Finite Group Databasebeta

← #515588

Subgroups — #515588

Order 512.

3212 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2322C211yesmaximal, characteristic
2C2×#2318C211yesmaximal, characteristic
3C2×#2274C211yesmaximal, characteristic, complemented
4#14140C212yesmaximal
5#14135C212yesmaximal
6#14131C212yesmaximal, complemented
7#14128C212yesmaximal, complemented
8#14085C212yesmaximal, complemented
9#14083C212yesmaximal, complemented
10#14081C212yesmaximal, complemented
11#14079C212yesmaximal, complemented
12#13989C212yesmaximal, complemented
13#13987C212yesmaximal, complemented
14#13985C212yesmaximal, complemented
15#13983C212yesmaximal, complemented
16#13782C211yesmaximal, characteristic, complemented
17C4×#386C211yesmaximal, characteristic
18C2×#1436C211yesmaximal, characteristic, complemented
19#13753C211yesmaximal, characteristic, complemented
20C22×#123C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×#117C2212yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2322C4116yescomplemented
26#2318—28no—
27C2×#389C2212yes—
28C2×#388C2212yes—
29C2×#388C2212yes—
30C2×#388C2212yes—
31C2×#387C2212yes—
32C2×#387C2212yes—
33C2×#387C2212yes—
34C2×#386C2212yes—
35C2×#386C2212yes—
36C2×#386C2211yescharacteristic
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2211yescharacteristic
40C2×#385C2212yes—
41C2×#383C2211yescharacteristic
42C2×#382C2211yescharacteristic
43C2×#381C2211yescharacteristic
44C2×#381C2211yescharacteristic
45C2×#380C2211yescharacteristic
46#2274—28no—
47C2×C4×C4⋊C4C2212yes—
48C2×C4×C4⋊C4C2212yes—
49C2×C4×C4⋊C4C2212yes—
50C2×C4×C4⋊C4C2212yes—
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2212yes—
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×#376C2212yes—
57C22×#95C2211yescharacteristic
58C22×#95C2212yes—
59C22×#95C2212yes—
60#1445C2212yes—
61#1444C2212yes—
62#1444C2212yes—
63#1443C2212yes—
64#1443C2212yes—
65#1442C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1441C2212yes—
70#1441C2212yes—
71#1441C2212yes—
72#1440C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1437C2211yescharacteristic
77#1437C2212yes—
78#1437C2212yes—
79#1437C2212yes—
80#1437C2211yescharacteristic
81#1436C2211yescharacteristic
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2211yescharacteristic
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98C4⋊#95C2212yes—
99#1434C2212yes—
100#1434C2212yes—
101#1434C2212yes—
102#1434C2212yes—
103#1434C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C4×#95C2212yes—
109C4×#95C2212yes—
110C23×D4C2311yescharacteristic
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2312yes—
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C24×C4C2311yescharacteristic
117C2×#123—28no—
118C2×#123C2×C418yes—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4C2×C418yes—
122C2×#117—28no—
123C2×#117—28no—
124C2×#117—28no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4C2×C418yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C42—24no—
152C22×C42—44no—
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2312yes—
163C22×C42C2312yes—
164#389C2×C4116yescomplemented
165#388—28no—
166#388—44no—
167#388C2×C4116yescomplemented
168#387—28no—
169#387—44no—
170#387C2×C4116yescomplemented
171#386—28no—
172#386—28no—
173#386C2×C418yes—
174#385—28no—
175#385—28no—
176#385C2×C418yes—
177#385C2×C4116yescomplemented
178#383—24no—
179#382—24no—
180#381—24no—
181#381C2×C418yes—
182#380—24no—
183C4×C4⋊C4—28no—
184C4×C4⋊C4—28no—
185C4×C4⋊C4—28no—
186C4×C4⋊C4—28no—
187C4×C22⋊C4—24no—
188C4×C22⋊C4—28no—
189C4×C22⋊C4—44no—
190C4×C22⋊C4C2×C418yes—
191C4×C22⋊C4D418yes—
192#376—44no—
193C2×#95—24no—
194C2×#95—28no—
195C2×#95—44no—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2311yescharacteristic
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2311yescharacteristic
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×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C2×#95C2311yescharacteristic
241C2×#95C2311yescharacteristic
242C25C2411yescharacteristic
243C25C2411yescharacteristic
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4C22×C414yes—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4C22×C414yes—
277C23×C4C22×C414yes—
278C23×C4C22×C414yes—
279C23×C4C22×C414yes—
280C23×C4C2×D414yes—
281C23×C4#4118yes—
282C23×C4#4114yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300#123—232no—
301C4×D4—232no—
302#117—264no—
303C2×C4⋊C4—232no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
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—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4C22×C418yes—
333C2×C4⋊C4C22×C418yes—
334C2×C4⋊C4C22×C414yes—
335C2×C4⋊C4C22×C418yes—
336C2×C4⋊C4C22×C418yes—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
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⋊C4C22×C414yes—
364C2×C22⋊C4C22×C414yes—
365C2×C22⋊C4C22×C414yes—
366C2×C22⋊C4C22×C418yes—
367C2×C22⋊C4C22×C414yes—
368C2×C22⋊C4C22×C418yes—
369C2×C22⋊C4C2×D418yes—
370C2×C22⋊C4#4118yes—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—416no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42C22×C414yes—
401C2×C42C22×C418yes—
402C2×C42C2×D418yes—
403#95—22no—
404#95—22no—
405#95—24no—
406#95—22no—
407#95—22no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95C22×C418yes—
443#95C22×C418yes—
444#95C22×C418yes—
445#95C22×C418yes—
446#95C22×C418yes—
447#95C2×D414yes—
448#95C2×D414yes—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—21no—
454C24—22no—
455C24—22no—
456C24—21no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24C23×C412yes—
462C24C23×C412yes—
463C24C22×D412yes—
464C24C2×#4114yes—
465C24C2×#4112yes—
466C24C2×#4114yes—
467C24C2511yescharacteristic
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—48no—
472C2×D4—48no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—216no—
476C22×C4—216no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—216no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
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—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
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—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—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—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—28no—
553C22×C4—28no—
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—44no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—44no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—82no—
584C22×C4—82no—
585C22×C4—84no—
586C22×C4—82no—
587C22×C4—82no—
588C22×C4—84no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—84no—
593C22×C4#117116yes—
594C22×C4C4×D4116yes—
595C22×C4C23×C412yes—
596C22×C4C23×C414yes—
597C22×C4C23×C414yes—
598C22×C4C23×C412yes—
599C22×C4C23×C412yes—
600C22×C4C23×C414yes—
601C22×C4C23×C414yes—
602C22×C4C23×C412yes—
603C22×C4C23×C412yes—
604C22×C4C22×D414yes—
605C22×C4C22×D414yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C2×#4114yes—
609C22×C4C2×#4114yes—
610C22×C4C2×#4114yes—
611C22×C4C2×#4114yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4H(5,𝔽2)14yes—
615C22×C42−1+414yes—
616C4⋊C4—216no—
617C4⋊C4—216no—
618C4⋊C4—216no—
619C4⋊C4—216no—
620C4⋊C4—216no—
621C4⋊C4—28no—
622C4⋊C4—48no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C4⋊C4—84no—
627C22⋊C4—28no—
628C22⋊C4—28no—
629C22⋊C4—28no—
630C22⋊C4—216no—
631C22⋊C4—216no—
632C22⋊C4—216no—
633C22⋊C4—28no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—84no—
638C22⋊C4—84no—
639C42—28no—
640C42—216no—
641C42—216no—
642C42—28no—
643C42—48no—
644C42—48no—
645C42—48no—
646C42—44no—
647C42—84no—
648C42—84no—
649C42—84no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23C2×#11714yes—
688C23C2×C4×D414yes—
689C23C4×#4114yes—
690C23#52518yes—
691C23#52918yes—
692C23C24×C411yescharacteristic
693C23C23×D411yescharacteristic
694C23C22×#4112yes—
695C23C22×#4111yescharacteristic
696C23C22×#4112yes—
697C23C2×H(5,𝔽2)12yes—
698C23C2×2−1+412yes—
699C23#58512yes—
700C23#58512yes—
701D4—416no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—232no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—416no—
752C2×C4—432no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—41no—
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—41no—
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—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—88no—
812C2×C4—88no—
813C2×C4—816no—
814C2×C4C2×#11718yes—
815C2×C4C2×C4×D414yes—
816C2×C4C2×C4×D414yes—
817C22—28no—
818C22—28no—
819C22—28no—
820C22—28no—
821C22—28no—
822C22—24no—
823C22—24no—
824C22—28no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—44no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22#229018yes—
835C22C22×#11711yescharacteristic
836C22C22×C4×D411yescharacteristic
837C22C2×C4×#4111yescharacteristic
838C22C4×H(5,𝔽2)12yes—
839C22C4×2−1+412yes—
840C22C2×#52512yes—
841C22C2×#52912yes—
842C22#349011yescharacteristic
843C22#349111yescharacteristic
844C22#349212yes—
845C22#349312yes—
846C22#349512yes—
847C22#349612yes—
848C22#349911yescharacteristic
849C22#350011yescharacteristic
850C22#350612yes—
851C22#350712yes—
852C22#351312yes—
853C22#351512yes—
854C22#352012yes—
855C22#352112yes—
856C4—28no—
857C4—24no—
858C4—24no—
859C4—44no—
860C4—44no—
861C4—44no—
862C4—44no—
863C4—44no—
864C4—44no—
865C4—44no—
866C4—42no—
867C4—42no—
868C4—44no—
869C4—42no—
870C4—44no—
871C4—82no—
872C4—82no—
873C2—28no—
874C2—82no—
875C2C2×#229011yescharacteristic
876C2#3425212yes—
877C2#3427311yescharacteristic
878C2#3427611yescharacteristic
879C2#3428212yes—
880C2#3536312yes—
881C2#3536412yes—
882C2#3537212yes—
883C2#3545812yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×#2274C2semidirect
6. #14131C2semidirect
7. #14128C2semidirect
8. #14085C2semidirect
9. #14083C2semidirect
10. #14081C2semidirect
11. #14079C2semidirect
12. #13989C2semidirect
13. #13987C2semidirect
14. #13985C2semidirect
15. #13983C2semidirect
16. #13782C2semidirect
18. C2×#1436C2semidirect
19. #13753C2semidirect
25. #2322C4semidirect
164. #389C2×C4semidirect
167. #388C2×C4semidirect
170. #387C2×C4semidirect
177. #385C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23222
C2×#23182
C2×#22742
#141402
#141352
#141312
#141282
#140852
#140832
#140812
#140792
#139892
#139872
#139852
#139832
#137822
C4×#3862
C2×#14362
#137532