Finite Group Databasebeta

← #582733

Subgroups — #582733

Order 512.

1786 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2508C211yesmaximal, characteristic
2#14672C212yesmaximal
3#14647C212yesmaximal
4#14644C212yesmaximal
5#14629C212yesmaximal
6#14585C212yesmaximal
7#14482C212yesmaximal
8#14477C212yesmaximal
9#14426C212yesmaximal
10#14266C211yesmaximal, characteristic
11#14266C211yesmaximal, characteristic
12#14150C211yesmaximal, characteristic
13#14133C211yesmaximal, characteristic
14#14046C211yesmaximal, characteristic
15#14045C211yesmaximal, characteristic
16#14042C211yesmaximal, characteristic
17#14041C211yesmaximal, characteristic
18#14030C211yesmaximal, characteristic
19#13982C211yesmaximal, characteristic
20#13955C211yesmaximal, characteristic
21#13933C211yesmaximal, characteristic
22#13885C211yesmaximal, characteristic
23#13848C211yesmaximal, characteristic
24#2508C4116yescomplemented
25C2×#400C2212yes—
26C2×#398C2212yes—
27C2×#389C2212yes—
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#387C2212yes—
37C2×#387C2212yes—
38C2×#387C2212yes—
39C2×#382C2211yescharacteristic
40C2×#382C2211yescharacteristic
41C2×#382C2212yes—
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×C4×C4⋊C4C2211yescharacteristic
50C2×#376C2211yescharacteristic
51#1445C2212yes—
52#1445C2212yes—
53#1445C2212yes—
54#1445C2212yes—
55#1445C2212yes—
56#1444C2211yescharacteristic
57#1444C2211yescharacteristic
58#1444C2212yes—
59#1444C2212yes—
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#1442C2212yes—
74#1442C2212yes—
75#1442C2212yes—
76#1442C2212yes—
77#1442C2212yes—
78#1442C2212yes—
79#1442C2212yes—
80#1441C2211yescharacteristic
81#1441C2211yescharacteristic
82#1441C2211yescharacteristic
83#1441C2211yescharacteristic
84#1441C2212yes—
85#1441C2212yes—
86#1441C2212yes—
87#1441C2212yes—
88#1441C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98#1436C2212yes—
99C4⋊#95C2211yescharacteristic
100C4⋊#95C2211yescharacteristic
101C4⋊#95C2211yescharacteristic
102C4⋊#95C2211yescharacteristic
103C4⋊#95C2211yescharacteristic
104C4⋊#95C2211yescharacteristic
105C4⋊#95C2211yescharacteristic
106C4⋊#95C2211yescharacteristic
107C4⋊#95C2211yescharacteristic
108C4⋊#95C2212yes—
109C4⋊#95C2211yescharacteristic
110C4⋊#95C2211yescharacteristic
111C4⋊#95C2211yescharacteristic
112C4⋊#95C2212yes—
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115#1434C2212yes—
116#1434C2212yes—
117#1434C2212yes—
118#1434C2212yes—
119#1434C2212yes—
120#1434C2212yes—
121#1434C2212yes—
122C4×#95C2211yescharacteristic
123C4×#95C2211yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2312yes—
159#400C2×C4116yes—
160#398C2×C4116yes—
161#389—42no—
162#389—42no—
163#389—42no—
164#389—42no—
165#389—44no—
166#389C2×C418yes—
167#389C2×C418yes—
168#389C2×C418yes—
169#389C2×C418yes—
170#387—44no—
171#387—44no—
172#387C2×C4116yes—
173#382—42no—
174#382C2×C4116yes—
175#382C2×C418yes—
176C4×C4⋊C4—42no—
177C4×C4⋊C4—42no—
178C4×C4⋊C4—42no—
179C4×C4⋊C4—42no—
180C4×C4⋊C4—42no—
181C4×C4⋊C4—42no—
182C4×C4⋊C4C2×C418yes—
183C4×C4⋊C4C2×C418yes—
184#376—42no—
185C2×#95C2311yescharacteristic
186C2×#95C2311yescharacteristic
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2311yescharacteristic
190C2×#95C2311yescharacteristic
191C2×#95C2311yescharacteristic
192C2×#95C2311yescharacteristic
193C2×#95C2311yescharacteristic
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
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×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2311yescharacteristic
231C2×#95C2312yes—
232C2×#95C2311yescharacteristic
233C2×#95C2311yescharacteristic
234C2×#95C2312yes—
235C2×#95C2311yescharacteristic
236C2×#95C2311yescharacteristic
237C2×#95C2312yes—
238C2×#95C2311yescharacteristic
239C2×#95C2312yes—
240C2×#95C2312yes—
241C2×#95C2312yes—
242C2×#95C2312yes—
243C2×#95C2311yescharacteristic
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2311yescharacteristic
248C2×#95C2312yes—
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C23×C4C2412yes—
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
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—24no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—41no—
311C2×C4⋊C4—41no—
312C2×C4⋊C4—41no—
313C2×C4⋊C4—41no—
314C2×C4⋊C4—41no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—41no—
318C2×C4⋊C4—41no—
319C2×C4⋊C4—41no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
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⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4C22×C414yes—
335C2×C4⋊C4C22×C414yes—
336C2×C4⋊C4C22×C414yes—
337C2×C4⋊C4C22×C414yes—
338C2×C4⋊C4C22×C414yes—
339C2×C4⋊C4C22×C414yes—
340C2×C4⋊C4C22×C418yes—
341C2×C4⋊C4C22×C418yes—
342C2×C4⋊C4C22×C418yes—
343C2×C4⋊C4C22×C418yes—
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—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—24no—
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—22no—
379#95—22no—
380#95—24no—
381#95—42no—
382#95—41no—
383#95—41no—
384#95—42no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—41no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—41no—
401#95—41no—
402#95—41no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—41no—
407#95—41no—
408#95—41no—
409#95—41no—
410#95—41no—
411#95—41no—
412#95—41no—
413#95—41no—
414#95—41no—
415#95—41no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
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#95C22×C414yes—
433#95C22×C418yes—
434#95C22×C414yes—
435#95C22×C418yes—
436#95C22×C418yes—
437#95C22×C418yes—
438#95C22×C418yes—
439#95C22×C418yes—
440#95C22×C418yes—
441C24C2511yescharacteristic
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C23×C412yes—
585C22×C4C23×C412yes—
586C22×C4C23×C414yes—
587C22×C4C23×C414yes—
588C22×C4C23×C412yes—
589C22×C4C23×C414yes—
590C22×C4C23×C412yes—
591C22×C4C23×C412yes—
592C22×C4C23×C414yes—
593C22×C4C23×C412yes—
594C22×C4C23×C412yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C42−1+412yes—
599C22×C42−1+412yes—
600C22×C42−1+412yes—
601C22×C42−1+412yes—
602C22×C42−1+412yes—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—48no—
610C4⋊C4—48no—
611C4⋊C4—48no—
612C4⋊C4—48no—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C4⋊C4—84no—
627C42—28no—
628C42—28no—
629C42—28no—
630C42—48no—
631C42—44no—
632C42—44no—
633C42—44no—
634C42—44no—
635C42—84no—
636C42—84no—
637C42—84no—
638C23C24×C411yescharacteristic
639C23C2×H(5,𝔽2)11yescharacteristic
640C23C2×H(5,𝔽2)11yescharacteristic
641C23C2×H(5,𝔽2)11yescharacteristic
642C23C2×2−1+411yescharacteristic
643C23C2×2−1+411yescharacteristic
644C23C2×2−1+411yescharacteristic
645C23C2×2−1+411yescharacteristic
646C23C2×2−1+411yescharacteristic
647C23#58511yescharacteristic
648C23#58511yescharacteristic
649C23#58511yescharacteristic
650C23#58511yescharacteristic
651C23#58511yescharacteristic
652C23#58511yescharacteristic
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4#51914yes—
808C2×C4#52014yes—
809C2×C4#52014yes—
810C2×C4#56214yes—
811C2×C4#56314yes—
812C2×C4#56314yes—
813C2×C4#56414yes—
814C22C2×#51911yescharacteristic
815C22C2×#52011yescharacteristic
816C22C2×#52011yescharacteristic
817C22#342811yescharacteristic
818C22#342811yescharacteristic
819C22C4×H(5,𝔽2)11yescharacteristic
820C22C4×2−1+411yescharacteristic
821C22C2×#56211yescharacteristic
822C22C2×#56311yescharacteristic
823C22C2×#56311yescharacteristic
824C22C2×#56411yescharacteristic
825C22#353911yescharacteristic
826C22#354011yescharacteristic
827C22#354111yescharacteristic
828C22#354111yescharacteristic
829C22#354211yescharacteristic
830C22#354211yescharacteristic
831C22#354711yescharacteristic
832C22#355011yescharacteristic
833C22#355111yescharacteristic
834C22#355111yescharacteristic
835C22#355411yescharacteristic
836C22#355511yescharacteristic
837C22#355511yescharacteristic
838C22#355711yescharacteristic
839C22#355711yescharacteristic
840C22#355711yescharacteristic
841C22#355711yescharacteristic
842C22#355711yescharacteristic
843C22#355911yescharacteristic
844C22#356311yescharacteristic
845C22#356511yescharacteristic
846C22#356511yescharacteristic
847C22#356511yescharacteristic
848C22#356511yescharacteristic
849C4—42no—
850C4—44no—
851C4—42no—
852C4—44no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—44no—
860C4—44no—
861C4—81no—
862C4—82no—
863C4—82no—
864C4—81no—
865C4—81no—
866C4—82no—
867C4—81no—
868C4—81no—
869C4—81no—
870C4—82no—
871C4#238218yes—
872C2C2×#238211yescharacteristic
873C2#3439711yescharacteristic
874C2#3442211yescharacteristic
875C2#3446211yescharacteristic
876C2#3446711yescharacteristic
877C2#3448911yescharacteristic
878C2#3449011yescharacteristic
879C2#5311111yescharacteristic
880C2#5311411yescharacteristic
881C2#5313111yescharacteristic
882C2#5313411yescharacteristic
883C2#5314211yescharacteristic
884C2#5314811yescharacteristic
885C2#5315311yescharacteristic
886C2#5315611yescharacteristic
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
24. #2508C4semidirect

Maximal subgroups

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

subgroupindex
C2×#25082
#146722
#146472
#146442
#146292
#145852
#144822
#144772
#144262
#142662
#141502
#141332
#140462
#140452
#140422
#140412
#140302
#139822
#139552
#139332
#138852
#138482