Finite Group Databasebeta

← #23761971

Subgroups — #23761971

Order 10112.

288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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
2C2×C22⋊(C79⋊C8)C211yesmaximal, characteristic
3#19098299C214yesmaximal, complemented
4#380×C79C211yesmaximal, characteristic
5C22×Dic158C411yescharacteristic, complemented
6C22×C79⋊C8—21no—
7#14579140—21no—
8#14579140—21no—
9#14579140C412yescomplemented
10#14579140C2212yes—
11C2×C4⋊Dic79C411yescharacteristic, complemented
12C2×Dic79⋊C4—21no—
13C2×C22⋊Dic79—21no—
14C22⋊(C79⋊C8)—21no—
15C22⋊(C79⋊C8)C2212yes—
16C23×C4×C79C2211yescharacteristic
17C2×C4⋊C4×C79—21no—
18C2×C22⋊C4×C79—21no—
19#95×C79C2212yes—
20C2×Dic158—21no—
21C2×Dic158—42no—
22C2×Dic158C2×C412yes—
23C22×Dic79—21no—
24C22×Dic79—21no—
25C2×C79⋊C8—22no—
26C2×C79⋊C8—42no—
27C4⋊Dic79—21no—
28C4⋊Dic79C2×C412yes—
29Dic79⋊C4—22no—
30Dic79⋊C4—22no—
31C22⋊Dic79—22no—
32C22⋊Dic79—22no—
33C24×C79D411yescharacteristic
34C22×C4×C79—22no—
35C22×C4×C79—42no—
36C22×C4×C79C2×C411yescharacteristic
37C22×C4×C79C2×C411yescharacteristic
38C22×C4×C79D411yescharacteristic
39C22×C4×C79D411yescharacteristic
40C22×C4×C79D411yescharacteristic
41C22×C4×C79C2311yescharacteristic
42C4⋊C4×C79—42no—
43C22⋊C4×C79—42no—
44C23×C79—41no—
45C23×C79—41no—
46C23×C79C22⋊C411yescharacteristic
47C23×C79C22⋊C411yescharacteristic
48C23×C79SD1612yes—
49C23×C79Q1612yes—
50C23×C79C2×D411yescharacteristic
51C2×C4×C79—22no—
52C2×C4×C79—22no—
53C2×C4×C79—22no—
54C2×C4×C79—41no—
55C2×C4×C79—41no—
56C2×C4×C79—41no—
57C2×C4×C79—42no—
58C2×C4×C79—42no—
59C2×C4×C79—42no—
60C2×C4×C79C22⋊C411yescharacteristic
61C2×C4×C79C22⋊C411yescharacteristic
62C2×C4×C79C22×C411yescharacteristic
63C2×C4×C79C2×D411yescharacteristic
64C2×Dic79—22no—
65C2×Dic79—22no—
66C2×Dic79—42no—
67C2×Dic79—42no—
68Dic158—42no—
69Dic158—42no—
70C79⋊C8—42no—
71C22×C79—21no—
72C22×C79—21no—
73C22×C79—21no—
74C22×C79—21no—
75C22×C79—21no—
76C22×C79—21no—
77C22×C79—42no—
78C22×C79—42no—
79C22×C79#10312yes—
80C22×C79#10312yes—
81C22×C79C2×C22⋊C411yescharacteristic
82C22×C79C2×SD1611yescharacteristic
83C22×C79C2×Q1611yescharacteristic
84C4×C79—21no—
85C4×C79—21no—
86C4×C79—21no—
87C4×C79—82no—
88C4×C79#9912yes—
89Dic79—42no—
90Dic79—42no—
91C2×C79—21no—
92C2×C79—22no—
93C2×C79—22no—
94C2×C79—21no—
95C2×C79C2×#9911yescharacteristic
96C2×C79C2×#10311yescharacteristic
97C2×C79#42111yescharacteristic
98#1520—791nomaximal, Sylow
99C79#152011yescharacteristic, complemented, Sylow
100C2×C22⋊Q8—791no—
101C2×C22⋊C8—791no—
102#380D7911yescharacteristic
103#328—794no—
104C22×Q8—791no—
105C23×C4C2×D7911yescharacteristic
106C22×C8—1581no—
107C22⋊Q8—792no—
108C22⋊Q8—792no—
109C22⋊Q8—1581no—
110C22⋊Q8—1581no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—791no—
113C2×C4⋊C4—1581no—
114C2×C22⋊C4—21no—
115C2×C22⋊C4—1581no—
116C22⋊C8—792no—
117C22⋊C8—1581no—
118#95C2×D7912yes—
119C24C22⋊D7911yescharacteristic
120C2×Q8—3162no—
121C2×Q8—792no—
122C2×Q8—1581no—
123C22×C4—22no—
124C22×C4—42no—
125C22×C4—1581no—
126C22×C4—1581no—
127C22×C4C4×D7911yescharacteristic
128C22×C4C4×D7911yescharacteristic
129C22×C4D31611yescharacteristic
130C22×C4D31611yescharacteristic
131C22×C4C22⋊D7911yescharacteristic
132C22×C4C22×D7911yescharacteristic
133C2×C8—3162no—
134C2×C8—1582no—
135C4⋊C4—42no—
136C4⋊C4—792no—
137C4⋊C4—1582no—
138C4⋊C4—1581no—
139C4⋊C4—1582no—
140C22⋊C4—42no—
141C22⋊C4—1582no—
142C22⋊C4—1582no—
143C23—41no—
144C23—41no—
145C23(C2×D79)⋊C411yescharacteristic
146C23(C2×D79)⋊C411yescharacteristic
147C23#1192961212yes—
148C23#1192961412yes—
149C23C2×C22⋊D7911yescharacteristic
150Q8—3162no—
151Q8—3162no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—3162no—
162C2×C4—3162no—
163C2×C4—1582no—
164C2×C4—1582no—
165C2×C4(C2×D79)⋊C411yescharacteristic
166C2×C4(C2×D79)⋊C411yescharacteristic
167C2×C4C2×C4×D7911yescharacteristic
168C2×C4C2×D31611yescharacteristic
169C8—3162no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22#1457908412yes—
179C22#1457908412yes—
180C22C2×(C2×D79)⋊C411yescharacteristic
181C22C2×#1192961211yescharacteristic
182C22C2×#1192961411yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—82no—
187C4—3162no—
188C4—3162no—
189C4#1457907512yes—
190C2—21no—
191C2—22no—
192C2—22no—
193C2—21no—
194C2C2×#1457907511yescharacteristic
195C2C2×#1457908411yescharacteristic
196C2#1909858111yescharacteristic
subgroupG/H
centerC22C2×(C2×D79)⋊C4
commutatorC2×C4×C79C22×C4
FrattiniC22×C4C22×D79
Fitting#380×C79C2
socleC22×C79C2×C22⋊C4
prime radicalC24×C79D4
cosocleC22×C4×C79C23
hypercenter#380D79
hypocenterC79#1520
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #19098299C2semidirect
5. C22×Dic158C4semidirect
9. #14579140C4semidirect
11. C2×C4⋊Dic79C4semidirect
99. C79#1520semidirect