Finite Group Databasebeta

← #23761728

Subgroups — #23761728

Order 10112.

312 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C2×C4⋊C4×D79C211yesmaximal, characteristic
2#19098525C212yesmaximal
3#19098289C211yesmaximal, characteristic, complemented
4#19098288C212yesmaximal, complemented
5#324×C79C211yesmaximal, characteristic, complemented
6C22×C4×D79C411yescharacteristic
7C22×C4×D79C411yescharacteristic
8C22×C4×D79C2211yescharacteristic
9C2×#11929607—22no—
10C2×C4⋊Dic79C411yescharacteristic
11C2×Dic79⋊C4C411yescharacteristic
12C2×Dic79⋊C4C2211yescharacteristic
13C4⋊C4×D79—22no—
14C4⋊C4×D79—22no—
15C22⋊(C79⋊C8)C2212yes—
16(C2×D79)⋊C8—22no—
17C2×C4⋊C4×C79C2211yescharacteristic
18C22⋊C8×C79C2212yes—
19C23×D79C2×C411yescharacteristic
20C22×Dic79C2×C411yescharacteristic
21C22×Dic79C2×C411yescharacteristic
22C22×Dic79C2×C411yescharacteristic
23C2×C4×D79—22no—
24C2×C4×D79—21no—
25C2×C4×D79—21no—
26C2×C4×D79—21no—
27C2×C4×D79—21no—
28C2×C4×D79—22no—
29C2×C4×D79—42no—
30C2×C4×D79—42no—
31C2×C4×D79D412yes—
32C2×C4×D79D412yes—
33#11929607—44no—
34C2×C79⋊C8—22no—
35C4⋊Dic79—22no—
36Dic79⋊C4—22no—
37Dic79⋊C4—22no—
38C22×C4×C79C2×C411yescharacteristic
39C22×C4×C79C2×C411yescharacteristic
40C22×C4×C79C2311yescharacteristic
41C2×C8×C79—22no—
42C4⋊C4×C79—22no—
43C23×C79C22×C411yescharacteristic
44C22×D79—21no—
45C22×D79—21no—
46C22×D79—22no—
47C22×D79—22no—
48C22×D79C22⋊C411yescharacteristic
49C22×D79C22⋊C411yescharacteristic
50C2×C4×C79—21no—
51C2×C4×C79—21no—
52C2×C4×C79—21no—
53C2×C4×C79—41no—
54C2×C4×C79—41no—
55C2×C4×C79M1612yescomplemented
56C2×C4×C79C2×D412yes—
57C2×Dic79—21no—
58C2×Dic79—21no—
59C2×Dic79—21no—
60C2×Dic79—41no—
61C2×Dic79—41no—
62C2×Dic79C22⋊C412yes—
63C2×Dic79M1612yescomplemented
64C4×D79—24no—
65C4×D79—24no—
66C4×D79—24no—
67C4×D79—42no—
68C4×D79—42no—
69C4×D79—42no—
70C8×C79—42no—
71C79⋊C8—42no—
72C22×C79—21no—
73C22×C79—21no—
74C22×C79C2×C22⋊C411yescharacteristic
75C22×C79C2×M1611yescharacteristic
76C22×C79C2×M1611yescharacteristic
77C2×D79—24no—
78C2×D79—24no—
79C2×D79—21no—
80C2×D79—21no—
81C2×D79—21no—
82C2×D79—21no—
83C2×D79#9912yes—
84C2×D79#10112yes—
85C4×C79—22no—
86C4×C79—22no—
87C4×C79—41no—
88Dic79—22no—
89Dic79—22no—
90Dic79—41no—
91C2×C79—21no—
92C2×C79—21no—
93C2×C79#40711yescharacteristic
94C2×C79C2×#9911yescharacteristic
95C2×C79C2×#10111yescharacteristic
96D79—22no—
97D79—22no—
98#1463—791nomaximal, Sylow
99C79#146311yescharacteristic, complemented, Sylow
100C22×C4⋊C4—791no—
101#407—792no—
102#324—791no—
103#324—792no—
104#324D7911yescharacteristic, complemented
105C23×C4—791no—
106C23×C4—791no—
107C23×C4—791no—
108C2×M16—1582no—
109C2×C4⋊C4—791no—
110C2×C4⋊C4—791no—
111C2×C4⋊C4—791no—
112C2×C4⋊C4—1582no—
113C2×C4⋊C4—1582no—
114C2×C4⋊C4C2×D7911yescharacteristic
115C22⋊C8—792no—
116C22⋊C8—1582no—
117C22⋊C8C2×D7912yes—
118C24—791no—
119C22×C4—3162no—
120C22×C4—3162no—
121C22×C4—791no—
122C22×C4—792no—
123C22×C4—791no—
124C22×C4—791no—
125C22×C4—792no—
126C22×C4—1581no—
127C22×C4—1581no—
128C22×C4—1582no—
129C22×C4—1581no—
130C22×C4—1581no—
131C22×C4—1582no—
132C22×C4C4×D7911yescharacteristic
133C22×C4C4×D7911yescharacteristic
134C22×C4C22×D7911yescharacteristic
135M16—3164no—
136C2×C8—22no—
137C2×C8—1582no—
138C4⋊C4—22no—
139C4⋊C4—1582no—
140C4⋊C4—1582no—
141C4⋊C4—1582no—
142C23—791no—
143C23—791no—
144C23—1582no—
145C23—1582no—
146C23—1581no—
147C23—1581no—
148C23C2×C4×D7911yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—3162no—
155C2×C4—3162no—
156C2×C4—3162no—
157C2×C4—3161no—
158C2×C4—3161no—
159C2×C4—792no—
160C2×C4—792no—
161C2×C4—1584no—
162C2×C4—1584no—
163C2×C4—1584no—
164C2×C4—1581no—
165C2×C4—1581no—
166C2×C4—1581no—
167C2×C4#1192960712yescomplemented
168C2×C4D4×D7912yes—
169C8—42no—
170C8—3162no—
171C22—21no—
172C22—21no—
173C22—792no—
174C22—792no—
175C22—1584no—
176C22—1584no—
177C22—1581no—
178C22—1581no—
179C22—1581no—
180C22—1581no—
181C22C22⋊C4×D7911yescharacteristic
182C22M16×D7911yescharacteristic
183C22C2×#1192960711yescharacteristic
184C4—22no—
185C4—22no—
186C4—41no—
187C4—3161no—
188C4—1582no—
189C4—1582no—
190C2—21no—
191C2—21no—
192C2—1582no—
193C2—1582no—
194C2#1909852511yescharacteristic
195C2#99×D7911yescharacteristic
196C2#101×D7911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D79
commutatorC23×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#324×C79C2
socleC22×C79C2×C22⋊C4
prime radicalC23×D79C2×C4
cosocleC22×C4×C79C23
hypercenter#324D79
hypocenterC79#1463
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
3. #19098289C2semidirect
4. #19098288C2semidirect
5. #324×C79C2semidirect
55. C2×C4×C79M16semidirect
63. C2×Dic79M16semidirect
99. C79#1463semidirect
104. #324D79semidirect
167. C2×C4#11929607semidirect