Finite Group Databasebeta

← #618040

Subgroups — #618040

Order 512.

3790 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#533C211yesmaximal, characteristic
2C2×#2567C211yesmaximal, characteristic, complemented
3C2×#2546C211yesmaximal, characteristic, complemented
4C2×#2628C211yesmaximal, characteristic
5#15850C212yesmaximal, complemented
6#15849C212yesmaximal, complemented
7#15783C212yesmaximal, complemented
8#15762C212yesmaximal, complemented
9#15671C212yesmaximal
10#15466C212yesmaximal
11#15430C212yesmaximal
12#15265C212yesmaximal
13#15202C212yesmaximal, complemented
14#15158C212yesmaximal, complemented
15#14697C212yesmaximal
16#14264C212yesmaximal
17#13925C211yesmaximal, characteristic, complemented
18#13925C211yesmaximal, characteristic, complemented
19#13777C211yesmaximal, characteristic
20C2×#533—28no—
21C2×#533—28no—
22C2×#533—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2212yes—
27C22×#125C2211yescharacteristic
28C22×#125C2211yescharacteristic
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37C22×#117C2211yescharacteristic
38C22×#117C2211yescharacteristic
39C23×C42C2211yescharacteristic
40#2628—28no—
41#2567—28no—
42#2546—28no—
43C2×#400C2212yes—
44C2×#399C2212yes—
45C2×#398C2212yes—
46C2×#398C2212yes—
47C2×#395C2212yes—
48C2×#395C2212yes—
49C2×#395C2212yes—
50C2×#395C2214yes—
51C2×#393C2212yes—
52C2×#391C2212yes—
53C2×#391C2212yes—
54C2×#389C2212yes—
55C2×#389C2212yes—
56C2×#389C2212yes—
57C2×#389C2212yes—
58C2×#389C2212yes—
59C2×#385C2214yes—
60C2×#384C2212yes—
61C2×#382C2211yescharacteristic
62C2×#380C2212yes—
63C2×#380C2212yes—
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66#1446C2214yes—
67#1446C2212yes—
68#1446C2212yes—
69#1445C2212yes—
70#1445C2212yes—
71#1444C2214yes—
72#1444C2214yes—
73#1444C2214yes—
74#1444C2214yes—
75#1442C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1437C2212yes—
82#1437C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2214yes—
88#1436C2214yes—
89#1436C2212yes—
90#1436C2212yes—
91C4⋊#95C2212yes—
92C4⋊#95C2212yes—
93C4⋊#95C2212yes—
94C4⋊#95C2212yes—
95C4⋊#95C2212yes—
96C22⋊#95C2214yes—
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2311yescharacteristic
100C23×Q8C2311yescharacteristic
101C23×Q8C2312yes—
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105#533—2128no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—28no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—48no—
117C2×#125—24no—
118C2×#125—24no—
119C2×#125—24no—
120C2×#125—24no—
121C2×#125—24no—
122C2×#125—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—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—24no—
134C2×C22⋊Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×Q8—24no—
138C2×C4×Q8—24no—
139C2×C4×Q8—24no—
140C2×C4×Q8—24no—
141C2×C4×Q8—24no—
142C2×C4×Q8—24no—
143C2×C4×Q8—24no—
144C2×C4×Q8—24no—
145C2×C4×Q8D418yes—
146C2×C4×Q8D418yes—
147C2×#117—24no—
148C2×#117—24no—
149C2×#117—24no—
150C2×#117—24no—
151C2×#117—24no—
152C2×#117D418yes—
153C22×C4⋊C4C2314yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
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⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2314yes—
176C22×C4⋊C4C2314yes—
177C22×C4⋊C4C2314yes—
178C22×C4⋊C4C2314yes—
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2314yes—
184C22×C22⋊C4C2314yes—
185C22×C42—24no—
186C22×C42—24no—
187C22×C42—24no—
188C22×C42C2311yescharacteristic
189C22×C42C2311yescharacteristic
190C22×C42C2311yescharacteristic
191C22×C42C2311yescharacteristic
192C22×C42C2311yescharacteristic
193C22×C42C2311yescharacteristic
194C22×C42C2311yescharacteristic
195C22×C42C2312yes—
196C22×C42C2312yes—
197C22×C42C2311yescharacteristic
198#400—28no—
199#399—28no—
200#398—28no—
201#398—28no—
202#395—28no—
203#395—28no—
204#395—28no—
205#395—48no—
206#393—28no—
207#391—28no—
208#391—28no—
209#389—28no—
210#389—28no—
211#389—28no—
212#389—28no—
213#389—28no—
214#385—48no—
215#384—28no—
216#382—24no—
217#380—28no—
218#380Q8116yescomplemented
219C4×C4⋊C4—24no—
220C4×C4⋊C4—24no—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2314yes—
241C2×#95C2314yes—
242C25C2411yescharacteristic
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—24no—
254C22×Q8—24no—
255C22×Q8—24no—
256C22×Q8—24no—
257C22×Q8—24no—
258C22×Q8—24no—
259C22×Q8—24no—
260C22×Q8—42no—
261C22×Q8—42no—
262C22×Q8—42no—
263C22×Q8—42no—
264C22×Q8—44no—
265C22×Q8—44no—
266C22×Q8C2×D414yes—
267C22×Q8C2×D414yes—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4C2×D414yes—
282C23×C4C2×Q818yes—
283C23×C4C2414yes—
284C23×C4C2414yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2414yes—
294C23×C4C2414yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C4⋊Q8—232no—
302C4⋊Q8—232no—
303C4⋊Q8—432no—
304C4⋊Q8—416no—
305#125—232no—
306#125—232no—
307C22⋊Q8—232no—
308C22⋊Q8—232no—
309C22⋊Q8—232no—
310C22⋊Q8—232no—
311C4×Q8—232no—
312C4×Q8—232no—
313C4×Q8—232no—
314C4×Q8—232no—
315#117—232no—
316#117—232no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
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—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
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—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—44no—
385C2×C4⋊C4C2×D414yes—
386C2×C4⋊C4C2×D414yes—
387C2×C4⋊C4C2×D414yes—
388C2×C4⋊C4C2×D414yes—
389C2×C4⋊C4C2×D414yes—
390C2×C4⋊C4C2×D414yes—
391C2×C4⋊C4C2×D414yes—
392C2×C4⋊C4C2×D414yes—
393C2×C4⋊C4C2×Q818yes—
394C2×C4⋊C4C2×Q818yes—
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—28no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4C2×D414yes—
411C2×C22⋊C4C2×D414yes—
412C2×C22⋊C4C2×Q8116yes—
413C2×C42—232no—
414C2×C42—22no—
415C2×C42—22no—
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—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—24no—
431C2×C42—24no—
432C2×C42—44no—
433C2×C42—44no—
434C2×C42C2×D414yes—
435C2×C42C2×D414yes—
436C2×C42C2×D414yes—
437C2×C42C2×D414yes—
438C2×C42C2×D414yes—
439C2×C42C2×D414yes—
440C2×C42C2×D414yes—
441C2×C42C2×D414yes—
442#95—24no—
443#95—24no—
444#95—28no—
445#95—24no—
446#95—24no—
447#95—28no—
448#95—28no—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—28no—
454#95—44no—
455#95—44no—
456#95—44no—
457#95—44no—
458#95—44no—
459#95—44no—
460#95—44no—
461#95—44no—
462#95C2×Q8116yes—
463C24—21no—
464C24—21no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C22×D412yes—
471C24C22×Q814yes—
472C24C2511yescharacteristic
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—28no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—48no—
482C2×Q8—48no—
483C2×Q8—48no—
484C2×Q8—48no—
485C2×Q8—48no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—48no—
492C2×Q8—48no—
493C2×Q8—48no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—88no—
497C2×Q8—88no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—216no—
514C22×C4—216no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
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—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4C4⋊Q8116yescomplemented
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×Q818yes—
605C22×C4C22×Q818yes—
606C22×C4C22×Q814yes—
607C22×C4C22×Q814yes—
608C22×C4H(5,𝔽2)14yes—
609C22×C42−1+414yes—
610C22×C42−1+414yes—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—28no—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—216no—
628C4⋊C4—216no—
629C4⋊C4—416no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—416no—
633C4⋊C4—48no—
634C4⋊C4—88no—
635C4⋊C4—88no—
636C4⋊C4—88no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—416no—
642C22⋊C4—88no—
643C42—28no—
644C42—28no—
645C42—28no—
646C42—28no—
647C42—28no—
648C42—28no—
649C42—28no—
650C42—48no—
651C42—48no—
652C42#120116yes—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23C2×C4⋊Q814yes—
674C23C23×D411yescharacteristic
675C23C23×D411yescharacteristic
676C23C23×D411yescharacteristic
677C23C23×Q812yes—
678C23C2×H(5,𝔽2)12yes—
679C23C2×2−1+412yes—
680C23C2×2−1+412yes—
681C23#58512yes—
682C23#58512yes—
683Q8—416no—
684Q8—416no—
685Q8—416no—
686Q8—416no—
687Q8—816no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
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—232no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—28no—
730C2×C4—28no—
731C2×C4—28no—
732C2×C4—28no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—44no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4C2×#12014yes—
780C2×C4C2×#12014yes—
781C2×C4C2×#12014yes—
782C2×C4C2×C4⋊Q814yes—
783C2×C4C2×C4⋊Q814yes—
784C2×C4#53514yes—
785C2×C4#53614yes—
786C2×C4#53614yes—
787C2×C4D4×Q818yes—
788C2×C4D4×Q818yes—
789C22—24no—
790C22—28no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22C22×#12011yescharacteristic
799C22C22×C4⋊Q811yescharacteristic
800C22C2×#53511yescharacteristic
801C22C2×#53611yescharacteristic
802C22C2×#53611yescharacteristic
803C22#344911yescharacteristic
804C22#344911yescharacteristic
805C22C2×D4×Q812yes—
806C22C2×D4×Q812yes—
807C22#348812yes—
808C22#348812yes—
809C22#348912yes—
810C22#348912yes—
811C22#350112yes—
812C22#350212yes—
813C22#350312yes—
814C22#350412yes—
815C22#355012yes—
816C22#355412yes—
817C22#355512yes—
818C22#355712yes—
819C4—24no—
820C4—24no—
821C4—24no—
822C4—24no—
823C4—24no—
824C4—48no—
825C4—48no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—84no—
835C4—84no—
836C4#243418yes—
837C2—44no—
838C2C2×#243411yescharacteristic
839C2#3525011yescharacteristic
840C2#3530511yescharacteristic
841C2#3556612yes—
842C2#3727512yes—
843C2#3959012yes—
844C2#3959112yes—
845C2#3959612yes—
846C2#3959712yes—
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×#2567C2semidirect
3. C2×#2546C2semidirect
5. #15850C2semidirect
6. #15849C2semidirect
7. #15783C2semidirect
8. #15762C2semidirect
13. #15202C2semidirect
14. #15158C2semidirect
17. #13925C2semidirect
18. #13925C2semidirect
218. #380Q8semidirect
583. C22×C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×#5332
C2×#25672
C2×#25462
C2×#26282
#158502
#158492
#157832
#157622
#156712
#154662
#154302
#152652
#152022
#151582
#146972
#142642
#139252
#137772