Finite Group Databasebeta

← #23774348

Subgroups — #23774348

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
1#19099120C211yesmaximal, characteristic
2#19098942C212yesmaximal, complemented
3#19098913C212yesmaximal, complemented
4#19098770C214yesmaximal, complemented
5#19098719C214yesmaximal
6#19098616C211yesmaximal, characteristic
7C2×C4⋊Q8×C79C211yesmaximal, characteristic
8C2×#11929614C2218yes—
9#14579161C2211yescharacteristic
10#14579161C2211yescharacteristic
11#14579153—21no—
12#14579140—21no—
13#14579140C2212yes—
14C4×Dic158—21no—
15C4×Dic158C2212yes—
16#14579120—21no—
17C4⋊(C79⋊C8)C2212yes—
18#14579085C2218yes—
19C22⋊(C79⋊C8)C2212yes—
20C4×C79⋊C8C2212yes—
21C22×Q8×C79C2212yes—
22C4⋊Q8×C79—21no—
23C4⋊Q8×C79—21no—
24C4⋊Q8×C79C2212yes—
25C4⋊Q8×C79C2212yes—
26C2×C4⋊C4×C79—21no—
27C2×C4⋊C4×C79—21no—
28C2×C42×C79C2211yescharacteristic
29C2×Dic158—21no—
30C2×Dic158C2312yes—
31#11929614—48no—
32C2×C79⋊C8C2314yes—
33C4⋊Dic79—21no—
34C4⋊Dic79—21no—
35C4⋊Dic79—21no—
36C4⋊Dic79C2312yes—
37Dic79⋊C4—22no—
38Dic79⋊C4—22no—
39C22⋊Dic79—22no—
40C4×Dic79—22no—
41C2×Q8×C79—22no—
42C2×Q8×C79—44no—
43C2×Q8×C79C2314yes—
44C22×C4×C79—22no—
45C22×C4×C79D411yescharacteristic
46C22×C4×C79D411yescharacteristic
47C22×C4×C79C2311yescharacteristic
48C4⋊C4×C79—22no—
49C4⋊C4×C79—22no—
50C4⋊C4×C79—22no—
51C4⋊C4×C79—22no—
52C42×C79D411yescharacteristic
53C42×C79D411yescharacteristic
54C42×C79C2311yescharacteristic
55C42×C79C2311yescharacteristic
56C23×C79C2×D411yescharacteristic
57Q8×C79—28no—
58Q8×C79—44no—
59C2×C4×C79—22no—
60C2×C4×C79—22no—
61C2×C4×C79—24no—
62C2×C4×C79—44no—
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—22no—
71C2×Dic79—22no—
72Dic158—24no—
73Dic158—42no—
74C79⋊C8—24no—
75C22×C79—21no—
76C22×C79—21no—
77C22×C79C2×Q1612yes—
78C22×C79C22×D411yescharacteristic
79C4×C79—21no—
80C4×C79—21no—
81C4×C79—44no—
82C4×C79C2×Q1612yes—
83C4×C79C2×Q1612yes—
84C4×C79#13712yes—
85C4×C79H(5,𝔽2)12yes—
86Dic79—42no—
87Dic79—42no—
88C2×C79—22no—
89C2×C79#53511yescharacteristic
90C2×C79C22×Q1611yescharacteristic
91C2×C79C2×#13711yescharacteristic
92#3209—791nomaximal, Sylow
93C79#320911yescharacteristic, complemented, Sylow
94#533—791no—
95C2×C4⋊Q8D7911yescharacteristic
96#494—792no—
97#487—792no—
98#462—794no—
99#451—794no—
100#431—791no—
101C22×Q8C2×D7912yes—
102C2×Q16—798no—
103C4⋊Q8—21no—
104C4⋊Q8—21no—
105C4⋊Q8—791no—
106C4⋊Q8—791no—
107C4⋊Q8C2×D7912yes—
108C4⋊Q8C2×D7912yes—
109#125—1581no—
110C22⋊Q8—792no—
111C22⋊Q8—1581no—
112C4×Q8—792no—
113C4×Q8—1581no—
114#117—1581no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C42C2×D7911yescharacteristic
118C4⋊C8—792no—
119#103—798no—
120C22⋊C8—792no—
121C4×C8—792no—
122C2×Q8—22no—
123C2×Q8—44no—
124C2×Q8—792no—
125C2×Q8—1581no—
126C2×Q8C22×D7914yes—
127C22×C4—22no—
128C22×C4C22⋊D7911yescharacteristic
129C22×C4C22⋊D7911yescharacteristic
130C22×C4C22×D7911yescharacteristic
131Q16—3168no—
132C2×C8—794no—
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—22no—
137C4⋊C4—792no—
138C4⋊C4—1582no—
139C4⋊C4—1582no—
140C4⋊C4—1581no—
141C4⋊C4—1581no—
142C4⋊C4—1581no—
143C22⋊C4—1582no—
144C42—1582no—
145C42C22⋊D7911yescharacteristic
146C42C22⋊D7911yescharacteristic
147C42C22×D7911yescharacteristic
148C42C22×D7911yescharacteristic
149C23C2×C22⋊D7911yescharacteristic
150Q8—28no—
151Q8—44no—
152Q8—3162no—
153Q8—1584no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—24no—
157C2×C4—44no—
158C2×C4—1582no—
159C2×C4—1582no—
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—44no—
175C4—3162no—
176C4—3162no—
177C4C2×#1192961412yes—
178C4C2×#1192961412yes—
179C4#1457919212yes—
180C4#1457920612yes—
181C2—22no—
182C2#1909913011yescharacteristic
183C2C22×#1192961411yescharacteristic
184C2C2×#1457919211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×C4⋊Q8×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenterC2×C4⋊Q8D79
hypocenterC79#3209
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #19098942C2semidirect
3. #19098913C2semidirect
4. #19098770C2semidirect
63. C2×C4×C79Q16semidirect
93. C79#3209semidirect
160. C2×C4#11929614semidirect