Finite Group Databasebeta

← #648728

Subgroups — #648728

Order 512.

5766 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Q8C211yesmaximal, characteristic
2C2×#2848C211yesmaximal, characteristic
3C2×#2429C212yesmaximal, complemented
4C2×#2434C211yesmaximal, characteristic, complemented
5C2×#2360C211yesmaximal, characteristic, complemented
6#15614C214yesmaximal, complemented
7#15354C214yesmaximal, complemented
8#15179C212yesmaximal, complemented
9#15178C212yesmaximal, complemented
10#14786C212yesmaximal, complemented
11#14726C212yesmaximal
12#14130C212yesmaximal, complemented
13#13997C212yesmaximal, complemented
14#13991C212yesmaximal
15#13922C211yesmaximal, characteristic, complemented
16#13907C211yesmaximal, characteristic, complemented
17C4×#379C211yesmaximal, characteristic
18C24×Q8C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×C4⋊Q8C2212yescomplemented
21C22×C22⋊Q8—216no—
22C22×C22⋊Q8—28no—
23C22×C22⋊Q8C2212yes—
24C22×C22⋊Q8C2214yes—
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2212yes—
28C22×C4×Q8C2211yescharacteristic, complemented
29C23×C4⋊C4C2212yes—
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2212yes—
32#2848—28no—
33#2434—28no—
34#2429—216no—
35C2×#398C2214yescomplemented
36C2×#396C2214yes—
37C2×#395C2214yescomplemented
38#2360—28no—
39C2×#391C2211yescharacteristic, complemented
40C2×#391C2212yescomplemented
41C2×#391C2212yescomplemented
42C2×#391C2212yescomplemented
43C2×#389C2214yescomplemented
44C2×#389C2211yescharacteristic, complemented
45C2×#389C2212yescomplemented
46C2×#389C2212yescomplemented
47C2×#388C2214yes—
48C2×#387C2212yescomplemented
49C2×#385C2212yes—
50C2×#385C2214yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#385C2212yes—
54C2×#380C2212yes—
55C2×#380C2211yescharacteristic
56C2×#380C2212yes—
57C2×#379C2212yes—
58C2×#379C2211yescharacteristic
59C2×#379C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic, complemented
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2212yes—
66#1446C2212yescomplemented
67#1446C2212yescomplemented
68#1445C2214yescomplemented
69#1444C2214yescomplemented
70#1444C2214yescomplemented
71#1442C2214yescomplemented
72#1441C2214yescomplemented
73#1441C2214yescomplemented
74#1440C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1437C2214yes—
80C4⋊#95C2214yescomplemented
81C4⋊#95C2212yescomplemented
82C22⋊#95C2211yescharacteristic
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2211yescharacteristic
87C22⋊#95C2212yes—
88C22⋊#95C2212yes—
89C26C2311yescharacteristic
90C23×Q8—28no—
91C23×Q8—24no—
92C23×Q8—24no—
93C23×Q8—24no—
94C23×Q8—44no—
95C23×Q8C2312yes—
96C23×Q8C2311yescharacteristic
97C23×Q8C2312yes—
98C24×C4—28no—
99C24×C4—24no—
100C24×C4—24no—
101C24×C4—24no—
102C24×C4—44no—
103C24×C4C2312yes—
104C24×C4C2311yescharacteristic
105C24×C4C2312yes—
106C24×C4C2312yes—
107C24×C4C2312yes—
108C24×C4C2311yescharacteristic
109C2×C4⋊Q8—28no—
110C2×C4⋊Q8—28no—
111C2×C4⋊Q8—44no—
112C2×C22⋊Q8—2128no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8—216no—
120C2×C22⋊Q8—216no—
121C2×C22⋊Q8—28no—
122C2×C22⋊Q8—28no—
123C2×C22⋊Q8—28no—
124C2×C22⋊Q8—216no—
125C2×C22⋊Q8—44no—
126C2×C22⋊Q8D418yes—
127C2×C22⋊Q8D4116yes—
128C2×C4×Q8—24no—
129C2×C4×Q8—28no—
130C22×C4⋊C4—28no—
131C22×C4⋊C4—216no—
132C22×C4⋊C4—28no—
133C22×C4⋊C4D418yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C22⋊C4—28no—
149C22×C22⋊C4—216no—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2311yescharacteristic
168C22×C42C2312yes—
169#398—216no—
170#396—216no—
171#395—216no—
172#391—28no—
173#391—24no—
174#391—28no—
175#391—44no—
176#389—24no—
177#389—28no—
178#389—216no—
179#389—28no—
180#388—216no—
181#387—28no—
182#385—28no—
183#385—216no—
184#385—28no—
185#385—28no—
186#385—28no—
187#380—24no—
188#380—28no—
189#380—28no—
190#379—28no—
191#379—24no—
192#379Q818yescomplemented
193C4×C4⋊C4—24no—
194C4×C22⋊C4—24no—
195C4×C22⋊C4—28no—
196C4×C22⋊C4—28no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—44no—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C25—24no—
222C25—22no—
223C25—24no—
224C25—22no—
225C25—22no—
226C25—22no—
227C25—22no—
228C25—22no—
229C25—42no—
230C25—42no—
231C25C2×Q814yes—
232C25C2412yes—
233C25C2411yescharacteristic
234C22×Q8—232no—
235C22×Q8—24no—
236C22×Q8—22no—
237C22×Q8—28no—
238C22×Q8—24no—
239C22×Q8—24no—
240C22×Q8—24no—
241C22×Q8—24no—
242C22×Q8—24no—
243C22×Q8—22no—
244C22×Q8—24no—
245C22×Q8—24no—
246C22×Q8—24no—
247C22×Q8—24no—
248C22×Q8—24no—
249C22×Q8—44no—
250C22×Q8—432no—
251C22×Q8—432no—
252C22×Q8—416no—
253C22×Q8—416no—
254C22×Q8C2×D414yes—
255C22×Q8C2×D418yes—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—232no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—28no—
265C23×C4—28no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—22no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—432no—
287C23×C4—432no—
288C23×C4—416no—
289C23×C4—416no—
290C23×C4C2×D418yes—
291C23×C4C2×D418yes—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4#4114yes—
295C23×C4C2411yescharacteristic
296C23×C4C2414yes—
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2414yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C4⋊Q8—432no—
311C22⋊Q8—264no—
312C22⋊Q8—2128no—
313C22⋊Q8—232no—
314C22⋊Q8—264no—
315C22⋊Q8—432no—
316C4×Q8—416no—
317C2×C4⋊C4—264no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—232no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4C2×D4116yes—
350C2×C4⋊C4C2×D418yes—
351C2×C4⋊C4C2×D414yes—
352C2×C4⋊C4C2×D414yes—
353C2×C4⋊C4C2×D418yes—
354C2×C4⋊C4C2×D418yes—
355C2×C4⋊C4C2×D414yes—
356C2×C22⋊C4—264no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4C2×D4116yes—
393C2×C22⋊C4C2×D418yes—
394C2×C22⋊C4C2×Q814yes—
395C2×C22⋊C4C2×Q814yes—
396C2×C22⋊C4C2×Q818yescomplemented
397C2×C22⋊C4C2×Q818yescomplemented
398C2×C22⋊C4#4114yes—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—24no—
402C2×C42—28no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—44no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—22no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—28no—
419#95—24no—
420#95—24no—
421#95—28no—
422#95—28no—
423#95—28no—
424#95—28no—
425#95—28no—
426#95—28no—
427#95—44no—
428#95—42no—
429#95—42no—
430#95—44no—
431#95—44no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—28no—
437C24—28no—
438C24—216no—
439C24—216no—
440C24—28no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—28no—
454C24—28no—
455C24—48no—
456C24—48no—
457C24—48no—
458C24—48no—
459C24—48no—
460C24—48no—
461C24—48no—
462C24—48no—
463C24—48no—
464C24—44no—
465C24—44no—
466C24—48no—
467C24—44no—
468C24—44no—
469C24—44no—
470C24—44no—
471C24C22×D414yes—
472C24C22×D412yes—
473C24C22×D412yes—
474C24C22×Q814yes—
475C24C22×Q812yes—
476C24C2×#4112yes—
477C24C2×#4112yes—
478C242−1+414yes—
479C242−1+412yes—
480C242−1+412yes—
481C24C2511yescharacteristic
482C2×Q8—216no—
483C2×Q8—216no—
484C2×Q8—28no—
485C2×Q8—216no—
486C2×Q8—216no—
487C2×Q8—216no—
488C2×Q8—416no—
489C2×Q8—416no—
490C2×Q8—48no—
491C2×Q8—4128no—
492C2×Q8—44no—
493C2×Q8—48no—
494C2×Q8—48no—
495C2×Q8—44no—
496C2×Q8—48no—
497C2×Q8—48no—
498C2×Q8—48no—
499C2×Q8—48no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—216no—
508C22×C4—216no—
509C22×C4—216no—
510C22×C4—28no—
511C22×C4—216no—
512C22×C4—216no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—216no—
558C22×C4—216no—
559C22×C4—216no—
560C22×C4—216no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—416no—
582C22×C4—416no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—416no—
588C22×C4—416no—
589C22×C4—48no—
590C22×C4—4128no—
591C22×C4—44no—
592C22×C4—48no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4#121116yes—
601C22×C4C22×D414yes—
602C22×C4C22×D414yes—
603C22×C4C22×D418yes—
604C22×C4C22×D414yes—
605C22×C4C22×D414yes—
606C22×C4C22×D414yes—
607C22×C4C22×D418yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D414yes—
612C22×C4C22×D412yes—
613C22×C4C22×Q812yes—
614C22×C4C22×Q814yes—
615C22×C4C22×Q812yes—
616C22×C4C2×#4114yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4H(5,𝔽2)14yes—
620C4⋊C4—232no—
621C4⋊C4—216no—
622C4⋊C4—28no—
623C4⋊C4—232no—
624C4⋊C4—28no—
625C4⋊C4—216no—
626C4⋊C4—416no—
627C4⋊C4—416no—
628C4⋊C4—416no—
629C4⋊C4—416no—
630C4⋊C4—48no—
631C4⋊C4—48no—
632C4⋊C4—84no—
633C4⋊C4#120116yes—
634C22⋊C4—232no—
635C22⋊C4—216no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—216no—
640C22⋊C4—232no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—416no—
644C22⋊C4—48no—
645C22⋊C4—416no—
646C22⋊C4—44no—
647C22⋊C4—48no—
648C42—48no—
649C42—44no—
650C42—44no—
651C42—48no—
652C42—84no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—232no—
670C23—24no—
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—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—432no—
689C23—432no—
690C23—416no—
691C23—416no—
692C23—432no—
693C23—416no—
694C23—416no—
695C23—432no—
696C23—416no—
697C23—42no—
698C23—42no—
699C23—416no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23C2×#12114yes—
715C23#53314yes—
716C23#54114yes—
717C23#54714yes—
718C23#54814yes—
719C23D4×Q818yes—
720C23D4×Q814yes—
721C23D4×Q814yes—
722C23C23×D411yescharacteristic
723C23C23×D412yes—
724C23C23×D411yescharacteristic
725C23C23×Q811yescharacteristic
726C23C22×#4111yescharacteristic
727C23C22×#4111yescharacteristic
728C23C2×H(5,𝔽2)12yes—
729C23C2×2−1+411yescharacteristic
730C23C2×2−1+411yescharacteristic
731C23C2×2−1+412yes—
732C23#58512yes—
733Q8—432no—
734Q8—416no—
735Q8—432no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—24no—
743C2×C4—28no—
744C2×C4—232no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—28no—
751C2×C4—24no—
752C2×C4—28no—
753C2×C4—24no—
754C2×C4—28no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—28no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—432no—
769C2×C4—432no—
770C2×C4—416no—
771C2×C4—432no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—432no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—44no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4C2×#12018yes—
821C2×C4C2×#12014yes—
822C2×C4C2×#12114yes—
823C2×C4C2×#12114yes—
824C2×C4#53514yes—
825C2×C4D4218yes—
826C2×C4#54618yes—
827C22—24no—
828C22—28no—
829C22—28no—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—28no—
834C22—28no—
835C22—24no—
836C22—24no—
837C22—28no—
838C22—28no—
839C22—28no—
840C22—464no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22#242918yescomplemented
854C22C22×#12011yescharacteristic
855C22C22×#12111yescharacteristic
856C22C2×#53311yescharacteristic
857C22C2×#53511yescharacteristic
858C22C2×#54111yescharacteristic
859C22C2×D4212yes—
860C22C2×#54612yes—
861C22C2×#54711yescharacteristic
862C22C2×#54811yescharacteristic
863C22C2×D4×Q812yes—
864C22C2×D4×Q811yescharacteristic
865C22C2×D4×Q811yescharacteristic
866C22D4×#4112yes—
867C22#348511yescharacteristic
868C22#348611yescharacteristic
869C22#348612yes—
870C22#348912yes—
871C22#348912yes—
872C22#349512yes—
873C22#350112yes—
874C22#352012yes—
875C22#353812yes—
876C22#354112yes—
877C4—24no—
878C4—28no—
879C4—44no—
880C4—44no—
881C4—48no—
882C4—44no—
883C4—44no—
884C4—44no—
885C4—44no—
886C4—42no—
887C4—42no—
888C4—81no—
889C4—81no—
890C4—84no—
891C4#240818yes—
892C2—28no—
893C2—48no—
894C2C2×#240811yescharacteristic
895C2C2×#242911yescharacteristic
896C2#3563311yescharacteristic
897C2#3613012yes—
898C2#3621311yescharacteristic
899C2Q8×#12011yescharacteristic
900C2#3766312yes—
901C2#3891711yescharacteristic
902C2#3959411yescharacteristic
903C2#5899812yes—
904C2#5900512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#2429C2semidirect
4. C2×#2434C2semidirect
5. C2×#2360C2semidirect
6. #15614C2semidirect
7. #15354C2semidirect
8. #15179C2semidirect
9. #15178C2semidirect
10. #14786C2semidirect
12. #14130C2semidirect
13. #13997C2semidirect
15. #13922C2semidirect
16. #13907C2semidirect
20. C22×C4⋊Q8C22semidirect
28. C22×C4×Q8C22semidirect
35. C2×#398C22semidirect
37. C2×#395C22semidirect
39. C2×#391C22semidirect
40. C2×#391C22semidirect
41. C2×#391C22semidirect
42. C2×#391C22semidirect
43. C2×#389C22semidirect
44. C2×#389C22semidirect
45. C2×#389C22semidirect
46. C2×#389C22semidirect
48. C2×#387C22semidirect
60. C2×C4×C4⋊C4C22semidirect
66. #1446C22semidirect
67. #1446C22semidirect
68. #1445C22semidirect
69. #1444C22semidirect
70. #1444C22semidirect
71. #1442C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
80. C4⋊#95C22semidirect
81. C4⋊#95C22semidirect
192. #379Q8semidirect
396. C2×C22⋊C4C2×Q8semidirect
397. C2×C22⋊C4C2×Q8semidirect
853. C22#2429semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Q82
C2×#28482
C2×#24292
C2×#24342
C2×#23602
#156142
#153542
#151792
#151782
#147862
#147262
#141302
#139972
#139912
#139222
#139072
C4×#3792