Finite Group Databasebeta

← #615938

Subgroups — #615938

Order 512.

3156 conjugacy classes of subgroups.

The subgroup lattice has 831 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#123C211yesmaximal, characteristic
2C22×C4×C4⋊C4C211yesmaximal, characteristic, complemented
3#15110C212yesmaximal, complemented
4#15101C212yesmaximal, complemented
5#15088C212yesmaximal, complemented
6#15079C212yesmaximal, complemented
7#14919C212yesmaximal, complemented
8#14912C212yesmaximal
9#14696C212yesmaximal
10#14695C212yesmaximal, complemented
11#14685C211yesmaximal, characteristic, complemented
12#14130C211yesmaximal, characteristic, complemented
13#14130C211yesmaximal, characteristic, complemented
14#14042C212yesmaximal, complemented
15#14041C212yesmaximal, complemented
16#13994C212yesmaximal, complemented
17#13993C212yesmaximal, complemented
18#13872C211yesmaximal, characteristic
19#13872C211yesmaximal, characteristic
20C22×#123C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25C23×C42C2212yes—
26C4×#123—28no—
27C2×#389C2212yes—
28C2×#389C2212yes—
29C2×#388C2211yescharacteristic
30C2×#388C2211yescharacteristic
31C2×#388C2214yes—
32C2×#387C2211yescharacteristic
33C2×#387C2211yescharacteristic
34C2×#387C2214yes—
35C2×#386C2212yes—
36C2×#386C2211yescharacteristic
37C2×#386C2212yes—
38C2×#385C2212yes—
39C2×#385C2211yescharacteristic
40C2×#385C2212yes—
41C2×#381C2211yescharacteristic
42C2×#381C2212yes—
43C2×#380C2211yescharacteristic
44C2×#380C2211yescharacteristic
45C2×#380C2212yes—
46C2×#380C2212yes—
47C2×C4×C4⋊C4—28no—
48C2×C4×C4⋊C4C2212yes—
49C2×C4×C4⋊C4C2212yes—
50C2×C4×C4⋊C4C2212yes—
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C22×#95C2212yes—
58#1445C2214yes—
59#1444C2212yes—
60#1444C2212yes—
61#1443C2214yes—
62#1443C2214yes—
63#1442C2212yes—
64#1442C2212yes—
65#1442C2214yes—
66#1442C2214yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2214yes—
70#1440C2214yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2214yes—
74#1437C2214yes—
75#1436C2214yes—
76#1436C2214yes—
77#1436C2214yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84#1434C2212yes—
85#1434C2212yes—
86#1434C2214yes—
87#1434C2214yes—
88C22⋊#95C2212yes—
89C22⋊#95C2212yes—
90C22⋊#95C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C23×D4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C2×#123—24no—
101C2×#123—24no—
102C2×#123—24no—
103C2×C4×D4—24no—
104C2×C4×D4—24no—
105C2×C4×D4—24no—
106C22×C4⋊C4—24no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—28no—
109C22×C4⋊C4—28no—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C22⋊C4C2311yescharacteristic
124C22×C22⋊C4C2311yescharacteristic
125C22×C22⋊C4C2311yescharacteristic
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2314yes—
135C22×C42—24no—
136C22×C42—24no—
137C22×C42—28no—
138C22×C42—48no—
139C22×C42D418yes—
140C22×C42C2314yes—
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2314yes—
149#389—28no—
150#389—28no—
151#388—24no—
152#388—24no—
153#388—48no—
154#387—24no—
155#387—24no—
156#387—48no—
157#386—28no—
158#386—24no—
159#386—44no—
160#385—24no—
161#385—28no—
162#385—44no—
163#381—24no—
164#381—44no—
165#380—24no—
166#380—24no—
167#380—28no—
168#380—28no—
169C4×C4⋊C4—28no—
170C4×C4⋊C4—28no—
171C4×C4⋊C4—28no—
172C4×C4⋊C4—28no—
173C4×C4⋊C4—24no—
174C4×C4⋊C4—24no—
175C4×C22⋊C4—24no—
176C4×C22⋊C4—24no—
177C4×C22⋊C4—24no—
178C2×#95—28no—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2311yescharacteristic
186C2×#95C2311yescharacteristic
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2311yescharacteristic
192C2×#95C2311yescharacteristic
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2311yescharacteristic
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
198C2×#95C2311yescharacteristic
199C2×#95C2311yescharacteristic
200C2×#95C2311yescharacteristic
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C25C2411yescharacteristic
210C25C2411yescharacteristic
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4#4114yes—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—24no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—28no—
233C23×C4—28no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—44no—
244C23×C4—44no—
245C23×C4C2×D414yes—
246C23×C4C2×D414yes—
247C23×C4C2×D414yes—
248C23×C4#4114yes—
249C23×C4#4114yes—
250C23×C4C2411yescharacteristic
251C23×C4C2414yes—
252C23×C4C2414yes—
253C23×C4C2411yescharacteristic
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C23×C4C2414yes—
261C23×C4C2414yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267#123—232no—
268C4×D4—416no—
269C2×C4⋊C4—232no—
270C2×C4⋊C4—232no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—28no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4#4118yes—
305C2×C4⋊C4#4118yes—
306C2×C22⋊C4—22no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4#4114yes—
340C2×C42—232no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—28no—
353C2×C42—28no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—28no—
359C2×C42—28no—
360C2×C42—44no—
361C2×C42—44no—
362C2×C42—432no—
363C2×C42C2×D414yes—
364C2×C42C2×D414yes—
365C2×C42C2×D414yes—
366C2×C42C2×D414yes—
367#95—28no—
368#95—28no—
369#95—22no—
370#95—22no—
371#95—22no—
372#95—22no—
373#95—22no—
374#95—22no—
375#95—22no—
376#95—22no—
377#95—22no—
378#95—22no—
379#95—28no—
380#95—28no—
381#95—24no—
382#95—24no—
383#95—28no—
384#95—28no—
385#95—28no—
386#95—28no—
387#95—28no—
388#95—28no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—21no—
402C24—22no—
403C24—22no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—22no—
408C24—21no—
409C24—22no—
410C24—21no—
411C24C22×D412yes—
412C24C2×#4112yes—
413C24C2×#4112yes—
414C24C2×#4112yes—
415C24C2×#4112yes—
416C24C2×#4112yes—
417C24H(5,𝔽2)12yes—
418C242−1+412yes—
419C24C2511yescharacteristic
420C2×D4—28no—
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C22×C4—216no—
428C22×C4—216no—
429C22×C4—28no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—28no—
439C22×C4—28no—
440C22×C4—216no—
441C22×C4—216no—
442C22×C4—28no—
443C22×C4—28no—
444C22×C4—216no—
445C22×C4—216no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—24no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—416no—
522C22×C4—416no—
523C22×C4—416no—
524C22×C4—416no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4#123116yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C2×#4112yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4118yes—
548C22×C4C2×#4118yes—
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4114yes—
555C22×C4C2×#4114yes—
556C22×C4H(5,𝔽2)14yes—
557C22×C42−1+414yes—
558C4⋊C4—216no—
559C4⋊C4—216no—
560C4⋊C4—28no—
561C4⋊C4—28no—
562C4⋊C4—216no—
563C4⋊C4—216no—
564C4⋊C4—416no—
565C4⋊C4—44no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—88no—
571C22⋊C4—28no—
572C22⋊C4—28no—
573C22⋊C4—28no—
574C22⋊C4—416no—
575C22⋊C4—44no—
576C22⋊C4—44no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—44no—
580C22⋊C4—44no—
581C22⋊C4—44no—
582C22⋊C4—88no—
583C42—28no—
584C42—28no—
585C42—28no—
586C42—28no—
587C42—416no—
588C42—44no—
589C42—44no—
590C42—44no—
591C42—416no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—24no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23C2×#12314yes—
632C23#52514yes—
633C23#53714yes—
634C23#55214yes—
635C23#55314yes—
636C23#55514yes—
637C23#55614yes—
638C23C23×D411yescharacteristic
639C23C22×#4111yescharacteristic
640C23C22×#4111yescharacteristic
641C23C22×#4112yes—
642C23C22×#4112yes—
643C23C22×#4111yescharacteristic
644C23C22×#4111yescharacteristic
645C23C2×H(5,𝔽2)12yes—
646C23C2×H(5,𝔽2)11yescharacteristic
647C23C2×2−1+412yes—
648C23C2×2−1+411yescharacteristic
649D4—416no—
650C2×C4—232no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—232no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—28no—
678C2×C4—24no—
679C2×C4—28no—
680C2×C4—24no—
681C2×C4—28no—
682C2×C4—28no—
683C2×C4—432no—
684C2×C4—432no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—44no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—88no—
747C2×C4C2×#12314yes—
748C2×C4C2×#12314yes—
749C2×C4#52514yes—
750C2×C4#52514yes—
751C2×C4#52918yes—
752C2×C4#52918yes—
753C2×C4#53514yes—
754C2×C4#53614yes—
755C22—24no—
756C22—28no—
757C22—28no—
758C22—24no—
759C22—24no—
760C22—24no—
761C22—28no—
762C22—28no—
763C22—24no—
764C22—24no—
765C22—44no—
766C22—42no—
767C22—42no—
768C22—44no—
769C22—42no—
770C22—81no—
771C22—82no—
772C22—81no—
773C22—82no—
774C22—81no—
775C22—81no—
776C22#248518yes—
777C22C22×#12311yescharacteristic
778C22C2×#52511yescharacteristic
779C22C2×#52511yescharacteristic
780C22C2×#52511yescharacteristic
781C22C2×#52912yes—
782C22C2×#52912yes—
783C22C2×#53511yescharacteristic
784C22C2×#53611yescharacteristic
785C22C2×#53711yescharacteristic
786C22C2×#55211yescharacteristic
787C22C2×#55311yescharacteristic
788C22C2×#55511yescharacteristic
789C22C2×#55611yescharacteristic
790C22#348112yes—
791C22#348112yes—
792C22#348212yes—
793C22#348212yes—
794C22#349212yes—
795C22#349212yes—
796C22#351912yes—
797C22#352012yes—
798C22#352212yes—
799C22#352312yes—
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—48no—
805C4—42no—
806C4—48no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—81no—
811C4—84no—
812C4—81no—
813C4—84no—
814C4—81no—
815C4—81no—
816C4#285318yes—
817C2—28no—
818C2—82no—
819C2C2×#248511yescharacteristic
820C2#3496311yescharacteristic
821C2#3497111yescharacteristic
822C2#3522711yescharacteristic
823C2#3523611yescharacteristic
824C2#3524711yescharacteristic
825C2#3625612yes—
826C2#3625712yes—
827C2#3648812yes—
828C2#3648912yes—
829C2C2×#285311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×C4×C4⋊C4C2semidirect
3. #15110C2semidirect
4. #15101C2semidirect
5. #15088C2semidirect
6. #15079C2semidirect
7. #14919C2semidirect
10. #14695C2semidirect
11. #14685C2semidirect
12. #14130C2semidirect
13. #14130C2semidirect
14. #14042C2semidirect
15. #14041C2semidirect
16. #13994C2semidirect
17. #13993C2semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1232
C22×C4×C4⋊C42
#151102
#151012
#150882
#150792
#149192
#149122
#146962
#146952
#146852
#141302
#140422
#140412
#139942
#139932
#138722