Finite Group Databasebeta

← #1295160

Subgroups — #1295160

Order 512.

2148 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2515C211yesmaximal, characteristic
2C2×#2451C211yesmaximal, characteristic, complemented
3#16962C211yesmaximal, characteristic, complemented
4#16900C211yesmaximal, characteristic, complemented
5#16694C211yesmaximal, characteristic, complemented
6#16511C211yesmaximal, characteristic
7#15712C212yesmaximal, complemented
8#15704C212yesmaximal
9#15401C212yesmaximal, complemented
10#15286C212yesmaximal
11#15161C211yesmaximal, characteristic
12#15053C211yesmaximal, characteristic, complemented
13#14910C211yesmaximal, characteristic
14#14902C211yesmaximal, characteristic
15#14875C211yesmaximal, characteristic
16#14816C212yesmaximal, complemented
17#14789C212yesmaximal
18#14575C212yesmaximal
19#14574C212yesmaximal, complemented
20#14274C211yesmaximal, characteristic, complemented
21#14230C211yesmaximal, characteristic
22#13961C211yesmaximal, characteristic, complemented
23#13810C211yesmaximal, characteristic, complemented
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26#2515—28no—
27#2451—28no—
28C2×#400C2211yescharacteristic
29C2×#399C2211yescharacteristic
30C2×#399C2211yescharacteristic
31C2×#398C2212yes—
32C2×#398C2211yescharacteristic
33C2×#397C2211yescharacteristic
34C2×#396C2211yescharacteristic
35C2×#395C2212yes—
36C2×#395C2212yes—
37C2×#393C2212yes—
38C2×#393C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2212yes—
42C2×#391C2212yes—
43C2×#391C2212yes—
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#389C2212yes—
47C2×#388C2211yescharacteristic
48C2×#388C2211yescharacteristic
49C2×#388C2212yes—
50C2×#387C2211yescharacteristic
51C2×#387C2211yescharacteristic
52C2×#387C2212yes—
53C2×#387C2211yescharacteristic
54C2×#387C2212yes—
55C2×#385C2211yescharacteristic
56C2×#385C2212yes—
57C2×#383C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#381C2211yescharacteristic
60C2×C4×C4⋊C4C2212yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×#376C2211yescharacteristic
64C2×#376C2211yescharacteristic
65#1446C2211yescharacteristic
66#1446C2211yescharacteristic
67#1446C2211yescharacteristic
68#1445C2211yescharacteristic
69#1445C2211yescharacteristic
70#1445C2212yes—
71#1445C2211yescharacteristic
72#1445C2212yes—
73#1445C2211yescharacteristic
74#1445C2211yescharacteristic
75#1445C2212yes—
76#1445C2211yescharacteristic
77#1444C2212yes—
78#1444C2211yescharacteristic
79#1444C2212yes—
80#1444C2212yes—
81#1444C2211yescharacteristic
82#1444C2212yes—
83#1443C2212yes—
84#1443C2212yes—
85#1443C2212yes—
86#1442C2211yescharacteristic
87#1442C2212yes—
88#1442C2212yes—
89#1442C2212yes—
90#1442C2212yes—
91#1442C2212yes—
92#1442C2212yes—
93#1442C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2212yes—
98#1440C2212yes—
99#1439C2212yes—
100#1439C2211yescharacteristic
101#1439C2212yes—
102#1439C2212yes—
103#1439C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1436C2212yes—
108#1436C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2212yes—
115C4⋊#95C2212yes—
116#1434C2211yescharacteristic
117#1434C2212yes—
118#1434C2211yescharacteristic
119#1434C2212yes—
120#1434C2212yes—
121#1434C2212yes—
122#1434C2212yes—
123C22⋊#95C2212yes—
124C4×#95C2211yescharacteristic
125C23×Q8C2311yescharacteristic
126C23×Q8C2312yes—
127C24×C4C2311yescharacteristic
128C2×C4⋊Q8—24no—
129C2×C4⋊Q8—24no—
130C2×C4⋊Q8—42no—
131C2×C4×Q8—24no—
132C2×C4×Q8—24no—
133C2×C4×Q8—42no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#400—24no—
173#399—24no—
174#399—42no—
175#398—24no—
176#398—28no—
177#397—24no—
178#396—24no—
179#395—28no—
180#395—28no—
181#393—28no—
182#393—42no—
183#391—24no—
184#391—24no—
185#391—28no—
186#391—44no—
187#391—44no—
188#389—24no—
189#389—24no—
190#389—44no—
191#388—24no—
192#388—24no—
193#388—44no—
194#387—28no—
195#387—24no—
196#387—24no—
197#387—24no—
198#387—44no—
199#385—24no—
200#385—44no—
201#383—24no—
202#382—24no—
203#381—24no—
204C4×C4⋊C4—28no—
205C4×C4⋊C4D418yes—
206C4×C22⋊C4—24no—
207#376—42no—
208#376—42no—
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2312yes—
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C2×#95C2312yes—
232C2×#95C2311yescharacteristic
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2311yescharacteristic
244C2×#95C2311yescharacteristic
245C2×#95C2311yescharacteristic
246C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
265C2×#95C2311yescharacteristic
266C2×#95C2312yes—
267C25C2411yescharacteristic
268C22×Q8—22no—
269C22×Q8—24no—
270C22×Q8—22no—
271C22×Q8—24no—
272C22×Q8—24no—
273C22×Q8—24no—
274C22×Q8—22no—
275C22×Q8—24no—
276C22×Q8—42no—
277C22×Q8—42no—
278C22×Q8—42no—
279C22×Q8—42no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—41no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C4⋊Q8—416no—
308C4×Q8—416no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
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⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4C2×D414yes—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4#4114yes—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—41no—
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×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42C2×D414yes—
410C2×C42C2×D414yes—
411C2×C42C2×D414yes—
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—22no—
422#95—22no—
423#95—22no—
424#95—22no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—22no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
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—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#95—42no—
466#95—42no—
467#95C2×D414yes—
468#95C2×D414yes—
469#95#4118yes—
470C24—21no—
471C24—22no—
472C24—21no—
473C24—21no—
474C24—22no—
475C24—21no—
476C24—22no—
477C24—21no—
478C24—21no—
479C24—22no—
480C242−1+412yes—
481C24C2511yescharacteristic
482C2×Q8—28no—
483C2×Q8—48no—
484C2×Q8—48no—
485C2×Q8—48no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—44no—
489C2×Q8—48no—
490C2×Q8—44no—
491C2×Q8—84no—
492C2×Q8—84no—
493C2×Q8—84no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—22no—
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—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
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—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—21no—
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—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—82no—
610C22×C4—84no—
611C22×C4—84no—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C2×#4114yes—
620C22×C4C2×#4114yes—
621C22×C4C2×#4114yes—
622C22×C4C2×#4114yes—
623C22×C4C2×#4112yes—
624C22×C4H(5,𝔽2)14yes—
625C22×C4H(5,𝔽2)12yes—
626C22×C42−1+414yes—
627C22×C42−1+412yes—
628C22×C42−1+412yes—
629C4⋊C4—28no—
630C4⋊C4—28no—
631C4⋊C4—28no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—44no—
637C4⋊C4—44no—
638C4⋊C4—48no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—82no—
643C4⋊C4—82no—
644C4⋊C4—84no—
645C4⋊C4—82no—
646C4⋊C4—84no—
647C4⋊C4—84no—
648C4⋊C4—84no—
649C22⋊C4—48no—
650C22⋊C4—44no—
651C22⋊C4—44no—
652C22⋊C4—48no—
653C22⋊C4—44no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—82no—
657C22⋊C4—84no—
658C22⋊C4—84no—
659C42—28no—
660C42—28no—
661C42—44no—
662C42—48no—
663C42—48no—
664C42—48no—
665C42—48no—
666C42—82no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—41no—
690C23C23×D411yescharacteristic
691C23C22×#4112yes—
692C23C22×#4111yescharacteristic
693C23C2×H(5,𝔽2)11yescharacteristic
694C23C2×H(5,𝔽2)12yes—
695C23C2×2−1+411yescharacteristic
696C23C2×2−1+411yescharacteristic
697C23C2×2−1+412yes—
698C23C2×2−1+411yescharacteristic
699C23#58512yes—
700C23#58511yescharacteristic
701Q8—416no—
702Q8—816no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
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—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
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—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—88no—
831C2×C4#53214yes—
832C2×C4#53614yes—
833C2×C4#54614yes—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—81no—
840C22—81no—
841C22—82no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#53211yescharacteristic
846C22C2×#53611yescharacteristic
847C22#344911yescharacteristic
848C22C2×#54611yescharacteristic
849C22#348112yes—
850C22#348611yescharacteristic
851C22#348911yescharacteristic
852C22#349512yes—
853C22#349512yes—
854C22#349512yes—
855C22#349811yescharacteristic
856C22#351512yes—
857C22#351811yescharacteristic
858C22#351912yes—
859C22#352311yescharacteristic
860C22#352312yes—
861C22#353512yes—
862C22#353512yes—
863C22#354012yes—
864C22#354412yes—
865C22#355012yes—
866C22#355211yescharacteristic
867C22#355411yescharacteristic
868C4—24no—
869C4—24no—
870C4—24no—
871C4—42no—
872C4—44no—
873C4—44no—
874C4—44no—
875C4—44no—
876C4—44no—
877C4—42no—
878C4—42no—
879C4—42no—
880C4—81no—
881C4—82no—
882C4—81no—
883C4—81no—
884C4—82no—
885C4—81no—
886C4—81no—
887C4—82no—
888C4—81no—
889C4—81no—
890C2—82no—
891C2#3532611yescharacteristic
892C2#3594911yescharacteristic
893C2#3636211yescharacteristic
894C2#3784111yescharacteristic
895C2#3891111yescharacteristic
896C2#4196011yescharacteristic
897C2#4278911yescharacteristic
898C2#4482912yes—
899C2#4485812yes—
900C2#4846312yes—
901C2#4847712yes—
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
2. C2×#2451C2semidirect
3. #16962C2semidirect
4. #16900C2semidirect
5. #16694C2semidirect
7. #15712C2semidirect
9. #15401C2semidirect
12. #15053C2semidirect
16. #14816C2semidirect
19. #14574C2semidirect
20. #14274C2semidirect
22. #13961C2semidirect
23. #13810C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25152
C2×#24512
#169622
#169002
#166942
#165112
#157122
#157042
#154012
#152862
#151612
#150532
#149102
#149022
#148752
#148162
#147892
#145752
#145742
#142742
#142302
#139612
#138102