Finite Group Databasebeta

← #3873889

Subgroups — #3873889

Order 512.

2692 conjugacy classes of subgroups.

The subgroup lattice has 901 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2546C211yesmaximal, characteristic, complemented
2C2×#2609C211yesmaximal, characteristic
3C2×#2439C212yesmaximal, complemented
4#17015C211yesmaximal, characteristic
5#16688C211yesmaximal, characteristic, complemented
6#16356C212yesmaximal, complemented
7#15963C212yesmaximal, complemented
8#15616C212yesmaximal, complemented
9#15431C212yesmaximal, complemented
10#15322C212yesmaximal, complemented
11#15322C212yesmaximal, complemented
12#15309C212yesmaximal
13#14883C211yesmaximal, characteristic
14#14817C212yesmaximal
15#14587C211yesmaximal, characteristic, complemented
16#14385C212yesmaximal, complemented
17#14204C212yesmaximal, complemented
18#14072C212yesmaximal, complemented
19#13978C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2212yes—
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×#117C2212yes—
24#2609—28no—
25#2546—28no—
26#2439—216no—
27C2×#398C2211yescharacteristic
28C2×#398C2211yescharacteristic
29C2×#398C2211yescharacteristic
30C2×#398C2211yescharacteristic
31C2×#396C2212yes—
32C2×#396C2212yes—
33C2×#396C2212yes—
34C2×#396C2212yes—
35C2×#396C2212yes—
36C2×#394C2211yescharacteristic
37C2×#394C2211yescharacteristic
38C2×#393C2212yes—
39C2×#393C2212yes—
40C2×#393C2212yes—
41C2×#391C2212yes—
42C2×#391C2212yes—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#389C2212yes—
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#389C2212yes—
50C2×#389C2212yes—
51C2×#389C2211yescharacteristic
52C2×#388C2212yes—
53C2×#388C2212yes—
54C2×#387C2212yes—
55C2×#387C2212yes—
56C2×#387C2212yes—
57C2×#386C2212yes—
58C2×#385C2212yes—
59C2×#385C2212yes—
60C2×#382C2211yescharacteristic
61C2×#382C2212yes—
62C2×#380C2212yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2212yes—
65#1446C2212yes—
66#1445C2212yes—
67#1444C2212yes—
68#1443C2212yes—
69#1442C2212yes—
70#1442C2212yes—
71#1442C2212yes—
72#1442C2212yes—
73#1442C2212yes—
74#1442C2212yes—
75#1441C2212yes—
76#1441C2212yes—
77#1441C2212yes—
78#1441C2212yes—
79#1441C2211yescharacteristic
80#1441C2211yescharacteristic
81#1441C2212yes—
82#1441C2212yes—
83#1441C2212yes—
84#1441C2212yes—
85#1440C2212yes—
86#1440C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1438C2212yes—
94#1437C2212yes—
95#1437C2212yes—
96#1437C2212yes—
97#1437C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103#1436C2212yes—
104#1436C2212yes—
105C4⋊#95C2211yescharacteristic
106#1434C2211yescharacteristic
107#1434C2212yes—
108C22⋊#95C2212yes—
109C4×#95C2211yescharacteristic
110C23×Q8C2312yes—
111C23×Q8C2311yescharacteristic
112C23×D4C2311yescharacteristic
113C24×C4C2312yes—
114C2×C4⋊Q8—28no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—28no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8—42no—
119C2×C4⋊Q8—44no—
120C2×C4×Q8—24no—
121C2×C4×Q8—42no—
122C2×C4×Q8—42no—
123C2×#117—28no—
124C2×#117—28no—
125C2×#117—44no—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2312yes—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168#398—24no—
169#398—24no—
170#398—24no—
171#398D418yes—
172#396—28no—
173#396—28no—
174#396—28no—
175#396—28no—
176#396—44no—
177#394—24no—
178#394—42no—
179#393—28no—
180#393—28no—
181#393—44no—
182#391—28no—
183#391—28no—
184#391—42no—
185#391D418yescomplemented
186#390—42no—
187#389—28no—
188#389—28no—
189#389—28no—
190#389—28no—
191#389—28no—
192#389—42no—
193#388—28no—
194#388—44no—
195#387—28no—
196#387—28no—
197#387—28no—
198#386—28no—
199#385—28no—
200#385—28no—
201#382—24no—
202#382—28no—
203#380—28no—
204C4×C4⋊C4—24no—
205C4×C22⋊C4—28no—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2311yescharacteristic
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2311yescharacteristic
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×#95C2312yes—
245C2×#95C2311yescharacteristic
246C2×#95C2312yes—
247C25C2412yes—
248C22×Q8—22no—
249C22×Q8—24no—
250C22×Q8—24no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—24no—
254C22×Q8—22no—
255C22×Q8—24no—
256C22×Q8—41no—
257C22×Q8—41no—
258C22×Q8—42no—
259C22×Q8—42no—
260C22×Q8—42no—
261C22×Q8C2×D414yes—
262C22×D4—24no—
263C22×D4—22no—
264C22×D4—42no—
265C22×D4—41no—
266C22×D4—41no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C4⋊Q8—416no—
293C4⋊Q8—432no—
294C4×Q8—416no—
295#117—432no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
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—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—41no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—41no—
339C2×C4⋊C4—41no—
340C2×C4⋊C4—41no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—41no—
345C2×C4⋊C4—41no—
346C2×C4⋊C4—41no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4C2×D418yes—
354C2×C4⋊C4C2×D414yes—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4C2×D414yes—
357C2×C4⋊C4#4118yes—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
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—42no—
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—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—24no—
403C2×C42—24no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—42no—
414C2×C42—41no—
415C2×C42—41no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42—41no—
419C2×C42—41no—
420C2×C42C2×D414yes—
421#95—24no—
422#95—22no—
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—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—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—41no—
457#95—42no—
458#95C2×D418yes—
459#95C2×D414yes—
460#95C2×D418yes—
461#95C2×D418yes—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C242−1+414yes—
477C24C2511yescharacteristic
478C2×Q8—28no—
479C2×Q8—28no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—48no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—84no—
490C2×Q8—84no—
491C2×Q8—84no—
492C2×D4—48no—
493C2×D4—44no—
494C2×D4—82no—
495C2×D4—84no—
496C2×D4—82no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—216no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
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—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
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—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
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—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4C22×D412yes—
605C22×C4C22×D414yes—
606C22×C4C22×D412yes—
607C22×C4C22×D414yes—
608C22×C4C22×D412yes—
609C22×C4C22×D414yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D414yes—
614C22×C4C2×#4114yes—
615C22×C4C2×#4114yes—
616C22×C4C2×#4114yes—
617C22×C4H(5,𝔽2)12yes—
618C22×C4H(5,𝔽2)12yes—
619C22×C4H(5,𝔽2)12yes—
620C22×C42−1+412yes—
621C22×C42−1+414yes—
622C4⋊C4—216no—
623C4⋊C4—216no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—48no—
631C4⋊C4—44no—
632C4⋊C4—48no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—82no—
641C4⋊C4—84no—
642C4⋊C4—82no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—84no—
652C22⋊C4—84no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C22⋊C4—84no—
656C42—28no—
657C42—28no—
658C42—48no—
659C42—48no—
660C42—44no—
661C42—44no—
662C42—48no—
663C42—82no—
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×D411yescharacteristic
701C23C22×#4112yes—
702C23C2×H(5,𝔽2)11yescharacteristic
703C23C2×H(5,𝔽2)11yescharacteristic
704C23C2×H(5,𝔽2)11yescharacteristic
705C23C2×2−1+411yescharacteristic
706C23C2×2−1+412yes—
707C23C2×2−1+412yes—
708C23#58512yes—
709C23#58511yescharacteristic
710Q8—416no—
711Q8—816no—
712D4—88no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—432no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—41no—
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—41no—
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—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4#53714yes—
829C2×C4D4214yes—
830C2×C4#54818yes—
831C2×C4#55514yes—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22C2×#53711yescharacteristic
848C22C2×D4211yescharacteristic
849C22C2×#54812yes—
850C22D4×#4112yes—
851C22C2×#55511yescharacteristic
852C22#348411yescharacteristic
853C22#348612yes—
854C22#348911yescharacteristic
855C22#348912yes—
856C22#349611yescharacteristic
857C22#351112yes—
858C22#352012yes—
859C22#352312yes—
860C22#352412yes—
861C22#353411yescharacteristic
862C22#353611yescharacteristic
863C22#353811yescharacteristic
864C22#354112yes—
865C22#354411yescharacteristic
866C22#355111yescharacteristic
867C22#355512yes—
868C22#356112yes—
869C22#356312yes—
870C4—24no—
871C4—24no—
872C4—28no—
873C4—24no—
874C4—42no—
875C4—44no—
876C4—44no—
877C4—44no—
878C4—44no—
879C4—42no—
880C4—42no—
881C4—82no—
882C4—82no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—81no—
887C4—82no—
888C2—84no—
889C2#3767311yescharacteristic
890C2#3987912yes—
891C2#4530012yes—
892C2#4538411yescharacteristic
893C2#4779911yescharacteristic
894C2#4822912yes—
895C2#5140911yescharacteristic
896C2#5671311yescharacteristic
897C2#5900512yes—
898C2#5913511yescharacteristic
899C2#5984111yescharacteristic
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
1. C2×#2546C2semidirect
3. C2×#2439C2semidirect
5. #16688C2semidirect
6. #16356C2semidirect
7. #15963C2semidirect
8. #15616C2semidirect
9. #15431C2semidirect
10. #15322C2semidirect
11. #15322C2semidirect
15. #14587C2semidirect
16. #14385C2semidirect
17. #14204C2semidirect
18. #14072C2semidirect
19. #13978C2semidirect
185. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25462
C2×#26092
C2×#24392
#170152
#166882
#163562
#159632
#156162
#154312
#153222
#153092
#148832
#148172
#145872
#143852
#142042
#140722
#139782