Finite Group Databasebeta

← #24915225

Subgroups — #24915225

Order 10624.

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

normal subgroups only

This group has 352 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
1C83⋊#401C212yesmaximal
2#19127640C212yesmaximal
3#19127631C211yesmaximal, characteristic
4#19127608C212yesmaximal
5#19127588C212yesmaximal
6#19127587C212yesmaximal
7#19127586C212yesmaximal
8#19127566C211yesmaximal, characteristic
9#395×C83C211yesmaximal, characteristic
10C2×C4⋊Dic83C2212yes—
11C2×C4⋊Dic83C2211yescharacteristic
12C2×C4⋊Dic83C2211yescharacteristic
13C2×Dic83⋊C4C2212yes—
14C2×C4×Dic83C2211yescharacteristic
15C2×C4×Dic83C2212yes—
16C83⋊#95C2212yes—
17C83⋊#95C2212yes—
18C83⋊#95C2212yes—
19C83⋊#95C2212yes—
20C83⋊#95C2212yes—
21C83⋊#95C2212yes—
22C83⋊#95C2212yes—
23C83⋊#95C2212yes—
24C83⋊#95C2212yes—
25C83⋊#95C2211yescharacteristic
26C22×Q8×C83C2211yescharacteristic
27C2×C4⋊C4×C83C2212yes—
28C2×C4⋊C4×C83C2211yescharacteristic
29#95×C83C2212yes—
30#95×C83C2211yescharacteristic
31C22×Dic83C2312yes—
32C22×Dic83C2312yes—
33C22×Dic83C2312yes—
34C22×Dic83C2312yes—
35C4⋊Dic83—24no—
36C4⋊Dic83—41no—
37C4⋊Dic83—41no—
38Dic83⋊C4—24no—
39C4×Dic83—22no—
40C4×Dic83—42no—
41C2×Q8×C83—24no—
42C2×Q8×C83—41no—
43C22×C4×C83C2312yes—
44C22×C4×C83C2311yescharacteristic
45C22×C4×C83C2311yescharacteristic
46C22×C4×C83C2311yescharacteristic
47C22×C4×C83C2312yes—
48C4⋊C4×C83—24no—
49C4⋊C4×C83—41no—
50C23×C83C2411yescharacteristic
51Q8×C83—44no—
52C2×C4×C83—22no—
53C2×C4×C83—21no—
54C2×C4×C83—22no—
55C2×C4×C83—21no—
56C2×C4×C83—22no—
57C2×C4×C83—22no—
58C2×C4×C83—22no—
59C2×C4×C83—21no—
60C2×C4×C83—21no—
61C2×C4×C83—22no—
62C2×C4×C83—22no—
63C2×C4×C83#4114yes—
64C2×C4×C83#4112yes—
65C2×Dic83—22no—
66C2×Dic83—22no—
67C2×Dic83—22no—
68C2×Dic83—22no—
69C2×Dic83—22no—
70C2×Dic83—22no—
71C2×Dic83—22no—
72C2×Dic83—22no—
73C2×Dic83—22no—
74C2×Dic83—22no—
75C2×Dic83—24no—
76C22×C83C2×#4112yes—
77C22×C83C2×#4111yescharacteristic
78C22×C83H(5,𝔽2)11yescharacteristic
79C22×C832−1+411yescharacteristic
80C22×C832−1+412yes—
81C4×C83—22no—
82C4×C83—24no—
83C4×C83—42no—
84C4×C83—41no—
85C4×C83—41no—
86Dic83—42no—
87Dic83—42no—
88Dic83—42no—
89Dic83—42no—
90C2×C83#53911yescharacteristic
91C2×C83#54112yes—
92C2×C83#55111yescharacteristic
93C2×C83#55612yes—
94C2×C83#56311yescharacteristic
95#2789—831nomaximal, Sylow
96C83#278911yescharacteristic, complemented, Sylow
97#401—832no—
98#400—832no—
99#398—831no—
100#395D8311yescharacteristic
101#391—832no—
102#387—832no—
103#387—832no—
104#387—832no—
105#382—831no—
106C22×Q8C2×D8311yescharacteristic
107C2×C4⋊C4—831no—
108C2×C4⋊C4—831no—
109C2×C4⋊C4—832no—
110C2×C4⋊C4—832no—
111C2×C4⋊C4C2×D8312yes—
112C2×C4⋊C4C2×D8311yescharacteristic
113C2×C42—832no—
114C2×C42—831no—
115#95—832no—
116#95—832no—
117#95—832no—
118#95—832no—
119#95—832no—
120#95—832no—
121#95—832no—
122#95—832no—
123#95—832no—
124#95—831no—
125#95C2×D8312yes—
126#95C2×D8311yescharacteristic
127C2×Q8—24no—
128C2×Q8—41no—
129C22×C4—832no—
130C22×C4—832no—
131C22×C4—832no—
132C22×C4—832no—
133C22×C4C22×D8312yes—
134C22×C4C22×D8311yescharacteristic
135C22×C4C22×D8311yescharacteristic
136C22×C4C22×D8312yes—
137C22×C4C22×D8311yescharacteristic
138C4⋊C4—24no—
139C4⋊C4—41no—
140C4⋊C4—3321no—
141C4⋊C4—3321no—
142C4⋊C4—1664no—
143C4⋊C4—1664no—
144C42—3322no—
145C42—1662no—
146C23C23×D8311yescharacteristic
147Q8—44no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—1662no—
160C2×C4—1662no—
161C2×C4—1662no—
162C2×C4—1662no—
163C2×C4—1662no—
164C2×C4—1662no—
165C2×C4—1662no—
166C2×C4—1662no—
167C2×C4—1662no—
168C2×C4—1662no—
169C2×C4—1664no—
170C2×C4#1305058914yes—
171C2×C4#1305059112yes—
172C22C2×#1305058912yes—
173C22C2×#1305059111yescharacteristic
174C22#1458183711yescharacteristic
175C22#1458183911yescharacteristic
176C22#1458184012yes—
177C4—24no—
178C4—22no—
179C4—41no—
180C4—41no—
181C4—42no—
182C4—3322no—
183C4—3322no—
184C4—3322no—
185C4—3322no—
186C2#1912830011yescharacteristic
187C2#1912831112yes—
188C2#1912838211yescharacteristic
189C2#1912842512yes—
190C2#1912845011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D83
commutator, socle, prime radical, cosocleC23×C83C24
Fitting#395×C83C2
hypercenter#395D83
hypocenterC83#2789
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
96. C83#2789semidirect

Maximal subgroups

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

subgroupindex
C83⋊#4012
#191276402
#191276312
#191276082
#191275882
#191275872
#191275862
#191275662
#395×C832
#278983