Finite Group Databasebeta

← #23762000

Subgroups — #23762000

Order 10112.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#125×D79C211yesmaximal, characteristic
2#19098618C211yesmaximal, characteristic
3#19098515C211yesmaximal, characteristic
4#19098305C211yesmaximal, characteristic, complemented
5#19098304C211yesmaximal, characteristic, complemented
6#19098304C211yesmaximal, characteristic, complemented
7#330×C79C211yesmaximal, characteristic, complemented
8C2×#11929607—21no—
9#14579153C2211yescharacteristic
10#14579152C411yescharacteristic
11#14579152C411yescharacteristic
12#14579151—21no—
13#14579151—21no—
14C4⋊C4×D79—21no—
15C4⋊C4×D79—21no—
16C4⋊C4×D79C411yescharacteristic
17C4⋊C4×D79C411yescharacteristic
18C42×D79C2211yescharacteristic
19Dic79⋊C8—21no—
20(C2×D79)⋊C8—21no—
21#14579072C2211yescharacteristic
22#14579072C2211yescharacteristic
23C8×Dic79—21no—
24#125×C79C2211yescharacteristic
25#97×C79C2211yescharacteristic
26#97×C79C2211yescharacteristic
27C2×C4×D79—21no—
28C2×C4×D79—21no—
29C2×C4×D79C2×C411yescharacteristic
30C2×C4×D79D411yescharacteristic
31C2×C4×D79D411yescharacteristic
32#11929607—24no—
33C2×C79⋊C8—21no—
34C2×C79⋊C8—21no—
35C4⋊Dic79—21no—
36C4⋊Dic79—21no—
37C4⋊Dic79C2×C411yescharacteristic
38C4⋊Dic79C2×C411yescharacteristic
39Dic79⋊C4—21no—
40Dic79⋊C4—21no—
41Dic79⋊C4—21no—
42Dic79⋊C4—21no—
43Dic79⋊C4—21no—
44Dic79⋊C4—21no—
45C4×Dic79C2×C411yescharacteristic
46C4×Dic79D411yescharacteristic
47C4×Dic79D411yescharacteristic
48C2×C8×C79—21no—
49C2×C8×C79—21no—
50C4⋊C4×C79—21no—
51C4⋊C4×C79—21no—
52C4⋊C4×C79C2×C411yescharacteristic
53C4⋊C4×C79C2×C411yescharacteristic
54C42×C79C2311yescharacteristic
55C22×D79C22⋊C411yescharacteristic
56C2×C4×C79—21no—
57C2×C4×C79—21no—
58C2×C4×C79C22×C411yescharacteristic
59C2×C4×C79C2×D411yescharacteristic
60C2×C4×C79C2×D411yescharacteristic
61C2×Dic79—21no—
62C2×Dic79—21no—
63C2×Dic79C22⋊C411yescharacteristic
64C2×Dic79C22⋊C411yescharacteristic
65C2×Dic79C22⋊C411yescharacteristic
66C4×D79—22no—
67C4×D79—22no—
68C4×D79—41no—
69C4×D79—42no—
70C4×D79—42no—
71C8×C79—22no—
72C8×C79—41no—
73C79⋊C8—22no—
74C79⋊C8—41no—
75C22×C79C2×C22⋊C411yescharacteristic
76C2×D79—21no—
77C2×D79—21no—
78C2×D79#10412yes—
79C4×C79—21no—
80C4×C79—21no—
81C4×C79—21no—
82C4×C79—41no—
83C4×C79—41no—
84Dic79—21no—
85Dic79—21no—
86Dic79—41no—
87Dic79—41no—
88Dic79#10112yes—
89C2×C79C2×#10111yescharacteristic
90C2×C79C2×#10411yescharacteristic
91C2×C79#42111yescharacteristic
92D79—22no—
93#1528—791nomaximal, Sylow
94C79#152811yescharacteristic, complemented, Sylow
95C2×#125—791no—
96#432—791no—
97C4×M16—791no—
98#330—791no—
99#330—791no—
100#330—791no—
101#330D7911yescharacteristic, complemented
102C2×M16—1581no—
103#125—791no—
104#125—791no—
105#125—791no—
106#125—1581no—
107#125—1581no—
108#125C2×D7911yescharacteristic
109C2×C4⋊C4—791no—
110C2×C4⋊C4—791no—
111C2×C4⋊C4—1581no—
112C2×C4⋊C4—1581no—
113C2×C42—791no—
114C4⋊C8—1581no—
115C22⋊C8—1581no—
116#97—791no—
117#97—791no—
118#97C2×D7911yescharacteristic
119#97C2×D7911yescharacteristic
120C4×C8—1581no—
121C22×C4—791no—
122C22×C4—791no—
123C22×C4—791no—
124C22×C4—1581no—
125C22×C4—1581no—
126M16—1584no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—1581no—
130C2×C8—1581no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—791no—
134C4⋊C4—791no—
135C4⋊C4—1581no—
136C4⋊C4—1581no—
137C4⋊C4—1581no—
138C4⋊C4—1581no—
139C4⋊C4—1581no—
140C4⋊C4—1581no—
141C4⋊C4—1581no—
142C4⋊C4—1581no—
143C4⋊C4C4×D7911yescharacteristic
144C4⋊C4C4×D7911yescharacteristic
145C42—791no—
146C42—791no—
147C42—791no—
148C42C22×D7911yescharacteristic
149C23—791no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—3161no—
153C2×C4—3162no—
154C2×C4—3162no—
155C2×C4—791no—
156C2×C4—791no—
157C2×C4—791no—
158C2×C4—1582no—
159C2×C4—1582no—
160C2×C4—1581no—
161C2×C4—1581no—
162C2×C4C2×C4×D7911yescharacteristic
163C2×C4D4×D7911yescharacteristic
164C2×C4D4×D7911yescharacteristic
165C8—22no—
166C8—41no—
167C8—3161no—
168C8—1582no—
169C22—792no—
170C22—1581no—
171C22—1581no—
172C22C22⋊C4×D7911yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—3161no—
179C4—3161no—
180C4—792no—
181C4—1581no—
182C4—1581no—
183C2—1582no—
184C2#101×D7911yescharacteristic
185C2#104×D7911yescharacteristic
186C2#1909857811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D79
commutatorC2×C4×C79C22×C4
FrattiniC42C22×D79
Fitting#330×C79C2
socleC22×C79C2×C22⋊C4
prime radicalC22×D79C22⋊C4
cosocleC42×C79C23
hypercenter#330D79
hypocenterC79#1528
LCSG ▷ C2×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #19098305C2semidirect
5. #19098304C2semidirect
6. #19098304C2semidirect
7. #330×C79C2semidirect
94. C79#1528semidirect
101. #330D79semidirect