Finite Group Databasebeta

← #37534860

Subgroups — #37534860

Order 23168.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 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×#19153815C211yesmaximal, characteristic
2C2×#19153740C211yesmaximal, characteristic
3#26041186C211yesmaximal, characteristic
4#26041042C211yesmaximal, characteristic
5#26041041C211yesmaximal, characteristic
6#26041033C211yesmaximal, characteristic
7C2×#103×C181C211yesmaximal, characteristic
8C22×Dic362—21no—
9C22×#13089678C2211yescharacteristic
10#19153815—22no—
11#19153815—22no—
12C2×C4⋊Dic181C2211yescharacteristic
13C2×C4⋊Dic181C2211yescharacteristic
14C2×#15668428—21no—
15C2×C4×Dic181C2211yescharacteristic
16#19153740—22no—
17#19153723—21no—
18#19153723—21no—
19C22×Q8×C181C2211yescharacteristic
20C22×C8×C181C2211yescharacteristic
21C2×C4⋊C4×C181C2211yescharacteristic
22#103×C181—22no—
23C2×Dic362—24no—
24C2×Dic362—42no—
25C2×Dic362—42no—
26C22×Dic181—21no—
27C22×Dic181—21no—
28C22×Dic181D411yescharacteristic
29C22×Dic181D411yescharacteristic
30C2×#13089678—21no—
31C2×#13089678—21no—
32C2×#13089678—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181—21no—
35C4⋊Dic181—21no—
36C4⋊Dic181D412yes—
37#15668428—24no—
38C4×Dic181—21no—
39C4×Dic181—21no—
40C2×Q8×C181—21no—
41C2×Q8×C181—21no—
42C2×Q8×C181—21no—
43C2×Q8×C181—21no—
44C2×Q8×C181—21no—
45C2×Q8×C181Q812yescomplemented
46C22×C4×C181—21no—
47C22×C4×C181—21no—
48C22×C4×C181C2311yescharacteristic
49C2×C8×C181—21no—
50C2×C8×C181—21no—
51C2×C8×C181—21no—
52C4⋊C4×C181—21no—
53C4⋊C4×C181D412yes—
54Dic362—48no—
55C2×Dic181—21no—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C2×Dic181—21no—
59C2×Dic181—22no—
60C2×Dic181—41no—
61C2×Dic181—41no—
62C2×Dic181—41no—
63C2×Dic181—41no—
64C2×Dic181—41no—
65C2×Dic181SD1612yes—
66C2×Dic181Q1612yes—
67#13089678—41no—
68C23×C181C2×D411yescharacteristic
69Q8×C181—22no—
70Q8×C181—22no—
71Q8×C181—41no—
72Q8×C181—41no—
73C2×C4×C181—22no—
74C2×C4×C181—22no—
75C2×C4×C181—41no—
76C2×C4×C181—41no—
77C2×C4×C181—41no—
78C2×C4×C181—41no—
79C2×C4×C181C2×D411yescharacteristic
80C2×C4×C181C2×D411yescharacteristic
81C2×C4×C181C2×Q811yescharacteristic
82C2×C4×C181#4111yescharacteristic
83C2×C4×C181#4111yescharacteristic
84C2×C4×C181#4111yescharacteristic
85C8×C181—41no—
86C22×C181#12011yescharacteristic
87C22×C181C22⋊Q811yescharacteristic
88C22×C181#12411yescharacteristic
89C22×C181C2×SD1611yescharacteristic
90C22×C181C2×Q1611yescharacteristic
91C22×C181AGL(1,ℤ/8)11yescharacteristic
92C22×C181#13711yescharacteristic
93C4×C181—42no—
94C4×C181—42no—
95C4×C181C22⋊Q811yescharacteristic
96C4×C181C22⋊Q811yescharacteristic
97C4×C181#12411yescharacteristic
98C4×C181#12411yescharacteristic
99Dic181—22no—
100Dic181—22no—
101Dic181—42no—
102Dic181—81no—
103C2×C181#39311yescharacteristic
104C2×C181#45011yescharacteristic
105C2×C181#45111yescharacteristic
106C2×C181#47511yescharacteristic
107C2×C181#47711yescharacteristic
108C2×C181#48711yescharacteristic
109C2×C181#48911yescharacteristic
110C181#202411yescharacteristic, complemented, Sylow
111#2024—1811nomaximal, Sylow
112C2×C4⋊Q8—1811no—
113C2×#103—1811no—
114C2×#103D18111yescharacteristic
115#391—1811no—
116#340—1811no—
117#340—1811no—
118#336—1811no—
119C22×Q8—3621no—
120C22×Q8C2×D18111yescharacteristic
121C22×C8—1811no—
122C22×C8C2×D18111yescharacteristic
123C4⋊Q8—3622no—
124C4⋊Q8—3622no—
125C2×C4⋊C4—3621no—
126C2×C4⋊C4—1811no—
127C2×C4⋊C4—1811no—
128C2×C4⋊C4C2×D18111yescharacteristic
129C2×C42—1811no—
130#103—22no—
131#103—3622no—
132#95—3621no—
133#95—3621no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—3624no—
140C2×Q8—7242no—
141C2×Q8—7242no—
142C2×Q8Dic36212yescomplemented
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—3621no—
146C22×C4—3621no—
147C22×C4—1811no—
148C22×C4—1811no—
149C22×C4C22×D18111yescharacteristic
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—3621no—
154C2×C8—3621no—
155C2×C8—3621no—
156C4⋊C4—21no—
157C4⋊C4—3624no—
158C4⋊C4—3621no—
159C4⋊C4—3621no—
160C4⋊C4—3621no—
161C4⋊C4—1812no—
162C4⋊C4C22⋊D18112yes—
163C42—3621no—
164C42—3621no—
165C23D4×D18111yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—7248no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—3621no—
178C2×C4—3621no—
179C2×C4—3621no—
180C2×C4—3621no—
181C2×C4—3622no—
182C2×C4—1812no—
183C2×C4—1812no—
184C2×C4—7241no—
185C2×C4—7241no—
186C2×C4—7241no—
187C2×C4—7241no—
188C2×C4—7241no—
189C2×C4D4×D18111yescharacteristic
190C2×C4C2×C22⋊D18111yescharacteristic
191C2×C4C2×Dic36211yescharacteristic
192C2×C4#1566844811yescharacteristic
193C2×C4#1566844811yescharacteristic
194C2×C4#1566844911yescharacteristic
195C8—41no—
196C8—7241no—
197C22#1915378411yescharacteristic
198C22#1915379311yescharacteristic
199C22#1915380211yescharacteristic
200C22SD16×D18111yescharacteristic
201C22Q16×D18111yescharacteristic
202C22#1915384311yescharacteristic
203C22#1915384811yescharacteristic
204C4—42no—
205C4—42no—
206C4—3622no—
207C4—3622no—
208C4—14481no—
209C4—7242no—
210C4#1915379311yescharacteristic
211C4#1915379511yescharacteristic
212C4#1915380211yescharacteristic
213C4#1915380311yescharacteristic
214C2#2604119111yescharacteristic
215C2#2604142811yescharacteristic
216C2#2604143311yescharacteristic
217C2#2604156211yescharacteristic
218C2#2604157211yescharacteristic
219C2#2604162811yescharacteristic
220C2#2604164011yescharacteristic
subgroupG/H
centerC23D4×D181
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
FittingC2×#103×C181C2
socle, prime radicalC23×C181C2×D4
hypercenterC2×#103D181
hypocenterC181#2024
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
45. C2×Q8×C181Q8semidirect
110. C181#2024semidirect
142. C2×Q8Dic362semidirect

Maximal subgroups

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

subgroupindex
C2×#191538152
C2×#191537402
#260411862
#260410422
#260410412
#260410332
C2×#103×C1812
#2024181