Finite Group Databasebeta

← #23774541

Subgroups — #23774541

Order 10112.

360 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14579161C211yesmaximal, characteristic
2#19098959C212yesmaximal, complemented
3#19098913C212yesmaximal, complemented
4#19098891C214yesmaximal
5#19098848C214yesmaximal, complemented
6#19098616C211yesmaximal, characteristic
7#533×C79C211yesmaximal, characteristic
8C22×Dic158—21no—
9#14579161—21no—
10#14579161—21no—
11#14579161C2212yes—
12#14579161C2212yes—
13C2×C4⋊Dic79—21no—
14C2×C4⋊Dic79C2212yes—
15#14579092C2218yes—
16C4⋊(C79⋊C8)C2212yes—
17#14579085C2218yes—
18C22⋊(C79⋊C8)C2212yes—
19C4×C79⋊C8C2212yes—
20C4⋊Q8×C79C2211yescharacteristic
21C4⋊Q8×C79C2211yescharacteristic
22#125×C79—21no—
23C22⋊Q8×C79—21no—
24C22⋊Q8×C79C2212yes—
25C4×Q8×C79—21no—
26C4×Q8×C79C2212yes—
27#117×C79—21no—
28C2×C42×C79C2211yescharacteristic
29C2×Dic158—22no—
30C2×Dic158—22no—
31C2×Dic158—44no—
32C22×Dic79—22no—
33C2×C79⋊C8C2314yes—
34C4⋊Dic79—22no—
35C4⋊Dic79—22no—
36C4⋊Dic79—22no—
37C4⋊Dic79C2314yes—
38C2×Q8×C79—21no—
39C2×Q8×C79C2312yes—
40C22×C4×C79D411yescharacteristic
41C22×C4×C79D411yescharacteristic
42C22×C4×C79C2311yescharacteristic
43C4⋊C4×C79—21no—
44C4⋊C4×C79—21no—
45C4⋊C4×C79—21no—
46C4⋊C4×C79—22no—
47C4⋊C4×C79—22no—
48C4⋊C4×C79C2312yes—
49C22⋊C4×C79—22no—
50C42×C79—22no—
51C42×C79D411yescharacteristic
52C42×C79D411yescharacteristic
53C42×C79C2311yescharacteristic
54C42×C79C2311yescharacteristic
55C23×C79C2×D411yescharacteristic
56Q8×C79—24no—
57Q8×C79—42no—
58C2×C4×C79—22no—
59C2×C4×C79—22no—
60C2×C4×C79—22no—
61C2×C4×C79—22no—
62C2×C4×C79SD1614yes—
63C2×C4×C79C2×D411yescharacteristic
64C2×C4×C79C2×D411yescharacteristic
65C2×C4×C79C2×D411yescharacteristic
66C2×C4×C79C2×D411yescharacteristic
67C2×C4×C79C2×D411yescharacteristic
68C2×C4×C79C2411yescharacteristic
69C2×Dic79—24no—
70C2×Dic79—44no—
71Dic158—44no—
72Dic158—44no—
73C79⋊C8—24no—
74C22×C79—21no—
75C22×C79—21no—
76C22×C79C2×SD1612yes—
77C22×C79C22×D411yescharacteristic
78C4×C79—21no—
79C4×C79—21no—
80C4×C79—42no—
81C4×C79—42no—
82C4×C79C2×SD1612yes—
83C4×C79C2×SD1612yes—
84C4×C79#13712yes—
85C4×C792−1+412yes—
86Dic79—44no—
87C2×C79—22no—
88C2×C79#53611yescharacteristic
89C2×C79C22×SD1611yescharacteristic
90C2×C79C2×#13711yescharacteristic
91#3229—791nomaximal, Sylow
92C79#322911yescharacteristic, complemented, Sylow
93#533D7911yescharacteristic
94C2×C4⋊Q8—791no—
95#498—792no—
96#487—792no—
97#483—794no—
98#475—794no—
99#431—791no—
100C22×Q8—1581no—
101C4⋊Q8—792no—
102C4⋊Q8—792no—
103C4⋊Q8—1581no—
104C4⋊Q8—1581no—
105C4⋊Q8C2×D7911yescharacteristic
106C4⋊Q8C2×D7911yescharacteristic
107#125—21no—
108C22⋊Q8—21no—
109C22⋊Q8C2×D7912yes—
110C4×Q8—21no—
111C4×Q8C2×D7912yes—
112#117—21no—
113C2×C4⋊C4—792no—
114C2×C4⋊C4—1581no—
115C2×C42C2×D7911yescharacteristic
116#106—798no—
117C4⋊C8—792no—
118#103—798no—
119C22⋊C8—792no—
120C4×C8—792no—
121C2×Q8—21no—
122C2×Q8—3164no—
123C2×Q8—1582no—
124C2×Q8—1582no—
125C2×Q8C22×D7912yes—
126C22×C4—1582no—
127C22×C4C22⋊D7911yescharacteristic
128C22×C4C22⋊D7911yescharacteristic
129C22×C4C22×D7911yescharacteristic
130C2×C8—794no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—22no—
135C4⋊C4—22no—
136C4⋊C4—794no—
137C4⋊C4—1582no—
138C4⋊C4—1582no—
139C4⋊C4—1582no—
140C4⋊C4C22×D7912yes—
141C22⋊C4—22no—
142C42—22no—
143C42C22⋊D7911yescharacteristic
144C42C22⋊D7911yescharacteristic
145C42C22×D7911yescharacteristic
146C42C22×D7911yescharacteristic
147C23C2×C22⋊D7911yescharacteristic
148Q8—24no—
149Q8—42no—
150Q8—3164no—
151Q8—3164no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—3164no—
157C2×C4—1584no—
158C2×C4#1192961114yes—
159C2×C4C2×C22⋊D7911yescharacteristic
160C2×C4C2×C22⋊D7911yescharacteristic
161C2×C4C2×C22⋊D7911yescharacteristic
162C2×C4C2×C22⋊D7911yescharacteristic
163C2×C4C2×C22⋊D7911yescharacteristic
164C2×C4C23×D7911yescharacteristic
165C8—1584no—
166C22—21no—
167C22—21no—
168C22C2×#1192961112yes—
169C22C22×C22⋊D7911yescharacteristic
170C4—21no—
171C4—21no—
172C4—42no—
173C4—42no—
174C4—3164no—
175C4C2×#1192961112yes—
176C4C2×#1192961112yes—
177C4#1457919112yes—
178C4#1457920812yes—
179C2—22no—
180C2#1909913411yescharacteristic
181C2C22×#1192961111yescharacteristic
182C2C2×#1457919111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#533×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#533D79
hypocenterC79#3229
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #19098959C2semidirect
3. #19098913C2semidirect
5. #19098848C2semidirect
92. C79#3229semidirect