Finite Group Databasebeta

← #4327976

Subgroups — #4327976

Order 512.

2398 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16932C211yesmaximal, characteristic, complemented
2#16881C212yesmaximal, complemented
3#16877C211yesmaximal, characteristic, complemented
4#16417C212yesmaximal, complemented
5#16369C212yesmaximal, complemented
6#16219C212yesmaximal, complemented
7#15870C212yesmaximal, complemented
8#15329C212yesmaximal, complemented
9#15305C212yesmaximal, complemented
10#14893C211yesmaximal, characteristic, complemented
11#14888C212yesmaximal, complemented
12#14886C211yesmaximal, characteristic
13#14801C212yesmaximal, complemented
14#14732C212yesmaximal
15#14603C211yesmaximal, characteristic, complemented
16#14535C211yesmaximal, characteristic, complemented
17#14398C212yesmaximal, complemented
18#14015C212yesmaximal, complemented
19#13795C211yesmaximal, characteristic, complemented
20C22×C4×D4C2212yes—
21C22×#117C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C2×#400C2211yescharacteristic
25C2×#400C2212yes—
26C2×#400C2212yes—
27C2×#399C2211yescharacteristic
28C2×#398C2212yes—
29C2×#396C2212yes—
30C2×#394C2211yescharacteristic
31C2×#394C2212yes—
32C2×#394C2212yes—
33C2×#392C2211yescharacteristic
34C2×#390C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#387C2212yes—
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#385C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#380C2212yes—
45#1445C2212yes—
46#1444C2212yes—
47#1444C2212yes—
48#1444C2212yes—
49#1444C2212yes—
50#1443C2212yes—
51#1443C2212yes—
52#1443C2212yes—
53#1443C2212yes—
54#1442C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1441C2211yescharacteristic
59#1441C2212yes—
60#1441C2212yes—
61#1441C2212yes—
62#1441C2211yescharacteristic
63#1441C2212yes—
64#1440C2212yes—
65#1440C2212yes—
66#1440C2212yes—
67#1440C2212yes—
68#1440C2212yes—
69#1439C2211yescharacteristic
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2211yescharacteristic
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1438C2212yes—
82#1438C2212yes—
83#1437C2212yes—
84#1437C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2211yescharacteristic
96C4⋊#95C2212yes—
97C4⋊#95C2212yes—
98C4⋊#95C2211yescharacteristic
99#1434C2212yes—
100#1434C2211yescharacteristic
101#1434C2211yescharacteristic
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C23×D4C2312yes—
108C23×D4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
112C2×C4×D4—44no—
113C2×C4×D4—44no—
114C2×C4×D4—44no—
115C2×#117—24no—
116C2×#117—24no—
117C2×#117—42no—
118C2×#117—42no—
119C2×#117—42no—
120C2×#117—42no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163#400—24no—
164#400—44no—
165#400—44no—
166#399—42no—
167#398—44no—
168#396—44no—
169#394—24no—
170#394—44no—
171#394—44no—
172#392—42no—
173#390—42no—
174#389—42no—
175#387—44no—
176#386—28no—
177#386—44no—
178#386—44no—
179#385—28no—
180#385—44no—
181#385—44no—
182#385—44no—
183#380—44no—
184C2×#95C2311yescharacteristic
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2311yescharacteristic
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2311yescharacteristic
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2311yescharacteristic
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C25C2412yes—
228C25C2411yescharacteristic
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—24no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4—41no—
240C22×D4—41no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4#4114yes—
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C4×D4—432no—
280#117—416no—
281#117—416no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—416no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4#4114yes—
328C2×C4⋊C4#4114yes—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—41no—
391C2×C42—41no—
392C2×C42—41no—
393C2×C42—41no—
394C2×C42—41no—
395C2×C42—41no—
396C2×C42—42no—
397C2×C42—42no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—22no—
403#95—22no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—41no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—41no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—22no—
446C24—21no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24C2×#4112yes—
464C24H(5,𝔽2)12yes—
465C24H(5,𝔽2)12yes—
466C242−1+414yes—
467C24C2511yescharacteristic
468C2×D4—216no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—44no—
477C2×D4—82no—
478C2×D4—84no—
479C2×D4—82no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—28no—
494C22×C4—28no—
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—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—84no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4H(5,𝔽2)14yes—
609C22×C4H(5,𝔽2)14yes—
610C22×C4H(5,𝔽2)12yes—
611C22×C42−1+412yes—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—44no—
619C4⋊C4—48no—
620C4⋊C4—44no—
621C4⋊C4—82no—
622C4⋊C4—84no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—82no—
626C4⋊C4—84no—
627C4⋊C4—84no—
628C22⋊C4—48no—
629C22⋊C4—44no—
630C22⋊C4—44no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—84no—
645C22⋊C4—84no—
646C42—44no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42—48no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23#53814yes—
709C23C22×#4111yescharacteristic
710C23C22×#4111yescharacteristic
711C23C22×#4111yescharacteristic
712C23C2×H(5,𝔽2)11yescharacteristic
713C23C2×H(5,𝔽2)11yescharacteristic
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×H(5,𝔽2)12yes—
716C23C2×H(5,𝔽2)12yes—
717C23C2×2−1+411yescharacteristic
718C23C2×2−1+412yes—
719C23#58512yes—
720D4—432no—
721D4—88no—
722C2×C4—232no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—816no—
833C2×C4—816no—
834C2×C4#52914yes—
835C2×C4#53914yes—
836C22—24no—
837C22—28no—
838C22—42no—
839C22—42no—
840C22—44no—
841C22—42no—
842C22—42no—
843C22—44no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22C2×#52911yescharacteristic
863C22C2×#53811yescharacteristic
864C22C2×#53911yescharacteristic
865C22#349011yescharacteristic
866C22#349011yescharacteristic
867C22#349212yes—
868C22#349211yescharacteristic
869C22#349211yescharacteristic
870C22#350612yes—
871C22#351612yes—
872C22#351712yes—
873C22#351912yes—
874C22#352012yes—
875C22#353212yes—
876C22#353412yes—
877C22#353512yes—
878C22#353612yes—
879C22#353711yescharacteristic
880C22#353811yescharacteristic
881C22#354712yes—
882C22#354911yescharacteristic
883C22#355111yescharacteristic
884C22#355212yes—
885C4—24no—
886C4—24no—
887C4—44no—
888C4—44no—
889C4—42no—
890C4—42no—
891C4—44no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—81no—
900C4—81no—
901C4—82no—
902C2—44no—
903C2—84no—
904C2#3499711yescharacteristic
905C2#3572512yes—
906C2#3679112yes—
907C2#4250211yescharacteristic
908C2#4252211yescharacteristic
909C2#4714812yes—
910C2#4717111yescharacteristic
911C2#4717711yescharacteristic
912C2#5162911yescharacteristic
913C2#5183712yes—
914C2#5193011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #16932C2semidirect
2. #16881C2semidirect
3. #16877C2semidirect
4. #16417C2semidirect
5. #16369C2semidirect
6. #16219C2semidirect
7. #15870C2semidirect
8. #15329C2semidirect
9. #15305C2semidirect
10. #14893C2semidirect
11. #14888C2semidirect
13. #14801C2semidirect
15. #14603C2semidirect
16. #14535C2semidirect
17. #14398C2semidirect
18. #14015C2semidirect
19. #13795C2semidirect

Maximal subgroups

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

subgroupindex
#169322
#168812
#168772
#164172
#163692
#162192
#158702
#153292
#153052
#148932
#148882
#148862
#148012
#147322
#146032
#145352
#143982
#140152
#137952