Finite Group Databasebeta

← #2609536

Subgroups — #2609536

Order 512.

2128 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2546C211yesmaximal, characteristic, complemented
2C2×#2574C211yesmaximal, characteristic
3#17080C211yesmaximal, characteristic, complemented
4#17025C211yesmaximal, characteristic, complemented
5#16829C212yesmaximal, complemented
6#16571C212yesmaximal, complemented
7#16560C211yesmaximal, characteristic, complemented
8#16560C211yesmaximal, characteristic, complemented
9#16506C211yesmaximal, characteristic
10#16506C211yesmaximal, characteristic
11#16378C212yesmaximal
12#16304C212yesmaximal
13#15895C212yesmaximal, complemented
14#15808C212yesmaximal
15#15699C212yesmaximal, complemented
16#15290C212yesmaximal
17#15214C211yesmaximal, characteristic, complemented
18#15191C211yesmaximal, characteristic, complemented
19#15125C211yesmaximal, characteristic
20#14625C211yesmaximal, characteristic
21#14301C211yesmaximal, characteristic
22#14243C211yesmaximal, characteristic
23#13928C211yesmaximal, characteristic, complemented
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28#2574—28no—
29#2546—28no—
30C2×#400C2212yes—
31C2×#400C2212yes—
32C2×#398C2211yescharacteristic
33C2×#398C2212yes—
34C2×#398C2212yes—
35C2×#397C2212yes—
36C2×#397C2212yes—
37C2×#396C2211yescharacteristic
38C2×#395C2211yescharacteristic
39C2×#393C2211yescharacteristic
40C2×#393C2211yescharacteristic
41C2×#393C2211yescharacteristic
42C2×#393C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2212yes—
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#388C2211yescharacteristic
50C2×#388C2211yescharacteristic
51C2×#388C2212yes—
52C2×#387C2211yescharacteristic
53C2×#387C2211yescharacteristic
54C2×#387C2211yescharacteristic
55C2×#387C2212yes—
56C2×#385C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#1446C2211yescharacteristic
63#1446C2211yescharacteristic
64#1446C2211yescharacteristic
65#1446C2212yes—
66#1446C2211yescharacteristic
67#1446C2211yescharacteristic
68#1446C2211yescharacteristic
69#1446C2211yescharacteristic
70#1446C2211yescharacteristic
71#1446C2211yescharacteristic
72#1445C2212yes—
73#1445C2212yes—
74#1445C2212yes—
75#1445C2212yes—
76#1445C2212yes—
77#1444C2211yescharacteristic
78#1444C2212yes—
79#1444C2211yescharacteristic
80#1444C2212yes—
81#1444C2212yes—
82#1443C2212yes—
83#1442C2212yes—
84#1442C2212yes—
85#1442C2212yes—
86#1442C2212yes—
87#1442C2212yes—
88#1442C2212yes—
89#1442C2212yes—
90#1442C2212yes—
91#1442C2211yescharacteristic
92#1442C2212yes—
93#1442C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2212yes—
98#1441C2212yes—
99#1441C2212yes—
100#1441C2212yes—
101#1441C2212yes—
102#1440C2212yes—
103#1439C2212yes—
104#1439C2211yescharacteristic
105#1439C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1439C2212yes—
109#1437C2212yes—
110#1436C2212yes—
111C4⋊#95C2212yes—
112C4⋊#95C2211yescharacteristic
113C4⋊#95C2212yes—
114#1434C2212yes—
115#1434C2212yes—
116#1434C2211yescharacteristic
117#1434C2212yes—
118#1434C2212yes—
119#1434C2211yescharacteristic
120#1434C2211yescharacteristic
121#1434C2211yescharacteristic
122#1434C2212yes—
123C22⋊#95C2212yes—
124C4×#95C2211yescharacteristic
125C23×Q8C2311yescharacteristic
126C23×Q8C2311yescharacteristic
127C23×Q8C2311yescharacteristic
128C23×Q8C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C2×C4⋊Q8—24no—
131C2×C4⋊Q8—24no—
132C2×C4⋊Q8—24no—
133C2×C4⋊Q8—44no—
134C2×C4⋊Q8—44no—
135C2×C4⋊Q8—44no—
136C2×C4×Q8—24no—
137C2×C4×Q8—44no—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C22⋊C4C2312yes—
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2312yes—
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174#400—44no—
175#400—44no—
176#398—24no—
177#398—28no—
178#398—28no—
179#397—44no—
180#397—44no—
181#396—24no—
182#395—24no—
183#393—24no—
184#393—24no—
185#393—24no—
186#393—24no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—44no—
191#389—28no—
192#389—28no—
193#388—24no—
194#388—24no—
195#388—44no—
196#387—24no—
197#387—24no—
198#387—24no—
199#387—44no—
200#385—24no—
201#382—24no—
202#380—24no—
203#380—44no—
204C4×C4⋊C4D418yes—
205C4×C22⋊C4—24no—
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2311yescharacteristic
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2311yescharacteristic
233C2×#95C2311yescharacteristic
234C2×#95C2311yescharacteristic
235C2×#95C2311yescharacteristic
236C2×#95C2311yescharacteristic
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
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×#95C2311yescharacteristic
263C2×#95C2311yescharacteristic
264C25C2411yescharacteristic
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—24no—
273C22×Q8—22no—
274C22×Q8—22no—
275C22×Q8—22no—
276C22×Q8—22no—
277C22×Q8—22no—
278C22×Q8—42no—
279C22×Q8—42no—
280C22×Q8—42no—
281C22×Q8—42no—
282C22×Q8—42no—
283C22×Q8—42no—
284C22×Q8—42no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—24no—
288C23×C4—41no—
289C23×C4—42no—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C4⋊Q8—416no—
313C4⋊Q8—416no—
314C4⋊Q8—416no—
315C4×Q8—416no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
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—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—41no—
345C2×C4⋊C4—41no—
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⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
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⋊C4C2×D414yes—
368C2×C4⋊C4C2×D414yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—42no—
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—42no—
394C2×C22⋊C4#4114yes—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42C2×D414yes—
407C2×C42C2×D414yes—
408C2×C42C2×D414yes—
409#95—22no—
410#95—22no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—22no—
418#95—22no—
419#95—22no—
420#95—22no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—22no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—42no—
465#95C2×D414yes—
466#95C2×D414yes—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24—21no—
477C24C2×#4112yes—
478C24C2511yescharacteristic
479C2×Q8—28no—
480C2×Q8—48no—
481C2×Q8—48no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—48no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—82no—
493C2×Q8—82no—
494C2×Q8—84no—
495C2×Q8—84no—
496C2×Q8—84no—
497C2×Q8—84no—
498C2×Q8—84no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
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—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—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
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—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—44no—
610C22×C4—48no—
611C22×C4—44no—
612C22×C4—82no—
613C22×C4—84no—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C2×#4112yes—
622C22×C4C2×#4112yes—
623C22×C4H(5,𝔽2)14yes—
624C22×C4H(5,𝔽2)14yes—
625C22×C42−1+412yes—
626C22×C42−1+412yes—
627C22×C42−1+414yes—
628C22×C42−1+412yes—
629C22×C42−1+412yes—
630C4⋊C4—28no—
631C4⋊C4—28no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—44no—
643C4⋊C4—48no—
644C4⋊C4—82no—
645C4⋊C4—84no—
646C4⋊C4—82no—
647C4⋊C4—82no—
648C4⋊C4—82no—
649C4⋊C4—84no—
650C22⋊C4—28no—
651C22⋊C4—48no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—82no—
655C22⋊C4—82no—
656C22⋊C4—82no—
657C22⋊C4—84no—
658C22⋊C4—84no—
659C22⋊C4—84no—
660C42—28no—
661C42—44no—
662C42—44no—
663C42—48no—
664C42—44no—
665C42—84no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23C23×D411yescharacteristic
690C23C22×#4111yescharacteristic
691C23C2×H(5,𝔽2)12yes—
692C23C2×H(5,𝔽2)12yes—
693C23C2×2−1+411yescharacteristic
694C23C2×2−1+411yescharacteristic
695C23C2×2−1+412yes—
696C23C2×2−1+411yescharacteristic
697C23C2×2−1+411yescharacteristic
698C23#58511yescharacteristic
699C23#58512yes—
700Q8—416no—
701Q8—88no—
702Q8—88no—
703Q8—88no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
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—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
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—42no—
825C2×C4—42no—
826C2×C4—88no—
827C2×C4#53514yes—
828C2×C4#53614yes—
829C2×C4#53614yes—
830C2×C4#54814yes—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—81no—
837C22—81no—
838C22—82no—
839C22—81no—
840C22—81no—
841C22—82no—
842C22C2×#53511yescharacteristic
843C22C2×#53611yescharacteristic
844C22C2×#53611yescharacteristic
845C22C2×#54811yescharacteristic
846C22#348411yescharacteristic
847C22#348911yescharacteristic
848C22#350011yescharacteristic
849C22#350711yescharacteristic
850C22#350911yescharacteristic
851C22#351512yes—
852C22#351912yes—
853C22#353612yes—
854C22#353812yes—
855C22#354012yes—
856C22#354112yes—
857C22#354412yes—
858C22#354412yes—
859C22#354712yes—
860C22#355512yes—
861C22#355511yescharacteristic
862C22#355611yescharacteristic
863C22#356112yes—
864C22#356112yes—
865C4—24no—
866C4—24no—
867C4—24no—
868C4—24no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—44no—
874C4—42no—
875C4—81no—
876C4—81no—
877C4—81no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—81no—
883C4—81no—
884C4—82no—
885C4—82no—
886C4—82no—
887C2—82no—
888C2#3763211yescharacteristic
889C2#3912011yescharacteristic
890C2#3917311yescharacteristic
891C2#3972411yescharacteristic
892C2#4049111yescharacteristic
893C2#4059511yescharacteristic
894C2#4299511yescharacteristic
895C2#5042712yes—
896C2#5042912yes—
897C2#5861412yes—
898C2#5875312yes—
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×#2546C2semidirect
3. #17080C2semidirect
4. #17025C2semidirect
5. #16829C2semidirect
6. #16571C2semidirect
7. #16560C2semidirect
8. #16560C2semidirect
13. #15895C2semidirect
15. #15699C2semidirect
17. #15214C2semidirect
18. #15191C2semidirect
23. #13928C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25462
C2×#25742
#170802
#170252
#168292
#165712
#165602
#165062
#163782
#163042
#158952
#158082
#156992
#152902
#152142
#151912
#151252
#146252
#143012
#142432
#139282