Finite Group Databasebeta

← #23774546

Subgroups — #23774546

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
1#19099120C211yesmaximal, characteristic
2C2×#14579161C211yesmaximal, characteristic
3#19098961C212yesmaximal, complemented
4#19098914C212yesmaximal, complemented
5#19098894C214yesmaximal
6#19098849C214yesmaximal, complemented
7#431×C79C211yesmaximal, characteristic
8C22×Dic158—21no—
9#14579161—21no—
10#14579161—21no—
11#14579161C2211yescharacteristic
12#14579161C2212yes—
13#14579161C2211yescharacteristic
14#14579161C2212yes—
15#14579153—21no—
16#14579140—21no—
17#14579140C2212yes—
18C4×Dic158—21no—
19C4×Dic158C2212yes—
20#14579120—21no—
21C2×C4⋊Dic79—21no—
22C2×C4⋊Dic79C2212yes—
23#14579093C2218yes—
24#14579086C2218yes—
25C2×C42×C79C2211yescharacteristic
26C4⋊C8×C79C2212yes—
27C22⋊C8×C79C2212yes—
28C4×C8×C79C2212yes—
29C2×Dic158—22no—
30C2×Dic158—22no—
31C2×Dic158—21no—
32C2×Dic158—44no—
33C2×Dic158C2312yes—
34C22×Dic79—22no—
35C4⋊Dic79—22no—
36C4⋊Dic79—22no—
37C4⋊Dic79—22no—
38C4⋊Dic79—21no—
39C4⋊Dic79—21no—
40C4⋊Dic79—21no—
41C4⋊Dic79C2314yes—
42C4⋊Dic79C2312yes—
43Dic79⋊C4—22no—
44Dic79⋊C4—22no—
45C22⋊Dic79—22no—
46C4×Dic79—22no—
47C22×C4×C79D411yescharacteristic
48C22×C4×C79D411yescharacteristic
49C22×C4×C79C2311yescharacteristic
50C2×C8×C79C2314yes—
51C42×C79D411yescharacteristic
52C42×C79D411yescharacteristic
53C42×C79C2311yescharacteristic
54C42×C79C2311yescharacteristic
55C23×C79C2×D411yescharacteristic
56C2×C4×C79—22no—
57C2×C4×C79—22no—
58C2×C4×C79SD1614yes—
59C2×C4×C79C2×D411yescharacteristic
60C2×C4×C79C2×D411yescharacteristic
61C2×C4×C79C2×D411yescharacteristic
62C2×C4×C79C2×D411yescharacteristic
63C2×C4×C79C2×D411yescharacteristic
64C2×C4×C79C2411yescharacteristic
65C2×Dic79—22no—
66C2×Dic79—22no—
67C2×Dic79—24no—
68C2×Dic79—44no—
69Dic158—24no—
70Dic158—44no—
71Dic158—44no—
72Dic158—42no—
73C8×C79—24no—
74C22×C79—21no—
75C22×C79—21no—
76C22×C79C2×SD1612yes—
77C22×C79C22×D411yescharacteristic
78C4×C79—21no—
79C4×C79—21no—
80C4×C79C2×SD1612yes—
81C4×C79C2×SD1612yes—
82C4×C79#13712yes—
83C4×C792−1+412yes—
84Dic79—42no—
85Dic79—44no—
86Dic79—42no—
87C2×C79—22no—
88C2×C79#53611yescharacteristic
89C2×C79C22×SD1611yescharacteristic
90C2×C79C2×#13711yescharacteristic
91#3229—791nomaximal, Sylow
92C79#322911yescharacteristic, complemented, Sylow
93#533—791no—
94C2×C4⋊Q8—791no—
95#498—792no—
96#487—792no—
97#483—794no—
98#475—794no—
99#431D7911yescharacteristic
100C22×Q8—1581no—
101C4⋊Q8—792no—
102C4⋊Q8—792no—
103C4⋊Q8—791no—
104C4⋊Q8—791no—
105C4⋊Q8—1581no—
106C4⋊Q8—1581no—
107#125—1581no—
108C22⋊Q8—792no—
109C22⋊Q8—1581no—
110C4×Q8—792no—
111C4×Q8—1581no—
112#117—1581no—
113C2×C4⋊C4—792no—
114C2×C4⋊C4—1581no—
115C2×C42C2×D7911yescharacteristic
116#106—798no—
117C4⋊C8C2×D7912yes—
118#103—798no—
119C22⋊C8C2×D7912yes—
120C4×C8C2×D7912yes—
121C2×Q8—3164no—
122C2×Q8—792no—
123C2×Q8—1581no—
124C2×Q8—1582no—
125C2×Q8—1582no—
126C22×C4—1582no—
127C22×C4D31611yescharacteristic
128C22×C4D31611yescharacteristic
129C22×C4C22×D7911yescharacteristic
130C2×C8C22×D7914yes—
131C4⋊C4—794no—
132C4⋊C4—792no—
133C4⋊C4—1582no—
134C4⋊C4—1582no—
135C4⋊C4—1582no—
136C4⋊C4—1582no—
137C4⋊C4—1582no—
138C4⋊C4—1581no—
139C4⋊C4—1581no—
140C4⋊C4—1581no—
141C22⋊C4—1582no—
142C42—1582no—
143C42D31611yescharacteristic
144C42D31611yescharacteristic
145C42C22×D7911yescharacteristic
146C42C22×D7911yescharacteristic
147C23C2×D31611yescharacteristic
148Q8—3164no—
149Q8—3164no—
150Q8—3162no—
151Q8—1584no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—3164no—
155C2×C4—1582no—
156C2×C4—1582no—
157C2×C4—1584no—
158C2×C4#1192961314yes—
159C2×C4C2×D31611yescharacteristic
160C2×C4C2×D31611yescharacteristic
161C2×C4C2×D31611yescharacteristic
162C2×C4C2×D31611yescharacteristic
163C2×C4C2×D31611yescharacteristic
164C2×C4C23×D7911yescharacteristic
165C8—24no—
166C22—21no—
167C22—21no—
168C22C2×#1192961312yes—
169C22C22×D31611yescharacteristic
170C4—21no—
171C4—21no—
172C4—3162no—
173C4—3164no—
174C4—3162no—
175C4C2×#1192961312yes—
176C4C2×#1192961312yes—
177C4#1457919412yes—
178C4#1457920812yes—
179C2—22no—
180C2#1909913911yescharacteristic
181C2C22×#1192961311yescharacteristic
182C2C2×#1457919411yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#431×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#431D79
hypocenterC79#3229
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
3. #19098961C2semidirect
4. #19098914C2semidirect
6. #19098849C2semidirect
92. C79#3229semidirect