Finite Group Databasebeta

← #36275147

Subgroups — #36275147

Order 21248.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128212C211yesmaximal, characteristic, complemented
2#24918277C214yesmaximal, complemented
3#24918269C212yesmaximal, complemented
4#24918260C212yesmaximal, complemented
5#24918228C214yesmaximal, complemented
6#24918220C212yesmaximal, complemented
7#24918211C212yesmaximal, complemented
8#24917399C212yesmaximal, complemented
9#24917386C212yesmaximal, complemented
10#24917078C214yesmaximal, complemented
11#24916713C212yesmaximal, complemented
12#24916690C212yesmaximal, complemented
13C2×#19127665C211yesmaximal, characteristic, complemented
14C22×#121×C83C211yesmaximal, characteristic, complemented
15C22×#13050590C2211yescharacteristic, complemented
16C2×#14581818C2214yescomplemented
17C22×#13050574C2212yescomplemented
18#19128212—21no—
19#19128212—21no—
20#19128212—21no—
21#19128212—21no—
22#19128212C2212yes—
23#19128212C2212yescomplemented
24#19128212C2212yescomplemented
25#19128212C2212yescomplemented
26C2×#14581775—21no—
27C2×#14581771C2211yescharacteristic, complemented
28C2×#14581771C2211yescharacteristic, complemented
29C2×#14581766C2211yescharacteristic, complemented
30C2×#14581766C2211yescharacteristic, complemented
31C2×#14581761—21no—
32C2×C4×C22⋊D83—21no—
33C2×C4×C22⋊D83—21no—
34C2×#14581751C2211yescharacteristic, complemented
35#19128036C2214yescomplemented
36#19128031C2214yescomplemented
37#19128022C2218yescomplemented
38#19128019C2214yescomplemented
39#19128017C2214yescomplemented
40#19128014C2214yescomplemented
41#19128012C2214yescomplemented
42#19127952C2218yescomplemented
43#19127945C2218yescomplemented
44#19127935C2218yescomplemented
45#19127928C2218yescomplemented
46#19127852C2214yescomplemented
47#19127852C2214yescomplemented
48#19127844C2218yescomplemented
49#19127839C2214yescomplemented
50#19127835C2214yescomplemented
51#19127835C2214yescomplemented
52#19127834C2214yescomplemented
53#19127741C2214yescomplemented
54#19127706C2214yescomplemented
55#19127700C2214yescomplemented
56#19127665C2212yescomplemented
57#19127665C2212yescomplemented
58#19127665C2212yescomplemented
59#19127665C2212yescomplemented
60C2×C22⋊(C83⋊C8)C2212yescomplemented
61C2×C22⋊(C83⋊C8)C2212yescomplemented
62C23×D4×C83—21no—
63C23×D4×C83C2211yescharacteristic, complemented
64C24×C4×C83C2211yescharacteristic
65C2×#121×C83—21no—
66C2×#121×C83—21no—
67C2×#121×C83—21no—
68C2×#121×C83—21no—
69C2×#121×C83—21no—
70C2×#121×C83—21no—
71C2×#121×C83C2212yes—
72C2×#121×C83C2212yes—
73C2×#121×C83C2212yes—
74C2×#121×C83C2212yescomplemented
75C2×#121×C83C2212yescomplemented
76C2×#121×C83C2212yescomplemented
77C22×C4⋊C4×C83C2211yescharacteristic, complemented
78C22×C22⋊C4×C83—21no—
79C2×#13050590—21no—
80C2×#13050590—21no—
81C2×#13050590—44no—
82C2×#13050590C2312yes—
83C2×#13050590C2312yescomplemented
84C22×Dic166C2311yescharacteristic, complemented
85C22×D332C2311yescharacteristic, complemented
86C22×C22⋊D83—21no—
87C22×C22⋊D83—21no—
88C22×C22⋊D83—21no—
89C22×C4×D83—21no—
90#14581818—48no—
91C2×#13050578C2318yescomplemented
92C2×#13050575C2318yescomplemented
93C2×#13050574—44no—
94C2×#13050574C2314yes—
95C2×#13050574C2314yescomplemented
96C22×C83⋊C8C2314yescomplemented
97#14581775—22no—
98#14581775—22no—
99#14581775—22no—
100#14581775—22no—
101#14581771—21no—
102#14581771—21no—
103#14581771—21no—
104#14581771—21no—
105#14581771C2312yes—
106#14581771C2312yes—
107#14581771C2312yescomplemented
108#14581771C2312yescomplemented
109#14581766—21no—
110#14581766—21no—
111#14581766—21no—
112#14581766—21no—
113#14581766C2312yes—
114#14581766C2312yes—
115#14581766C2312yescomplemented
116#14581766C2312yescomplemented
117#14581761—22no—
118#14581761—22no—
119#14581761—22no—
120#14581761—22no—
121C4×C22⋊D83—22no—
122C4×C22⋊D83—22no—
123C4×C22⋊D83—22no—
124C4×C22⋊D83—22no—
125C4×C22⋊D83—22no—
126C4×C22⋊D83—22no—
127C4×C22⋊D83—22no—
128C4×C22⋊D83—22no—
129#14581751—21no—
130#14581751—21no—
131#14581751C2312yes—
132#14581751C2312yescomplemented
133C2×C4⋊Dic83C2311yescharacteristic, complemented
134C2×C4⋊Dic83C2311yescharacteristic, complemented
135C2×Dic83⋊C4—21no—
136C2×Dic83⋊C4—21no—
137C2×C22⋊Dic83—21no—
138C2×C22⋊Dic83—21no—
139C2×C22⋊Dic83—21no—
140C2×(C2×D83)⋊C4—21no—
141C2×(C2×D83)⋊C4—21no—
142C2×C4×Dic83—21no—
143#14581725C2318yescomplemented
144#14581723C2318yescomplemented
145#14581715C2318yescomplemented
146#14581713C2318yescomplemented
147#14581713C2318yescomplemented
148#14581712C2318yescomplemented
149C22⋊(C83⋊C8)C2314yes—
150C22⋊(C83⋊C8)C2314yes—
151C22⋊(C83⋊C8)C2314yescomplemented
152C22⋊(C83⋊C8)C2314yescomplemented
153C25×C83—21no—
154C25×C83D411yescharacteristic
155C22×D4×C83—22no—
156C22×D4×C83—22no—
157C22×D4×C83—22no—
158C22×D4×C83—22no—
159C22×D4×C83—22no—
160C22×D4×C83—22no—
161C22×D4×C83—21no—
162C22×D4×C83—21no—
163C22×D4×C83—21no—
164C22×D4×C83—44no—
165C22×D4×C83—48no—
166C22×D4×C83C2312yes—
167C22×D4×C83C2312yes—
168C22×D4×C83C2312yes—
169C23×C4×C83—21no—
170C23×C4×C83—44no—
171C23×C4×C83D411yescharacteristic
172C23×C4×C83D411yescharacteristic
173C23×C4×C83D411yescharacteristic
174C23×C4×C83D411yescharacteristic
175C23×C4×C83D411yescharacteristic
176C23×C4×C83D411yescharacteristic
177C23×C4×C83D411yescharacteristic
178C23×C4×C83C2311yescharacteristic
179C23×C4×C83C2311yescharacteristic
180C23×C4×C83C2311yescharacteristic
181C23×C4×C83C2311yescharacteristic
182C23×C4×C83C2311yescharacteristic
183C23×C4×C83C2311yescharacteristic
184C23×C4×C83C2311yescharacteristic
185#121×C83—22no—
186#121×C83—22no—
187#121×C83—22no—
188#121×C83—22no—
189#121×C83—22no—
190#121×C83—22no—
191#121×C83—22no—
192#121×C83—22no—
193#121×C83—22no—
194#121×C83—22no—
195#121×C83—22no—
196#121×C83—22no—
197#121×C83C2314yes—
198#121×C83C2314yes—
199#121×C83C2314yes—
200#121×C83C2314yes—
201C2×C4⋊C4×C83—21no—
202C2×C4⋊C4×C83—21no—
203C2×C4⋊C4×C83—21no—
204C2×C4⋊C4×C83C2312yes—
205C2×C4⋊C4×C83C2312yes—
206C2×C4⋊C4×C83C2312yes—
207C2×C22⋊C4×C83—22no—
208C2×C22⋊C4×C83—22no—
209C2×C22⋊C4×C83—22no—
210C2×C22⋊C4×C83—22no—
211C2×C22⋊C4×C83—22no—
212C2×C22⋊C4×C83—22no—
213C23×D83—21no—
214#13050590—28no—
215#13050590—44no—
216#13050590—44no—
217#13050590—44no—
218C2×Dic166—21no—
219C2×Dic166—42no—
220C2×Dic166C2412yes—
221C2×D332—21no—
222C2×D332—42no—
223C2×D332C2412yes—
224C2×C22⋊D83—22no—
225C2×C22⋊D83—22no—
226C2×C22⋊D83—22no—
227C2×C22⋊D83—22no—
228C2×C22⋊D83—22no—
229C2×C22⋊D83—22no—
230C2×C22⋊D83—44no—
231C2×C22⋊D83—44no—
232C2×C22⋊D83—44no—
233C22×Dic83—21no—
234C22×Dic83—21no—
235C22×Dic83—21no—
236C2×C4×D83—22no—
237C2×C4×D83—22no—
238C2×C4×D83—44no—
239#13050578—48no—
240#13050575—48no—
241#13050574—28no—
242#13050574—44no—
243C2×C83⋊C8—44no—
244C2×C83⋊C8C2418yes—
245C4⋊Dic83—21no—
246C4⋊Dic83—21no—
247C4⋊Dic83C2412yes—
248C4⋊Dic83C2412yes—
249Dic83⋊C4—22no—
250Dic83⋊C4—22no—
251Dic83⋊C4—22no—
252Dic83⋊C4—22no—
253C22⋊Dic83—22no—
254C22⋊Dic83—22no—
255C22⋊Dic83—22no—
256C22⋊Dic83—22no—
257C22⋊Dic83—22no—
258C22⋊Dic83—22no—
259(C2×D83)⋊C4—22no—
260(C2×D83)⋊C4—22no—
261(C2×D83)⋊C4—22no—
262(C2×D83)⋊C4—22no—
263C4×Dic83—22no—
264C4×Dic83—22no—
265C24×C83—24no—
266C24×C83—22no—
267C24×C83—22no—
268C24×C83—22no—
269C24×C83—42no—
270C24×C83—42no—
271C24×C83—44no—
272C24×C83—44no—
273C24×C83—44no—
274C24×C83C2×D411yescharacteristic
275C24×C83C2×D411yescharacteristic
276C24×C83C2×D411yescharacteristic
277C24×C83C2×D411yescharacteristic
278C24×C83C2×D411yescharacteristic
279C24×C83C2×D411yescharacteristic
280C24×C83C2×D411yescharacteristic
281C2×D4×C83—24no—
282C2×D4×C83—24no—
283C2×D4×C83—24no—
284C2×D4×C83—24no—
285C2×D4×C83—22no—
286C2×D4×C83—22no—
287C2×D4×C83—22no—
288C2×D4×C83—28no—
289C2×D4×C83—44no—
290C2×D4×C83—44no—
291C2×D4×C83—44no—
292C2×D4×C83—44no—
293C2×D4×C83—44no—
294C2×D4×C83—48no—
295C2×D4×C83—48no—
296C2×D4×C83—48no—
297C2×D4×C83—48no—
298C2×D4×C83—48no—
299C2×D4×C83—48no—
300C2×D4×C83C2414yes—
301C22×C4×C83—24no—
302C22×C4×C83—24no—
303C22×C4×C83—24no—
304C22×C4×C83—22no—
305C22×C4×C83—22no—
306C22×C4×C83—22no—
307C22×C4×C83—42no—
308C22×C4×C83—42no—
309C22×C4×C83—42no—
310C22×C4×C83—42no—
311C22×C4×C83—42no—
312C22×C4×C83—42no—
313C22×C4×C83—42no—
314C22×C4×C83—42no—
315C22×C4×C83—42no—
316C22×C4×C83—42no—
317C22×C4×C83—42no—
318C22×C4×C83—44no—
319C22×C4×C83C2×D411yescharacteristic
320C22×C4×C83C2×D411yescharacteristic
321C22×C4×C83C2×D411yescharacteristic
322C22×C4×C83C2×D411yescharacteristic
323C22×C4×C83C2×D411yescharacteristic
324C22×C4×C83C2×D411yescharacteristic
325C22×C4×C83C2×D411yescharacteristic
326C22×C4×C83C2×D411yescharacteristic
327C22×C4×C83C2×D411yescharacteristic
328C22×C4×C83C2×D411yescharacteristic
329C22×C4×C83C2×D411yescharacteristic
330C22×C4×C83C2×D411yescharacteristic
331C22×C4×C83C2×D411yescharacteristic
332C22×C4×C83C2×D411yescharacteristic
333C22×C4×C83C2×D411yescharacteristic
334C22×C4×C83C2×D411yescharacteristic
335C22×C4×C83C2×D411yescharacteristic
336C22×C4×C83C2×D411yescharacteristic
337C22×C4×C83C2×D411yescharacteristic
338C22×C4×C83C2×D411yescharacteristic
339C22×C4×C83C2×D411yescharacteristic
340C22×C4×C83C2411yescharacteristic
341C22×C4×C83C2411yescharacteristic
342C22×C4×C83C2411yescharacteristic
343C22×C4×C83C2411yescharacteristic
344C22×C4×C83C2411yescharacteristic
345C22×C4×C83C2411yescharacteristic
346C22×C4×C83C2411yescharacteristic
347C4⋊C4×C83—22no—
348C4⋊C4×C83—22no—
349C4⋊C4×C83—22no—
350C4⋊C4×C83C2414yes—
351C22⋊C4×C83—24no—
352C22⋊C4×C83—24no—
353C22⋊C4×C83—24no—
354C22⋊C4×C83—24no—
355C23×C83—22no—
356C23×C83—22no—
357C23×C83—22no—
358C23×C83—22no—
359C23×C83—22no—
360C23×C83—22no—
361C23×C83—22no—
362C23×C83—22no—
363C23×C83—22no—
364C23×C83—22no—
365C23×C83—22no—
366C23×C83—22no—
367C23×C83—24no—
368C23×C83—41no—
369C23×C83—41no—
370C23×C83—41no—
371C23×C83—41no—
372C23×C83—41no—
373C23×C83—41no—
374C23×C83—41no—
375C23×C83—41no—
376C23×C83—416no—
377C23×C83—44no—
378C23×C83—44no—
379C23×C83—44no—
380C23×C83—44no—
381C23×C83—44no—
382C23×C83—44no—
383C23×C83—44no—
384C23×C83—44no—
385C23×C83—44no—
386C23×C83—816no—
387C23×C83AGL(1,ℤ/8)14yescomplemented
388C23×C83C22×D411yescharacteristic
389C23×C83C22×D411yescharacteristic
390C23×C83C22×D411yescharacteristic
391C23×C83C22×D411yescharacteristic
392C23×C83C22×D411yescharacteristic
393C23×C83C22×D411yescharacteristic
394C23×C83C22×D411yescharacteristic
395C22×D83—22no—
396C22×D83—42no—
397C22×D83—42no—
398C22×D83—42no—
399D4×C83—28no—
400D4×C83—44no—
401D4×C83—44no—
402D4×C83—48no—
403D4×C83—48no—
404D4×C83—48no—
405D4×C83—48no—
406D4×C83—44no—
407C2×C4×C83—22no—
408C2×C4×C83—22no—
409C2×C4×C83—22no—
410C2×C4×C83—22no—
411C2×C4×C83—22no—
412C2×C4×C83—22no—
413C2×C4×C83—22no—
414C2×C4×C83—22no—
415C2×C4×C83—22no—
416C2×C4×C83—22no—
417C2×C4×C83—22no—
418C2×C4×C83—22no—
419C2×C4×C83—22no—
420C2×C4×C83—22no—
421C2×C4×C83—22no—
422C2×C4×C83—24no—
423C2×C4×C83—41no—
424C2×C4×C83—41no—
425C2×C4×C83—41no—
426C2×C4×C83—41no—
427C2×C4×C83—41no—
428C2×C4×C83—41no—
429C2×C4×C83—41no—
430C2×C4×C83—41no—
431C2×C4×C83—41no—
432C2×C4×C83—41no—
433C2×C4×C83—41no—
434C2×C4×C83—41no—
435C2×C4×C83—44no—
436C2×C4×C83—44no—
437C2×C4×C83—44no—
438C2×C4×C83C22×D411yescharacteristic
439C2×C4×C83C22×D411yescharacteristic
440C2×C4×C83C22×D411yescharacteristic
441C2×C4×C83C22×D411yescharacteristic
442C2×C4×C83C22×D411yescharacteristic
443C2×C4×C83C22×D411yescharacteristic
444C2×C4×C83C22×D411yescharacteristic
445C2×C4×C83H(5,𝔽2)14yes—
446C2×C4×C83C2511yescharacteristic
447C22⋊D83—44no—
448C22⋊D83—44no—
449C22⋊D83—44no—
450C22⋊D83—44no—
451C22⋊D83—44no—
452C22⋊D83—44no—
453C2×Dic83—22no—
454C2×Dic83—22no—
455C2×Dic83—22no—
456C2×Dic83—42no—
457C2×Dic83—42no—
458C2×Dic83—42no—
459D332—24no—
460D332—42no—
461C4×D83—44no—
462C4×D83—44no—
463Dic166—24no—
464Dic166—42no—
465C83⋊C8—28no—
466C22×C83—28no—
467C22×C83—21no—
468C22×C83—21no—
469C22×C83—21no—
470C22×C83—21no—
471C22×C83—21no—
472C22×C83—21no—
473C22×C83—21no—
474C22×C83—21no—
475C22×C83—21no—
476C22×C83—21no—
477C22×C83—21no—
478C22×C83—21no—
479C22×C83—21no—
480C22×C83—21no—
481C22×C83—21no—
482C22×C83—21no—
483C22×C83—44no—
484C22×C83—44no—
485C22×C83—44no—
486C22×C83—44no—
487C22×C83—44no—
488C22×C83—44no—
489C22×C83—44no—
490C22×C83—44no—
491C22×C83—44no—
492C22×C83—88no—
493C22×C83—88no—
494C22×C83—88no—
495C22×C83#53412yes—
496C22×C83C2×AGL(1,ℤ/8)12yes—
497C22×C83C2×AGL(1,ℤ/8)12yes—
498C22×C83C2×AGL(1,ℤ/8)12yes—
499C22×C83#57512yes—
500C22×C83C23×D411yescharacteristic
501C2×D83—42no—
502C2×D83—42no—
503C2×D83—42no—
504C2×D83—84no—
505C4×C83—21no—
506C4×C83—21no—
507C4×C83—21no—
508C4×C83—21no—
509C4×C83—21no—
510C4×C83—21no—
511C4×C83—44no—
512C4×C83#53412yes—
513C4×C83C2×H(5,𝔽2)12yes—
514Dic83—42no—
515Dic83—42no—
516Dic83—42no—
517#60750—831nomaximal, Sylow
518C2×C83—22no—
519C2×C83—22no—
520C2×C83—22no—
521C2×C83—22no—
522C2×C83—22no—
523C2×C83—41no—
524C2×C83—41no—
525C2×C83—84no—
526C2×C83C2×#53411yescharacteristic
527C2×C83C22×AGL(1,ℤ/8)11yescharacteristic
528C2×C83C2×#57511yescharacteristic
529D83—82no—
530C2×#525—831no—
531C22×#121D8311yescharacteristic, complemented
532#3194—834no—
533#3193—832no—
534#3192—832no—
535#3188—834no—
536#3187—832no—
537#3186—832no—
538#3094—832no—
539#3092—832no—
540#3055—834no—
541#3006—832no—
542#3003—832no—
543C2×#407—831no—
544C83#6075011yescharacteristic, complemented, Sylow
545C22×#41—831no—
546C23×D4—21no—
547C23×D4C2×D8311yescharacteristic, complemented
548C24×C4C2×D8311yescharacteristic
549C2×AGL(1,ℤ/8)—834no—
550C22×M16—832no—
551#525—832no—
552#525—832no—
553#525—832no—
554#525—832no—
555#525—1661no—
556#525—1661no—
557#525—1661no—
558#525—1661no—
559C2×#123—1661no—
560C2×C22⋊Q8—831no—
561C2×C22⋊Q8—831no—
562C2×#121—21no—
563C2×#121—21no—
564C2×#121—21no—
565C2×#121—21no—
566C2×#121—21no—
567C2×#121—21no—
568C2×#121—831no—
569C2×#121—831no—
570C2×#121C2×D8312yes—
571C2×#121C2×D8312yes—
572C2×#121C2×D8312yes—
573C2×#121C2×D8312yescomplemented
574C2×#121C2×D8312yescomplemented
575C2×#121C2×D8312yescomplemented
576C2×#120—1661no—
577C2×C4×D4—1661no—
578C2×C4×D4—1661no—
579C2×#117—831no—
580C22×C4⋊C4C2×D8311yescharacteristic, complemented
581C22×C22⋊C4—21no—
582#484—834no—
583#483—834no—
584#482—838no—
585#481—834no—
586#481—834no—
587#480—834no—
588#480—834no—
589#469—838no—
590#468—838no—
591#466—838no—
592#465—838no—
593#450—834no—
594#450—834no—
595#449—838no—
596#448—834no—
597#447—834no—
598#447—834no—
599#447—834no—
600#428—834no—
601#418—834no—
602#417—834no—
603#407—832no—
604#407—832no—
605#407—832no—
606#407—832no—
607C2×C22⋊C8—832no—
608C2×C22⋊C8—832no—
609C25—21no—
610C25C22⋊D8311yescharacteristic
611C2×#41—3324no—
612C2×#41—832no—
613C2×#41—832no—
614C2×#41—1661no—
615C2×#41—1661no—
616C22×Q8—831no—
617C22×D4—22no—
618C22×D4—22no—
619C22×D4—22no—
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—22no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—21no—
626C22×D4—44no—
627C22×D4—48no—
628C22×D4—831no—
629C22×D4—1661no—
630C22×D4—1661no—
631C22×D4—1661no—
632C22×D4C22×D8312yes—
633C22×D4C22×D8312yes—
634C22×D4C22×D8312yes—
635C23×C4—21no—
636C23×C4—44no—
637C23×C4—1661no—
638C23×C4C22⋊D8311yescharacteristic
639C23×C4C22⋊D8311yescharacteristic
640C23×C4C22⋊D8311yescharacteristic
641C23×C4C22⋊D8311yescharacteristic
642C23×C4C22⋊D8311yescharacteristic
643C23×C4C22⋊D8311yescharacteristic
644C23×C4C22⋊D8311yescharacteristic
645C23×C4C22×D8311yescharacteristic
646C23×C4C22×D8311yescharacteristic
647C23×C4C22×D8311yescharacteristic
648C23×C4C22×D8311yescharacteristic
649C23×C4C22×D8311yescharacteristic
650C23×C4C22×D8311yescharacteristic
651C23×C4C22×D8311yescharacteristic
652AGL(1,ℤ/8)—3328no—
653C2×SD16—838no—
654C2×D8—838no—
655C2×M16—3324no—
656C2×M16—834no—
657C2×M16—834no—
658C22×C8—834no—
659#123—1662no—
660#123—1662no—
661#123—1662no—
662#123—1662no—
663C22⋊Q8—832no—
664C22⋊Q8—832no—
665C22⋊Q8—832no—
666C22⋊Q8—832no—
667C22⋊Q8—1661no—
668C22⋊Q8—1661no—
669C22⋊Q8—1661no—
670C22⋊Q8—1661no—
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—22no—
681#121—22no—
682#121—22no—
683#121—832no—
684#121—832no—
685#121—832no—
686#121—832no—
687#121—1661no—
688#121—1661no—
689#121—1661no—
690#121—1661no—
691#121C22×D8314yes—
692#121C22×D8314yes—
693#121C22×D8314yes—
694#121C22×D8314yes—
695#120—1662no—
696#120—1662no—
697#120—1662no—
698#120—1662no—
699C4×D4—1662no—
700C4×D4—1662no—
701C4×D4—1662no—
702C4×D4—1662no—
703C4×D4—1662no—
704C4×D4—1662no—
705C4×D4—1662no—
706C4×D4—1662no—
707#117—832no—
708#117—832no—
709#117—1661no—
710#117—1661no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—831no—
715C2×C4⋊C4—831no—
716C2×C4⋊C4—1661no—
717C2×C4⋊C4—1661no—
718C2×C4⋊C4C22×D8312yes—
719C2×C4⋊C4C22×D8312yes—
720C2×C4⋊C4C22×D8312yes—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—1661no—
728C2×C22⋊C4—1661no—
729C2×C22⋊C4—1661no—
730C2×C22⋊C4—1661no—
731C2×C22⋊C4—1661no—
732C2×C42—1661no—
733#107—838no—
734#106—838no—
735#103—838no—
736#102—838no—
737#102—838no—
738#102—838no—
739C22⋊C8—834no—
740C22⋊C8—834no—
741C22⋊C8—834no—
742C22⋊C8—834no—
743C24—24no—
744C24—22no—
745C24—22no—
746C24—22no—
747C24—42no—
748C24—42no—
749C24—44no—
750C24—44no—
751C24—44no—
752C24—1661no—
753C24C2×C22⋊D8311yescharacteristic
754C24C2×C22⋊D8311yescharacteristic
755C24C2×C22⋊D8311yescharacteristic
756C24C2×C22⋊D8311yescharacteristic
757C24C2×C22⋊D8311yescharacteristic
758C24C2×C22⋊D8311yescharacteristic
759C24C2×C22⋊D8311yescharacteristic
760#41—3324no—
761#41—3324no—
762#41—3324no—
763#41—1668no—
764C2×Q8—3322no—
765C2×Q8—832no—
766C2×Q8—1661no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—24no—
771C2×D4—22no—
772C2×D4—22no—
773C2×D4—22no—
774C2×D4—28no—
775C2×D4—44no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—3322no—
787C2×D4—3324no—
788C2×D4—3324no—
789C2×D4—3324no—
790C2×D4—832no—
791C2×D4—1662no—
792C2×D4—1662no—
793C2×D4—1662no—
794C2×D4—1662no—
795C2×D4—1662no—
796C2×D4—1662no—
797C2×D4—1661no—
798C2×D4C23×D8314yes—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—44no—
817C22×C4—3324no—
818C22×C4—1661no—
819C22×C4—1661no—
820C22×C4—1661no—
821C22×C4—1662no—
822C22×C4—1662no—
823C22×C4C2×C22⋊D8311yescharacteristic
824C22×C4C2×C22⋊D8311yescharacteristic
825C22×C4C2×C22⋊D8311yescharacteristic
826C22×C4C2×C22⋊D8311yescharacteristic
827C22×C4C2×C22⋊D8311yescharacteristic
828C22×C4C2×C22⋊D8311yescharacteristic
829C22×C4C2×C22⋊D8311yescharacteristic
830C22×C4C2×C22⋊D8311yescharacteristic
831C22×C4C2×C22⋊D8311yescharacteristic
832C22×C4C2×C22⋊D8311yescharacteristic
833C22×C4C2×C22⋊D8311yescharacteristic
834C22×C4C2×C22⋊D8311yescharacteristic
835C22×C4C2×C22⋊D8311yescharacteristic
836C22×C4C2×C22⋊D8311yescharacteristic
837C22×C4C2×C22⋊D8311yescharacteristic
838C22×C4C2×C22⋊D8311yescharacteristic
839C22×C4C2×C22⋊D8311yescharacteristic
840C22×C4C2×C22⋊D8311yescharacteristic
841C22×C4C2×C22⋊D8311yescharacteristic
842C22×C4C2×C22⋊D8311yescharacteristic
843C22×C4C2×C22⋊D8311yescharacteristic
844C22×C4C23×D8311yescharacteristic
845C22×C4C23×D8311yescharacteristic
846C22×C4C23×D8311yescharacteristic
847C22×C4C23×D8311yescharacteristic
848C22×C4C23×D8311yescharacteristic
849C22×C4C23×D8311yescharacteristic
850C22×C4C23×D8311yescharacteristic
851SD16—3328no—
852D8—3328no—
853M16—3324no—
854M16—1668no—
855C2×C8—3324no—
856C2×C8—838no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—832no—
861C4⋊C4—832no—
862C4⋊C4—1661no—
863C4⋊C4—1661no—
864C4⋊C4—1662no—
865C4⋊C4—1662no—
866C4⋊C4—1662no—
867C4⋊C4—1662no—
868C4⋊C4C23×D8314yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—24no—
872C22⋊C4—24no—
873C22⋊C4—1662no—
874C22⋊C4—1662no—
875C22⋊C4—1662no—
876C22⋊C4—1662no—
877C22⋊C4—1662no—
878C22⋊C4—1662no—
879C22⋊C4—1662no—
880C22⋊C4—1662no—
881C22⋊C4—1662no—
882C22⋊C4—1662no—
883C42—1662no—
884C42—1662no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—24no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—416no—
907C23—44no—
908C23—44no—
909C23—44no—
910C23—44no—
911C23—44no—
912C23—44no—
913C23—44no—
914C23—44no—
915C23—44no—
916C23—816no—
917C23—3322no—
918C23—3322no—
919C23—3322no—
920C23—1662no—
921C23#1458181814yescomplemented
922C23C22×C22⋊D8311yescharacteristic
923C23C22×C22⋊D8311yescharacteristic
924C23C22×C22⋊D8311yescharacteristic
925C23C22×C22⋊D8311yescharacteristic
926C23C22×C22⋊D8311yescharacteristic
927C23C22×C22⋊D8311yescharacteristic
928C23C22×C22⋊D8311yescharacteristic
929Q8—3322no—
930Q8—1664no—
931D4—28no—
932D4—44no—
933D4—44no—
934D4—48no—
935D4—48no—
936D4—48no—
937D4—48no—
938D4—44no—
939D4—3322no—
940D4—3324no—
941D4—3324no—
942D4—3324no—
943D4—3324no—
944D4—3324no—
945D4—3324no—
946D4—1664no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—44no—
976C2×C4—44no—
977C2×C4—44no—
978C2×C4—3324no—
979C2×C4—3322no—
980C2×C4—3322no—
981C2×C4—3322no—
982C2×C4—3324no—
983C2×C4—1662no—
984C2×C4—1662no—
985C2×C4—1662no—
986C2×C4C22×C22⋊D8311yescharacteristic
987C2×C4C22×C22⋊D8311yescharacteristic
988C2×C4C22×C22⋊D8311yescharacteristic
989C2×C4C22×C22⋊D8311yescharacteristic
990C2×C4C22×C22⋊D8311yescharacteristic
991C2×C4C22×C22⋊D8311yescharacteristic
992C2×C4C22×C22⋊D8311yescharacteristic
993C2×C4#1458183714yes—
994C2×C4C24×D8311yescharacteristic
995C8—1668no—
996C22—28no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—88no—
1023C22—88no—
1024C22—88no—
1025C22—3322no—
1026C22—3322no—
1027C22—3322no—
1028C22—6644no—
1029C22#1912826012yes—
1030C22C2×#1458181812yes—
1031C22C2×#1458181812yes—
1032C22C2×#1458181812yes—
1033C22#1912849912yes—
1034C22C23×C22⋊D8311yescharacteristic
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—44no—
1042C4—3322no—
1043C4—3322no—
1044C4—3322no—
1045C4#1912826012yes—
1046C4C2×#1458183712yes—
1047C2—22no—
1048C2—22no—
1049C2—22no—
1050C2—22no—
1051C2—22no—
1052C2—41no—
1053C2—41no—
1054C2—84no—
1055C2—6642no—
1056C2C2×#1912826011yescharacteristic
1057C2C22×#1458181811yescharacteristic
1058C2C2×#1912849911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC22×#121×C83C2
socleC22×C83C23×D4
hypercenterC22×#121D83
hypocenterC83#60750
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#19128212C2semidirect
2. #24918277C2semidirect
3. #24918269C2semidirect
4. #24918260C2semidirect
5. #24918228C2semidirect
6. #24918220C2semidirect
7. #24918211C2semidirect
8. #24917399C2semidirect
9. #24917386C2semidirect
10. #24917078C2semidirect
11. #24916713C2semidirect
12. #24916690C2semidirect
13. C2×#19127665C2semidirect
14. C22×#121×C83C2semidirect
15. C22×#13050590C22semidirect
16. C2×#14581818C22semidirect
17. C22×#13050574C22semidirect
23. #19128212C22semidirect
24. #19128212C22semidirect
25. #19128212C22semidirect
27. C2×#14581771C22semidirect
28. C2×#14581771C22semidirect
29. C2×#14581766C22semidirect
30. C2×#14581766C22semidirect
34. C2×#14581751C22semidirect
35. #19128036C22semidirect
36. #19128031C22semidirect
37. #19128022C22semidirect
38. #19128019C22semidirect
39. #19128017C22semidirect
40. #19128014C22semidirect
41. #19128012C22semidirect
42. #19127952C22semidirect
43. #19127945C22semidirect
44. #19127935C22semidirect
45. #19127928C22semidirect
46. #19127852C22semidirect
47. #19127852C22semidirect
48. #19127844C22semidirect
49. #19127839C22semidirect
50. #19127835C22semidirect
51. #19127835C22semidirect
52. #19127834C22semidirect
53. #19127741C22semidirect
54. #19127706C22semidirect
55. #19127700C22semidirect
56. #19127665C22semidirect
57. #19127665C22semidirect
58. #19127665C22semidirect
59. #19127665C22semidirect
60. C2×C22⋊(C83⋊C8)C22semidirect
61. C2×C22⋊(C83⋊C8)C22semidirect
63. C23×D4×C83C22semidirect
74. C2×#121×C83C22semidirect
75. C2×#121×C83C22semidirect
76. C2×#121×C83C22semidirect
77. C22×C4⋊C4×C83C22semidirect
83. C2×#13050590C23semidirect
84. C22×Dic166C23semidirect
85. C22×D332C23semidirect
91. C2×#13050578C23semidirect
92. C2×#13050575C23semidirect
95. C2×#13050574C23semidirect
96. C22×C83⋊C8C23semidirect
107. #14581771C23semidirect
108. #14581771C23semidirect
115. #14581766C23semidirect
116. #14581766C23semidirect
132. #14581751C23semidirect
133. C2×C4⋊Dic83C23semidirect
134. C2×C4⋊Dic83C23semidirect
143. #14581725C23semidirect
144. #14581723C23semidirect
145. #14581715C23semidirect
146. #14581713C23semidirect
147. #14581713C23semidirect
148. #14581712C23semidirect
151. C22⋊(C83⋊C8)C23semidirect
152. C22⋊(C83⋊C8)C23semidirect
387. C23×C83AGL(1,ℤ/8)semidirect
531. C22×#121D83semidirect
544. C83#60750semidirect
547. C23×D4C2×D83semidirect
573. C2×#121C2×D83semidirect
574. C2×#121C2×D83semidirect
575. C2×#121C2×D83semidirect
580. C22×C4⋊C4C2×D83semidirect
921. C23#14581818semidirect

Maximal subgroups

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

subgroupindex
C2×#191282122
#249182772
#249182692
#249182602
#249182282
#249182202
#249182112
#249173992
#249173862
#249170782
#249167132
#249166902
C2×#191276652
C22×#121×C832
#6075083