Finite Group Databasebeta

← #35293248

Subgroups — #35293248

Order 21248.

424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915451C211yesmaximal, characteristic
2#24908797C212yesmaximal
3#24908562C211yesmaximal, characteristic
4#24905287C212yesmaximal
5C83×#1272C211yesmaximal, characteristic
6C22×#13050580—21no—
7C2×#14581792C2211yescharacteristic
8C2×#14581724—22no—
9C2×#14581715—21no—
10#19127640—21no—
11#19127633—22no—
12#19127608—21no—
13#19127599C2212yes—
14#19127588—22no—
15#19127464—22no—
16#19127456C2211yescharacteristic
17#391×C83C2211yescharacteristic
18#336×C83C2212yes—
19C22×Dic166—21no—
20C2×#13050580—42no—
21C2×#13050580—42no—
22C2×#13050580—42no—
23C22×C83⋊C8—21no—
24#14581792—42no—
25C2×C4⋊Dic83—21no—
26C2×C4⋊Dic83—21no—
27C2×C4⋊Dic83—22no—
28C2×C4⋊Dic83D412yes—
29C2×C4⋊Dic83D412yes—
30C2×Dic83⋊C4—22no—
31C2×C4×Dic83—21no—
32#14581724—44no—
33#14581715—42no—
34C83⋊#95—21no—
35C83⋊#95—22no—
36C83⋊#95—22no—
37C83⋊#95—22no—
38C22×Q8×C83D411yescharacteristic
39C22×C8×C83—22no—
40C2×C4⋊C4×C83D411yescharacteristic
41C2×C42×C83C2311yescharacteristic
42#95×C83—22no—
43C2×Dic166—22no—
44C2×Dic166—41no—
45C2×Dic166—41no—
46C2×Dic166—41no—
47C2×Dic166—41no—
48C2×Dic166—41no—
49C22×Dic83—22no—
50C22×Dic83—22no—
51C22×Dic83—41no—
52#13050580—48no—
53C2×C83⋊C8—22no—
54C2×C83⋊C8—41no—
55C2×C83⋊C8—41no—
56C4⋊Dic83—24no—
57C4⋊Dic83—22no—
58C4⋊Dic83—22no—
59C4⋊Dic83—42no—
60C4⋊Dic83—42no—
61C4⋊Dic83—81no—
62C4⋊Dic83—81no—
63Dic83⋊C4—42no—
64Dic83⋊C4—42no—
65C4×Dic83—81no—
66C2×Q8×C83—21no—
67C2×Q8×C83—41no—
68C2×Q8×C83—41no—
69C2×Q8×C83SD1612yes—
70C22×C4×C83—21no—
71C22×C4×C83—21no—
72C22×C4×C83C2×D412yes—
73C22×C4×C83C2×D411yescharacteristic
74C2×C8×C83—24no—
75C2×C8×C83—42no—
76C2×C8×C83—42no—
77C4⋊C4×C83—41no—
78C42×C83—41no—
79C23×C83#12011yescharacteristic
80Q8×C83—42no—
81Q8×C83—81no—
82C2×C4×C83—21no—
83C2×C4×C83—22no—
84C2×C4×C83—22no—
85C2×C4×C83—21no—
86C2×C4×C83—22no—
87C2×C4×C83—41no—
88C2×C4×C83—41no—
89C2×C4×C83—41no—
90C2×C4×C83—42no—
91C2×C4×C83C2×SD1611yescharacteristic
92C2×C4×C83#13512yes—
93C2×C4×C83#13712yes—
94C2×C4×C83#13711yescharacteristic
95C2×Dic83—42no—
96C2×Dic83—42no—
97C2×Dic83—42no—
98C2×Dic83—42no—
99C2×Dic83—42no—
100C2×Dic83—42no—
101C2×Dic83—42no—
102C2×Dic83—81no—
103C2×Dic83—81no—
104Dic166—42no—
105Dic166—42no—
106Dic166—81no—
107Dic166—81no—
108C8×C83—44no—
109C83⋊C8—42no—
110C22×C83#44811yescharacteristic
111C22×C83#45212yes—
112C22×C83#45311yescharacteristic
113C22×C83#45612yes—
114C22×C83B(4,𝔽2)11yescharacteristic
115C4×C83—21no—
116C4×C83—21no—
117C4×C83—22no—
118C4×C83—22no—
119C4×C83—42no—
120C4×C83—81no—
121Dic83—82no—
122Dic83—82no—
123Dic83—82no—
124#7760—831nomaximal, Sylow
125C2×C83#159611yescharacteristic
126C2×C83#160312yes—
127C2×C83#163411yescharacteristic
128C2×C83#165312yes—
129C2×C83#166011yescharacteristic
130#2809—831no—
131#2058—832no—
132#2016—831no—
133#1272D8311yescharacteristic
134#1271—832no—
135C83#776011yescharacteristic, complemented, Sylow
136C22×Q16—1661no—
137C2×C4⋊Q8—831no—
138C2×#106—1662no—
139C2×#103—1661no—
140#400—1661no—
141#398—1662no—
142#391—1661no—
143#391C2×D8311yescharacteristic
144#389—832no—
145#387—1662no—
146#340—1662no—
147#336—831no—
148#336C2×D8312yes—
149C22×Q8—1661no—
150C22×Q8D33211yescharacteristic
151C2×Q16—3322no—
152C2×Q16—3322no—
153C2×Q16—3322no—
154C22×C8—22no—
155C22×C8—1661no—
156C4⋊Q8—3322no—
157C2×C4⋊C4—832no—
158C2×C4⋊C4—832no—
159C2×C4⋊C4—1662no—
160C2×C4⋊C4—1662no—
161C2×C4⋊C4—1661no—
162C2×C4⋊C4—1661no—
163C2×C4⋊C4D33211yescharacteristic
164C2×C42—1661no—
165C2×C42C22×D8311yescharacteristic
166#106—3324no—
167#103—3322no—
168#95—22no—
169#95—1661no—
170#95—1662no—
171#95—1662no—
172#95—1662no—
173C2×Q8—21no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—3321no—
177C2×Q8—3321no—
178C2×Q8—3321no—
179C2×Q8—3321no—
180C2×Q8—3321no—
181C2×Q8—1662no—
182C2×Q8#1305057912yes—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—3321no—
186C22×C4—1662no—
187C22×C4—1662no—
188C22×C4D4×D8312yes—
189C22×C4C2×D33211yescharacteristic
190Q16—3328no—
191C2×C8—24no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—3321no—
195C2×C8—3321no—
196C2×C8—1662no—
197C4⋊C4—41no—
198C4⋊C4—3322no—
199C4⋊C4—3322no—
200C4⋊C4—3322no—
201C4⋊C4—3322no—
202C4⋊C4—6641no—
203C4⋊C4—6641no—
204C4⋊C4—1664no—
205C4⋊C4—1662no—
206C4⋊C4—1662no—
207C42—41no—
208C42—6641no—
209C23#1458176211yescharacteristic
210Q8—42no—
211Q8—81no—
212Q8—3322no—
213Q8—3322no—
214Q8—6641no—
215Q8—6641no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—42no—
225C2×C4—3322no—
226C2×C4—3322no—
227C2×C4—3322no—
228C2×C4—3322no—
229C2×C4—3322no—
230C2×C4—3322no—
231C2×C4—3322no—
232C2×C4—6641no—
233C2×C4—6641no—
234C2×C4C2×#1305057911yescharacteristic
235C2×C4#1458181312yes—
236C2×C4#1458182412yes—
237C2×C4#1458182511yescharacteristic
238C8—44no—
239C8—3322no—
240C22#1912784211yescharacteristic
241C22#1912786612yes—
242C22#1912787111yescharacteristic
243C22#1912788512yes—
244C22#1912788911yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—42no—
250C4—81no—
251C4—6642no—
252C4—6642no—
253C4—6642no—
254C2#2490638811yescharacteristic
255C2#2490642912yes—
256C2#2490660911yescharacteristic
257C2#2490674212yes—
258C2#2490677511yescharacteristic
subgroupG/H
centerC23#14581762
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1272C2
socle, prime radicalC23×C83#120
hypercenter#1272D83
hypocenterC83#7760
LCSG ▷ C2×C42×C83 ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
135. C83#7760semidirect

Maximal subgroups

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

subgroupindex
#249154512
#249087972
#249085622
#249052872
C83×#12722
#776083