Finite Group Databasebeta

← #37542092

Subgroups — #37542092

Order 23168.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C2×#19153807C211yesmaximal, characteristic, complemented
2C2×#19153803C211yesmaximal, characteristic
3#26041185C211yesmaximal, characteristic, complemented
4#26041184C211yesmaximal, characteristic, complemented
5#26041182C211yesmaximal, characteristic
6#26041172C214yesmaximal, complemented
7#26041167C214yesmaximal, complemented
8C42×Dic181C211yesmaximal, characteristic, complemented
9#390×C181C211yesmaximal, characteristic
10C22×Dic362C2211yescharacteristic
11#19153807—24no—
12#19153803—24no—
13C2×C4⋊Dic181C2212yes—
14C2×C4⋊Dic181C2211yescharacteristic
15C2×#15668428C2212yes—
16C2×C22⋊Dic181C2212yes—
17C2×C22⋊Dic181C2214yes—
18C2×C22⋊Dic181C2212yes—
19C2×C4×Dic181C2212yes—
20C2×C4×Dic181C2212yes—
21C2×C4×Dic181C2211yescharacteristic
22C2×C4×Dic181C2211yescharacteristic
23#19153723C2214yes—
24#19153723C2214yes—
25C22×D4×C181C2211yescharacteristic
26C2×C4⋊C4×C181C2211yescharacteristic
27C2×C22⋊C4×C181C2214yes—
28C2×C42×C181C2211yescharacteristic
29C2×Dic362—22no—
30C2×Dic362—22no—
31C2×Dic362—22no—
32C22×Dic181C2312yes—
33C22×Dic181C2312yes—
34C22×Dic181C2311yescharacteristic
35C22×Dic181C2311yescharacteristic
36C22×Dic181C2312yes—
37C4⋊Dic181—24no—
38C4⋊Dic181—22no—
39#15668428—24no—
40C22⋊Dic181—24no—
41C22⋊Dic181—24no—
42C22⋊Dic181—28no—
43C4×Dic181—24no—
44C4×Dic181—24no—
45C4×Dic181—22no—
46C4×Dic181D414yes—
47C24×C181C2312yes—
48C2×D4×C181—22no—
49C2×D4×C181—22no—
50C2×D4×C181—22no—
51C22×C4×C181C2312yes—
52C22×C4×C181C2312yes—
53C22×C4×C181C2311yescharacteristic
54C4⋊C4×C181—22no—
55C22⋊C4×C181—28no—
56C42×C181—22no—
57Dic362—44no—
58C2×Dic181—22no—
59C2×Dic181—22no—
60C2×Dic181—22no—
61C2×Dic181—22no—
62C2×Dic181—22no—
63C2×Dic181—22no—
64C2×Dic181—24no—
65C2×Dic181—22no—
66C2×Dic181—22no—
67C2×Dic181C2×D412yes—
68C2×Dic181C2×D412yes—
69C2×Dic181#4114yes—
70C23×C181—22no—
71C23×C181—24no—
72C23×C181—22no—
73C23×C181—22no—
74C23×C181—24no—
75C23×C181C2411yescharacteristic
76D4×C181—44no—
77C2×C4×C181—22no—
78C2×C4×C181—22no—
79C2×C4×C181—22no—
80C2×C4×C181—24no—
81C2×C4×C181C2×D412yes—
82C2×C4×C181#4114yes—
83C2×C4×C181#4112yes—
84C2×C4×C181#4112yes—
85C22×C181—42no—
86C22×C181—44no—
87C22×C181—44no—
88C22×C181—42no—
89C22×C181—42no—
90C22×C181C22×D411yescharacteristic
91C22×C181C2×#4112yes—
92C22×C181C2×#4111yescharacteristic
93C22×C181C2×#4112yes—
94C22×C181C2×#4111yescharacteristic
95C4×C181—24no—
96C4×C181—42no—
97C4×C181#12414yes—
98Dic181—24no—
99Dic181—22no—
100Dic181—22no—
101Dic181—42no—
102Dic181—42no—
103C2×C181—82no—
104C2×C181C2×#12411yescharacteristic
105C2×C181#52912yes—
106C2×C181#52912yes—
107C2×C181#53211yescharacteristic
108C2×C181#53211yescharacteristic
109C181#286111yescharacteristic, complemented, Sylow
110#2861—1811nomaximal, Sylow
111C2×#125—1811no—
112C2×#124—1811no—
113#391—1811no—
114#391—1811no—
115#390—1811no—
116#390D18111yescharacteristic
117#388—1814no—
118#388—1814no—
119C43—1811no—
120C22×Q8—1811no—
121C22×D4C2×D18111yescharacteristic
122#125—3624no—
123#124—3624no—
124C2×C4⋊C4—1812no—
125C2×C4⋊C4—1812no—
126C2×C4⋊C4—1811no—
127C2×C4⋊C4C2×D18111yescharacteristic
128C2×C22⋊C4—1812no—
129C2×C22⋊C4—1812no—
130C2×C22⋊C4—1814no—
131C2×C22⋊C4C2×D18114yes—
132C2×C42—1812no—
133C2×C42—1812no—
134C2×C42—1811no—
135C2×C42—1811no—
136C2×C42C2×D18111yescharacteristic
137#95—1814no—
138#95—1814no—
139C24C22×D18112yes—
140C2×Q8—3622no—
141C2×Q8—3622no—
142C2×Q8—3622no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4—22no—
146C22×C4—1812no—
147C22×C4—1812no—
148C22×C4—1812no—
149C22×C4—1811no—
150C22×C4—1811no—
151C22×C4C22×D18112yes—
152C22×C4C22×D18112yes—
153C22×C4C22×D18111yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—3624no—
156C4⋊C4—3624no—
157C4⋊C4—3622no—
158C22⋊C4—28no—
159C22⋊C4—3624no—
160C22⋊C4—3624no—
161C22⋊C4—3628no—
162C42—22no—
163C42—3624no—
164C42—3624no—
165C42—3622no—
166C42—1814no—
167C23—22no—
168C23—24no—
169C23—24no—
170C23—22no—
171C23—22no—
172C23C23×D18111yescharacteristic
173Q8—7244no—
174D4—44no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—24no—
179C2×C4—3622no—
180C2×C4—3622no—
181C2×C4—3622no—
182C2×C4—3622no—
183C2×C4—3622no—
184C2×C4—3622no—
185C2×C4—3624no—
186C2×C4—3622no—
187C2×C4—3622no—
188C2×C4—1812no—
189C2×C4—1812no—
190C2×C4—1814no—
191C2×C4D4×D18112yes—
192C2×C4#1566844814yes—
193C2×C4#1566844812yes—
194C2×C4#1566844912yes—
195C22—42no—
196C22—44no—
197C22—44no—
198C22—42no—
199C22—42no—
200C22C2×D4×D18111yescharacteristic
201C22#41×D18112yes—
202C22C2×#1566844811yescharacteristic
203C22C2×#1566844812yes—
204C22C2×#1566844911yescharacteristic
205C4—24no—
206C4—42no—
207C4—3624no—
208C4—3622no—
209C4—3622no—
210C4—7242no—
211C4—7242no—
212C4#1915380214yes—
213C2—82no—
214C2C2×#1915380211yescharacteristic
215C2#2604181012yes—
216C2#2604181112yes—
217C2#2604182711yescharacteristic
218C2#2604182811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D181
commutator, socle, cosocleC23×C181C24
Fitting#390×C181C2
prime radicalC22×D4×C181C22
hypercenter#390D181
hypocenterC181#2861
LCSG ▷ C23×C181 ▷ C181
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#19153807C2semidirect
3. #26041185C2semidirect
4. #26041184C2semidirect
6. #26041172C2semidirect
7. #26041167C2semidirect
8. C42×Dic181C2semidirect
109. C181#2861semidirect

Maximal subgroups

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

subgroupindex
C2×#191538072
C2×#191538032
#260411852
#260411842
#260411822
#260411722
#260411672
C42×Dic1812
#390×C1812
#2861181