Finite Group Databasebeta

← #576646

Subgroups — #576646

Order 512.

3002 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2609C211yesmaximal, characteristic
2C2×#2317C212yesmaximal, complemented
3#14677C211yesmaximal, characteristic, complemented
4#14587C211yesmaximal, characteristic, complemented
5#14549C212yesmaximal, complemented
6#14535C211yesmaximal, characteristic
7#14406C212yesmaximal, complemented
8#14405C212yesmaximal, complemented
9#14394C212yesmaximal, complemented
10#14393C212yesmaximal, complemented
11#14226C211yesmaximal, characteristic, complemented
12#14204C212yesmaximal, complemented
13#14176C211yesmaximal, characteristic
14#14072C212yesmaximal, complemented
15#14064C212yesmaximal
16#14043C212yesmaximal, complemented
17#14015C212yesmaximal
18#13957C212yesmaximal, complemented
19#13779C211yesmaximal, characteristic, complemented
20C22×C4×D4C2211yescharacteristic
21C22×#117C2212yes—
22C22×#117C2212yes—
23C23×C4⋊C4C2212yes—
24#2609C4116yescomplemented
25C2×#398C2211yescharacteristic
26C2×#396C2212yes—
27C2×#394C2211yescharacteristic
28#2317—216no—
29C2×#389C2212yes—
30C2×#389C2212yes—
31C2×#389C2212yes—
32C2×#389C2212yes—
33C2×#389C2211yescharacteristic
34C2×#389C2212yes—
35C2×#388C2212yes—
36C2×#388C2212yes—
37C2×#387C2212yes—
38C2×#387C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#385C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#384C2212yes—
50C2×#384C2211yescharacteristic
51C2×#382C2212yes—
52C2×#382C2212yes—
53C2×#382C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57C2×#376C2211yescharacteristic
58#1445C2211yescharacteristic
59#1444C2212yes—
60#1444C2212yes—
61#1444C2211yescharacteristic
62#1444C2212yes—
63#1444C2212yes—
64#1444C2211yescharacteristic
65#1443C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1441C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1441C2212yes—
74#1441C2211yescharacteristic
75#1441C2212yes—
76#1441C2211yescharacteristic
77#1440C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1438C2211yescharacteristic
83#1437C2212yes—
84#1437C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98C4⋊#95C2211yescharacteristic
99C4⋊#95C2211yescharacteristic
100#1434C2212yes—
101#1434C2211yescharacteristic
102#1434C2212yes—
103#1434C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C4×#95C2211yescharacteristic
109C23×D4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
112C24×C4C2312yes—
113C2×C4×D4—42no—
114C2×C4×D4—44no—
115C2×#117—28no—
116C2×#117—28no—
117C2×#117—28no—
118C2×#117—44no—
119C2×#117—44no—
120C2×#117C2×C4116yescomplemented
121C22×C4⋊C4—28no—
122C22×C4⋊C4—44no—
123C22×C4⋊C4—44no—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊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⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165#398C2×C418yescomplemented
166#396C2×C4116yescomplemented
167#394C2×C418yes—
168#389—28no—
169#389—28no—
170#389—28no—
171#389—28no—
172#389—42no—
173#389—44no—
174#388—44no—
175#388C2×C4116yescomplemented
176#387—44no—
177#387C2×C4116yescomplemented
178#386—44no—
179#386C2×C4116yes—
180#385—28no—
181#385—28no—
182#385—28no—
183#385—28no—
184#385—44no—
185#385—44no—
186#385—44no—
187#385C2×C4116yescomplemented
188#384—28no—
189#384D418yescomplemented
190#382—28no—
191#382—28no—
192#382C2×C418yescomplemented
193C4×C4⋊C4—42no—
194C4×C4⋊C4—42no—
195C4×C22⋊C4—44no—
196#376—24no—
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×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2311yescharacteristic
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2311yescharacteristic
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2311yescharacteristic
234C2×#95C2312yes—
235C2×#95C2311yescharacteristic
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C25C2412yes—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—41no—
243C22×D4—41no—
244C22×D4C22×C414yes—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4C22×C418yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C4×D4—416no—
285#117—264no—
286#117—432no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
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—41no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—432no—
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⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—41no—
339C2×C4⋊C4C22×C418yes—
340C2×C4⋊C4C22×C418yes—
341C2×C4⋊C4C22×C418yes—
342C2×C4⋊C4C22×C414yes—
343C2×C4⋊C4C22×C414yes—
344C2×C4⋊C4C22×C414yes—
345C2×C4⋊C4C2×D418yes—
346C2×C4⋊C4C2×D418yes—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4C2×D414yes—
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—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—42no—
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⋊C4C22×C418yes—
378C2×C22⋊C4C22×C418yes—
379C2×C22⋊C4C22×C418yes—
380C2×C22⋊C4C22×C418yes—
381C2×C22⋊C4C22×C418yes—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—41no—
398C2×C42—41no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42C22×C418yes—
404C2×C42C22×C414yes—
405C2×C42C2×D414yes—
406C2×C42#4114yes—
407#95—24no—
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—42no—
425#95—42no—
426#95—41no—
427#95—42no—
428#95—41no—
429#95—42no—
430#95—41no—
431#95—41no—
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#95—42no—
443#95C22×C418yes—
444#95C22×C418yes—
445#95C22×C414yes—
446#95C22×C418yes—
447#95C22×C414yes—
448#95C22×C418yes—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24C23×C414yes—
462C24H(5,𝔽2)14yes—
463C242−1+414yes—
464C24C2511yescharacteristic
465C2×D4—216no—
466C2×D4—44no—
467C2×D4—44no—
468C2×D4—48no—
469C2×D4—44no—
470C22×C4—216no—
471C22×C4—216no—
472C22×C4—216no—
473C22×C4—216no—
474C22×C4—216no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—216no—
488C22×C4—216no—
489C22×C4—22no—
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—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
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—21no—
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—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
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—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4—84no—
583C22×C4—84no—
584C22×C4—84no—
585C22×C4—84no—
586C22×C4C23×C412yes—
587C22×C4C23×C412yes—
588C22×C4C23×C414yes—
589C22×C4C23×C414yes—
590C22×C4C23×C414yes—
591C22×C4C23×C414yes—
592C22×C4C23×C412yes—
593C22×C4C23×C414yes—
594C22×C4C22×D412yes—
595C22×C4C22×D414yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D414yes—
599C22×C4C2×#4114yes—
600C22×C4C2×#4112yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C4H(5,𝔽2)14yes—
603C22×C42−1+412yes—
604C22×C42−1+414yes—
605C4⋊C4—216no—
606C4⋊C4—216no—
607C4⋊C4—216no—
608C4⋊C4—48no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—44no—
620C4⋊C4—84no—
621C4⋊C4—84no—
622C4⋊C4—84no—
623C4⋊C4—84no—
624C4⋊C4—82no—
625C4⋊C4—84no—
626C22⋊C4—216no—
627C22⋊C4—216no—
628C22⋊C4—216no—
629C22⋊C4—216no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C42—28no—
638C42—216no—
639C42—48no—
640C42—48no—
641C42—44no—
642C42—44no—
643C42—82no—
644C42—84no—
645C42C4×D4116yescomplemented
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
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#52018yes—
681C23C24×C411yescharacteristic
682C23C23×D411yescharacteristic
683C23C22×#4111yescharacteristic
684C23C2×H(5,𝔽2)12yes—
685C23C2×H(5,𝔽2)12yes—
686C23C2×H(5,𝔽2)11yescharacteristic
687C23C2×2−1+412yes—
688C23C2×2−1+412yes—
689C23C2×2−1+411yescharacteristic
690C23#58511yescharacteristic
691C23#58511yescharacteristic
692D4—416no—
693C2×C4—264no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
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—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
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—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
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—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—816no—
806C2×C4—816no—
807C2×C4C2×C4×D418yes—
808C2×C4C2×C4×D414yes—
809C2×C4#52018yes—
810C22—28no—
811C22—28no—
812C22—28no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22C22×C4×D411yescharacteristic
826C22C2×#52012yes—
827C22C2×#52012yes—
828C22C4×H(5,𝔽2)11yescharacteristic
829C22C4×2−1+411yescharacteristic
830C22#348412yes—
831C22#348612yes—
832C22#349212yes—
833C22#349212yes—
834C22#349211yescharacteristic
835C22#349311yescharacteristic
836C22#349611yescharacteristic
837C22#349711yescharacteristic
838C22#353211yescharacteristic
839C22#353512yes—
840C22#353811yescharacteristic
841C22#353812yes—
842C22#354212yes—
843C22#354412yes—
844C22#354411yescharacteristic
845C22#354712yes—
846C22#354911yescharacteristic
847C22#356312yes—
848C4—28no—
849C4—28no—
850C4—24no—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—44no—
856C4—42no—
857C4—44no—
858C4—42no—
859C4—42no—
860C4—44no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C2—48no—
867C2#3420012yes—
868C2#3427411yescharacteristic
869C2#3445711yescharacteristic
870C2#3446512yes—
871C2#3448511yescharacteristic
872C2#4779411yescharacteristic
873C2#4779512yes—
874C2#4779911yescharacteristic
875C2#4780211yescharacteristic
876C2#4780312yes—
877C2#4780411yescharacteristic
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
2. C2×#2317C2semidirect
3. #14677C2semidirect
4. #14587C2semidirect
5. #14549C2semidirect
7. #14406C2semidirect
8. #14405C2semidirect
9. #14394C2semidirect
10. #14393C2semidirect
11. #14226C2semidirect
12. #14204C2semidirect
14. #14072C2semidirect
16. #14043C2semidirect
18. #13957C2semidirect
19. #13779C2semidirect
24. #2609C4semidirect
120. C2×#117C2×C4semidirect
165. #398C2×C4semidirect
166. #396C2×C4semidirect
175. #388C2×C4semidirect
177. #387C2×C4semidirect
187. #385C2×C4semidirect
189. #384D4semidirect
192. #382C2×C4semidirect
645. C42C4×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#26092
C2×#23172
#146772
#145872
#145492
#145352
#144062
#144052
#143942
#143932
#142262
#142042
#141762
#140722
#140642
#140432
#140152
#139572
#137792