Finite Group Databasebeta

← #874551

Subgroups — #874551

Order 512.

3238 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2546C211yesmaximal, characteristic, complemented
2C2×#2423C211yesmaximal, characteristic
3C2×#2434C211yesmaximal, characteristic
4C2×#2434C211yesmaximal, characteristic
5#16827C214yesmaximal, complemented
6#15627C214yesmaximal, complemented
7#15545C214yesmaximal
8#15190C211yesmaximal, characteristic, complemented
9#15188C211yesmaximal, characteristic, complemented
10#15185C211yesmaximal, characteristic, complemented
11#15184C211yesmaximal, characteristic, complemented
12#15182C211yesmaximal, characteristic
13#15178C211yesmaximal, characteristic
14#14714C211yesmaximal, characteristic, complemented
15#14714C211yesmaximal, characteristic, complemented
16#14442C214yesmaximal
17#14024C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic
19C4×#388C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29#2546—28no—
30#2434—28no—
31#2434—28no—
32#2423—28no—
33C2×#399C2212yes—
34C2×#398C2214yes—
35C2×#398C2212yes—
36C2×#395C2212yes—
37C2×#395C2214yes—
38C2×#395C2212yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#389C2214yes—
53C2×#389C2211yescharacteristic
54C2×#388C2212yes—
55C2×#388C2212yes—
56C2×#387C2212yes—
57C2×#385C2212yes—
58C2×#385C2214yes—
59C2×#385C2212yes—
60C2×#384C2211yescharacteristic
61C2×#384C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C43C2211yescharacteristic
68#1446C2214yes—
69#1445C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1442C2214yes—
74#1442C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1437C2212yes—
83#1436C2212yes—
84#1436C2214yes—
85C4⋊#95C2214yes—
86C4⋊#95C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2214yes—
90C4⋊#95C2214yes—
91#1434C2212yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—42no—
99C23×Q8—42no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×Q8C2311yescharacteristic
106C23×Q8C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
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—42no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8—42no—
119C2×C4⋊Q8—42no—
120C2×C4⋊Q8—42no—
121C2×C4⋊Q8—42no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8D418yes—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—24no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×C22⋊Q8—42no—
130C2×C4×Q8—24no—
131C2×C4×Q8—24no—
132C2×C4×Q8—42no—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2314yes—
151C22×C4⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2312yes—
168#399—28no—
169#398—216no—
170#398—28no—
171#395—216no—
172#395—28no—
173#395—28no—
174#391—24no—
175#391—24no—
176#391—24no—
177#391—24no—
178#391—24no—
179#391—24no—
180#391—24no—
181#391—42no—
182#391—42no—
183#391—42no—
184#391—42no—
185#391—42no—
186#391—42no—
187#389—216no—
188#389—24no—
189#388—28no—
190#388Q8116yescomplemented
191#387—28no—
192#385—216no—
193#385—28no—
194#385—28no—
195#384—24no—
196#384—42no—
197#380—24no—
198C4×C4⋊C4—24no—
199C4×C22⋊C4—24no—
200C4×C22⋊C4—42no—
201C4×C22⋊C4D418yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C2×#95C2312yes—
230C2×#95C2312yes—
231C43—42no—
232C25C2411yescharacteristic
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—24no—
240C22×Q8—24no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—24no—
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—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—42no—
262C22×Q8—42no—
263C22×Q8—42no—
264C22×Q8—42no—
265C22×Q8—416no—
266C22×Q8—416no—
267C22×Q8—416no—
268C22×Q8—416no—
269C22×Q8—416no—
270C22×Q8—416no—
271C22×Q8—416no—
272C22×Q8C2×D414yes—
273C22×Q8C2×D414yes—
274C22×Q8#4114yes—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4C2×D414yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2412yes—
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C4⋊Q8—416no—
308C4⋊Q8—416no—
309C4⋊Q8—416no—
310C4⋊Q8—416no—
311C4⋊Q8—416no—
312C22⋊Q8—416no—
313C22⋊Q8—416no—
314C4×Q8—416no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—28no—
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—28no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4C2×D4116yes—
368C2×C4⋊C4C2×Q818yescomplemented
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4C2×D414yes—
383C2×C22⋊C4C2×D414yes—
384C2×C22⋊C4C2×Q818yes—
385C2×C22⋊C4C2×Q818yes—
386C2×C22⋊C4C2×Q818yes—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42C2×D414yes—
411C2×C42C2×D414yes—
412C2×C42C2×D414yes—
413C2×C42C2×Q818yescomplemented
414#95—24no—
415#95—24no—
416#95—24no—
417#95—28no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—28no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—28no—
427#95—28no—
428#95—24no—
429#95—42no—
430#95—44no—
431#95—44no—
432#95—42no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95—44no—
439#95C2×D414yes—
440#95C2×D414yes—
441#95C2×Q818yescomplemented
442#95C2×Q818yescomplemented
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24C22×D412yes—
453C24C22×Q814yes—
454C24C2511yescharacteristic
455C2×Q8—28no—
456C2×Q8—28no—
457C2×Q8—28no—
458C2×Q8—28no—
459C2×Q8—28no—
460C2×Q8—28no—
461C2×Q8—28no—
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—48no—
465C2×Q8—48no—
466C2×Q8—48no—
467C2×Q8—48no—
468C2×Q8—48no—
469C2×Q8—48no—
470C2×Q8—4128no—
471C2×Q8—48no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
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—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4C22×D414yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D414yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D414yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×Q814yes—
602C22×C4C22×Q814yes—
603C22×C4C22×Q814yes—
604C22×C4C22×Q814yes—
605C22×C4C22×Q814yes—
606C22×C4C22×Q814yes—
607C22×C4C2×#4114yes—
608C22×C4C2×#4112yes—
609C22×C4H(5,𝔽2)12yes—
610C22×C4H(5,𝔽2)12yes—
611C22×C4H(5,𝔽2)12yes—
612C22×C4H(5,𝔽2)12yes—
613C22×C42−1+414yes—
614C22×C42−1+414yes—
615C4⋊C4—216no—
616C4⋊C4—416no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—416no—
624C4⋊C4—48no—
625C4⋊C4—416no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—48no—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—84no—
632C4⋊C4—88no—
633C4⋊C4—84no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—84no—
640C22⋊C4C4⋊Q8116yescomplemented
641C42—28no—
642C42—28no—
643C42—28no—
644C42—48no—
645C42—48no—
646C42—48no—
647C42—44no—
648C42—44no—
649C42—44no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23C2×C4⋊Q814yes—
673C23C23×D411yescharacteristic
674C23C23×D411yescharacteristic
675C23C23×Q812yes—
676C23C22×#4111yescharacteristic
677C23C2×H(5,𝔽2)11yescharacteristic
678C23C2×H(5,𝔽2)11yescharacteristic
679C23C2×H(5,𝔽2)11yescharacteristic
680C23C2×H(5,𝔽2)11yescharacteristic
681C23C2×2−1+412yes—
682C23C2×2−1+412yes—
683C23#58512yes—
684Q8—432no—
685Q8—416no—
686Q8—416no—
687Q8—416no—
688Q8—88no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
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—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—432no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
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—416no—
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—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4C2×C4⋊Q814yes—
791C2×C4C2×C4⋊Q814yes—
792C2×C4#53414yes—
793C2×C4#53514yes—
794C2×C4#53614yes—
795C2×C4#53814yes—
796C2×C4D4214yes—
797C2×C4#54614yes—
798C2×C4#54614yes—
799C2×C4D4×Q818yes—
800C2×C4#56014yes—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—42no—
805C22—44no—
806C22—42no—
807C22—44no—
808C22—44no—
809C22—42no—
810C22—42no—
811C22—44no—
812C22C22×C4⋊Q811yescharacteristic
813C22C2×#53411yescharacteristic
814C22C2×#53511yescharacteristic
815C22C2×#53611yescharacteristic
816C22C2×#53811yescharacteristic
817C22C2×D4211yescharacteristic
818C22C2×#54611yescharacteristic
819C22C2×#54611yescharacteristic
820C22C2×D4×Q812yes—
821C22Q8×#4112yes—
822C22#349712yes—
823C22#349911yescharacteristic
824C22#350011yescharacteristic
825C22#350112yes—
826C22#350312yes—
827C22#350312yes—
828C22#350312yes—
829C22#352312yes—
830C22C2×#56011yescharacteristic
831C22#353812yes—
832C22#355412yes—
833C22#355412yes—
834C22#356112yes—
835C4—24no—
836C4—24no—
837C4—28no—
838C4—24no—
839C4—44no—
840C4—44no—
841C4—42no—
842C4—44no—
843C4—44no—
844C4—44no—
845C4—44no—
846C4—42no—
847C4—82no—
848C4—82no—
849C4—82no—
850C4—82no—
851C4—82no—
852C4#267818yes—
853C2—44no—
854C2#3528111yescharacteristic
855C2D4×C4⋊Q811yescharacteristic
856C2#3627611yescharacteristic
857C2#3739111yescharacteristic
858C2#3808111yescharacteristic
859C2#3936311yescharacteristic
860C2#3961512yes—
861C2#3966312yes—
862C2#4550312yes—
863C2C2×#267811yescharacteristic
864C2#5941312yes—
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. C2×#2546C2semidirect
5. #16827C2semidirect
6. #15627C2semidirect
8. #15190C2semidirect
9. #15188C2semidirect
10. #15185C2semidirect
11. #15184C2semidirect
14. #14714C2semidirect
15. #14714C2semidirect
17. #14024C2semidirect
190. #388Q8semidirect
368. C2×C4⋊C4C2×Q8semidirect
413. C2×C42C2×Q8semidirect
441. #95C2×Q8semidirect
442. #95C2×Q8semidirect
640. C22⋊C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25462
C2×#24232
C2×#24342
#168272
#156272
#155452
#151902
#151882
#151852
#151842
#151822
#151782
#147142
#144422
#140242
#139222
C4×#3882