Finite Group Databasebeta

← #921973

Subgroups — #921973

Order 512.

3148 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2579C211yesmaximal, characteristic, complemented
2C2×#2388C211yesmaximal, characteristic
3#17099C212yesmaximal, complemented
4#17092C212yesmaximal, complemented
5#16851C212yesmaximal, complemented
6#16467C212yesmaximal, complemented
7#16270C212yesmaximal, complemented
8#16266C212yesmaximal, complemented
9#15635C211yesmaximal, characteristic, complemented
10#15622C211yesmaximal, characteristic, complemented
11#15568C211yesmaximal, characteristic, complemented
12#15420C211yesmaximal, characteristic, complemented
13#14925C212yesmaximal, complemented
14#14889C212yesmaximal, complemented
15#14825C212yesmaximal, complemented
16#14304C212yesmaximal, complemented
17#14080C212yesmaximal, complemented
18#14015C212yesmaximal, complemented
19#13959C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24#2579—28no—
25C2×#400C2212yes—
26C2×#399C2212yes—
27C2×#398C2212yes—
28C2×#397C2212yes—
29C2×#396C2212yes—
30#2388—28no—
31C2×#395C2211yescharacteristic
32C2×#395C2212yes—
33C2×#394C2212yes—
34C2×#394C2211yescharacteristic
35C2×#394C2212yes—
36C2×#394C2212yes—
37C2×#394C2212yes—
38C2×#393C2211yescharacteristic
39C2×#392C2211yescharacteristic
40C2×#392C2212yes—
41C2×#388C2212yes—
42C2×#387C2212yes—
43C2×#386C2211yescharacteristic
44C2×#386C2211yescharacteristic
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#385C2211yescharacteristic
48C2×#385C2212yes—
49C2×#385C2211yescharacteristic
50C2×#385C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#383C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×#376C2211yescharacteristic
58#1446C2212yes—
59#1445C2212yes—
60#1445C2212yes—
61#1444C2212yes—
62#1444C2212yes—
63#1443C2212yes—
64#1443C2212yes—
65#1443C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1441C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1440C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1438C2212yes—
88#1438C2212yes—
89#1438C2212yes—
90#1438C2212yes—
91#1438C2212yes—
92#1438C2212yes—
93#1437C2212yes—
94#1437C2211yescharacteristic
95#1437C2211yescharacteristic
96#1437C2211yescharacteristic
97#1437C2211yescharacteristic
98#1436C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103C4⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2212yes—
109C22×#41—24no—
110C22×#41—42no—
111C22×#41—42no—
112C22×#41—44no—
113C22×#41—44no—
114C23×Q8C2311yescharacteristic
115C23×D4C2312yes—
116C23×D4C2311yescharacteristic
117C23×D4C2312yes—
118C23×D4C2311yescharacteristic
119C24×C4C2312yes—
120C24×C4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C24×C4C2311yescharacteristic
123C24×C4C2311yescharacteristic
124C2×C4×D4—28no—
125C2×C4×D4—42no—
126C2×C4×D4—42no—
127C2×C4×D4—44no—
128C2×C4×D4—44no—
129C2×C4×D4D418yes—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—42no—
132C22×C4⋊C4—42no—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
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×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2312yes—
170C22×C42C2311yescharacteristic
171#400—44no—
172#399—44no—
173#398—28no—
174#397—28no—
175#396—28no—
176#395—24no—
177#395—44no—
178#394—24no—
179#394—28no—
180#394—44no—
181#394—44no—
182#394—44no—
183#393—24no—
184#392—28no—
185#392—24no—
186#388—28no—
187#387—28no—
188#386—24no—
189#386—24no—
190#386—28no—
191#386—44no—
192#385—28no—
193#385—24no—
194#385—24no—
195#385—44no—
196#385—44no—
197#385—44no—
198#383—42no—
199#380—24no—
200C4×C22⋊C4—24no—
201C4×C22⋊C4—28no—
202#376—42no—
203C2×#95C2311yescharacteristic
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
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—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2311yescharacteristic
238C2×#95C2311yescharacteristic
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C25C2411yescharacteristic
243C25C2412yes—
244C25C2411yescharacteristic
245C2×#41—432no—
246C2×#41—416no—
247C2×#41—416no—
248C2×#41—432no—
249C2×#41—416no—
250C22×Q8—22no—
251C22×Q8—24no—
252C22×Q8—41no—
253C22×Q8—41no—
254C22×Q8—42no—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—24no—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4—24no—
263C22×D4—22no—
264C22×D4—24no—
265C22×D4—24no—
266C22×D4—41no—
267C22×D4—41no—
268C22×D4—42no—
269C22×D4—42no—
270C22×D4—42no—
271C22×D4—42no—
272C22×D4—42no—
273C22×D4—42no—
274C22×D4—42no—
275C22×D4—42no—
276C22×D4—41no—
277C22×D4—41no—
278C22×D4C2×D414yes—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—41no—
292C23×C4—41no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—41no—
299C23×C4—41no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4C2×D414yes—
305C23×C4C2×D414yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2411yescharacteristic
322C4×D4—416no—
323C4×D4—432no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—41no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—416no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4C2×D414yes—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—42no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4C2×D414yes—
424C2×C22⋊C4C2×D414yes—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—24no—
429C2×C42—42no—
430C2×C42—42no—
431C2×C42—41no—
432C2×C42—41no—
433C2×C42—42no—
434C2×C42C2×D414yes—
435#95—22no—
436#95—24no—
437#95—24no—
438#95—22no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—41no—
457#95—41no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—42no—
465#95—42no—
466#95—42no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95—42no—
472#95—42no—
473#95#4118yescomplemented
474C24—22no—
475C24—22no—
476C24—22no—
477C24—21no—
478C24—21no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—21no—
492C24—21no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24C22×D412yes—
504C24C22×D412yes—
505C24H(5,𝔽2)14yes—
506C242−1+414yes—
507C24C2511yescharacteristic
508#41—4128no—
509C2×Q8—48no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—48no—
513C2×Q8—44no—
514C2×D4—216no—
515C2×D4—28no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—48no—
519C2×D4—48no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—44no—
524C2×D4—48no—
525C2×D4—48no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—44no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—44no—
537C2×D4—48no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—216no—
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—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
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—28no—
582C22×C4—28no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—48no—
633C22×C4—44no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—48no—
639C22×C4—48no—
640C22×C4—48no—
641C22×C4—48no—
642C22×C4—44no—
643C22×C4—48no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—48no—
648C22×C4—44no—
649C22×C4—82no—
650C22×C4—84no—
651C22×C4—82no—
652C22×C4—84no—
653C22×C4—82no—
654C22×C4—84no—
655C22×C4—82no—
656C22×C4C22×D412yes—
657C22×C4C22×D412yes—
658C22×C4C22×D412yes—
659C22×C4C22×D412yes—
660C22×C4C22×D412yes—
661C22×C4C2×#4114yes—
662C22×C4C2×#4114yes—
663C22×C4C2×#4114yes—
664C22×C4H(5,𝔽2)14yes—
665C22×C4H(5,𝔽2)12yes—
666C22×C4H(5,𝔽2)12yes—
667C4⋊C4—44no—
668C4⋊C4—48no—
669C4⋊C4—48no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—84no—
673C4⋊C4—84no—
674C4⋊C4—84no—
675C4⋊C4—84no—
676C4⋊C4—84no—
677C4⋊C4—84no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—48no—
686C22⋊C4—48no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—84no—
693C22⋊C4—84no—
694C22⋊C4—84no—
695C22⋊C4—84no—
696C22⋊C4—84no—
697C22⋊C4—84no—
698C22⋊C4—84no—
699C22⋊C4—84no—
700C22⋊C4—84no—
701C42—28no—
702C42—44no—
703C42—48no—
704C42—44no—
705C23—22no—
706C23—22no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—42no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—41no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—41no—
760C23—41no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—41no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23#53614yes—
782C23C23×D411yescharacteristic
783C23C22×#4112yes—
784C23C2×H(5,𝔽2)11yescharacteristic
785C23C2×H(5,𝔽2)11yescharacteristic
786C23C2×H(5,𝔽2)12yes—
787C23C2×H(5,𝔽2)12yes—
788C23C2×2−1+412yes—
789C23#58512yes—
790C23#58512yes—
791Q8—416no—
792D4—416no—
793D4—432no—
794D4—416no—
795D4—432no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—432no—
822C2×C4—416no—
823C2×C4—416no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—41no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—88no—
901C2×C4—88no—
902C2×C4#53414yes—
903C22—24no—
904C22—28no—
905C22—44no—
906C22—42no—
907C22—44no—
908C22—44no—
909C22—42no—
910C22—44no—
911C22—44no—
912C22—44no—
913C22—44no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—42no—
920C22—44no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—82no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22C2×#53411yescharacteristic
937C22C2×#53611yescharacteristic
938C22#344911yescharacteristic
939C22#346012yes—
940C22D4×#4112yes—
941C22#348111yescharacteristic
942C22#348412yes—
943C22#349212yes—
944C22#349412yes—
945C22#351712yes—
946C22#352012yes—
947C22#352911yescharacteristic
948C22#353211yescharacteristic
949C22#353212yes—
950C22#353211yescharacteristic
951C22#353512yes—
952C22#354112yes—
953C22#354112yes—
954C22#354112yes—
955C22#356012yes—
956C22#356212yes—
957C4—24no—
958C4—42no—
959C4—42no—
960C4—44no—
961C4—42no—
962C4—44no—
963C4—42no—
964C4—44no—
965C4—44no—
966C4—82no—
967C4—82no—
968C4—82no—
969C4—82no—
970C4—82no—
971C4—82no—
972C4—82no—
973C2—44no—
974C2—84no—
975C2—82no—
976C2#3671411yescharacteristic
977C2#3743811yescharacteristic
978C2#3835912yes—
979C2#3837312yes—
980C2#4098212yes—
981C2#4118212yes—
982C2#4422412yes—
983C2#5216511yescharacteristic
984C2#5240112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2388C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2579C2semidirect
3. #17099C2semidirect
4. #17092C2semidirect
5. #16851C2semidirect
6. #16467C2semidirect
7. #16270C2semidirect
8. #16266C2semidirect
9. #15635C2semidirect
10. #15622C2semidirect
11. #15568C2semidirect
12. #15420C2semidirect
13. #14925C2semidirect
14. #14889C2semidirect
15. #14825C2semidirect
16. #14304C2semidirect
17. #14080C2semidirect
18. #14015C2semidirect
19. #13959C2semidirect
473. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25792
C2×#23882
#170992
#170922
#168512
#164672
#162702
#162662
#156352
#156222
#155682
#154202
#149252
#148892
#148252
#143042
#140802
#140152
#139592