Finite Group Databasebeta

← #37532869

Subgroups — #37532869

Order 23168.

234 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 55 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#26041932C211yesmaximal, characteristic
2#26041566C211yesmaximal, characteristic, complemented
3#26041566C211yesmaximal, characteristic, complemented
4#26041025C211yesmaximal, characteristic, complemented
5#26041008C211yesmaximal, characteristic, complemented
6#26041008C211yesmaximal, characteristic, complemented
7#487×C181C211yesmaximal, characteristic, complemented
8C2×#15668450—21no—
9#19153801—22no—
10#19153792—21no—
11#19153791—21no—
12C4×D724C2211yescharacteristic
13C4×D724C2211yescharacteristic
14C4⋊C4×D181—21no—
15#19153747—21no—
16#19153747—21no—
17C4⋊#13089678C2211yescharacteristic
18C4⋊#13089678C2211yescharacteristic
19#19153736—21no—
20#19153736—21no—
21C4⋊Q8×C181C2211yescharacteristic
22C4⋊Q8×C181C2211yescharacteristic
23#103×C181—22no—
24C4×C8×C181C2211yescharacteristic
25#15668450—42no—
26#15668450—42no—
27C2×D724—22no—
28C2×D724D411yescharacteristic
29C2×D724D411yescharacteristic
30C2×C4×D181—22no—
31C2×C4×D181—21no—
32C2×C4×D181—21no—
33C2×#13089678—21no—
34C2×#13089678—21no—
35C4⋊Dic181D411yescharacteristic
36C4⋊Dic181D411yescharacteristic
37#15668428—22no—
38#15668426—22no—
39#15668426—21no—
40#15668426—21no—
41C2×Q8×C181—21no—
42C2×Q8×C181—21no—
43C2×C8×C181—21no—
44C4⋊C4×C181—21no—
45C4⋊C4×C181—21no—
46C4⋊C4×C181—21no—
47C4⋊C4×C181D412yes—
48C42×C181C2311yescharacteristic
49C22×D181—21no—
50C22×D181—21no—
51D724—21no—
52D724—21no—
53D724—21no—
54D724—44no—
55D724SD1612yes—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C4×D181—44no—
59C4×D181—41no—
60C4×D181—41no—
61C4×D181—41no—
62C4×D181—41no—
63#13089678—41no—
64#13089678—41no—
65Q8×C181—42no—
66Q8×C181—41no—
67Q8×C181—41no—
68C2×C4×C181—22no—
69C2×C4×C181—41no—
70C2×C4×C181C2×D411yescharacteristic
71C2×C4×C181C2×D411yescharacteristic
72C2×C4×C181C2×D411yescharacteristic
73C8×C181—41no—
74C22×C181#12011yescharacteristic
75C2×D181—22no—
76C2×D181—41no—
77C2×D181—41no—
78C2×D181—41no—
79C2×D181—41no—
80C2×D181—41no—
81C4×C181—21no—
82C4×C181—42no—
83C4×C181—81no—
84C4×C181C2×SD1611yescharacteristic
85C4×C181#13511yescharacteristic
86C4×C181AGL(1,ℤ/8)11yescharacteristic
87C4×C181#13711yescharacteristic
88Dic181—41no—
89Dic181—41no—
90C2×C181#45011yescharacteristic
91C2×C181#45211yescharacteristic
92C2×C181#45411yescharacteristic
93D181—42no—
94D181—81no—
95C181#163511yescharacteristic, complemented, Sylow
96#1635—1811nomaximal, Sylow
97#547—1811no—
98#487D18111yescharacteristic, complemented
99#476—1811no—
100#476—1811no—
101#332—1811no—
102D4⋊C8—1811no—
103D4⋊C8—1811no—
104C2×#41—3621no—
105C4⋊Q8C2×D18111yescharacteristic
106C4⋊Q8C2×D18111yescharacteristic
107#123—3622no—
108C22⋊Q8—3621no—
109#121—3621no—
110C4×D4—1811no—
111C4×D4—1811no—
112C2×C4⋊C4—3621no—
113#106—3621no—
114#106—3621no—
115C4⋊C8—1811no—
116C4⋊C8—1811no—
117#103—22no—
118#102—3621no—
119#102—3621no—
120C4×C8C2×D18111yescharacteristic
121#41—7242no—
122#41—7242no—
123C2×Q8—21no—
124C2×Q8—21no—
125C2×D4—3622no—
126C2×D4—1811no—
127C2×D4—1811no—
128C22×C4—3622no—
129C22×C4—3621no—
130C22×C4—3621no—
131C2×C8—21no—
132C2×C8—3621no—
133C2×C8—3621no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—3622no—
138C4⋊C4—1811no—
139C4⋊C4—1811no—
140C4⋊C4C22⋊D18112yes—
141C22⋊C4—3622no—
142C22⋊C4—3621no—
143C22⋊C4—3621no—
144C42C22×D18111yescharacteristic
145C23—3621no—
146C23—3621no—
147Q8—42no—
148Q8—41no—
149Q8—41no—
150D4—3621no—
151D4—3621no—
152D4—3621no—
153D4—1812no—
154D4—7244no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—3621no—
158C2×C4—3621no—
159C2×C4—7244no—
160C2×C4—7241no—
161C2×C4—7241no—
162C2×C4—7241no—
163C2×C4—7241no—
164C2×C4D4×D18111yescharacteristic
165C2×C4D4×D18111yescharacteristic
166C2×C4C2×C22⋊D18111yescharacteristic
167C8—41no—
168C8—7241no—
169C8—7241no—
170C22—3622no—
171C22—7241no—
172C22—7241no—
173C22—7241no—
174C22—7241no—
175C22—7241no—
176C22#1915378411yescharacteristic
177C4—21no—
178C4—42no—
179C4—81no—
180C4—7241no—
181C4—7241no—
182C4SD16×D18111yescharacteristic
183C4#1915383911yescharacteristic
184C4#1915384311yescharacteristic
185C4#1915384811yescharacteristic
186C2—14481no—
187C2—7242no—
188C2#2604142811yescharacteristic
189C2#2604144011yescharacteristic
190C2#2604145111yescharacteristic
subgroupG/H
centerC22#19153784
commutator, cosocleC42×C181C23
FrattiniC42C22×D181
Fitting#487×C181C2
socleC22×C181#120
prime radical#26041932C2
hypercenter#487D181
hypocenterC181#1635
LCSG ▷ C42×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #26041566C2semidirect
3. #26041566C2semidirect
4. #26041025C2semidirect
5. #26041008C2semidirect
6. #26041008C2semidirect
7. #487×C181C2semidirect
95. C181#1635semidirect
98. #487D181semidirect

Maximal subgroups

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

subgroupindex
#260419322
#260415662
#260410252
#260410082
#487×C1812
#1635181