Finite Group Databasebeta

← #37532787

Subgroups — #37532787

Order 23168.

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

normal subgroups only

This group has 278 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#26041949C211yesmaximal, characteristic, complemented
2#26041655C211yesmaximal, characteristic, complemented
3#26041480C211yesmaximal, characteristic, complemented
4#26041475C211yesmaximal, characteristic, complemented
5#26041009C211yesmaximal, characteristic, complemented
6#26041006C211yesmaximal, characteristic, complemented
7#331×C181C211yesmaximal, characteristic, complemented
8C2×#15668448—21no—
9C2×#15668438—21no—
10C2×D1448—21no—
11C2×#15668434—22no—
12#19153813C2211yescharacteristic
13#19153812—21no—
14#19153788—22no—
15#19153787—21no—
16C4×Dic362C2211yescharacteristic
17C4×D724C2211yescharacteristic
18D4×Dic181—21no—
19#19153738—21no—
20#19153738—21no—
21C4×#13089678C2211yescharacteristic
22#127×C181C2211yescharacteristic
23C4⋊C8×C181C2211yescharacteristic
24C4⋊C8×C181C2211yescharacteristic
25#15668448—42no—
26#15668448—42no—
27C2×Dic362D411yescharacteristic
28C2×D724—21no—
29C2×D724—21no—
30C2×D724—21no—
31C2×D724D411yescharacteristic
32C2×C22⋊D181—22no—
33C2×C22⋊D181—22no—
34C22×Dic181—22no—
35C2×C4×D181—21no—
36#15668438—42no—
37D1448—42no—
38#15668434—44no—
39C2×#13089678—21no—
40C4⋊Dic181D411yescharacteristic
41C4⋊Dic181D411yescharacteristic
42#15668428—21no—
43C22⋊Dic181—22no—
44#15668426—21no—
45C4×Dic181—21no—
46C2×D4×C181—21no—
47C2×D4×C181—21no—
48C2×D4×C181D412yes—
49C2×C8×C181—21no—
50C2×C8×C181—21no—
51C42×C181C2311yescharacteristic
52C22×D181—21no—
53C22×D181—41no—
54Dic362—21no—
55Dic362D812yescomplemented
56D724—21no—
57D724—21no—
58D724—42no—
59D724—41no—
60D724—41no—
61D724—41no—
62D724—41no—
63C22⋊D181—44no—
64C22⋊D181—82no—
65C2×Dic181—21no—
66C2×Dic181—21no—
67C2×Dic181—21no—
68C2×Dic181—44no—
69C4×D181—41no—
70C4×D181—41no—
71#13089678—22no—
72C23×C181—22no—
73D4×C181—42no—
74D4×C181—41no—
75D4×C181—41no—
76D4×C181—41no—
77D4×C181—41no—
78C2×C4×C181C2×D411yescharacteristic
79C2×C4×C181C2×D411yescharacteristic
80C2×C4×C181C2×D411yescharacteristic
81C8×C181—41no—
82C8×C181—41no—
83C22×C181—42no—
84C22×C181—42no—
85C22×C181—42no—
86C22×C181#12011yescharacteristic
87C2×D181—41no—
88C2×D181—41no—
89C2×D181—41no—
90C2×D181—81no—
91C2×D181—81no—
92C2×D181—81no—
93C4×C181—21no—
94C4×C181C2×D811yescharacteristic
95C4×C181#13511yescharacteristic
96C4×C181AGL(1,ℤ/8)11yescharacteristic
97C4×C181AGL(1,ℤ/8)11yescharacteristic
98Dic181—22no—
99Dic181—41no—
100Dic181—41no—
101C2×C181—82no—
102C2×C181#44711yescharacteristic
103C2×C181#44911yescharacteristic
104C2×C181#45311yescharacteristic
105D181—81no—
106D181—161no—
107C181#162111yescharacteristic, complemented, Sylow
108#1621—1811nomaximal, Sylow
109#550—1811no—
110#493—1811no—
111#460—1811no—
112#459—1811no—
113#331D18111yescharacteristic, complemented
114Q8⋊C8—1811no—
115D4⋊C8—1811no—
116C2×#41—3621no—
117C2×SD16—3621no—
118C2×D8—3621no—
119C2×D8—3622no—
120#127—3621no—
121#127—1811no—
122#127C2×D18111yescharacteristic
123#121—3622no—
124#121—3621no—
125C4×Q8—1811no—
126C4×D4—3621no—
127C4×D4—1811no—
128C4⋊C8C2×D18111yescharacteristic
129C4⋊C8C2×D18111yescharacteristic
130#102—3621no—
131#102—3621no—
132C4×C8—1811no—
133#41—7242no—
134#41—7242no—
135C2×Q8—1811no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—3622no—
139C2×D4—3622no—
140C2×D4—3621no—
141C2×D4—3621no—
142C2×D4—3621no—
143C2×D4—1811no—
144C2×D4D72412yes—
145C22×C4—3622no—
146C22×C4—3621no—
147SD16—7242no—
148D8—7242no—
149D8—7244no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—3621no—
153C4⋊C4—3621no—
154C4⋊C4—1811no—
155C4⋊C4—1811no—
156C22⋊C4—3622no—
157C22⋊C4—3621no—
158C42—3621no—
159C42C22×D18111yescharacteristic
160C23—22no—
161C23—3621no—
162C23—7241no—
163Q8—3621no—
164Q8—1812no—
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—3621no—
171D4—3621no—
172D4—14482no—
173D4—7242no—
174D4—7244no—
175D4—7241no—
176D4—7241no—
177D4—7241no—
178D4—7241no—
179C2×C4—3621no—
180C2×C4—3621no—
181C2×C4—3621no—
182C2×C4—7244no—
183C2×C4—7241no—
184C2×C4—7241no—
185C2×C4D4×D18111yescharacteristic
186C2×C4D4×D18111yescharacteristic
187C2×C4C2×D72411yescharacteristic
188C8—41no—
189C8—41no—
190C8—3622no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—14481no—
195C22—14481no—
196C22—14481no—
197C22—7241no—
198C22—7241no—
199C22—7241no—
200C22#1915378611yescharacteristic
201C4—21no—
202C4—3622no—
203C4—7241no—
204C4—7241no—
205C4D8×D18111yescharacteristic
206C4#1915383711yescharacteristic
207C4#1915384011yescharacteristic
208C4#1915384311yescharacteristic
209C2—82no—
210C2—28961no—
211C2—14481no—
212C2#2604141411yescharacteristic
213C2#2604142511yescharacteristic
214C2#2604144911yescharacteristic
subgroupG/H
centerC22#19153786
commutator, cosocleC42×C181C23
FrattiniC42C22×D181
Fitting#331×C181C2
socleC22×C181#120
hypercenter#331D181
hypocenterC181#1621
LCSG ▷ C42×C181 ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #26041949C2semidirect
2. #26041655C2semidirect
3. #26041480C2semidirect
4. #26041475C2semidirect
5. #26041009C2semidirect
6. #26041006C2semidirect
7. #331×C181C2semidirect
55. Dic362D8semidirect
107. C181#1621semidirect
113. #331D181semidirect

Maximal subgroups

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

subgroupindex
#260419492
#260416552
#260414802
#260414752
#260410092
#260410062
#331×C1812
#1621181