Finite Group Databasebeta

← #23774350

Subgroups — #23774350

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
2C2×#14579161C211yesmaximal, characteristic
3#19098943C212yesmaximal, complemented
4#19098914C212yesmaximal, complemented
5#19098774C214yesmaximal, complemented
6#19098721C214yesmaximal
7#431×C79C211yesmaximal, characteristic
8C22×Dic158C2212yes—
9C2×Dic316C2218yes—
10#14579161—21no—
11#14579161—21no—
12#14579161C2212yes—
13#14579161C2211yescharacteristic
14#14579161C2212yes—
15#14579161C2211yescharacteristic
16#14579153—21no—
17#14579140—21no—
18#14579140C2212yes—
19C4×Dic158—21no—
20C4×Dic158C2212yes—
21#14579120—21no—
22C2×C4⋊Dic79—21no—
23C2×C4⋊Dic79—21no—
24#14579086C2218yes—
25C2×C42×C79C2211yescharacteristic
26C4⋊C8×C79C2212yes—
27C22⋊C8×C79C2212yes—
28C4×C8×C79C2212yes—
29C2×Dic158—22no—
30C2×Dic158—21no—
31C2×Dic158—44no—
32C2×Dic158C2314yes—
33C2×Dic158C2312yes—
34C22×Dic79—22no—
35Dic316—48no—
36C4⋊Dic79—22no—
37C4⋊Dic79—22no—
38C4⋊Dic79—22no—
39C4⋊Dic79—22no—
40C4⋊Dic79—21no—
41C4⋊Dic79—21no—
42C4⋊Dic79—21no—
43C4⋊Dic79C2312yes—
44Dic79⋊C4—22no—
45Dic79⋊C4—22no—
46C22⋊Dic79—22no—
47C4×Dic79—22no—
48C22×C4×C79D411yescharacteristic
49C22×C4×C79D411yescharacteristic
50C22×C4×C79C2311yescharacteristic
51C2×C8×C79C2314yes—
52C42×C79D411yescharacteristic
53C42×C79D411yescharacteristic
54C42×C79C2311yescharacteristic
55C42×C79C2311yescharacteristic
56C23×C79C2×D411yescharacteristic
57C2×C4×C79—22no—
58C2×C4×C79—22no—
59C2×C4×C79Q1614yescomplemented
60C2×C4×C79C2×D411yescharacteristic
61C2×C4×C79C2×D411yescharacteristic
62C2×C4×C79C2×D411yescharacteristic
63C2×C4×C79C2×D411yescharacteristic
64C2×C4×C79C2×D411yescharacteristic
65C2×C4×C79C2411yescharacteristic
66C2×Dic79—22no—
67C2×Dic79—22no—
68C2×Dic79—24no—
69C2×Dic79—44no—
70Dic158—24no—
71Dic158—28no—
72Dic158—44no—
73Dic158—42no—
74C8×C79—24no—
75C22×C79—21no—
76C22×C79—21no—
77C22×C79C2×Q1612yes—
78C22×C79C22×D411yescharacteristic
79C4×C79—21no—
80C4×C79—21no—
81C4×C79C2×Q1612yes—
82C4×C79C2×Q1612yes—
83C4×C79#13712yes—
84C4×C79H(5,𝔽2)12yes—
85Dic79—44no—
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⋊Q8—791no—
96#494—792no—
97#487—792no—
98#462—794no—
99#451—794no—
100#431D7911yescharacteristic
101C22×Q8—792no—
102C2×Q16—798no—
103C4⋊Q8—791no—
104C4⋊Q8—792no—
105C4⋊Q8—792no—
106C4⋊Q8—791no—
107C4⋊Q8—1581no—
108C4⋊Q8—1581no—
109#125—1581no—
110C22⋊Q8—792no—
111C22⋊Q8—1581no—
112C4×Q8—792no—
113C4×Q8—1581no—
114#117—1581no—
115C2×C4⋊C4—1581no—
116C2×C4⋊C4—1581no—
117C2×C42C2×D7911yescharacteristic
118C4⋊C8C2×D7912yes—
119#103—798no—
120C22⋊C8C2×D7912yes—
121C4×C8C2×D7912yes—
122C2×Q8—3164no—
123C2×Q8—794no—
124C2×Q8—792no—
125C2×Q8—1581no—
126C2×Q8—1582no—
127C22×C4—1582no—
128C22×C4D31611yescharacteristic
129C22×C4D31611yescharacteristic
130C22×C4C22×D7911yescharacteristic
131Q16—3168no—
132C2×C8C22×D7914yes—
133C4⋊C4—792no—
134C4⋊C4—1582no—
135C4⋊C4—1582no—
136C4⋊C4—1582no—
137C4⋊C4—1582no—
138C4⋊C4—1582no—
139C4⋊C4—1582no—
140C4⋊C4—1581no—
141C4⋊C4—1581no—
142C4⋊C4—1581no—
143C22⋊C4—1582no—
144C42—1582no—
145C42D31611yescharacteristic
146C42D31611yescharacteristic
147C42C22×D7911yescharacteristic
148C42C22×D7911yescharacteristic
149C23C2×D31611yescharacteristic
150Q8—3164no—
151Q8—3162no—
152Q8—1584no—
153Q8—1588no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—3164no—
157C2×C4—1582no—
158C2×C4—1582no—
159C2×C4—1584no—
160C2×C4Dic31614yescomplemented
161C2×C4C2×D31611yescharacteristic
162C2×C4C2×D31611yescharacteristic
163C2×C4C2×D31611yescharacteristic
164C2×C4C2×D31611yescharacteristic
165C2×C4C2×D31611yescharacteristic
166C2×C4C23×D7911yescharacteristic
167C8—24no—
168C22—21no—
169C22—21no—
170C22C2×Dic31612yes—
171C22C22×D31611yescharacteristic
172C4—21no—
173C4—21no—
174C4—3162no—
175C4—3164no—
176C4—3162no—
177C4C2×Dic31612yes—
178C4C2×Dic31612yes—
179C4#1457919412yes—
180C4#1457920712yes—
181C2—22no—
182C2#1909913211yescharacteristic
183C2C22×Dic31611yescharacteristic
184C2C2×#1457919411yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#431×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#431D79
hypocenterC79#3209
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
3. #19098943C2semidirect
4. #19098914C2semidirect
5. #19098774C2semidirect
59. C2×C4×C79Q16semidirect
93. C79#3209semidirect
160. C2×C4Dic316semidirect