Finite Group Databasebeta

← #37535732

Subgroups — #37535732

Order 23168.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#26042032C211yesmaximal, characteristic, complemented
2#26041469C211yesmaximal, characteristic
3#26041457C211yesmaximal, characteristic
4#26041073C211yesmaximal, characteristic, complemented
5#26041069C211yesmaximal, characteristic, complemented
6#26041068C211yesmaximal, characteristic, complemented
7#458×C181C211yesmaximal, characteristic
8#19153846—21no—
9#19153815—21no—
10#19153809—21no—
11#19153809—21no—
12#19153806—21no—
13#19153803C2211yescharacteristic
14#19153797—21no—
15#19153797C2211yescharacteristic
16#19153795—21no—
17#19153793—21no—
18#19153743—21no—
19#19153733C2211yescharacteristic
20#19153731—21no—
21#19153731C2211yescharacteristic
22H(5,𝔽2)×C181C2211yescharacteristic
23#123×C181—21no—
24#123×C181C2211yescharacteristic
25#99×C181—21no—
26#99×C181C2211yescharacteristic
27C2×Dic362—21no—
28C2×Dic362D411yescharacteristic
29C22×Dic181D411yescharacteristic
30#15668439—41no—
31#15668437—41no—
32#15668433—21no—
33C4⋊Dic181—21no—
34C4⋊Dic181—21no—
35#15668428—21no—
36#15668428—21no—
37#15668428—21no—
38#15668428—21no—
39#15668428—21no—
40#15668428—41no—
41C22⋊Dic181—21no—
42C22⋊Dic181—21no—
43C22⋊Dic181—21no—
44C22⋊Dic181—21no—
45C22⋊Dic181—41no—
46C22⋊Dic181D411yescharacteristic
47C4×Dic181—21no—
48C4×Dic181D411yescharacteristic
49#41×C181—21no—
50#41×C181—41no—
51C2×D4×C181—21no—
52C2×D4×C181—21no—
53C2×D4×C181—41no—
54C2×D4×C181C2311yescharacteristic
55C22×C4×C181D411yescharacteristic
56C4⋊C4×C181—21no—
57C4⋊C4×C181—41no—
58C22⋊C4×C181—21no—
59C22⋊C4×C181—21no—
60C22⋊C4×C181—41no—
61C22⋊C4×C181D411yescharacteristic
62Dic362—41no—
63Dic362—81no—
64C2×Dic181—21no—
65C2×Dic181—21no—
66C2×Dic181—21no—
67C2×Dic181—21no—
68C2×Dic181—41no—
69C2×Dic181—41no—
70#13089678—41no—
71C23×C181—21no—
72C23×C181—21no—
73C23×C181C2×D411yescharacteristic
74C23×C181C2×D411yescharacteristic
75Q8×C181—21no—
76D4×C181—21no—
77D4×C181—41no—
78D4×C181—41no—
79D4×C181—41no—
80D4×C181—41no—
81C2×C4×C181—21no—
82C2×C4×C181—21no—
83C2×C4×C181—21no—
84C2×C4×C181—21no—
85C2×C4×C181—41no—
86C2×C4×C181—41no—
87C2×C4×C181—41no—
88C2×C4×C181C2×D411yescharacteristic
89C22×C181—21no—
90C22×C181—21no—
91C22×C181—41no—
92C22×C181—41no—
93C22×C181—41no—
94C22×C181—81no—
95C22×C181—81no—
96C22×C181#12011yescharacteristic
97C4×C181—21no—
98C4×C181—41no—
99C4×C181—41no—
100C4×C181—41no—
101C4×C181—81no—
102Dic181—41no—
103Dic181—41no—
104Dic181—41no—
105Dic181—41no—
106Dic181—81no—
107C2×C181—21no—
108C2×C181—41no—
109C2×C181—41no—
110C2×C181—81no—
111C2×C181B(4,𝔽2)11yescharacteristic
112C181#220111yescharacteristic, complemented, Sylow
113#2201—1811nomaximal, Sylow
114#563—1811no—
115#458—1811no—
116#458D18111yescharacteristic
117#455—1811no—
118#354—1811no—
119#352—1811no—
120#352—1811no—
121H(5,𝔽2)C2×D18111yescharacteristic
122#137—3621no—
123C4⋊Q8—3621no—
124#126—3621no—
125#126—3621no—
126#125—3621no—
127#124—1811no—
128#123—21no—
129#123—3621no—
130#123—1811no—
131#123C2×D18111yescharacteristic
132C22⋊Q8—3621no—
133C22⋊Q8—3621no—
134#104—3621no—
135#100—1811no—
136#99—21no—
137#99—3621no—
138#99—1811no—
139#99C2×D18111yescharacteristic
140#41—21no—
141#41—41no—
142C2×Q8—3621no—
143C2×Q8—1811no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—41no—
147C2×D4C22×D18111yescharacteristic
148C22×C4—1811no—
149C22×C4C22⋊D18111yescharacteristic
150Q16—7241no—
151SD16—7241no—
152M16—3621no—
153C4⋊C4—21no—
154C4⋊C4—41no—
155C4⋊C4—3621no—
156C4⋊C4—3621no—
157C4⋊C4—3621no—
158C4⋊C4—3621no—
159C4⋊C4—3621no—
160C4⋊C4—3621no—
161C4⋊C4—3621no—
162C4⋊C4—7241no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—41no—
166C22⋊C4—3621no—
167C22⋊C4—3621no—
168C22⋊C4—3621no—
169C22⋊C4—3621no—
170C22⋊C4—1811no—
171C22⋊C4—7241no—
172C22⋊C4C22⋊D18111yescharacteristic
173C42—3621no—
174C42—1811no—
175C23—21no—
176C23—21no—
177C23D4×D18111yescharacteristic
178C23C2×C22⋊D18111yescharacteristic
179Q8—21no—
180Q8—14481no—
181Q8—7241no—
182D4—21no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—41no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—3621no—
195C2×C4—3621no—
196C2×C4—3621no—
197C2×C4—3621no—
198C2×C4—7241no—
199C2×C4—7241no—
200C2×C4D4×D18111yescharacteristic
201C8—7241no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—81no—
209C22#1915378411yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—81no—
215C4—14481no—
216C4—7241no—
217C4—7241no—
218C4—7241no—
219C4—7241no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—81no—
224C2#2604146511yescharacteristic
subgroupG/H
centerC2#26041465
commutator, cosocleC2×D4×C181C23
FrattiniC2×D4C22×D181
Fitting#458×C181C2
socleC2×C181B(4,𝔽2)
prime radicalH(5,𝔽2)×C181C22
hypercenter#458D181
hypocenterC181#2201
LCSG ▷ C2×D4×C181 ▷ C22×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #26042032C2semidirect
4. #26041073C2semidirect
5. #26041069C2semidirect
6. #26041068C2semidirect
112. C181#2201semidirect

Maximal subgroups

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

subgroupindex
#260420322
#260414692
#260414572
#260410732
#260410692
#260410682
#458×C1812
#2201181