Finite Group Databasebeta

← #23765062

Subgroups — #23765062

Order 10112.

258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 55 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#19099111C211yesmaximal, characteristic
2#19098535C212yesmaximal, complemented
3#19098357C212yesmaximal, complemented
4#19098356C211yesmaximal, characteristic, complemented
5#353×C79C211yesmaximal, characteristic, complemented
6C2×#11929623C411yescharacteristic, complemented
7C2×#11929623C2211yescharacteristic
8#14579161C411yescharacteristic, complemented
9#14579148C411yescharacteristic, complemented
10#14579148C2211yescharacteristic
11#14579132—22no—
12D4×Dic79—22no—
13#14579117—22no—
14C42×D79C411yescharacteristic, complemented
15#14579076C2212yes—
16#14579075—22no—
17#127×C79C2211yescharacteristic
18#99×C79C2212yes—
19#11929623—41no—
20#11929623—41no—
21#11929623—41no—
22#11929623—41no—
23C2×Dic158C2×C411yescharacteristic
24C2×Dic158C2×C411yescharacteristic
25C2×C22⋊D79—21no—
26C2×C22⋊D79D412yes—
27C22×Dic79—21no—
28C22×Dic79D412yes—
29C2×C4×D79—21no—
30C2×C4×D79C2×C411yescharacteristic
31C4⋊Dic79—22no—
32Dic79⋊C4—42no—
33C22⋊Dic79—22no—
34C22⋊Dic79—22no—
35C22⋊Dic79—22no—
36C4×Dic79—21no—
37C4×Dic79—42no—
38C4×Dic79C2×C411yescharacteristic
39C2×D4×C79—22no—
40C2×D4×C79C2×C411yescharacteristic
41C2×D4×C79C2311yescharacteristic
42C22⋊C4×C79—22no—
43C42×C79C2×C411yescharacteristic
44C23×C79—21no—
45C23×C79C2×D412yes—
46C22×D79C22⋊C411yescharacteristic
47D4×C79—41no—
48D4×C79—41no—
49D4×C79—44no—
50C2×C4×C79—21no—
51C2×C4×C79—42no—
52C2×C4×C79C22×C411yescharacteristic
53C22⋊D79—42no—
54C22⋊D79—42no—
55C2×Dic79—22no—
56C2×Dic79—22no—
57C2×Dic79—21no—
58C2×Dic79—21no—
59C2×Dic79—41no—
60C2×Dic79—41no—
61C2×Dic79—42no—
62C2×Dic79C22⋊C412yes—
63C2×Dic79C22⋊C411yescharacteristic
64C4×D79—21no—
65C4×D79—21no—
66C4×D79—42no—
67Dic158—41no—
68Dic158—41no—
69C22×C79—22no—
70C22×C79—42no—
71C22×C79—42no—
72C22×C79—41no—
73C22×C79C2×C22⋊C411yescharacteristic
74C2×D79—21no—
75C2×D79—41no—
76C4×C79—22no—
77C4×C79—21no—
78C4×C79—82no—
79Dic79—22no—
80Dic79—41no—
81Dic79—41no—
82Dic79—82no—
83Dic79#9911yescharacteristic
84Dic79#9911yescharacteristic
85C2×C79—21no—
86C2×C79—42no—
87C2×C79—81no—
88C2×C79C2×#9911yescharacteristic
89D79—41no—
90#2126—791nomaximal, Sylow
91C79#212611yescharacteristic, complemented, Sylow
92#532—791no—
93#410—792no—
94#354—792no—
95#353—791no—
96#353D7911yescharacteristic, complemented
97C2×#41—791no—
98C2×#41—791no—
99C4⋊Q8—791no—
100#127C2×D7911yescharacteristic
101#124—791no—
102#124—791no—
103#121—1582no—
104C4×D4—1582no—
105#117—1582no—
106C2×C42—791no—
107#99—792no—
108#99—1582no—
109#99C2×D7912yes—
110#41—3161no—
111#41—3161no—
112#41—3161no—
113#41—3161no—
114C2×Q8—791no—
115C2×Q8—791no—
116C2×D4—22no—
117C2×D4—792no—
118C2×D4—1581no—
119C2×D4C4×D7911yescharacteristic
120C2×D4C22×D7911yescharacteristic
121C22×C4—792no—
122C22×C4—791no—
123C22×C4—1581no—
124C22×C4—1581no—
125C4⋊C4—3162no—
126C4⋊C4—1582no—
127C22⋊C4—22no—
128C22⋊C4—1582no—
129C22⋊C4—1582no—
130C22⋊C4—1582no—
131C42—3162no—
132C42—791no—
133C42—1581no—
134C42C4×D7911yescharacteristic
135C23—21no—
136C23—791no—
137C23D4×D7912yes—
138Q8—3161no—
139Q8—3161no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—3162no—
144D4—3162no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—3162no—
148C2×C4—3161no—
149C2×C4—3161no—
150C2×C4—3162no—
151C2×C4—791no—
152C2×C4—792no—
153C2×C4—1581no—
154C2×C4—1581no—
155C2×C4—1581no—
156C2×C4—1581no—
157C2×C4—1582no—
158C2×C4—1582no—
159C2×C4C2×C4×D7911yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—3161no—
165C22—1581no—
166C22C22⋊C4×D7911yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—3161no—
171C4—3161no—
172C4—791no—
173C4—791no—
174C4—6322no—
175C4—1582no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—3161no—
180C2#99×D7911yescharacteristic
subgroupG/H
centerC2#99×D79
commutatorC2×C4×C79C22×C4
FrattiniC2×D4C22×D79
Fitting#353×C79C2
socleC2×C79C2×#99
prime radical#19099111C2
cosocleC2×D4×C79C23
hypercenter#353D79
hypocenterC79#2126
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #19098535C2semidirect
3. #19098357C2semidirect
4. #19098356C2semidirect
5. #353×C79C2semidirect
6. C2×#11929623C4semidirect
8. #14579161C4semidirect
9. #14579148C4semidirect
14. C42×D79C4semidirect
91. C79#2126semidirect
96. #353D79semidirect