Finite Group Databasebeta

← #674883

Subgroups — #674883

Order 512.

2894 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2441C212yesmaximal, complemented
2C2×#2354C211yesmaximal, characteristic
3C2×C4×#125C211yesmaximal, characteristic, complemented
4#15866C214yesmaximal, complemented
5#15365C214yesmaximal, complemented
6#15220C212yesmaximal, complemented
7#15148C212yesmaximal
8#15134C212yesmaximal
9#15131C212yesmaximal, complemented
10#14712C211yesmaximal, characteristic, complemented
11#14151C212yesmaximal, complemented
12#14042C212yesmaximal, complemented
13#13951C212yesmaximal, complemented
14#13910C211yesmaximal, characteristic, complemented
15#13910C211yesmaximal, characteristic, complemented
16#13906C211yesmaximal, characteristic
17C4×#390C211yesmaximal, characteristic
18C22×#125C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×#117C2212yes—
21#2441—216no—
22C2×#399C2214yes—
23C2×#396C2214yes—
24C2×#396C2214yes—
25#2354—28no—
26C4×#125—28no—
27C2×#390C2211yescharacteristic
28C2×#390C2212yes—
29C2×#390C2211yescharacteristic
30C2×#390C2212yes—
31C2×#389C2214yes—
32C2×#389C2211yescharacteristic
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2211yescharacteristic
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#388C2214yes—
42C2×#387C2212yes—
43C2×#387C2214yes—
44C2×#387C2212yes—
45C2×#384C2212yes—
46C2×#384C2212yes—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#382C2211yescharacteristic
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61C2×C43C2211yescharacteristic
62#1444C2214yes—
63#1444C2214yes—
64#1443C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1437C2212yes—
75#1437C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2212yes—
81C4⋊#95C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2211yescharacteristic
85#1434C2214yes—
86C23×D4C2311yescharacteristic
87C24×C4C2312yes—
88C2×#125—24no—
89C2×#125—24no—
90C2×#125D418yescomplemented
91C2×C4×D4—24no—
92C2×C4×D4—24no—
93C2×C4×D4Q818yes—
94C2×#117—28no—
95C2×#117—28no—
96C2×#117—28no—
97C22×C4⋊C4C2312yes—
98C22×C4⋊C4C2312yes—
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2314yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2314yes—
128C22×C42C2314yes—
129C22×C42C2311yescharacteristic
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C22×C42C2312yes—
133C22×C42C2312yes—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2312yes—
138C22×C42C2311yescharacteristic
139#399—216no—
140#396—216no—
141#396—48no—
142#390—24no—
143#390—24no—
144#390—28no—
145#390—44no—
146#389—24no—
147#389—24no—
148#389—216no—
149#389—28no—
150#389—28no—
151#389—28no—
152#389—44no—
153#389—44no—
154#389—44no—
155#389—44no—
156#388—216no—
157#387—216no—
158#387—28no—
159#387—28no—
160#384—28no—
161#384—28no—
162#384—24no—
163#384—24no—
164#382—24no—
165#380—28no—
166#380—28no—
167#380—44no—
168C4×C4⋊C4—28no—
169C4×C4⋊C4—28no—
170C4×C4⋊C4—24no—
171C4×C4⋊C4—28no—
172C4×C4⋊C4—24no—
173C4×C4⋊C4D418yes—
174C4×C22⋊C4—28no—
175C4×C22⋊C4—44no—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C43—24no—
198C25C2412yes—
199C22×D4—22no—
200C22×D4—22no—
201C22×D4—22no—
202C22×D4—22no—
203C22×D4—22no—
204C22×D4—22no—
205C22×D4C2×Q814yes—
206C23×C4—24no—
207C23×C4—24no—
208C23×C4—24no—
209C23×C4—24no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4C2×Q818yes—
213C23×C4C2414yes—
214C23×C4C2414yes—
215C23×C4C2412yes—
216C23×C4C2412yes—
217C23×C4C2411yescharacteristic
218C23×C4C2412yes—
219C23×C4C2411yescharacteristic
220C23×C4C2412yes—
221C23×C4C2412yes—
222C23×C4C2412yes—
223C23×C4C2411yescharacteristic
224C23×C4C2411yescharacteristic
225C23×C4C2412yes—
226C23×C4C2411yescharacteristic
227C23×C4C2411yescharacteristic
228C23×C4C2411yescharacteristic
229#125—232no—
230C4×D4—232no—
231#117—432no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—24no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—22no—
236C2×C4⋊C4—22no—
237C2×C4⋊C4—24no—
238C2×C4⋊C4—24no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—28no—
254C2×C4⋊C4—28no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—28no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—28no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—44no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—44no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—44no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4C2×D414yes—
289C2×C4⋊C4C2×D418yes—
290C2×C4⋊C4C2×D418yes—
291C2×C4⋊C4C2×D414yes—
292C2×C4⋊C4C2×D414yes—
293C2×C4⋊C4C2×D414yes—
294C2×C4⋊C4C2×Q814yes—
295C2×C4⋊C4#4114yes—
296C2×C4⋊C4#4114yes—
297C2×C4⋊C4#4114yes—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—28no—
301C2×C22⋊C4—28no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—28no—
312C2×C22⋊C4—28no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4C2×Q818yes—
325C2×C42—22no—
326C2×C42—22no—
327C2×C42—24no—
328C2×C42—24no—
329C2×C42—28no—
330C2×C42—28no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—28no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—24no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—24no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—41no—
352C2×C42—41no—
353C2×C42C2×D414yes—
354C2×C42C2×D418yes—
355C2×C42C2×D414yes—
356C2×C42C2×Q814yes—
357C2×C42#4114yes—
358#95—24no—
359#95—24no—
360#95—28no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—24no—
370#95—28no—
371#95—28no—
372#95—42no—
373#95—42no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95C2×D418yes—
379C24—22no—
380C24—22no—
381C24—22no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24C22×Q814yes—
394C24C2511yescharacteristic
395C2×D4—28no—
396C2×D4—28no—
397C2×D4—28no—
398C2×D4—44no—
399C2×D4—44no—
400C2×D4—44no—
401C2×D4—44no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—216no—
465C22×C4—216no—
466C22×C4—216no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4C22×D412yes—
493C22×C4C22×D414yes—
494C22×C4C22×D412yes—
495C22×C4C22×D414yes—
496C22×C4C22×D414yes—
497C22×C4C22×D414yes—
498C22×C4C22×D412yes—
499C22×C4C22×D412yes—
500C22×C4C22×D412yes—
501C22×C4C22×D412yes—
502C22×C4C22×Q814yes—
503C22×C4C22×Q812yes—
504C22×C4C22×Q812yes—
505C22×C4C22×Q812yes—
506C22×C4C2×#4114yes—
507C22×C4C2×#4114yes—
508C22×C4C2×#4114yes—
509C22×C4C2×#4112yes—
510C22×C4C2×#4112yes—
511C22×C4C2×#4112yes—
512C22×C4C2×#4112yes—
513C22×C4C2×#4112yes—
514C22×C4C2×#4112yes—
515C22×C4H(5,𝔽2)12yes—
516C22×C4H(5,𝔽2)12yes—
517C22×C4H(5,𝔽2)12yes—
518C22×C42−1+412yes—
519C22×C42−1+412yes—
520C22×C42−1+412yes—
521C4⋊C4—216no—
522C4⋊C4—216no—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—28no—
528C4⋊C4—416no—
529C4⋊C4—48no—
530C4⋊C4—416no—
531C4⋊C4—48no—
532C4⋊C4—48no—
533C4⋊C4—48no—
534C4⋊C4—44no—
535C4⋊C4—48no—
536C4⋊C4—48no—
537C4⋊C4—48no—
538C4⋊C4—84no—
539C4⋊C4—88no—
540C4⋊C4—88no—
541C4⋊C4—88no—
542C4⋊C4#121116yes—
543C22⋊C4—216no—
544C22⋊C4—48no—
545C22⋊C4—48no—
546C22⋊C4—48no—
547C22⋊C4—48no—
548C22⋊C4—416no—
549C22⋊C4—88no—
550C22⋊C4—88no—
551C22⋊C4—88no—
552C42—28no—
553C42—216no—
554C42—44no—
555C42—44no—
556C42—416no—
557C42—44no—
558C42—44no—
559C42—44no—
560C42—48no—
561C42—48no—
562C42C22⋊Q8116yes—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23C23×D411yescharacteristic
599C23C23×D411yescharacteristic
600C23C23×Q811yescharacteristic
601C23C22×#4111yescharacteristic
602C23C22×#4111yescharacteristic
603C23C22×#4111yescharacteristic
604C23C22×#4111yescharacteristic
605C23C2×H(5,𝔽2)11yescharacteristic
606C23C2×H(5,𝔽2)11yescharacteristic
607C23C2×H(5,𝔽2)11yescharacteristic
608C23C2×2−1+411yescharacteristic
609C23C2×2−1+411yescharacteristic
610C23C2×2−1+411yescharacteristic
611C23#58511yescharacteristic
612C23#58511yescharacteristic
613D4—416no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—432no—
690C2×C4—44no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4C2×#12118yes—
712C2×C4C2×#12114yes—
713C2×C4C2×C22⋊Q814yes—
714C2×C4C2×C22⋊Q814yes—
715C2×C4C2×C22⋊Q814yes—
716C2×C4#53314yes—
717C2×C4#53714yes—
718C2×C4#54414yes—
719C2×C4#54714yes—
720C2×C4D4×Q814yes—
721C2×C4#55014yes—
722C2×C4#55014yes—
723C2×C4#55214yes—
724C2×C4#55314yes—
725C2×C4#55414yes—
726C2×C4#55614yes—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—82no—
735C22—82no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22C22×#12111yescharacteristic
743C22C22×C22⋊Q811yescharacteristic
744C22C2×#53311yescharacteristic
745C22C2×#53711yescharacteristic
746C22C2×#54411yescharacteristic
747C22C2×#54711yescharacteristic
748C22C2×D4×Q811yescharacteristic
749C22C2×#55011yescharacteristic
750C22C2×#55011yescharacteristic
751C22D4×#4111yescharacteristic
752C22D4×#4111yescharacteristic
753C22C2×#55211yescharacteristic
754C22C2×#55311yescharacteristic
755C22C2×#55411yescharacteristic
756C22C2×#55611yescharacteristic
757C22#348211yescharacteristic
758C22#348311yescharacteristic
759C22#348811yescharacteristic
760C22#348911yescharacteristic
761C22#349811yescharacteristic
762C22#349911yescharacteristic
763C22#350311yescharacteristic
764C22#350411yescharacteristic
765C22#350611yescharacteristic
766C22#350711yescharacteristic
767C22#351511yescharacteristic
768C22#351711yescharacteristic
769C22#351811yescharacteristic
770C22#351811yescharacteristic
771C22#351911yescharacteristic
772C22#352011yescharacteristic
773C22#354411yescharacteristic
774C22#354611yescharacteristic
775C22#354711yescharacteristic
776C22#355211yescharacteristic
777C4—28no—
778C4—24no—
779C4—44no—
780C4—42no—
781C4—44no—
782C4—44no—
783C4—42no—
784C4—44no—
785C4—44no—
786C4—42no—
787C4—42no—
788C4—84no—
789C4—84no—
790C4—82no—
791C4#244118yescomplemented
792C4#253818yes—
793C2—84no—
794C2C2×#244111yescharacteristic
795C2C2×#253811yescharacteristic
796C2#3551911yescharacteristic
797C2#3613211yescharacteristic
798C2#3625911yescharacteristic
799C2#3640711yescharacteristic
800C2#3645511yescharacteristic
801C2#3892211yescharacteristic
802C2#3896611yescharacteristic
803C2#3913611yescharacteristic
804C2#3936911yescharacteristic
805C2#5943411yescharacteristic
806C2#5943511yescharacteristic
807C2#5944411yescharacteristic
808C2#5968011yescharacteristic
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
1. C2×#2441C2semidirect
3. C2×C4×#125C2semidirect
4. #15866C2semidirect
5. #15365C2semidirect
6. #15220C2semidirect
9. #15131C2semidirect
10. #14712C2semidirect
11. #14151C2semidirect
12. #14042C2semidirect
13. #13951C2semidirect
14. #13910C2semidirect
15. #13910C2semidirect
90. C2×#125D4semidirect
791. C4#2441semidirect

Maximal subgroups

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

subgroupindex
C2×#24412
C2×#23542
C2×C4×#1252
#158662
#153652
#152202
#151482
#151342
#151312
#147122
#141512
#140422
#139512
#139102
#139062
C4×#3902