Finite Group Databasebeta

← #37549038

Subgroups — #37549038

Order 23168.

234 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 64 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×C4⋊#13089685C211yesmaximal, characteristic, complemented
2C4×#15668458C211yesmaximal, characteristic, complemented
3Q8⋊#13089685C212yesmaximal, complemented
4#26042127C212yesmaximal, complemented
5#26041815C211yesmaximal, characteristic
6C2×#15668458—21no—
7C22×#13089685—21no—
8C4⋊#13089685—21no—
9C4⋊#13089685C2212yes—
10#19153871—21no—
11C4×#13089685C2212yes—
12#19153811—21no—
13#19153807C411yescharacteristic
14#19153805C411yescharacteristic
15#19153800—21no—
16#19153790C411yescharacteristic
17Q8×Dic181C2211yescharacteristic
18#19153778C2211yescharacteristic
19#19153776—21no—
20#19153774—21no—
21C2×C4×Dic181C2211yescharacteristic
22C22⋊Q8×C181C411yescharacteristic
23#15668458—24no—
24C2×#13089685—22no—
25C2×#13089685—22no—
26C2×#13089685—42no—
27C2×D724C2×C411yescharacteristic
28C2×C22⋊D181—21no—
29C22×Dic181D411yescharacteristic
30C22×Dic181D411yescharacteristic
31C2×C4×D181—21no—
32C4⋊Dic181—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181C2×C411yescharacteristic
35#15668428—21no—
36#15668426—21no—
37#15668426—21no—
38#15668426—21no—
39#15668426—21no—
40C4×Dic181—21no—
41C4×Dic181C2×C411yescharacteristic
42C4×Dic181D411yescharacteristic
43C4×Dic181D411yescharacteristic
44C4×Dic181C2311yescharacteristic
45C2×Q8×C181C2×C411yescharacteristic
46C22×C4×C181C2×C411yescharacteristic
47C4⋊C4×C181—21no—
48C4⋊C4×C181C2×C411yescharacteristic
49C22⋊C4×C181—21no—
50#13089685—24no—
51#13089685—42no—
52C22×D181—21no—
53D724—22no—
54C22⋊D181—42no—
55C2×Dic181—22no—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C2×Dic181—21no—
59C2×Dic181C22⋊C411yescharacteristic
60C2×Dic181C22⋊C411yescharacteristic
61C2×Dic181C2×D411yescharacteristic
62C2×Dic181C2×D411yescharacteristic
63C4×D181—41no—
64C4×D181—41no—
65C23×C181C22⋊C411yescharacteristic
66Q8×C181—22no—
67C2×C4×C181—22no—
68C2×C4×C181—21no—
69C2×C4×C181—21no—
70C2×C4×C181C22⋊C411yescharacteristic
71C2×C4×C181C22×C411yescharacteristic
72C22×C181—21no—
73C22×C181—21no—
74C22×C181#10412yes—
75C22×C181C2×C22⋊C411yescharacteristic
76C2×D181—41no—
77C2×D181—41no—
78C2×D181—41no—
79C4×C181—21no—
80C4×C181—41no—
81C4×C181—41no—
82C4×C181#13112yes—
83Dic181—21no—
84Dic181—21no—
85Dic181—21no—
86Dic181—41no—
87Dic181AGL(1,ℤ/8)11yescharacteristic
88Dic181#13711yescharacteristic
89C2×C181—22no—
90C2×C181#40811yescharacteristic
91C2×C181#41711yescharacteristic
92C2×C181C2×#10411yescharacteristic
93D181—81no—
94C181#148311yescharacteristic, complemented, Sylow
95#1483—1811nomaximal, Sylow
96#529—1811no—
97C2×C4⋊C8—1811no—
98C4×M16—1811no—
99Q8⋊C8—1812no—
100D4⋊C8—1812no—
101C2×M16—3621no—
102C22×C8—3621no—
103#126—3621no—
104#125—1811no—
105#124—1811no—
106#123—3621no—
107C22⋊Q8#1062438211yescharacteristic
108#121—1811no—
109C4×Q8—1811no—
110C4×D4—3621no—
111C4×D4—1811no—
112#117—3621no—
113C2×C42—1811no—
114C4⋊C8—3621no—
115C4⋊C8—1812no—
116#97—3621no—
117C4×C8—1812no—
118C2×Q8C2×#1062438211yescharacteristic
119C2×D4—3621no—
120C2×D4—1811no—
121C22×C4—3621no—
122C22×C4—1811no—
123C22×C4—1811no—
124C22×C4C2×#1062438211yescharacteristic
125M16—3624no—
126C2×C8—3622no—
127C2×C8—3622no—
128C2×C8—7242no—
129C4⋊C4—21no—
130C4⋊C4—3621no—
131C4⋊C4—3621no—
132C4⋊C4—3621no—
133C4⋊C4—1811no—
134C4⋊C4C2×#1062438211yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—3621no—
137C22⋊C4—3621no—
138C22⋊C4—3621no—
139C22⋊C4—3621no—
140C42—3621no—
141C42—1811no—
142C42—1811no—
143C42—1811no—
144C42—1811no—
145C23—3621no—
146C23C22⋊#1062438211yescharacteristic
147Q8—22no—
148D4—3622no—
149D4—7242no—
150C2×C4—22no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—3622no—
154C2×C4—3621no—
155C2×C4—3621no—
156C2×C4—3621no—
157C2×C4—1811no—
158C2×C4—1811no—
159C2×C4—1811no—
160C2×C4—1811no—
161C2×C4—7241no—
162C2×C4—7241no—
163C2×C4C22⋊#1062438211yescharacteristic
164C2×C4C22×#1062438211yescharacteristic
165C8—3624no—
166C8—7242no—
167C22—21no—
168C22—21no—
169C22—7241no—
170C22—7241no—
171C22—7241no—
172C22#1915388112yes—
173C22C2×C22⋊#1062438211yescharacteristic
174C4—21no—
175C4—41no—
176C4—41no—
177C4—3621no—
178C4—3621no—
179C4—3621no—
180C4—1811no—
181C4—1811no—
182C4—7241no—
183C4#1915390312yes—
184C2—22no—
185C2—14481no—
186C2#2604225211yescharacteristic
187C2#2604227011yescharacteristic
188C2C2×#1915388111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC22⋊Q8×C181C4
socleC22×C181C2×C22⋊C4
prime radical#19153790C4
cosocleC4×Dic181C23
hypercenterC22⋊Q8#10624382
hypocenterC181#1483
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#13089685C2semidirect
2. C4×#15668458C2semidirect
3. Q8⋊#13089685C2semidirect
4. #26042127C2semidirect
94. C181#1483semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4⋊#130896852
C4×#156684582
Q8⋊#130896852
#260421272
#260418152
#1483181