Finite Group Databasebeta

← #37532865

Subgroups — #37532865

Order 23168.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#26041994C211yesmaximal, characteristic
2#26041658C211yesmaximal, characteristic, complemented
3#26041566C211yesmaximal, characteristic, complemented
4#26041027C211yesmaximal, characteristic, complemented
5D4⋊#13089678C211yesmaximal, characteristic, complemented
6#26041006C211yesmaximal, characteristic, complemented
7#476×C181C211yesmaximal, characteristic, complemented
8C2×#15668439—22no—
9#19153816C2211yescharacteristic
10#19153802—22no—
11#19153790—21no—
12#19153787—21no—
13C4×D724C2211yescharacteristic
14#19153775—21no—
15#19153774—21no—
16#19153747—21no—
17C4⋊#13089678C2211yescharacteristic
18#19153736—21no—
19C4×#13089678C2211yescharacteristic
20C4⋊Q8×C181C2211yescharacteristic
21C4×D4×C181C2211yescharacteristic
22#106×C181—21no—
23C4⋊C8×C181C2211yescharacteristic
24#102×C181—21no—
25C2×Dic362D412yes—
26C2×D724D411yescharacteristic
27C2×C22⋊D181—22no—
28C2×C4×D181—21no—
29#15668439—44no—
30C2×#13089678—21no—
31C2×#13089678—21no—
32C4⋊Dic181—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181D411yescharacteristic
35C22⋊Dic181—22no—
36#15668426—22no—
37#15668426—21no—
38C4×Dic181—22no—
39C2×Q8×C181—21no—
40C2×D4×C181D411yescharacteristic
41C22×C4×C181—21no—
42C2×C8×C181—21no—
43C4⋊C4×C181—21no—
44C4⋊C4×C181—21no—
45C4⋊C4×C181D411yescharacteristic
46C22⋊C4×C181—21no—
47C42×C181C2311yescharacteristic
48C22×D181—21no—
49Dic362—42no—
50D724—21no—
51D724—21no—
52C22⋊D181—82no—
53C2×Dic181—21no—
54C2×Dic181—22no—
55C4×D181—41no—
56C4×D181—41no—
57#13089678—22no—
58#13089678—41no—
59C23×C181—21no—
60Q8×C181—42no—
61D4×C181—21no—
62D4×C181—21no—
63C2×C4×C181—21no—
64C2×C4×C181—41no—
65C2×C4×C181—41no—
66C2×C4×C181—41no—
67C2×C4×C181C2×D411yescharacteristic
68C2×C4×C181C2×D411yescharacteristic
69C2×C4×C181C2×D411yescharacteristic
70C8×C181—41no—
71C22×C181—41no—
72C22×C181—41no—
73C22×C181—41no—
74C22×C181#12011yescharacteristic
75C2×D181—41no—
76C2×D181—41no—
77C2×D181—41no—
78C4×C181—21no—
79C4×C181—41no—
80C4×C181—81no—
81C4×C181#13511yescharacteristic
82C4×C181#13511yescharacteristic
83C4×C181#13711yescharacteristic
84C4×C181#13711yescharacteristic
85Dic181—41no—
86Dic181—42no—
87C2×C181—81no—
88C2×C181#45211yescharacteristic
89C2×C181#45211yescharacteristic
90C2×C181#45311yescharacteristic
91D181—81no—
92C181#163411yescharacteristic, complemented, Sylow
93#1634—1811nomaximal, Sylow
94#555—1811no—
95#494—1811no—
96#476—1811no—
97#476D18111yescharacteristic, complemented
98#333—1811no—
99D4⋊C8—1811no—
100D4⋊C8—1811no—
101C2×Q16—3622no—
102C4⋊Q8—1811no—
103C4⋊Q8C2×D18111yescharacteristic
104#124—3622no—
105#121—3621no—
106#121—3621no—
107C4×D4—1811no—
108C4×D4C2×D18111yescharacteristic
109#117—3621no—
110#117—3621no—
111#106—21no—
112#106—3621no—
113C4⋊C8—1811no—
114C4⋊C8C2×D18111yescharacteristic
115#102—21no—
116#102—3621no—
117C4×C8—1811no—
118C2×Q8—21no—
119C2×Q8—1812no—
120C2×D4—3622no—
121C2×D4—1811no—
122C2×D4C22⋊D18111yescharacteristic
123C22×C4—21no—
124C22×C4—3621no—
125Q16—7244no—
126C2×C8—21no—
127C2×C8—3621no—
128C2×C8—3621no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—3621no—
132C4⋊C4—3621no—
133C4⋊C4—1811no—
134C4⋊C4C22⋊D18111yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—3622no—
137C22⋊C4—3622no—
138C22⋊C4—3621no—
139C42—3622no—
140C42C22×D18111yescharacteristic
141C23—21no—
142C23—3621no—
143Q8—42no—
144Q8—7242no—
145D4—21no—
146D4—21no—
147D4—3621no—
148D4—3621no—
149D4—14482no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—3621no—
155C2×C4—3622no—
156C2×C4—7241no—
157C2×C4—7241no—
158C2×C4D4×D18111yescharacteristic
159C2×C4D4×D18111yescharacteristic
160C2×C4C2×C22⋊D18111yescharacteristic
161C8—41no—
162C8—3622no—
163C8—7241no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—7241no—
168C22—7241no—
169C22—7241no—
170C22#1915378411yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—7241no—
175C4—7242no—
176C4#1915383611yescharacteristic
177C4#1915383711yescharacteristic
178C4#1915384511yescharacteristic
179C4#1915384711yescharacteristic
180C2—81no—
181C2—14481no—
182C2#2604143811yescharacteristic
183C2#2604143911yescharacteristic
184C2#2604144511yescharacteristic
subgroupG/H
centerC22#19153784
commutator, cosocleC42×C181C23
FrattiniC42C22×D181
Fitting#476×C181C2
socleC22×C181#120
prime radical#26041994C2
hypercenter#476D181
hypocenterC181#1634
LCSG ▷ C42×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #26041658C2semidirect
3. #26041566C2semidirect
4. #26041027C2semidirect
5. D4⋊#13089678C2semidirect
6. #26041006C2semidirect
7. #476×C181C2semidirect
92. C181#1634semidirect
97. #476D181semidirect

Maximal subgroups

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

subgroupindex
#260419942
#260416582
#260415662
#260410272
D4⋊#130896782
#260410062
#476×C1812
#1634181