62C2×#381C2212yes—
63C2×#380C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65#1446C2212yes—
66#1445C2212yes—
67#1444C2214yes—
68#1444C2214yes—
69#1444C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1441C2212yes—
73#1441C2214yes—
74#1441C2212yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2212yes—
78#1440C2214yes—
79#1440C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1440C2212yes—
83#1439C2214yes—
84#1439C2212yes—
85#1439C2214yes—
86#1438C2214yes—
87#1438C2212yes—
88#1438C2212yes—
89#1437C2212yes—
90#1437C2212yes—
91#1436C2212yes—
92#1436C2214yes—
93#1436C2212yes—
94#1434C2212yes—
95C22⋊#95C2214yes—
96C22⋊#95C2212yes—
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—24no—
100C23×Q8—48no—
101C23×Q8C2312yes—
102C23×Q8C2312yes—
103C23×Q8C2311yescharacteristic
104C23×D4C2311yescharacteristic
105C23×D4C2311yescharacteristic
106C23×D4C2311yescharacteristic
107C24×C4C2312yes—
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113#539—2128no—
114C2×C4⋊Q8—28no—
115C2×C4⋊Q8—48no—
116C2×#126—24no—
117C2×#126—24no—
118C2×#126—24no—
119C2×#126—24no—
120C2×#126—24no—
121C2×#126—24no—
122C2×#125—24no—
123C2×#125—24no—
124C2×#125—24no—
125C2×#125—24no—
126C2×#125—24no—
127C2×#125—24no—
128C2×#123—24no—
129C2×#123—24no—
130C2×#123—24no—
131C2×#123—24no—
132C2×#123—28no—
133C2×#123—24no—
134C2×#123—24no—
135C2×#123—24no—
136C2×#123—24no—
137C2×#123—24no—
138C2×#123—24no—
139C2×#123—24no—
140C2×#123—48no—
141C2×#123D418yes—
142C2×C22⋊Q8—24no—
143C2×C22⋊Q8—24no—
144C2×C22⋊Q8—24no—
145C2×C22⋊Q8—24no—
146C2×C22⋊Q8—28no—
147C2×C22⋊Q8—24no—
148C2×C22⋊Q8—24no—
149C2×C22⋊Q8—24no—
150C2×C22⋊Q8—24no—
151C2×C22⋊Q8—48no—
152C2×C22⋊Q8D418yes—
153C2×#121—24no—
154C2×#121—24no—
155C2×#121—24no—
156C2×C4×D4—24no—
157C2×C4×D4—24no—
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4D418yes—
162C22×C4⋊C4—24no—
163C22×C4⋊C4—24no—
164C22×C4⋊C4—24no—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2314yes—
174C22×C4⋊C4C2314yes—
175C22×C4⋊C4C2314yes—
176C22×C4⋊C4C2314yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2314yes—
189C22×C22⋊C4C2314yes—
190C22×C22⋊C4C2314yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2314yes—
200C22×C22⋊C4C2312yes—
201C22×C42C2311yescharacteristic
202C22×C42C2311yescharacteristic
203C22×C42C2312yes—
204#395—28no—
205#395—28no—
206#395—28no—
207#395—28no—
208#395—28no—
209#393—28no—
210#393—28no—
211#393—28no—
212#391—28no—
213#391—28no—
214#386—28no—
215#385—28no—
216#385—28no—
217#385—28no—
218#385—48no—
219#385—48no—
220#381—24no—
221#381—28no—
222#380—24no—
223C4×C22⋊C4—24no—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
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—
244C25C2411yescharacteristic
245C25C2411yescharacteristic
246C25C2411yescharacteristic
247C22×Q8—24no—
248C22×Q8—24no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—24no—
252C22×Q8—24no—
253C22×Q8—24no—
254C22×Q8—24no—
255C22×Q8—28no—
256C22×Q8—28no—
257C22×Q8—44no—
258C22×Q8—44no—
259C22×Q8—44no—
260C22×Q8—432no—
261C22×Q8—432no—
262C22×Q8—432no—
263C22×Q8—416no—
264C22×Q8C2×D414yes—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—24no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—24no—
273C22×D4—22no—
274C22×D4—42no—
275C22×D4—42no—
276C22×D4—44no—
277C22×D4C2×D414yes—
278C22×D4C2×D414yes—
279C23×C4—22no—
280C23×C4—24no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—28no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—42no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4—44no—
299C23×C4—44no—
300C23×C4—44no—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4C2×D414yes—
304C23×C4C2×D414yes—
305C23×C4C2414yes—
306C23×C4C2414yes—
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2414yes—
318C23×C4C2414yes—
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C4⋊Q8—432no—
322#126—232no—
323#126—232no—
324#125—232no—
325#125—232no—
326#123—232no—
327#123—232no—
328#123—232no—
329#123—232no—
330#123—432no—
331C22⋊Q8—232no—
332C22⋊Q8—232no—
333C22⋊Q8—232no—
334C22⋊Q8—432no—
335#121—232no—
336C4×D4—232no—
337C4×D4—232no—
338C2×C4⋊C4—232no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
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—24no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—28no—
379C2×C4⋊C4—28no—
380C2×C4⋊C4—28no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—28no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—44no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4C2×D414yes—
390C2×C4⋊C4C2×D414yes—
391C2×C4⋊C4C2×D414yes—
392C2×C4⋊C4C2×D414yes—
393C2×C4⋊C4C2×D414yes—
394C2×C4⋊C4C2×D414yes—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—28no—
420C2×C22⋊C4—28no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—28no—
427C2×C22⋊C4—28no—
428C2×C22⋊C4—28no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—44no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4—44no—
434C2×C22⋊C4—44no—
435C2×C22⋊C4—44no—
436C2×C22⋊C4C2×D414yes—
437C2×C22⋊C4C2×D414yes—
438C2×C22⋊C4C2×D414yes—
439C2×C22⋊C4C2×D414yes—
440C2×C22⋊C4C2×D414yes—
441C2×C22⋊C4C2×D414yes—
442C2×C22⋊C4C2×D414yes—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—24no—
449C2×C42—44no—
450C2×C42C2×D414yes—
451#95—24no—
452#95—24no—
453#95—28no—
454#95—28no—
455#95—24no—
456#95—24no—
457#95—28no—
458#95—28no—
459#95—28no—
460#95—28no—
461#95—28no—
462#95—28no—
463#95—44no—
464#95—44no—
465#95—44no—
466#95—44no—
467#95—44no—
468#95—44no—
469#95—44no—
470#95—44no—
471C24—21no—
472C24—21no—
473C24—24no—
474C24—24no—
475C24—24no—
476C24—24no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—21no—
481C24—21no—
482C24—24no—
483C24—24no—
484C24—22no—
485C24—22no—
486C24C22×D412yes—
487C24C22×D412yes—
488C24C22×D412yes—
489C24C22×D412yes—
490C24C22×D412yes—
491C242−1+414yes—
492C24C2511yescharacteristic
493C2×Q8—216no—
494C2×Q8—216no—
495C2×Q8—28no—
496C2×Q8—48no—
497C2×Q8—416no—
498C2×Q8—416no—
499C2×Q8—416no—
500C2×Q8—416no—
501C2×Q8—48no—
502C2×Q8—48no—
503C2×Q8—4128no—
504C2×Q8—48no—
505C2×Q8—48no—
506C2×Q8—84no—
507C2×Q8—84no—
508C2×D4—28no—
509C2×D4—28no—
510C2×D4—28no—
511C2×D4—28no—
512C2×D4—44no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—84no—
521C2×D4—84no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—28no—
525C22×C4—216no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
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—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—416no—
596C22×C4—416no—
597C22×C4—44no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—44no—
601C22×C4—84no—
602C22×C4—84no—
603C22×C4—84no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4#120116yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4H(5,𝔽2)18yes—
627C22×C42−1+418yes—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—28no—
632C4⋊C4—28no—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—416no—
643C4⋊C4—416no—
644C4⋊C4—416no—
645C4⋊C4—416no—
646C4⋊C4—48no—
647C22⋊C4—216no—
648C22⋊C4—28no—
649C22⋊C4—28no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—28no—
658C22⋊C4—416no—
659C22⋊C4—416no—
660C22⋊C4—416no—
661C22⋊C4—416no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C42—28no—
665C42—28no—
666C42—48no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—28no—
684C23—28no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—41no—
700C23—41no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23C2×#12014yes—
711C23#53614yes—
712C23C23×D411yescharacteristic
713C23C23×D411yescharacteristic
714C23C23×D411yescharacteristic
715C23C2×H(5,𝔽2)14yes—
716C23C2×2−1+412yes—
717C23C2×2−1+414yes—
718C23#58512yes—
719Q8—432no—
720Q8—432no—
721Q8—88no—
722D4—416no—
723D4—416no—
724D4—88no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—28no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—28no—
757C2×C4—28no—
758C2×C4—416no—
759C2×C4—416no—
760C2×C4—432no—
761C2×C4—44no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
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—44no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—88no—
807C2×C4—88no—
808C2×C4—88no—
809C2×C4C2×#12014yes—
810C2×C4C2×#12014yes—
811C22—24no—
812C22—28no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—42no—
817C22—48no—
818C22—48no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—42no—
823C22—48no—
824C22—48no—
825C22—42no—
826C22—48no—
827C22—42no—
828C22—42no—
829C22—82no—
830C22—82no—
831C22—84no—
832C22C22×#12011yescharacteristic
833C22C2×#53611yescharacteristic
834C22#344911yescharacteristic
835C22#348412yes—
836C22#348412yes—
837C22#348412yes—
838C22#348612yes—
839C22#348912yes—
840C22#348912yes—
841C22#349912yes—
842C22#349912yes—
843C22#353814yes—
844C22#354114yes—
845C22#355214yes—
846C22#355414yes—
847C4—24no—
848C4—24no—
849C4—48no—
850C4—42no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—48no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—84no—
862C4—84no—
863C2—44no—
864C2—44no—
865C2—82no—
866C2#3530511yescharacteristic
867C2#3534611yescharacteristic
868C2#3566611yescharacteristic
869C2#4049512yes—
870C2#4050312yes—
871C2#4636314yes—
872C2#4784114yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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
3. C2×#2409C2semidirect
4. C2×#2614C2semidirect
5. #16656C2semidirect
6. #16608C2semidirect
7. #16024C2semidirect
8. #15982C2semidirect
10. #15949C2semidirect
11. #15849C2semidirect
12. #15668C2semidirect
13. #15265C2semidirect
14. #15265C2semidirect
15. #14723C2semidirect
16. #14720C2semidirect
17. #14660C2semidirect
18. #14287C2semidirect
19. #13940C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5392
C2×#24342
C2×#24092
C2×#26142
#166562
#166082
#160242
#159822
#159502
#159492
#158492
#156682
#152652
#147232
#147202
#146602
#142872
#139402