Finite Group Databasebeta

← #23766116

Subgroups — #23766116

Order 10112.

516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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×#14579159C211yesmaximal, characteristic
2C2×C4×Dic158C211yesmaximal, characteristic
3#19098470C211yesmaximal, characteristic
4#19098468C211yesmaximal, characteristic
5#19098447C214yesmaximal
6#19098444C214yesmaximal
7#19098428C211yesmaximal, characteristic
8#19098409C211yesmaximal, characteristic
9C2×C4×Q8×C79C211yesmaximal, characteristic
10C22×Dic158C2211yescharacteristic
11#14579159C418yescomplemented
12C4×Dic158—24no—
13C2×C4⋊Dic79C2211yescharacteristic
14C2×Dic79⋊C4C2212yes—
15C2×Dic79⋊C4C2214yes—
16C2×C4×Dic79C2211yescharacteristic
17C2×C4×Dic79C2212yes—
18C2×C4×Dic79C2211yescharacteristic
19C79⋊#95C2212yes—
20C79⋊#95C2212yes—
21C79⋊#95C2214yes—
22C79⋊#95C2214yes—
23C79⋊#95C2214yes—
24C22×Q8×C79C2211yescharacteristic
25C4×Q8×C79—24no—
26C2×C4⋊C4×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2212yes—
28C2×C42×C79C2212yes—
29C2×C42×C79C2211yescharacteristic
30C2×Dic158—22no—
31C2×Dic158—22no—
32C2×Dic158C2×C414yes—
33C22×Dic79C2312yes—
34C22×Dic79C2312yes—
35C22×Dic79C2312yes—
36C22×Dic79C2312yes—
37C4⋊Dic79—22no—
38Dic79⋊C4—24no—
39Dic79⋊C4C2×C4116yes—
40C4×Dic79—24no—
41C4×Dic79—22no—
42C4×Dic79C2×C414yes—
43C2×Q8×C79—22no—
44C2×Q8×C79—22no—
45C2×Q8×C79C2×C414yes—
46C22×C4×C79C2312yes—
47C22×C4×C79C2312yes—
48C22×C4×C79C2311yescharacteristic
49C22×C4×C79C2311yescharacteristic
50C22×C4×C79C2311yescharacteristic
51C4⋊C4×C79—24no—
52C4⋊C4×C79—22no—
53C42×C79—24no—
54C42×C79D414yes—
55C23×C79C2411yescharacteristic
56Q8×C79—28no—
57C2×C4×C79—22no—
58C2×C4×C79—22no—
59C2×C4×C79—22no—
60C2×C4×C79—22no—
61C2×C4×C79—22no—
62C2×C4×C79—24no—
63C2×C4×C79C22×C414yes—
64C2×C4×C79C22×C412yes—
65C2×C4×C79C2×D412yes—
66C2×C4×C79C2×D412yes—
67C2×C4×C79C2×D412yes—
68C2×C4×C79#4112yes—
69C2×Dic79—22no—
70C2×Dic79—22no—
71C2×Dic79—22no—
72C2×Dic79—22no—
73C2×Dic79—22no—
74C2×Dic79—22no—
75C2×Dic79—22no—
76C2×Dic79—24no—
77C2×Dic79—22no—
78C2×Dic79C22×C414yes—
79C2×Dic79C22×C414yes—
80Dic158—28no—
81C22×C79C23×C411yescharacteristic
82C22×C79C22×D411yescharacteristic
83C22×C79C2×#4111yescharacteristic
84C22×C792−1+412yes—
85C22×C792−1+412yes—
86C4×C79—24no—
87C4×C79—22no—
88C4×C79—22no—
89C4×C79—42no—
90C4×C79C4×D414yes—
91Dic79—24no—
92Dic79—24no—
93Dic79—42no—
94Dic79—42no—
95C2×C79C2×C4×D411yescharacteristic
96C2×C79#51912yes—
97C2×C79#53611yescharacteristic
98C2×C79#53611yescharacteristic
99C2×C79#54112yes—
100#2327—791nomaximal, Sylow
101C79#232711yescharacteristic, complemented, Sylow
102C2×C4⋊Q8—791no—
103C2×C4×Q8—791no—
104C2×C4×Q8D7911yescharacteristic
105#391—791no—
106#391—791no—
107#387—794no—
108#387—794no—
109#382—791no—
110#376—791no—
111C22×Q8—791no—
112C22×Q8C2×D7911yescharacteristic
113C4⋊Q8—798no—
114C4×Q8—24no—
115C4×Q8—1584no—
116C2×C4⋊C4—794no—
117C2×C4⋊C4—791no—
118C2×C4⋊C4—792no—
119C2×C4⋊C4C2×D7911yescharacteristic
120C2×C4⋊C4C2×D7912yes—
121C2×C42—791no—
122C2×C42—792no—
123C2×C42—791no—
124C2×C42C2×D7912yes—
125C2×C42C2×D7911yescharacteristic
126#95—792no—
127#95—792no—
128#95—794no—
129#95—794no—
130#95—794no—
131C2×Q8—22no—
132C2×Q8—22no—
133C2×Q8—794no—
134C2×Q8—1582no—
135C2×Q8—1582no—
136C2×Q8C4×D7914yes—
137C22×C4—792no—
138C22×C4—792no—
139C22×C4—792no—
140C22×C4—792no—
141C22×C4C22×D7912yes—
142C22×C4C22×D7912yes—
143C22×C4C22×D7911yescharacteristic
144C22×C4C22×D7911yescharacteristic
145C22×C4C22×D7911yescharacteristic
146C4⋊C4—24no—
147C4⋊C4—22no—
148C4⋊C4—7916no—
149C4⋊C4—1584no—
150C4⋊C4—1582no—
151C42—24no—
152C42—794no—
153C42—1584no—
154C42—1582no—
155C42C22⋊D7914yes—
156C23C23×D7911yescharacteristic
157Q8—28no—
158Q8—1588no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—794no—
166C2×C4—794no—
167C2×C4—1582no—
168C2×C4—1582no—
169C2×C4—1584no—
170C2×C4—1582no—
171C2×C4—1582no—
172C2×C4—1582no—
173C2×C4—1582no—
174C2×C4—1582no—
175C2×C4—1582no—
176C2×C4C2×C4×D7914yes—
177C2×C4C2×C4×D7912yes—
178C2×C4C2×C22⋊D7912yes—
179C2×C4C2×C22⋊D7912yes—
180C2×C4C2×C22⋊D7912yes—
181C2×C4#1192962412yes—
182C22C22×C4×D7911yescharacteristic
183C22C22×C22⋊D7911yescharacteristic
184C22C2×#1192962411yescharacteristic
185C22#1457920812yes—
186C22#1457920912yes—
187C4—22no—
188C4—24no—
189C4—22no—
190C4—42no—
191C4—3162no—
192C4—3162no—
193C4—1584no—
194C4—1584no—
195C4C4×C22⋊D7914yes—
196C2C2×C4×C22⋊D7911yescharacteristic
197C2#1909903912yes—
198C2#1909913411yescharacteristic
199C2#1909913711yescharacteristic
200C2#1909917112yes—
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
FittingC2×C4×Q8×C79C2
socle, prime radical, cosocleC23×C79C24
hypercenterC2×C4×Q8D79
hypocenterC79#2327
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
11. #14579159C4semidirect
101. C79#2327semidirect