Finite Group Databasebeta

← #657643

Subgroups — #657643

Order 512.

2856 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C211yesmaximal, characteristic
2C2×#2352C211yesmaximal, characteristic
3#15716C214yesmaximal, complemented
4#15542C214yesmaximal, complemented
5#15239C211yesmaximal, characteristic, complemented
6#15233C211yesmaximal, characteristic, complemented
7#15231C211yesmaximal, characteristic, complemented
8#15195C211yesmaximal, characteristic, complemented
9#14927C214yesmaximal
10#14686C211yesmaximal, characteristic, complemented
11#14051C211yesmaximal, characteristic, complemented
12#14048C211yesmaximal, characteristic, complemented
13#13939C211yesmaximal, characteristic, complemented
14#13904C211yesmaximal, characteristic, complemented
15#13881C211yesmaximal, characteristic, complemented
16#13879C211yesmaximal, characteristic, complemented
17#13874C214yesmaximal, complemented
18C4×#386C211yesmaximal, characteristic
19C2×C4⋊#95C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×C4×D4C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2486—28no—
27C2×#398C2212yes—
28C2×#397C2212yes—
29#2352—28no—
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#388C2212yes—
33C2×#387C2212yes—
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#384C2211yescharacteristic
37C2×#384C2211yescharacteristic
38C2×#382C2211yescharacteristic
39C2×#382C2211yescharacteristic
40C2×#382C2211yescharacteristic
41C2×#381C2212yes—
42C2×#381C2214yes—
43C2×#380C2211yescharacteristic
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2214yes—
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2212yes—
51C2×C4×C22⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C22×#95C2214yes—
55#1445C2214yes—
56#1443C2214yes—
57#1443C2214yes—
58#1442C2214yes—
59#1442C2214yes—
60#1442C2214yes—
61#1442C2214yes—
62#1442C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1440C2214yes—
66#1440C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1437C2212yes—
70#1436C2214yes—
71#1436C2214yes—
72#1436C2212yes—
73C4⋊#95C2211yescharacteristic
74C4⋊#95C2211yescharacteristic
75C4⋊#95C2211yescharacteristic
76C4⋊#95C2211yescharacteristic
77C4⋊#95C2211yescharacteristic
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2214yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2214yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87#1434C2214yes—
88#1434C2214yes—
89C22⋊#95C2212yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×D4C2311yescharacteristic
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C2×#123—28no—
100C2×#123—48no—
101C2×C4×D4—24no—
102C2×C4×D4—24no—
103C2×C4×D4D418yes—
104C2×#117—24no—
105C2×#117—24no—
106C2×#117—42no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—24no—
112C22×C4⋊C4—42no—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C42—24no—
140C22×C42—24no—
141C22×C42—42no—
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150#398—28no—
151#397—28no—
152#389—24no—
153#389—24no—
154#388—28no—
155#387—28no—
156#386—28no—
157#386—28no—
158#384—24no—
159#384—42no—
160#382—24no—
161#382—24no—
162#382—42no—
163#381—28no—
164#381—48no—
165#380—24no—
166#380—24no—
167#380—24no—
168#380—24no—
169#380—24no—
170#380—48no—
171C4×C4⋊C4—24no—
172C4×C22⋊C4—24no—
173C4×C22⋊C4—28no—
174C4×C22⋊C4—24no—
175C4×C22⋊C4—42no—
176C2×#95—216no—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C25C2411yescharacteristic
209C25C2411yescharacteristic
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4C2×D414yes—
215C23×C4—22no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—24no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—28no—
233C23×C4—28no—
234C23×C4—24no—
235C23×C4—28no—
236C23×C4—24no—
237C23×C4—42no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—44no—
241C23×C4C2×D414yes—
242C23×C4C2×D414yes—
243C23×C4#4118yes—
244C23×C4#4114yes—
245C23×C4#4114yes—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263#123—432no—
264C4×D4—232no—
265#117—416no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—416no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—416no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4C2×D414yes—
310C2×C4⋊C4#4114yes—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4C2×D414yes—
338C2×C22⋊C4C2×D414yes—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—24no—
344C2×C42—24no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—416no—
358C2×C42—42no—
359C2×C42—42no—
360C2×C42—44no—
361C2×C42C2×D414yes—
362C2×C42#4114yes—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—28no—
374#95—28no—
375#95—28no—
376#95—28no—
377#95—24no—
378#95—24no—
379#95—28no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—42no—
384#95—44no—
385#95—44no—
386#95—42no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95—44no—
391#95—44no—
392#95—44no—
393#95—44no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—22no—
399C24—22no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—22no—
407C24—22no—
408C24—21no—
409C24—22no—
410C24C22×D412yes—
411C24C22×D412yes—
412C24C2×#4112yes—
413C24C2×#4112yes—
414C24C2×#4114yes—
415C24H(5,𝔽2)14yes—
416C24C2511yescharacteristic
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—48no—
421C2×D4—48no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—28no—
431C22×C4—28no—
432C22×C4—28no—
433C22×C4—28no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—216no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—216no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
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—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—416no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—416no—
530C22×C4—416no—
531C22×C4—84no—
532C22×C4—88no—
533C22×C4#123116yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C2×#4114yes—
540C22×C4C2×#4114yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4114yes—
544C22×C4C2×#4114yes—
545C22×C4C2×#4112yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C4C2×#4112yes—
549C22×C4H(5,𝔽2)12yes—
550C22×C42−1+414yes—
551C22×C42−1+412yes—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C4⋊C4—48no—
555C4⋊C4—48no—
556C4⋊C4—48no—
557C4⋊C4—48no—
558C4⋊C4—44no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—44no—
565C4⋊C4—88no—
566C4⋊C4—88no—
567C22⋊C4—28no—
568C22⋊C4—28no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—48no—
573C22⋊C4—48no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—84no—
578C42—28no—
579C42—28no—
580C42—48no—
581C42—48no—
582C42—44no—
583C42—44no—
584C42—44no—
585C42—84no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—24no—
592C23—22no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—41no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23C2×#12314yes—
628C23#53214yes—
629C23#53514yes—
630C23#55318yes—
631C23#55518yes—
632C23C23×D411yescharacteristic
633C23C22×#4111yescharacteristic
634C23C22×#4111yescharacteristic
635C23C22×#4111yescharacteristic
636C23C22×#4111yescharacteristic
637C23C22×#4112yes—
638C23C2×H(5,𝔽2)12yes—
639C23C2×H(5,𝔽2)11yescharacteristic
640C23C2×2−1+411yescharacteristic
641C23C2×2−1+412yes—
642C23#58512yes—
643D4—416no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—232no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—28no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—432no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—44no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—416no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—816no—
738C2×C4—816no—
739C2×C4C2×#12314yes—
740C2×C4C2×#12314yes—
741C2×C4#52914yes—
742C2×C4#53914yes—
743C2×C4#54614yes—
744C2×C4#54714yes—
745C2×C4#55114yes—
746C2×C4#55218yes—
747C2×C4#55214yes—
748C22—24no—
749C22—24no—
750C22—28no—
751C22—28no—
752C22—28no—
753C22—24no—
754C22—24no—
755C22—28no—
756C22—24no—
757C22—24no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22#250018yes—
770C22C22×#12311yescharacteristic
771C22C2×#52911yescharacteristic
772C22C2×#53211yescharacteristic
773C22C2×#53511yescharacteristic
774C22C2×#53911yescharacteristic
775C22C2×#54611yescharacteristic
776C22C2×#54711yescharacteristic
777C22C2×#55111yescharacteristic
778C22C2×#55212yes—
779C22C2×#55211yescharacteristic
780C22C2×#55312yes—
781C22C2×#55512yes—
782C22#347512yes—
783C22#349412yes—
784C22#349512yes—
785C22#349911yescharacteristic
786C22#350011yescharacteristic
787C22#350512yes—
788C22#350712yes—
789C22#350912yes—
790C22#352212yes—
791C22#353612yes—
792C22#355912yes—
793C4—28no—
794C4—24no—
795C4—44no—
796C4—42no—
797C4—44no—
798C4—42no—
799C4—42no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4#241918yes—
810C2—28no—
811C2—82no—
812C2C2×#241911yescharacteristic
813C2C2×#250011yescharacteristic
814C2#3561911yescharacteristic
815C2#3617612yes—
816C2#3618111yescharacteristic
817C2#3638611yescharacteristic
818C2#3786411yescharacteristic
819C2#3807911yescharacteristic
820C2#3950412yes—
821C2#5919712yes—
822C2#5928912yes—
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
3. #15716C2semidirect
4. #15542C2semidirect
5. #15239C2semidirect
6. #15233C2semidirect
7. #15231C2semidirect
8. #15195C2semidirect
10. #14686C2semidirect
11. #14051C2semidirect
12. #14048C2semidirect
13. #13939C2semidirect
14. #13904C2semidirect
15. #13881C2semidirect
16. #13879C2semidirect
17. #13874C2semidirect
19. C2×C4⋊#95C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24862
C2×#23522
#157162
#155422
#152392
#152332
#152312
#151952
#149272
#146862
#140512
#140482
#139392
#139042
#138812
#138792
#138742
C4×#3862
C2×C4⋊#952