Finite Group Databasebeta

← #37535065

Subgroups — #37535065

Order 23168.

246 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 75 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#26041907C211yesmaximal, characteristic
2#26041322C211yesmaximal, characteristic
3#26041321C211yesmaximal, characteristic
4#26041149C211yesmaximal, characteristic
5#26041047C211yesmaximal, characteristic
6#26041039C211yesmaximal, characteristic
7#339×C181C211yesmaximal, characteristic
8C2×#15668433C2211yescharacteristic
9#19153816—21no—
10#19153815—21no—
11#19153808—21no—
12#19153807—21no—
13#19153793—22no—
14#19153775C2211yescharacteristic
15C2×C4⋊Dic181—22no—
16C2×C4⋊Dic181C2211yescharacteristic
17C2×C4⋊Dic181C2211yescharacteristic
18#19153750—21no—
19#19153749—21no—
20#19153748—21no—
21#19153747—21no—
22C2×M16×C181C2211yescharacteristic
23#117×C181C2211yescharacteristic
24C2×C42×C181C2211yescharacteristic
25C2×Dic362—22no—
26C22×Dic181—21no—
27C22×Dic181D412yes—
28#15668433—21no—
29#15668433Q812yescomplemented
30C2×#13089678—21no—
31C4⋊Dic181—22no—
32C4⋊Dic181—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181—21no—
35C4⋊Dic181—21no—
36C4⋊Dic181—44no—
37C4⋊Dic181D411yescharacteristic
38C4⋊Dic181D411yescharacteristic
39#15668428—22no—
40#15668428—22no—
41C22⋊Dic181—21no—
42C4×Dic181—21no—
43C22×C4×C181—21no—
44C22×C4×C181C2311yescharacteristic
45M16×C181—21no—
46M16×C181Q812yescomplemented
47C2×C8×C181—21no—
48C4⋊C4×C181D411yescharacteristic
49C4⋊C4×C181D411yescharacteristic
50C22⋊C4×C181—21no—
51C42×C181—21no—
52C42×C181—21no—
53C42×C181Q812yescomplemented
54Dic362—82no—
55C2×Dic181—21no—
56C2×Dic181—21no—
57C2×Dic181—22no—
58C2×Dic181—42no—
59C2×Dic181—42no—
60C2×Dic181—41no—
61#13089678—22no—
62C23×C181C2×D411yescharacteristic
63C2×C4×C181—22no—
64C2×C4×C181—22no—
65C2×C4×C181—22no—
66C2×C4×C181—21no—
67C2×C4×C181—21no—
68C2×C4×C181C2×D411yescharacteristic
69C2×C4×C181C2×D411yescharacteristic
70C2×C4×C181C2×Q811yescharacteristic
71C2×C4×C181C2×Q811yescharacteristic
72C2×C4×C181C2×Q811yescharacteristic
73C2×C4×C181#4111yescharacteristic
74C8×C181—22no—
75C22×C181—21no—
76C22×C181—21no—
77C22×C181#12011yescharacteristic
78C22×C181C22⋊Q811yescharacteristic
79C22×C181C4⋊Q811yescharacteristic
80C4×C181—24no—
81C4×C181—41no—
82C4×C181—41no—
83C4×C181C22⋊Q811yescharacteristic
84C4×C181C22⋊Q811yescharacteristic
85C4×C181C4⋊Q811yescharacteristic
86C4×C181C4⋊Q811yescharacteristic
87Dic181—42no—
88Dic181—41no—
89Dic181—41no—
90Dic181—81no—
91C2×C181—21no—
92C2×C181—21no—
93C2×C181#39511yescharacteristic
94C2×C181#45311yescharacteristic
95C2×C181#45611yescharacteristic
96C181#206011yescharacteristic, complemented, Sylow
97#2060—1811nomaximal, Sylow
98#544—1811no—
99#428—1811no—
100#428—1811no—
101#384—1811no—
102#343—1811no—
103#339—1811no—
104#339D18111yescharacteristic
105C2×M16—1811no—
106C2×M16C2×D18111yescharacteristic
107C4⋊Q8—3621no—
108C4⋊Q8—3621no—
109#125—3621no—
110#125—3621no—
111C22⋊Q8—3622no—
112#117—1811no—
113#117C2×D18111yescharacteristic
114C2×C4⋊C4—3622no—
115C2×C4⋊C4—1811no—
116C2×C4⋊C4—1811no—
117C2×C42C2×D18111yescharacteristic
118#107—3621no—
119#107—3621no—
120#106—3621no—
121#106—3621no—
122C2×Q8—3622no—
123C22×C4—21no—
124C22×C4—3621no—
125C22×C4—1812no—
126C22×C4C22×D18111yescharacteristic
127M16—21no—
128M16—3621no—
129M16—1812no—
130M16Dic36212yescomplemented
131C2×C8—21no—
132C2×C8—3621no—
133C4⋊C4—3622no—
134C4⋊C4—3622no—
135C4⋊C4—3622no—
136C4⋊C4—3621no—
137C4⋊C4—3621no—
138C4⋊C4—3621no—
139C4⋊C4—3621no—
140C4⋊C4—1811no—
141C4⋊C4—1811no—
142C4⋊C4—7244no—
143C4⋊C4D72411yescharacteristic
144C4⋊C4D72411yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—3621no—
147C42—21no—
148C42—21no—
149C42—3621no—
150C42Dic36212yescomplemented
151C23D4×D18111yescharacteristic
152Q8—14482no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—3621no—
159C2×C4—3621no—
160C2×C4—3622no—
161C2×C4—7242no—
162C2×C4—7241no—
163C2×C4—7242no—
164C2×C4D4×D18111yescharacteristic
165C2×C4C2×D72411yescharacteristic
166C2×C4Q8×D18111yescharacteristic
167C2×C4C2×Dic36211yescharacteristic
168C2×C4C2×Dic36211yescharacteristic
169C2×C4#1566844811yescharacteristic
170C8—22no—
171C8—3622no—
172C22—21no—
173C22—21no—
174C22#1915378611yescharacteristic
175C22#1915379311yescharacteristic
176C22#1915381511yescharacteristic
177C4—24no—
178C4—41no—
179C4—41no—
180C4—14481no—
181C4—7242no—
182C4—7241no—
183C4—7241no—
184C4#1915379311yescharacteristic
185C4#1915379611yescharacteristic
186C4#1915381511yescharacteristic
187C4#1915381611yescharacteristic
188C2—21no—
189C2—21no—
190C2#2604120011yescharacteristic
191C2#2604144811yescharacteristic
192C2#2604146311yescharacteristic
subgroupG/H
centerC22#19153786
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#339×C181C2
socleC22×C181#120
prime radicalC23×C181C2×D4
hypercenter#339D181
hypocenterC181#2060
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
29. #15668433Q8semidirect
46. M16×C181Q8semidirect
53. C42×C181Q8semidirect
96. C181#2060semidirect
130. M16Dic362semidirect
150. C42Dic362semidirect

Maximal subgroups

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

subgroupindex
#260419072
#260413222
#260413212
#260411492
#260410472
#260410392
#339×C1812
#2060181