Finite Group Databasebeta

← #4944198

Subgroups — #4944198

Order 512.

3418 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#563C211yesmaximal, characteristic
2C2×#2453C211yesmaximal, characteristic, complemented
3C2×#2469C212yesmaximal, complemented
4#16659C212yesmaximal, complemented
5#16608C211yesmaximal, characteristic, complemented
6#16560C212yesmaximal, complemented
7#16559C211yesmaximal, characteristic
8#15672C212yesmaximal, complemented
9#15671C212yesmaximal, complemented
10#15667C212yesmaximal
11#15397C212yesmaximal
12#15354C212yesmaximal, complemented
13#15354C212yesmaximal, complemented
14#15128C212yesmaximal, complemented
15#15072C212yesmaximal, complemented
16#15071C211yesmaximal, characteristic, complemented
17#15070C211yesmaximal, characteristic
18#14493C212yesmaximal, complemented
19#14474C211yesmaximal, characteristic, complemented
20C2×#563—216no—
21C2×#563—28no—
22C22×C4⋊Q8C2212yes—
23C22×#126C2212yes—
24C22×#126C2212yes—
25C22×#125C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C22×#123C2212yes—
29C22×C22⋊Q8C2212yes—
30C22×C22⋊Q8C2212yes—
31C22×C4×Q8C2211yescharacteristic
32#2469—216no—
33#2453—28no—
34C2×#400C2212yes—
35C2×#400C2212yes—
36C2×#398C2212yes—
37C2×#396C2212yes—
38C2×#395C2212yes—
39C2×#395C2211yescharacteristic
40C2×#395C2212yes—
41C2×#394C2211yescharacteristic
42C2×#393C2212yes—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#389C2212yes—
46C2×#389C2212yes—
47C2×#389C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#388C2212yes—
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#388C2212yes—
53C2×#387C2212yes—
54C2×#387C2212yes—
55C2×#387C2212yes—
56C2×#387C2212yes—
57C2×#385C2212yes—
58C2×C4×C4⋊C4C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60#1446C2212yes—
61#1446C2212yes—
62#1446C2212yes—
63#1446C2212yes—
64#1446C2211yescharacteristic
65#1445C2212yes—
66#1445C2212yes—
67#1445C2212yes—
68#1444C2212yes—
69#1444C2212yes—
70#1444C2212yes—
71#1444C2211yescharacteristic
72#1442C2212yes—
73#1442C2212yes—
74#1442C2212yes—
75#1442C2211yescharacteristic
76#1441C2211yescharacteristic
77#1441C2212yes—
78#1441C2212yes—
79#1441C2212yes—
80#1441C2212yes—
81#1441C2212yes—
82#1441C2211yescharacteristic
83#1441C2212yes—
84#1440C2212yes—
85#1440C2212yes—
86#1440C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1438C2212yes—
97#1438C2211yescharacteristic
98#1437C2212yes—
99#1437C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102C4⋊#95C2212yes—
103C4⋊#95C2212yes—
104C4⋊#95C2212yes—
105#1434C2211yescharacteristic
106#1434C2211yescharacteristic
107#1434C2212yes—
108C22⋊#95C2212yes—
109C22⋊#95C2212yes—
110C22⋊#95C2212yes—
111C23×Q8C2311yescharacteristic
112C23×Q8C2312yes—
113C23×Q8C2311yescharacteristic
114C23×D4C2311yescharacteristic
115C24×C4C2312yes—
116#563—2128no—
117C2×C4⋊Q8—28no—
118C2×C4⋊Q8—28no—
119C2×C4⋊Q8—28no—
120C2×#126—28no—
121C2×#126—28no—
122C2×#126—28no—
123C2×#126—28no—
124C2×#126—28no—
125C2×#126D4116yes—
126C2×#125—28no—
127C2×#125—28no—
128C2×#125—24no—
129C2×#125D418yes—
130C2×#124—28no—
131C2×#124—24no—
132C2×#123—28no—
133C2×#123—28no—
134C2×#123—28no—
135C2×C22⋊Q8—28no—
136C2×C22⋊Q8—28no—
137C2×C22⋊Q8—28no—
138C2×C22⋊Q8—28no—
139C2×C22⋊Q8—28no—
140C2×C22⋊Q8—28no—
141C2×C4×Q8—24no—
142C2×C4×Q8—28no—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C42C2311yescharacteristic
178C22×C42C2312yes—
179C22×C42C2312yes—
180C22×C42C2311yescharacteristic
181C22×C42C2312yes—
182C22×C42C2311yescharacteristic
183#400—28no—
184#400—28no—
185#398—28no—
186#396—28no—
187#395—28no—
188#395—44no—
189#395—42no—
190#394—42no—
191#393—28no—
192#391—24no—
193#391—24no—
194#389—24no—
195#389—28no—
196#389—24no—
197#389—28no—
198#388—28no—
199#388—28no—
200#388—28no—
201#388—28no—
202#387—28no—
203#387—28no—
204#387—28no—
205#387—28no—
206#385—44no—
207C4×C4⋊C4—24no—
208C4×C4⋊C4—28no—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2311yescharacteristic
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2311yescharacteristic
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2311yescharacteristic
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2311yescharacteristic
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2311yescharacteristic
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C25C2412yes—
252C22×Q8—22no—
253C22×Q8—24no—
254C22×Q8—24no—
255C22×Q8—24no—
256C22×Q8—22no—
257C22×Q8—24no—
258C22×Q8—24no—
259C22×Q8—24no—
260C22×Q8—41no—
261C22×Q8—41no—
262C22×Q8—42no—
263C22×Q8—42no—
264C22×Q8—42no—
265C22×Q8—42no—
266C22×Q8—41no—
267C22×Q8—42no—
268C22×Q8—41no—
269C22×D4—24no—
270C22×D4—22no—
271C22×D4—42no—
272C22×D4—41no—
273C22×D4—41no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C4⋊Q8—264no—
300#126—264no—
301#126—264no—
302#125—232no—
303#125—232no—
304#124—232no—
305#123—264no—
306C22⋊Q8—264no—
307C22⋊Q8—264no—
308C4×Q8—416no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
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—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—41no—
355C2×C4⋊C4—41no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—41no—
360C2×C4⋊C4—41no—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D418yes—
363C2×C4⋊C4C2×D418yes—
364C2×C4⋊C4C2×D418yes—
365C2×C4⋊C4C2×D418yes—
366C2×C4⋊C4C2×D418yes—
367C2×C4⋊C4C2×D414yes—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
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⋊C4C2×D418yes—
405C2×C22⋊C4C2×D418yes—
406C2×C22⋊C4C2×D418yes—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—22no—
417C2×C42—24no—
418C2×C42—42no—
419C2×C42—41no—
420C2×C42—41no—
421C2×C42C2×D414yes—
422C2×C42C2×D418yes—
423#95—22no—
424#95—24no—
425#95—24no—
426#95—22no—
427#95—24no—
428#95—24no—
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—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—41no—
449#95—42no—
450#95—41no—
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—41no—
460#95—41no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—42no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24C22×D414yes—
480C24C2511yescharacteristic
481C2×Q8—28no—
482C2×Q8—216no—
483C2×Q8—28no—
484C2×Q8—48no—
485C2×Q8—48no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—84no—
489C2×Q8—84no—
490C2×Q8—82no—
491C2×Q8—84no—
492C2×Q8—84no—
493C2×Q8—84no—
494C2×Q8—84no—
495C2×Q8—82no—
496C2×Q8—84no—
497C2×Q8—84no—
498C2×D4—28no—
499C2×D4—82no—
500C2×D4—82no—
501C2×D4—84no—
502C2×D4—84no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
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—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
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—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—216no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
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—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—22no—
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—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—84no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—84no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4C22×D412yes—
610C22×C4C22×D414yes—
611C22×C4C22×D412yes—
612C22×C4C22×D414yes—
613C22×C4C22×D414yes—
614C22×C4C22×D414yes—
615C22×C4C22×D414yes—
616C22×C4C22×D414yes—
617C22×C4C22×D414yes—
618C22×C4C22×D414yes—
619C22×C4C22×D412yes—
620C22×C4H(5,𝔽2)12yes—
621C22×C42−1+414yes—
622C22×C42−1+412yes—
623C22×C42−1+414yes—
624C4⋊C4—28no—
625C4⋊C4—216no—
626C4⋊C4—216no—
627C4⋊C4—28no—
628C4⋊C4—28no—
629C4⋊C4—216no—
630C4⋊C4—216no—
631C4⋊C4—216no—
632C4⋊C4—216no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—48no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—48no—
644C4⋊C4#120116yes—
645C22⋊C4—216no—
646C22⋊C4—216no—
647C22⋊C4—216no—
648C22⋊C4—216no—
649C22⋊C4—216no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C22⋊C4—84no—
658C42—28no—
659C42—216no—
660C42—48no—
661C42—44no—
662C42—48no—
663C42—44no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23C23×D411yescharacteristic
700C23C23×D412yes—
701C23C2×H(5,𝔽2)11yescharacteristic
702C23C2×2−1+412yes—
703C23C2×2−1+412yes—
704C23C2×2−1+411yescharacteristic
705C23#58511yescharacteristic
706C23#58511yescharacteristic
707C23#58511yescharacteristic
708C23#58512yes—
709C23#58511yescharacteristic
710Q8—416no—
711Q8—816no—
712Q8—88no—
713D4—88no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—41no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
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—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
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—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
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—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
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—816no—
827C2×C4C2×#12018yes—
828C2×C4C2×#12014yes—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22C22×#12011yescharacteristic
845C22#348611yescharacteristic
846C22#348711yescharacteristic
847C22#348811yescharacteristic
848C22#348812yes—
849C22#348912yes—
850C22#348912yes—
851C22#348911yescharacteristic
852C22#348912yes—
853C22#349911yescharacteristic
854C22#349912yes—
855C22#350012yes—
856C22#350011yescharacteristic
857C22#352911yescharacteristic
858C22#355212yes—
859C22#355311yescharacteristic
860C22#355512yes—
861C22#355512yes—
862C22#355712yes—
863C22#356111yescharacteristic
864C22#356412yes—
865C22#356512yes—
866C22#356811yescharacteristic
867C4—24no—
868C4—28no—
869C4—44no—
870C4—44no—
871C4—44no—
872C4—42no—
873C4—42no—
874C4—44no—
875C4—44no—
876C4—42no—
877C4—44no—
878C4—42no—
879C4—82no—
880C4—81no—
881C4—82no—
882C4—82no—
883C4—81no—
884C4—82no—
885C2—84no—
886C2#3565911yescharacteristic
887C2#3608211yescharacteristic
888C2#3608511yescharacteristic
889C2#4596912yes—
890C2#4597511yescharacteristic
891C2#5068612yes—
892C2#5069211yescharacteristic
893C2#5120512yes—
894C2#5121011yescharacteristic
895C2#5133112yes—
896C2#5154811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
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×#2453C2semidirect
3. C2×#2469C2semidirect
4. #16659C2semidirect
5. #16608C2semidirect
6. #16560C2semidirect
8. #15672C2semidirect
9. #15671C2semidirect
12. #15354C2semidirect
13. #15354C2semidirect
14. #15128C2semidirect
15. #15072C2semidirect
16. #15071C2semidirect
18. #14493C2semidirect
19. #14474C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5632
C2×#24532
C2×#24692
#166592
#166082
#165602
#165592
#156722
#156712
#156672
#153972
#153542
#151282
#150722
#150712
#150702
#144932
#144742