Finite Group Databasebeta

← #37544859

Subgroups — #37544859

Order 23168.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#26041836C211yesmaximal, characteristic, complemented
2#26041829C211yesmaximal, characteristic
3#26041684C211yesmaximal, characteristic, complemented
4#26041677C211yesmaximal, characteristic, complemented
5#26041626C211yesmaximal, characteristic, complemented
6#26041626C211yesmaximal, characteristic, complemented
7#26041604C214yesmaximal, complemented
8#26041580C214yesmaximal, complemented
9#431×C181C211yesmaximal, characteristic, complemented
10C2×#15668449—21no—
11#19153816C2211yescharacteristic
12#19153816C2211yescharacteristic
13#19153816C2211yescharacteristic
14#19153813C2211yescharacteristic
15#19153808C2212yes—
16#19153804—21no—
17#19153795—21no—
18#19153795—21no—
19#19153790—21no—
20#19153790C2212yes—
21C4×Dic362—21no—
22C4×Dic362—21no—
23C4×D724—21no—
24C4×D724C2212yes—
25#19153775C2212yes—
26#19153750C2214yes—
27#19153748C2214yes—
28#19153738C2214yes—
29#19153738C2214yes—
30C2×C42×C181C2211yescharacteristic
31C4⋊C8×C181C2212yes—
32C22⋊C8×C181C2212yes—
33C4×C8×C181C2211yescharacteristic
34C4×C8×C181C2211yescharacteristic
35#15668449—44no—
36C2×Dic362—21no—
37C2×Dic362—21no—
38C2×Dic362—21no—
39C2×D724—21no—
40C2×D724—21no—
41C2×D724C2312yes—
42C2×C22⋊D181—22no—
43C2×C4×D181—22no—
44C4⋊Dic181—21no—
45C4⋊Dic181—21no—
46C4⋊Dic181—21no—
47C4⋊Dic181C2312yes—
48C4⋊Dic181C2312yes—
49C4⋊Dic181C2312yes—
50#15668428—22no—
51#15668428—22no—
52C22⋊Dic181—22no—
53#15668426—22no—
54#15668426—22no—
55C4×Dic181—22no—
56C22×C4×C181D411yescharacteristic
57C22×C4×C181D411yescharacteristic
58C22×C4×C181C2311yescharacteristic
59C2×C8×C181C2312yes—
60C2×C8×C181C2312yes—
61C42×C181D411yescharacteristic
62C42×C181D411yescharacteristic
63C42×C181C2311yescharacteristic
64C42×C181C2311yescharacteristic
65C22×D181—22no—
66Dic362—42no—
67Dic362—42no—
68Dic362—42no—
69D724—24no—
70D724—42no—
71D724—42no—
72C22⋊D181—44no—
73C2×Dic181—22no—
74C2×Dic181—22no—
75C2×Dic181—22no—
76C4×D181—44no—
77C23×C181C2×D411yescharacteristic
78C2×C4×C181—22no—
79C2×C4×C181—22no—
80C2×C4×C181—22no—
81C2×C4×C181C2×D411yescharacteristic
82C2×C4×C181C2×D411yescharacteristic
83C2×C4×C181C2×D411yescharacteristic
84C2×C4×C181C2×D411yescharacteristic
85C2×C4×C181C2×D411yescharacteristic
86C2×C4×C181C2411yescharacteristic
87C8×C181—22no—
88C8×C181—22no—
89C22×C181—21no—
90C22×C181—21no—
91C22×C181—21no—
92C22×C181C22×D411yescharacteristic
93C2×D181—42no—
94C2×D181—42no—
95C2×D181—42no—
96C4×C181—21no—
97C4×C181—21no—
98C4×C181—21no—
99C4×C181#13512yes—
100C4×C181AGL(1,ℤ/8)12yes—
101C4×C1812−1+412yes—
102Dic181—42no—
103Dic181—42no—
104Dic181—42no—
105C2×C181—41no—
106C2×C181#53611yescharacteristic
107C2×C181C2×#13511yescharacteristic
108C2×C181C2×AGL(1,ℤ/8)11yescharacteristic
109D181—82no—
110C181#322811yescharacteristic, complemented, Sylow
111#3228—1811nomaximal, Sylow
112#533—1811no—
113#532—1811no—
114#500—1811no—
115#498—1811no—
116#486—1811no—
117#486—1811no—
118#482—1814no—
119#478—1814no—
120#431D18111yescharacteristic, complemented
121C2×#41—3621no—
122C4⋊Q8—1811no—
123C4⋊Q8—1811no—
124C4⋊Q8—1811no—
125#127—1811no—
126#125—1812no—
127#124—3621no—
128C22⋊Q8—3621no—
129C22⋊Q8—3621no—
130#121—3621no—
131#121—1812no—
132C4×Q8—3621no—
133C4×Q8—3621no—
134C4×D4—3621no—
135C4×D4—1812no—
136#117—1812no—
137C2×C42C2×D18111yescharacteristic
138#107—1814no—
139#106—1814no—
140C4⋊C8C2×D18112yes—
141#102—1814no—
142#102—1814no—
143C22⋊C8C2×D18112yes—
144C4×C8C2×D18111yescharacteristic
145C4×C8C2×D18111yescharacteristic
146#41—7244no—
147C2×Q8—3621no—
148C2×Q8—3621no—
149C2×Q8—3621no—
150C2×D4—3622no—
151C2×D4—3621no—
152C2×D4—3621no—
153C2×D4—1812no—
154C22×C4—3622no—
155C22×C4D72411yescharacteristic
156C22×C4D72411yescharacteristic
157C22×C4C22×D18111yescharacteristic
158C2×C8C22×D18112yes—
159C2×C8C22×D18112yes—
160C4⋊C4—3621no—
161C4⋊C4—3622no—
162C4⋊C4—3622no—
163C4⋊C4—3621no—
164C4⋊C4—3621no—
165C4⋊C4—1812no—
166C4⋊C4—1812no—
167C4⋊C4—1812no—
168C22⋊C4—3622no—
169C22⋊C4—3622no—
170C22⋊C4—3622no—
171C42—3622no—
172C42D72411yescharacteristic
173C42D72411yescharacteristic
174C42C22×D18111yescharacteristic
175C42C22×D18111yescharacteristic
176C23—3622no—
177C23C2×D72411yescharacteristic
178Q8—7242no—
179Q8—7242no—
180Q8—7242no—
181D4—3624no—
182D4—7244no—
183D4—7242no—
184D4—7242no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—3622no—
189C2×C4—3622no—
190C2×C4—3622no—
191C2×C4—7244no—
192C2×C4C2×D72411yescharacteristic
193C2×C4C2×D72411yescharacteristic
194C2×C4C2×D72411yescharacteristic
195C2×C4C2×D72411yescharacteristic
196C2×C4C2×D72411yescharacteristic
197C2×C4C23×D18111yescharacteristic
198C8—22no—
199C8—22no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—7242no—
204C22—7242no—
205C22—7242no—
206C22C22×D72411yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—7242no—
211C4—7242no—
212C4—7242no—
213C4#1915383812yes—
214C4#1915384412yes—
215C4#1915386312yes—
216C2—41no—
217C2—14482no—
218C2#2604185511yescharacteristic
219C2C2×#1915383811yescharacteristic
220C2C2×#1915384411yescharacteristic
subgroupG/H
centerC22C22×D724
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#431×C181C2
socleC22×C181C22×D4
prime radical#26041829C2
hypercenter#431D181
hypocenterC181#3228
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
1. #26041836C2semidirect
3. #26041684C2semidirect
4. #26041677C2semidirect
5. #26041626C2semidirect
6. #26041626C2semidirect
7. #26041604C2semidirect
8. #26041580C2semidirect
9. #431×C181C2semidirect
110. C181#3228semidirect
120. #431D181semidirect

Maximal subgroups

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

subgroupindex
#260418362
#260418292
#260416842
#260416772
#260416262
#260416042
#260415802
#431×C1812
#3228181