Finite Group Databasebeta

← #2007×C181 #37529950

Subgroups — #2007×C181 #37529950

Order 23168.

370 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 92 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×#137×C181C212yesmaximal, complemented
2#537×C181C211yesmaximal, characteristic
3C2×#104×C181C212yesmaximal, complemented
4#391×C181C211yesmaximal, characteristic, complemented
5#343×C181C211yesmaximal, characteristic, complemented
6C2×#41×C181C2212yes—
7C22×Q8×C181C2211yescharacteristic
8#137×C181—24no—
9#137×C181—24no—
10C2×Q16×C181—22no—
11C2×SD16×C181—22no—
12C2×M16×C181C2212yes—
13C22⋊Q8×C181—22no—
14#121×C181—22no—
15#121×C181—22no—
16C2×C4⋊C4×C181C2211yescharacteristic
17C2×C42×C181C2211yescharacteristic
18#104×C181—24no—
19#95×C181—22no—
20#41×C181—22no—
21#41×C181—22no—
22#41×C181—22no—
23#41×C181—22no—
24C2×Q8×C181—21no—
25C2×Q8×C181—22no—
26C2×Q8×C181—22no—
27C2×Q8×C181D412yes—
28C2×Q8×C181D412yescomplemented
29C2×D4×C181—22no—
30C2×D4×C181—22no—
31C2×D4×C181D412yes—
32C22×C4×C181—21no—
33C22×C4×C181—21no—
34C22×C4×C181—22no—
35C22×C4×C181D412yes—
36C22×C4×C181C2311yescharacteristic
37Q16×C181—28no—
38SD16×C181—28no—
39M16×C181—22no—
40M16×C181D414yescomplemented
41C2×C8×C181—22no—
42C4⋊C4×C181—22no—
43C4⋊C4×C181—22no—
44C22⋊C4×C181—24no—
45C42×C181—22no—
46C23×C181—22no—
47C23×C181C2×D411yescharacteristic
48Q8×C181—24no—
49Q8×C181—22no—
50Q8×C181—22no—
51Q8×C181—42no—
52D4×C181—22no—
53D4×C181—22no—
54D4×C181—42no—
55D4×C181—42no—
56D4×C181—82no—
57C2×C4×C181—22no—
58C2×C4×C181—22no—
59C2×C4×C181—22no—
60C2×C4×C181—22no—
61C2×C4×C181—41no—
62C2×C4×C181—41no—
63C2×C4×C181—41no—
64C2×C4×C181—41no—
65C2×C4×C181—42no—
66C2×C4×C181—42no—
67C2×C4×C181—42no—
68C2×C4×C181C2×D411yescharacteristic
69C2×C4×C181C2×D412yes—
70C2×C4×C181C2×D412yes—
71C2×C4×C181#4111yescharacteristic
72C8×C181—24no—
73C22×C181—21no—
74C22×C181—21no—
75C22×C181—42no—
76C22×C181—42no—
77C22×C181—42no—
78C22×C181#12011yescharacteristic
79C22×C181#12111yescharacteristic
80C22×C181#12711yescharacteristic
81C4×C181—42no—
82C4×C181—42no—
83C4×C181—42no—
84C4×C181—42no—
85C4×C181#12012yes—
86C4×C181#12112yes—
87C2×C181—21no—
88C2×C181—21no—
89C2×C181—82no—
90C2×C181#39211yescharacteristic
91C2×C181#45511yescharacteristic
92C2×C181#45611yescharacteristic
93C181#200711yescharacteristic, direct product factor, Sylow
94#2007C18111yesmaximal, characteristic, direct product factor, Sylow
95C2×#137C2×C18112yescomplemented
96#537C2×C18111yescharacteristic
97C2×#104C2×C18112yescomplemented
98#391C2×C18111yescharacteristic, complemented
99#343C2×C18111yescharacteristic, complemented
100C2×#41C22×C18112yes—
101C22×Q8C22×C18111yescharacteristic
102#137—24no—
103#137—24no—
104C2×Q16—22no—
105C2×SD16—22no—
106C2×M16C22×C18112yes—
107C22⋊Q8—22no—
108#121—22no—
109#121—22no—
110C2×C4⋊C4C22×C18111yescharacteristic
111C2×C42C22×C18111yescharacteristic
112#104—24no—
113#95—22no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8D4×C18112yes—
122C2×Q8D4×C18112yescomplemented
123C2×D4—22no—
124C2×D4—22no—
125C2×D4D4×C18112yes—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—22no—
129C22×C4D4×C18112yes—
130C22×C4C23×C18111yescharacteristic
131Q16—28no—
132SD16—28no—
133M16—22no—
134M16D4×C18114yescomplemented
135C2×C8—22no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C22⋊C4—24no—
139C42—22no—
140C23—22no—
141C23C2×D4×C18111yescharacteristic
142Q8—24no—
143Q8—22no—
144Q8—22no—
145Q8—42no—
146D4—22no—
147D4—22no—
148D4—42no—
149D4—42no—
150D4—82no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4C2×D4×C18111yescharacteristic
163C2×C4C2×D4×C18112yes—
164C2×C4C2×D4×C18112yes—
165C2×C4#41×C18111yescharacteristic
166C8—24no—
167C22—21no—
168C22—21no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22#120×C18111yescharacteristic
173C22#121×C18111yescharacteristic
174C22#127×C18111yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—42no—
179C4#120×C18112yes—
180C4#121×C18112yes—
181C2—21no—
182C2—21no—
183C2—82no—
184C2#392×C18111yescharacteristic
185C2#455×C18111yescharacteristic
186C2#456×C18111yescharacteristic
subgroupG/H
center, socleC22×C181#120
commutator, Frattini, cosocleC22×C4C23×C181
prime radical#537×C181C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C181 ◁ C22×C4×C181 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#137×C181C2semidirect
3. C2×#104×C181C2semidirect
4. #391×C181C2semidirect
5. #343×C181C2semidirect
28. C2×Q8×C181D4semidirect
40. M16×C181D4semidirect
93. C181#2007direct (N × H)
94. #2007C181direct (N × H)
95. C2×#137C2×C181semidirect
97. C2×#104C2×C181semidirect
98. #391C2×C181semidirect
99. #343C2×C181semidirect
122. C2×Q8D4×C181semidirect
134. M16D4×C181semidirect

Maximal subgroups

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

subgroupindex
C2×#137×C1812
#537×C1812
C2×#104×C1812
#391×C1812
#343×C1812
#2007181