Finite Group Databasebeta

← #687688

Subgroups — #687688

Order 512.

3838 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic, complemented
2C2×#2440C211yesmaximal, characteristic, complemented
3C2×#2339C211yesmaximal, characteristic
4C2×#2311C211yesmaximal, characteristic
5#16300C214yesmaximal, complemented
6#15951C214yesmaximal, complemented
7#15327C214yesmaximal, complemented
8#15237C211yesmaximal, characteristic, complemented
9#15199C211yesmaximal, characteristic, complemented
10#15191C211yesmaximal, characteristic, complemented
11#15184C211yesmaximal, characteristic, complemented
12#14758C214yesmaximal, complemented
13#14340C211yesmaximal, characteristic, complemented
14#13979C211yesmaximal, characteristic, complemented
15#13977C211yesmaximal, characteristic, complemented
16#13937C211yesmaximal, characteristic
17#13906C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic, complemented
19#13844C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2212yes—
23C22×C22⋊Q8C2214yes—
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#2542—28no—
29#2440—28no—
30C2×#399C2214yes—
31C2×#398C2212yes—
32C2×#395C2212yes—
33#2339—28no—
34#2311—28no—
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2214yes—
50C2×#385C2212yes—
51C2×#385C2214yes—
52C2×#385C2214yes—
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#381C2212yes—
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2214yes—
62C2×#380C2214yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C22×#95C2212yes—
68#1446C2214yes—
69#1444C2212yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1443C2214yes—
74#1442C2212yes—
75#1442C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1439C2214yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2214yes—
84#1439C2214yes—
85#1439C2214yes—
86#1438C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—24no—
99C22×#41—42no—
100C22×#41—42no—
101C22×#41Q818yescomplemented
102C23×Q8C2311yescharacteristic
103C23×Q8C2312yes—
104C23×D4C2312yes—
105C23×D4C2311yescharacteristic
106C24×C4C2312yes—
107C24×C4C2312yes—
108C24×C4C2312yes—
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—42no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—216no—
116C2×C22⋊Q8—48no—
117C2×C22⋊Q8—48no—
118C2×C22⋊Q8—48no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4—24no—
122C2×C4×D4—24no—
123C2×C4×D4—42no—
124C2×C4×D4—42no—
125C2×#117—24no—
126C2×#117—24no—
127C2×#117—42no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—42no—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2314yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167#399—216no—
168#398—28no—
169#395—28no—
170#391—24no—
171#391—24no—
172#391—24no—
173#391—24no—
174#391—42no—
175#391—42no—
176#390—24no—
177#390—24no—
178#390—24no—
179#390D418yes—
180#389—24no—
181#389—24no—
182#386—216no—
183#386—28no—
184#386—28no—
185#385—28no—
186#385—48no—
187#385—48no—
188#384—24no—
189#384—24no—
190#384—24no—
191#384—42no—
192#382—42no—
193#381—28no—
194#380—24no—
195#380—24no—
196#380—216no—
197#380—48no—
198C4×C4⋊C4—24no—
199C4×C4⋊C4—42no—
200C4×C22⋊C4—24no—
201C4×C22⋊C4D418yes—
202C2×#95—28no—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C25C2411yescharacteristic
230C25C2412yes—
231C2×#41—232no—
232C2×#41—232no—
233C2×#41—416no—
234C2×#41—416no—
235C2×#41—416no—
236C2×#41—416no—
237C2×#41—416no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—24no—
241C22×Q8—24no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—28no—
247C22×Q8—44no—
248C22×Q8—42no—
249C22×Q8C2×Q814yes—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4—24no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4C2×D414yes—
261C22×D4C2×Q818yes—
262C22×D4C2×Q814yes—
263C22×D4#4114yes—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—28no—
278C23×C4—28no—
279C23×C4—24no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4C2×D414yes—
290C23×C4C2×Q818yes—
291C23×C4C2×Q814yes—
292C23×C4#4114yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C4⋊Q8—416no—
311C22⋊Q8—432no—
312C22⋊Q8—464no—
313C4×D4—416no—
314C4×D4—416no—
315#117—416no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—416no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4C2×D414yes—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4C2×D414yes—
397C2×C22⋊C4C2×D414yes—
398C2×C22⋊C4C2×D4116yes—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42C2×D414yes—
415C2×C42C2×D414yes—
416C2×C42C2×D414yes—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—28no—
422#95—28no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—28no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—42no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95C2×D414yes—
442#95C2×D414yes—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—24no—
449C24—22no—
450C24—24no—
451C24—21no—
452C24—22no—
453C24—22no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24—24no—
458C24—24no—
459C24C22×D414yes—
460C24C22×D412yes—
461C24C22×Q812yes—
462C24C22×Q814yes—
463C24C2×#4112yes—
464C24C2×#4114yes—
465C24C2511yescharacteristic
466#41—4128no—
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—416no—
471C2×Q8—48no—
472C2×Q8—48no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—84no—
478C2×Q8—88no—
479C2×D4—216no—
480C2×D4—216no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—28no—
485C2×D4—28no—
486C2×D4—28no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4C22⋊Q8116yescomplemented
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—216no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—216no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
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—24no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—416no—
588C22×C4—416no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—88no—
595C22×C4—88no—
596C22×C4—88no—
597C22×C4—84no—
598C22×C4—88no—
599C22×C4C22⋊Q8116yescomplemented
600C22×C4C22×D412yes—
601C22×C4C22×D414yes—
602C22×C4C22×D412yes—
603C22×C4C22×D414yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×Q814yes—
610C22×C4C22×Q812yes—
611C22×C4C22×Q812yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4H(5,𝔽2)14yes—
616C22×C4H(5,𝔽2)14yes—
617C22×C4H(5,𝔽2)12yes—
618C22×C4H(5,𝔽2)12yes—
619C22×C42−1+414yes—
620C22×C42−1+414yes—
621C4⋊C4—216no—
622C4⋊C4—28no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—416no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—416no—
631C4⋊C4—48no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—84no—
638C4⋊C4—88no—
639C22⋊C4—216no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—416no—
643C22⋊C4—416no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—416no—
648C22⋊C4—48no—
649C22⋊C4—88no—
650C22⋊C4—84no—
651C42—28no—
652C42—28no—
653C42—28no—
654C42—44no—
655C42—44no—
656C42—44no—
657C23—22no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—22no—
665C23—22no—
666C23—24no—
667C23—22no—
668C23—24no—
669C23—22no—
670C23—24no—
671C23—28no—
672C23—24no—
673C23—22no—
674C23—28no—
675C23—22no—
676C23—28no—
677C23—28no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—28no—
682C23—28no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—44no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—44no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—42no—
695C23—42no—
696C23—44no—
697C23—42no—
698C23—44no—
699C23—44no—
700C23—42no—
701C23C2×C22⋊Q818yes—
702C23C2×C22⋊Q814yes—
703C23C23×D411yescharacteristic
704C23C23×D411yescharacteristic
705C23C23×Q811yescharacteristic
706C23C22×#4111yescharacteristic
707C23C22×#4111yescharacteristic
708C23C2×H(5,𝔽2)12yes—
709C23C2×H(5,𝔽2)11yescharacteristic
710C23C2×H(5,𝔽2)11yescharacteristic
711C23C2×H(5,𝔽2)12yes—
712C23C2×2−1+412yes—
713C23C2×2−1+412yes—
714Q8—416no—
715Q8—816no—
716D4—232no—
717D4—432no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—232no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—432no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
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—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—816no—
810C2×C4—816no—
811C2×C4—816no—
812C2×C4C2×C22⋊Q814yes—
813C2×C4C2×C22⋊Q814yes—
814C2×C4C2×C22⋊Q814yes—
815C2×C4#53514yes—
816C2×C4#53614yes—
817C2×C4#54314yes—
818C2×C4D4214yes—
819C2×C4#54614yes—
820C2×C4#54614yes—
821C2×C4#55114yes—
822C22—24no—
823C22—28no—
824C22—216no—
825C22—24no—
826C22—24no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—44no—
831C22—44no—
832C22—48no—
833C22—44no—
834C22—44no—
835C22—48no—
836C22—44no—
837C22—48no—
838C22—44no—
839C22—42no—
840C22—42no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22C22×C22⋊Q811yescharacteristic
845C22C22×C22⋊Q811yescharacteristic
846C22C2×#53511yescharacteristic
847C22C2×#53611yescharacteristic
848C22C2×#54311yescharacteristic
849C22C2×D4211yescharacteristic
850C22C2×#54611yescharacteristic
851C22C2×#54611yescharacteristic
852C22C2×#55111yescharacteristic
853C22#348412yes—
854C22#349212yes—
855C22#349811yescharacteristic
856C22#349911yescharacteristic
857C22#349912yes—
858C22#350312yes—
859C22#350312yes—
860C22#351112yes—
861C22#352012yes—
862C22#352012yes—
863C22#353612yes—
864C22#354312yes—
865C22#354812yes—
866C22#355212yes—
867C4—24no—
868C4—24no—
869C4—24no—
870C4—42no—
871C4—44no—
872C4—44no—
873C4—44no—
874C4—44no—
875C4—44no—
876C4—42no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—82no—
883C4#243718yes—
884C2—44no—
885C2—48no—
886C2C2×#243711yescharacteristic
887C2#3527911yescharacteristic
888C2#3553211yescharacteristic
889C2#3573912yes—
890C2#3767411yescharacteristic
891C2#3807811yescharacteristic
892C2#3895111yescharacteristic
893C2#3936011yescharacteristic
894C2#4293112yes—
895C2#4486912yes—
896C2#4498812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
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×#2542C2semidirect
2. C2×#2440C2semidirect
5. #16300C2semidirect
6. #15951C2semidirect
7. #15327C2semidirect
8. #15237C2semidirect
9. #15199C2semidirect
10. #15191C2semidirect
11. #15184C2semidirect
12. #14758C2semidirect
13. #14340C2semidirect
14. #13979C2semidirect
15. #13977C2semidirect
17. #13906C2semidirect
18. #13880C2semidirect
19. #13844C2semidirect
101. C22×#41Q8semidirect
492. C2×D4C22⋊Q8semidirect
599. C22×C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
C2×#24402
C2×#23392
C2×#23112
#163002
#159512
#153272
#152372
#151992
#151912
#151842
#147582
#143402
#139792
#139772
#139372
#139062
#138802
#138442