Finite Group Databasebeta

← #734800

Subgroups — #734800

Order 512.

5310 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Q8C211yesmaximal, characteristic, complemented
2C2×#2561C211yesmaximal, characteristic, complemented
3C2×#2534C211yesmaximal, characteristic
4C22×#393C211yesmaximal, characteristic, complemented
5#16632C212yesmaximal, complemented
6#16602C212yesmaximal, complemented
7#15322C214yesmaximal, complemented
8#15275C214yesmaximal, complemented
9#14934C212yesmaximal, complemented
10#14882C212yesmaximal, complemented
11#14873C212yesmaximal, complemented
12#14717C212yesmaximal, complemented
13#14281C211yesmaximal, characteristic, complemented
14#13968C212yesmaximal, complemented
15#13967C212yesmaximal
16#13922C211yesmaximal, characteristic, complemented
17#13784C211yesmaximal, characteristic, complemented
18C24×Q8C2211yescharacteristic
19C24×Q8C2211yescharacteristic, complemented
20C2×D4×Q8—28no—
21C2×D4×Q8—28no—
22C2×D4×Q8—28no—
23C22×C4⋊Q8C2212yescomplemented
24C22×C4⋊Q8C2211yescharacteristic, complemented
25C22×#123C2211yescharacteristic
26C22×C22⋊Q8C2212yes—
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2212yescomplemented
29C22×C22⋊Q8C2211yescharacteristic, complemented
30C22×#120C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic, complemented
32C22×C4×D4C2212yes—
33C22×C4×D4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2212yes—
36#2561—28no—
37#2534—28no—
38C2×#397C2212yes—
39C2×#396C2212yes—
40C2×#394C2212yes—
41C2×#393—28no—
42C2×#393C2212yes—
43C2×#393C2212yes—
44C2×#393C2214yes—
45C2×#393C2212yes—
46C2×#393C2214yes—
47C2×#391C2214yescomplemented
48C2×#388C2212yes—
49C2×#388C2214yes—
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2214yes—
53C2×#381C2211yescharacteristic
54C2×#381C2212yes—
55C2×#380C2211yescharacteristic
56C2×#379C2211yescharacteristic
57C2×#379C2212yes—
58C2×C4×C22⋊C4C2211yescharacteristic
59C22×#95C2212yes—
60C22×#95C2211yescharacteristic
61#1446C2212yescomplemented
62#1446C2214yescomplemented
63#1446C2212yescomplemented
64#1446C2212yescomplemented
65#1445C2212yescomplemented
66#1442C2214yescomplemented
67#1442C2214yescomplemented
68#1442C2214yescomplemented
69#1441C2214yescomplemented
70#1441C2214yescomplemented
71#1440C2214yescomplemented
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1438C2214yes—
77#1437C2214yes—
78#1437C2212yescomplemented
79#1436C2214yescomplemented
80#1436C2212yescomplemented
81#1434C2212yescomplemented
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22⋊#95C2214yescomplemented
88C22⋊#95C2212yescomplemented
89C26C2311yescharacteristic
90C23×Q8—24no—
91C23×Q8—24no—
92C23×Q8—24no—
93C23×Q8—24no—
94C23×Q8—24no—
95C23×Q8—48no—
96C23×Q8—48no—
97C23×Q8D418yescomplemented
98C23×Q8C2311yescharacteristic
99C23×Q8C2312yes—
100C23×Q8C2312yes—
101C23×Q8C2311yescharacteristic
102C23×Q8C2311yescharacteristic
103C23×D4C2312yes—
104C23×D4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2312yes—
107C24×C4C2312yes—
108C24×C4C2312yes—
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111D4×Q8—2128no—
112C2×C4⋊Q8—28no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—28no—
116C2×C4⋊Q8—28no—
117C2×C4⋊Q8—24no—
118C2×#123—24no—
119C2×#123—28no—
120C2×C22⋊Q8—28no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—28no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—28no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—28no—
129C2×C22⋊Q8—28no—
130C2×C22⋊Q8—28no—
131C2×C22⋊Q8D418yescomplemented
132C2×#120—24no—
133C2×#120—28no—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×D4—28no—
138C2×C4×D4—28no—
139C2×C4×D4—24no—
140C2×C4×D4—24no—
141C2×C4×D4—28no—
142C2×C4×D4D418yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C22⋊C4—24no—
153C22×C22⋊C4—28no—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—24no—
156C22×C22⋊C4—48no—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2314yes—
173C22×C22⋊C4C2314yes—
174C22×C22⋊C4C2314yes—
175C22×C42C2312yes—
176C22×C42C2311yescharacteristic
177C22×C42C2312yes—
178#397—28no—
179#396—28no—
180#394—28no—
181#393—28no—
182#393—28no—
183#393—216no—
184#393—28no—
185#393—48no—
186#391—48no—
187#388—216no—
188#388—28no—
189#386—28no—
190#386—28no—
191#386—48no—
192#381—28no—
193#381—24no—
194#380—24no—
195#379—28no—
196#379—24no—
197C4×C22⋊C4—24no—
198C2×#95—28no—
199C2×#95—24no—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C25—22no—
222C25—24no—
223C25—22no—
224C25—22no—
225C25—24no—
226C25—24no—
227C25—44no—
228C25—42no—
229C25C2412yes—
230C25C2411yescharacteristic
231C25C2411yescharacteristic
232C22×Q8—232no—
233C22×Q8—232no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—24no—
237C22×Q8—24no—
238C22×Q8—24no—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—24no—
245C22×Q8—28no—
246C22×Q8—28no—
247C22×Q8—28no—
248C22×Q8—44no—
249C22×Q8—44no—
250C22×Q8—44no—
251C22×Q8—44no—
252C22×Q8—432no—
253C22×Q8—432no—
254C22×Q8—432no—
255C22×Q8—432no—
256C22×Q8—432no—
257C22×Q8—432no—
258C22×Q8C2×D414yes—
259C22×Q8C2×D418yes—
260C22×Q8C2×D414yes—
261C22×Q8C2×D414yes—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—24no—
265C22×D4—24no—
266C22×D4—24no—
267C22×D4—28no—
268C22×D4—42no—
269C22×D4—44no—
270C22×D4C2×D414yes—
271C22×D4#4118yes—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—28no—
280C23×C4—22no—
281C23×C4—24no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—28no—
289C23×C4—44no—
290C23×C4—44no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4—44no—
294C23×C4—44no—
295C23×C4C2×D418yes—
296C23×C4C2×D414yes—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4C2412yes—
301C23×C4C2414yes—
302C23×C4C2412yes—
303C23×C4C2414yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2412yes—
314C4⋊Q8—264no—
315C4⋊Q8—232no—
316#123—416no—
317C22⋊Q8—232no—
318C22⋊Q8—264no—
319C22⋊Q8—264no—
320C22⋊Q8—232no—
321#120—416no—
322C4×Q8—232no—
323C4×D4—264no—
324C4×D4—232no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2×D418yes—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
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—28no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—432no—
392C2×C22⋊C4—416no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×D418yes—
399C2×C22⋊C4C2×D414yes—
400C2×C22⋊C4C2×D414yes—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42—44no—
408C2×C42C2×D414yes—
409#95—28no—
410#95—24no—
411#95—24no—
412#95—28no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—28no—
417#95—24no—
418#95—28no—
419#95—28no—
420#95—28no—
421#95—28no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95—44no—
429#95—44no—
430C24—24no—
431C24—22no—
432C24—22no—
433C24—21no—
434C24—21no—
435C24—24no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—28no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—22no—
447C24—24no—
448C24—22no—
449C24—22no—
450C24—48no—
451C24—48no—
452C24—416no—
453C24—416no—
454C24—48no—
455C24—44no—
456C24—44no—
457C24—48no—
458C24—44no—
459C24—44no—
460C24—48no—
461C24—84no—
462C24—84no—
463C24—88no—
464C24—88no—
465C24C22×D412yes—
466C24C22×D412yes—
467C24C22×D412yes—
468C24C22×D412yes—
469C24C2×#4114yes—
470C24C2×#4114yes—
471C242−1+414yes—
472C242−1+414yes—
473C24C2511yescharacteristic
474C2×Q8—216no—
475C2×Q8—216no—
476C2×Q8—216no—
477C2×Q8—28no—
478C2×Q8—216no—
479C2×Q8—28no—
480C2×Q8—28no—
481C2×Q8—216no—
482C2×Q8—216no—
483C2×Q8—48no—
484C2×Q8—48no—
485C2×Q8—48no—
486C2×Q8—416no—
487C2×Q8—416no—
488C2×Q8—416no—
489C2×Q8—416no—
490C2×Q8—48no—
491C2×Q8—48no—
492C2×Q8—48no—
493C2×Q8—48no—
494C2×Q8—48no—
495C2×Q8—4128no—
496C2×Q8—4128no—
497C2×Q8—48no—
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—216no—
501C2×D4—216no—
502C2×D4—48no—
503C2×D4—416no—
504C2×D4—48no—
505C2×D4—84no—
506C2×D4—88no—
507C2×D4#124116yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—216no—
517C22×C4—216no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—28no—
538C22×C4—216no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—416no—
574C22×C4—416no—
575C22×C4—416no—
576C22×C4—416no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—88no—
590C22×C4—88no—
591C22×C4#120116yes—
592C22×C4C22×D414yes—
593C22×C4C22×D412yes—
594C22×C4C22×D414yes—
595C22×C4C22×D414yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D414yes—
605C22×C4C2×#4114yes—
606C22×C4H(5,𝔽2)18yes—
607C4⋊C4—216no—
608C4⋊C4—216no—
609C4⋊C4—216no—
610C4⋊C4—216no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—216no—
614C4⋊C4—48no—
615C4⋊C4—84no—
616C22⋊C4—216no—
617C22⋊C4—216no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—416no—
621C22⋊C4—48no—
622C22⋊C4—416no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—416no—
631C22⋊C4—88no—
632C22⋊C4—84no—
633C22⋊C4—88no—
634C42—216no—
635C42—28no—
636C42—84no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—28no—
655C23—28no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—28no—
660C23—28no—
661C23—416no—
662C23—432no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—44no—
669C23—44no—
670C23—42no—
671C23—42no—
672C23—44no—
673C23—42no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—832no—
689C23—816no—
690C23—816no—
691C23—88no—
692C23—816no—
693C23—88no—
694C23C2×#12014yes—
695C23C2×#12414yes—
696C23C2×#12414yes—
697C23#53614yes—
698C23#54818yes—
699C23#54818yes—
700C23C23×D411yescharacteristic
701C23C23×D411yescharacteristic
702C23C23×D411yescharacteristic
703C23C22×#4112yes—
704C23C2×H(5,𝔽2)14yes—
705C23C2×2−1+412yes—
706C23C2×2−1+412yes—
707C23#58512yes—
708Q8—232no—
709Q8—432no—
710Q8—416no—
711Q8—416no—
712Q8—432no—
713D4—232no—
714D4—816no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—28no—
737C2×C4—24no—
738C2×C4—28no—
739C2×C4—24no—
740C2×C4—416no—
741C2×C4—432no—
742C2×C4—416no—
743C2×C4—432no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—816no—
787C2×C4—88no—
788C2×C4C2×#12014yes—
789C2×C4C2×#12014yes—
790C2×C4C2×#12414yes—
791C2×C4#53418yes—
792C22—24no—
793C22—216no—
794C22—28no—
795C22—28no—
796C22—24no—
797C22—28no—
798C22—28no—
799C22—28no—
800C22—24no—
801C22—42no—
802C22—48no—
803C22—44no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—48no—
809C22—44no—
810C22—44no—
811C22—48no—
812C22—832no—
813C22—84no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—82no—
818C22—84no—
819C22#243618yes—
820C22C22×#12011yescharacteristic
821C22C22×#12411yescharacteristic
822C22C2×#53412yes—
823C22C2×#53611yescharacteristic
824C22C2×#54812yes—
825C22C2×#54812yes—
826C22#348412yes—
827C22#348412yes—
828C22#348611yescharacteristic
829C22#348711yescharacteristic
830C22#348912yes—
831C22#348912yes—
832C22#351414yes—
833C22#352014yes—
834C22#353814yes—
835C22#356114yes—
836C4—24no—
837C4—24no—
838C4—28no—
839C4—24no—
840C4—44no—
841C4—42no—
842C4—44no—
843C4—44no—
844C4—42no—
845C4—84no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—84no—
850C2—28no—
851C2—44no—
852C2—84no—
853C2C2×#243611yescharacteristic
854C2#3498011yescharacteristic
855C2#3565911yescharacteristic
856C2#3593912yes—
857C2#3912112yes—
858C2#3912312yes—
859C2#4059512yes—
860C2#4310414yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
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×D4×Q8C2semidirect
2. C2×#2561C2semidirect
4. C22×#393C2semidirect
5. #16632C2semidirect
6. #16602C2semidirect
7. #15322C2semidirect
8. #15275C2semidirect
9. #14934C2semidirect
10. #14882C2semidirect
11. #14873C2semidirect
12. #14717C2semidirect
13. #14281C2semidirect
14. #13968C2semidirect
16. #13922C2semidirect
17. #13784C2semidirect
19. C24×Q8C22semidirect
23. C22×C4⋊Q8C22semidirect
24. C22×C4⋊Q8C22semidirect
28. C22×C22⋊Q8C22semidirect
29. C22×C22⋊Q8C22semidirect
31. C22×C4×Q8C22semidirect
47. C2×#391C22semidirect
61. #1446C22semidirect
62. #1446C22semidirect
63. #1446C22semidirect
64. #1446C22semidirect
65. #1445C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1440C22semidirect
78. #1437C22semidirect
79. #1436C22semidirect
80. #1436C22semidirect
81. #1434C22semidirect
87. C22⋊#95C22semidirect
88. C22⋊#95C22semidirect
97. C23×Q8D4semidirect
131. C2×C22⋊Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Q82
C2×#25612
C2×#25342
C22×#3932
#166322
#166022
#153222
#152752
#149342
#148822
#148732
#147172
#142812
#139682
#139672
#139222
#137842