Finite Group Databasebeta

← #37535111

Subgroups — #37535111

Order 23168.

248 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19153745C211yesmaximal, characteristic
2C2×#19153741C211yesmaximal, characteristic
3C2×#19153739C211yesmaximal, characteristic
4#26041184C211yesmaximal, characteristic
5#26041178C211yesmaximal, characteristic
6#26041041C211yesmaximal, characteristic
7C2×#107×C181C211yesmaximal, characteristic
8C22×Dic362C2211yescharacteristic
9C22×#13089678C2211yescharacteristic
10C2×C4⋊Dic181—21no—
11C2×C4⋊Dic181C2211yescharacteristic
12C2×C4×Dic181C2211yescharacteristic
13#19153745—22no—
14#19153741—22no—
15#19153739—22no—
16#19153723—21no—
17#19153723—21no—
18#19153723—21no—
19C22×C8×C181C2211yescharacteristic
20C2×C4⋊C4×C181C2211yescharacteristic
21C2×C4⋊C4×C181C2211yescharacteristic
22#107×C181—22no—
23C2×Dic362—21no—
24C2×Dic362—21no—
25C2×Dic362—21no—
26C2×Dic362—21no—
27C2×Dic362—21no—
28C2×Dic362Q812yes—
29C22×Dic181—21no—
30C22×Dic181—21no—
31C22×Dic181D411yescharacteristic
32C22×Dic181D411yescharacteristic
33C2×#13089678—21no—
34C2×#13089678—21no—
35C2×#13089678—21no—
36C4⋊Dic181—21no—
37C4⋊Dic181—21no—
38C4⋊Dic181—42no—
39C4×Dic181—21no—
40C4×Dic181—21no—
41C22×C4×C181—21no—
42C22×C4×C181—21no—
43C22×C4×C181C2311yescharacteristic
44C2×C8×C181—21no—
45C2×C8×C181—21no—
46C2×C8×C181D412yes—
47C4⋊C4×C181—21no—
48C4⋊C4×C181—21no—
49C4⋊C4×C181—21no—
50C4⋊C4×C181D412yes—
51Dic362—22no—
52Dic362—22no—
53Dic362—41no—
54Dic362—41no—
55C2×Dic181—21no—
56C2×Dic181—21no—
57C2×Dic181—21no—
58C2×Dic181—22no—
59C2×Dic181—21no—
60C2×Dic181—21no—
61C2×Dic181—41no—
62C2×Dic181—41no—
63C2×Dic181—41no—
64C2×Dic181—41no—
65C2×Dic181—41no—
66C2×Dic181Q1612yes—
67#13089678—41no—
68C23×C181C2×D411yescharacteristic
69C2×C4×C181—22no—
70C2×C4×C181—41no—
71C2×C4×C181—41no—
72C2×C4×C181—41no—
73C2×C4×C181—41no—
74C2×C4×C181—41no—
75C2×C4×C181C2×D411yescharacteristic
76C2×C4×C181C2×D411yescharacteristic
77C2×C4×C181C2×Q811yescharacteristic
78C2×C4×C181#4111yescharacteristic
79C2×C4×C181#4111yescharacteristic
80C2×C4×C181#4111yescharacteristic
81C8×C181—22no—
82C22×C181#12111yescharacteristic
83C22×C181#12111yescharacteristic
84C22×C181C22⋊Q811yescharacteristic
85C22×C181C2×Q1611yescharacteristic
86C22×C181#13511yescharacteristic
87C22×C181AGL(1,ℤ/8)11yescharacteristic
88C22×C181#13711yescharacteristic
89C4×C181—42no—
90C4×C181—81no—
91C4×C181#12111yescharacteristic
92C4×C181C22⋊Q811yescharacteristic
93C4×C181C22⋊Q811yescharacteristic
94C4×C181#12611yescharacteristic
95Dic181—22no—
96Dic181—42no—
97Dic181—41no—
98Dic181—81no—
99C2×C181#39611yescharacteristic
100C2×C181#46211yescharacteristic
101C2×C181#46311yescharacteristic
102C2×C181#46711yescharacteristic
103C2×C181#46811yescharacteristic
104C2×C181#47711yescharacteristic
105C2×C181#47911yescharacteristic
106C181#206811yescharacteristic, complemented, Sylow
107#2068—1811nomaximal, Sylow
108C2×#107D18111yescharacteristic
109C2×C4⋊C8—1811no—
110C2×#103—1811no—
111C2×#103—1811no—
112#391—1811no—
113#389—1811no—
114#340—1811no—
115C22×Q8—1811no—
116C22×C8—1811no—
117C22×C8C2×D18111yescharacteristic
118C2×C4⋊C4—3621no—
119C2×C4⋊C4—1811no—
120C2×C4⋊C4C2×D18111yescharacteristic
121C2×C4⋊C4C2×D18111yescharacteristic
122C2×C42—1811no—
123#107—22no—
124C4⋊C8—3622no—
125#103—3622no—
126#103—3622no—
127#95—3621no—
128#95—3621no—
129#95—3621no—
130C2×Q8—3621no—
131C2×Q8—3621no—
132C2×Q8—3621no—
133C2×Q8—3621no—
134C2×Q8—3621no—
135C2×Q8—1812no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—3621no—
139C22×C4—3621no—
140C22×C4—1811no—
141C22×C4—1811no—
142C22×C4C22×D18111yescharacteristic
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—3621no—
146C2×C8—3621no—
147C2×C8—3621no—
148C2×C8D72412yes—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—3621no—
153C4⋊C4—3621no—
154C4⋊C4—7242no—
155C4⋊C4C22⋊D18112yes—
156C42—3621no—
157C42—3621no—
158C23D4×D18111yescharacteristic
159Q8—3622no—
160Q8—3622no—
161Q8—7241no—
162Q8—7241no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—3621no—
170C2×C4—3621no—
171C2×C4—3621no—
172C2×C4—3622no—
173C2×C4—3621no—
174C2×C4—3621no—
175C2×C4—1812no—
176C2×C4—7241no—
177C2×C4—7241no—
178C2×C4—7241no—
179C2×C4—7241no—
180C2×C4—7241no—
181C2×C4C2×C22⋊D18111yescharacteristic
182C2×C4C2×D72411yescharacteristic
183C2×C4Q8×D18111yescharacteristic
184C2×C4#1566844811yescharacteristic
185C2×C4#1566844911yescharacteristic
186C2×C4#1566845011yescharacteristic
187C8—22no—
188C8—7241no—
189C22#1915378811yescharacteristic
190C22#1915379111yescharacteristic
191C22#1915379411yescharacteristic
192C22Q16×D18111yescharacteristic
193C22#1915383511yescharacteristic
194C22#1915384011yescharacteristic
195C22#1915384811yescharacteristic
196C4—42no—
197C4—81no—
198C4—3622no—
199C4—14481no—
200C4—7242no—
201C4—7241no—
202C4#1915379011yescharacteristic
203C4#1915379211yescharacteristic
204C4#1915379611yescharacteristic
205C4#1915381111yescharacteristic
206C2#2604120111yescharacteristic
207C2#2604148711yescharacteristic
208C2#2604149211yescharacteristic
209C2#2604152111yescharacteristic
210C2#2604152611yescharacteristic
211C2#2604157311yescharacteristic
212C2#2604158511yescharacteristic
subgroupG/H
centerC23D4×D181
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
FittingC2×#107×C181C2
socle, prime radicalC23×C181C2×D4
hypercenterC2×#107D181
hypocenterC181#2068
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
106. C181#2068semidirect

Maximal subgroups

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

subgroupindex
C2×#191537452
C2×#191537412
C2×#191537392
#260411842
#260411782
#260410412
C2×#107×C1812
#2068181