Finite Group Databasebeta

← #37545074

Subgroups — #37545074

Order 23168.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#26041815C212yesmaximal, complemented
2#26041588C212yesmaximal, complemented
3#26041582C212yesmaximal, complemented
4#26041515C211yesmaximal, characteristic
5#26041510C212yesmaximal, complemented
6#26041503C212yesmaximal, complemented
7#26041497C212yesmaximal, complemented
8C2×#19153745C211yesmaximal, characteristic, complemented
9#467×C181C211yesmaximal, characteristic, complemented
10C2×#15668436C2212yes—
11C2×D1448C2211yescharacteristic
12C22×#13089678C2211yescharacteristic
13#19153811—22no—
14#19153807C2212yes—
15#19153805C2212yes—
16#19153800—22no—
17#19153790C2212yes—
18Q8×Dic181C2212yes—
19#19153778C2212yes—
20#19153776—22no—
21#19153774—22no—
22C2×C4×Dic181C2211yescharacteristic
23#19153750C2211yescharacteristic
24#19153747C2212yes—
25#19153745C2212yes—
26#19153745C2212yes—
27#19153740C2212yes—
28#19153738C2212yes—
29#19153736C2212yes—
30C2×Q16×C181C2211yescharacteristic
31C22×C8×C181C2211yescharacteristic
32C22⋊Q8×C181C2212yes—
33#107×C181C2211yescharacteristic
34#103×C181C2212yes—
35C2×D724C2312yes—
36C2×C22⋊D181—22no—
37C22×Dic181D411yescharacteristic
38C22×Dic181D411yescharacteristic
39C2×C4×D181—22no—
40#15668436—42no—
41D1448—41no—
42C2×#13089678—41no—
43C2×#13089678C2312yes—
44C4⋊Dic181—22no—
45C4⋊Dic181—22no—
46C4⋊Dic181C2312yes—
47#15668428—22no—
48#15668426—22no—
49#15668426—22no—
50#15668426—22no—
51#15668426—22no—
52C4×Dic181—22no—
53C4×Dic181D412yes—
54C4×Dic181C2312yes—
55C2×Q8×C181C2312yes—
56C22×C4×C181C2311yescharacteristic
57Q16×C181—41no—
58C2×C8×C181—41no—
59C2×C8×C181C2311yescharacteristic
60C2×C8×C181C2311yescharacteristic
61C4⋊C4×C181—22no—
62C4⋊C4×C181C2312yes—
63C22⋊C4×C181—22no—
64C22×D181—22no—
65D724—22no—
66D724—22no—
67C22⋊D181—44no—
68C2×Dic181—22no—
69C2×Dic181—22no—
70C2×Dic181—41no—
71C2×Dic181C2×D412yes—
72C2×Dic181C2×D412yes—
73C4×D181—44no—
74#13089678—22no—
75C23×C181C2×D411yescharacteristic
76Q8×C181—22no—
77Q8×C181—22no—
78C2×C4×C181—21no—
79C2×C4×C181—21no—
80C2×C4×C181—22no—
81C2×C4×C181—22no—
82C2×C4×C181C2×D411yescharacteristic
83C2×C4×C181C2411yescharacteristic
84C8×C181—21no—
85C8×C181—21no—
86C22×C181—21no—
87C22×C181—21no—
88C22×C181#13512yes—
89C22×C181C22×D411yescharacteristic
90C2×D181—42no—
91C2×D181—42no—
92C2×D181—42no—
93C4×C181—21no—
94C4×C181—42no—
95C4×C181—42no—
96C4×C181H(5,𝔽2)11yescharacteristic
97C4×C1812−1+411yescharacteristic
98Dic181—22no—
99Dic181—22no—
100Dic181—42no—
101C2×C181—22no—
102C2×C181#53711yescharacteristic
103C2×C181C2×#13511yescharacteristic
104C2×C181#57511yescharacteristic
105D181—82no—
106C181#325011yescharacteristic, complemented, Sylow
107#3250—1811nomaximal, Sylow
108#529—1812no—
109#479—1812no—
110#478—1812no—
111#467D18111yescharacteristic, complemented
112#466—1811no—
113#465—1812no—
114#464—1812no—
115#463—1812no—
116C2×C4⋊C8—1811no—
117C2×Q16C2×D18111yescharacteristic
118C2×SD16—1812no—
119C2×D8—1811no—
120C22×C8—1811no—
121C22×C8C2×D18111yescharacteristic
122#126—3622no—
123#125—1812no—
124#124—1812no—
125#123—3622no—
126C22⋊Q8C2×D18112yes—
127#121—1812no—
128C4×Q8—1812no—
129C4×D4—3622no—
130C4×D4—1812no—
131#117—3622no—
132C2×C42—1811no—
133#107—1811no—
134#107C2×D18111yescharacteristic
135#106—1812no—
136C4⋊C8—1812no—
137C4⋊C8—1812no—
138#103—1812no—
139#103C2×D18112yes—
140#102—1812no—
141#102—1812no—
142C2×Q8C22×D18112yes—
143C2×D4—3622no—
144C2×D4—1812no—
145C22×C4—3622no—
146C22×C4—1811no—
147C22×C4—1811no—
148C22×C4C22×D18111yescharacteristic
149Q16—41no—
150SD16—7242no—
151D8—7241no—
152C2×C8—41no—
153C2×C8—1812no—
154C2×C8—7241no—
155C2×C8C22×D18111yescharacteristic
156C2×C8C22×D18111yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—3622no—
159C4⋊C4—3622no—
160C4⋊C4—3622no—
161C4⋊C4—1812no—
162C4⋊C4C22×D18112yes—
163C22⋊C4—22no—
164C22⋊C4—3622no—
165C22⋊C4—3622no—
166C22⋊C4—3622no—
167C22⋊C4—3622no—
168C42—3622no—
169C42—1812no—
170C42—1812no—
171C23—3622no—
172C23D4×D18111yescharacteristic
173Q8—22no—
174Q8—22no—
175D4—3622no—
176D4—3622no—
177D4—7244no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—3622no—
183C2×C4—3622no—
184C2×C4—1812no—
185C2×C4—1812no—
186C2×C4—7244no—
187C2×C4—7241no—
188C2×C4D4×D18111yescharacteristic
189C2×C4C23×D18111yescharacteristic
190C8—21no—
191C8—21no—
192C8—3622no—
193C22—21no—
194C22—21no—
195C22—7242no—
196C22—7242no—
197C22—7242no—
198C22#1915383912yes—
199C22C2×D4×D18111yescharacteristic
200C4—21no—
201C4—42no—
202C4—42no—
203C4—3622no—
204C4—3622no—
205C4—7242no—
206C4#1915386111yescharacteristic
207C4#1915386311yescharacteristic
208C2—22no—
209C2—14482no—
210C2#2604185611yescharacteristic
211C2C2×#1915383911yescharacteristic
212C2#2604207611yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#467×C181C2
socleC22×C181C22×D4
prime radical#26041515C2
hypercenter#467D181
hypocenterC181#3250
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #26041815C2semidirect
2. #26041588C2semidirect
3. #26041582C2semidirect
5. #26041510C2semidirect
6. #26041503C2semidirect
7. #26041497C2semidirect
8. C2×#19153745C2semidirect
9. #467×C181C2semidirect
106. C181#3250semidirect
111. #467D181semidirect

Maximal subgroups

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

subgroupindex
#260418152
#260415882
#260415822
#260415152
#260415102
#260415032
#260414972
C2×#191537452
#467×C1812
#3250181