Finite Group Databasebeta

← #555633

Subgroups — #555633

Order 512.

3290 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2735C211yesmaximal, characteristic
2#14693C212yesmaximal
3#14591C212yesmaximal, complemented
4#14577C211yesmaximal, characteristic, complemented
5#14551C211yesmaximal, characteristic, complemented
6#14525C212yesmaximal, complemented
7#14442C212yesmaximal, complemented
8#14389C212yesmaximal, complemented
9#14389C212yesmaximal, complemented
10#14366C212yesmaximal
11#14366C211yesmaximal, characteristic
12#14317C211yesmaximal, characteristic, complemented
13#14313C211yesmaximal, characteristic, complemented
14#14204C212yesmaximal, complemented
15#14177C212yesmaximal, complemented
16#14116C212yesmaximal, complemented
17#13990C212yesmaximal, complemented
18#13789C212yesmaximal, complemented
19C4×#379C211yesmaximal, characteristic
20C25×C4C2211yescharacteristic
21#2735C4116yescomplemented
22C2×#399C2211yescharacteristic
23C2×#397C2212yes—
24C2×#397C2211yescharacteristic
25C2×#396C2212yes—
26C2×#389C2211yescharacteristic, complemented
27C2×#389C2212yescomplemented
28C2×#389C2211yescharacteristic, complemented
29C2×#388C2212yes—
30C2×#388C2212yes—
31C2×#388C2212yes—
32C2×#388C2212yes—
33C2×#388C2212yes—
34C2×#388C2212yes—
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#385C2212yes—
40C2×#385C2212yes—
41C2×#383C2212yescomplemented
42C2×#379C2211yescharacteristic
43C2×#379C2212yes—
44C2×#379C2212yes—
45C2×#379C2211yescharacteristic
46C2×C4×C4⋊C4C2212yescomplemented
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2211yescharacteristic
51#1445C2211yescharacteristic, complemented
52#1445C2212yescomplemented
53#1445C2212yescomplemented
54#1445C2211yescharacteristic, complemented
55#1444C2211yescharacteristic, complemented
56#1442C2212yescomplemented
57#1442C2212yescomplemented
58#1442C2212yescomplemented
59#1442C2212yescomplemented
60#1442C2212yescomplemented
61#1442C2211yescharacteristic, complemented
62#1441C2212yescomplemented
63#1441C2212yescomplemented
64#1441C2212yescomplemented
65#1440C2212yes—
66#1440C2212yes—
67#1440C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1439C2211yescharacteristic
74#1439C2211yescharacteristic
75#1437C2212yes—
76#1437C2212yes—
77#1437C2212yes—
78#1437C2212yes—
79#1437C2212yes—
80#1437C2212yes—
81#1436C2212yescomplemented
82#1436C2212yescomplemented
83#1436C2212yescomplemented
84#1436C2212yescomplemented
85#1436C2212yescomplemented
86#1436C2212yescomplemented
87#1436C2212yescomplemented
88#1436C2212yescomplemented
89#1436C2212yescomplemented
90#1436C2212yescomplemented
91C4⋊#95C2212yescomplemented
92C4⋊#95C2212yescomplemented
93#1434C2212yescomplemented
94#1434C2212yescomplemented
95#1434C2211yescharacteristic, complemented
96#1434C2211yescharacteristic, complemented
97C22⋊#95C2212yes—
98C22⋊#95C2211yescharacteristic
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2211yescharacteristic
107C4×#95C2212yescomplemented
108C26C2311yescharacteristic
109C24×C4—24no—
110C24×C4—44no—
111C24×C4—42no—
112C24×C4—42no—
113C24×C4—44no—
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C24×C4C2312yes—
117C24×C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊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⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2312yes—
157#399C2×C418yescomplemented
158#397C2×C418yescomplemented
159#397C2×C4116yescomplemented
160#396C2×C4116yescomplemented
161#389—42no—
162#389—44no—
163#389—42no—
164#388—28no—
165#388—44no—
166#388—44no—
167#388C2×C4116yescomplemented
168#388C2×C4116yescomplemented
169#388C2×C4116yescomplemented
170#385—28no—
171#385—44no—
172#385—44no—
173#385—44no—
174#385—44no—
175#385—44no—
176#383—44no—
177#379—24no—
178#379—44no—
179#379C2×C418yes—
180#379C2×C4116yes—
181C4×C4⋊C4—44no—
182C4×C22⋊C4—44no—
183C4×C22⋊C4—42no—
184C4×C22⋊C4—42no—
185C4×C22⋊C4—44no—
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×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2311yescharacteristic
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2311yescharacteristic
229C25—22no—
230C25—22no—
231C25—24no—
232C25—24no—
233C25—41no—
234C25—42no—
235C25—41no—
236C25—41no—
237C25—42no—
238C25—41no—
239C25C22×C414yes—
240C25C2411yescharacteristic
241C25C2412yes—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—41no—
263C23×C4—42no—
264C23×C4—41no—
265C23×C4—432no—
266C23×C4—416no—
267C23×C4—416no—
268C23×C4—432no—
269C23×C4—416no—
270C23×C4#4114yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
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—41no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
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—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4C22×C414yescomplemented
319C2×C4⋊C4C22×C418yescomplemented
320C2×C4⋊C4C22×C418yescomplemented
321C2×C4⋊C4C22×C414yescomplemented
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—41no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—41no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—41no—
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—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4C22×C418yes—
372C2×C22⋊C4C22×C418yes—
373C2×C22⋊C4C22×C418yes—
374C2×C22⋊C4C22×C418yes—
375C2×C22⋊C4C22×C414yes—
376C2×C22⋊C4C22×C418yes—
377C2×C22⋊C4C22×C418yes—
378C2×C22⋊C4C22×C418yes—
379C2×C22⋊C4C22×C418yes—
380C2×C22⋊C4C22×C414yes—
381C2×C22⋊C4#4114yes—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—42no—
387C2×C42—42no—
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×C418yescomplemented
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—42no—
412#95—42no—
413#95—41no—
414#95—42no—
415#95—42no—
416#95—41no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—41no—
422#95—41no—
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—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95C22×C418yescomplemented
440#95C22×C414yescomplemented
441#95C22×C418yescomplemented
442#95C22×C418yescomplemented
443#95C22×C414yescomplemented
444C24—22no—
445C24—22no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—28no—
465C24—216no—
466C24—44no—
467C24—48no—
468C24—44no—
469C24—48no—
470C24—44no—
471C24—48no—
472C24—48no—
473C24—48no—
474C24—48no—
475C24—44no—
476C24—44no—
477C24—48no—
478C24—44no—
479C24—44no—
480C24—44no—
481C24—48no—
482C24—48no—
483C24—48no—
484C24—44no—
485C24—48no—
486C24—44no—
487C24C23×C412yes—
488C24C23×C414yes—
489C24C2×#4112yes—
490C24C2×#4112yes—
491C24H(5,𝔽2)14yes—
492C242−1+414yes—
493C24C2511yescharacteristic
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—216no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
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—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
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—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—21no—
541C22×C4—22no—
542C22×C4—21no—
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—28no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
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—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—44no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—44no—
602C22×C4—48no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—44no—
608C22×C4—48no—
609C22×C4—4128no—
610C22×C4—48no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4C23×C414yes—
614C22×C4C23×C412yes—
615C22×C4C23×C414yes—
616C22×C4C23×C414yes—
617C22×C4C23×C414yes—
618C22×C4C23×C414yes—
619C22×C4C23×C412yes—
620C22×C4C2×#4114yes—
621C22×C4C2×#4112yes—
622C22×C4C2×#4112yes—
623C22×C4H(5,𝔽2)14yes—
624C22×C4H(5,𝔽2)12yes—
625C22×C4H(5,𝔽2)12yes—
626C4⋊C4—48no—
627C4⋊C4—44no—
628C4⋊C4—48no—
629C4⋊C4—44no—
630C4⋊C4—48no—
631C4⋊C4—84no—
632C4⋊C4—84no—
633C4⋊C4—84no—
634C4⋊C4—84no—
635C4⋊C4—82no—
636C4⋊C4—82no—
637C4⋊C4—84no—
638C22⋊C4—216no—
639C22⋊C4—216no—
640C22⋊C4—216no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—44no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—44no—
652C22⋊C4—84no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C22⋊C4—84no—
658C42—48no—
659C42—48no—
660C42—84no—
661C42—82no—
662C42—82no—
663C42—84no—
664C42—84no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—416no—
696C23—432no—
697C23—416no—
698C23—432no—
699C23—416no—
700C23—416no—
701C23—416no—
702C23—432no—
703C23—416no—
704C23—416no—
705C23—432no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—41no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—41no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—41no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23C4×#4114yes—
733C23#52018yes—
734C23C24×C411yescharacteristic
735C23C22×#4111yescharacteristic
736C23C22×#4111yescharacteristic
737C23C2×H(5,𝔽2)12yes—
738C23C2×H(5,𝔽2)11yescharacteristic
739C23C2×H(5,𝔽2)11yescharacteristic
740C23C2×H(5,𝔽2)12yes—
741C23C2×2−1+412yes—
742C23#58511yescharacteristic
743C23#58511yescharacteristic
744C23#58512yes—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—432no—
777C2×C4—416no—
778C2×C4—432no—
779C2×C4—416no—
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—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
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—41no—
821C2×C4—41no—
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—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4#53814yes—
856C22—24no—
857C22—28no—
858C22—28no—
859C22—28no—
860C22—28no—
861C22—464no—
862C22—42no—
863C22—44no—
864C22—44no—
865C22—42no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—42no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—42no—
875C22—42no—
876C22—44no—
877C22—42no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22C2×C4×#4111yescharacteristic
884C22C2×#52012yes—
885C22C4×H(5,𝔽2)11yescharacteristic
886C22C4×H(5,𝔽2)11yescharacteristic
887C22C4×H(5,𝔽2)12yes—
888C22C2×#53811yescharacteristic
889C22#345511yescharacteristic
890C22#345911yescharacteristic
891C22#346011yescharacteristic
892C22#349012yes—
893C22#349512yes—
894C22#351312yes—
895C22#352012yes—
896C22#353211yescharacteristic
897C22#353212yes—
898C22#353211yescharacteristic
899C22#353312yes—
900C22#353512yes—
901C22#353811yescharacteristic
902C22#353912yes—
903C22#354011yescharacteristic
904C22#354112yes—
905C22#354112yes—
906C4—24no—
907C4—44no—
908C4—44no—
909C4—44no—
910C4—42no—
911C4—44no—
912C4—42no—
913C4—44no—
914C4—42no—
915C4—44no—
916C4—44no—
917C4—81no—
918C4—82no—
919C4—82no—
920C4—81no—
921C4—82no—
922C4—82no—
923C2—44no—
924C2—48no—
925C2C4×#53811yescharacteristic
926C2#3429612yes—
927C2#3441612yes—
928C2#3445711yescharacteristic
929C2#3451111yescharacteristic
930C2#3672511yescharacteristic
931C2#3673612yes—
932C2#3684211yescharacteristic
933C2#3685512yes—
934C2#3693011yescharacteristic
935C2#3738111yescharacteristic
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
3. #14591C2semidirect
4. #14577C2semidirect
5. #14551C2semidirect
6. #14525C2semidirect
7. #14442C2semidirect
8. #14389C2semidirect
9. #14389C2semidirect
12. #14317C2semidirect
13. #14313C2semidirect
14. #14204C2semidirect
15. #14177C2semidirect
16. #14116C2semidirect
17. #13990C2semidirect
18. #13789C2semidirect
21. #2735C4semidirect
26. C2×#389C22semidirect
27. C2×#389C22semidirect
28. C2×#389C22semidirect
41. C2×#383C22semidirect
46. C2×C4×C4⋊C4C22semidirect
51. #1445C22semidirect
52. #1445C22semidirect
53. #1445C22semidirect
54. #1445C22semidirect
55. #1444C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
81. #1436C22semidirect
82. #1436C22semidirect
83. #1436C22semidirect
84. #1436C22semidirect
85. #1436C22semidirect
86. #1436C22semidirect
87. #1436C22semidirect
88. #1436C22semidirect
89. #1436C22semidirect
90. #1436C22semidirect
91. C4⋊#95C22semidirect
92. C4⋊#95C22semidirect
93. #1434C22semidirect
94. #1434C22semidirect
95. #1434C22semidirect
96. #1434C22semidirect
107. C4×#95C22semidirect
157. #399C2×C4semidirect
158. #397C2×C4semidirect
159. #397C2×C4semidirect
160. #396C2×C4semidirect
167. #388C2×C4semidirect
168. #388C2×C4semidirect
169. #388C2×C4semidirect
318. C2×C4⋊C4C22×C4semidirect
319. C2×C4⋊C4C22×C4semidirect
320. C2×C4⋊C4C22×C4semidirect
321. C2×C4⋊C4C22×C4semidirect
400. C2×C42C22×C4semidirect
439. #95C22×C4semidirect
440. #95C22×C4semidirect
441. #95C22×C4semidirect
442. #95C22×C4semidirect
443. #95C22×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#27352
#146932
#145912
#145772
#145512
#145252
#144422
#143892
#143662
#143172
#143132
#142042
#141772
#141162
#139902
#137892
C4×#3792