Finite Group Databasebeta

← #846862

Subgroups — #846862

Order 512.

2722 conjugacy classes of subgroups.

The subgroup lattice has 973 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2583C211yesmaximal, characteristic
2C2×#2484C211yesmaximal, characteristic
3C2×#2438C211yesmaximal, characteristic
4C22×#382C211yesmaximal, characteristic
5#16524C212yesmaximal, complemented
6#16517C212yesmaximal, complemented
7#15767C212yesmaximal, complemented
8#15685C212yesmaximal, complemented
9#15437C212yesmaximal, complemented
10#15395C212yesmaximal, complemented
11#15092C211yesmaximal, characteristic
12#15073C211yesmaximal, characteristic
13#14936C211yesmaximal, characteristic
14#14935C211yesmaximal, characteristic
15#14934C211yesmaximal, characteristic
16#14919C211yesmaximal, characteristic
17#14697C211yesmaximal, characteristic
18#14695C211yesmaximal, characteristic
19#14404C212yesmaximal, complemented
20#14385C212yesmaximal, complemented
21#14128C211yesmaximal, characteristic
22#13972C211yesmaximal, characteristic
23#13874C211yesmaximal, characteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2583—28no—
30#2484—28no—
31#2438—28no—
32C2×#400C2212yes—
33C2×#400C2211yescharacteristic
34C2×#398C2212yes—
35C2×#398C2211yescharacteristic
36C2×#398C2211yescharacteristic
37C2×#398C2212yes—
38C2×#395C2212yes—
39C2×#395C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#389C2212yes—
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#389C2211yescharacteristic
45C2×#387C2211yescharacteristic
46C2×#387C2212yes—
47C2×#387C2211yescharacteristic
48C2×#387C2212yes—
49C2×#387C2212yes—
50C2×#385C2211yescharacteristic
51C2×#385C2211yescharacteristic
52C2×#385C2211yescharacteristic
53C2×#385C2211yescharacteristic
54C2×#385C2211yescharacteristic
55C2×#385C2211yescharacteristic
56C2×#385C2211yescharacteristic
57C2×#385C2211yescharacteristic
58C2×#382—28no—
59C2×#382C2212yes—
60C2×#382C2212yes—
61C2×#382C2212yes—
62C2×#382C2212yes—
63C2×#381C2211yescharacteristic
64C2×#381C2211yescharacteristic
65C2×#381C2211yescharacteristic
66C2×#381C2211yescharacteristic
67C2×#381C2211yescharacteristic
68C2×#381C2211yescharacteristic
69C2×#381C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C22×#95C2211yescharacteristic
74C22×#95C2211yescharacteristic
75C22×#95C2211yescharacteristic
76C22×#95C2211yescharacteristic
77#1446C2212yes—
78#1445C2212yes—
79#1445C2212yes—
80#1445C2212yes—
81#1445C2212yes—
82#1444C2212yes—
83#1444C2212yes—
84#1444C2212yes—
85#1444C2212yes—
86#1443C2212yes—
87#1443C2212yes—
88#1443C2212yes—
89#1443C2212yes—
90#1443C2212yes—
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#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2212yes—
115C4⋊#95C2212yes—
116#1434C2212yes—
117#1434C2212yes—
118#1434C2212yes—
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C23×Q8C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2311yescharacteristic
131C24×C4C2311yescharacteristic
132C24×C4C2311yescharacteristic
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C2×C22⋊Q8—24no—
136C2×C22⋊Q8—24no—
137C2×C22⋊Q8—42no—
138C2×#117—24no—
139C2×#117—24no—
140C2×#117—42no—
141C22×C4⋊C4—24no—
142C22×C4⋊C4—24no—
143C22×C4⋊C4—24no—
144C22×C4⋊C4—24no—
145C22×C4⋊C4—42no—
146C22×C4⋊C4—42no—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2311yescharacteristic
177C22×C42—24no—
178C22×C42—28no—
179C22×C42C2312yes—
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182C22×C42C2312yes—
183C22×C42C2312yes—
184#400—24no—
185#400—28no—
186#398—28no—
187#398—28no—
188#398—24no—
189#398—24no—
190#395—28no—
191#395—24no—
192#391—24no—
193#389—28no—
194#389—28no—
195#389—28no—
196#389—24no—
197#387—28no—
198#387—28no—
199#387—24no—
200#387—24no—
201#387—28no—
202#385—24no—
203#385—24no—
204#385—24no—
205#385—24no—
206#385—24no—
207#385—24no—
208#385—42no—
209#385D418yes—
210#382—28no—
211#382—28no—
212#382—28no—
213#382—28no—
214#381—24no—
215#381—24no—
216#381—24no—
217#381—24no—
218#381—24no—
219#381—24no—
220#381—42no—
221#380—24no—
222#380—24no—
223C4×C22⋊C4—24no—
224C2×#95—24no—
225C2×#95—24no—
226C2×#95—24no—
227C2×#95D418yes—
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C2×#95C2312yes—
232C2×#95C2311yescharacteristic
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2311yescharacteristic
236C2×#95C2312yes—
237C2×#95C2311yescharacteristic
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2311yescharacteristic
241C2×#95C2312yes—
242C2×#95C2311yescharacteristic
243C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2311yescharacteristic
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C25C2411yescharacteristic
285C22×Q8—22no—
286C22×Q8—22no—
287C22×Q8—41no—
288C22×Q8—42no—
289C22×Q8—42no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—22no—
305C23×C4—24no—
306C23×C4—24no—
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—42no—
320C23×C4—42no—
321C23×C4—42no—
322C23×C4—42no—
323C23×C4—42no—
324C23×C4—42no—
325C23×C4C2×D414yes—
326C23×C4C2×D414yes—
327C23×C4C2×D414yes—
328C23×C4C2×D414yes—
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2411yescharacteristic
332C23×C4C2411yescharacteristic
333C23×C4C2411yescharacteristic
334C23×C4C2412yes—
335C23×C4C2411yescharacteristic
336C23×C4C2412yes—
337C23×C4C2412yes—
338C23×C4C2412yes—
339C23×C4C2411yescharacteristic
340C23×C4C2411yescharacteristic
341C23×C4C2412yes—
342C23×C4C2411yescharacteristic
343C23×C4C2411yescharacteristic
344C23×C4C2411yescharacteristic
345C23×C4C2411yescharacteristic
346C23×C4C2411yescharacteristic
347C23×C4C2412yes—
348C23×C4C2412yes—
349C23×C4C2411yescharacteristic
350C23×C4C2412yes—
351C22⋊Q8—416no—
352#117—416no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—24no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—24no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—24no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—42no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4—42no—
395C2×C4⋊C4—42no—
396C2×C4⋊C4—42no—
397C2×C4⋊C4—41no—
398C2×C4⋊C4—41no—
399C2×C4⋊C4—41no—
400C2×C4⋊C4—41no—
401C2×C4⋊C4—41no—
402C2×C4⋊C4—416no—
403C2×C4⋊C4—416no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—42no—
407C2×C4⋊C4—42no—
408C2×C4⋊C4—42no—
409C2×C4⋊C4—42no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4C2×D418yes—
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×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4C2×D414yes—
437C2×C22⋊C4C2×D414yes—
438C2×C22⋊C4#4114yes—
439C2×C42—232no—
440C2×C42—24no—
441C2×C42—24no—
442C2×C42—24no—
443C2×C42—24no—
444C2×C42—24no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—24no—
450C2×C42—41no—
451C2×C42—41no—
452C2×C42—42no—
453C2×C42—42no—
454C2×C42#4118yes—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—24no—
462#95—22no—
463#95—22no—
464#95—24no—
465#95—22no—
466#95—24no—
467#95—24no—
468#95—24no—
469#95—24no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—24no—
474#95—22no—
475#95—22no—
476#95—24no—
477#95—22no—
478#95—24no—
479#95—24no—
480#95—24no—
481#95—22no—
482#95—24no—
483#95—24no—
484#95—24no—
485#95—24no—
486#95—24no—
487#95—24no—
488#95—24no—
489#95—24no—
490#95—24no—
491#95—24no—
492#95—24no—
493#95—24no—
494#95—42no—
495#95—42no—
496#95—42no—
497#95—42no—
498#95—42no—
499#95—42no—
500#95—42no—
501#95—42no—
502#95—42no—
503#95—42no—
504#95—42no—
505#95—42no—
506#95C2×D414yes—
507#95C2×D414yes—
508#95C2×D414yes—
509#95C2×D414yes—
510#95C2×D418yes—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24C22×D412yes—
516C24C22×D412yes—
517C24C2×#4112yes—
518C24H(5,𝔽2)12yes—
519C242−1+412yes—
520C242−1+412yes—
521C242−1+412yes—
522C24C2511yescharacteristic
523C2×Q8—44no—
524C2×Q8—44no—
525C2×Q8—82no—
526C2×Q8—84no—
527C2×Q8—84no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—216no—
531C22×C4—28no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—216no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
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—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
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—28no—
596C22×C4—28no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—21no—
633C22×C4—21no—
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—44no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—48no—
659C22×C4—48no—
660C22×C4—48no—
661C22×C4—48no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—84no—
679C22×C4—84no—
680C22×C4—84no—
681C22×C4—84no—
682C22×C4C22×D414yes—
683C22×C4C22×D412yes—
684C22×C4C22×D412yes—
685C22×C4C22×D412yes—
686C22×C4C22×D412yes—
687C22×C4C22×D412yes—
688C22×C4C22×D412yes—
689C22×C4C22×D412yes—
690C22×C4C22×D412yes—
691C22×C4C22×D414yes—
692C22×C4C2×#4114yes—
693C22×C4C2×#4114yes—
694C22×C4C2×#4114yes—
695C22×C4C2×#4114yes—
696C22×C42−1+414yes—
697C4⋊C4—216no—
698C4⋊C4—48no—
699C4⋊C4—48no—
700C4⋊C4—48no—
701C4⋊C4—48no—
702C4⋊C4—48no—
703C4⋊C4—44no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C4⋊C4—44no—
707C4⋊C4—44no—
708C4⋊C4—44no—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—48no—
712C4⋊C4—48no—
713C4⋊C4—82no—
714C4⋊C4—82no—
715C4⋊C4—82no—
716C4⋊C4—84no—
717C4⋊C4—84no—
718C4⋊C4—84no—
719C22⋊C4—28no—
720C22⋊C4—28no—
721C22⋊C4—28no—
722C22⋊C4—44no—
723C22⋊C4—44no—
724C22⋊C4—44no—
725C22⋊C4—44no—
726C22⋊C4—44no—
727C42—216no—
728C42—216no—
729C42—44no—
730C42—44no—
731C42—84no—
732C23—22no—
733C23—22no—
734C23—24no—
735C23—24no—
736C23—22no—
737C23—22no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23#53614yes—
749C23#53614yes—
750C23#54214yes—
751C23D4214yes—
752C23#54714yes—
753C23#54814yes—
754C23#56314yes—
755C23C23×D411yescharacteristic
756C23C23×D411yescharacteristic
757C23C22×#4112yes—
758C23C22×#4111yescharacteristic
759C23C2×H(5,𝔽2)11yescharacteristic
760C23C2×2−1+411yescharacteristic
761C23C2×2−1+411yescharacteristic
762C23C2×2−1+411yescharacteristic
763C23C2×2−1+412yes—
764C23#58512yes—
765C23#58512yes—
766Q8—88no—
767C2×C4—232no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—416no—
807C2×C4—416no—
808C2×C4—41no—
809C2×C4—416no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—41no—
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—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—42no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
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—88no—
901C2×C4—88no—
902C2×C4#52514yes—
903C2×C4#54718yes—
904C22—24no—
905C22—28no—
906C22—28no—
907C22—24no—
908C22—24no—
909C22—24no—
910C22—28no—
911C22—28no—
912C22—24no—
913C22—24no—
914C22#267418yes—
915C22C2×#52511yescharacteristic
916C22C2×#53611yescharacteristic
917C22C2×#53611yescharacteristic
918C22#344911yescharacteristic
919C22C2×#54211yescharacteristic
920C22C2×D4211yescharacteristic
921C22C2×#54712yes—
922C22C2×#54711yescharacteristic
923C22C2×#54811yescharacteristic
924C22#347512yes—
925C22#348511yescharacteristic
926C22#348611yescharacteristic
927C22#349212yes—
928C22#349512yes—
929C22#349512yes—
930C22#349512yes—
931C22#350012yes—
932C22#351512yes—
933C22C2×#56311yescharacteristic
934C22#354512yes—
935C22#356312yes—
936C22#356312yes—
937C22#356312yes—
938C4—28no—
939C4—24no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—42no—
945C4—42no—
946C4—44no—
947C4—44no—
948C4—42no—
949C4—44no—
950C4—81no—
951C4—81no—
952C4—82no—
953C4—82no—
954C4—81no—
955C4—81no—
956C4—82no—
957C4—81no—
958C4—82no—
959C4—81no—
960C2—28no—
961C2#3532511yescharacteristic
962C2#3610311yescharacteristic
963C2#3634111yescharacteristic
964C2#3695911yescharacteristic
965C2#3786512yes—
966C2#3790712yes—
967C2#3804511yescharacteristic
968C2#3933311yescharacteristic
969C2#4614512yes—
970C2C2×#267411yescharacteristic
971C2#5931712yes—
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
5. #16524C2semidirect
6. #16517C2semidirect
7. #15767C2semidirect
8. #15685C2semidirect
9. #15437C2semidirect
10. #15395C2semidirect
19. #14404C2semidirect
20. #14385C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25832
C2×#24842
C2×#24382
C22×#3822
#165242
#165172
#157672
#156852
#154372
#153952
#150922
#150732
#149362
#149352
#149342
#149192
#146972
#146952
#144042
#143852
#141282
#139722
#138742