Finite Group Databasebeta

← #646666

Subgroups — #646666

Order 512.

5662 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#123C211yesmaximal, characteristic
2C2×#2848C211yesmaximal, characteristic, complemented
3C2×#2663C212yesmaximal, complemented
4#16657C214yesmaximal, complemented
5#16360C212yesmaximal, complemented
6#16251C212yesmaximal, complemented
7#14822C211yesmaximal, characteristic, complemented
8#14761C214yesmaximal, complemented
9#14734C211yesmaximal, characteristic, complemented
10#14727C212yesmaximal, complemented
11#14724C212yesmaximal
12#14720C211yesmaximal, characteristic, complemented
13#14717C211yesmaximal, characteristic, complemented
14#14287C212yesmaximal, complemented
15#14043C212yesmaximal, complemented
16#13971C212yesmaximal, complemented
17C4×#379C211yesmaximal, characteristic, complemented
18C24×D4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×#123—28no—
21C22×#123—216no—
22C22×#123C2212yes—
23C22×#123C2212yes—
24C22×#123C2212yes—
25C22×#123C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic, complemented
28C22×C22⋊Q8C2211yescharacteristic, complemented
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34#2848—28no—
35#2663—216no—
36C2×#400C2212yescomplemented
37C2×#399C2212yescomplemented
38C2×#397C2214yescomplemented
39C2×#395C2212yescomplemented
40C2×#394C2214yes—
41C2×#394C2214yes—
42C2×#393C2212yescomplemented
43C2×#389C2214yescomplemented
44C2×#388C2214yescomplemented
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yescomplemented
49C2×#385C2212yescomplemented
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic, complemented
52C2×#380C2211yescharacteristic, complemented
53C2×#379C2212yes—
54C2×#379C2212yes—
55C2×#379C2212yes—
56C2×#379C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yescomplemented
59C2×C4×C22⋊C4C2212yescomplemented
60#1444C2214yescomplemented
61#1444C2214yescomplemented
62#1442C2214yescomplemented
63#1441C2214yescomplemented
64#1441C2212yescomplemented
65#1441C2212yescomplemented
66#1440C2214yescomplemented
67#1440C2214yescomplemented
68#1440C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1439C2214yescomplemented
72#1439C2212yescomplemented
73#1439C2212yescomplemented
74#1439C2214yescomplemented
75#1438C2214yes—
76#1438C2214yes—
77#1437C2214yescomplemented
78#1436C2214yescomplemented
79C22⋊#95C2212yes—
80C22⋊#95C2211yescharacteristic
81C22⋊#95C2212yes—
82C22⋊#95C2211yescharacteristic
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yescomplemented
86C22⋊#95C2212yescomplemented
87C26C2311yescharacteristic
88C26C2311yescharacteristic
89C23×Q8C2311yescharacteristic
90C23×D4—24no—
91C23×D4—28no—
92C23×D4—44no—
93C23×D4—44no—
94C23×D4C2312yes—
95C23×D4C2312yes—
96C24×C4—28no—
97C24×C4—44no—
98C24×C4—44no—
99C24×C4D418yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C2×#123—2128no—
110C2×#123—28no—
111C2×#123—28no—
112C2×#123—28no—
113C2×#123—28no—
114C2×#123—28no—
115C2×#123—28no—
116C2×#123—28no—
117C2×#123—28no—
118C2×#123—28no—
119C2×#123—28no—
120C2×#123—28no—
121C2×#123D4116yes—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—28no—
126C2×C22⋊Q8—44no—
127C2×C22⋊Q8—44no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—28no—
131C22×C4⋊C4—28no—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C22⋊C4—24no—
145C22×C22⋊C4—24no—
146C22×C22⋊C4—24no—
147C22×C22⋊C4—28no—
148C22×C22⋊C4—28no—
149C22×C22⋊C4—28no—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2314yes—
170C22×C42C2314yes—
171#400—28no—
172#399—28no—
173#397—216no—
174#395—28no—
175#394—216no—
176#394—48no—
177#393—28no—
178#389—216no—
179#388—216no—
180#385—28no—
181#385—28no—
182#385—28no—
183#385—28no—
184#385—44no—
185#380—24no—
186#380—24no—
187#380—24no—
188#379—28no—
189#379—28no—
190#379—28no—
191#379—44no—
192C4×C22⋊C4—28no—
193C4×C22⋊C4—44no—
194C4×C22⋊C4—44no—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C25—24no—
214C25—24no—
215C25—24no—
216C25—24no—
217C25—22no—
218C25—24no—
219C25—22no—
220C25—22no—
221C25—24no—
222C25—24no—
223C25—22no—
224C25—22no—
225C25—42no—
226C25—42no—
227C25—42no—
228C25—42no—
229C25—42no—
230C25C2×D414yes—
231C25C2412yes—
232C25C2411yescharacteristic
233C25C2411yescharacteristic
234C25C2411yescharacteristic
235C22×Q8—22no—
236C22×Q8—24no—
237C22×Q8—42no—
238C22×Q8—42no—
239C22×D4—232no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—28no—
245C22×D4—24no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—464no—
250C22×D4—416no—
251C22×D4—416no—
252C22×D4C2×D418yes—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—232no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—416no—
274C23×C4—416no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—464no—
287C23×C4C2×D414yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D418yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2414yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2414yes—
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307#123—264no—
308#123—264no—
309#123—264no—
310#123—264no—
311C22⋊Q8—416no—
312C22⋊Q8—416no—
313C22⋊Q8—416no—
314C2×C4⋊C4—232no—
315C2×C4⋊C4—232no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
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—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—28no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4C2×D418yes—
346C2×C4⋊C4C2×D418yes—
347C2×C22⋊C4—232no—
348C2×C22⋊C4—232no—
349C2×C22⋊C4—232no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
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⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4C2×D418yes—
403C2×C22⋊C4C2×D418yes—
404C2×C22⋊C4C2×D418yes—
405C2×C22⋊C4#4118yes—
406C2×C42—28no—
407C2×C42—44no—
408C2×C42—44no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—28no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—28no—
419#95—44no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—42no—
424#95—42no—
425#95—44no—
426#95—44no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—232no—
432C24—28no—
433C24—28no—
434C24—28no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—28no—
450C24—28no—
451C24—28no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—24no—
456C24—24no—
457C24—22no—
458C24—22no—
459C24—24no—
460C24—22no—
461C24—22no—
462C24—44no—
463C24—44no—
464C24—416no—
465C24—48no—
466C24—48no—
467C24—416no—
468C24—48no—
469C24—48no—
470C24—416no—
471C24—416no—
472C24—48no—
473C24—48no—
474C24—416no—
475C24—44no—
476C24—44no—
477C24—44no—
478C24—48no—
479C24—48no—
480C24—44no—
481C24—44no—
482C24—44no—
483C24—48no—
484C24—48no—
485C24—88no—
486C24—88no—
487C24—84no—
488C24—84no—
489C24C22×D414yes—
490C24C22×D412yes—
491C24C22×D414yes—
492C24C22×D412yes—
493C24C22×D412yes—
494C24C2×#4114yes—
495C24H(5,𝔽2)14yes—
496C24H(5,𝔽2)14yes—
497C242−1+412yes—
498C242−1+412yes—
499C24C2511yescharacteristic
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—88no—
504C2×D4—216no—
505C2×D4—216no—
506C2×D4—416no—
507C2×D4—416no—
508C2×D4—416no—
509C2×D4—4128no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—416no—
514C2×D4—48no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—416no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—416no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—416no—
597C22×C4—416no—
598C22×C4—416no—
599C22×C4—416no—
600C22×C4—416no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—4128no—
604C22×C4—416no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4#120116yes—
610C22×C4C22×D414yes—
611C22×C4C22×D414yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D414yes—
615C22×C4C22×D412yes—
616C22×C4C22×D414yes—
617C22×C4C22×D414yes—
618C22×C4C22×D412yes—
619C22×C4C2×#4118yes—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C4⋊C4—216no—
623C4⋊C4—216no—
624C4⋊C4—416no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—44no—
630C4⋊C4—48no—
631C4⋊C4—88no—
632C22⋊C4—216no—
633C22⋊C4—216no—
634C22⋊C4—216no—
635C22⋊C4—216no—
636C22⋊C4—216no—
637C22⋊C4—216no—
638C22⋊C4—216no—
639C22⋊C4—416no—
640C22⋊C4—416no—
641C22⋊C4—416no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—88no—
650C22⋊C4—88no—
651C22⋊C4—88no—
652C42—88no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—28no—
658C23—28no—
659C23—24no—
660C23—24no—
661C23—28no—
662C23—28no—
663C23—24no—
664C23—24no—
665C23—232no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—28no—
679C23—28no—
680C23—28no—
681C23—24no—
682C23—24no—
683C23—28no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—28no—
688C23—28no—
689C23—24no—
690C23—24no—
691C23—416no—
692C23—416no—
693C23—416no—
694C23—416no—
695C23—416no—
696C23—464no—
697C23—464no—
698C23—416no—
699C23—416no—
700C23—416no—
701C23—416no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—44no—
707C23—42no—
708C23—42no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—42no—
725C23—42no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—832no—
733C23—832no—
734C23—88no—
735C23—88no—
736C23—88no—
737C23—88no—
738C23C2×#12014yes—
739C23#53214yes—
740C23#53414yes—
741C23#53414yes—
742C23#53614yes—
743C23#53918yes—
744C23#54218yes—
745C23C23×D411yescharacteristic
746C23C23×D412yes—
747C23C22×#4112yes—
748C23C2×H(5,𝔽2)12yes—
749C23C2×H(5,𝔽2)12yes—
750C23C2×2−1+411yescharacteristic
751C23C2×2−1+411yescharacteristic
752C23#58512yes—
753C23#58512yes—
754Q8—88no—
755D4—432no—
756D4—432no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—28no—
773C2×C4—28no—
774C2×C4—28no—
775C2×C4—28no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—28no—
779C2×C4—416no—
780C2×C4—416no—
781C2×C4—416no—
782C2×C4—416no—
783C2×C4—416no—
784C2×C4—416no—
785C2×C4—416no—
786C2×C4—416no—
787C2×C4—416no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4C2×#12014yes—
832C2×C4C2×#12014yes—
833C22—24no—
834C22—24no—
835C22—216no—
836C22—216no—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—464no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—48no—
854C22—48no—
855C22—48no—
856C22—48no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—48no—
861C22—48no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—832no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—84no—
870C22—84no—
871C22—82no—
872C22#266318yescomplemented
873C22C22×#12011yescharacteristic
874C22C2×#53211yescharacteristic
875C22C2×#53411yescharacteristic
876C22C2×#53411yescharacteristic
877C22C2×#53611yescharacteristic
878C22#344911yescharacteristic
879C22#344911yescharacteristic
880C22C2×#53912yes—
881C22C2×#54212yes—
882C22D4×#4114yes—
883C22#348414yes—
884C22#348912yes—
885C22#348912yes—
886C22#351314yes—
887C22#353314yes—
888C22#353512yes—
889C22#353512yes—
890C4—24no—
891C4—24no—
892C4—48no—
893C4—42no—
894C4—42no—
895C4—44no—
896C4—44no—
897C4—44no—
898C4—82no—
899C4—84no—
900C4—82no—
901C4—82no—
902C4—82no—
903C2—28no—
904C2—44no—
905C2—44no—
906C2—84no—
907C2C2×#266311yescharacteristic
908C2#3473811yescharacteristic
909C2#3498011yescharacteristic
910C2#3506411yescharacteristic
911C2#3530511yescharacteristic
912C2#3744111yescharacteristic
913C2#3744311yescharacteristic
914C2#3771214yes—
915C2#3771514yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2848C2semidirect
3. C2×#2663C2semidirect
4. #16657C2semidirect
5. #16360C2semidirect
6. #16251C2semidirect
7. #14822C2semidirect
8. #14761C2semidirect
9. #14734C2semidirect
10. #14727C2semidirect
12. #14720C2semidirect
13. #14717C2semidirect
14. #14287C2semidirect
15. #14043C2semidirect
16. #13971C2semidirect
17. C4×#379C2semidirect
27. C22×C22⋊Q8C22semidirect
28. C22×C22⋊Q8C22semidirect
36. C2×#400C22semidirect
37. C2×#399C22semidirect
38. C2×#397C22semidirect
39. C2×#395C22semidirect
42. C2×#393C22semidirect
43. C2×#389C22semidirect
44. C2×#388C22semidirect
48. C2×#385C22semidirect
49. C2×#385C22semidirect
51. C2×#380C22semidirect
52. C2×#380C22semidirect
58. C2×C4×C22⋊C4C22semidirect
59. C2×C4×C22⋊C4C22semidirect
60. #1444C22semidirect
61. #1444C22semidirect
62. #1442C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1440C22semidirect
67. #1440C22semidirect
68. #1440C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
74. #1439C22semidirect
77. #1437C22semidirect
78. #1436C22semidirect
85. C22⋊#95C22semidirect
86. C22⋊#95C22semidirect
872. C22#2663semidirect

Maximal subgroups

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

subgroupindex
C23×#1232
C2×#28482
C2×#26632
#166572
#163602
#162512
#148222
#147612
#147342
#147272
#147242
#147202
#147172
#142872
#140432
#139712
C4×#3792