Finite Group Databasebeta

← #4606374

Subgroups — #4606374

Order 512.

2314 conjugacy classes of subgroups.

The subgroup lattice has 921 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2735C211yesmaximal, characteristic
2C2×#2482C211yesmaximal, characteristic
3#17190C212yesmaximal, complemented
4#17116C212yesmaximal, complemented
5#16579C212yesmaximal, complemented
6#16473C211yesmaximal, characteristic, complemented
7#16470C211yesmaximal, characteristic, complemented
8#16458C212yesmaximal, complemented
9#16434C212yesmaximal, complemented
10#16391C212yesmaximal
11#16316C212yesmaximal, complemented
12#16077C212yesmaximal, complemented
13#16015C212yesmaximal, complemented
14#15717C212yesmaximal, complemented
15#15350C212yesmaximal, complemented
16#14907C211yesmaximal, characteristic, complemented
17#14893C211yesmaximal, characteristic, complemented
18#14727C212yesmaximal
19#14673C211yesmaximal, characteristic
20C22×#117C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22#2735—28no—
23#2482—28no—
24C2×#400C2211yescharacteristic, complemented
25C2×#399C2212yes—
26C2×#399C2211yescharacteristic
27C2×#398C2211yescharacteristic, complemented
28C2×#397C2212yes—
29C2×#397C2211yescharacteristic
30C2×#397C2212yes—
31C2×#397C2212yes—
32C2×#397C2212yes—
33C2×#397C2212yes—
34C2×#396C2212yes—
35C2×#389C2211yescharacteristic, complemented
36C2×#389C2211yescharacteristic, complemented
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#385C2211yescharacteristic
43C2×#385C2211yescharacteristic
44C2×#385C2212yes—
45C2×#381C2211yescharacteristic
46C2×#379C2211yescharacteristic
47C2×#379C2212yes—
48C2×#379C2212yes—
49C2×#379C2211yescharacteristic
50#1445C2212yescomplemented
51#1445C2212yescomplemented
52#1444C2212yescomplemented
53#1443C2212yescomplemented
54#1443C2212yescomplemented
55#1442C2212yescomplemented
56#1442C2212yescomplemented
57#1442C2212yescomplemented
58#1442C2212yescomplemented
59#1442C2212yescomplemented
60#1442C2212yescomplemented
61#1441C2211yescharacteristic, complemented
62#1441C2212yescomplemented
63#1441C2212yescomplemented
64#1441C2212yescomplemented
65#1441C2212yescomplemented
66#1441C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2212yescomplemented
69#1441C2211yescharacteristic, complemented
70#1441C2212yescomplemented
71#1441C2212yescomplemented
72#1441C2212yescomplemented
73#1441C2212yescomplemented
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1440C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1440C2212yes—
83#1440C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2211yescharacteristic
92#1439C2212yes—
93#1439C2211yescharacteristic
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1436C2212yescomplemented
99#1436C2212yescomplemented
100#1436C2212yescomplemented
101#1436C2212yescomplemented
102C4⋊#95C2212yescomplemented
103#1434C2211yescharacteristic, complemented
104#1434C2211yescharacteristic, complemented
105#1434C2212yescomplemented
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2212yes—
109C26C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C2×#117—24no—
113C2×#117—42no—
114C2×#117—42no—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4—24no—
131C22×C22⋊C4—42no—
132C22×C22⋊C4—42no—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158#400—42no—
159#399—24no—
160#399—28no—
161#398—42no—
162#397—24no—
163#397—28no—
164#397—28no—
165#397—44no—
166#397—44no—
167#397—44no—
168#396—28no—
169#389—42no—
170#389—42no—
171#388—28no—
172#388—28no—
173#388—28no—
174#388—28no—
175#388—28no—
176#385—24no—
177#385—24no—
178#385—44no—
179#381—24no—
180#379—28no—
181#379—24no—
182#379—44no—
183#379D418yes—
184C2×#95C2312yes—
185C2×#95C2311yescharacteristic
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2311yescharacteristic
203C2×#95C2312yes—
204C2×#95C2311yescharacteristic
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C25—22no—
229C25—22no—
230C25—41no—
231C25—41no—
232C25—42no—
233C25—42no—
234C25—41no—
235C25—41no—
236C25—42no—
237C25—42no—
238C25C2×D414yes—
239C25C2412yes—
240C25C2411yescharacteristic
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—41no—
248C23×C4—41no—
249C23×C4—41no—
250C23×C4—41no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4C2412yes—
254C23×C4C2411yescharacteristic
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270#117—416no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4—41no—
287C2×C4⋊C4—41no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—41no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—41no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—41no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—416no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4C2×D414yes—
378C2×C22⋊C4C2×D414yes—
379C2×C22⋊C4C2×D418yes—
380C2×C22⋊C4C2×D418yes—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—41no—
387C2×C42—41no—
388C2×C42—42no—
389C2×C42—42no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—22no—
396#95—24no—
397#95—24no—
398#95—22no—
399#95—24no—
400#95—24no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—41no—
431#95—42no—
432#95—41no—
433#95—42no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—28no—
457C24—44no—
458C24—48no—
459C24—44no—
460C24—48no—
461C24—44no—
462C24—48no—
463C24—44no—
464C24—84no—
465C24—82no—
466C24—82no—
467C24—82no—
468C24—82no—
469C24—84no—
470C24—84no—
471C24—84no—
472C24—82no—
473C24—82no—
474C24—84no—
475C24—84no—
476C24—84no—
477C24—84no—
478C24—84no—
479C24C22×D414yes—
480C24C22×D412yes—
481C24H(5,𝔽2)12yes—
482C242−1+412yes—
483C24C2511yescharacteristic
484C22×C4—28no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
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—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
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—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
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—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—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—84no—
599C22×C4—82no—
600C22×C4—82no—
601C22×C4—84no—
602C22×C4C22×D414yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4H(5,𝔽2)12yes—
606C22×C4H(5,𝔽2)12yes—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—82no—
612C4⋊C4—82no—
613C4⋊C4—84no—
614C4⋊C4—84no—
615C4⋊C4—84no—
616C4⋊C4—84no—
617C4⋊C4—84no—
618C4⋊C4—84no—
619C4⋊C4—84no—
620C4⋊C4—84no—
621C4⋊C4—84no—
622C22⋊C4—48no—
623C22⋊C4—44no—
624C22⋊C4—48no—
625C22⋊C4—44no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C22⋊C4—48no—
634C22⋊C4—84no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C42—44no—
645C42—44no—
646C42—84no—
647C23—22no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—41no—
667C23—42no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—416no—
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—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—88no—
706C23—816no—
707C23—816no—
708C23—88no—
709C23—88no—
710C23—816no—
711C23—88no—
712C23—88no—
713C23—88no—
714C23—816no—
715C23#53714yes—
716C23C23×D411yescharacteristic
717C23C2×H(5,𝔽2)11yescharacteristic
718C23C2×H(5,𝔽2)11yescharacteristic
719C23C2×H(5,𝔽2)11yescharacteristic
720C23C2×2−1+411yescharacteristic
721C23#58512yes—
722C23#58512yes—
723C23#58511yescharacteristic
724C23#58511yescharacteristic
725C23#58512yes—
726C23#58512yes—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—416no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
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—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
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—41no—
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—41no—
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—42no—
839C2×C4—88no—
840C22—24no—
841C22—28no—
842C22—42no—
843C22—42no—
844C22—44no—
845C22—44no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—832no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22C2×#53711yescharacteristic
868C22#348411yescharacteristic
869C22#348511yescharacteristic
870C22#348512yes—
871C22#348512yes—
872C22#352911yescharacteristic
873C22#353312yes—
874C22#353411yescharacteristic
875C22#353411yescharacteristic
876C22#353511yescharacteristic
877C22#353511yescharacteristic
878C22#353912yes—
879C22#354011yescharacteristic
880C22#354011yescharacteristic
881C22#354512yes—
882C22#355111yescharacteristic
883C22#356212yes—
884C22#356412yes—
885C22#356412yes—
886C22#356612yes—
887C22#356612yes—
888C22#356612yes—
889C22#356812yes—
890C4—42no—
891C4—42no—
892C4—42no—
893C4—44no—
894C4—42no—
895C4—82no—
896C4—82no—
897C4—81no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4—81no—
904C4—82no—
905C4—82no—
906C4—82no—
907C2—44no—
908C2—84no—
909C2#3670911yescharacteristic
910C2#4140512yes—
911C2#4544111yescharacteristic
912C2#4877512yes—
913C2#5016511yescharacteristic
914C2#5271711yescharacteristic
915C2#5291111yescharacteristic
916C2#5468312yes—
917C2#5480511yescharacteristic
918C2#5733312yes—
919C2#5879711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #17190C2semidirect
4. #17116C2semidirect
5. #16579C2semidirect
6. #16473C2semidirect
7. #16470C2semidirect
8. #16458C2semidirect
9. #16434C2semidirect
11. #16316C2semidirect
12. #16077C2semidirect
13. #16015C2semidirect
14. #15717C2semidirect
15. #15350C2semidirect
16. #14907C2semidirect
17. #14893C2semidirect
24. C2×#400C22semidirect
27. C2×#398C22semidirect
35. C2×#389C22semidirect
36. C2×#389C22semidirect
50. #1445C22semidirect
51. #1445C22semidirect
52. #1444C22semidirect
53. #1443C22semidirect
54. #1443C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
98. #1436C22semidirect
99. #1436C22semidirect
100. #1436C22semidirect
101. #1436C22semidirect
102. C4⋊#95C22semidirect
103. #1434C22semidirect
104. #1434C22semidirect
105. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#27352
C2×#24822
#171902
#171162
#165792
#164732
#164702
#164582
#164342
#163912
#163162
#160772
#160152
#157172
#153502
#149072
#148932
#147272
#146732