Finite Group Databasebeta

← #917583

Subgroups — #917583

Order 512.

2774 conjugacy classes of subgroups.

The subgroup lattice has 971 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2493C211yesmaximal, characteristic
2C22×#395C211yesmaximal, characteristic
3#17155C212yesmaximal, complemented
4#17154C212yesmaximal, complemented
5#16833C212yesmaximal, complemented
6#16826C212yesmaximal, complemented
7#16669C212yesmaximal, complemented
8#16475C212yesmaximal, complemented
9#15861C212yesmaximal, complemented
10#15592C212yesmaximal, complemented
11#15073C211yesmaximal, characteristic
12#15073C211yesmaximal, characteristic
13#15073C211yesmaximal, characteristic
14#15073C211yesmaximal, characteristic
15#14936C211yesmaximal, characteristic
16#14935C211yesmaximal, characteristic
17#14336C211yesmaximal, characteristic
18#14336C211yesmaximal, characteristic
19#13992C211yesmaximal, characteristic
20#13972C211yesmaximal, characteristic
21#13904C211yesmaximal, characteristic
22#13904C211yesmaximal, characteristic
23#13874C211yesmaximal, characteristic
24C24×Q8C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#2493—28no—
29C2×#401C2211yescharacteristic
30C2×#400C2211yescharacteristic
31C2×#400C2211yescharacteristic
32C2×#400C2211yescharacteristic
33C2×#395—28no—
34C2×#395C2212yes—
35C2×#395C2212yes—
36C2×#395C2212yes—
37C2×#395C2212yes—
38C2×#387C2211yescharacteristic
39C2×#387C2211yescharacteristic
40C2×#387C2211yescharacteristic
41C2×#385C2211yescharacteristic
42C2×#385C2211yescharacteristic
43C2×#385C2211yescharacteristic
44C2×#385C2211yescharacteristic
45C2×#383C2211yescharacteristic
46C2×#381C2211yescharacteristic
47C2×#381C2211yescharacteristic
48C2×#381C2211yescharacteristic
49C2×#381C2211yescharacteristic
50C2×#381C2211yescharacteristic
51C2×#381C2211yescharacteristic
52C2×#381C2211yescharacteristic
53C2×#381C2211yescharacteristic
54C2×#381C2211yescharacteristic
55C2×#381C2211yescharacteristic
56C2×#381C2211yescharacteristic
57C2×#381C2211yescharacteristic
58C2×#381C2211yescharacteristic
59C2×#381C2211yescharacteristic
60C2×#381C2211yescharacteristic
61C2×#381C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C22×#95C2211yescharacteristic
67C22×#95C2211yescharacteristic
68C22×#95C2211yescharacteristic
69#1446C2212yes—
70#1446C2212yes—
71#1446C2212yes—
72#1446C2212yes—
73#1446C2212yes—
74#1446C2212yes—
75#1446C2212yes—
76#1446C2212yes—
77#1445C2212yes—
78#1445C2212yes—
79#1445C2212yes—
80#1445C2212yes—
81#1445C2212yes—
82#1445C2212yes—
83#1445C2212yes—
84#1444C2212yes—
85#1443C2212yes—
86#1443C2212yes—
87#1443C2212yes—
88#1443C2212yes—
89#1442C2212yes—
90#1442C2212yes—
91#1442C2212yes—
92#1442C2212yes—
93#1442C2212yes—
94#1442C2212yes—
95#1442C2212yes—
96#1442C2212yes—
97#1442C2212yes—
98#1442C2212yes—
99#1442C2212yes—
100#1441C2212yes—
101#1441C2212yes—
102#1441C2212yes—
103#1441C2212yes—
104#1441C2212yes—
105#1441C2212yes—
106#1441C2212yes—
107#1441C2212yes—
108#1441C2212yes—
109#1441C2212yes—
110#1441C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114C4⋊#95C2212yes—
115C4⋊#95C2212yes—
116C4⋊#95C2212yes—
117C4⋊#95C2212yes—
118#1434C2212yes—
119#1434C2212yes—
120#1434C2212yes—
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C23×Q8—24no—
126C23×Q8—24no—
127C23×Q8—24no—
128C23×Q8—42no—
129C23×Q8—42no—
130C23×Q8—42no—
131C23×Q8—42no—
132C23×Q8C2312yes—
133C23×Q8C2312yes—
134C24×C4C2311yescharacteristic
135C24×C4C2311yescharacteristic
136C24×C4C2311yescharacteristic
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C22×C4⋊C4—24no—
142C22×C4⋊C4—24no—
143C22×C4⋊C4—24no—
144C22×C4⋊C4—24no—
145C22×C4⋊C4—24no—
146C22×C4⋊C4—42no—
147C22×C4⋊C4—42no—
148C22×C4⋊C4—42no—
149C22×C4⋊C4—42no—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2312yes—
175C22×C42C2311yescharacteristic
176#401—24no—
177#400—24no—
178#400—24no—
179#400—24no—
180#395—28no—
181#395—28no—
182#395—28no—
183#395—28no—
184#387—24no—
185#387—24no—
186#387—24no—
187#385—24no—
188#385—24no—
189#385—42no—
190#385—42no—
191#383—24no—
192#381—24no—
193#381—24no—
194#381—24no—
195#381—24no—
196#381—42no—
197#381—42no—
198#381—42no—
199#381—42no—
200#381—42no—
201#381—42no—
202#381—42no—
203#381—42no—
204#381—42no—
205#381—42no—
206#381—42no—
207#381—42no—
208#380—24no—
209#380—42no—
210C4×C22⋊C4—24no—
211C4×C22⋊C4—42no—
212C2×#95—24no—
213C2×#95—24no—
214C2×#95D418yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C2×#95C2311yescharacteristic
232C2×#95C2311yescharacteristic
233C2×#95C2311yescharacteristic
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2311yescharacteristic
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C25C2411yescharacteristic
280C22×Q8—24no—
281C22×Q8—24no—
282C22×Q8—24no—
283C22×Q8—24no—
284C22×Q8—24no—
285C22×Q8—24no—
286C22×Q8—42no—
287C22×Q8—42no—
288C22×Q8—42no—
289C22×Q8—42no—
290C22×Q8—42no—
291C22×Q8—42no—
292C22×Q8—42no—
293C22×Q8—42no—
294C22×Q8—416no—
295C22×Q8—416no—
296C22×Q8—416no—
297C22×Q8—416no—
298C22×Q8—416no—
299C22×Q8—416no—
300C22×Q8—416no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—22no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—22no—
310C23×C4—22no—
311C23×C4—22no—
312C23×C4—22no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—22no—
316C23×C4—22no—
317C23×C4—22no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—22no—
322C23×C4—22no—
323C23×C4—22no—
324C23×C4—24no—
325C23×C4—24no—
326C23×C4—24no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—22no—
331C23×C4—22no—
332C23×C4—22no—
333C23×C4—22no—
334C23×C4—22no—
335C23×C4—22no—
336C23×C4—42no—
337C23×C4—42no—
338C23×C4—42no—
339C23×C4C2×D414yes—
340C23×C4C2×D414yes—
341C23×C4C2×D414yes—
342C23×C4#4114yes—
343C23×C4#4114yes—
344C23×C4C2411yescharacteristic
345C23×C4C2411yescharacteristic
346C23×C4C2411yescharacteristic
347C23×C4C2411yescharacteristic
348C23×C4C2412yes—
349C23×C4C2411yescharacteristic
350C23×C4C2411yescharacteristic
351C23×C4C2412yes—
352C23×C4C2411yescharacteristic
353C23×C4C2412yes—
354C23×C4C2411yescharacteristic
355C23×C4C2412yes—
356C23×C4C2412yes—
357C23×C4C2411yescharacteristic
358C23×C4C2411yescharacteristic
359C23×C4C2411yescharacteristic
360C23×C4C2411yescharacteristic
361C23×C4C2412yes—
362C23×C4C2412yes—
363C23×C4C2412yes—
364C23×C4C2411yescharacteristic
365C23×C4C2411yescharacteristic
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—42no—
389C2×C4⋊C4—42no—
390C2×C4⋊C4—42no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—416no—
397C2×C4⋊C4—416no—
398C2×C4⋊C4—416no—
399C2×C4⋊C4—42no—
400C2×C4⋊C4—42no—
401C2×C4⋊C4—42no—
402C2×C4⋊C4—42no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—22no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—22no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—22no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—22no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C42—22no—
433C2×C42—24no—
434C2×C42—22no—
435C2×C42—24no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42—42no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95—24no—
463#95—24no—
464#95—24no—
465#95—24no—
466#95—24no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95—42no—
472#95—42no—
473#95—42no—
474#95—42no—
475#95—42no—
476#95—42no—
477#95—42no—
478#95—42no—
479#95—42no—
480#95—42no—
481#95—42no—
482#95—42no—
483#95—42no—
484#95—42no—
485#95—42no—
486#95—42no—
487#95—42no—
488#95—42no—
489#95—42no—
490#95—42no—
491#95—42no—
492#95—42no—
493#95—42no—
494#95—42no—
495#95—42no—
496#95—42no—
497#95—42no—
498#95—42no—
499#95C2×D414yes—
500#95C2×D414yes—
501#95C2×D414yes—
502#95C2×D414yes—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24C22×D412yes—
508C24C2×#4112yes—
509C24C2×#4112yes—
510C24H(5,𝔽2)12yes—
511C24H(5,𝔽2)12yes—
512C24H(5,𝔽2)12yes—
513C24H(5,𝔽2)12yes—
514C24C2511yescharacteristic
515C2×Q8—48no—
516C2×Q8—48no—
517C2×Q8—48no—
518C2×Q8—48no—
519C2×Q8—48no—
520C2×Q8—48no—
521C2×Q8—48no—
522C2×Q8—48no—
523C2×Q8—48no—
524C2×Q8—48no—
525C2×Q8—48no—
526C2×Q8—48no—
527C2×Q8—4128no—
528C2×Q8—48no—
529C2×Q8—48no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
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—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
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—28no—
587C22×C4—28no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
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—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—48no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—48no—
669C22×C4—48no—
670C22×C4—48no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4C22×D412yes—
693C22×C4C22×D412yes—
694C22×C4C22×D412yes—
695C22×C4C22×D412yes—
696C22×C4C22×D412yes—
697C22×C4C22×D412yes—
698C22×C4C2×#4114yes—
699C22×C4C2×#4114yes—
700C22×C42−1+414yes—
701C22×C42−1+414yes—
702C22×C42−1+414yes—
703C4⋊C4—48no—
704C4⋊C4—48no—
705C4⋊C4—48no—
706C4⋊C4—48no—
707C4⋊C4—48no—
708C4⋊C4—48no—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—44no—
712C4⋊C4—82no—
713C4⋊C4—84no—
714C4⋊C4—82no—
715C4⋊C4—82no—
716C4⋊C4—84no—
717C4⋊C4—84no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—44no—
721C22⋊C4—44no—
722C22⋊C4—44no—
723C22⋊C4—44no—
724C22⋊C4—44no—
725C22⋊C4—44no—
726C42—44no—
727C42—82no—
728C42—84no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23#53514yes—
746C23#53814yes—
747C23#53814yes—
748C23#54614yes—
749C23#54614yes—
750C23#55114yes—
751C23#56014yes—
752C23C23×D411yescharacteristic
753C23C22×#4111yescharacteristic
754C23C22×#4111yescharacteristic
755C23C2×H(5,𝔽2)11yescharacteristic
756C23C2×H(5,𝔽2)11yescharacteristic
757C23C2×H(5,𝔽2)11yescharacteristic
758C23C2×H(5,𝔽2)11yescharacteristic
759C23C2×2−1+412yes—
760C23C2×2−1+412yes—
761C23C2×2−1+412yes—
762C23#58512yes—
763Q8—432no—
764Q8—432no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—416no—
795C2×C4—416no—
796C2×C4—416no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—416no—
807C2×C4—416no—
808C2×C4—416no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
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—41no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
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—88no—
900C2×C4#53614yes—
901C2×C4#53614yes—
902C22—24no—
903C22—24no—
904C22—24no—
905C22—28no—
906C22—28no—
907C22—28no—
908C22—24no—
909C22—24no—
910C22—28no—
911C22—24no—
912C22#268518yes—
913C22C2×#53511yescharacteristic
914C22C2×#53611yescharacteristic
915C22C2×#53611yescharacteristic
916C22C2×#53811yescharacteristic
917C22C2×#53811yescharacteristic
918C22C2×#54611yescharacteristic
919C22C2×#54611yescharacteristic
920C22C2×#55111yescharacteristic
921C22#348511yescharacteristic
922C22#348611yescharacteristic
923C22#349512yes—
924C22#349512yes—
925C22#350912yes—
926C22#350912yes—
927C22C2×#56011yescharacteristic
928C22#353512yes—
929C22#353512yes—
930C22#353512yes—
931C22#353512yes—
932C22#354412yes—
933C22#354412yes—
934C22#354412yes—
935C22#354412yes—
936C4—24no—
937C4—24no—
938C4—42no—
939C4—42no—
940C4—44no—
941C4—44no—
942C4—42no—
943C4—42no—
944C4—44no—
945C4—81no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4—82no—
950C4—82no—
951C4—82no—
952C4—82no—
953C4—82no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—28no—
959C2#3711811yescharacteristic
960C2#3763211yescharacteristic
961C2#3783511yescharacteristic
962C2#3783511yescharacteristic
963C2#3946511yescharacteristic
964C2#3946511yescharacteristic
965C2#4231912yes—
966C2#4231912yes—
967C2#4479512yes—
968C2C2×#268511yescharacteristic
969C2#5291312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #17155C2semidirect
4. #17154C2semidirect
5. #16833C2semidirect
6. #16826C2semidirect
7. #16669C2semidirect
8. #16475C2semidirect
9. #15861C2semidirect
10. #15592C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24932
C22×#3952
#171552
#171542
#168332
#168262
#166692
#164752
#158612
#155922
#150732
#149362
#149352
#143362
#139922
#139722
#139042
#138742