Finite Group Databasebeta

← #1664×C181 #37529607

Subgroups — #1664×C181 #37529607

Order 23168.

184 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 60 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#563×C181C211yesmaximal, characteristic
2#501×C181C211yesmaximal, characteristic, complemented
3#491×C181C211yesmaximal, characteristic, complemented
4#489×C181C211yesmaximal, characteristic
5#330×C181C211yesmaximal, characteristic, complemented
6#330×C181C211yesmaximal, characteristic, complemented
7#329×C181C211yesmaximal, characteristic
8C4⋊Q8×C181—21no—
9C4⋊Q8×C181C2211yescharacteristic
10#126×C181—21no—
11#126×C181—21no—
12#125×C181C2211yescharacteristic
13#125×C181C2211yescharacteristic
14#124×C181C2211yescharacteristic
15#123×C181—21no—
16C22⋊Q8×C181—21no—
17C22⋊Q8×C181—21no—
18#107×C181—21no—
19#106×C181—21no—
20#103×C181—21no—
21#103×C181—21no—
22#103×C181—21no—
23#102×C181—21no—
24#97×C181C2211yescharacteristic
25#97×C181C2211yescharacteristic
26#97×C181C2211yescharacteristic
27C2×Q8×C181—21no—
28C2×Q8×C181—21no—
29C2×Q8×C181D411yescharacteristic
30C2×D4×C181D411yescharacteristic
31C22×C4×C181—21no—
32C2×C8×C181—21no—
33C2×C8×C181—21no—
34C2×C8×C181—21no—
35C4⋊C4×C181—21no—
36C4⋊C4×C181—21no—
37C4⋊C4×C181—21no—
38C4⋊C4×C181—21no—
39C4⋊C4×C181—21no—
40C4⋊C4×C181—21no—
41C4⋊C4×C181—21no—
42C4⋊C4×C181—21no—
43C4⋊C4×C181D411yescharacteristic
44C4⋊C4×C181D411yescharacteristic
45C4⋊C4×C181D411yescharacteristic
46C4⋊C4×C181D411yescharacteristic
47C22⋊C4×C181—21no—
48C22⋊C4×C181—21no—
49C22⋊C4×C181—21no—
50C22⋊C4×C181—21no—
51C22⋊C4×C181—21no—
52C42×C181—21no—
53C42×C181C2311yescharacteristic
54C23×C181—21no—
55Q8×C181—41no—
56Q8×C181—42no—
57Q8×C181—81no—
58D4×C181—41no—
59C2×C4×C181—21no—
60C2×C4×C181—21no—
61C2×C4×C181—21no—
62C2×C4×C181—21no—
63C2×C4×C181—21no—
64C2×C4×C181—41no—
65C2×C4×C181—81no—
66C2×C4×C181C2×D411yescharacteristic
67C2×C4×C181C2×D411yescharacteristic
68C2×C4×C181C2×D411yescharacteristic
69C8×C181—22no—
70C8×C181—41no—
71C8×C181—41no—
72C22×C181—41no—
73C22×C181—41no—
74C22×C181—41no—
75C22×C181#12011yescharacteristic
76C4×C181—21no—
77C4×C181—21no—
78C4×C181—21no—
79C4×C181—41no—
80C4×C181—41no—
81C4×C181—41no—
82C4×C181—41no—
83C4×C181—41no—
84C4×C181—81no—
85C2×C181—81no—
86C2×C181#45411yescharacteristic
87C2×C181#45511yescharacteristic
88C2×C181#45611yescharacteristic
89C181#166411yescharacteristic, direct product factor, Sylow
90#1664C18111yesmaximal, characteristic, direct product factor, Sylow
91#563C2×C18111yescharacteristic
92#501C2×C18111yescharacteristic, complemented
93#491C2×C18111yescharacteristic, complemented
94#489C2×C18111yescharacteristic
95#330C2×C18111yescharacteristic, complemented
96#330C2×C18111yescharacteristic, complemented
97#329C2×C18111yescharacteristic
98C4⋊Q8—21no—
99C4⋊Q8C22×C18111yescharacteristic
100#126—21no—
101#126—21no—
102#125C22×C18111yescharacteristic
103#125C22×C18111yescharacteristic
104#124C22×C18111yescharacteristic
105#123—21no—
106C22⋊Q8—21no—
107C22⋊Q8—21no—
108#107—21no—
109#106—21no—
110#103—21no—
111#103—21no—
112#103—21no—
113#102—21no—
114#97C22×C18111yescharacteristic
115#97C22×C18111yescharacteristic
116#97C22×C18111yescharacteristic
117C2×Q8—21no—
118C2×Q8—21no—
119C2×Q8D4×C18111yescharacteristic
120C2×D4D4×C18111yescharacteristic
121C22×C4—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4D4×C18111yescharacteristic
134C4⋊C4D4×C18111yescharacteristic
135C4⋊C4D4×C18111yescharacteristic
136C4⋊C4D4×C18111yescharacteristic
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C42—21no—
143C42C23×C18111yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—42no—
147Q8—81no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—81no—
156C2×C4C2×D4×C18111yescharacteristic
157C2×C4C2×D4×C18111yescharacteristic
158C2×C4C2×D4×C18111yescharacteristic
159C8—22no—
160C8—41no—
161C8—41no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#120×C18111yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—41no—
172C4—41no—
173C4—41no—
174C4—81no—
175C2—81no—
176C2#454×C18111yescharacteristic
177C2#455×C18111yescharacteristic
178C2#456×C18111yescharacteristic
subgroupG/H
center, socleC22×C181#120
commutator, Frattini, cosocleC42C23×C181
prime radicalC2×D4×C181D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C181 ◁ C42×C181 ◁ G

Complements

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

NH ≅ G/Ntype
2. #501×C181C2semidirect
3. #491×C181C2semidirect
5. #330×C181C2semidirect
6. #330×C181C2semidirect
89. C181#1664direct (N × H)
90. #1664C181direct (N × H)
92. #501C2×C181semidirect
93. #491C2×C181semidirect
95. #330C2×C181semidirect
96. #330C2×C181semidirect

Maximal subgroups

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

subgroupindex
#563×C1812
#501×C1812
#491×C1812
#489×C1812
#330×C1812
#329×C1812
#1664181