Finite Group Databasebeta

← #35307251

Subgroups — #35307251

Order 21248.

602 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128099C211yesmaximal, characteristic
2C2×#19128080C211yesmaximal, characteristic
3C2×#19128053C211yesmaximal, characteristic
4#24908423C211yesmaximal, characteristic
5#24908423C211yesmaximal, characteristic
6C83⋊#1273C211yesmaximal, characteristic
7C83×#1990C211yesmaximal, characteristic
8C22×#13050580—22no—
9C2×#14581792C2211yescharacteristic
10C2×#14581792C2211yescharacteristic
11#19128099—22no—
12#19128099—22no—
13#19128080—22no—
14#19128080—22no—
15#19128053—22no—
16#19128053—22no—
17C2×#14581724—22no—
18C2×#14581715—22no—
19C2×C4×C83⋊C8C2211yescharacteristic
20C2×C4×C83⋊C8C2211yescharacteristic
21#19127463—22no—
22#19127463—22no—
23C2×C4⋊Q8×C83C2211yescharacteristic
24C2×C4×C8×C83C2211yescharacteristic
25#384×C83C2211yescharacteristic
26#340×C83—22no—
27C22×Dic166—21no—
28C22×Dic166—21no—
29C2×#13050580—28no—
30C2×#13050580—44no—
31C2×#13050580—44no—
32C22×C83⋊C8D412yes—
33C22×C83⋊C8D412yes—
34#14581792—21no—
35#14581792—21no—
36#14581792—21no—
37#14581792—21no—
38#14581792—21no—
39#14581792—21no—
40#14581792D412yes—
41#14581792D412yes—
42C2×C4⋊Dic83—21no—
43C2×C4⋊Dic83—21no—
44C2×C4⋊Dic83—21no—
45C2×C4⋊Dic83—21no—
46#14581724—28no—
47#14581715—28no—
48C4×C83⋊C8—21no—
49C4×C83⋊C8—21no—
50C4×C83⋊C8—21no—
51C4×C83⋊C8—21no—
52C22×Q8×C83—21no—
53C22×C8×C83D412yes—
54C4⋊Q8×C83—21no—
55C4⋊Q8×C83—21no—
56C4⋊Q8×C83—21no—
57C4⋊Q8×C83D412yes—
58C2×C4⋊C4×C83—21no—
59C2×C4⋊C4×C83—21no—
60C2×C4⋊C4×C83—21no—
61C2×C4⋊C4×C83—21no—
62C2×C4⋊C4×C83—21no—
63C2×C42×C83C2311yescharacteristic
64C4×C8×C83—21no—
65C4×C8×C83—21no—
66C2×Dic166—22no—
67C2×Dic166—22no—
68C2×Dic166—42no—
69C2×Dic166—42no—
70C2×Dic166—42no—
71C2×Dic166—42no—
72C2×Dic166—41no—
73C2×Dic166—41no—
74C22×Dic83—41no—
75C22×Dic83—41no—
76#13050580—416no—
77C2×C83⋊C8—22no—
78C2×C83⋊C8—22no—
79C2×C83⋊C8—22no—
80C2×C83⋊C8—22no—
81C2×C83⋊C8—22no—
82C2×C83⋊C8SD1614yes—
83C4⋊Dic83—22no—
84C4⋊Dic83—22no—
85C4⋊Dic83—22no—
86C4⋊Dic83—22no—
87C4⋊Dic83—41no—
88C4⋊Dic83—41no—
89C4⋊Dic83—41no—
90C4⋊Dic83—41no—
91C2×Q8×C83—22no—
92C2×Q8×C83—41no—
93C2×Q8×C83—42no—
94C2×Q8×C83—42no—
95C22×C4×C83—41no—
96C22×C4×C83—41no—
97C22×C4×C83C2×D411yescharacteristic
98C22×C4×C83C2×D411yescharacteristic
99C22×C4×C83C2×D411yescharacteristic
100C2×C8×C83—22no—
101C2×C8×C83—22no—
102C2×C8×C83Q1614yescomplemented
103C4⋊C4×C83—22no—
104C4⋊C4×C83—22no—
105C4⋊C4×C83—41no—
106C4⋊C4×C83—41no—
107C4⋊C4×C83—42no—
108C4⋊C4×C83—42no—
109C4⋊C4×C83—42no—
110C42×C83C2×D411yescharacteristic
111C42×C83C2×D411yescharacteristic
112C42×C83C2×D411yescharacteristic
113C42×C83#4111yescharacteristic
114C23×C83#12711yescharacteristic
115Q8×C83—44no—
116Q8×C83—82no—
117C2×C4×C83—42no—
118C2×C4×C83—81no—
119C2×C4×C83—81no—
120C2×C4×C83—81no—
121C2×C4×C83—81no—
122C2×C4×C83—81no—
123C2×C4×C83#12011yescharacteristic
124C2×C4×C83#12011yescharacteristic
125C2×C4×C83#12011yescharacteristic
126C2×C4×C83#12111yescharacteristic
127C2×C4×C83#12111yescharacteristic
128C2×C4×C83#12111yescharacteristic
129C2×C4×C83C2×SD1612yes—
130C2×C4×C83C2×Q1612yes—
131C2×C4×C83#13512yes—
132C2×C4×C83AGL(1,ℤ/8)12yes—
133C2×C4×C83#13712yes—
134C2×C4×C83#13712yes—
135C2×Dic83—42no—
136C2×Dic83—42no—
137C2×Dic83—81no—
138C2×Dic83—81no—
139C2×Dic83—81no—
140C2×Dic83—81no—
141Dic166—44no—
142Dic166—44no—
143Dic166—82no—
144Dic166—82no—
145C8×C83—24no—
146C83⋊C8—24no—
147C83⋊C8—42no—
148C22×C83#39211yescharacteristic
149C22×C83#49211yescharacteristic
150C22×C83#49411yescharacteristic
151C22×C83#49511yescharacteristic
152C22×C83#49611yescharacteristic
153C22×C83#49711yescharacteristic
154C22×C83#49711yescharacteristic
155C4×C83—82no—
156C4×C83—161no—
157C4×C83#45012yes—
158C4×C83#45112yes—
159C4×C83#45212yes—
160C4×C83#46012yes—
161C4×C83#46212yes—
162C4×C83#46412yes—
163Dic83—82no—
164Dic83—82no—
165#10318—831nomaximal, Sylow
166C2×C83#170711yescharacteristic
167C2×C83#171611yescharacteristic
168C2×C83#172011yescharacteristic
169C2×C83#172311yescharacteristic
170C2×C83#201411yescharacteristic
171C2×C83#201511yescharacteristic
172C2×C83#201611yescharacteristic
173C2×#498—831no—
174C2×#494—831no—
175C2×#487—831no—
176#1990—831no—
177#1990—831no—
178#1990D8311yescharacteristic
179#1273—831no—
180C83#1031811yescharacteristic, complemented, Sylow
181C22×Q16—1662no—
182C2×C4⋊Q8—831no—
183C2×C4⋊Q8—831no—
184C2×C4⋊Q8C2×D8311yescharacteristic
185#498—1662no—
186#498—1662no—
187#494—1662no—
188#494—1662no—
189#487—1662no—
190#487—1662no—
191C2×#106—1662no—
192C2×#103—1662no—
193C2×C4×C8—831no—
194C2×C4×C8—831no—
195C2×C4×C8C2×D8311yescharacteristic
196#384C2×D8311yescharacteristic
197#340—22no—
198#340—1662no—
199#340—1662no—
200C22×Q8—21no—
201C22×Q8—1661no—
202C22×Q8—1661no—
203C2×Q16—3324no—
204C2×Q16—3324no—
205C2×Q16—1668no—
206C22×C8—832no—
207C22×C8—832no—
208C22×C8C22⋊D8312yes—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—832no—
213C4⋊Q8—832no—
214C4⋊Q8—1661no—
215C4⋊Q8—1661no—
216C4⋊Q8—1661no—
217C4⋊Q8—1661no—
218C4⋊Q8—1661no—
219C4⋊Q8—1661no—
220C4⋊Q8D33212yes—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—1661no—
227C2×C4⋊C4—1661no—
228C2×C4⋊C4—1661no—
229C2×C4⋊C4—1661no—
230C2×C42C22×D8311yescharacteristic
231#106—1668no—
232#103—1668no—
233C4×C8—21no—
234C4×C8—21no—
235C4×C8—1661no—
236C4×C8—1661no—
237C4×C8—1661no—
238C4×C8—1661no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×Q8—42no—
242C2×Q8—42no—
243C2×Q8—3321no—
244C2×Q8—3321no—
245C2×Q8—3322no—
246C2×Q8—3322no—
247C2×Q8—3322no—
248C2×Q8—3322no—
249C2×Q8—1662no—
250C2×Q8—1662no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—3321no—
254C22×C4—3321no—
255C22×C4D4×D8311yescharacteristic
256C22×C4D4×D8311yescharacteristic
257C22×C4C2×C22⋊D8311yescharacteristic
258Q16—33216no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—834no—
262C2×C8—1662no—
263C2×C8—1662no—
264C2×C8—1662no—
265C2×C8—1662no—
266C2×C8—1662no—
267C2×C8#1305058014yescomplemented
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4—42no—
275C4⋊C4—3321no—
276C4⋊C4—3321no—
277C4⋊C4—3321no—
278C4⋊C4—3321no—
279C4⋊C4—1662no—
280C4⋊C4—1662no—
281C4⋊C4—1662no—
282C4⋊C4—1662no—
283C42D4×D8311yescharacteristic
284C42D4×D8311yescharacteristic
285C42C2×D33211yescharacteristic
286C42#1305059011yescharacteristic
287C23#1458178811yescharacteristic
288Q8—44no—
289Q8—82no—
290Q8—3324no—
291Q8—3324no—
292Q8—6642no—
293Q8—6642no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—3322no—
301C2×C4—3322no—
302C2×C4—6641no—
303C2×C4—6641no—
304C2×C4—6641no—
305C2×C4—6641no—
306C2×C4#1458176011yescharacteristic
307C2×C4#1458176211yescharacteristic
308C2×C4#1458176211yescharacteristic
309C2×C4#1458176511yescharacteristic
310C2×C4#1458176511yescharacteristic
311C2×C4#1458176611yescharacteristic
312C2×C4SD16×D8312yes—
313C2×C4C2×#1305058012yes—
314C2×C4#1458181312yes—
315C2×C4#1458181612yes—
316C2×C4#1458182212yes—
317C2×C4#1458182412yes—
318C8—24no—
319C8—3322no—
320C8—1664no—
321C22#1912761011yescharacteristic
322C22#1912807211yescharacteristic
323C22#1912808011yescharacteristic
324C22#1912808211yescharacteristic
325C22#1912808911yescharacteristic
326C22#1912809411yescharacteristic
327C22#1912809611yescharacteristic
328C4—82no—
329C4—161no—
330C4—6642no—
331C4—6642no—
332C4#1912785312yes—
333C4#1912785612yes—
334C4#1912786612yes—
335C4#1912790012yes—
336C4#1912791112yes—
337C4#1912792612yes—
338C2#2490705811yescharacteristic
339C2#2490709811yescharacteristic
340C2#2490712511yescharacteristic
341C2#2490714111yescharacteristic
342C2#2490855211yescharacteristic
343C2#2490855811yescharacteristic
344C2#2490856211yescharacteristic
subgroupG/H
centerC23#14581788
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1990C2
socle, prime radicalC23×C83#127
hypercenter#1990D83
hypocenterC83#10318
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
102. C2×C8×C83Q16semidirect
180. C83#10318semidirect
267. C2×C8#13050580semidirect

Maximal subgroups

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

subgroupindex
C2×#191280992
C2×#191280802
C2×#191280532
#249084232
C83⋊#12732
C83×#19902
#1031883