Finite Group Databasebeta

← #5083502

Subgroups — #5083502

Order 512.

2276 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2735C211yesmaximal, characteristic
2C2×#2664C211yesmaximal, characteristic, complemented
3#17229C211yesmaximal, characteristic, complemented
4#17133C212yesmaximal, complemented
5#17130C212yesmaximal, complemented
6#16538C212yesmaximal, complemented
7#16494C212yesmaximal, complemented
8#16298C212yesmaximal
9#16087C212yesmaximal, complemented
10#15986C211yesmaximal, characteristic
11#15928C211yesmaximal, characteristic, complemented
12#15846C212yesmaximal, complemented
13#15765C212yesmaximal, complemented
14#15597C212yesmaximal, complemented
15#15480C211yesmaximal, characteristic
16#15443C212yesmaximal, complemented
17#15284C212yesmaximal
18#14783C212yesmaximal, complemented
19#14646C211yesmaximal, characteristic, complemented
20C22×#126C2211yescharacteristic
21C22×#125C2211yescharacteristic, complemented
22#2735—28no—
23#2664—28no—
24C2×#400C2211yescharacteristic, complemented
25C2×#400C2211yescharacteristic, complemented
26C2×#399C2212yes—
27C2×#399C2212yes—
28C2×#399C2211yescharacteristic
29C2×#398C2211yescharacteristic, complemented
30C2×#398C2212yescomplemented
31C2×#398C2212yescomplemented
32C2×#397C2211yescharacteristic
33C2×#397C2211yescharacteristic
34C2×#397C2212yes—
35C2×#397C2212yes—
36C2×#396C2212yes—
37C2×#396C2212yes—
38C2×#396C2212yes—
39C2×#389C2212yescomplemented
40C2×#388C2212yes—
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#387C2212yescomplemented
46C2×#384C2211yescharacteristic, complemented
47C2×#379C2211yescharacteristic
48C2×#379C2212yes—
49C2×#379C2211yescharacteristic
50C2×#379C2211yescharacteristic
51C2×#379C2212yes—
52C2×C4×C4⋊C4C2211yescharacteristic, complemented
53#1445C2211yescharacteristic, complemented
54#1445C2212yescomplemented
55#1444C2212yescomplemented
56#1444C2212yescomplemented
57#1444C2212yescomplemented
58#1444C2212yescomplemented
59#1443C2212yescomplemented
60#1443C2212yescomplemented
61#1443C2212yescomplemented
62#1443C2212yescomplemented
63#1442C2212yescomplemented
64#1442C2212yescomplemented
65#1441C2212yescomplemented
66#1441C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2212yescomplemented
69#1441C2212yescomplemented
70#1441C2212yescomplemented
71#1440C2211yescharacteristic
72#1440C2212yes—
73#1440C2211yescharacteristic
74#1440C2212yes—
75#1440C2212yes—
76#1440C2211yescharacteristic
77#1440C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1437C2211yescharacteristic
98#1437C2212yes—
99#1437C2212yes—
100#1437C2212yes—
101#1436C2212yescomplemented
102#1436C2212yescomplemented
103#1436C2211yescharacteristic, complemented
104#1436C2212yescomplemented
105#1436C2212yescomplemented
106#1436C2212yescomplemented
107C4⋊#95C2212yescomplemented
108#1434C2212yescomplemented
109C26C2311yescharacteristic
110C2×#126—24no—
111C2×#126—42no—
112C2×#126—42no—
113C2×#125—24no—
114C2×#125—42no—
115C2×#125—42no—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162#400—24no—
163#400—42no—
164#399—44no—
165#399—44no—
166#399D418yes—
167#398—28no—
168#398—24no—
169#398—44no—
170#397—24no—
171#397—24no—
172#397—28no—
173#397—44no—
174#396—28no—
175#396—28no—
176#396—44no—
177#389—28no—
178#388—28no—
179#388—28no—
180#388—28no—
181#388—28no—
182#388—44no—
183#387—44no—
184#384—42no—
185#379—28no—
186#379—24no—
187#379—42no—
188#379—42no—
189#379—44no—
190C4×C4⋊C4—24no—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2311yescharacteristic
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—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2311yescharacteristic
231C25—22no—
232C25—24no—
233C25—42no—
234C25—42no—
235C25—42no—
236C25—42no—
237C25—41no—
238C25—42no—
239C25—41no—
240C25C2411yescharacteristic
241C25C2412yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2411yescharacteristic
245C23×C4C2411yescharacteristic
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259#126—416no—
260#125—416no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—41no—
288C2×C4⋊C4—41no—
289C2×C4⋊C4—41no—
290C2×C4⋊C4—41no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—41no—
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—41no—
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—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4C2×D414yes—
314C2×C4⋊C4C2×D418yes—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
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—22no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—22no—
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—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—41no—
345C2×C22⋊C4—41no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—41no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
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—41no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4C2×D414yes—
383C2×C22⋊C4C2×D418yes—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—41no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395#95—22no—
396#95—24no—
397#95—22no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
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—42no—
431#95—42no—
432#95—41no—
433#95—42no—
434#95C2×D414yes—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—22no—
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—22no—
457C24—48no—
458C24—44no—
459C24—44no—
460C24—48no—
461C24—44no—
462C24—82no—
463C24—84no—
464C24—82no—
465C24—84no—
466C24—84no—
467C24—84no—
468C24—84no—
469C24—84no—
470C24—84no—
471C24—82no—
472C24—82no—
473C24—84no—
474C24—84no—
475C24—84no—
476C24—84no—
477C24—84no—
478C24C22×D412yes—
479C242−1+414yes—
480C24C2511yescharacteristic
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
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—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
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—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
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—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×C4C22×D412yes—
582C22×C4C22×D414yes—
583C22×C4C22×D412yes—
584C22×C4C22×D414yes—
585C22×C4H(5,𝔽2)14yes—
586C22×C4H(5,𝔽2)12yes—
587C22×C4H(5,𝔽2)12yes—
588C4⋊C4—48no—
589C4⋊C4—44no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C4⋊C4—48no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—48no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—82no—
599C4⋊C4—84no—
600C4⋊C4—84no—
601C4⋊C4—84no—
602C4⋊C4—84no—
603C4⋊C4—84no—
604C4⋊C4—84no—
605C4⋊C4—84no—
606C22⋊C4—48no—
607C22⋊C4—44no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—48no—
614C22⋊C4—84no—
615C22⋊C4—84no—
616C22⋊C4—84no—
617C22⋊C4—84no—
618C22⋊C4—84no—
619C22⋊C4—84no—
620C22⋊C4—84no—
621C22⋊C4—84no—
622C22⋊C4—84no—
623C22⋊C4—82no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—82no—
628C22⋊C4—82no—
629C22⋊C4—84no—
630C42—28no—
631C42—44no—
632C42—84no—
633C42—84no—
634C23—22no—
635C23—24no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—41no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—41no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
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—88no—
691C23—816no—
692C23—816no—
693C23—816no—
694C23—88no—
695C23—816no—
696C23—816no—
697C23—88no—
698C23—816no—
699C23C23×D411yescharacteristic
700C23C2×H(5,𝔽2)11yescharacteristic
701C23C2×H(5,𝔽2)11yescharacteristic
702C23C2×H(5,𝔽2)12yes—
703C23C2×2−1+412yes—
704C23#58512yes—
705C23#58512yes—
706C23#58512yes—
707C23#58512yes—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
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—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
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—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
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—42no—
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—41no—
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—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—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—42no—
820C22—44no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—832no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22#348411yescharacteristic
841C22#348512yes—
842C22#348711yescharacteristic
843C22#348912yes—
844C22#349811yescharacteristic
845C22#352911yescharacteristic
846C22#353412yes—
847C22#353512yes—
848C22#353811yescharacteristic
849C22#354112yes—
850C22#354612yes—
851C22#355111yescharacteristic
852C22#355111yescharacteristic
853C22#356012yes—
854C22#356012yes—
855C22#356112yes—
856C22#356212yes—
857C22#356412yes—
858C22#356412yes—
859C22#356612yes—
860C22#356612yes—
861C4—42no—
862C4—44no—
863C4—42no—
864C4—42no—
865C4—44no—
866C4—42no—
867C4—44no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—81no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4—81no—
876C4—82no—
877C4—82no—
878C2—84no—
879C2—82no—
880C2#4627611yescharacteristic
881C2#4642511yescharacteristic
882C2#4682412yes—
883C2#5140911yescharacteristic
884C2#5152812yes—
885C2#5259312yes—
886C2#5381412yes—
887C2#5565512yes—
888C2#5608312yes—
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
2. C2×#2664C2semidirect
3. #17229C2semidirect
4. #17133C2semidirect
5. #17130C2semidirect
6. #16538C2semidirect
7. #16494C2semidirect
9. #16087C2semidirect
11. #15928C2semidirect
12. #15846C2semidirect
13. #15765C2semidirect
14. #15597C2semidirect
16. #15443C2semidirect
18. #14783C2semidirect
19. #14646C2semidirect
21. C22×#125C22semidirect
24. C2×#400C22semidirect
25. C2×#400C22semidirect
29. C2×#398C22semidirect
30. C2×#398C22semidirect
31. C2×#398C22semidirect
39. C2×#389C22semidirect
45. C2×#387C22semidirect
46. C2×#384C22semidirect
52. C2×C4×C4⋊C4C22semidirect
53. #1445C22semidirect
54. #1445C22semidirect
55. #1444C22semidirect
56. #1444C22semidirect
57. #1444C22semidirect
58. #1444C22semidirect
59. #1443C22semidirect
60. #1443C22semidirect
61. #1443C22semidirect
62. #1443C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
101. #1436C22semidirect
102. #1436C22semidirect
103. #1436C22semidirect
104. #1436C22semidirect
105. #1436C22semidirect
106. #1436C22semidirect
107. C4⋊#95C22semidirect
108. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#27352
C2×#26642
#172292
#171332
#171302
#165382
#164942
#162982
#160872
#159862
#159282
#158462
#157652
#155972
#154802
#154432
#152842
#147832
#146462