Finite Group Databasebeta

← #675005

Subgroups — #675005

Order 512.

3006 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2542C211yesmaximal, characteristic
2C2×#2423C212yesmaximal, complemented
3C2×#2365C211yesmaximal, characteristic, complemented
4#15653C214yesmaximal, complemented
5#15649C214yesmaximal, complemented
6#15182C212yesmaximal, complemented
7#15179C212yesmaximal, complemented
8#15148C212yesmaximal
9#15133C212yesmaximal, complemented
10#14714C211yesmaximal, characteristic, complemented
11#14151C211yesmaximal, characteristic, complemented
12#14022C212yesmaximal
13#13969C212yesmaximal, complemented
14#13906C211yesmaximal, characteristic
15#13884C212yesmaximal, complemented
16C4×#384C211yesmaximal, characteristic, complemented
17C4×#390C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C4×Q8C2212yes—
22C22×C4×D4C2211yescharacteristic
23#2542—28no—
24#2423—216no—
25C2×#399C2214yes—
26C2×#399C2214yes—
27C2×#398C2214yes—
28#2365—28no—
29C2×#391C2212yes—
30C2×#391C2212yes—
31C2×#391C2212yes—
32C2×#390C2211yescharacteristic
33C2×#390C2212yes—
34C2×#390C2212yes—
35C2×#390C2211yescharacteristic
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#388C2214yes—
40C2×#387C2214yes—
41C2×#387C2214yes—
42C2×#384C2212yes—
43C2×#384C2211yescharacteristic
44C2×#384C2211yescharacteristic
45C2×#384C2211yescharacteristic
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×C4×C4⋊C4C2212yes—
49C2×C4×C4⋊C4C2212yes—
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2211yescharacteristic
53C2×C4×C4⋊C4C2212yes—
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2212yes—
56C2×C43C2211yescharacteristic
57#1442C2214yes—
58#1441C2214yes—
59#1441C2214yes—
60#1441C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1440C2214yes—
64#1439C2214yes—
65#1439C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1437C2212yes—
70#1437C2214yes—
71#1437C2212yes—
72#1436C2214yes—
73C4⋊#95C2211yescharacteristic
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C23×Q8C2312yes—
87C23×D4C2311yescharacteristic
88C24×C4C2312yes—
89C2×C4⋊Q8—24no—
90C2×C4⋊Q8—24no—
91C2×C4⋊Q8D418yes—
92C2×C22⋊Q8—28no—
93C2×C22⋊Q8—28no—
94C2×C22⋊Q8—28no—
95C2×C22⋊Q8—28no—
96C2×C22⋊Q8—44no—
97C2×C22⋊Q8—44no—
98C2×C4×Q8—28no—
99C2×C4×Q8—28no—
100C2×C4×Q8—44no—
101C2×C4×D4—24no—
102C2×C4×D4—24no—
103C2×C4×D4—24no—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C42C2312yes—
134C22×C42C2311yescharacteristic
135C22×C42C2312yes—
136C22×C42C2312yes—
137C22×C42C2314yes—
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144#399—216no—
145#399—216no—
146#398—216no—
147#391—28no—
148#391—28no—
149#391—44no—
150#390—28no—
151#390—24no—
152#390—44no—
153#390Q818yescomplemented
154#389—28no—
155#389—28no—
156#389—44no—
157#388—216no—
158#387—216no—
159#387—216no—
160#384—28no—
161#384—24no—
162#384—24no—
163#384D418yescomplemented
164#380—28no—
165#380—44no—
166C4×C4⋊C4—28no—
167C4×C4⋊C4—24no—
168C4×C4⋊C4—24no—
169C4×C4⋊C4—24no—
170C4×C4⋊C4—28no—
171C4×C4⋊C4—44no—
172C4×C22⋊C4—28no—
173C4×C22⋊C4—44no—
174C2×#95C2312yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C43—24no—
197C25C2412yes—
198C22×Q8—24no—
199C22×Q8—24no—
200C22×Q8—24no—
201C22×Q8—24no—
202C22×Q8—24no—
203C22×Q8—24no—
204C22×Q8C2×D418yes—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4C2×Q814yes—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—24no—
217C23×C4—24no—
218C23×C4—24no—
219C23×C4C2412yes—
220C23×C4C2414yes—
221C23×C4C2412yes—
222C23×C4C2412yes—
223C23×C4C2412yes—
224C23×C4C2414yes—
225C23×C4C2412yes—
226C23×C4C2412yes—
227C23×C4C2411yescharacteristic
228C23×C4C2412yes—
229C23×C4C2411yescharacteristic
230C23×C4C2411yescharacteristic
231C23×C4C2411yescharacteristic
232C23×C4C2411yescharacteristic
233C23×C4C2411yescharacteristic
234C23×C4C2411yescharacteristic
235C4⋊Q8—232no—
236C22⋊Q8—432no—
237C22⋊Q8—432no—
238C4×Q8—432no—
239C4×D4—416no—
240C2×C4⋊C4—22no—
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—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—28no—
256C2×C4⋊C4—28no—
257C2×C4⋊C4—28no—
258C2×C4⋊C4—28no—
259C2×C4⋊C4—28no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—28no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—44no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—44no—
291C2×C4⋊C4—44no—
292C2×C4⋊C4C2×D414yes—
293C2×C4⋊C4C2×D414yes—
294C2×C4⋊C4C2×D418yes—
295C2×C4⋊C4C2×D418yes—
296C2×C4⋊C4C2×D418yes—
297C2×C4⋊C4C2×D418yes—
298C2×C4⋊C4C2×Q814yes—
299C2×C4⋊C4#4114yes—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—28no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—28no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4C2×Q818yes—
326C2×C22⋊C4C2×Q818yes—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—24no—
334C2×C42—28no—
335C2×C42—24no—
336C2×C42—28no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—24no—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—22no—
346C2×C42—24no—
347C2×C42—24no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—44no—
352C2×C42—41no—
353C2×C42—41no—
354C2×C42C2×D414yes—
355C2×C42C2×D414yes—
356C2×C42C2×Q814yes—
357C2×C42#4114yes—
358C2×C42#4114yes—
359C2×C42#4114yes—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—28no—
365#95—24no—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—28no—
370#95—28no—
371#95—24no—
372#95—24no—
373#95—44no—
374#95—42no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382C24—22no—
383C24—22no—
384C24—22no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—22no—
396C24C22×Q814yes—
397C24C2511yescharacteristic
398C2×Q8—216no—
399C2×Q8—216no—
400C2×Q8—216no—
401C2×Q8—48no—
402C2×Q8—48no—
403C2×Q8—48no—
404C2×Q8—48no—
405C2×D4—28no—
406C2×D4—28no—
407C2×D4—28no—
408C2×D4—44no—
409C2×D4—44no—
410C2×D4—44no—
411C2×D4—44no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—24no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4—48no—
497C22×C4—48no—
498C22×C4—48no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4C22×D414yes—
502C22×C4C22×D418yes—
503C22×C4C22×D414yes—
504C22×C4C22×D412yes—
505C22×C4C22×D412yes—
506C22×C4C22×D412yes—
507C22×C4C22×D412yes—
508C22×C4C22×D412yes—
509C22×C4C22×D412yes—
510C22×C4C22×Q812yes—
511C22×C4C22×Q814yes—
512C22×C4C22×Q812yes—
513C22×C4C22×Q812yes—
514C22×C4C2×#4112yes—
515C22×C4C2×#4114yes—
516C22×C4C2×#4112yes—
517C22×C4C2×#4112yes—
518C22×C4C2×#4112yes—
519C22×C4C2×#4112yes—
520C22×C4C2×#4112yes—
521C22×C4C2×#4112yes—
522C22×C4C2×#4112yes—
523C22×C4C2×#4112yes—
524C22×C4C2×#4112yes—
525C22×C4H(5,𝔽2)12yes—
526C22×C4H(5,𝔽2)12yes—
527C22×C4H(5,𝔽2)12yes—
528C22×C42−1+412yes—
529C22×C42−1+412yes—
530C22×C42−1+412yes—
531C4⋊C4—216no—
532C4⋊C4—216no—
533C4⋊C4—28no—
534C4⋊C4—28no—
535C4⋊C4—28no—
536C4⋊C4—216no—
537C4⋊C4—28no—
538C4⋊C4—48no—
539C4⋊C4—48no—
540C4⋊C4—48no—
541C4⋊C4—416no—
542C4⋊C4—416no—
543C4⋊C4—416no—
544C4⋊C4—44no—
545C4⋊C4—48no—
546C4⋊C4—44no—
547C4⋊C4—44no—
548C4⋊C4—48no—
549C4⋊C4—84no—
550C4⋊C4—88no—
551C22⋊C4—216no—
552C22⋊C4—48no—
553C22⋊C4—416no—
554C22⋊C4—416no—
555C22⋊C4—48no—
556C22⋊C4—48no—
557C22⋊C4—48no—
558C22⋊C4—88no—
559C22⋊C4—88no—
560C42—28no—
561C42—28no—
562C42—28no—
563C42—44no—
564C42—44no—
565C42—416no—
566C42—44no—
567C42—48no—
568C42—48no—
569C42—48no—
570C42#123116yes—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
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—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23C23×D411yescharacteristic
607C23C23×D411yescharacteristic
608C23C23×Q811yescharacteristic
609C23C22×#4111yescharacteristic
610C23C22×#4111yescharacteristic
611C23C22×#4111yescharacteristic
612C23C22×#4111yescharacteristic
613C23C2×H(5,𝔽2)11yescharacteristic
614C23C2×H(5,𝔽2)11yescharacteristic
615C23C2×H(5,𝔽2)11yescharacteristic
616C23C2×2−1+411yescharacteristic
617C23C2×2−1+411yescharacteristic
618C23C2×2−1+411yescharacteristic
619C23#58511yescharacteristic
620C23#58511yescharacteristic
621Q8—432no—
622D4—416no—
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—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—28no—
642C2×C4—24no—
643C2×C4—28no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—28no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—44no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—44no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—816no—
719C2×C4C2×#12314yes—
720C2×C4C2×#12314yes—
721C2×C4C2×#12314yes—
722C2×C4#53214yes—
723C2×C4#53314yes—
724C2×C4#54014yes—
725C2×C4#54214yes—
726C2×C4D4214yes—
727C2×C4#54614yes—
728C2×C4#54714yes—
729C2×C4D4×Q814yes—
730C2×C4D4×Q814yes—
731C2×C4#55014yes—
732C2×C4#55014yes—
733C2×C4#55214yes—
734C2×C4#55414yes—
735C2×C4#55914yes—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—82no—
744C22—82no—
745C22—82no—
746C22—82no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22C22×#12311yescharacteristic
752C22C2×#53211yescharacteristic
753C22C2×#53311yescharacteristic
754C22C2×#54011yescharacteristic
755C22C2×#54211yescharacteristic
756C22C2×D4211yescharacteristic
757C22C2×#54611yescharacteristic
758C22C2×#54711yescharacteristic
759C22C2×D4×Q811yescharacteristic
760C22C2×D4×Q811yescharacteristic
761C22C2×#55011yescharacteristic
762C22C2×#55011yescharacteristic
763C22C2×#55211yescharacteristic
764C22C2×#55411yescharacteristic
765C22#347511yescharacteristic
766C22Q8×#4111yescharacteristic
767C22C2×#55911yescharacteristic
768C22#349511yescharacteristic
769C22#349511yescharacteristic
770C22#349611yescharacteristic
771C22#349711yescharacteristic
772C22#349711yescharacteristic
773C22#349711yescharacteristic
774C22#350111yescharacteristic
775C22#350311yescharacteristic
776C22#350611yescharacteristic
777C22#350911yescharacteristic
778C22#351011yescharacteristic
779C22#351111yescharacteristic
780C22#352011yescharacteristic
781C22#352311yescharacteristic
782C22#354611yescharacteristic
783C22#354811yescharacteristic
784C22#355011yescharacteristic
785C22#355411yescharacteristic
786C4—24no—
787C4—24no—
788C4—24no—
789C4—44no—
790C4—42no—
791C4—48no—
792C4—44no—
793C4—44no—
794C4—44no—
795C4—42no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—84no—
800C4#242318yescomplemented
801C4#244518yes—
802C2—84no—
803C2C2×#244511yescharacteristic
804C2C2×#242311yescharacteristic
805C2#3567311yescharacteristic
806C2#3613411yescharacteristic
807C2#3618611yescharacteristic
808C2#3647611yescharacteristic
809C2#3656111yescharacteristic
810C2#3920011yescharacteristic
811C2#3938711yescharacteristic
812C2#3948111yescharacteristic
813C2#3960611yescharacteristic
814C2#5941011yescharacteristic
815C2#5941311yescharacteristic
816C2#5981511yescharacteristic
817C2#5981711yescharacteristic
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. C2×#2423C2semidirect
3. C2×#2365C2semidirect
4. #15653C2semidirect
5. #15649C2semidirect
6. #15182C2semidirect
7. #15179C2semidirect
9. #15133C2semidirect
10. #14714C2semidirect
11. #14151C2semidirect
13. #13969C2semidirect
15. #13884C2semidirect
16. C4×#384C2semidirect
153. #390Q8semidirect
163. #384D4semidirect
800. C4#2423semidirect

Maximal subgroups

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

subgroupindex
C2×#25422
C2×#24232
C2×#23652
#156532
#156492
#151822
#151792
#151482
#151332
#147142
#141512
#140222
#139692
#139062
#138842
C4×#3842
C4×#3902