Finite Group Databasebeta

← #674502

Subgroups — #674502

Order 512.

2914 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2551C211yesmaximal, characteristic, complemented
2C2×#2492C212yesmaximal
3C2×C4×C22⋊Q8C211yesmaximal, characteristic
4#15858C214yesmaximal, complemented
5#15426C214yesmaximal
6#15186C212yesmaximal, complemented
7#15183C212yesmaximal
8#15156C212yesmaximal, complemented
9#15125C212yesmaximal
10#14686C211yesmaximal, characteristic
11#14155C212yesmaximal, complemented
12#14053C212yesmaximal, complemented
13#13974C212yesmaximal
14#13926C211yesmaximal, characteristic, complemented
15#13926C211yesmaximal, characteristic, complemented
16C4⋊C42C211yesmaximal, characteristic, complemented
17C4×#380C211yesmaximal, characteristic
18C22×C4⋊Q8C2212yes—
19C22×C4⋊Q8C2212yes—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C23×C42C2211yescharacteristic
23#2551—28no—
24#2492—216no—
25C2×#400C2214yes—
26C2×#395C2214yes—
27C2×#393C2214yes—
28C4×C22⋊Q8—28no—
29C2×#391C2214yes—
30C2×#391C2211yescharacteristic
31C2×#391C2212yes—
32C2×#391C2212yes—
33C2×#391C2214yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2211yescharacteristic
37C2×#388C2214yes—
38C2×#387C2212yes—
39C2×#385C2212yes—
40C2×#384C2211yescharacteristic
41C2×#384C2211yescharacteristic
42C2×#380C2211yescharacteristic
43C2×#380C2211yescharacteristic
44C2×#380C2212yes—
45C2×#380C2212yes—
46C2×#380C2212yes—
47C2×#380C2211yescharacteristic
48C2×C4×C4⋊C4C2212yes—
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2212yes—
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2212yes—
56#1446C2214yes—
57#1445C2214yes—
58#1445C2214yes—
59#1443C2214yes—
60#1443C2214yes—
61#1443C2214yes—
62#1442C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1440C2214yes—
67#1439C2214yes—
68#1436C2214yes—
69#1436C2214yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2211yescharacteristic
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83#1434C2212yes—
84C22⋊#95C2212yes—
85C4×#95C2212yes—
86C23×Q8C2311yescharacteristic
87C23×Q8C2314yes—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C2×C4⋊Q8—28no—
92C2×C4⋊Q8—28no—
93C2×C4⋊Q8—28no—
94C2×C4⋊Q8—28no—
95C2×C4⋊Q8—28no—
96C2×C4⋊Q8—44no—
97C2×C22⋊Q8—24no—
98C2×C22⋊Q8—24no—
99C2×C22⋊Q8D418yes—
100C2×C4×Q8—24no—
101C2×C4×Q8—24no—
102C2×C4×Q8—24no—
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C42—24no—
127C22×C42—24no—
128C22×C42—24no—
129C22×C42C2311yescharacteristic
130C22×C42C2311yescharacteristic
131C22×C42C2311yescharacteristic
132C22×C42C2312yes—
133C22×C42C2312yes—
134C22×C42C2312yes—
135C22×C42C2312yes—
136C22×C42C2314yes—
137C22×C42C2311yescharacteristic
138#400—216no—
139#395—216no—
140#393—216no—
141#391—28no—
142#391—28no—
143#391—216no—
144#391—24no—
145#391—48no—
146#389—28no—
147#389—24no—
148#389—28no—
149#388—216no—
150#387—28no—
151#385—28no—
152#384—24no—
153#384—24no—
154#380—28no—
155#380—24no—
156#380—24no—
157#380—44no—
158#380—44no—
159#380Q818yescomplemented
160C4×C4⋊C4—28no—
161C4×C4⋊C4—24no—
162C4×C4⋊C4—28no—
163C4×C4⋊C4—24no—
164C4×C4⋊C4—44no—
165C4×C4⋊C4D418yes—
166C4×C22⋊C4—28no—
167C4×C22⋊C4—28no—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2312yes—
172C2×#95C2314yes—
173C2×#95C2312yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C25C2411yescharacteristic
197C22×Q8—22no—
198C22×Q8—28no—
199C22×Q8—28no—
200C22×Q8—22no—
201C22×Q8—22no—
202C22×Q8—22no—
203C22×Q8—28no—
204C22×Q8—28no—
205C22×Q8—22no—
206C22×Q8—22no—
207C22×Q8—44no—
208C22×Q8—44no—
209C22×Q8—44no—
210C22×Q8C2×D414yes—
211C23×C4—22no—
212C23×C4—22no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—41no—
229C23×C4—41no—
230C23×C4C2×D414yes—
231C23×C4C2×Q814yes—
232C23×C4C2414yes—
233C23×C4C2414yes—
234C23×C4C2412yes—
235C23×C4C2412yes—
236C23×C4C2412yes—
237C23×C4C2412yes—
238C23×C4C2411yescharacteristic
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2411yescharacteristic
242C23×C4C2412yes—
243C23×C4C2411yescharacteristic
244C23×C4C2412yes—
245C23×C4C2411yescharacteristic
246C23×C4C2411yescharacteristic
247C23×C4C2411yescharacteristic
248C4⋊Q8—432no—
249C4⋊Q8—432no—
250C22⋊Q8—232no—
251C4×Q8—416no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—28no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—28no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4C2×D418yes—
299C2×C4⋊C4C2×D414yes—
300C2×C4⋊C4C2×D414yes—
301C2×C4⋊C4C2×D414yes—
302C2×C4⋊C4C2×Q814yes—
303C2×C4⋊C4C2×Q814yes—
304C2×C4⋊C4#4114yes—
305C2×C4⋊C4#4114yes—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4C2×D418yes—
320C2×C22⋊C4C2×Q818yes—
321C2×C42—24no—
322C2×C42—24no—
323C2×C42—24no—
324C2×C42—24no—
325C2×C42—24no—
326C2×C42—24no—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—24no—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—24no—
341C2×C42—28no—
342C2×C42—416no—
343C2×C42—44no—
344C2×C42—44no—
345C2×C42C2×D418yes—
346C2×C42C2×D414yes—
347C2×C42#4114yes—
348C2×C42#4114yes—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—24no—
354#95—24no—
355#95—28no—
356#95—24no—
357#95—28no—
358#95—28no—
359#95—28no—
360#95—28no—
361#95—28no—
362#95—28no—
363#95—24no—
364#95—24no—
365#95—28no—
366#95—24no—
367#95—42no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95C2×D418yes—
376#95C2×Q818yes—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24C22×D412yes—
390C24C22×Q812yes—
391C242−1+412yes—
392C24C2511yescharacteristic
393C2×Q8—28no—
394C2×Q8—28no—
395C2×Q8—28no—
396C2×Q8—416no—
397C2×Q8—416no—
398C2×Q8—416no—
399C2×Q8—416no—
400C2×Q8—44no—
401C2×Q8—44no—
402C2×Q8—44no—
403C2×Q8—44no—
404C2×Q8—88no—
405C2×Q8—88no—
406C2×Q8—88no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—28no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
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—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—24no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4—44no—
501C22×C4—44no—
502C22×C4—44no—
503C22×C4—44no—
504C22×C4—44no—
505C22×C4—44no—
506C22×C4—44no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4C22×D414yes—
513C22×C4C22×D412yes—
514C22×C4C22×D414yes—
515C22×C4C22×D414yes—
516C22×C4C22×D414yes—
517C22×C4C22×D412yes—
518C22×C4C22×D412yes—
519C22×C4C22×D412yes—
520C22×C4C22×D412yes—
521C22×C4C22×Q812yes—
522C22×C4C22×Q814yes—
523C22×C4C22×Q814yes—
524C22×C4C22×Q812yes—
525C22×C4C2×#4114yes—
526C22×C4C2×#4114yes—
527C22×C4C2×#4112yes—
528C22×C4C2×#4112yes—
529C22×C4C2×#4112yes—
530C22×C4C2×#4112yes—
531C22×C4C2×#4112yes—
532C22×C4C2×#4112yes—
533C22×C4C2×#4112yes—
534C22×C4C2×#4112yes—
535C22×C4H(5,𝔽2)12yes—
536C22×C4H(5,𝔽2)12yes—
537C22×C42−1+412yes—
538C22×C42−1+412yes—
539C22×C42−1+412yes—
540C4⋊C4—216no—
541C4⋊C4—28no—
542C4⋊C4—28no—
543C4⋊C4—28no—
544C4⋊C4—28no—
545C4⋊C4—48no—
546C4⋊C4—416no—
547C4⋊C4—416no—
548C4⋊C4—48no—
549C4⋊C4—48no—
550C4⋊C4—44no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—48no—
554C4⋊C4—44no—
555C4⋊C4—84no—
556C4⋊C4—84no—
557C4⋊C4#121116yes—
558C22⋊C4—216no—
559C22⋊C4—216no—
560C22⋊C4—48no—
561C22⋊C4—48no—
562C22⋊C4—88no—
563C42—216no—
564C42—48no—
565C42—44no—
566C42—44no—
567C42—44no—
568C42—48no—
569C42—48no—
570C42—88no—
571C42#124116yes—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23D4×Q814yes—
607C23C23×D411yescharacteristic
608C23C23×D411yescharacteristic
609C23C23×Q811yescharacteristic
610C23C22×#4111yescharacteristic
611C23C22×#4111yescharacteristic
612C23C22×#4111yescharacteristic
613C23C22×#4111yescharacteristic
614C23C2×H(5,𝔽2)11yescharacteristic
615C23C2×H(5,𝔽2)11yescharacteristic
616C23C2×2−1+411yescharacteristic
617C23C2×2−1+411yescharacteristic
618C23C2×2−1+411yescharacteristic
619C23C2×2−1+411yescharacteristic
620C23#58511yescharacteristic
621C23#58511yescharacteristic
622Q8—416no—
623Q8—832no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—24no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—416no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
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—416no—
694C2×C4—416no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4C2×#12118yes—
724C2×C4C2×#12114yes—
725C2×C4C2×#12414yes—
726C2×C4C2×#12414yes—
727C2×C4C2×#12414yes—
728C2×C4#53314yes—
729C2×C4#53614yes—
730C2×C4#54214yes—
731C2×C4#54614yes—
732C2×C4#54714yes—
733C2×C4#54714yes—
734C2×C4D4×Q814yes—
735C2×C4#55414yes—
736C2×C4#55614yes—
737C2×C4#55614yes—
738C2×C4#55614yes—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C22×#12111yescharacteristic
755C22C22×#12411yescharacteristic
756C22C2×#53311yescharacteristic
757C22C2×#53611yescharacteristic
758C22C2×#54211yescharacteristic
759C22C2×#54611yescharacteristic
760C22C2×#54711yescharacteristic
761C22C2×#54711yescharacteristic
762C22C2×D4×Q811yescharacteristic
763C22C2×D4×Q811yescharacteristic
764C22D4×#4111yescharacteristic
765C22C2×#55411yescharacteristic
766C22C2×#55611yescharacteristic
767C22C2×#55611yescharacteristic
768C22C2×#55611yescharacteristic
769C22Q8×#4111yescharacteristic
770C22#348111yescharacteristic
771C22#348811yescharacteristic
772C22#348911yescharacteristic
773C22#349211yescharacteristic
774C22#349311yescharacteristic
775C22#349411yescharacteristic
776C22#349511yescharacteristic
777C22#349711yescharacteristic
778C22#349811yescharacteristic
779C22#350211yescharacteristic
780C22#350311yescharacteristic
781C22#351411yescharacteristic
782C22#351811yescharacteristic
783C22#352311yescharacteristic
784C22#352311yescharacteristic
785C22#355011yescharacteristic
786C22#355211yescharacteristic
787C22#355411yescharacteristic
788C22#355511yescharacteristic
789C4—28no—
790C4—24no—
791C4—42no—
792C4—44no—
793C4—44no—
794C4—44no—
795C4—44no—
796C4—42no—
797C4—42no—
798C4—44no—
799C4—82no—
800C4—84no—
801C4—84no—
802C4—82no—
803C4#249218yescomplemented
804C4#254718yes—
805C2—44no—
806C2C2×#249211yescharacteristic
807C2C2×#254711yescharacteristic
808C2#3554211yescharacteristic
809C2#3613311yescharacteristic
810C2#3625811yescharacteristic
811C2#3648011yescharacteristic
812C2Q8×#12111yescharacteristic
813C2#3891111yescharacteristic
814C2#3915911yescharacteristic
815C2#3935111yescharacteristic
816C2#3959711yescharacteristic
817C2#5924411yescharacteristic
818C2#5924511yescharacteristic
819C2#5924811yescharacteristic
820C2#5931411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
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×#2551C2semidirect
4. #15858C2semidirect
6. #15186C2semidirect
8. #15156C2semidirect
11. #14155C2semidirect
12. #14053C2semidirect
14. #13926C2semidirect
15. #13926C2semidirect
16. C4⋊C42C2semidirect
159. #380Q8semidirect
803. C4#2492semidirect

Maximal subgroups

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

subgroupindex
C2×#25512
C2×#24922
C2×C4×C22⋊Q82
#158582
#154262
#151862
#151832
#151562
#151252
#146862
#141552
#140532
#139742
#139262
C4⋊C422
C4×#3802