Finite Group Databasebeta

← #24914413

Subgroups — #24914413

Order 10624.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14581782C212yesmaximal
2#19127635C212yesmaximal
3#19127634C212yesmaximal
4#19127632C212yesmaximal
5#19127599C211yesmaximal, characteristic
6#19127599C211yesmaximal, characteristic
7#19127596C212yesmaximal
8#19127584C212yesmaximal
9#389×C83C211yesmaximal, characteristic
10#14581782—28no—
11C2×C4⋊Dic83C2211yescharacteristic
12C2×C4⋊Dic83C2211yescharacteristic
13C2×C4⋊Dic83C2211yescharacteristic
14C2×C4⋊Dic83C2211yescharacteristic
15C2×Dic83⋊C4C2212yes—
16C2×Dic83⋊C4C2212yes—
17C2×Dic83⋊C4C2212yes—
18C2×Dic83⋊C4C2212yes—
19C2×Dic83⋊C4C2212yes—
20C2×Dic83⋊C4C2212yes—
21C2×C4×Dic83C2212yes—
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2212yes—
25C83⋊#95C2212yes—
26C83⋊#95C2212yes—
27C2×C4⋊C4×C83C2211yescharacteristic
28C2×C4⋊C4×C83C2212yes—
29C2×C4⋊C4×C83C2211yescharacteristic
30C2×C42×C83C2211yescharacteristic
31#95×C83C2212yes—
32C22×Dic83C2312yes—
33C22×Dic83C2312yes—
34C22×Dic83C2312yes—
35C22×Dic83C2312yes—
36C4⋊Dic83—41no—
37C4⋊Dic83—41no—
38C4⋊Dic83D414yes—
39C4⋊Dic83Q814yes—
40Dic83⋊C4—24no—
41Dic83⋊C4—24no—
42Dic83⋊C4—24no—
43Dic83⋊C4—24no—
44Dic83⋊C4—24no—
45Dic83⋊C4—42no—
46C4×Dic83—24no—
47C22×C4×C83C2312yes—
48C22×C4×C83C2312yes—
49C22×C4×C83C2311yescharacteristic
50C22×C4×C83C2311yescharacteristic
51C22×C4×C83C2311yescharacteristic
52C4⋊C4×C83—24no—
53C4⋊C4×C83—22no—
54C4⋊C4×C83—41no—
55C42×C83—41no—
56C23×C83C2411yescharacteristic
57C2×C4×C83—21no—
58C2×C4×C83—21no—
59C2×C4×C83—21no—
60C2×C4×C83—21no—
61C2×C4×C83—21no—
62C2×C4×C83—21no—
63C2×C4×C83—22no—
64C2×C4×C83—22no—
65C2×C4×C83—22no—
66C2×C4×C83—22no—
67C2×C4×C83—22no—
68C2×C4×C83—22no—
69C2×C4×C83C2×D412yes—
70C2×C4×C83C2×Q812yes—
71C2×C4×C83#4112yes—
72C2×Dic83—22no—
73C2×Dic83—22no—
74C2×Dic83—22no—
75C2×Dic83—22no—
76C2×Dic83—22no—
77C2×Dic83—22no—
78C2×Dic83—22no—
79C2×Dic83—22no—
80C2×Dic83—22no—
81C2×Dic83—22no—
82C2×Dic83C2×D414yes—
83C2×Dic83C2×Q814yes—
84C22×C83C22×D411yescharacteristic
85C22×C83C22×Q811yescharacteristic
86C22×C83C2×#4111yescharacteristic
87C22×C83H(5,𝔽2)11yescharacteristic
88C22×C832−1+411yescharacteristic
89C22×C832−1+411yescharacteristic
90C22×C832−1+411yescharacteristic
91C4×C83—22no—
92C4×C83—22no—
93C4×C83—22no—
94C4×C83—42no—
95C4×C83—42no—
96Dic83—24no—
97Dic83—24no—
98Dic83—42no—
99Dic83—42no—
100C2×C83#53711yescharacteristic
101C2×C83#53911yescharacteristic
102C2×C83#54411yescharacteristic
103C2×C83#54711yescharacteristic
104C2×C83D4×Q811yescharacteristic
105C2×C83#55711yescharacteristic
106C2×C83#56411yescharacteristic
107#2726—831nomaximal, Sylow
108C83#272611yescharacteristic, complemented, Sylow
109C2×#125—832no—
110#398—832no—
111#398—832no—
112#398—832no—
113#389—832no—
114#389—831no—
115#389—831no—
116#389D8311yescharacteristic
117#387—832no—
118#125—1668no—
119C2×C4⋊C4—832no—
120C2×C4⋊C4—831no—
121C2×C4⋊C4—831no—
122C2×C4⋊C4—831no—
123C2×C4⋊C4—831no—
124C2×C4⋊C4—832no—
125C2×C4⋊C4—832no—
126C2×C4⋊C4—832no—
127C2×C4⋊C4—832no—
128C2×C4⋊C4—832no—
129C2×C4⋊C4C2×D8312yes—
130C2×C4⋊C4C2×D8311yescharacteristic
131C2×C4⋊C4C2×D8311yescharacteristic
132C2×C42—832no—
133C2×C42C2×D8311yescharacteristic
134#95—832no—
135#95—832no—
136#95—832no—
137#95—832no—
138#95—832no—
139#95C2×D8312yes—
140C22×C4—832no—
141C22×C4—832no—
142C22×C4—832no—
143C22×C4—832no—
144C22×C4C22×D8312yes—
145C22×C4C22×D8312yes—
146C22×C4C22×D8311yescharacteristic
147C22×C4C22×D8311yescharacteristic
148C22×C4C22×D8311yescharacteristic
149C4⋊C4—24no—
150C4⋊C4—22no—
151C4⋊C4—41no—
152C4⋊C4—3322no—
153C4⋊C4—3321no—
154C4⋊C4—3321no—
155C4⋊C4—834no—
156C4⋊C4—834no—
157C4⋊C4—1664no—
158C4⋊C4—1664no—
159C4⋊C4—1664no—
160C4⋊C4—1664no—
161C4⋊C4—1664no—
162C42—41no—
163C42—1664no—
164C23C23×D8311yescharacteristic
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—834no—
178C2×C4—834no—
179C2×C4—1662no—
180C2×C4—1662no—
181C2×C4—1662no—
182C2×C4—1662no—
183C2×C4—1662no—
184C2×C4—1662no—
185C2×C4—1662no—
186C2×C4—1662no—
187C2×C4—1662no—
188C2×C4—1662no—
189C2×C4D4×D8312yes—
190C2×C4Q8×D8312yes—
191C2×C4#1305059012yes—
192C22C2×D4×D8311yescharacteristic
193C22C2×Q8×D8311yescharacteristic
194C22C2×#1305059011yescharacteristic
195C22#1458183711yescharacteristic
196C22#1458183911yescharacteristic
197C22#1458183911yescharacteristic
198C22#1458184011yescharacteristic
199C4—22no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—42no—
204C4—3322no—
205C4—3322no—
206C4—1664no—
207C4—1664no—
208C2#1912827811yescharacteristic
209C2#1912829811yescharacteristic
210C2#1912833011yescharacteristic
211C2#1912835611yescharacteristic
212C2#1912836611yescharacteristic
213C2#1912842911yescharacteristic
214C2C83⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#389×C83C2
hypercenter#389D83
hypocenterC83#2726
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
108. C83#2726semidirect

Maximal subgroups

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

subgroupindex
C2×#145817822
#191276352
#191276342
#191276322
#191275992
#191275962
#191275842
#389×C832
#272683