Finite Group Databasebeta

← #23763858

Subgroups — #23763858

Order 10112.

378 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14579144C211yesmaximal, characteristic
2C2×#14579075C212yesmaximal
3#19098426C211yesmaximal, characteristic, complemented
4#19098329C212yesmaximal, complemented
5C2×#117×C79C211yesmaximal, characteristic, complemented
6C22×C22⋊D79C2211yescharacteristic
7#14579144—21no—
8#14579144—21no—
9#14579144—22no—
10C2×Dic79⋊C4C412yescomplemented
11C2×C22⋊Dic79C2212yes—
12C2×C22⋊Dic79C2211yescharacteristic
13C2×(C2×D79)⋊C4C412yescomplemented
14#14579075—24no—
15C79⋊#95—22no—
16C23×C4×C79C2211yescharacteristic
17#117×C79—24no—
18C2×C4⋊C4×C79—21no—
19C2×C22⋊C4×C79C2212yes—
20C2×C42×C79—21no—
21C23×D79C2×C411yescharacteristic
22C2×C22⋊D79—22no—
23C2×C22⋊D79—21no—
24C2×C22⋊D79—21no—
25C2×C22⋊D79—22no—
26C22×Dic79—22no—
27C22×Dic79C2×C411yescharacteristic
28C22×Dic79C2×C412yes—
29Dic79⋊C4—22no—
30Dic79⋊C4—22no—
31C22⋊Dic79—21no—
32C22⋊Dic79—21no—
33C22⋊Dic79—22no—
34C22⋊Dic79—22no—
35(C2×D79)⋊C4—22no—
36(C2×D79)⋊C4—22no—
37C24×C79C2311yescharacteristic
38C22×C4×C79—22no—
39C22×C4×C79—22no—
40C22×C4×C79—22no—
41C22×C4×C79C2×C412yes—
42C22×C4×C79D411yescharacteristic
43C22×C4×C79D411yescharacteristic
44C22×C4×C79D412yes—
45C4⋊C4×C79—24no—
46C22⋊C4×C79—22no—
47C22⋊C4×C79D414yes—
48C42×C79—24no—
49C23×C79—42no—
50C23×C79C22×C411yescharacteristic
51C23×C79C2×D411yescharacteristic
52C23×C79C2×D412yes—
53C23×C79C2×D411yescharacteristic
54C23×C79#4112yes—
55C22×D79—21no—
56C22×D79—22no—
57C22×D79—42no—
58C2×C4×C79—24no—
59C2×C4×C79—21no—
60C2×C4×C79—21no—
61C2×C4×C79—24no—
62C2×C4×C79—21no—
63C2×C4×C79—21no—
64C2×C4×C79—24no—
65C2×C4×C79—44no—
66C2×C4×C79C22⋊C412yes—
67C2×C4×C79C22⋊C412yes—
68C22⋊D79—41no—
69C22⋊D79—42no—
70C22⋊D79—41no—
71C2×Dic79—22no—
72C2×Dic79—21no—
73C2×Dic79—22no—
74C2×Dic79—42no—
75C2×Dic79—44no—
76C2×Dic79—42no—
77C22×C79—22no—
78C22×C79—22no—
79C22×C79—22no—
80C22×C79—42no—
81C22×C79—42no—
82C22×C79C2×C22⋊C411yescharacteristic
83C22×C79C4×D412yes—
84C22×C79#12011yescharacteristic
85C22×C79#12112yes—
86C22×C79#12311yescharacteristic
87C2×D79—41no—
88C2×D79—42no—
89C2×D79—82no—
90C4×C79—22no—
91C4×C79—22no—
92C4×C79—44no—
93Dic79—41no—
94Dic79—42no—
95Dic79—82no—
96C2×C79—22no—
97C2×C79—21no—
98C2×C79—22no—
99C2×C79—21no—
100C2×C79#38611yescharacteristic
101C2×C79#41012yes—
102D79—81no—
103#1899—791nomaximal, Sylow
104C79#189911yescharacteristic, complemented, Sylow
105C2×#123—791no—
106C2×#117D7911yescharacteristic, complemented
107C2×#99—792no—
108#381—791no—
109#342—792no—
110C22×D4—791no—
111C23×C4C2×D7911yescharacteristic
112#123—1581no—
113#123—1581no—
114#123—1582no—
115#117—24no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—792no—
118C2×C22⋊C4—791no—
119C2×C22⋊C4—792no—
120C2×C22⋊C4—792no—
121C2×C22⋊C4C2×D7912yes—
122C2×C42—21no—
123#99—1584no—
124#95—1582no—
125C24—791no—
126C24C22×D7911yescharacteristic
127C2×D4—1582no—
128C2×D4—1581no—
129C2×D4—1581no—
130C2×D4—1582no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—792no—
135C22×C4—791no—
136C22×C4—1582no—
137C22×C4C4×D7912yes—
138C22×C4D31612yes—
139C22×C4C22⋊D7911yescharacteristic
140C22×C4C22⋊D7911yescharacteristic
141C4⋊C4—24no—
142C4⋊C4—1582no—
143C4⋊C4—1582no—
144C22⋊C4—22no—
145C22⋊C4—1582no—
146C22⋊C4—1582no—
147C22⋊C4—1581no—
148C22⋊C4—1581no—
149C22⋊C4—1582no—
150C22⋊C4—1582no—
151C22⋊C4C22⋊D7914yes—
152C42—24no—
153C23—42no—
154C23—3162no—
155C23—1581no—
156C23—1582no—
157C23C2×C4×D7911yescharacteristic
158C23C2×C22⋊D7911yescharacteristic
159C23C2×C22⋊D7912yes—
160C23C2×D31611yescharacteristic
161C23#1192962412yes—
162D4—3161no—
163D4—3162no—
164D4—3161no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—24no—
172C2×C4—44no—
173C2×C4—3162no—
174C2×C4—3164no—
175C2×C4—3162no—
176C2×C4—1582no—
177C2×C4—1581no—
178C2×C4—1582no—
179C2×C4(C2×D79)⋊C412yes—
180C2×C4(C2×D79)⋊C412yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—3161no—
187C22—3162no—
188C22—6322no—
189C22C2×(C2×D79)⋊C411yescharacteristic
190C22C4×C22⋊D7912yes—
191C22#1457913011yescharacteristic
192C22#1457913512yes—
193C22#1457914411yescharacteristic
194C4—22no—
195C4—22no—
196C4—44no—
197C4—3161no—
198C4—3162no—
199C4—6322no—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2—6321no—
205C2#1909844211yescharacteristic
206C2#1909853612yes—
subgroupG/H
centerC22C2×(C2×D79)⋊C4
commutatorC23×C79C22×C4
FrattiniC24C22×D79
FittingC2×#117×C79C2
socleC22×C79C2×C22⋊C4
prime radicalC22×C22⋊D79C22
cosocleC24×C79C23
hypercenterC2×#117D79
hypocenterC79#1899
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #19098426C2semidirect
4. #19098329C2semidirect
5. C2×#117×C79C2semidirect
10. C2×Dic79⋊C4C4semidirect
13. C2×(C2×D79)⋊C4C4semidirect
104. C79#1899semidirect
106. C2×#117D79semidirect