Finite Group Databasebeta

← #23774345

Subgroups — #23774345

Order 10112.

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

normal subgroups only

This group has 384 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×#14579161C211yesmaximal, characteristic
2#19098942C212yesmaximal, complemented
3#19098915C212yesmaximal, complemented
4#19098773C214yesmaximal, complemented
5#19098718C214yesmaximal
6#19098616C211yesmaximal, characteristic
7#533×C79C211yesmaximal, characteristic
8C22×Dic158C2212yes—
9C2×#11929614C2218yes—
10#14579161—21no—
11#14579161—21no—
12#14579161C2212yes—
13#14579161C2212yes—
14C2×C4⋊Dic79—21no—
15C2×C4⋊Dic79—21no—
16C4⋊(C79⋊C8)C2212yes—
17#14579084C2218yes—
18C22⋊(C79⋊C8)C2212yes—
19C4×C79⋊C8C2212yes—
20C4⋊Q8×C79C2211yescharacteristic
21C4⋊Q8×C79C2211yescharacteristic
22#125×C79—21no—
23C22⋊Q8×C79—21no—
24C22⋊Q8×C79C2212yes—
25C4×Q8×C79—21no—
26C4×Q8×C79C2212yes—
27#117×C79—21no—
28C2×C42×C79C2211yescharacteristic
29C2×Dic158—22no—
30C2×Dic158—44no—
31C2×Dic158C2314yes—
32C22×Dic79—22no—
33#11929614—48no—
34C2×C79⋊C8C2314yes—
35C4⋊Dic79—22no—
36C4⋊Dic79—22no—
37C4⋊Dic79—22no—
38C4⋊Dic79—22no—
39C2×Q8×C79—21no—
40C2×Q8×C79C2312yes—
41C22×C4×C79D411yescharacteristic
42C22×C4×C79D411yescharacteristic
43C22×C4×C79C2311yescharacteristic
44C4⋊C4×C79—21no—
45C4⋊C4×C79—21no—
46C4⋊C4×C79—21no—
47C4⋊C4×C79—22no—
48C4⋊C4×C79—22no—
49C4⋊C4×C79C2312yes—
50C22⋊C4×C79—22no—
51C42×C79—22no—
52C42×C79D411yescharacteristic
53C42×C79D411yescharacteristic
54C42×C79C2311yescharacteristic
55C42×C79C2311yescharacteristic
56C23×C79C2×D411yescharacteristic
57Q8×C79—24no—
58Q8×C79—42no—
59C2×C4×C79—22no—
60C2×C4×C79—22no—
61C2×C4×C79—22no—
62C2×C4×C79—22no—
63C2×C4×C79Q1614yescomplemented
64C2×C4×C79C2×D411yescharacteristic
65C2×C4×C79C2×D411yescharacteristic
66C2×C4×C79C2×D411yescharacteristic
67C2×C4×C79C2×D411yescharacteristic
68C2×C4×C79C2×D411yescharacteristic
69C2×C4×C79C2411yescharacteristic
70C2×Dic79—24no—
71C2×Dic79—44no—
72Dic158—28no—
73Dic158—44no—
74C79⋊C8—24no—
75C22×C79—21no—
76C22×C79—21no—
77C22×C79C2×Q1612yes—
78C22×C79C22×D411yescharacteristic
79C4×C79—21no—
80C4×C79—21no—
81C4×C79—42no—
82C4×C79—42no—
83C4×C79C2×Q1612yes—
84C4×C79C2×Q1612yes—
85C4×C79#13712yes—
86C4×C79H(5,𝔽2)12yes—
87Dic79—44no—
88C2×C79—22no—
89C2×C79#53511yescharacteristic
90C2×C79C22×Q1611yescharacteristic
91C2×C79C2×#13711yescharacteristic
92#3209—791nomaximal, Sylow
93C79#320911yescharacteristic, complemented, Sylow
94#533D7911yescharacteristic
95C2×C4⋊Q8—791no—
96#494—792no—
97#487—792no—
98#462—794no—
99#451—794no—
100#431—791no—
101C22×Q8—792no—
102C2×Q16—798no—
103C4⋊Q8—792no—
104C4⋊Q8—792no—
105C4⋊Q8—1581no—
106C4⋊Q8—1581no—
107C4⋊Q8C2×D7911yescharacteristic
108C4⋊Q8C2×D7911yescharacteristic
109#125—21no—
110C22⋊Q8—21no—
111C22⋊Q8C2×D7912yes—
112C4×Q8—21no—
113C4×Q8C2×D7912yes—
114#117—21no—
115C2×C4⋊C4—1581no—
116C2×C4⋊C4—1581no—
117C2×C42C2×D7911yescharacteristic
118C4⋊C8—792no—
119#103—798no—
120C22⋊C8—792no—
121C4×C8—792no—
122C2×Q8—21no—
123C2×Q8—3164no—
124C2×Q8—794no—
125C2×Q8—1582no—
126C2×Q8C22×D7912yes—
127C22×C4—1582no—
128C22×C4C22⋊D7911yescharacteristic
129C22×C4C22⋊D7911yescharacteristic
130C22×C4C22×D7911yescharacteristic
131Q16—3168no—
132C2×C8—794no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C4⋊C4—1582no—
139C4⋊C4—1582no—
140C4⋊C4—1582no—
141C4⋊C4—1582no—
142C4⋊C4C22×D7912yes—
143C22⋊C4—22no—
144C42—22no—
145C42C22⋊D7911yescharacteristic
146C42C22⋊D7911yescharacteristic
147C42C22×D7911yescharacteristic
148C42C22×D7911yescharacteristic
149C23C2×C22⋊D7911yescharacteristic
150Q8—24no—
151Q8—42no—
152Q8—3164no—
153Q8—1588no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—3164no—
159C2×C4—1584no—
160C2×C4#1192961414yescomplemented
161C2×C4C2×C22⋊D7911yescharacteristic
162C2×C4C2×C22⋊D7911yescharacteristic
163C2×C4C2×C22⋊D7911yescharacteristic
164C2×C4C2×C22⋊D7911yescharacteristic
165C2×C4C2×C22⋊D7911yescharacteristic
166C2×C4C23×D7911yescharacteristic
167C8—1584no—
168C22—21no—
169C22—21no—
170C22C2×#1192961412yes—
171C22C22×C22⋊D7911yescharacteristic
172C4—21no—
173C4—21no—
174C4—42no—
175C4—42no—
176C4—3164no—
177C4C2×#1192961412yes—
178C4C2×#1192961412yes—
179C4#1457919112yes—
180C4#1457920712yes—
181C2—22no—
182C2#1909912711yescharacteristic
183C2C22×#1192961411yescharacteristic
184C2C2×#1457919111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#533×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#533D79
hypocenterC79#3209
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #19098942C2semidirect
3. #19098915C2semidirect
4. #19098773C2semidirect
63. C2×C4×C79Q16semidirect
93. C79#3209semidirect
160. C2×C4#11929614semidirect