Finite Group Databasebeta

← #522787

Subgroups — #522787

Order 512.

1986 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2647C211yesmaximal, characteristic
2#14699C211yesmaximal, characteristic
3#14608C212yesmaximal
4#14598C212yesmaximal
5#14583C212yesmaximal
6#14545C212yesmaximal
7#14266C211yesmaximal, characteristic
8#14252C212yesmaximal
9#14250C212yesmaximal
10#14223C212yesmaximal
11#14212C212yesmaximal
12#14133C211yesmaximal, characteristic
13#14132C211yesmaximal, characteristic
14#14051C211yesmaximal, characteristic
15#14051C211yesmaximal, characteristic
16#14029C211yesmaximal, characteristic
17#14029C211yesmaximal, characteristic
18#13821C211yesmaximal, characteristic
19#13818C211yesmaximal, characteristic
20#13797C211yesmaximal, characteristic
21#13783C211yesmaximal, characteristic
22C4×#389C211yesmaximal, characteristic
23#13757C211yesmaximal, characteristic
24#2647C4116yescomplemented
25C2×#400C2212yes—
26C2×#400C2212yes—
27C2×#398C2212yes—
28C2×#398C2212yes—
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#389C2211yescharacteristic
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#387C2212yes—
38C2×#387C2212yes—
39C2×#387C2212yes—
40C2×#387C2212yes—
41C2×#384C2211yescharacteristic
42C2×#382C2211yescharacteristic
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⋊C4C2212yes—
50C2×C4×C4⋊C4C2212yes—
51C2×#376C2211yescharacteristic
52C2×#376C2211yescharacteristic
53C2×C43C2211yescharacteristic
54#1445C2212yes—
55#1445C2212yes—
56#1445C2212yes—
57#1445C2212yes—
58#1443C2212yes—
59#1443C2212yes—
60#1442C2212yes—
61#1442C2212yes—
62#1442C2212yes—
63#1442C2212yes—
64#1442C2212yes—
65#1442C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2212yes—
70#1436C2212yes—
71#1436C2212yes—
72#1436C2212yes—
73#1436C2212yes—
74#1436C2212yes—
75#1436C2212yes—
76#1436C2212yes—
77#1436C2212yes—
78#1436C2212yes—
79#1436C2212yes—
80#1436C2212yes—
81#1436C2212yes—
82#1436C2212yes—
83#1436C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2212yes—
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2211yescharacteristic
96C4⋊#95C2211yescharacteristic
97C4⋊#95C2211yescharacteristic
98#1434C2211yescharacteristic
99#1434C2212yes—
100#1434C2212yes—
101#1434C2211yescharacteristic
102#1434C2212yes—
103#1434C2212yes—
104#1434C2212yes—
105#1434C2212yes—
106#1434C2211yescharacteristic
107#1434C2212yes—
108#1434C2212yes—
109#1434C2211yescharacteristic
110#1434C2212yes—
111#1434C2211yescharacteristic
112#1434C2212yes—
113#1434C2212yes—
114#1434C2211yescharacteristic
115#1434C2212yes—
116#1434C2211yescharacteristic
117#1434C2211yescharacteristic
118C4×#95C2211yescharacteristic
119C4×#95C2212yes—
120C4×#95C2212yes—
121C4×#95C2211yescharacteristic
122C4×#95C2211yescharacteristic
123C4×#95C2211yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2312yes—
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2312yes—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2312yes—
159#400C2×C4116yes—
160#400C2×C4116yes—
161#398C2×C4116yes—
162#398C2×C4116yes—
163#389—24no—
164#389—24no—
165#389—24no—
166#389—24no—
167#389C2×C418yes—
168#389C2×C418yes—
169#389C2×C418yes—
170#389C2×C418yes—
171#387—44no—
172#387—44no—
173#387—44no—
174#387—44no—
175#384C2×C418yes—
176#382C2×C418yes—
177C4×C4⋊C4—24no—
178C4×C4⋊C4—24no—
179C4×C4⋊C4—24no—
180C4×C4⋊C4—24no—
181C4×C4⋊C4—24no—
182C4×C4⋊C4—24no—
183C4×C4⋊C4—44no—
184C4×C4⋊C4—44no—
185#376—24no—
186#376C2×C418yes—
187C2×#95C2311yescharacteristic
188C2×#95C2311yescharacteristic
189C2×#95C2311yescharacteristic
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2311yescharacteristic
193C2×#95C2311yescharacteristic
194C2×#95C2311yescharacteristic
195C2×#95C2311yescharacteristic
196C2×#95C2312yes—
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2311yescharacteristic
205C2×#95C2311yescharacteristic
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
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×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2311yescharacteristic
249C2×#95C2311yescharacteristic
250C2×#95C2312yes—
251C43—24no—
252C23×C4C2411yescharacteristic
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
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—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
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—42no—
317C2×C4⋊C4C22×C414yes—
318C2×C4⋊C4C22×C414yes—
319C2×C4⋊C4C22×C414yes—
320C2×C4⋊C4C22×C414yes—
321C2×C4⋊C4C22×C418yes—
322C2×C4⋊C4C22×C418yes—
323C2×C4⋊C4C22×C418yes—
324C2×C4⋊C4C22×C418yes—
325C2×C4⋊C4C22×C418yes—
326C2×C4⋊C4C22×C418yes—
327C2×C4⋊C4#4114yes—
328C2×C4⋊C4#4114yes—
329C2×C42—22no—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—22no—
336C2×C42—22no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—24no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—41no—
363C2×C42—42no—
364C2×C42—41no—
365C2×C42—41no—
366C2×C42—41no—
367C2×C42—42no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—42no—
374C2×C42—42no—
375C2×C42C22×C414yes—
376C2×C42C22×C414yes—
377C2×C42C22×C414yes—
378C2×C42#4114yes—
379C2×C42#4114yes—
380#95—22no—
381#95—22no—
382#95—22no—
383#95—22no—
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—24no—
393#95—24no—
394#95—22no—
395#95—24no—
396#95—22no—
397#95—22no—
398#95—24no—
399#95—24no—
400#95—22no—
401#95—22no—
402#95—22no—
403#95—22no—
404#95—24no—
405#95—22no—
406#95—42no—
407#95—41no—
408#95—42no—
409#95—41no—
410#95—41no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—41no—
416#95—41no—
417#95—41no—
418#95—41no—
419#95—42no—
420#95—41no—
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#95—42no—
433#95—42no—
434#95C22×C414yes—
435#95C22×C414yes—
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
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
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—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4C23×C412yes—
580C22×C4C23×C412yes—
581C22×C4C23×C412yes—
582C22×C4C23×C412yes—
583C22×C4C23×C412yes—
584C22×C4C23×C414yes—
585C22×C4C23×C414yes—
586C22×C4C23×C412yes—
587C22×C4C23×C414yes—
588C22×C4C23×C414yes—
589C22×C4C23×C412yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C4H(5,𝔽2)12yes—
602C22×C42−1+412yes—
603C22×C42−1+412yes—
604C22×C42−1+412yes—
605C22×C42−1+412yes—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—84no—
623C4⋊C4—84no—
624C42—28no—
625C42—28no—
626C42—28no—
627C42—28no—
628C42—28no—
629C42—44no—
630C42—48no—
631C42—44no—
632C42—44no—
633C42—44no—
634C42—48no—
635C42—44no—
636C42—44no—
637C42—84no—
638C42—84no—
639C42—84no—
640C42—84no—
641C23C24×C411yescharacteristic
642C23C22×#4111yescharacteristic
643C23C22×#4111yescharacteristic
644C23C22×#4111yescharacteristic
645C23C22×#4111yescharacteristic
646C23C2×H(5,𝔽2)11yescharacteristic
647C23C2×H(5,𝔽2)11yescharacteristic
648C23C2×2−1+411yescharacteristic
649C23C2×2−1+411yescharacteristic
650C23C2×2−1+411yescharacteristic
651C23C2×2−1+411yescharacteristic
652C23#58511yescharacteristic
653C23#58511yescharacteristic
654C23#58511yescharacteristic
655C23#58511yescharacteristic
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4C4×#4114yes—
810C2×C4C4×#4114yes—
811C2×C4#51914yes—
812C2×C4#54214yes—
813C2×C4#55214yes—
814C2×C4#55214yes—
815C2×C4#55214yes—
816C2×C4#55214yes—
817C22C2×C4×#4111yescharacteristic
818C22C2×C4×#4111yescharacteristic
819C22C2×#51911yescharacteristic
820C22C4×H(5,𝔽2)11yescharacteristic
821C22C4×H(5,𝔽2)11yescharacteristic
822C22C4×2−1+411yescharacteristic
823C22C4×2−1+411yescharacteristic
824C22C2×#54211yescharacteristic
825C22#345511yescharacteristic
826C22#346011yescharacteristic
827C22#346111yescharacteristic
828C22C2×#55211yescharacteristic
829C22C2×#55211yescharacteristic
830C22C2×#55211yescharacteristic
831C22C2×#55211yescharacteristic
832C22#349411yescharacteristic
833C22#349511yescharacteristic
834C22#351011yescharacteristic
835C22#351111yescharacteristic
836C22#351311yescharacteristic
837C22#351511yescharacteristic
838C22#351611yescharacteristic
839C22#351711yescharacteristic
840C22#351911yescharacteristic
841C22#352111yescharacteristic
842C22#352311yescharacteristic
843C22#352411yescharacteristic
844C22#354411yescharacteristic
845C22#354411yescharacteristic
846C22#354711yescharacteristic
847C22#354711yescharacteristic
848C22#356311yescharacteristic
849C22#356311yescharacteristic
850C22#356511yescharacteristic
851C22#356511yescharacteristic
852C4—24no—
853C4—42no—
854C4—44no—
855C4—42no—
856C4—42no—
857C4—44no—
858C4—42no—
859C4—42no—
860C4—44no—
861C4—42no—
862C4—42no—
863C4—42no—
864C4—42no—
865C4—44no—
866C4—42no—
867C4—42no—
868C4—44no—
869C4—44no—
870C4—81no—
871C4—81no—
872C4—82no—
873C4—82no—
874C4#237118yes—
875C2C4×#54211yescharacteristic
876C2C2×#237111yescharacteristic
877C2#3427911yescharacteristic
878C2#3428611yescharacteristic
879C2#3428711yescharacteristic
880C2#3443511yescharacteristic
881C2#3443511yescharacteristic
882C2#3806911yescharacteristic
883C2#3807311yescharacteristic
884C2#3827511yescharacteristic
885C2#3827611yescharacteristic
886C2#3892711yescharacteristic
887C2#3893211yescharacteristic
888C2#3907911yescharacteristic
889C2#3908111yescharacteristic
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. #2647C4semidirect

Maximal subgroups

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

subgroupindex
C2×#26472
#146992
#146082
#145982
#145832
#145452
#142662
#142522
#142502
#142232
#142122
#141332
#141322
#140512
#140292
#138212
#138182
#137972
#137832
C4×#3892
#137572