Finite Group Databasebeta

← #4422410

Subgroups — #4422410

Order 512.

2202 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2451C211yesmaximal, characteristic, complemented
2C2×#2343C211yesmaximal, characteristic
3#16965C211yesmaximal, characteristic, complemented
4#16806C211yesmaximal, characteristic, complemented
5#16696C211yesmaximal, characteristic, complemented
6#16617C212yesmaximal, complemented
7#16603C211yesmaximal, characteristic, complemented
8#16318C212yesmaximal
9#16022C212yesmaximal, complemented
10#15960C212yesmaximal
11#15437C212yesmaximal, complemented
12#15371C212yesmaximal
13#15125C211yesmaximal, characteristic
14#15050C211yesmaximal, characteristic
15#14907C211yesmaximal, characteristic
16#14895C212yesmaximal, complemented
17#14887C211yesmaximal, characteristic
18#14736C212yesmaximal
19#14631C211yesmaximal, characteristic, complemented
20#14352C211yesmaximal, characteristic, complemented
21#14313C211yesmaximal, characteristic
22#14302C211yesmaximal, characteristic, complemented
23#14172C211yesmaximal, characteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×#117C2211yescharacteristic
27#2451—28no—
28C2×#398C2211yescharacteristic
29C2×#398C2212yes—
30C2×#397C2211yescharacteristic
31C2×#395C2211yescharacteristic
32C2×#395C2212yes—
33C2×#395C2212yes—
34C2×#393C2211yescharacteristic
35C2×#393C2212yes—
36#2343—28no—
37C2×#391C2212yes—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#387C2211yescharacteristic
43C2×#387C2211yescharacteristic
44C2×#387C2211yescharacteristic
45C2×#387C2211yescharacteristic
46C2×#387C2212yes—
47C2×#387C2212yes—
48C2×#385C2211yescharacteristic
49C2×#385C2211yescharacteristic
50C2×#385C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#383C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#381C2211yescharacteristic
56C2×#380C2212yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×#376C2211yescharacteristic
61C22×#95C2211yescharacteristic
62#1446C2212yes—
63#1446C2212yes—
64#1446C2211yescharacteristic
65#1446C2211yescharacteristic
66#1445C2212yes—
67#1445C2212yes—
68#1445C2211yescharacteristic
69#1445C2212yes—
70#1445C2212yes—
71#1445C2211yescharacteristic
72#1444C2211yescharacteristic
73#1444C2211yescharacteristic
74#1444C2212yes—
75#1443C2212yes—
76#1443C2212yes—
77#1443C2212yes—
78#1443C2212yes—
79#1443C2212yes—
80#1442C2212yes—
81#1442C2212yes—
82#1442C2212yes—
83#1442C2211yescharacteristic
84#1442C2211yescharacteristic
85#1442C2212yes—
86#1442C2212yes—
87#1442C2212yes—
88#1442C2212yes—
89#1442C2212yes—
90#1442C2212yes—
91#1442C2212yes—
92#1441C2212yes—
93#1441C2211yescharacteristic
94#1441C2212yes—
95#1441C2212yes—
96#1441C2212yes—
97#1441C2212yes—
98#1441C2211yescharacteristic
99#1441C2212yes—
100#1441C2212yes—
101#1441C2212yes—
102#1440C2212yes—
103#1440C2212yes—
104#1440C2212yes—
105#1439C2211yescharacteristic
106#1439C2211yescharacteristic
107#1439C2212yes—
108#1437C2212yes—
109#1436C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2212yes—
116#1434C2212yes—
117#1434C2211yescharacteristic
118#1434C2211yescharacteristic
119#1434C2211yescharacteristic
120#1434C2211yescharacteristic
121#1434C2211yescharacteristic
122#1434C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C23×Q8C2311yescharacteristic
126C23×Q8C2312yes—
127C24×C4C2311yescharacteristic
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C2×C4⋊Q8—24no—
131C2×C4⋊Q8—44no—
132C2×C4×Q8—24no—
133C2×C4×Q8—44no—
134C2×#117—24no—
135C2×#117—24no—
136C2×#117—24no—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#398—24no—
171#398—28no—
172#397—24no—
173#395—28no—
174#395—24no—
175#395—44no—
176#393—24no—
177#393—44no—
178#391—24no—
179#391—24no—
180#391—28no—
181#389—24no—
182#389—24no—
183#387—24no—
184#387—24no—
185#387—28no—
186#387—24no—
187#387—24no—
188#387—44no—
189#385—24no—
190#385—24no—
191#385—44no—
192#385—44no—
193#385—44no—
194#383—24no—
195#382—24no—
196#381—24no—
197#380—44no—
198C4×C4⋊C4D418yes—
199C4×C22⋊C4—24no—
200C4×C22⋊C4—24no—
201#376—24no—
202C2×#95—24no—
203C2×#95C2311yescharacteristic
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2311yescharacteristic
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2311yescharacteristic
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C2×#95C2311yescharacteristic
231C2×#95C2311yescharacteristic
232C2×#95C2311yescharacteristic
233C2×#95C2311yescharacteristic
234C2×#95C2311yescharacteristic
235C2×#95C2311yescharacteristic
236C2×#95C2312yes—
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—24no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—24no—
270C22×Q8—24no—
271C22×Q8—42no—
272C22×Q8—42no—
273C22×Q8—42no—
274C22×Q8—42no—
275C22×Q8—42no—
276C22×Q8—42no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—24no—
287C23×C4—41no—
288C23×C4—41no—
289C23×C4—41no—
290C23×C4—42no—
291C23×C4—41no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C4⋊Q8—416no—
317C4×Q8—416no—
318#117—232no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
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⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4C2×D414yes—
365C2×C4⋊C4C2×D414yes—
366C2×C4⋊C4#4114yes—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4#4114yes—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42C2×D414yes—
406C2×C42C2×D414yes—
407C2×C42C2×D414yes—
408#95—22no—
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—22no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—22no—
430#95—24no—
431#95—22no—
432#95—22no—
433#95—24no—
434#95—22no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
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#95—42no—
466#95—42no—
467#95C2×D414yes—
468#95C2×D414yes—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—21no—
476C24—21no—
477C24C2×#4112yes—
478C24H(5,𝔽2)12yes—
479C242−1+412yes—
480C24C2511yescharacteristic
481C2×Q8—28no—
482C2×Q8—48no—
483C2×Q8—48no—
484C2×Q8—48no—
485C2×Q8—44no—
486C2×Q8—48no—
487C2×Q8—44no—
488C2×Q8—84no—
489C2×Q8—84no—
490C2×Q8—84no—
491C2×Q8—84no—
492C2×Q8—84no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—28no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
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—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
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—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—48no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—82no—
621C22×C4—84no—
622C22×C4—82no—
623C22×C4—84no—
624C22×C4—84no—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C2×#4112yes—
633C22×C4C2×#4112yes—
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4C2×#4112yes—
637C22×C4H(5,𝔽2)14yes—
638C22×C42−1+414yes—
639C22×C42−1+414yes—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—28no—
643C4⋊C4—28no—
644C4⋊C4—44no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—84no—
651C4⋊C4—82no—
652C4⋊C4—82no—
653C4⋊C4—84no—
654C4⋊C4—84no—
655C4⋊C4—84no—
656C4⋊C4—84no—
657C4⋊C4—84no—
658C22⋊C4—28no—
659C22⋊C4—28no—
660C22⋊C4—44no—
661C22⋊C4—44no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—84no—
666C42—28no—
667C42—28no—
668C42—44no—
669C42—44no—
670C42—48no—
671C42—44no—
672C42—44no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23#54214yes—
696C23C23×D411yescharacteristic
697C23C22×#4111yescharacteristic
698C23C22×#4111yescharacteristic
699C23C2×H(5,𝔽2)11yescharacteristic
700C23C2×H(5,𝔽2)12yes—
701C23C2×2−1+412yes—
702C23C2×2−1+411yescharacteristic
703C23C2×2−1+412yes—
704C23#58512yes—
705C23#58511yescharacteristic
706C23#58511yescharacteristic
707Q8—416no—
708Q8—816no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—416no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
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—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
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—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—88no—
839C2×C4—88no—
840C2×C4#52514yes—
841C2×C4#53614yes—
842C22—28no—
843C22—24no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—44no—
848C22—42no—
849C22—44no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22C2×#52511yescharacteristic
854C22C2×#53611yescharacteristic
855C22#344911yescharacteristic
856C22C2×#54211yescharacteristic
857C22#345511yescharacteristic
858C22#348411yescharacteristic
859C22#348611yescharacteristic
860C22#348811yescharacteristic
861C22#348911yescharacteristic
862C22#349411yescharacteristic
863C22#349511yescharacteristic
864C22#351512yes—
865C22#351812yes—
866C22#352012yes—
867C22#352012yes—
868C22#353412yes—
869C22#353812yes—
870C22#354412yes—
871C22#354512yes—
872C22#355512yes—
873C22#355712yes—
874C22#356112yes—
875C22#356312yes—
876C4—24no—
877C4—24no—
878C4—42no—
879C4—44no—
880C4—42no—
881C4—42no—
882C4—44no—
883C4—42no—
884C4—42no—
885C4—42no—
886C4—42no—
887C4—42no—
888C4—82no—
889C4—82no—
890C4—81no—
891C4—82no—
892C4—81no—
893C4—82no—
894C4—82no—
895C4—81no—
896C4—81no—
897C4—82no—
898C2—44no—
899C2#3520011yescharacteristic
900C2#3526011yescharacteristic
901C2#3535711yescharacteristic
902C2#4059511yescharacteristic
903C2#4084712yes—
904C2#4158312yes—
905C2#4198911yescharacteristic
906C2#4217111yescharacteristic
907C2#4281311yescharacteristic
908C2#5145912yes—
909C2#5149312yes—
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×#2451C2semidirect
3. #16965C2semidirect
4. #16806C2semidirect
5. #16696C2semidirect
6. #16617C2semidirect
7. #16603C2semidirect
9. #16022C2semidirect
11. #15437C2semidirect
16. #14895C2semidirect
19. #14631C2semidirect
20. #14352C2semidirect
22. #14302C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24512
C2×#23432
#169652
#168062
#166962
#166172
#166032
#163182
#160222
#159602
#154372
#153712
#151252
#150502
#149072
#148952
#148872
#147362
#146312
#143522
#143132
#143022
#141722