Finite Group Databasebeta

← #24913581

Subgroups — #24913581

Order 10624.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C2×#14581790C211yesmaximal, characteristic
2C2×#14581782C211yesmaximal, characteristic
3#19127635C212yesmaximal
4#19127634C212yesmaximal
5#19127622C211yesmaximal, characteristic
6#19127621C211yesmaximal, characteristic
7#19127620C211yesmaximal, characteristic
8#19127570C212yesmaximal
9#19127565C212yesmaximal
10#19127546C211yesmaximal, characteristic
11#395×C83C211yesmaximal, characteristic
12C22×Dic166C2211yescharacteristic
13#14581790—24no—
14#14581782—24no—
15C2×C4⋊Dic83C2211yescharacteristic
16C2×C4⋊Dic83C2212yes—
17C2×Dic83⋊C4C2211yescharacteristic
18C2×Dic83⋊C4C2212yes—
19C2×Dic83⋊C4C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2212yes—
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2212yes—
24C2×Dic83⋊C4C2212yes—
25C2×C4×Dic83C2211yescharacteristic
26C2×C4×Dic83C2212yes—
27C83⋊#95C2212yes—
28C83⋊#95C2212yes—
29C83⋊#95C2212yes—
30C83⋊#95C2211yescharacteristic
31C83⋊#95C2212yes—
32C22×Q8×C83C2211yescharacteristic
33C2×C4⋊C4×C83C2211yescharacteristic
34C2×C4⋊C4×C83C2212yes—
35#95×C83C2212yes—
36#95×C83C2211yescharacteristic
37C2×Dic166—22no—
38C2×Dic166—42no—
39C22×Dic83C2312yes—
40C22×Dic83C2311yescharacteristic
41C22×Dic83C2311yescharacteristic
42C22×Dic83C2311yescharacteristic
43C22×Dic83C2312yes—
44C22×Dic83C2311yescharacteristic
45C4⋊Dic83—22no—
46C4⋊Dic83—42no—
47Dic83⋊C4—22no—
48Dic83⋊C4—22no—
49Dic83⋊C4—22no—
50Dic83⋊C4—22no—
51Dic83⋊C4—24no—
52Dic83⋊C4—24no—
53Dic83⋊C4—42no—
54Dic83⋊C4—42no—
55C4×Dic83D414yes—
56C4×Dic83Q818yescomplemented
57C2×Q8×C83—22no—
58C2×Q8×C83—42no—
59C22×C4×C83C2311yescharacteristic
60C22×C4×C83C2312yes—
61C22×C4×C83C2311yescharacteristic
62C22×C4×C83C2311yescharacteristic
63C22×C4×C83C2312yes—
64C4⋊C4×C83—22no—
65C4⋊C4×C83—42no—
66C23×C83C2411yescharacteristic
67Q8×C83—44no—
68C2×C4×C83—22no—
69C2×C4×C83—22no—
70C2×C4×C83—22no—
71C2×C4×C83—21no—
72C2×C4×C83—21no—
73C2×C4×C83—22no—
74C2×C4×C83—22no—
75C2×C4×C83—22no—
76C2×C4×C83—22no—
77C2×C4×C83—21no—
78C2×C4×C83—21no—
79C2×C4×C83C2×D412yes—
80C2×C4×C83C2×Q814yes—
81C2×Dic83—22no—
82C2×Dic83—21no—
83C2×Dic83—21no—
84C2×Dic83—22no—
85C2×Dic83—21no—
86C2×Dic83—21no—
87C2×Dic83—22no—
88C2×Dic83—22no—
89C2×Dic83—22no—
90C2×Dic83—22no—
91C2×Dic83—21no—
92C2×Dic83—21no—
93C2×Dic83C2×D412yes—
94C2×Dic83C2×D412yes—
95C2×Dic83C2×Q814yes—
96C2×Dic83C2×Q814yes—
97Dic166—44no—
98C22×C83C22×D411yescharacteristic
99C22×C83C22×Q812yes—
100C22×C83H(5,𝔽2)12yes—
101C22×C832−1+411yescharacteristic
102C22×C832−1+411yescharacteristic
103C4×C83—22no—
104C4×C83—24no—
105C4×C83—41no—
106C4×C83—42no—
107C4×C83—41no—
108Dic83—22no—
109Dic83—24no—
110Dic83—42no—
111Dic83—41no—
112Dic83—41no—
113Dic83C4⋊Q814yes—
114C2×C83C2×C4⋊Q811yescharacteristic
115C2×C83#53511yescharacteristic
116C2×C83#53611yescharacteristic
117C2×C83#54412yes—
118C2×C83#54412yes—
119#2660—831nomaximal, Sylow
120C83#266011yescharacteristic, complemented, Sylow
121C2×C4⋊Q8—831no—
122C2×#125—831no—
123#398—832no—
124#398—832no—
125#395—831no—
126#395—831no—
127#395—831no—
128#395D8311yescharacteristic
129#384—832no—
130#382—832no—
131#376—831no—
132C22×Q8—831no—
133C22×Q8C2×D8311yescharacteristic
134C4⋊Q8—1664no—
135#125—1664no—
136C2×C4⋊C4—832no—
137C2×C4⋊C4—832no—
138C2×C4⋊C4—832no—
139C2×C4⋊C4—831no—
140C2×C4⋊C4—831no—
141C2×C4⋊C4—831no—
142C2×C4⋊C4—831no—
143C2×C4⋊C4—831no—
144C2×C4⋊C4—832no—
145C2×C4⋊C4—832no—
146C2×C4⋊C4C2×D8311yescharacteristic
147C2×C4⋊C4C2×D8312yes—
148C2×C42—831no—
149C2×C42—832no—
150#95—831no—
151#95—832no—
152#95—832no—
153#95—832no—
154#95—832no—
155#95C2×D8311yescharacteristic
156#95C2×D8312yes—
157C2×Q8—22no—
158C2×Q8—42no—
159C2×Q8—3322no—
160C2×Q8—1662no—
161C22×C4—831no—
162C22×C4—832no—
163C22×C4—831no—
164C22×C4—831no—
165C22×C4—832no—
166C22×C4—831no—
167C22×C4C22×D8311yescharacteristic
168C22×C4C22×D8312yes—
169C22×C4C22×D8311yescharacteristic
170C22×C4C22×D8311yescharacteristic
171C22×C4C22×D8312yes—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—3322no—
175C4⋊C4—3322no—
176C4⋊C4—3322no—
177C4⋊C4—1662no—
178C4⋊C4—1662no—
179C4⋊C4—1662no—
180C4⋊C4—1662no—
181C4⋊C4—1664no—
182C4⋊C4—1664no—
183C4⋊C4—1662no—
184C42—834no—
185C42—838no—
186C23C23×D8311yescharacteristic
187Q8—44no—
188Q8—3324no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—832no—
201C2×C4—834no—
202C2×C4—832no—
203C2×C4—834no—
204C2×C4—1661no—
205C2×C4—1661no—
206C2×C4—1662no—
207C2×C4—1662no—
208C2×C4—1662no—
209C2×C4—1662no—
210C2×C4—1661no—
211C2×C4—1661no—
212C2×C4—1662no—
213C2×C4—1661no—
214C2×C4—1662no—
215C2×C4—1661no—
216C2×C4D4×D8312yes—
217C2×C4Q8×D8314yes—
218C22C2×D4×D8311yescharacteristic
219C22C2×Q8×D8312yes—
220C22#1458183712yes—
221C22#1458183911yescharacteristic
222C22#1458184011yescharacteristic
223C4—24no—
224C4—22no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—3322no—
229C4—3321no—
230C4—3321no—
231C4—834no—
232C4—1664no—
233C4—1662no—
234C2C4⋊Q8×D8311yescharacteristic
235C2#1912826611yescharacteristic
236C2#1912827411yescharacteristic
237C2#1912832812yes—
238C2#1912833012yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#395×C83C2
hypercenter#395D83
hypocenterC83#2660
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
56. C4×Dic83Q8semidirect
120. C83#2660semidirect

Maximal subgroups

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

subgroupindex
C2×#145817902
C2×#145817822
#191276352
#191276342
#191276222
#191276212
#191276202
#191275702
#191275652
#191275462
#395×C832
#266083