Finite Group Databasebeta

← #874129

Subgroups — #874129

Order 512.

2720 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2547C211yesmaximal, characteristic
2C2×#2415C211yesmaximal, characteristic
3#16858C214yesmaximal, complemented
4#15485C214yesmaximal, complemented
5#15311C214yesmaximal
6#15236C211yesmaximal, characteristic, complemented
7#15191C211yesmaximal, characteristic, complemented
8#15182C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic, complemented
10#15150C211yesmaximal, characteristic, complemented
11#15143C211yesmaximal, characteristic, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14686C211yesmaximal, characteristic, complemented
14#14554C214yesmaximal, complemented
15#14050C211yesmaximal, characteristic, complemented
16#14000C211yesmaximal, characteristic, complemented
17#13939C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×#124C2212yes—
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C42C2211yescharacteristic
27#2547—28no—
28#2415—28no—
29C2×#397C2212yes—
30C2×#397C2212yes—
31C2×#397C2212yes—
32C2×#397C2214yes—
33C2×#395C2214yes—
34C2×#394C2212yes—
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2212yes—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2212yes—
43C2×#388C2212yes—
44C2×#386C2212yes—
45C2×#384C2211yescharacteristic
46C2×#384C2211yescharacteristic
47C2×#384C2211yescharacteristic
48C2×#382C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2214yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59#1446C2214yes—
60#1445C2214yes—
61#1444C2214yes—
62#1443C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1437C2212yes—
74#1436C2214yes—
75#1436C2214yes—
76#1436C2214yes—
77#1436C2212yes—
78#1436C2214yes—
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2214yes—
87C4⋊#95C2211yescharacteristic
88#1434C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2212yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×Q8C2312yes—
95C23×D4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—42no—
101C2×C4⋊Q8—42no—
102C2×#124—28no—
103C2×#124—48no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—42no—
108C2×C22⋊Q8—42no—
109C2×C22⋊Q8—42no—
110C2×C4×D4—42no—
111C2×C4×D4—42no—
112C2×C4×D4D418yes—
113C2×#117—24no—
114C2×#117—24no—
115C2×#117—42no—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C42—24no—
145C22×C42—42no—
146C22×C42—42no—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2312yes—
154C22×C42C2312yes—
155#397—28no—
156#397—28no—
157#397—28no—
158#397—48no—
159#395—216no—
160#394—28no—
161#391—28no—
162#391—24no—
163#391—24no—
164#391—42no—
165#391—42no—
166#391—42no—
167#389—28no—
168#389—24no—
169#388—28no—
170#386—28no—
171#384—42no—
172#384—42no—
173#384—42no—
174#382—24no—
175#380—24no—
176#380—24no—
177#380—24no—
178#380—24no—
179#380—24no—
180#380—48no—
181C4×C4⋊C4—24no—
182C4×C22⋊C4—24no—
183C4×C22⋊C4—42no—
184C4×C22⋊C4—42no—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C25C2411yescharacteristic
215C25C2411yescharacteristic
216C22×Q8—22no—
217C22×Q8—24no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—28no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—44no—
226C22×Q8—42no—
227C22×Q8—42no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—41no—
231C22×D4—41no—
232C22×D4C2×D414yes—
233C23×C4—24no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4C2×D414yes—
253C23×C4C2×D414yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C4⋊Q8—416no—
272#124—432no—
273C22⋊Q8—416no—
274C22⋊Q8—416no—
275C4×D4—416no—
276#117—416no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4C2×D414yes—
320C2×C4⋊C4#4114yes—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—41no—
345C2×C22⋊C4—41no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4C2×D414yes—
354C2×C22⋊C4C2×D414yes—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—24no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—416no—
373C2×C42—42no—
374C2×C42—44no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42C2×D414yes—
378C2×C42#4114yes—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—28no—
390#95—24no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—24no—
395#95—24no—
396#95—28no—
397#95—42no—
398#95—42no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95#4118yes—
408C24—21no—
409C24—22no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—22no—
417C24—21no—
418C24—21no—
419C24—22no—
420C24—21no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24C22×D412yes—
428C24C22×D412yes—
429C24H(5,𝔽2)14yes—
430C24C2511yescharacteristic
431C2×Q8—48no—
432C2×Q8—48no—
433C2×Q8—48no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—88no—
442C2×Q8—88no—
443C2×D4—28no—
444C2×D4—28no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—216no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
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—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—48no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C2×#4114yes—
558C22×C4C2×#4114yes—
559C22×C4C2×#4114yes—
560C22×C4C2×#4114yes—
561C22×C4C2×#4114yes—
562C22×C4C2×#4112yes—
563C22×C4C2×#4112yes—
564C22×C4H(5,𝔽2)12yes—
565C22×C4H(5,𝔽2)12yes—
566C22×C4H(5,𝔽2)12yes—
567C22×C42−1+414yes—
568C22×C42−1+414yes—
569C22×C42−1+412yes—
570C4⋊C4—28no—
571C4⋊C4—44no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—88no—
583C4⋊C4—88no—
584C4⋊C4—88no—
585C22⋊C4—44no—
586C22⋊C4—44no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C42—28no—
599C42—28no—
600C42—48no—
601C42—48no—
602C42—48no—
603C42—44no—
604C42—44no—
605C42—44no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—24no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—41no—
633C23—42no—
634C23—42no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23#53514yes—
652C23C23×D411yescharacteristic
653C23C22×#4112yes—
654C23C22×#4111yescharacteristic
655C23C22×#4111yescharacteristic
656C23C2×H(5,𝔽2)11yescharacteristic
657C23C2×H(5,𝔽2)11yescharacteristic
658C23C2×H(5,𝔽2)12yes—
659C23C2×H(5,𝔽2)11yescharacteristic
660C23C2×2−1+411yescharacteristic
661C23C2×2−1+412yes—
662C23C2×2−1+412yes—
663Q8—816no—
664Q8—88no—
665D4—416no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—28no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—432no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—416no—
716C2×C4—416no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4#53214yes—
762C2×C4#53414yes—
763C2×C4#53814yes—
764C2×C4#54214yes—
765C2×C4#54614yes—
766C2×C4#54714yes—
767C2×C4#55514yes—
768C2×C4#55618yes—
769C2×C4#56214yes—
770C22—24no—
771C22—24no—
772C22—24no—
773C22—42no—
774C22—42no—
775C22—44no—
776C22—42no—
777C22—44no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22C2×#53211yescharacteristic
793C22C2×#53411yescharacteristic
794C22C2×#53511yescharacteristic
795C22C2×#53811yescharacteristic
796C22C2×#54211yescharacteristic
797C22C2×#54611yescharacteristic
798C22C2×#54711yescharacteristic
799C22C2×#55511yescharacteristic
800C22C2×#55612yes—
801C22#348212yes—
802C22#349212yes—
803C22#349911yescharacteristic
804C22#349911yescharacteristic
805C22#350912yes—
806C22#351912yes—
807C22#351912yes—
808C22#352012yes—
809C22#352212yes—
810C22C2×#56211yescharacteristic
811C22#353612yes—
812C22#353812yes—
813C22#354412yes—
814C22#355012yes—
815C4—24no—
816C4—28no—
817C4—42no—
818C4—44no—
819C4—44no—
820C4—42no—
821C4—42no—
822C4—44no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4—82no—
829C4—82no—
830C4—82no—
831C4#268618yes—
832C2—44no—
833C2—82no—
834C2#3507811yescharacteristic
835C2#3618811yescharacteristic
836C2#3640611yescharacteristic
837C2#3738611yescharacteristic
838C2#3786311yescharacteristic
839C2#3807911yescharacteristic
840C2#3915412yes—
841C2#4007812yes—
842C2#4563112yes—
843C2C2×#268611yescharacteristic
844C2#5923412yes—
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. #16858C2semidirect
4. #15485C2semidirect
6. #15236C2semidirect
7. #15191C2semidirect
8. #15182C2semidirect
9. #15182C2semidirect
10. #15150C2semidirect
11. #15143C2semidirect
12. #14702C2semidirect
13. #14686C2semidirect
14. #14554C2semidirect
15. #14050C2semidirect
16. #14000C2semidirect
17. #13939C2semidirect
18. #13879C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25472
C2×#24152
#168582
#154852
#153112
#152362
#151912
#151822
#151502
#151432
#147022
#146862
#145542
#140502
#140002
#139392
#138792
C4×#3862