Finite Group Databasebeta

← #545692

Subgroups — #545692

Order 512.

1926 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2453C211yesmaximal, characteristic
2#14644C212yesmaximal
3#14490C212yesmaximal
4#14485C212yesmaximal
5#14482C212yesmaximal
6#14459C212yesmaximal
7#14334C212yesmaximal
8#14329C212yesmaximal
9#14266C211yesmaximal, characteristic
10#14252C212yesmaximal
11#14160C211yesmaximal, characteristic
12#14142C211yesmaximal, characteristic
13#14142C211yesmaximal, characteristic
14#14132C211yesmaximal, characteristic
15#14054C211yesmaximal, characteristic
16#14021C211yesmaximal, characteristic
17#14003C211yesmaximal, characteristic
18#13982C211yesmaximal, characteristic
19#13931C211yesmaximal, characteristic
20#13846C211yesmaximal, characteristic
21#13818C211yesmaximal, characteristic
22#13804C211yesmaximal, characteristic
23#13786C211yesmaximal, characteristic
24C22×#125C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26#2453C4116yescomplemented
27C2×#400C2212yes—
28C2×#398C2212yes—
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2212yes—
39C2×#389C2211yescharacteristic
40C2×#387C2212yes—
41C2×#382C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2211yescharacteristic
49C2×#376C2211yescharacteristic
50#1445C2211yescharacteristic
51#1445C2211yescharacteristic
52#1445C2212yes—
53#1445C2212yes—
54#1445C2212yes—
55#1445C2212yes—
56#1445C2212yes—
57#1445C2212yes—
58#1443C2211yescharacteristic
59#1443C2211yescharacteristic
60#1443C2212yes—
61#1443C2212yes—
62#1443C2212yes—
63#1443C2212yes—
64#1443C2212yes—
65#1443C2212yes—
66#1443C2212yes—
67#1442C2211yescharacteristic
68#1442C2211yescharacteristic
69#1442C2212yes—
70#1442C2212yes—
71#1442C2212yes—
72#1442C2212yes—
73#1441C2211yescharacteristic
74#1441C2211yescharacteristic
75#1441C2212yes—
76#1441C2212yes—
77#1441C2212yes—
78#1441C2212yes—
79#1441C2212yes—
80#1436C2212yes—
81#1436C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2211yescharacteristic
96C4⋊#95C2211yescharacteristic
97C4⋊#95C2211yescharacteristic
98C4⋊#95C2211yescharacteristic
99C4⋊#95C2211yescharacteristic
100C4⋊#95C2211yescharacteristic
101C4⋊#95C2211yescharacteristic
102C4⋊#95C2212yes—
103C4⋊#95C2212yes—
104C4⋊#95C2211yescharacteristic
105C4⋊#95C2211yescharacteristic
106#1434C2212yes—
107#1434C2212yes—
108#1434C2212yes—
109#1434C2212yes—
110#1434C2212yes—
111#1434C2212yes—
112#1434C2212yes—
113#1434C2212yes—
114#1434C2212yes—
115#1434C2212yes—
116#1434C2212yes—
117#1434C2212yes—
118C4×#95C2211yescharacteristic
119C4×#95C2211yescharacteristic
120C4×#95C2211yescharacteristic
121C4×#95C2211yescharacteristic
122C4×#95C2212yes—
123C4×#95C2212yes—
124C23×Q8C2311yescharacteristic
125C2×#125—42no—
126C2×#125—42no—
127C2×#125C2×C418yes—
128C2×C4×Q8—42no—
129C2×C4×Q8—42no—
130C2×C4×Q8C2×C418yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162#400C2×C4116yes—
163#398C2×C4116yes—
164#391—24no—
165#391—24no—
166#391—42no—
167#391—42no—
168#391C2×C418yes—
169#391C2×C418yes—
170#389—24no—
171#389—42no—
172#389C2×C418yes—
173#389C2×C4116yes—
174#389C2×C418yes—
175#387C2×C4116yes—
176#382—24no—
177C4×C4⋊C4—24no—
178C4×C4⋊C4—24no—
179C4×C4⋊C4—42no—
180C4×C4⋊C4—42no—
181C4×C4⋊C4—42no—
182C4×C4⋊C4—42no—
183C4×C4⋊C4C2×C418yes—
184#376—42no—
185C2×#95C2311yescharacteristic
186C2×#95C2311yescharacteristic
187C2×#95C2311yescharacteristic
188C2×#95C2312yes—
189C2×#95C2311yescharacteristic
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2311yescharacteristic
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2311yescharacteristic
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
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×#95C2312yes—
241C2×#95C2311yescharacteristic
242C2×#95C2311yescharacteristic
243C2×#95C2311yescharacteristic
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2311yescharacteristic
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2311yescharacteristic
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8C22×C414yes—
259C23×C4C2411yescharacteristic
260C23×C4C2412yes—
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282#125—416no—
283C4×Q8—416no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—41no—
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—42no—
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—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4C22×C414yes—
327C2×C4⋊C4C22×C414yes—
328C2×C4⋊C4C22×C414yes—
329C2×C4⋊C4C22×C418yes—
330C2×C4⋊C4C22×C418yes—
331C2×C4⋊C4C22×C418yes—
332C2×C4⋊C4C22×C414yes—
333C2×C4⋊C4C22×C414yes—
334C2×C4⋊C4C22×C418yes—
335C2×C4⋊C4C22×C418yes—
336C2×C4⋊C4#4114yes—
337C2×C4⋊C4#4114yes—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—42no—
360C2×C42—42no—
361C2×C42—42no—
362C2×C42—42no—
363C2×C42—42no—
364C2×C42—42no—
365C2×C42—42no—
366C2×C42—42no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42C22×C414yes—
374C2×C42C22×C414yes—
375C2×C42C22×C414yes—
376C2×C42C22×C418yes—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—22no—
387#95—22no—
388#95—24no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95—41no—
393#95—42no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—41no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—41no—
402#95—42no—
403#95—42no—
404#95—41no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—41no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—41no—
415#95—41no—
416#95—41no—
417#95—41no—
418#95—41no—
419#95—42no—
420#95—42no—
421#95—41no—
422#95—41no—
423#95—41no—
424#95—41no—
425#95—41no—
426#95—41no—
427#95—42no—
428#95—42no—
429#95—41no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95C22×C414yes—
437#95C22×C414yes—
438#95C22×C418yes—
439#95C22×C418yes—
440#95C22×C418yes—
441#95C22×C418yes—
442#95C22×C418yes—
443#95C22×C418yes—
444C24C2511yescharacteristic
445C2×Q8—28no—
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4C23×C412yes—
593C22×C4C23×C414yes—
594C22×C4C23×C414yes—
595C22×C4C23×C412yes—
596C22×C4C23×C412yes—
597C22×C4C23×C412yes—
598C22×C4C23×C414yes—
599C22×C4C23×C412yes—
600C22×C4C23×C412yes—
601C22×C4C23×C414yes—
602C22×C4C23×C412yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4H(5,𝔽2)12yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C42−1+412yes—
610C22×C42−1+412yes—
611C22×C42−1+412yes—
612C22×C42−1+412yes—
613C4⋊C4—28no—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—28no—
617C4⋊C4—28no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—84no—
630C4⋊C4—84no—
631C42—28no—
632C42—28no—
633C42—28no—
634C42—48no—
635C42—44no—
636C42—44no—
637C42—44no—
638C42—44no—
639C42—84no—
640C42—84no—
641C42—84no—
642C42—84no—
643C42—84no—
644C23C24×C411yescharacteristic
645C23C22×#4111yescharacteristic
646C23C22×#4111yescharacteristic
647C23C2×H(5,𝔽2)11yescharacteristic
648C23C2×H(5,𝔽2)11yescharacteristic
649C23C2×2−1+411yescharacteristic
650C23C2×2−1+411yescharacteristic
651C23C2×2−1+411yescharacteristic
652C23C2×2−1+411yescharacteristic
653C23#58511yescharacteristic
654C23#58511yescharacteristic
655C23#58511yescharacteristic
656C23#58511yescharacteristic
657C23#58511yescharacteristic
658C23#58511yescharacteristic
659Q8—416no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4C4×#4114yes—
815C2×C4#51814yes—
816C2×C4#51914yes—
817C2×C4#53914yes—
818C2×C4#53914yes—
819C2×C4#54214yes—
820C2×C4#54214yes—
821C22C2×C4×#4111yescharacteristic
822C22C2×#51811yescharacteristic
823C22C2×#51911yescharacteristic
824C22#342811yescharacteristic
825C22#342811yescharacteristic
826C22C4×2−1+411yescharacteristic
827C22C4×2−1+411yescharacteristic
828C22C2×#53911yescharacteristic
829C22C2×#53911yescharacteristic
830C22C2×#54211yescharacteristic
831C22C2×#54211yescharacteristic
832C22#351511yescharacteristic
833C22#351611yescharacteristic
834C22#352111yescharacteristic
835C22#352111yescharacteristic
836C22#352111yescharacteristic
837C22#352311yescharacteristic
838C22#352411yescharacteristic
839C22#352411yescharacteristic
840C22#353911yescharacteristic
841C22#354111yescharacteristic
842C22#354711yescharacteristic
843C22#355111yescharacteristic
844C22#355411yescharacteristic
845C22#355511yescharacteristic
846C22#355511yescharacteristic
847C22#355711yescharacteristic
848C22#355711yescharacteristic
849C22#356111yescharacteristic
850C22#356211yescharacteristic
851C22#356211yescharacteristic
852C22#356311yescharacteristic
853C22#356311yescharacteristic
854C22#356511yescharacteristic
855C22#356511yescharacteristic
856C4—44no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—44no—
861C4—42no—
862C4—44no—
863C4—42no—
864C4—42no—
865C4—44no—
866C4—42no—
867C4—44no—
868C4—44no—
869C4—42no—
870C4—81no—
871C4—81no—
872C4—81no—
873C4—82no—
874C4—81no—
875C4—81no—
876C4—82no—
877C4—81no—
878C4#233218yes—
879C2C2×#233211yescharacteristic
880C2#3423711yescharacteristic
881C2#3428611yescharacteristic
882C2#3447311yescharacteristic
883C2#3449011yescharacteristic
884C2#3449011yescharacteristic
885C2#3449611yescharacteristic
886C2#4272011yescharacteristic
887C2#4272111yescharacteristic
888C2#4272511yescharacteristic
889C2#4272711yescharacteristic
890C2#4277711yescharacteristic
891C2#4277911yescharacteristic
892C2#4284511yescharacteristic
893C2#4286311yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC24C25
commutatorC23C24×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
26. #2453C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24532
#146442
#144902
#144852
#144822
#144592
#143342
#143292
#142662
#142522
#141602
#141422
#141322
#140542
#140212
#140032
#139822
#139312
#138462
#138182
#138042
#137862