Finite Group Databasebeta

← #37535064

Subgroups — #37535064

Order 23168.

246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 73 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#26041319C211yesmaximal, characteristic
3#26041148C211yesmaximal, characteristic
4#26041047C211yesmaximal, characteristic
5#26041040C211yesmaximal, characteristic
6#26041038C211yesmaximal, characteristic
7#428×C181C211yesmaximal, characteristic
8C2×#15668433C2211yescharacteristic
9#19153816—21no—
10#19153815—21no—
11#19153808—21no—
12#19153807—21no—
13#19153793—22no—
14#19153775C2211yescharacteristic
15C2×C4⋊Dic181C2211yescharacteristic
16C2×#15668428—22no—
17C2×C4×Dic181C2211yescharacteristic
18#19153749—21no—
19#19153747—21no—
20C2×M16×C181C2211yescharacteristic
21#117×C181C2211yescharacteristic
22C2×C4⋊C4×C181C2211yescharacteristic
23#107×C181—21no—
24#106×C181—21no—
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⋊Dic181D411yescharacteristic
35C4⋊Dic181D411yescharacteristic
36#15668428—22no—
37#15668428—22no—
38#15668428—44no—
39C22⋊Dic181—21no—
40C4×Dic181—21no—
41C4×Dic181—21no—
42C4×Dic181Q812yescomplemented
43C22×C4×C181—21no—
44C22×C4×C181C2311yescharacteristic
45M16×C181—21no—
46M16×C181Q812yescomplemented
47C2×C8×C181—21no—
48C4⋊C4×C181—21no—
49C4⋊C4×C181—21no—
50C4⋊C4×C181D411yescharacteristic
51C4⋊C4×C181D411yescharacteristic
52C22⋊C4×C181—21no—
53C42×C181—21no—
54Dic362—82no—
55C2×Dic181—22no—
56C2×Dic181—22no—
57C2×Dic181—22no—
58C2×Dic181—21no—
59C2×Dic181—21no—
60C2×Dic181—22no—
61C2×Dic181—42no—
62#13089678—22no—
63C23×C181C2×D411yescharacteristic
64C2×C4×C181—21no—
65C2×C4×C181—21no—
66C2×C4×C181—42no—
67C2×C4×C181—41no—
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—41no—
81C4×C181—41no—
82C4×C181—81no—
83C4×C181C22⋊Q811yescharacteristic
84C4×C181C22⋊Q811yescharacteristic
85C4×C181C4⋊Q811yescharacteristic
86C4×C181C4⋊Q811yescharacteristic
87Dic181—24no—
88Dic181—42no—
89Dic181—41no—
90Dic181—41no—
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#428D18111yescharacteristic
101#384—1811no—
102#343—1811no—
103#339—1811no—
104#339—1811no—
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⋊C4C2×D18111yescharacteristic
117C2×C42—1811no—
118#107—21no—
119#107—3621no—
120#106—21no—
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—21no—
134C4⋊C4—21no—
135C4⋊C4—3622no—
136C4⋊C4—3622no—
137C4⋊C4—3622no—
138C4⋊C4—3621no—
139C4⋊C4—3621no—
140C4⋊C4—1811no—
141C4⋊C4—1811no—
142C4⋊C4—7244no—
143C4⋊C4C22⋊D18111yescharacteristic
144C4⋊C4C22⋊D18111yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—3621no—
147C42—21no—
148C42—3621no—
149C42—3621no—
150C42—1812no—
151C23D4×D18111yescharacteristic
152Q8—14482no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—3622no—
158C2×C4—3622no—
159C2×C4—3622no—
160C2×C4—3621no—
161C2×C4—3621no—
162C2×C4—3622no—
163C2×C4—7242no—
164C2×C4D4×D18111yescharacteristic
165C2×C4C2×C22⋊D18111yescharacteristic
166C2×C4Q8×D18111yescharacteristic
167C2×C4Q8×D18111yescharacteristic
168C2×C4C2×Dic36211yescharacteristic
169C2×C4#1566844911yescharacteristic
170C8—22no—
171C8—3622no—
172C22—21no—
173C22—21no—
174C22#1915378411yescharacteristic
175C22#1915379411yescharacteristic
176C22#1915381511yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—3624no—
181C4—7242no—
182C4—7241no—
183C4—7241no—
184C4#1915379411yescharacteristic
185C4#1915379511yescharacteristic
186C4#1915381411yescharacteristic
187C4#1915381511yescharacteristic
188C2—21no—
189C2—21no—
190C2#2604119911yescharacteristic
191C2#2604144511yescharacteristic
192C2#2604146011yescharacteristic
subgroupG/H
centerC22#19153784
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#428×C181C2
socleC22×C181#120
prime radicalC23×C181C2×D4
hypercenter#428D181
hypocenterC181#2060
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
29. #15668433Q8semidirect
42. C4×Dic181Q8semidirect
46. M16×C181Q8semidirect
96. C181#2060semidirect
130. M16Dic362semidirect

Maximal subgroups

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

subgroupindex
#260419072
#260413192
#260411482
#260410472
#260410402
#260410382
#428×C1812
#2060181