Finite Group Databasebeta

← #575566

Subgroups — #575566

Order 512.

2514 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
1C2×#2377C211yesmaximal, characteristic
2#14497C212yesmaximal, complemented
3#14400C212yesmaximal, complemented
4#14392C212yesmaximal, complemented
5#14377C212yesmaximal, complemented
6#14375C212yesmaximal, complemented
7#14374C212yesmaximal, complemented
8#14297C211yesmaximal, characteristic, complemented
9#14290C211yesmaximal, characteristic
10#14137C211yesmaximal, characteristic
11#14130C211yesmaximal, characteristic, complemented
12#14093C212yesmaximal, complemented
13#14076C212yesmaximal, complemented
14#14034C212yesmaximal, complemented
15#14010C212yesmaximal, complemented
16#14008C212yesmaximal, complemented
17#13988C212yesmaximal, complemented
18#13807C211yesmaximal, characteristic, complemented
19#13776C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22#2377C4116yescomplemented
23C2×#390C2212yes—
24C2×#390C2212yes—
25C2×#389C2212yes—
26C2×#388C2212yes—
27C2×#388C2212yes—
28C2×#388C2212yes—
29C2×#388C2212yes—
30C2×#387C2212yes—
31C2×#387C2212yes—
32C2×#386C2212yes—
33C2×#386C2212yes—
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#385C2211yescharacteristic
37C2×#385C2211yescharacteristic
38C2×#385C2212yes—
39C2×#382C2212yes—
40C2×#381C2211yescharacteristic
41C2×#381C2212yes—
42C2×#381C2211yescharacteristic
43C2×#380C2212yes—
44C2×#380C2211yescharacteristic
45C2×C4×C22⋊C4C2211yescharacteristic
46C2×C4×C22⋊C4C2211yescharacteristic
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2212yes—
49#1445C2211yescharacteristic
50#1445C2212yes—
51#1445C2211yescharacteristic
52#1444C2212yes—
53#1443C2212yes—
54#1443C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1441C2212yes—
59#1441C2212yes—
60#1441C2212yes—
61#1440C2212yes—
62#1440C2212yes—
63#1440C2212yes—
64#1439C2212yes—
65#1439C2212yes—
66#1439C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1438C2211yescharacteristic
72#1438C2212yes—
73#1438C2212yes—
74#1438C2211yescharacteristic
75#1437C2212yes—
76#1437C2212yes—
77#1437C2212yes—
78#1437C2212yes—
79#1437C2212yes—
80#1437C2212yes—
81#1437C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91C4⋊#95C2212yes—
92C4⋊#95C2212yes—
93#1434C2212yes—
94#1434C2212yes—
95#1434C2212yes—
96#1434C2212yes—
97#1434C2211yescharacteristic
98#1434C2212yes—
99#1434C2211yescharacteristic
100C22⋊#95C2211yescharacteristic
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2211yescharacteristic
104C4×#95C2212yes—
105C4×#95C2212yes—
106C4×#95C2211yescharacteristic
107C4×#95C2211yescharacteristic
108C23×D4C2312yes—
109C23×D4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C2×#121—24no—
115C2×#121—24no—
116C2×#121C2×C418yes—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—44no—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C22⋊C4C2311yescharacteristic
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C42C2312yes—
148C22×C42C2312yes—
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2312yes—
155#390—44no—
156#390C2×C4116yes—
157#389—44no—
158#388—44no—
159#388—44no—
160#388—44no—
161#388C2×C4116yescomplemented
162#387—44no—
163#387C2×C4116yescomplemented
164#386—44no—
165#386—44no—
166#386C2×C4116yes—
167#386C2×C4116yescomplemented
168#385—42no—
169#385—42no—
170#385C2×C4116yescomplemented
171#382—44no—
172#381—24no—
173#381—44no—
174#381C2×C418yes—
175#380—44no—
176#380C2×C418yes—
177C4×C22⋊C4—24no—
178C4×C22⋊C4—24no—
179C4×C22⋊C4—44no—
180C4×C22⋊C4—44no—
181C2×#95C2311yescharacteristic
182C2×#95C2311yescharacteristic
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2311yescharacteristic
189C2×#95C2311yescharacteristic
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2311yescharacteristic
196C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C25C2412yes—
227C25C2411yescharacteristic
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—42no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4C22×C418yes—
239C22×D4C22×C414yes—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—41no—
253C23×C4—41no—
254C23×C4—41no—
255C23×C4—41no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4C22×C418yes—
259C23×C4C22×C414yes—
260C23×C4#4114yes—
261C23×C4#4114yes—
262C23×C4C2411yescharacteristic
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279#121—232no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—416no—
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⋊C4C22×C414yes—
306C2×C4⋊C4C22×C418yes—
307C2×C4⋊C4C22×C418yes—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—41no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—41no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—42no—
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—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⋊C4C22×C418yes—
359C2×C22⋊C4C22×C414yes—
360C2×C22⋊C4C22×C414yes—
361C2×C22⋊C4C22×C418yes—
362C2×C22⋊C4C22×C418yes—
363C2×C22⋊C4C22×C418yes—
364C2×C22⋊C4C22×C418yes—
365C2×C42—24no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42C22×C418yes—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—24no—
392#95—22no—
393#95—22no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
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#95C22×C418yes—
427#95C22×C414yes—
428#95C22×C418yes—
429#95C22×C414yes—
430#95C22×C418yes—
431#95C22×C418yes—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—21no—
436C24—21no—
437C24—22no—
438C24—21no—
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—
454C24C23×C414yes—
455C24C23×C412yes—
456C24C2×#4112yes—
457C24C2×#4112yes—
458C24C2511yescharacteristic
459C2×D4—216no—
460C2×D4—28no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—82no—
465C2×D4—82no—
466C2×D4—84no—
467C2×D4—84no—
468C2×D4—84no—
469C2×D4—84no—
470C2×D4—84no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
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—21no—
505C22×C4—21no—
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—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—28no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
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—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
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—21no—
563C22×C4—21no—
564C22×C4—44no—
565C22×C4—48no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—44no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4—82no—
575C22×C4—82no—
576C22×C4—82no—
577C22×C4—82no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4#117116yes—
585C22×C4C23×C414yes—
586C22×C4C23×C414yes—
587C22×C4C23×C414yes—
588C22×C4C23×C414yes—
589C22×C4C23×C414yes—
590C22×C4C23×C412yes—
591C22×C4C23×C412yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4H(5,𝔽2)14yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4H(5,𝔽2)14yes—
599C22×C42−1+412yes—
600C4⋊C4—28no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—84no—
606C4⋊C4—84no—
607C4⋊C4—84no—
608C4⋊C4—84no—
609C22⋊C4—216no—
610C22⋊C4—48no—
611C22⋊C4—44no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—44no—
618C22⋊C4—48no—
619C22⋊C4—44no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—84no—
623C22⋊C4—84no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C42—48no—
629C42—82no—
630C42—82no—
631C42—84no—
632C42—84no—
633C42—84no—
634C42—84no—
635C42—84no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
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—42no—
691C23—42no—
692C23—42no—
693C23C2×#11714yes—
694C23C24×C411yescharacteristic
695C23C22×#4111yescharacteristic
696C23C22×#4111yescharacteristic
697C23C2×H(5,𝔽2)12yes—
698C23C2×H(5,𝔽2)12yes—
699C23C2×H(5,𝔽2)11yescharacteristic
700C23C2×2−1+411yescharacteristic
701C23#58512yes—
702C23#58512yes—
703C23#58511yescharacteristic
704C23#58511yescharacteristic
705D4—88no—
706D4—816no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
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—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—416no—
741C2×C4—41no—
742C2×C4—41no—
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—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—41no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
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—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—88no—
814C2×C4—816no—
815C2×C4—88no—
816C2×C4C2×#11714yes—
817C2×C4C2×#11714yes—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—44no—
822C22—44no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—42no—
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×#11711yescharacteristic
845C22C4×H(5,𝔽2)12yes—
846C22C4×H(5,𝔽2)11yescharacteristic
847C22C4×H(5,𝔽2)12yes—
848C22C4×2−1+411yescharacteristic
849C22#349011yescharacteristic
850C22#349111yescharacteristic
851C22#349412yes—
852C22#349411yescharacteristic
853C22#349511yescharacteristic
854C22#350512yes—
855C22#350811yescharacteristic
856C22#351011yescharacteristic
857C22#351111yescharacteristic
858C22#351211yescharacteristic
859C22#353312yes—
860C22#353712yes—
861C22#355812yes—
862C22#355912yes—
863C22#356112yes—
864C22#356212yes—
865C22#356212yes—
866C22#356712yes—
867C4—24no—
868C4—24no—
869C4—44no—
870C4—42no—
871C4—44no—
872C4—44no—
873C4—44no—
874C4—44no—
875C4—44no—
876C4—42no—
877C4—44no—
878C4—82no—
879C4—82no—
880C4—82no—
881C4—81no—
882C4—82no—
883C4—81no—
884C2—44no—
885C2—84no—
886C2#3425111yescharacteristic
887C2#3425311yescharacteristic
888C2#3425511yescharacteristic
889C2#3451812yes—
890C2#3452712yes—
891C2#5067411yescharacteristic
892C2#5067511yescharacteristic
893C2#5070912yes—
894C2#5071012yes—
895C2#5104211yescharacteristic
896C2#5142711yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#121C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14497C2semidirect
3. #14400C2semidirect
4. #14392C2semidirect
5. #14377C2semidirect
6. #14375C2semidirect
7. #14374C2semidirect
8. #14297C2semidirect
11. #14130C2semidirect
12. #14093C2semidirect
13. #14076C2semidirect
14. #14034C2semidirect
15. #14010C2semidirect
16. #14008C2semidirect
17. #13988C2semidirect
18. #13807C2semidirect
19. #13776C2semidirect
22. #2377C4semidirect
161. #388C2×C4semidirect
163. #387C2×C4semidirect
167. #386C2×C4semidirect
170. #385C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23772
#144972
#144002
#143922
#143772
#143752
#143742
#142972
#142902
#141372
#141302
#140932
#140762
#140342
#140102
#140082
#139882
#138072
#137762