Finite Group Databasebeta

← #572214

Subgroups — #572214

Order 512.

2608 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2483C211yesmaximal, characteristic
2#14619C212yesmaximal, complemented
3#14544C212yesmaximal, complemented
4#14507C211yesmaximal, characteristic, complemented
5#14409C211yesmaximal, characteristic, complemented
6#14398C212yesmaximal, complemented
7#14367C212yesmaximal, complemented
8#14365C212yesmaximal
9#14332C212yesmaximal, complemented
10#14233C212yesmaximal, complemented
11#14104C212yesmaximal, complemented
12#14104C212yesmaximal, complemented
13#14008C212yesmaximal, complemented
14#14008C212yesmaximal, complemented
15#13903C211yesmaximal, characteristic
16#13873C212yesmaximal
17#13831C211yesmaximal, characteristic, complemented
18#13807C211yesmaximal, characteristic, complemented
19#13775C211yesmaximal, characteristic
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22#2483C4116yescomplemented
23C2×#397C2212yes—
24C2×#397C2212yes—
25C2×#388C2212yes—
26C2×#388C2212yes—
27C2×#388C2212yes—
28C2×#388C2212yes—
29C2×#387C2212yescomplemented
30C2×#387C2212yescomplemented
31C2×#385C2211yescharacteristic
32C2×#385C2211yescharacteristic
33C2×#385C2212yes—
34C2×#381C2212yes—
35C2×#381C2211yescharacteristic
36C2×#381C2212yes—
37C2×#381C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×#380C2212yes—
40C2×#379C2212yes—
41C2×#379C2212yes—
42C2×#379C2211yescharacteristic
43C2×C4×C22⋊C4C2212yes—
44C2×C4×C22⋊C4C2211yescharacteristic
45C2×C4×C22⋊C4C2211yescharacteristic
46C2×C4×C22⋊C4C2211yescharacteristic
47#1444C2212yescomplemented
48#1443C2212yescomplemented
49#1443C2212yescomplemented
50#1443C2212yescomplemented
51#1443C2212yescomplemented
52#1442C2212yescomplemented
53#1442C2212yescomplemented
54#1442C2212yescomplemented
55#1441C2212yescomplemented
56#1441C2212yescomplemented
57#1440C2212yes—
58#1440C2212yes—
59#1440C2212yes—
60#1440C2212yes—
61#1439C2212yes—
62#1439C2212yes—
63#1439C2212yes—
64#1439C2212yes—
65#1439C2212yes—
66#1439C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1437C2211yescharacteristic
70#1437C2211yescharacteristic
71#1437C2212yes—
72#1437C2212yes—
73#1437C2211yescharacteristic
74#1437C2212yes—
75#1437C2212yes—
76#1437C2212yes—
77#1437C2212yes—
78#1437C2212yes—
79#1437C2212yes—
80#1437C2211yescharacteristic
81#1437C2211yescharacteristic
82#1437C2211yescharacteristic
83#1437C2211yescharacteristic
84#1437C2211yescharacteristic
85#1436C2212yescomplemented
86#1436C2212yescomplemented
87#1436C2212yescomplemented
88#1436C2212yescomplemented
89#1436C2212yescomplemented
90#1436C2212yescomplemented
91#1436C2212yescomplemented
92#1436C2212yescomplemented
93#1436C2212yescomplemented
94#1436C2212yescomplemented
95C4⋊#95C2212yescomplemented
96C4⋊#95C2212yescomplemented
97#1434C2212yescomplemented
98#1434C2212yescomplemented
99#1434C2212yescomplemented
100#1434C2212yescomplemented
101#1434C2212yescomplemented
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C4×#95C2212yescomplemented
106C4×#95C2212yescomplemented
107C4×#95C2212yescomplemented
108C26C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
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×C22⋊C4—42no—
121C22×C22⋊C4—42no—
122C22×C22⋊C4—42no—
123C22×C22⋊C4—42no—
124C22×C22⋊C4C2×C418yes—
125C22×C22⋊C4C2×C418yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#397C2×C4116yes—
158#397C2×C4116yes—
159#388—28no—
160#388—44no—
161#388—44no—
162#388—44no—
163#387—44no—
164#387—44no—
165#385C2×C4116yes—
166#385C2×C418yes—
167#385C2×C418yes—
168#381—44no—
169#381C2×C4116yes—
170#381C2×C418yes—
171#381C2×C418yes—
172#380—44no—
173#380—42no—
174#379—28no—
175#379—44no—
176#379C2×C418yes—
177C4×C22⋊C4—28no—
178C4×C22⋊C4—42no—
179C4×C22⋊C4—42no—
180C4×C22⋊C4—42no—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2311yescharacteristic
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2311yescharacteristic
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C25—22no—
226C25—22no—
227C25—24no—
228C25—42no—
229C25—42no—
230C25—42no—
231C25—42no—
232C25—42no—
233C25C22×C414yes—
234C25C2411yescharacteristic
235C25C2411yescharacteristic
236C25C2411yescharacteristic
237C23×C4—24no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—41no—
243C23×C4—41no—
244C23×C4—41no—
245C23×C4—41no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4C22×C414yes—
254C23×C4C22×C414yes—
255C23×C4C22×C414yes—
256C23×C4C22×C414yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
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⋊C4C22×C418yes—
293C2×C4⋊C4C22×C418yes—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—24no—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—416no—
312C2×C22⋊C4—416no—
313C2×C22⋊C4—41no—
314C2×C22⋊C4—41no—
315C2×C22⋊C4—41no—
316C2×C22⋊C4—41no—
317C2×C22⋊C4—41no—
318C2×C22⋊C4—41no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—41no—
322C2×C22⋊C4—41no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
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—42no—
339C2×C22⋊C4—42no—
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⋊C4C22×C418yes—
350C2×C22⋊C4C22×C414yes—
351C2×C22⋊C4C22×C414yes—
352C2×C22⋊C4C22×C414yes—
353C2×C22⋊C4C22×C414yes—
354C2×C22⋊C4C22×C418yes—
355C2×C22⋊C4C22×C414yes—
356C2×C22⋊C4C22×C414yes—
357C2×C22⋊C4C22×C418yes—
358C2×C22⋊C4C22×C418yes—
359C2×C22⋊C4#4118yes—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—41no—
364C2×C42—42no—
365C2×C42—41no—
366C2×C42—41no—
367C2×C42—41no—
368C2×C42—42no—
369C2×C42—42no—
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—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—41no—
406#95—42no—
407#95—42no—
408#95—41no—
409#95—42no—
410#95—41no—
411#95—41no—
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#95C22×C418yes—
422#95C22×C418yes—
423#95C22×C418yes—
424#95C22×C418yes—
425#95C22×C418yes—
426#95C22×C418yes—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—21no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—28no—
449C24—28no—
450C24—44no—
451C24—48no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24—44no—
456C24—48no—
457C24—44no—
458C24—84no—
459C24—84no—
460C24—84no—
461C24—84no—
462C24—84no—
463C24—82no—
464C24—82no—
465C24—84no—
466C24—84no—
467C24—84no—
468C24—84no—
469C24C23×C412yes—
470C24C23×C412yes—
471C24C23×C412yes—
472C24C2×#4114yes—
473C24H(5,𝔽2)12yes—
474C24H(5,𝔽2)12yes—
475C24C2511yescharacteristic
476C22×C4—22no—
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—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
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—21no—
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—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—28no—
535C22×C4—28no—
536C22×C4—28no—
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—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—44no—
573C22×C4—44no—
574C22×C4—48no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—82no—
581C22×C4—82no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4—82no—
585C22×C4—82no—
586C22×C4—84no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4C23×C414yes—
590C22×C4C23×C412yes—
591C22×C4C23×C412yes—
592C22×C4C23×C414yes—
593C22×C4C23×C414yes—
594C22×C4C23×C414yes—
595C22×C4C23×C412yes—
596C22×C4C23×C412yes—
597C22×C4C2×#4114yes—
598C22×C4C2×#4114yes—
599C22×C4H(5,𝔽2)14yes—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—84no—
603C4⋊C4—84no—
604C4⋊C4—84no—
605C4⋊C4—84no—
606C4⋊C4—84no—
607C22⋊C4—28no—
608C22⋊C4—216no—
609C22⋊C4—48no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—48no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—84no—
623C22⋊C4—84no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C22⋊C4—84no—
629C42—84no—
630C42—84no—
631C42—84no—
632C42—82no—
633C42—82no—
634C42—84no—
635C42—82no—
636C42—82no—
637C42—84no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—22no—
642C23—22no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—24no—
656C23—22no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—416no—
666C23—416no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—42no—
673C23—41no—
674C23—42no—
675C23—41no—
676C23—41no—
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—41no—
692C23—42no—
693C23—41no—
694C23—42no—
695C23—41no—
696C23—41no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—88no—
702C23—816no—
703C23—816no—
704C23—816no—
705C23—816no—
706C23—816no—
707C23—816no—
708C23C4×#4114yes—
709C23#51814yes—
710C23C24×C411yescharacteristic
711C23C22×#4112yes—
712C23C2×H(5,𝔽2)11yescharacteristic
713C23C2×H(5,𝔽2)11yescharacteristic
714C23C2×H(5,𝔽2)12yes—
715C23#58512yes—
716C23#58512yes—
717C23#58512yes—
718C23#58512yes—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
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—42no—
749C2×C4—42no—
750C2×C4—42no—
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—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
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—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—88no—
824C2×C4—88no—
825C2×C4—88no—
826C2×C4—88no—
827C22—24no—
828C22—24no—
829C22—24no—
830C22—24no—
831C22—28no—
832C22—42no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—42no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—44no—
849C22—44no—
850C22—832no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22C2×C4×#4111yescharacteristic
856C22C2×#51811yescharacteristic
857C22#342812yes—
858C22#342811yescharacteristic
859C22C4×H(5,𝔽2)12yes—
860C22#349112yes—
861C22#349412yes—
862C22#351312yes—
863C22#351312yes—
864C22#351412yes—
865C22#352112yes—
866C22#353311yescharacteristic
867C22#353312yes—
868C22#353311yescharacteristic
869C22#353412yes—
870C22#354311yescharacteristic
871C22#354511yescharacteristic
872C22#356012yes—
873C22#356212yes—
874C22#356612yes—
875C22#356812yes—
876C4—42no—
877C4—42no—
878C4—44no—
879C4—44no—
880C4—42no—
881C4—42no—
882C4—44no—
883C4—44no—
884C4—44no—
885C4—44no—
886C4—44no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C2—44no—
893C2—44no—
894C2—82no—
895C2#3423811yescharacteristic
896C2#3430312yes—
897C2#3435711yescharacteristic
898C2#3440811yescharacteristic
899C2#3450412yes—
900C2#4928612yes—
901C2#4929312yes—
902C2#4946412yes—
903C2#5075512yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC26C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14619C2semidirect
3. #14544C2semidirect
4. #14507C2semidirect
5. #14409C2semidirect
6. #14398C2semidirect
7. #14367C2semidirect
9. #14332C2semidirect
10. #14233C2semidirect
11. #14104C2semidirect
12. #14104C2semidirect
13. #14008C2semidirect
14. #14008C2semidirect
17. #13831C2semidirect
18. #13807C2semidirect
22. #2483C4semidirect
29. C2×#387C22semidirect
30. C2×#387C22semidirect
47. #1444C22semidirect
48. #1443C22semidirect
49. #1443C22semidirect
50. #1443C22semidirect
51. #1443C22semidirect
52. #1442C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1441C22semidirect
56. #1441C22semidirect
85. #1436C22semidirect
86. #1436C22semidirect
87. #1436C22semidirect
88. #1436C22semidirect
89. #1436C22semidirect
90. #1436C22semidirect
91. #1436C22semidirect
92. #1436C22semidirect
93. #1436C22semidirect
94. #1436C22semidirect
95. C4⋊#95C22semidirect
96. C4⋊#95C22semidirect
97. #1434C22semidirect
98. #1434C22semidirect
99. #1434C22semidirect
100. #1434C22semidirect
101. #1434C22semidirect
105. C4×#95C22semidirect
106. C4×#95C22semidirect
107. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24832
#146192
#145442
#145072
#144092
#143982
#143672
#143652
#143322
#142332
#141042
#140082
#139032
#138732
#138312
#138072
#137752