Finite Group Databasebeta

← #674277

Subgroups — #674277

Order 512.

2914 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×#2857C211yesmaximal, characteristic
2C2×#2551C211yesmaximal, characteristic, complemented
3C2×#2492C212yesmaximal
4#15770C214yesmaximal
5#15699C214yesmaximal, complemented
6#15191C212yesmaximal, complemented
7#15179C212yesmaximal
8#15139C212yesmaximal, complemented
9#15125C212yesmaximal
10#14155C211yesmaximal, characteristic, complemented
11#14155C211yesmaximal, characteristic, complemented
12#14142C212yesmaximal, complemented
13#14053C212yesmaximal, complemented
14#13994C212yesmaximal
15C4⋊C42C211yesmaximal, characteristic, complemented
16C4×#380C211yesmaximal, characteristic
17C4×#380C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C4⋊Q8C2212yes—
20C22×C4⋊Q8C2212yes—
21C22×C22⋊Q8C2212yes—
22C23×C42C2211yescharacteristic
23#2857—28no—
24#2551—28no—
25#2492—216no—
26C2×#400C2214yes—
27C2×#395C2214yes—
28C2×#393C2214yes—
29C2×#391C2212yes—
30C2×#391C2212yes—
31C2×#391C2212yes—
32C2×#391C2212yes—
33C2×#391C2214yes—
34C2×#391C2212yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#388C2214yes—
40C2×#384C2211yescharacteristic
41C2×#380C2212yes—
42C2×#380C2212yes—
43C2×#380C2211yescharacteristic
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×C4×C4⋊C4C2212yes—
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C22⋊C4C2212yes—
54C2×C4×C22⋊C4C2212yes—
55#1446C2214yes—
56#1446C2214yes—
57#1445C2214yes—
58#1445C2214yes—
59#1443C2214yes—
60#1442C2214yes—
61#1442C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1441C2214yes—
65#1440C2214yes—
66#1439C2214yes—
67#1436C2214yes—
68#1436C2214yes—
69C4⋊#95C2212yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2211yescharacteristic
73C4⋊#95C2212yes—
74C4⋊#95C2211yescharacteristic
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2211yescharacteristic
79#1434C2214yes—
80#1434C2212yes—
81#1434C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C4×#95C2212yes—
85C4×#95C2212yes—
86C23×Q8C2312yes—
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—24no—
96C2×C4⋊Q8—24no—
97C2×C4⋊Q8—24no—
98C2×C4⋊Q8—44no—
99C2×C4⋊Q8—44no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—44no—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2314yes—
109C22×C4⋊C4C2314yes—
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C42—24no—
125C22×C42—24no—
126C22×C42—24no—
127C22×C42C2311yescharacteristic
128C22×C42C2311yescharacteristic
129C22×C42C2311yescharacteristic
130C22×C42C2312yes—
131C22×C42C2312yes—
132C22×C42C2312yes—
133C22×C42C2312yes—
134C22×C42C2314yes—
135C22×C42C2311yescharacteristic
136#400—216no—
137#395—216no—
138#393—216no—
139#391—28no—
140#391—28no—
141#391—28no—
142#391—28no—
143#391—216no—
144#391—44no—
145#389—28no—
146#389—28no—
147#389—28no—
148#389—28no—
149#388—216no—
150#384D418yes—
151#380—28no—
152#380—28no—
153#380—24no—
154#380—24no—
155#380D418yes—
156#380Q818yescomplemented
157C4×C4⋊C4—28no—
158C4×C4⋊C4—24no—
159C4×C4⋊C4—24no—
160C4×C4⋊C4—24no—
161C4×C4⋊C4—24no—
162C4×C4⋊C4—44no—
163C4×C22⋊C4—28no—
164C4×C22⋊C4—44no—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2312yes—
169C2×#95C2312yes—
170C2×#95C2314yes—
171C2×#95C2312yes—
172C2×#95C2314yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2314yes—
184C2×#95C2314yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C25C2411yescharacteristic
196C22×Q8—24no—
197C22×Q8—24no—
198C22×Q8—28no—
199C22×Q8—28no—
200C22×Q8—24no—
201C22×Q8—24no—
202C22×Q8—24no—
203C22×Q8—28no—
204C22×Q8—24no—
205C22×Q8—24no—
206C22×Q8—44no—
207C22×Q8—44no—
208C22×Q8—44no—
209C22×Q8—44no—
210C23×C4—22no—
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—41no—
228C23×C4—41no—
229C23×C4C2×D414yes—
230C23×C4C2×Q814yes—
231C23×C4C2414yes—
232C23×C4C2412yes—
233C23×C4C2412yes—
234C23×C4C2414yes—
235C23×C4C2412yes—
236C23×C4C2412yes—
237C23×C4C2411yescharacteristic
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2411yescharacteristic
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2411yescharacteristic
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C23×C4C2411yescharacteristic
247C4⋊Q8—432no—
248C4⋊Q8—432no—
249C4⋊Q8—416no—
250C22⋊Q8—432no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—22no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—22no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—24no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—28no—
268C2×C4⋊C4—28no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—28no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—44no—
288C2×C4⋊C4—44no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4C2×D418yes—
291C2×C4⋊C4C2×D414yes—
292C2×C4⋊C4C2×D418yes—
293C2×C4⋊C4C2×D414yes—
294C2×C4⋊C4C2×D418yes—
295C2×C4⋊C4C2×Q814yes—
296C2×C4⋊C4C2×Q814yes—
297C2×C4⋊C4#4114yes—
298C2×C4⋊C4#4114yes—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
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—42no—
308C2×C22⋊C4—42no—
309C2×C22⋊C4—44no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4C2×D418yes—
313C2×C22⋊C4C2×Q818yes—
314C2×C42—24no—
315C2×C42—24no—
316C2×C42—24no—
317C2×C42—24no—
318C2×C42—22no—
319C2×C42—22no—
320C2×C42—22no—
321C2×C42—24no—
322C2×C42—24no—
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—24no—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—24no—
335C2×C42—28no—
336C2×C42—416no—
337C2×C42—44no—
338C2×C42—44no—
339C2×C42C2×D414yes—
340C2×C42#4114yes—
341C2×C42#4114yes—
342#95—24no—
343#95—24no—
344#95—28no—
345#95—24no—
346#95—24no—
347#95—28no—
348#95—28no—
349#95—28no—
350#95—28no—
351#95—28no—
352#95—28no—
353#95—28no—
354#95—24no—
355#95—24no—
356#95—24no—
357#95—24no—
358#95—28no—
359#95—28no—
360#95—24no—
361#95—24no—
362#95—42no—
363#95—42no—
364#95—44no—
365#95—42no—
366#95—42no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95C2×D418yes—
371#95C2×Q818yes—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—21no—
378C24—21no—
379C24—21no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—21no—
384C24C22×D412yes—
385C24C22×Q812yes—
386C242−1+412yes—
387C24C2511yescharacteristic
388C2×Q8—416no—
389C2×Q8—416no—
390C2×Q8—416no—
391C2×Q8—48no—
392C2×Q8—48no—
393C2×Q8—48no—
394C2×Q8—48no—
395C2×Q8—48no—
396C2×Q8—48no—
397C2×Q8—48no—
398C2×Q8—88no—
399C2×Q8—88no—
400C2×Q8—88no—
401C2×Q8—88no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—28no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
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—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
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×C4C22×D414yes—
509C22×C4C22×D412yes—
510C22×C4C22×D414yes—
511C22×C4C22×D418yes—
512C22×C4C22×D412yes—
513C22×C4C22×D412yes—
514C22×C4C22×D412yes—
515C22×C4C22×D412yes—
516C22×C4C22×Q812yes—
517C22×C4C22×Q814yes—
518C22×C4C22×Q814yes—
519C22×C4C22×Q812yes—
520C22×C4C2×#4114yes—
521C22×C4C2×#4114yes—
522C22×C4C2×#4112yes—
523C22×C4C2×#4112yes—
524C22×C4C2×#4112yes—
525C22×C4C2×#4112yes—
526C22×C4C2×#4112yes—
527C22×C4C2×#4112yes—
528C22×C4C2×#4112yes—
529C22×C4C2×#4112yes—
530C22×C4H(5,𝔽2)12yes—
531C22×C4H(5,𝔽2)12yes—
532C22×C42−1+412yes—
533C22×C42−1+412yes—
534C22×C42−1+412yes—
535C4⋊C4—216no—
536C4⋊C4—28no—
537C4⋊C4—216no—
538C4⋊C4—28no—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—28no—
542C4⋊C4—28no—
543C4⋊C4—48no—
544C4⋊C4—416no—
545C4⋊C4—416no—
546C4⋊C4—416no—
547C4⋊C4—48no—
548C4⋊C4—48no—
549C4⋊C4—44no—
550C4⋊C4—44no—
551C22⋊C4—216no—
552C22⋊C4—48no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C22⋊C4—416no—
556C42—44no—
557C42—44no—
558C42—44no—
559C42—48no—
560C42—48no—
561C42—48no—
562C42—48no—
563C42—88no—
564C42#124116yes—
565C23—22no—
566C23—22no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23D4×Q814yes—
600C23C23×D411yescharacteristic
601C23C23×D411yescharacteristic
602C23C23×Q811yescharacteristic
603C23C22×#4111yescharacteristic
604C23C22×#4111yescharacteristic
605C23C22×#4111yescharacteristic
606C23C22×#4111yescharacteristic
607C23C2×H(5,𝔽2)11yescharacteristic
608C23C2×H(5,𝔽2)11yescharacteristic
609C23C2×2−1+411yescharacteristic
610C23C2×2−1+411yescharacteristic
611C23C2×2−1+411yescharacteristic
612C23C2×2−1+411yescharacteristic
613C23#58511yescharacteristic
614C23#58511yescharacteristic
615Q8—832no—
616Q8—816no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—28no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—28no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—416no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—44no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—416no—
695C2×C4—416no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4C2×#12414yes—
718C2×C4C2×#12414yes—
719C2×C4C2×#12414yes—
720C2×C4#53214yes—
721C2×C4#53314yes—
722C2×C4#54214yes—
723C2×C4#54214yes—
724C2×C4D4214yes—
725C2×C4#54614yes—
726C2×C4#54714yes—
727C2×C4#54814yes—
728C2×C4D4×Q814yes—
729C2×C4#55414yes—
730C2×C4#55514yes—
731C2×C4#55614yes—
732C22—24no—
733C22—24no—
734C22—24no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22C22×#12411yescharacteristic
748C22C2×#53211yescharacteristic
749C22C2×#53311yescharacteristic
750C22C2×#54211yescharacteristic
751C22C2×#54211yescharacteristic
752C22C2×D4211yescharacteristic
753C22C2×#54611yescharacteristic
754C22C2×#54711yescharacteristic
755C22C2×#54811yescharacteristic
756C22C2×D4×Q811yescharacteristic
757C22C2×D4×Q811yescharacteristic
758C22D4×#4111yescharacteristic
759C22C2×#55411yescharacteristic
760C22C2×#55511yescharacteristic
761C22C2×#55611yescharacteristic
762C22Q8×#4111yescharacteristic
763C22#348211yescharacteristic
764C22#348511yescharacteristic
765C22#348611yescharacteristic
766C22#349511yescharacteristic
767C22#349511yescharacteristic
768C22#349511yescharacteristic
769C22#349511yescharacteristic
770C22#349611yescharacteristic
771C22#349911yescharacteristic
772C22#350211yescharacteristic
773C22#350311yescharacteristic
774C22#351411yescharacteristic
775C22#351811yescharacteristic
776C22#352011yescharacteristic
777C22#352311yescharacteristic
778C22#354611yescharacteristic
779C22#355011yescharacteristic
780C22#355211yescharacteristic
781C22#355511yescharacteristic
782C4—24no—
783C4—42no—
784C4—48no—
785C4—44no—
786C4—44no—
787C4—44no—
788C4—44no—
789C4—42no—
790C4—42no—
791C4—44no—
792C4—44no—
793C4—82no—
794C4—82no—
795C4—84no—
796C4#249118yes—
797C4#249218yescomplemented
798C2—44no—
799C2C2×#249111yescharacteristic
800C2C2×#249211yescharacteristic
801C2#3564411yescharacteristic
802C2#3613311yescharacteristic
803C2#3628811yescharacteristic
804C2#3647311yescharacteristic
805C2#3656111yescharacteristic
806C2#3894011yescharacteristic
807C2#3915911yescharacteristic
808C2#3935011yescharacteristic
809C2#3960911yescharacteristic
810C2#5903511yescharacteristic
811C2#5904211yescharacteristic
812C2#5908111yescharacteristic
813C2#5912711yescharacteristic
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
2. C2×#2551C2semidirect
5. #15699C2semidirect
6. #15191C2semidirect
8. #15139C2semidirect
10. #14155C2semidirect
11. #14155C2semidirect
12. #14142C2semidirect
13. #14053C2semidirect
15. C4⋊C42C2semidirect
156. #380Q8semidirect
797. C4#2492semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25512
C2×#24922
#157702
#156992
#151912
#151792
#151392
#151252
#141552
#141422
#140532
#139942
C4⋊C422
C4×#3802