Finite Group Databasebeta

← #23771435

Subgroups — #23771435

Order 10112.

444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14579140C211yesmaximal, characteristic
2#19098502C212yesmaximal, complemented
3#19098501C212yesmaximal, complemented
4#19098491C214yesmaximal
5#19098483C212yesmaximal, complemented
6#19098482C212yesmaximal, complemented
7#19098426C211yesmaximal, characteristic
8C2×C22⋊Q8×C79C211yesmaximal, characteristic
9C22×Dic158C2211yescharacteristic
10#14579140—24no—
11C2×C4⋊Dic79C2211yescharacteristic
12C2×Dic79⋊C4C2212yes—
13C2×Dic79⋊C4C2214yes—
14C2×C22⋊Dic79C2212yes—
15C2×C22⋊Dic79C2212yes—
16C79⋊#95C2212yes—
17C79⋊#95C2212yes—
18C79⋊#95C2214yes—
19C79⋊#95C2214yes—
20C79⋊#95C2214yes—
21C22×Q8×C79C2211yescharacteristic
22C23×C4×C79C2211yescharacteristic
23C22⋊Q8×C79—24no—
24C2×C4⋊C4×C79C2212yes—
25C2×C4⋊C4×C79C2211yescharacteristic
26C2×C22⋊C4×C79C2212yes—
27C2×Dic158—22no—
28C2×Dic158—42no—
29C22×Dic79C2312yes—
30C22×Dic79C2314yes—
31C22×Dic79C2312yes—
32C4⋊Dic79—22no—
33Dic79⋊C4—24no—
34Dic79⋊C4—44no—
35C22⋊Dic79—24no—
36C22⋊Dic79—42no—
37C24×C79C2311yescharacteristic
38C2×Q8×C79—22no—
39C2×Q8×C79—42no—
40C22×C4×C79—42no—
41C22×C4×C79D414yes—
42C22×C4×C79C2312yes—
43C22×C4×C79C2312yes—
44C22×C4×C79C2311yescharacteristic
45C22×C4×C79C2311yescharacteristic
46C4⋊C4×C79—22no—
47C4⋊C4×C79—24no—
48C22⋊C4×C79—24no—
49C23×C79—22no—
50C23×C79—22no—
51C23×C79—22no—
52C23×C79C2×D412yes—
53C23×C79C2411yescharacteristic
54Q8×C79—44no—
55C2×C4×C79—22no—
56C2×C4×C79—22no—
57C2×C4×C79—22no—
58C2×C4×C79—22no—
59C2×C4×C79—24no—
60C2×C4×C79—24no—
61C2×C4×C79—44no—
62C2×C4×C79C2×D412yes—
63C2×C4×C79C2×D412yes—
64C2×Dic79—22no—
65C2×Dic79—22no—
66C2×Dic79—24no—
67C2×Dic79—24no—
68C2×Dic79—24no—
69C2×Dic79—24no—
70C2×Dic79—24no—
71Dic158—44no—
72C22×C79—22no—
73C22×C79—22no—
74C22×C79—22no—
75C22×C79—44no—
76C22×C79C22×D411yescharacteristic
77C22×C79H(5,𝔽2)12yes—
78C22×C792−1+412yes—
79C22×C792−1+412yes—
80C4×C79—22no—
81C4×C79—22no—
82C4×C79—42no—
83C4×C79—42no—
84Dic79—42no—
85Dic79—42no—
86Dic79—44no—
87C2×C79—42no—
88C2×C79#53411yescharacteristic
89C2×C79#53611yescharacteristic
90C2×C79#53611yescharacteristic
91C2×C79#56314yes—
92#2817—791nomaximal, Sylow
93C79#281711yescharacteristic, complemented, Sylow
94C2×C22⋊Q8—791no—
95C2×C22⋊Q8D7911yescharacteristic
96#400—792no—
97#400—792no—
98#397—794no—
99#395—792no—
100#395—792no—
101#381—791no—
102C22×Q8—791no—
103C22×Q8C2×D7911yescharacteristic
104C23×C4C2×D7911yescharacteristic
105C22⋊Q8—24no—
106C22⋊Q8—1584no—
107C2×C4⋊C4—794no—
108C2×C4⋊C4—792no—
109C2×C4⋊C4—791no—
110C2×C4⋊C4C2×D7912yes—
111C2×C4⋊C4C2×D7911yescharacteristic
112C2×C22⋊C4—792no—
113C2×C22⋊C4—792no—
114C2×C22⋊C4C2×D7912yes—
115#95—792no—
116#95—792no—
117#95—794no—
118#95—794no—
119#95—794no—
120C24C22×D7911yescharacteristic
121C2×Q8—22no—
122C2×Q8—42no—
123C2×Q8—3162no—
124C2×Q8—1582no—
125C22×C4—42no—
126C22×C4—794no—
127C22×C4—792no—
128C22×C4—792no—
129C22×C4C22⋊D7914yes—
130C22×C4C22×D7912yes—
131C22×C4C22×D7912yes—
132C22×C4C22×D7911yescharacteristic
133C22×C4C22×D7911yescharacteristic
134C4⋊C4—22no—
135C4⋊C4—24no—
136C4⋊C4—3164no—
137C4⋊C4—1584no—
138C4⋊C4—1582no—
139C22⋊C4—24no—
140C22⋊C4—3162no—
141C22⋊C4—1584no—
142C23—22no—
143C23—22no—
144C23—22no—
145C23C2×C22⋊D7912yes—
146C23C23×D7911yescharacteristic
147Q8—44no—
148Q8—3164no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—24no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—44no—
156C2×C4—1584no—
157C2×C4—1584no—
158C2×C4—1584no—
159C2×C4—1584no—
160C2×C4—1584no—
161C2×C4—1582no—
162C2×C4—1582no—
163C2×C4C2×C22⋊D7912yes—
164C2×C4C2×C22⋊D7912yes—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—44no—
169C22C22×C22⋊D7911yescharacteristic
170C22#1457920612yes—
171C22#1457920812yes—
172C22#1457920912yes—
173C4—22no—
174C4—22no—
175C4—42no—
176C4—42no—
177C4—3162no—
178C4—3164no—
179C4—3162no—
180C2—42no—
181C2#1909912211yescharacteristic
182C2#1909913411yescharacteristic
183C2#1909913711yescharacteristic
184C2#1909931414yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×C22⋊Q8×C79C2
prime radicalC24×C79C23
hypercenterC2×C22⋊Q8D79
hypocenterC79#2817
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #19098502C2semidirect
3. #19098501C2semidirect
5. #19098483C2semidirect
6. #19098482C2semidirect
93. C79#2817semidirect