Finite Group Databasebeta

← #23766708

Subgroups — #23766708

Order 10112.

400 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 161 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#19098505C212yesmaximal
2#19098502C212yesmaximal
3#19098496C212yesmaximal
4#19098495C212yesmaximal
5C4×Dic79⋊C4C212yesmaximal
6C4×C4⋊Dic79C212yesmaximal
7C4×C4⋊Dic79C211yesmaximal, characteristic
8#19098409C211yesmaximal, characteristic
9C4×C4⋊C4×C79C211yesmaximal, characteristic
10C2×C4⋊Dic79C2212yes—
11C2×C4⋊Dic79C2212yes—
12C2×C4⋊Dic79C2212yes—
13C2×Dic79⋊C4C2212yes—
14C2×Dic79⋊C4C2212yes—
15C2×C4×Dic79C2211yescharacteristic
16C2×C4×Dic79C2211yescharacteristic
17C2×C4×Dic79C2212yes—
18C79⋊#95C2212yes—
19C79⋊#95C2212yes—
20C79⋊#95C2211yescharacteristic
21C79⋊#95C2212yes—
22C79⋊#95C2211yescharacteristic
23C79⋊#95C2212yes—
24C79⋊#95C2212yes—
25C79⋊#95C2212yes—
26C2×C4⋊C4×C79C2212yes—
27C2×C42×C79C2212yes—
28C2×C42×C79C2211yescharacteristic
29#95×C79C2211yescharacteristic
30#95×C79C2211yescharacteristic
31C22×Dic79C2312yes—
32C22×Dic79C2312yes—
33C22×Dic79C2312yes—
34C22×Dic79C2312yes—
35C4⋊Dic79—24no—
36C4⋊Dic79—24no—
37C4⋊Dic79—24no—
38Dic79⋊C4—24no—
39Dic79⋊C4—24no—
40C4×Dic79—22no—
41C4×Dic79—24no—
42C4×Dic79—22no—
43C22×C4×C79C2312yes—
44C22×C4×C79C2311yescharacteristic
45C22×C4×C79C2311yescharacteristic
46C22×C4×C79C2312yes—
47C22×C4×C79C2311yescharacteristic
48C4⋊C4×C79—24no—
49C42×C79—24no—
50C42×C79Q814yes—
51C23×C79C2411yescharacteristic
52C2×C4×C79—22no—
53C2×C4×C79—22no—
54C2×C4×C79—22no—
55C2×C4×C79—22no—
56C2×C4×C79—22no—
57C2×C4×C79—22no—
58C2×C4×C79—22no—
59C2×C4×C79C2×Q812yes—
60C2×C4×C79C2×Q812yes—
61C2×C4×C79C2×Q812yes—
62C2×C4×C79#4112yes—
63C2×C4×C79#4114yes—
64C2×C4×C79#4112yes—
65C2×Dic79—22no—
66C2×Dic79—22no—
67C2×Dic79—22no—
68C2×Dic79—22no—
69C2×Dic79—22no—
70C2×Dic79—22no—
71C2×Dic79—22no—
72C2×Dic79—22no—
73C2×Dic79—22no—
74C2×Dic79—22no—
75C2×Dic79—22no—
76C2×Dic79#4114yes—
77C22×C79C22×Q811yescharacteristic
78C22×C79C2×#4112yes—
79C22×C79C2×#4111yescharacteristic
80C22×C79C2×#4112yes—
81C22×C79C2×#4111yescharacteristic
82C4×C79—24no—
83C4×C79—22no—
84C4×C79—22no—
85C4×C79—42no—
86C4×C79#12514yes—
87Dic79—24no—
88Dic79—42no—
89Dic79—42no—
90Dic79—42no—
91C2×C79C2×#12511yescharacteristic
92C2×C79#52912yes—
93C2×C79#52912yes—
94C2×C79#53311yescharacteristic
95C2×C79#53311yescharacteristic
96#2402—791nomaximal, Sylow
97C79#240211yescharacteristic, complemented, Sylow
98#400—792no—
99#400—792no—
100#398—792no—
101#398—792no—
102C4×C4⋊C4—791no—
103C4×C4⋊C4—792no—
104C4×C4⋊C4—792no—
105C4×C4⋊C4D7911yescharacteristic
106#376—791no—
107C2×C4⋊C4—792no—
108C2×C4⋊C4—792no—
109C2×C4⋊C4—792no—
110C2×C4⋊C4—792no—
111C2×C4⋊C4—792no—
112C2×C4⋊C4C2×D7912yes—
113C2×C42—791no—
114C2×C42—791no—
115C2×C42—792no—
116C2×C42C2×D7912yes—
117C2×C42C2×D7911yescharacteristic
118#95—792no—
119#95—792no—
120#95—791no—
121#95—792no—
122#95—792no—
123#95—792no—
124#95—792no—
125#95—791no—
126#95C2×D7911yescharacteristic
127#95C2×D7911yescharacteristic
128C22×C4—792no—
129C22×C4—792no—
130C22×C4—792no—
131C22×C4—792no—
132C22×C4C22×D7912yes—
133C22×C4C22×D7911yescharacteristic
134C22×C4C22×D7911yescharacteristic
135C22×C4C22×D7912yes—
136C22×C4C22×D7911yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—1584no—
139C4⋊C4—1584no—
140C4⋊C4—1584no—
141C4⋊C4—1584no—
142C4⋊C4—1584no—
143C42—24no—
144C42—1582no—
145C42—1582no—
146C42—1584no—
147C42Dic15814yes—
148C23C23×D7911yescharacteristic
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—794no—
157C2×C4—1582no—
158C2×C4—1582no—
159C2×C4—1582no—
160C2×C4—1582no—
161C2×C4—1582no—
162C2×C4—1582no—
163C2×C4—1582no—
164C2×C4—1582no—
165C2×C4—1582no—
166C2×C4—1582no—
167C2×C4—1582no—
168C2×C4C2×Dic15812yes—
169C2×C4C2×Dic15812yes—
170C2×C4C2×Dic15812yes—
171C2×C4#1192962312yes—
172C2×C4#1192962414yes—
173C2×C4#1192962512yes—
174C22C22×Dic15811yescharacteristic
175C22#41×D7912yes—
176C22C2×#1192962311yescharacteristic
177C22C2×#1192962412yes—
178C22C2×#1192962511yescharacteristic
179C4—24no—
180C4—22no—
181C4—22no—
182C4—42no—
183C4—3162no—
184C4—3162no—
185C4—3162no—
186C4—1584no—
187C4#1457915214yes—
188C2C2×#1457915211yescharacteristic
189C2#1909909312yes—
190C2#1909910012yes—
191C2#1909911611yescharacteristic
192C2#1909912011yescharacteristic
subgroupG/H
centerC22×C4C22×D79
commutator, socle, prime radical, cosocleC23×C79C24
FrattiniC23C23×D79
FittingC4×C4⋊C4×C79C2
hypercenterC4×C4⋊C4D79
hypocenterC79#2402
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
97. C79#2402semidirect