Finite Group Databasebeta

← #556609

Subgroups — #556609

Order 512.

2874 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic
2C2×#2295C211yesmaximal, characteristic, complemented
3C2×#2293C211yesmaximal, characteristic
4#14633C214yesmaximal, complemented
5#14310C214yesmaximal, complemented
6#14266C212yesmaximal, complemented
7#14264C212yesmaximal, complemented
8#14260C212yesmaximal
9#14258C212yesmaximal, complemented
10#14151C211yesmaximal, characteristic, complemented
11#14045C212yesmaximal, complemented
12#14022C212yesmaximal
13#13997C212yesmaximal, complemented
14#13974C212yesmaximal, complemented
15#13926C211yesmaximal, characteristic, complemented
16#13906C211yesmaximal, characteristic
17C4×#384C211yesmaximal, characteristic, complemented
18C22×C22⋊Q8C2212yes—
19C22×C4×Q8C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×#117C2212yes—
22#2538C4116yescomplemented
23C2×#396C2214yes—
24#2295—28no—
25C2×#391C2211yescharacteristic
26C2×#391C2211yescharacteristic
27C2×#391C2212yes—
28#2293—28no—
29C2×#390C2211yescharacteristic
30C2×#390C2211yescharacteristic
31C2×#390C2212yes—
32C2×#390C2212yes—
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#388C2214yes—
43C2×#387C2212yes—
44C2×#387C2212yes—
45C2×#384C2211yescharacteristic
46C2×#384C2211yescharacteristic
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C2×#376C2212yes—
58C2×C43C2211yescharacteristic
59#1445C2214yes—
60#1444C2214yes—
61#1443C2214yes—
62#1442C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1437C2214yes—
75#1436C2214yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2214yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C23×Q8C2311yescharacteristic
87C23×D4C2311yescharacteristic
88C24×C4C2312yes—
89C2×C22⋊Q8—44no—
90C2×C22⋊Q8—44no—
91C2×C22⋊Q8C2×C4116yes—
92C2×C4×Q8—24no—
93C2×C4×Q8—24no—
94C2×C4×Q8C2×C418yes—
95C2×C4×D4—24no—
96C2×C4×D4—24no—
97C2×C4×D4C2×C418yes—
98C2×#117—28no—
99C2×#117—44no—
100C2×#117—44no—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊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×C22⋊C4C2314yes—
129C22×C42C2312yes—
130C22×C42C2312yes—
131C22×C42C2312yes—
132C22×C42C2311yescharacteristic
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2314yes—
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140#396C2×C4132yes—
141#391—24no—
142#391—24no—
143#391—44no—
144#390—24no—
145#390—24no—
146#390—44no—
147#390C2×C4116yes—
148#389—24no—
149#389—24no—
150#389—24no—
151#389—24no—
152#389—44no—
153#389—44no—
154#389C2×C4116yes—
155#388—28no—
156#388—28no—
157#388—48no—
158#387—28no—
159#387—28no—
160#384—24no—
161#384C2×C418yes—
162#380—44no—
163#380—44no—
164#380C2×C4116yes—
165C4×C4⋊C4—24no—
166C4×C4⋊C4—24no—
167C4×C4⋊C4—28no—
168C4×C4⋊C4—44no—
169C4×C4⋊C4—44no—
170C4×C4⋊C4—44no—
171C4×C22⋊C4—28no—
172#376—28no—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C43D418yes—
197C25C2412yes—
198C22×Q8—22no—
199C22×Q8—22no—
200C22×Q8—22no—
201C22×Q8—22no—
202C22×Q8—22no—
203C22×Q8—22no—
204C22×Q8C22×C414yes—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4C22×C414yes—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4C22×C418yes—
219C23×C4C2412yes—
220C23×C4C2412yes—
221C23×C4C2414yes—
222C23×C4C2412yes—
223C23×C4C2412yes—
224C23×C4C2414yes—
225C23×C4C2412yes—
226C23×C4C2412yes—
227C23×C4C2412yes—
228C23×C4C2411yescharacteristic
229C23×C4C2411yescharacteristic
230C23×C4C2411yescharacteristic
231C23×C4C2411yescharacteristic
232C23×C4C2411yescharacteristic
233C23×C4C2411yescharacteristic
234C23×C4C2411yescharacteristic
235C22⋊Q8—432no—
236C4×Q8—232no—
237C4×D4—232no—
238#117—432no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—22no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
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—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4C22×C414yes—
290C2×C4⋊C4C22×C414yes—
291C2×C4⋊C4C22×C418yes—
292C2×C4⋊C4C22×C418yes—
293C2×C4⋊C4C22×C418yes—
294C2×C4⋊C4C22×C4116yes—
295C2×C4⋊C4C22×C418yes—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—44no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—44no—
312C2×C22⋊C4—44no—
313C2×C22⋊C4—44no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4C22×C418yes—
321C2×C22⋊C4C22×C4116yes—
322C2×C22⋊C4C22×C4116yes—
323C2×C42—24no—
324C2×C42—24no—
325C2×C42—22no—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—24no—
341C2×C42—28no—
342C2×C42—41no—
343C2×C42—41no—
344C2×C42—44no—
345C2×C42—44no—
346C2×C42C22×C418yes—
347C2×C42C22×C414yes—
348C2×C42C2×D414yes—
349C2×C42C2×D414yes—
350C2×C42C2×D414yes—
351C2×C42C2×D414yes—
352C2×C42C2×D414yes—
353C2×C42C2×D414yes—
354C2×C42C2×D414yes—
355C2×C42#4114yes—
356#95—24no—
357#95—24no—
358#95—24no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—44no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95C22×C4116yes—
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—
393C24C23×C414yes—
394C24C2511yescharacteristic
395C2×Q8—28no—
396C2×Q8—28no—
397C2×Q8—28no—
398C2×Q8—44no—
399C2×Q8—44no—
400C2×Q8—44no—
401C2×Q8—44no—
402C2×D4—28no—
403C2×D4—28no—
404C2×D4—28no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—44no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—24no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—216no—
460C22×C4—216no—
461C22×C4—216no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4C23×C414yes—
502C22×C4C23×C414yes—
503C22×C4C23×C418yes—
504C22×C4C23×C414yes—
505C22×C4C23×C412yes—
506C22×C4C23×C412yes—
507C22×C4C23×C412yes—
508C22×C4C22×D412yes—
509C22×C4C22×D412yes—
510C22×C4C22×D412yes—
511C22×C4C22×D412yes—
512C22×C4C22×D412yes—
513C22×C4C22×D412yes—
514C22×C4C22×D412yes—
515C22×C4C2×#4112yes—
516C22×C4C2×#4112yes—
517C22×C4C2×#4112yes—
518C22×C4H(5,𝔽2)12yes—
519C22×C4H(5,𝔽2)12yes—
520C22×C4H(5,𝔽2)12yes—
521C22×C4H(5,𝔽2)12yes—
522C22×C4H(5,𝔽2)12yes—
523C22×C42−1+412yes—
524C22×C42−1+412yes—
525C22×C42−1+412yes—
526C22×C42−1+412yes—
527C22×C42−1+412yes—
528C4⋊C4—28no—
529C4⋊C4—28no—
530C4⋊C4—216no—
531C4⋊C4—216no—
532C4⋊C4—216no—
533C4⋊C4—48no—
534C4⋊C4—416no—
535C4⋊C4—48no—
536C4⋊C4—48no—
537C4⋊C4—48no—
538C4⋊C4—48no—
539C4⋊C4—44no—
540C4⋊C4—44no—
541C4⋊C4—48no—
542C4⋊C4—44no—
543C4⋊C4—44no—
544C4⋊C4—48no—
545C4⋊C4—48no—
546C4⋊C4—88no—
547C22⋊C4—216no—
548C22⋊C4—416no—
549C22⋊C4—416no—
550C22⋊C4—48no—
551C22⋊C4—48no—
552C22⋊C4—48no—
553C22⋊C4—48no—
554C22⋊C4—88no—
555C22⋊C4—88no—
556C42—216no—
557C42—28no—
558C42—28no—
559C42—28no—
560C42—28no—
561C42—28no—
562C42—44no—
563C42—48no—
564C42—48no—
565C42—88no—
566C42C4×D4116yes—
567C23—24no—
568C23—24no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
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—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23C24×C411yescharacteristic
603C23C23×D411yescharacteristic
604C23C22×#4111yescharacteristic
605C23C2×H(5,𝔽2)11yescharacteristic
606C23C2×H(5,𝔽2)11yescharacteristic
607C23C2×H(5,𝔽2)11yescharacteristic
608C23C2×H(5,𝔽2)11yescharacteristic
609C23C2×H(5,𝔽2)11yescharacteristic
610C23C2×2−1+411yescharacteristic
611C23C2×2−1+411yescharacteristic
612C23C2×2−1+411yescharacteristic
613C23C2×2−1+411yescharacteristic
614C23C2×2−1+411yescharacteristic
615C23#58511yescharacteristic
616C23#58511yescharacteristic
617Q8—416no—
618D4—416no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—28no—
636C2×C4—24no—
637C2×C4—28no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—28no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—44no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—44no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—432no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4C2×C4×D414yes—
717C2×C4C2×C4×D414yes—
718C2×C4C2×C4×D414yes—
719C2×C4#51814yes—
720C2×C4#51914yes—
721C2×C4#52014yes—
722C2×C4#52014yes—
723C2×C4#53514yes—
724C2×C4#53614yes—
725C2×C4#53714yes—
726C2×C4#53714yes—
727C2×C4#53714yes—
728C2×C4#54014yes—
729C2×C4#54114yes—
730C2×C4#54214yes—
731C2×C4#54214yes—
732C22—44no—
733C22—44no—
734C22—44no—
735C22—44no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22—82no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22C22×C4×D411yescharacteristic
748C22C2×#51811yescharacteristic
749C22C2×#51911yescharacteristic
750C22C2×#52011yescharacteristic
751C22C2×#52011yescharacteristic
752C22C4×H(5,𝔽2)11yescharacteristic
753C22C4×2−1+411yescharacteristic
754C22C2×#53511yescharacteristic
755C22C2×#53611yescharacteristic
756C22C2×#53711yescharacteristic
757C22C2×#53711yescharacteristic
758C22C2×#53711yescharacteristic
759C22#344911yescharacteristic
760C22C2×#54011yescharacteristic
761C22C2×#54111yescharacteristic
762C22C2×#54211yescharacteristic
763C22C2×#54211yescharacteristic
764C22#346011yescharacteristic
765C22#346111yescharacteristic
766C22#354311yescharacteristic
767C22#354411yescharacteristic
768C22#354611yescharacteristic
769C22#354611yescharacteristic
770C22#354711yescharacteristic
771C22#354711yescharacteristic
772C22#354811yescharacteristic
773C22#354811yescharacteristic
774C22#355011yescharacteristic
775C22#355011yescharacteristic
776C22#355211yescharacteristic
777C22#355211yescharacteristic
778C22#355411yescharacteristic
779C22#355411yescharacteristic
780C22#355511yescharacteristic
781C22#355511yescharacteristic
782C4—24no—
783C4—24no—
784C4—42no—
785C4—44no—
786C4—44no—
787C4—44no—
788C4—48no—
789C4—42no—
790C4—42no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—84no—
796C4#232318yes—
797C4#232418yes—
798C2—84no—
799C2C2×#232311yescharacteristic
800C2C2×#232411yescharacteristic
801C2C4×#53711yescharacteristic
802C2#3448111yescharacteristic
803C2#3448411yescharacteristic
804C2#3448711yescharacteristic
805C2#3449411yescharacteristic
806C2#3762011yescharacteristic
807C2#3762111yescharacteristic
808C2#3762211yescharacteristic
809C2#3762511yescharacteristic
810C2#3762811yescharacteristic
811C2#3763111yescharacteristic
812C2#3763711yescharacteristic
813C2#3764011yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2295C2semidirect
4. #14633C2semidirect
5. #14310C2semidirect
6. #14266C2semidirect
7. #14264C2semidirect
9. #14258C2semidirect
10. #14151C2semidirect
11. #14045C2semidirect
13. #13997C2semidirect
14. #13974C2semidirect
15. #13926C2semidirect
17. C4×#384C2semidirect
22. #2538C4semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#22952
C2×#22932
#146332
#143102
#142662
#142642
#142602
#142582
#141512
#140452
#140222
#139972
#139742
#139262
#139062
C4×#3842