Finite Group Databasebeta

← #4457337

Subgroups — #4457337

Order 512.

2236 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2565C211yesmaximal, characteristic, complemented
2C2×#2611C211yesmaximal, characteristic
3C2×#2599C211yesmaximal, characteristic
4C2×#2314C211yesmaximal, characteristic
5#17061C211yesmaximal, characteristic, complemented
6#17060C211yesmaximal, characteristic
7#16806C211yesmaximal, characteristic, complemented
8#16805C211yesmaximal, characteristic
9#16804C211yesmaximal, characteristic, complemented
10#16803C211yesmaximal, characteristic
11#16705C211yesmaximal, characteristic, complemented
12#16701C211yesmaximal, characteristic
13#16688C212yesmaximal, complemented
14#16563C212yesmaximal, complemented
15#16561C212yesmaximal
16#16561C212yesmaximal
17#15005C212yesmaximal, complemented
18#14988C212yesmaximal
19#14970C212yesmaximal
20#14967C212yesmaximal, complemented
21#14289C211yesmaximal, characteristic, complemented
22#13964C211yesmaximal, characteristic, complemented
23#13850C211yesmaximal, characteristic, complemented
24C22×#125C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#2611—28no—
28#2599—28no—
29#2565—28no—
30C2×#400C2211yescharacteristic
31C2×#399C2211yescharacteristic
32C2×#398C2212yes—
33C2×#398C2211yescharacteristic
34C2×#398C2211yescharacteristic
35C2×#398C2212yes—
36C2×#397C2211yescharacteristic
37C2×#397C2211yescharacteristic
38C2×#395C2211yescharacteristic
39C2×#393C2211yescharacteristic
40#2314—28no—
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#389C2212yes—
44C2×#388C2212yes—
45C2×#388C2212yes—
46C2×#388C2211yescharacteristic
47C2×#388C2211yescharacteristic
48C2×#388C2211yescharacteristic
49C2×#388C2211yescharacteristic
50C2×#387C2212yes—
51C2×#387C2212yes—
52C2×#387C2212yes—
53C2×#387C2211yescharacteristic
54C2×#387C2212yes—
55C2×#387C2212yes—
56C2×#387C2211yescharacteristic
57C2×#387C2211yescharacteristic
58C2×#387C2211yescharacteristic
59C2×#385C2212yes—
60C2×#385C2212yes—
61C2×#384C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C2×#383C2211yescharacteristic
64C2×#382C2211yescharacteristic
65C2×#382C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#380C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×#376C2211yescharacteristic
71#1446C2211yescharacteristic
72#1446C2211yescharacteristic
73#1445C2211yescharacteristic
74#1445C2211yescharacteristic
75#1445C2211yescharacteristic
76#1445C2211yescharacteristic
77#1445C2211yescharacteristic
78#1445C2211yescharacteristic
79#1444C2212yes—
80#1444C2212yes—
81#1443C2212yes—
82#1443C2212yes—
83#1443C2212yes—
84#1443C2212yes—
85#1442C2212yes—
86#1442C2212yes—
87#1442C2212yes—
88#1442C2212yes—
89#1442C2212yes—
90#1442C2212yes—
91#1441C2212yes—
92#1441C2212yes—
93#1441C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2212yes—
98#1441C2212yes—
99#1441C2212yes—
100#1441C2212yes—
101#1441C2212yes—
102#1441C2212yes—
103#1441C2212yes—
104#1441C2212yes—
105#1441C2212yes—
106#1441C2212yes—
107#1441C2212yes—
108#1441C2212yes—
109#1440C2212yes—
110#1440C2212yes—
111#1440C2212yes—
112#1440C2212yes—
113#1439C2212yes—
114#1439C2212yes—
115#1439C2212yes—
116#1439C2212yes—
117#1436C2212yes—
118#1436C2212yes—
119#1436C2212yes—
120#1436C2212yes—
121C4⋊#95C2211yescharacteristic
122C4⋊#95C2211yescharacteristic
123#1434C2211yescharacteristic
124#1434C2211yescharacteristic
125C4×#95C2212yes—
126C4×#95C2212yes—
127C23×Q8C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C2×#125—24no—
130C2×#125—24no—
131C2×#125—24no—
132C2×C4×Q8—24no—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×#117—24no—
136C2×#117—24no—
137C2×#117D418yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2311yescharacteristic
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180#400—24no—
181#399—24no—
182#398—28no—
183#398—28no—
184#398—24no—
185#398—24no—
186#397—24no—
187#397—24no—
188#395—24no—
189#393—24no—
190#391—24no—
191#391—24no—
192#389—28no—
193#388—28no—
194#388—28no—
195#388—24no—
196#388—24no—
197#388—24no—
198#388—24no—
199#387—28no—
200#387—24no—
201#387—24no—
202#387—28no—
203#387—28no—
204#387—28no—
205#387—28no—
206#387—24no—
207#387—24no—
208#385—28no—
209#385—28no—
210#384—24no—
211#384—24no—
212#383—24no—
213#382—24no—
214#382—24no—
215#380—24no—
216#380—24no—
217C4×C4⋊C4—24no—
218C4×C4⋊C4D418yes—
219#376—24no—
220C2×#95C2311yescharacteristic
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2312yes—
224C2×#95C2311yescharacteristic
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2311yescharacteristic
245C2×#95C2311yescharacteristic
246C2×#95C2311yescharacteristic
247C2×#95C2311yescharacteristic
248C2×#95C2311yescharacteristic
249C2×#95C2311yescharacteristic
250C2×#95C2311yescharacteristic
251C2×#95C2311yescharacteristic
252C2×#95C2311yescharacteristic
253C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
274C2×#95C2311yescharacteristic
275C25C2411yescharacteristic
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—22no—
279C22×Q8—24no—
280C22×Q8—42no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—41no—
284C23×C4—41no—
285C23×C4—41no—
286C23×C4—41no—
287C23×C4C2×D414yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310#125—416no—
311C4×Q8—416no—
312#117—232no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
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—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—41no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—41no—
359C2×C4⋊C4—41no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2×D414yes—
379C2×C4⋊C4C2×D414yes—
380C2×C4⋊C4C2×D414yes—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
406C2×C22⋊C4C2×D414yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—42no—
419C2×C42—42no—
420C2×C42—42no—
421C2×C42C2×D414yes—
422C2×C42C2×D414yes—
423C2×C42C2×D414yes—
424C2×C42C2×D414yes—
425C2×C42C2×D414yes—
426C2×C42#4114yes—
427#95—24no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—22no—
445#95—22no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—24no—
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—42no—
474#95—42no—
475#95—42no—
476#95—42no—
477#95—42no—
478#95—42no—
479#95—42no—
480#95C2×D414yes—
481#95C2×D414yes—
482C24—21no—
483C24—21no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24C22×D412yes—
493C24C2511yescharacteristic
494C2×Q8—28no—
495C2×Q8—48no—
496C2×Q8—48no—
497C2×Q8—44no—
498C2×Q8—44no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—28no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
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—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
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—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C2×#4112yes—
632C22×C4C2×#4112yes—
633C22×C4C2×#4112yes—
634C22×C42−1+414yes—
635C22×C42−1+414yes—
636C4⋊C4—28no—
637C4⋊C4—28no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—48no—
649C4⋊C4—44no—
650C4⋊C4—48no—
651C4⋊C4—48no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—82no—
655C4⋊C4—82no—
656C4⋊C4—82no—
657C4⋊C4—82no—
658C4⋊C4—84no—
659C4⋊C4—84no—
660C22⋊C4—28no—
661C22⋊C4—28no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—82no—
667C22⋊C4—82no—
668C22⋊C4—82no—
669C22⋊C4—82no—
670C42—28no—
671C42—44no—
672C42—44no—
673C42—48no—
674C42—48no—
675C42—82no—
676C42—82no—
677C42#121116yes—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—42no—
690C23—41no—
691C23—41no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23C23×D411yescharacteristic
702C23C23×D411yescharacteristic
703C23C22×#4111yescharacteristic
704C23C2×2−1+412yes—
705C23C2×2−1+412yes—
706C23#58511yescharacteristic
707C23#58511yescharacteristic
708C23#58511yescharacteristic
709C23#58511yescharacteristic
710C23#58512yes—
711C23#58512yes—
712Q8—416no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
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—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—416no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
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—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
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—41no—
815C2×C4—41no—
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—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—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4C2×#12114yes—
842C2×C4C2×#12114yes—
843C2×C4C2×#12114yes—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—44no—
848C22—44no—
849C22—81no—
850C22—81no—
851C22—82no—
852C22—82no—
853C22—81no—
854C22—81no—
855C22C22×#12111yescharacteristic
856C22#344911yescharacteristic
857C22#344911yescharacteristic
858C22#344911yescharacteristic
859C22#344911yescharacteristic
860C22#345511yescharacteristic
861C22#345511yescharacteristic
862C22#348511yescharacteristic
863C22#348611yescharacteristic
864C22#348912yes—
865C22#348912yes—
866C22#349512yes—
867C22#349911yescharacteristic
868C22#350011yescharacteristic
869C22#350712yes—
870C22#355512yes—
871C22#355712yes—
872C22#356312yes—
873C22#356412yes—
874C22#356512yes—
875C22#356512yes—
876C22#356612yes—
877C22#356712yes—
878C4—24no—
879C4—24no—
880C4—24no—
881C4—42no—
882C4—42no—
883C4—44no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—42no—
889C4—44no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—82no—
898C4—82no—
899C4—82no—
900C2—82no—
901C2#3463311yescharacteristic
902C2#3562111yescharacteristic
903C2#3563311yescharacteristic
904C2#3700112yes—
905C2#3700812yes—
906C2#4215111yescharacteristic
907C2#4215411yescharacteristic
908C2#4217612yes—
909C2#4217912yes—
910C2#4231011yescharacteristic
911C2#4231311yescharacteristic
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
1. C2×#2565C2semidirect
5. #17061C2semidirect
7. #16806C2semidirect
9. #16804C2semidirect
11. #16705C2semidirect
13. #16688C2semidirect
14. #16563C2semidirect
17. #15005C2semidirect
20. #14967C2semidirect
21. #14289C2semidirect
22. #13964C2semidirect
23. #13850C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25652
C2×#26112
C2×#25992
C2×#23142
#170612
#170602
#168062
#168052
#168042
#168032
#167052
#167012
#166882
#165632
#165612
#150052
#149882
#149702
#149672
#142892
#139642
#138502