Finite Group Databasebeta

← #23776369

Subgroups — #23776369

Order 10112.

320 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 129 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#19099291C212yesmaximal
2#19098972C212yesmaximal
3#19098965C211yesmaximal, characteristic
4#19098871C212yesmaximal
5#19098871C212yesmaximal
6#19098859C212yesmaximal
7#19098671C212yesmaximal
8C4×Dic316C211yesmaximal, characteristic
9#446×C79C211yesmaximal, characteristic
10C2×Dic316C2211yescharacteristic
11#14579161C2212yes—
12#14579159—22no—
13#14579153C2212yes—
14#14579153C2212yes—
15#14579151—22no—
16#14579151—22no—
17C4×Dic158C2212yes—
18C4×Dic158C2212yes—
19C4×Dic158C2212yes—
20#14579126—22no—
21#14579095C2211yescharacteristic
22#14579095C2211yescharacteristic
23#14579095C2211yescharacteristic
24#14579095C2212yes—
25#14579093C2212yes—
26#14579093C2212yes—
27#14579086C2212yes—
28#14579086C2212yes—
29#14579086C2212yes—
30C4×Q8×C79C2211yescharacteristic
31C4⋊C8×C79C2212yes—
32C4⋊C8×C79C2211yescharacteristic
33#97×C79C2212yes—
34C4×C8×C79C2211yescharacteristic
35C2×Dic158—22no—
36C2×Dic158C2312yes—
37Dic316Q814yescomplemented
38C4⋊Dic79—22no—
39C4⋊Dic79C2312yes—
40C4⋊Dic79C2312yes—
41C4⋊Dic79C2312yes—
42Dic79⋊C4—22no—
43Dic79⋊C4—22no—
44Dic79⋊C4—22no—
45Dic79⋊C4—22no—
46Dic79⋊C4—22no—
47Dic79⋊C4—22no—
48Dic79⋊C4—22no—
49C4×Dic79—22no—
50C4×Dic79—22no—
51C4×Dic79—22no—
52C2×Q8×C79D411yescharacteristic
53C2×C8×C79C2311yescharacteristic
54C2×C8×C79C2312yes—
55C2×C8×C79C2311yescharacteristic
56C4⋊C4×C79D412yes—
57C4⋊C4×C79D411yescharacteristic
58C42×C79C2311yescharacteristic
59C42×C79C2312yes—
60Q8×C79—41no—
61C2×C4×C79C2×D411yescharacteristic
62C2×C4×C79C2×D412yes—
63C2×C4×C79C2×D412yes—
64C2×C4×C79C2×D411yescharacteristic
65C2×C4×C79C2411yescharacteristic
66C2×Dic79—22no—
67C2×Dic79—22no—
68C2×Dic79—22no—
69C2×Dic79—22no—
70Dic158—22no—
71Dic158—44no—
72Dic158C2×Q814yes—
73C8×C79—21no—
74C8×C79—22no—
75C8×C79C2×Q812yes—
76C22×C79C22×D411yescharacteristic
77C4×C79—21no—
78C4×C79—22no—
79C4×C79—21no—
80C4×C79—22no—
81C4×C79C22×Q811yescharacteristic
82C4×C792−1+411yescharacteristic
83Dic79—24no—
84Dic79—42no—
85Dic79—42no—
86Dic79—42no—
87C2×C79D4×Q811yescharacteristic
88C2×C79#57511yescharacteristic
89C2×C79#57811yescharacteristic
90#3390—791nomaximal, Sylow
91C79#339011yescharacteristic, complemented, Sylow
92#557—792no—
93#501—792no—
94#499—791no—
95#479—792no—
96#479—792no—
97#477—792no—
98#446D7911yescharacteristic
99#441—792no—
100C4×Q16—791no—
101C2×Q16—791no—
102C4⋊Q8—792no—
103C4⋊Q8—1582no—
104#125—792no—
105#125—792no—
106#125—1582no—
107#125—1582no—
108C4×Q8—792no—
109C4×Q8—792no—
110C4×Q8—792no—
111C4×Q8—1582no—
112C4×Q8C2×D7911yescharacteristic
113#107—791no—
114#107—791no—
115#107—792no—
116#107—791no—
117#106—792no—
118#106—792no—
119C4⋊C8C2×D7912yes—
120C4⋊C8C2×D7911yescharacteristic
121#103—792no—
122#103—792no—
123#103—792no—
124#97C2×D7912yes—
125C4×C8C2×D7911yescharacteristic
126C2×Q8—792no—
127C2×Q8—1582no—
128C2×Q8D31611yescharacteristic
129Q16—794no—
130C2×C8C22×D7911yescharacteristic
131C2×C8C22×D7912yes—
132C2×C8C22×D7911yescharacteristic
133C4⋊C4—792no—
134C4⋊C4—792no—
135C4⋊C4—792no—
136C4⋊C4—1582no—
137C4⋊C4—1582no—
138C4⋊C4—1582no—
139C4⋊C4—1582no—
140C4⋊C4—1582no—
141C4⋊C4—1582no—
142C4⋊C4—1582no—
143C4⋊C4—1582no—
144C4⋊C4D31612yes—
145C4⋊C4D31611yescharacteristic
146C42—1582no—
147C42—1582no—
148C42—1582no—
149C42C22×D7911yescharacteristic
150C42C22×D7912yes—
151Q8—41no—
152Q8—3164no—
153Q8—794no—
154Q8—1582no—
155C2×C4—1582no—
156C2×C4—1582no—
157C2×C4—1582no—
158C2×C4—1582no—
159C2×C4C2×D31611yescharacteristic
160C2×C4C2×D31612yes—
161C2×C4C2×D31612yes—
162C2×C4C2×D31611yescharacteristic
163C2×C4C23×D7911yescharacteristic
164C8—21no—
165C8—22no—
166C8Q8×D7912yes—
167C22C22×D31611yescharacteristic
168C4—22no—
169C4—21no—
170C4—21no—
171C4—22no—
172C4—3162no—
173C4—3162no—
174C4—3162no—
175C4—1584no—
176C4C2×Q8×D7911yescharacteristic
177C4#1457920811yescharacteristic
178C2Q8×D31611yescharacteristic
179C2#1909936311yescharacteristic
180C2#1909938011yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#446×C79C2
socle, prime radicalC22×C79C22×D4
hypercenter#446D79
hypocenterC79#3390
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
37. Dic316Q8semidirect
91. C79#3390semidirect