Finite Group Databasebeta

← #37535069

Subgroups — #37535069

Order 23168.

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

normal subgroups only

This group has 230 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#26041144C211yesmaximal, 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×C4×Dic181C2211yescharacteristic
17#19153749—21no—
18#19153747—21no—
19#19153723—22no—
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—
38C22⋊Dic181—21no—
39C4×Dic181—21no—
40C4×Dic181—21no—
41C4×Dic181Q812yescomplemented
42C22×C4×C181—21no—
43C22×C4×C181C2311yescharacteristic
44M16×C181—21no—
45M16×C181Q812yescomplemented
46C2×C8×C181—21no—
47C4⋊C4×C181—21no—
48C4⋊C4×C181—21no—
49C4⋊C4×C181D411yescharacteristic
50C4⋊C4×C181D411yescharacteristic
51C22⋊C4×C181—21no—
52C42×C181—21no—
53Dic362—82no—
54C2×Dic181—21no—
55C2×Dic181—21no—
56C2×Dic181—22no—
57C2×Dic181—22no—
58C2×Dic181—41no—
59C2×Dic181—41no—
60C2×Dic181—42no—
61#13089678—22no—
62C23×C181C2×D411yescharacteristic
63C2×C4×C181—21no—
64C2×C4×C181—21no—
65C2×C4×C181—42no—
66C2×C4×C181—41no—
67C2×C4×C181C2×D411yescharacteristic
68C2×C4×C181C2×D411yescharacteristic
69C2×C4×C181C2×Q811yescharacteristic
70C2×C4×C181C2×Q811yescharacteristic
71C2×C4×C181C2×Q811yescharacteristic
72C2×C4×C181#4111yescharacteristic
73C8×C181—22no—
74C22×C181—21no—
75C22×C181—21no—
76C22×C181#12011yescharacteristic
77C22×C181C22⋊Q811yescharacteristic
78C22×C181C4⋊Q811yescharacteristic
79C4×C181—41no—
80C4×C181—41no—
81C4×C181—81no—
82C4×C181C22⋊Q811yescharacteristic
83C4×C181C22⋊Q811yescharacteristic
84C4×C181C4⋊Q811yescharacteristic
85C4×C181C4⋊Q811yescharacteristic
86Dic181—42no—
87Dic181—41no—
88Dic181—42no—
89Dic181—41no—
90C2×C181—21no—
91C2×C181—21no—
92C2×C181#39511yescharacteristic
93C2×C181#45411yescharacteristic
94C2×C181#45511yescharacteristic
95C181#206111yescharacteristic, complemented, Sylow
96#2061—1811nomaximal, Sylow
97#544—1811no—
98#428—1811no—
99#428D18111yescharacteristic
100#382—1811no—
101#343—1811no—
102#339—1811no—
103#339—1811no—
104C2×M16—1811no—
105C2×M16C2×D18111yescharacteristic
106C4⋊Q8—3621no—
107C4⋊Q8—3621no—
108#125—3621no—
109#125—3621no—
110C22⋊Q8—3622no—
111#117—1811no—
112#117C2×D18111yescharacteristic
113C2×C4⋊C4—1811no—
114C2×C4⋊C4C2×D18111yescharacteristic
115C2×C42—1811no—
116#107—21no—
117#107—3621no—
118#106—21no—
119#106—3621no—
120#95—3622no—
121C2×Q8—3622no—
122C22×C4—21no—
123C22×C4—3621no—
124C22×C4—1812no—
125C22×C4C22×D18111yescharacteristic
126M16—21no—
127M16—3621no—
128M16—1812no—
129M16Dic36212yescomplemented
130C2×C8—21no—
131C2×C8—3621no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—3622no—
135C4⋊C4—3622no—
136C4⋊C4—3622no—
137C4⋊C4—3621no—
138C4⋊C4—3621no—
139C4⋊C4—1811no—
140C4⋊C4—1811no—
141C4⋊C4C22⋊D18111yescharacteristic
142C4⋊C4C22⋊D18111yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—3621no—
145C42—21no—
146C42—3621no—
147C42—3621no—
148C42—1812no—
149C23D4×D18111yescharacteristic
150Q8—14482no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—3621no—
156C2×C4—3621no—
157C2×C4—3622no—
158C2×C4—3622no—
159C2×C4—7241no—
160C2×C4—7241no—
161C2×C4—7242no—
162C2×C4D4×D18111yescharacteristic
163C2×C4C2×C22⋊D18111yescharacteristic
164C2×C4Q8×D18111yescharacteristic
165C2×C4Q8×D18111yescharacteristic
166C2×C4C2×Dic36211yescharacteristic
167C2×C4#1566844911yescharacteristic
168C8—22no—
169C8—3622no—
170C22—21no—
171C22—21no—
172C22#1915378411yescharacteristic
173C22#1915379411yescharacteristic
174C22#1915381511yescharacteristic
175C4—41no—
176C4—41no—
177C4—81no—
178C4—7242no—
179C4—7241no—
180C4—7242no—
181C4—7241no—
182C4#1915379411yescharacteristic
183C4#1915379511yescharacteristic
184C4#1915381411yescharacteristic
185C4#1915381511yescharacteristic
186C2—21no—
187C2—21no—
188C2#2604119911yescharacteristic
189C2#2604145011yescharacteristic
190C2#2604145511yescharacteristic
subgroupG/H
centerC22#19153784
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
Fitting#428×C181C2
socleC22×C181#120
prime radicalC23×C181C2×D4
hypercenter#428D181
hypocenterC181#2061
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
41. C4×Dic181Q8semidirect
45. M16×C181Q8semidirect
95. C181#2061semidirect
129. M16Dic362semidirect

Maximal subgroups

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

subgroupindex
#260419072
#260413192
#260411442
#260410472
#260410402
#260410382
#428×C1812
#2061181