Finite Group Databasebeta

← #23776370

Subgroups — #23776370

Order 10112.

320 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 121 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#19099290C212yesmaximal
2#19098970C212yesmaximal
3#19098869C212yesmaximal
4#19098867C212yesmaximal
5#19098857C212yesmaximal
6#19098693C211yesmaximal, characteristic
7#19098669C212yesmaximal
8C4×Dic316C211yesmaximal, characteristic
9#499×C79C211yesmaximal, characteristic
10C2×Dic316C2211yescharacteristic
11#14579160—22no—
12#14579160C2212yes—
13#14579152C2212yes—
14#14579151—22no—
15#14579151—22no—
16C4×Dic158C2212yes—
17C4×Dic158C2211yescharacteristic
18#14579126—22no—
19#14579126C2212yes—
20#14579126C2212yes—
21#14579095C2211yescharacteristic
22#14579094C2212yes—
23#14579092C2212yes—
24C4⋊(C79⋊C8)C2211yescharacteristic
25Dic79⋊C8C2212yes—
26#14579086C2212yes—
27#14579084C2212yes—
28#14579084C2212yes—
29#14579071C2212yes—
30#125×C79C2212yes—
31#107×C79C2211yescharacteristic
32#107×C79C2211yescharacteristic
33#106×C79C2212yes—
34C4×C8×C79C2211yescharacteristic
35C2×Dic158—22no—
36C2×Dic158D411yescharacteristic
37C2×Dic158C2312yes—
38Dic316Q814yescomplemented
39C2×C79⋊C8C2312yes—
40C4⋊Dic79—22no—
41C4⋊Dic79D411yescharacteristic
42C4⋊Dic79C2312yes—
43Dic79⋊C4—22no—
44Dic79⋊C4—22no—
45Dic79⋊C4—22no—
46Dic79⋊C4—22no—
47Dic79⋊C4—22no—
48Dic79⋊C4D412yes—
49C4×Dic79—22no—
50C4×Dic79—22no—
51C4×Dic79—22no—
52C4×Dic79C2312yes—
53C2×C8×C79C2311yescharacteristic
54C2×C8×C79C2311yescharacteristic
55C4⋊C4×C79—22no—
56C4⋊C4×C79—22no—
57C4⋊C4×C79C2312yes—
58C4⋊C4×C79C2312yes—
59C42×C79C2311yescharacteristic
60C2×C4×C79—22no—
61C2×C4×C79—22no—
62C2×C4×C79C2×D411yescharacteristic
63C2×C4×C79C2×D411yescharacteristic
64C2×C4×C79C2411yescharacteristic
65C2×Dic79—22no—
66C2×Dic79—22no—
67C2×Dic79C2×D412yes—
68C2×Dic79C2×D412yes—
69Dic158—22no—
70Dic158—41no—
71Dic158—44no—
72Dic158C2×Q814yes—
73C8×C79—21no—
74C8×C79C2×Q812yes—
75C79⋊C8—22no—
76C22×C79C22×D411yescharacteristic
77C4×C79—21no—
78C4×C79—21no—
79C4×C79—42no—
80C4×C79—42no—
81C4×C79C22×Q811yescharacteristic
82C4×C792−1+411yescharacteristic
83Dic79—24no—
84Dic79—22no—
85Dic79—22no—
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#499D7911yescharacteristic
95#479—792no—
96#479—792no—
97#477—792no—
98#446—791no—
99#441—792no—
100C4×Q16—791no—
101C2×Q16—791no—
102C4⋊Q8—792no—
103C4⋊Q8—1582no—
104#125—792no—
105#125—1582no—
106#125—1582no—
107#125C2×D7912yes—
108C4×Q8—791no—
109C4×Q8—792no—
110C4×Q8—792no—
111C4×Q8—792no—
112C4×Q8—1582no—
113#107—791no—
114#107—792no—
115#107C2×D7911yescharacteristic
116#107C2×D7911yescharacteristic
117#106—792no—
118#106C2×D7912yes—
119C4⋊C8—792no—
120C4⋊C8—791no—
121#103—792no—
122#103—792no—
123#103—792no—
124#97—792no—
125C4×C8C2×D7911yescharacteristic
126C2×Q8—791no—
127C2×Q8—792no—
128C2×Q8—1582no—
129Q16—794no—
130C2×C8—792no—
131C2×C8C22×D7911yescharacteristic
132C2×C8C22×D7911yescharacteristic
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—792no—
136C4⋊C4—791no—
137C4⋊C4—792no—
138C4⋊C4—1582no—
139C4⋊C4—1582no—
140C4⋊C4—1582no—
141C4⋊C4—1582no—
142C4⋊C4—1582no—
143C4⋊C4—1582no—
144C4⋊C4C22×D7912yes—
145C4⋊C4C22×D7912yes—
146C42—792no—
147C42—1582no—
148C42—1582no—
149C42—1582no—
150C42C22×D7911yescharacteristic
151Q8—3161no—
152Q8—3164no—
153Q8—794no—
154Q8—1582no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—792no—
158C2×C4—792no—
159C2×C4—1582no—
160C2×C4—1582no—
161C2×C4D4×D7911yescharacteristic
162C2×C4D4×D7911yescharacteristic
163C2×C4C23×D7911yescharacteristic
164C8—21no—
165C8—1582no—
166C8Q8×D7912yes—
167C22C2×D4×D7911yescharacteristic
168C4—21no—
169C4—21no—
170C4—42no—
171C4—42no—
172C4—3162no—
173C4—1584no—
174C4—1582no—
175C4—1582no—
176C4C2×Q8×D7911yescharacteristic
177C4#1457920911yescharacteristic
178C2#1909922811yescharacteristic
179C2#1909936011yescharacteristic
180C2#1909937711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#499×C79C2
socle, prime radicalC22×C79C22×D4
hypercenter#499D79
hypocenterC79#3390
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

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