Finite Group Databasebeta

← #24915532

Subgroups — #24915532

Order 10624.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14581783C211yesmaximal, characteristic
2C2×#14581782C211yesmaximal, characteristic
3#19127642C212yesmaximal
4#19127639C211yesmaximal, characteristic
5#19127635C212yesmaximal
6#19127635C212yesmaximal
7#19127633C211yesmaximal, characteristic
8#19127633C212yesmaximal
9#19127631C211yesmaximal, characteristic
10#19127565C211yesmaximal, characteristic
11#400×C83C211yesmaximal, characteristic
12#14581783—24no—
13#14581782—24no—
14C2×C4⋊Dic83C2211yescharacteristic
15C2×C4⋊Dic83C2211yescharacteristic
16C2×C4⋊Dic83C2212yes—
17C2×C4⋊Dic83C2212yes—
18C2×Dic83⋊C4C2211yescharacteristic
19C2×Dic83⋊C4C2211yescharacteristic
20C2×Dic83⋊C4C2211yescharacteristic
21C2×Dic83⋊C4C2212yes—
22C2×Dic83⋊C4C2211yescharacteristic
23C2×Dic83⋊C4C2212yes—
24C2×Dic83⋊C4C2212yes—
25C2×C4×Dic83C2211yescharacteristic
26C83⋊#95C2211yescharacteristic
27C83⋊#95C2212yes—
28C83⋊#95C2212yes—
29C83⋊#95C2212yes—
30C83⋊#95C2212yes—
31C83⋊#95C2212yes—
32C2×C4⋊C4×C83C2211yescharacteristic
33C2×C4⋊C4×C83C2211yescharacteristic
34#95×C83C2211yescharacteristic
35#95×C83C2212yes—
36#95×C83C2212yes—
37C22×Dic83C2312yes—
38C22×Dic83C2311yescharacteristic
39C22×Dic83C2311yescharacteristic
40C22×Dic83C2312yes—
41C22×Dic83C2311yescharacteristic
42C22×Dic83C2311yescharacteristic
43C4⋊Dic83—22no—
44C4⋊Dic83—22no—
45C4⋊Dic83—24no—
46C4⋊Dic83—42no—
47Dic83⋊C4—22no—
48Dic83⋊C4—22no—
49Dic83⋊C4—22no—
50Dic83⋊C4—22no—
51Dic83⋊C4—24no—
52Dic83⋊C4—42no—
53Dic83⋊C4—42no—
54C4×Dic83D414yes—
55C22×C4×C83C2312yes—
56C22×C4×C83C2311yescharacteristic
57C22×C4×C83C2312yes—
58C22×C4×C83C2311yescharacteristic
59C22×C4×C83C2311yescharacteristic
60C4⋊C4×C83—22no—
61C4⋊C4×C83—22no—
62C23×C83C2411yescharacteristic
63C2×C4×C83—22no—
64C2×C4×C83—21no—
65C2×C4×C83—21no—
66C2×C4×C83—22no—
67C2×C4×C83—21no—
68C2×C4×C83—22no—
69C2×C4×C83—24no—
70C2×C4×C83—22no—
71C2×C4×C83—22no—
72C2×C4×C83—22no—
73C2×C4×C83—21no—
74C2×C4×C83C2×D412yes—
75C2×Dic83—21no—
76C2×Dic83—22no—
77C2×Dic83—21no—
78C2×Dic83—21no—
79C2×Dic83—21no—
80C2×Dic83—22no—
81C2×Dic83—22no—
82C2×Dic83—22no—
83C2×Dic83—21no—
84C2×Dic83—22no—
85C2×Dic83—22no—
86C2×Dic83—22no—
87C2×Dic83—21no—
88C2×Dic83—22no—
89C2×Dic83C2×D412yes—
90C2×Dic83C2×D412yes—
91C22×C83C22×D411yescharacteristic
92C22×C83H(5,𝔽2)11yescharacteristic
93C22×C832−1+412yes—
94C22×C832−1+412yes—
95C22×C832−1+411yescharacteristic
96C4×C83—22no—
97C4×C83—42no—
98C4×C83—41no—
99C4×C83—41no—
100C4×C83—42no—
101Dic83—22no—
102Dic83—22no—
103Dic83—41no—
104Dic83—41no—
105Dic83—42no—
106Dic83—42no—
107C2×C83#53611yescharacteristic
108C2×C83#53611yescharacteristic
109C2×C83#53711yescharacteristic
110C2×C83#56312yes—
111C2×C83#56412yes—
112#2822—831nomaximal, Sylow
113C83#282211yescharacteristic, complemented, Sylow
114C2×#125—831no—
115C2×#125—831no—
116#400—831no—
117#400—832no—
118#400D8311yescharacteristic
119#398—831no—
120#398—831no—
121#398—832no—
122#398—832no—
123#398—832no—
124#382—831no—
125#125—1664no—
126#125—1664no—
127C2×C4⋊C4—832no—
128C2×C4⋊C4—832no—
129C2×C4⋊C4—832no—
130C2×C4⋊C4—831no—
131C2×C4⋊C4—831no—
132C2×C4⋊C4—831no—
133C2×C4⋊C4—832no—
134C2×C4⋊C4—831no—
135C2×C4⋊C4—832no—
136C2×C4⋊C4—831no—
137C2×C4⋊C4—831no—
138C2×C4⋊C4C2×D8311yescharacteristic
139C2×C4⋊C4C2×D8311yescharacteristic
140C2×C42—831no—
141#95—832no—
142#95—831no—
143#95—832no—
144#95—832no—
145#95—832no—
146#95—832no—
147#95C2×D8311yescharacteristic
148#95C2×D8312yes—
149#95C2×D8312yes—
150C22×C4—831no—
151C22×C4—831no—
152C22×C4—832no—
153C22×C4—831no—
154C22×C4—832no—
155C22×C4—831no—
156C22×C4C22×D8312yes—
157C22×C4C22×D8311yescharacteristic
158C22×C4C22×D8312yes—
159C22×C4C22×D8311yescharacteristic
160C22×C4C22×D8311yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—3322no—
164C4⋊C4—3322no—
165C4⋊C4—3322no—
166C4⋊C4—1662no—
167C4⋊C4—1662no—
168C4⋊C4—1664no—
169C4⋊C4—1662no—
170C4⋊C4—1662no—
171C4⋊C4—1664no—
172C4⋊C4—1662no—
173C4⋊C4—1662no—
174C42—834no—
175C23C23×D8311yescharacteristic
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—832no—
188C2×C4—832no—
189C2×C4—1661no—
190C2×C4—1661no—
191C2×C4—1662no—
192C2×C4—1662no—
193C2×C4—1662no—
194C2×C4—1661no—
195C2×C4—1662no—
196C2×C4—1662no—
197C2×C4—1662no—
198C2×C4—1662no—
199C2×C4—1661no—
200C2×C4—1661no—
201C2×C4—1662no—
202C2×C4—1661no—
203C2×C4D4×D8312yes—
204C22C2×D4×D8311yescharacteristic
205C22#1458183811yescharacteristic
206C22#1458183912yes—
207C22#1458183912yes—
208C22#1458184011yescharacteristic
209C4—22no—
210C4—42no—
211C4—42no—
212C4—41no—
213C4—41no—
214C4—3322no—
215C4—3321no—
216C4—3321no—
217C4—3322no—
218C4—1662no—
219C4—1662no—
220C2#1912827111yescharacteristic
221C2#1912827311yescharacteristic
222C2#1912828111yescharacteristic
223C2#1912845312yes—
224C2C83⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#400×C83C2
hypercenter#400D83
hypocenterC83#2822
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
113. C83#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#145817832
C2×#145817822
#191276422
#191276392
#191276352
#191276332
#191276312
#191275652
#400×C832
#282283