Finite Group Databasebeta

← #705200

Subgroups — #705200

Order 512.

2702 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2417C211yesmaximal, characteristic
2C2×#2352C211yesmaximal, characteristic
3#16444C214yesmaximal, complemented
4#15956C214yesmaximal, complemented
5#15954C214yesmaximal
6#15241C211yesmaximal, characteristic, complemented
7#15239C211yesmaximal, characteristic, complemented
8#15195C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic, complemented
10#14773C214yesmaximal, complemented
11#14258C211yesmaximal, characteristic, complemented
12#14139C211yesmaximal, characteristic, complemented
13#14138C211yesmaximal, characteristic, complemented
14#14049C211yesmaximal, characteristic, complemented
15#14000C211yesmaximal, characteristic, complemented
16#13904C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13839C211yesmaximal, characteristic
19#13795C211yesmaximal, characteristic, complemented
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2417—28no—
28C2×#398C2212yes—
29C2×#396C2212yes—
30#2352—28no—
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#388C2212yes—
38C2×#387C2212yes—
39C2×#387C2214yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#385C2214yes—
43C2×#384C2211yescharacteristic
44C2×#384C2211yescharacteristic
45C2×#382C2211yescharacteristic
46C2×#381C2214yes—
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2212yes—
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2212yes—
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56#1445C2214yes—
57#1445C2214yes—
58#1444C2214yes—
59#1443C2214yes—
60#1443C2214yes—
61#1443C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1441C2212yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1440C2212yes—
70#1440C2214yes—
71#1440C2214yes—
72#1439C2212yes—
73#1439C2214yes—
74#1439C2214yes—
75#1438C2212yes—
76#1436C2214yes—
77#1436C2214yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C2×C22⋊Q8—24no—
100C2×C22⋊Q8—24no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—42no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4D418yes—
108C2×#117—24no—
109C2×#117—24no—
110C2×#117—24no—
111C2×#117—42no—
112C2×#117—42no—
113C2×#117—42no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
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×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155#398—28no—
156#396—28no—
157#391—24no—
158#391—24no—
159#391—42no—
160#391—42no—
161#391—42no—
162#389—24no—
163#388—28no—
164#387—28no—
165#387—48no—
166#386—28no—
167#386—28no—
168#385—48no—
169#384—24no—
170#384—42no—
171#382—24no—
172#381—48no—
173#380—24no—
174#380—24no—
175#380—24no—
176#380—28no—
177C4×C4⋊C4—24no—
178C4×C22⋊C4—24no—
179C4×C22⋊C4—28no—
180C4×C22⋊C4—42no—
181C4×C22⋊C4—42no—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C25C2411yescharacteristic
213C25C2411yescharacteristic
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—24no—
224C22×D4—42no—
225C22×D4C2×D414yes—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—28no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—44no—
244C23×C4—44no—
245C23×C4—44no—
246C23×C4C2×D414yes—
247C23×C4C2×D414yes—
248C23×C4#4114yes—
249C23×C4#4114yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C22⋊Q8—416no—
268C22⋊Q8—416no—
269C4×D4—232no—
270#117—416no—
271#117—416no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—416no—
307C2×C4⋊C4—416no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4C2×D414yes—
319C2×C4⋊C4#4114yes—
320C2×C4⋊C4#4114yes—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
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—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4C2×D414yes—
353C2×C22⋊C4C2×D414yes—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—42no—
372C2×C42—44no—
373C2×C42C2×D414yes—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—28no—
385#95—28no—
386#95—28no—
387#95—24no—
388#95—24no—
389#95—28no—
390#95—42no—
391#95—42no—
392#95—44no—
393#95—44no—
394#95—42no—
395#95—42no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24C22×D412yes—
422C24C22×D412yes—
423C24C2×#4112yes—
424C24C2×#4112yes—
425C242−1+414yes—
426C24C2511yescharacteristic
427C2×Q8—44no—
428C2×Q8—44no—
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8—44no—
432C2×Q8—44no—
433C2×Q8—44no—
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—44no—
437C2×D4—48no—
438C2×D4—48no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
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—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—416no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—88no—
542C22×C4—84no—
543C22×C4—84no—
544C22×C4—88no—
545C22×C4—88no—
546C22×C4#123116yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C2×#4114yes—
553C22×C4C2×#4114yes—
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4112yes—
559C22×C4C2×#4112yes—
560C22×C4H(5,𝔽2)14yes—
561C22×C4H(5,𝔽2)12yes—
562C22×C4H(5,𝔽2)12yes—
563C22×C42−1+414yes—
564C4⋊C4—28no—
565C4⋊C4—28no—
566C4⋊C4—28no—
567C4⋊C4—416no—
568C4⋊C4—48no—
569C4⋊C4—48no—
570C4⋊C4—48no—
571C4⋊C4—48no—
572C4⋊C4—44no—
573C4⋊C4—48no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—84no—
579C4⋊C4—88no—
580C22⋊C4—216no—
581C22⋊C4—28no—
582C22⋊C4—28no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—84no—
591C22⋊C4—84no—
592C42—28no—
593C42—48no—
594C42—44no—
595C42—44no—
596C42—44no—
597C42—44no—
598C42—84no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23C2×#12314yes—
644C23#53614yes—
645C23C23×D411yescharacteristic
646C23C22×#4111yescharacteristic
647C23C22×#4111yescharacteristic
648C23C22×#4111yescharacteristic
649C23C22×#4111yescharacteristic
650C23C2×H(5,𝔽2)11yescharacteristic
651C23C2×H(5,𝔽2)11yescharacteristic
652C23C2×H(5,𝔽2)12yes—
653C23C2×2−1+412yes—
654C23C2×2−1+412yes—
655C23#58512yes—
656Q8—88no—
657D4—416no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—232no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—28no—
680C2×C4—24no—
681C2×C4—28no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
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—44no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—416no—
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×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—44no—
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—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—816no—
754C2×C4—816no—
755C2×C4C2×#12314yes—
756C2×C4C2×#12314yes—
757C2×C4#52914yes—
758C2×C4#53814yes—
759C2×C4#54614yes—
760C2×C4#54614yes—
761C2×C4#55314yes—
762C2×C4#55314yes—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—42no—
778C22—44no—
779C22—44no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—44no—
784C22—44no—
785C22C22×#12311yescharacteristic
786C22C2×#52911yescharacteristic
787C22C2×#53611yescharacteristic
788C22#344911yescharacteristic
789C22C2×#53811yescharacteristic
790C22C2×#54611yescharacteristic
791C22C2×#54611yescharacteristic
792C22C2×#55311yescharacteristic
793C22C2×#55311yescharacteristic
794C22#349212yes—
795C22#349512yes—
796C22#349512yes—
797C22#349811yescharacteristic
798C22#349911yescharacteristic
799C22#351112yes—
800C22#351312yes—
801C22#351612yes—
802C22#352012yes—
803C22#352312yes—
804C22#353612yes—
805C22#353812yes—
806C22#354612yes—
807C22#354712yes—
808C4—24no—
809C4—44no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—44no—
814C4—42no—
815C4—42no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4—82no—
822C4—82no—
823C4—82no—
824C4#244418yes—
825C2—44no—
826C2—44no—
827C2C2×#244411yescharacteristic
828C2#3531111yescharacteristic
829C2#3553011yescharacteristic
830C2#3599312yes—
831C2#3807811yescharacteristic
832C2#3808111yescharacteristic
833C2#3894511yescharacteristic
834C2#3894611yescharacteristic
835C2#4299112yes—
836C2#4537112yes—
837C2#4537212yes—
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. #16444C2semidirect
4. #15956C2semidirect
6. #15241C2semidirect
7. #15239C2semidirect
8. #15195C2semidirect
9. #15182C2semidirect
10. #14773C2semidirect
11. #14258C2semidirect
12. #14139C2semidirect
13. #14138C2semidirect
14. #14049C2semidirect
15. #14000C2semidirect
16. #13904C2semidirect
17. #13880C2semidirect
19. #13795C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24172
C2×#23522
#164442
#159562
#159542
#152412
#152392
#151952
#151822
#147732
#142582
#141392
#141382
#140492
#140002
#139042
#138802
#138392
#137952