Finite Group Databasebeta

← #23762399

Subgroups — #23762399

Order 10112.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#19099160C211yesmaximal, characteristic
2#19098894C211yesmaximal, characteristic, complemented
3#19098877C211yesmaximal, characteristic
4#19098493C211yesmaximal, characteristic, complemented
5#19098301C211yesmaximal, characteristic, complemented
6#19098298C211yesmaximal, characteristic
7#324×C79C211yesmaximal, characteristic, complemented
8#14579156—21no—
9#14579151—21no—
10#14579146—21no—
11#14579144—21no—
12#14579140C2211yescharacteristic
13#14579139—21no—
14#14579135C2211yescharacteristic
15C4×C22⋊D79—21no—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4—21no—
18#14579095—21no—
19#14579093—21no—
20#14579086—21no—
21#14579083—21no—
22C79⋊#95—21no—
23C79⋊#95C2211yescharacteristic
24C2×C4⋊C4×C79C2211yescharacteristic
25C22⋊C8×C79C2211yescharacteristic
26C22⋊C8×C79C2211yescharacteristic
27C2×Dic158D411yescharacteristic
28C2×D316D411yescharacteristic
29C2×C22⋊D79—21no—
30C22×Dic79—21no—
31C22×Dic79—21no—
32C2×C4×D79—21no—
33C4⋊Dic79—21no—
34C4⋊Dic79—21no—
35C4⋊Dic79D411yescharacteristic
36C4⋊Dic79D411yescharacteristic
37Dic79⋊C4—21no—
38Dic79⋊C4—21no—
39Dic79⋊C4—21no—
40Dic79⋊C4—21no—
41Dic79⋊C4—42no—
42C22⋊Dic79—21no—
43(C2×D79)⋊C4—21no—
44(C2×D79)⋊C4—21no—
45(C2×D79)⋊C4—21no—
46(C2×D79)⋊C4—21no—
47C4×Dic79—21no—
48C22×C4×C79D411yescharacteristic
49C22×C4×C79D411yescharacteristic
50C22×C4×C79C2311yescharacteristic
51C2×C8×C79—21no—
52C2×C8×C79—21no—
53C4⋊C4×C79—21no—
54C4⋊C4×C79—21no—
55C23×C79C2×D411yescharacteristic
56C22×D79—21no—
57C2×C4×C79—21no—
58C2×C4×C79—21no—
59C2×C4×C79—21no—
60C2×C4×C79—21no—
61C2×C4×C79—41no—
62C2×C4×C79—41no—
63C2×C4×C79C2×D411yescharacteristic
64C2×C4×C79C2×D411yescharacteristic
65C22⋊D79—41no—
66C22⋊D79—41no—
67C2×Dic79—22no—
68C2×Dic79—21no—
69C2×Dic79—21no—
70C2×Dic79—21no—
71C2×Dic79—41no—
72C2×Dic79—41no—
73C2×Dic79—41no—
74C2×Dic79—41no—
75C2×Dic79—41no—
76D316—41no—
77C4×D79—81no—
78Dic158—41no—
79C8×C79—41no—
80C8×C79—41no—
81C22×C79—21no—
82C22×C79—21no—
83C22×C79#12011yescharacteristic
84C22×C79#13511yescharacteristic
85C22×C79AGL(1,ℤ/8)11yescharacteristic
86C2×D79—41no—
87C2×D79—41no—
88C2×D79—41no—
89C4×C79—21no—
90C4×C79—21no—
91C4×C79—41no—
92C4×C79—41no—
93Dic79—42no—
94Dic79—41no—
95Dic79—41no—
96Dic79—41no—
97Dic79—81no—
98C2×C79—21no—
99C2×C79—21no—
100C2×C79#44911yescharacteristic
101C2×C79#45611yescharacteristic
102C2×C79#45811yescharacteristic
103D79—81no—
104#1609—791nomaximal, Sylow
105C79#160911yescharacteristic, complemented, Sylow
106#539—791no—
107#483—791no—
108#480—791no—
109#398—791no—
110#328—791no—
111#327—791no—
112#324D7911yescharacteristic, complemented
113#126—1581no—
114#125—1581no—
115#123—1581no—
116#123—1581no—
117C22⋊Q8—791no—
118C22⋊Q8—1581no—
119#121—791no—
120C4×D4—1581no—
121C2×C4⋊C4—791no—
122C2×C4⋊C4—1581no—
123C2×C4⋊C4C2×D7911yescharacteristic
124#107—1581no—
125#106—1581no—
126#103—1581no—
127#102—1581no—
128C22⋊C8C2×D7911yescharacteristic
129C22⋊C8C2×D7911yescharacteristic
130#95—791no—
131#95—1581no—
132C2×Q8—791no—
133C2×D4—791no—
134C2×D4—1581no—
135C22×C4—1581no—
136C22×C4—1581no—
137C22×C4—1581no—
138C22×C4D31611yescharacteristic
139C22×C4D31611yescharacteristic
140C22×C4C22×D7911yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—3162no—
146C4⋊C4—791no—
147C4⋊C4—791no—
148C4⋊C4—1581no—
149C4⋊C4—1581no—
150C4⋊C4—1581no—
151C4⋊C4—1581no—
152C4⋊C4—1581no—
153C4⋊C4—1581no—
154C22⋊C4—1581no—
155C22⋊C4—1581no—
156C22⋊C4—1581no—
157C22⋊C4—1581no—
158C22⋊C4—1581no—
159C42—1581no—
160C23—1581no—
161C23C2×D31611yescharacteristic
162Q8—3161no—
163D4—3161no—
164D4—3161no—
165D4—3161no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—3161no—
173C2×C4—3161no—
174C2×C4—3161no—
175C2×C4—3161no—
176C2×C4—3161no—
177C2×C4—6321no—
178C2×C4—1582no—
179C2×C4—1581no—
180C2×C4—1581no—
181C2×C4—1581no—
182C2×C4D4×D7911yescharacteristic
183C2×C4D4×D7911yescharacteristic
184C8—41no—
185C8—41no—
186C22—21no—
187C22—21no—
188C22—3161no—
189C22—3161no—
190C22—3161no—
191C22#1457913111yescharacteristic
192C22#1457918311yescharacteristic
193C22#1457918911yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—3162no—
199C4—3161no—
200C4—3161no—
201C4—3161no—
202C4—6321no—
203C2—21no—
204C2—21no—
205C2—6321no—
206C2#1909871011yescharacteristic
207C2#1909874811yescharacteristic
208C2#1909875411yescharacteristic
subgroupG/H
centerC22#14579131
commutator, cosocleC22×C4×C79C23
FrattiniC22×C4C22×D79
Fitting#324×C79C2
socleC22×C79#120
prime radical#14579135C22
hypercenter#324D79
hypocenterC79#1609
LCSG ▷ C22×C4×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #19098894C2semidirect
4. #19098493C2semidirect
5. #19098301C2semidirect
7. #324×C79C2semidirect
105. C79#1609semidirect
112. #324D79semidirect