Finite Group Databasebeta

← #4664507

Subgroups — #4664507

Order 512.

2334 conjugacy classes of subgroups.

The subgroup lattice has 915 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2736C211yesmaximal, characteristic
2C2×#2842C211yesmaximal, characteristic
3#17122C212yesmaximal, complemented
4#17111C212yesmaximal, complemented
5#16830C211yesmaximal, characteristic, complemented
6#16786C212yesmaximal, complemented
7#16455C212yesmaximal, complemented
8#16391C212yesmaximal
9#16316C212yesmaximal, complemented
10#16303C211yesmaximal, characteristic, complemented
11#16295C212yesmaximal, complemented
12#15828C212yesmaximal, complemented
13#15706C212yesmaximal, complemented
14#15621C212yesmaximal, complemented
15#15294C212yesmaximal, complemented
16#15161C211yesmaximal, characteristic, complemented
17#15016C211yesmaximal, characteristic, complemented
18#14820C212yesmaximal
19#13991C211yesmaximal, characteristic
20C23×C22⋊C4C2211yescharacteristic
21#2842—28no—
22#2736—28no—
23C2×#399C2211yescharacteristic
24C2×#399C2211yescharacteristic
25C2×#399C2212yes—
26C2×#398C2212yescomplemented
27C2×#397C2212yes—
28C2×#397C2211yescharacteristic
29C2×#397C2212yes—
30C2×#397C2212yes—
31C2×#397C2212yes—
32C2×#396C2212yes—
33C2×#396C2212yes—
34C2×#396C2212yes—
35C2×#396C2212yes—
36C2×#395C2212yescomplemented
37C2×#393C2211yescharacteristic
38C2×#393C2212yes—
39C2×#391C2211yescharacteristic, complemented
40C2×#389C2212yescomplemented
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#385C2211yescharacteristic
46C2×#382C2211yescharacteristic, complemented
47C2×#380C2212yes—
48C2×#379C2212yes—
49C2×#379C2212yes—
50C2×#379C2211yescharacteristic
51C2×#379C2211yescharacteristic
52C2×C4×C22⋊C4C2211yescharacteristic
53#1446C2211yescharacteristic, complemented
54#1445C2211yescharacteristic, complemented
55#1445C2212yescomplemented
56#1445C2212yescomplemented
57#1445C2211yescharacteristic, complemented
58#1445C2211yescharacteristic, complemented
59#1444C2212yescomplemented
60#1444C2212yescomplemented
61#1443C2212yescomplemented
62#1442C2212yescomplemented
63#1442C2212yescomplemented
64#1442C2212yescomplemented
65#1442C2212yescomplemented
66#1442C2212yescomplemented
67#1442C2212yescomplemented
68#1442C2212yescomplemented
69#1441C2212yescomplemented
70#1441C2212yescomplemented
71#1441C2212yescomplemented
72#1441C2212yescomplemented
73#1441C2212yescomplemented
74#1441C2212yescomplemented
75#1441C2212yescomplemented
76#1441C2212yescomplemented
77#1440C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1440C2212yes—
83#1440C2212yes—
84#1440C2212yes—
85#1440C2212yes—
86#1440C2212yes—
87#1440C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1437C2212yes—
97#1436C2212yescomplemented
98#1436C2212yescomplemented
99#1436C2212yescomplemented
100#1436C2212yescomplemented
101C4⋊#95C2211yescharacteristic, complemented
102#1434C2212yescomplemented
103#1434C2211yescharacteristic, complemented
104C22⋊#95C2212yes—
105C22⋊#95C2211yescharacteristic
106C22⋊#95C2211yescharacteristic
107C22⋊#95C2212yes—
108C22⋊#95C2212yes—
109C26C2311yescharacteristic
110C23×Q8C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C22⋊C4—44no—
128C22×C22⋊C4—42no—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154#399—28no—
155#399—24no—
156#399—24no—
157#398—44no—
158#397—24no—
159#397—28no—
160#397—44no—
161#397—44no—
162#397—44no—
163#396—28no—
164#396—28no—
165#396—28no—
166#396—28no—
167#395—44no—
168#393—24no—
169#393—28no—
170#391—42no—
171#389—44no—
172#388—28no—
173#388—28no—
174#388—28no—
175#388—44no—
176#385—42no—
177#382—42no—
178#380—44no—
179#379—28no—
180#379—28no—
181#379—42no—
182#379D418yes—
183C4×C22⋊C4—42no—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2311yescharacteristic
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2311yescharacteristic
193C2×#95C2311yescharacteristic
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
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×#95C2311yescharacteristic
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C25—22no—
229C25—22no—
230C25—41no—
231C25—42no—
232C25—41no—
233C25—42no—
234C25—42no—
235C25—42no—
236C25—41no—
237C25—41no—
238C25C2×D414yes—
239C25C2412yes—
240C25C2411yescharacteristic
241C22×Q8—22no—
242C22×Q8—42no—
243C22×Q8—41no—
244C22×Q8—41no—
245C22×Q8—42no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—42no—
251C23×C4—41no—
252C23×C4—41no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—41no—
256C23×C4C2412yes—
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
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—41no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
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—24no—
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—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—41no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—416no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—41no—
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—41no—
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⋊C4—42no—
378C2×C22⋊C4C2×D414yes—
379C2×C22⋊C4C2×D418yes—
380C2×C22⋊C4C2×D418yes—
381C2×C22⋊C4C2×D414yes—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389#95—24no—
390#95—22no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—22no—
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—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—41no—
420#95—41no—
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—42no—
433C24—21no—
434C24—21no—
435C24—22no—
436C24—21no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—21no—
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—28no—
456C24—44no—
457C24—48no—
458C24—48no—
459C24—44no—
460C24—44no—
461C24—44no—
462C24—48no—
463C24—84no—
464C24—82no—
465C24—82no—
466C24—82no—
467C24—84no—
468C24—84no—
469C24—84no—
470C24—82no—
471C24—82no—
472C24—84no—
473C24—84no—
474C24—82no—
475C24—84no—
476C24—84no—
477C24—84no—
478C24C22×D414yes—
479C24C22×D412yes—
480C242−1+412yes—
481C242−1+412yes—
482C24C2511yescharacteristic
483C2×Q8—44no—
484C2×Q8—84no—
485C2×Q8—82no—
486C2×Q8—82no—
487C2×Q8—84no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
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—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
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—22no—
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—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
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—21no—
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—21no—
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—44no—
590C22×C4—48no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—82no—
594C22×C4—84no—
595C22×C4—82no—
596C22×C4—84no—
597C22×C4—82no—
598C22×C4—84no—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D414yes—
602C22×C4H(5,𝔽2)12yes—
603C22×C4H(5,𝔽2)14yes—
604C22×C4H(5,𝔽2)12yes—
605C4⋊C4—48no—
606C4⋊C4—84no—
607C4⋊C4—84no—
608C4⋊C4—84no—
609C4⋊C4—82no—
610C4⋊C4—84no—
611C4⋊C4—82no—
612C4⋊C4—84no—
613C4⋊C4—82no—
614C4⋊C4—84no—
615C4⋊C4—84no—
616C4⋊C4—84no—
617C4⋊C4—84no—
618C4⋊C4—84no—
619C22⋊C4—48no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—44no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C22⋊C4—84no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C22⋊C4—82no—
640C22⋊C4—84no—
641C42—44no—
642C42—84no—
643C42—82no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—416no—
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—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—816no—
703C23—88no—
704C23—88no—
705C23—816no—
706C23—88no—
707C23—88no—
708C23—88no—
709C23—816no—
710C23—88no—
711C23—816no—
712C23#53614yes—
713C23C23×D411yescharacteristic
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×H(5,𝔽2)12yes—
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×2−1+411yescharacteristic
718C23C2×2−1+411yescharacteristic
719C23#58512yes—
720C23#58512yes—
721C23#58512yes—
722C23#58511yescharacteristic
723C23#58511yescharacteristic
724Q8—88no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
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—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—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—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
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—41no—
799C2×C4—41no—
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—88no—
833C2×C4—88no—
834C22—28no—
835C22—24no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—44no—
842C22—42no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—832no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22C2×#53611yescharacteristic
862C22#348512yes—
863C22#349612yes—
864C22#349611yescharacteristic
865C22#349611yescharacteristic
866C22#352911yescharacteristic
867C22#353211yescharacteristic
868C22#353311yescharacteristic
869C22#353412yes—
870C22#353511yescharacteristic
871C22#353512yes—
872C22#353611yescharacteristic
873C22#354012yes—
874C22#355112yes—
875C22#355111yescharacteristic
876C22#356112yes—
877C22#356111yescharacteristic
878C22#356212yes—
879C22#356412yes—
880C22#356412yes—
881C22#356411yescharacteristic
882C22#356612yes—
883C22#356612yes—
884C4—42no—
885C4—42no—
886C4—44no—
887C4—42no—
888C4—42no—
889C4—44no—
890C4—81no—
891C4—81no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C2—44no—
902C2—84no—
903C2#3674011yescharacteristic
904C2#4051112yes—
905C2#4547711yescharacteristic
906C2#4785112yes—
907C2#4881111yescharacteristic
908C2#5275111yescharacteristic
909C2#5292711yescharacteristic
910C2#5714711yescharacteristic
911C2#5825911yescharacteristic
912C2#5879712yes—
913C2#5886312yes—
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. #17122C2semidirect
4. #17111C2semidirect
5. #16830C2semidirect
6. #16786C2semidirect
7. #16455C2semidirect
9. #16316C2semidirect
10. #16303C2semidirect
11. #16295C2semidirect
12. #15828C2semidirect
13. #15706C2semidirect
14. #15621C2semidirect
15. #15294C2semidirect
16. #15161C2semidirect
17. #15016C2semidirect
26. C2×#398C22semidirect
36. C2×#395C22semidirect
39. C2×#391C22semidirect
40. C2×#389C22semidirect
46. C2×#382C22semidirect
53. #1446C22semidirect
54. #1445C22semidirect
55. #1445C22semidirect
56. #1445C22semidirect
57. #1445C22semidirect
58. #1445C22semidirect
59. #1444C22semidirect
60. #1444C22semidirect
61. #1443C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
74. #1441C22semidirect
75. #1441C22semidirect
76. #1441C22semidirect
97. #1436C22semidirect
98. #1436C22semidirect
99. #1436C22semidirect
100. #1436C22semidirect
101. C4⋊#95C22semidirect
102. #1434C22semidirect
103. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#27362
C2×#28422
#171222
#171112
#168302
#167862
#164552
#163912
#163162
#163032
#162952
#158282
#157062
#156212
#152942
#151612
#150162
#148202
#139912