Finite Group Databasebeta

← #676268

Subgroups — #676268

Order 512.

3962 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#557C211yesmaximal, characteristic, complemented
2C2×#2857C211yesmaximal, characteristic
3C2×C4×C22⋊Q8C211yesmaximal, characteristic
4C2×C4×C22⋊Q8C211yesmaximal, characteristic
5#16104C214yesmaximal, complemented
6#15996C214yesmaximal
7#15218C212yesmaximal, complemented
8#15216C212yesmaximal
9#15180C212yesmaximal, complemented
10#15178C212yesmaximal
11#14155C211yesmaximal, characteristic, complemented
12#14017C212yesmaximal, complemented
13#14017C212yesmaximal, complemented
14#13969C212yesmaximal
15#13969C212yesmaximal
16#13926C211yesmaximal, characteristic, complemented
17#13926C211yesmaximal, characteristic, complemented
18C2×#557—28no—
19C2×#557—28no—
20C2×#557—28no—
21C22×C4⋊Q8C2212yes—
22C22×C4⋊Q8C2211yescharacteristic
23C22×#125C2212yes—
24C22×#125C2214yes—
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2212yes—
29C22×C4×Q8C2212yes—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C23×C42C2211yescharacteristic
33#2857—28no—
34C4×C22⋊Q8—28no—
35C4×C22⋊Q8—28no—
36C2×#391C2212yes—
37C2×#391C2212yes—
38C2×#391C2211yescharacteristic
39C2×#391C2212yes—
40C2×#391C2211yescharacteristic
41C2×#391C2212yes—
42C2×#391C2212yes—
43C2×#389C2212yes—
44C2×#389C2212yes—
45C2×#389C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#387C2212yes—
48C2×#387C2212yes—
49C2×#385C2212yes—
50C2×#385C2212yes—
51C2×#384C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61C2×C4×C22⋊C4C2212yes—
62#1445C2214yes—
63#1444C2214yes—
64#1444C2214yes—
65#1444C2214yes—
66#1442C2214yes—
67#1442C2214yes—
68#1442C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1437C2214yes—
78#1436C2214yes—
79#1436C2214yes—
80#1436C2214yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C4⋊#95C2212yes—
88C4⋊#95C2212yes—
89C23×Q8C2311yescharacteristic
90C23×Q8C2312yes—
91C23×Q8C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95#557—2128no—
96C2×C4⋊Q8—28no—
97C2×C4⋊Q8—28no—
98C2×C4⋊Q8—28no—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8D418yes—
102C2×#125—216no—
103C2×#125—28no—
104C2×#125—28no—
105C2×#125—216no—
106C2×#125—216no—
107C2×#125—28no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—28no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—44no—
116C2×C22⋊Q8Q818yescomplemented
117C2×C4×Q8—28no—
118C2×C4×Q8—28no—
119C2×C4×Q8—28no—
120C2×C4×Q8—28no—
121C2×C4×Q8—28no—
122C2×C4×Q8—28no—
123C2×C4×Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×Q8—24no—
126C2×C4×Q8—24no—
127C2×C4×Q8D418yes—
128C2×C4×Q8D418yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C42—24no—
156C22×C42—24no—
157C22×C42—24no—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2314yes—
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167#391—28no—
168#391—24no—
169#391—24no—
170#391—28no—
171#391—28no—
172#391—44no—
173#391—44no—
174#389—28no—
175#389—28no—
176#389—24no—
177#389—24no—
178#387—28no—
179#387—28no—
180#385—28no—
181#385—28no—
182#384—24no—
183#380—28no—
184#380—28no—
185#380—24no—
186#380—24no—
187C4×C4⋊C4—28no—
188C4×C4⋊C4—28no—
189C4×C4⋊C4—24no—
190C4×C4⋊C4—24no—
191C4×C22⋊C4—28no—
192C4×C22⋊C4—28no—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C25C2411yescharacteristic
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—24no—
221C22×Q8—22no—
222C22×Q8—24no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—24no—
226C22×Q8—22no—
227C22×Q8—24no—
228C22×Q8—24no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—24no—
234C22×Q8C2×D418yes—
235C22×Q8C2×D414yes—
236C22×Q8C2×D414yes—
237C22×Q8C2×Q814yes—
238C22×Q8#4114yes—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—41no—
257C23×C4—41no—
258C23×C4C2×Q814yes—
259C23×C4#4114yes—
260C23×C4C2414yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2414yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C4⋊Q8—264no—
277C4⋊Q8—232no—
278#125—2128no—
279#125—264no—
280C22⋊Q8—232no—
281C22⋊Q8—232no—
282C22⋊Q8—432no—
283C4×Q8—264no—
284C4×Q8—264no—
285C4×Q8—232no—
286C4×Q8—232no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4C2×D414yes—
342C2×C4⋊C4C2×D418yes—
343C2×C4⋊C4C2×D414yes—
344C2×C4⋊C4C2×D418yes—
345C2×C4⋊C4C2×D418yes—
346C2×C4⋊C4C2×D418yes—
347C2×C4⋊C4C2×Q814yes—
348C2×C4⋊C4C2×Q818yes—
349C2×C4⋊C4#4114yes—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4C2×Q818yes—
365C2×C42—28no—
366C2×C42—28no—
367C2×C42—28no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—416no—
388C2×C42C2×D418yes—
389C2×C42C2×D418yes—
390C2×C42C2×D414yes—
391C2×C42C2×D414yes—
392C2×C42C2×D414yes—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—28no—
404#95—28no—
405#95—28no—
406#95—28no—
407#95—28no—
408#95—28no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24C22×Q812yes—
430C24C2×#4112yes—
431C242−1+412yes—
432C24C2511yescharacteristic
433C2×Q8—28no—
434C2×Q8—216no—
435C2×Q8—28no—
436C2×Q8—28no—
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—216no—
440C2×Q8—216no—
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—28no—
445C2×Q8—48no—
446C2×Q8—48no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—48no—
451C2×Q8—44no—
452C2×Q8—48no—
453C2×Q8C22⋊Q8116yescomplemented
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—28no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—24no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4C22×D414yes—
559C22×C4C22×D418yes—
560C22×C4C22×D414yes—
561C22×C4C22×D414yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D414yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C22×D412yes—
570C22×C4C22×D412yes—
571C22×C4C22×D412yes—
572C22×C4C22×Q814yes—
573C22×C4C22×Q812yes—
574C22×C4C22×Q814yes—
575C22×C4C22×Q812yes—
576C22×C4C2×#4114yes—
577C22×C4C2×#4112yes—
578C22×C4C2×#4114yes—
579C22×C4C2×#4112yes—
580C22×C4C2×#4112yes—
581C22×C4C2×#4112yes—
582C22×C4H(5,𝔽2)12yes—
583C22×C42−1+412yes—
584C22×C42−1+412yes—
585C22×C42−1+412yes—
586C22×C42−1+412yes—
587C4⋊C4—232no—
588C4⋊C4—232no—
589C4⋊C4—216no—
590C4⋊C4—232no—
591C4⋊C4—28no—
592C4⋊C4—216no—
593C4⋊C4—216no—
594C4⋊C4—28no—
595C4⋊C4—216no—
596C4⋊C4—216no—
597C4⋊C4—28no—
598C4⋊C4—216no—
599C4⋊C4—28no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—416no—
603C4⋊C4—48no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C22⋊C4—216no—
609C22⋊C4—216no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—416no—
613C42—232no—
614C42—216no—
615C42—216no—
616C42—44no—
617C42—44no—
618C42—44no—
619C42—48no—
620C42—48no—
621C42#120116yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23#55714yescomplemented
657C23C23×D411yescharacteristic
658C23C23×D411yescharacteristic
659C23C23×D411yescharacteristic
660C23C23×Q811yescharacteristic
661C23C22×#4111yescharacteristic
662C23C22×#4111yescharacteristic
663C23C22×#4111yescharacteristic
664C23C2×H(5,𝔽2)11yescharacteristic
665C23C2×2−1+411yescharacteristic
666C23C2×2−1+411yescharacteristic
667C23C2×2−1+411yescharacteristic
668C23C2×2−1+411yescharacteristic
669C23C2×2−1+411yescharacteristic
670C23#58511yescharacteristic
671C23#58511yescharacteristic
672Q8—232no—
673Q8—416no—
674Q8—432no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—28no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—28no—
698C2×C4—22no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—416no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—416no—
752C2×C4—416no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4C2×#12014yes—
775C2×C4C2×#12014yes—
776C2×C4C2×#12014yes—
777C2×C4C2×C22⋊Q818yes—
778C2×C4C2×C22⋊Q814yes—
779C2×C4#52514yes—
780C2×C4#53614yes—
781C2×C4#53714yes—
782C2×C4#54614yes—
783C2×C4#54714yes—
784C2×C4#54814yes—
785C2×C4#54814yes—
786C2×C4#54814yes—
787C2×C4D4×Q814yes—
788C2×C4D4×Q814yes—
789C2×C4#55014yes—
790C22—24no—
791C22—24no—
792C22—24no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22C22×#12011yescharacteristic
806C22C22×C22⋊Q811yescharacteristic
807C22C2×#52511yescharacteristic
808C22C2×#53611yescharacteristic
809C22C2×#53711yescharacteristic
810C22C2×#54611yescharacteristic
811C22C2×#54711yescharacteristic
812C22C2×#54811yescharacteristic
813C22C2×#54811yescharacteristic
814C22C2×#54811yescharacteristic
815C22C2×D4×Q811yescharacteristic
816C22C2×D4×Q811yescharacteristic
817C22C2×#55011yescharacteristic
818C22C2×#55711yescharacteristic
819C22Q8×#4111yescharacteristic
820C22#348011yescharacteristic
821C22#348211yescharacteristic
822C22#348611yescharacteristic
823C22#348711yescharacteristic
824C22#348911yescharacteristic
825C22#348911yescharacteristic
826C22#348911yescharacteristic
827C22#348911yescharacteristic
828C22#350211yescharacteristic
829C22#350311yescharacteristic
830C22#350711yescharacteristic
831C22#350911yescharacteristic
832C22#351511yescharacteristic
833C22#351711yescharacteristic
834C22#352311yescharacteristic
835C22#352311yescharacteristic
836C22#355211yescharacteristic
837C22#355411yescharacteristic
838C22#355511yescharacteristic
839C22#355611yescharacteristic
840C4—24no—
841C4—28no—
842C4—44no—
843C4—44no—
844C4—42no—
845C4—44no—
846C4—42no—
847C4—42no—
848C4—44no—
849C4—48no—
850C4—44no—
851C4—84no—
852C4—82no—
853C4—82no—
854C4#240718yes—
855C4#240918yes—
856C2—44no—
857C2C2×#240911yescharacteristic
858C2C2×#240711yescharacteristic
859C2#3565911yescharacteristic
860C2#3644511yescharacteristic
861C2#3650511yescharacteristic
862C2#3654511yescharacteristic
863C2#3657711yescharacteristic
864C2#3912711yescharacteristic
865C2#3913911yescharacteristic
866C2#3959911yescharacteristic
867C2#3972411yescharacteristic
868C2#5906711yescharacteristic
869C2#5907111yescharacteristic
870C2#5907811yescharacteristic
871C2#5914411yescharacteristic
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
1. C22×#557C2semidirect
5. #16104C2semidirect
7. #15218C2semidirect
9. #15180C2semidirect
11. #14155C2semidirect
12. #14017C2semidirect
13. #14017C2semidirect
16. #13926C2semidirect
17. #13926C2semidirect
116. C2×C22⋊Q8Q8semidirect
453. C2×Q8C22⋊Q8semidirect
656. C23#557semidirect

Maximal subgroups

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

subgroupindex
C22×#5572
C2×#28572
C2×C4×C22⋊Q82
#161042
#159962
#152182
#152162
#151802
#151782
#141552
#140172
#139692
#139262