Finite Group Databasebeta

← #37546523

Subgroups — #37546523

Order 23168.

326 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 115 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#26042007C211yesmaximal, characteristic
2#26042004C211yesmaximal, characteristic
3#26041646C212yesmaximal
4#26041631C211yesmaximal, characteristic
5#26041589C212yesmaximal
6#26041490C211yesmaximal, characteristic
7#26041488C212yesmaximal
8#26041406C211yesmaximal, characteristic
9#26041385C212yesmaximal
10C4×#15668439C211yesmaximal, characteristic
11#475×C181C211yesmaximal, characteristic
12C2×Dic724C2212yes—
13C2×#15668439C2211yescharacteristic
14#19153816C2211yescharacteristic
15#19153814—21no—
16#19153814C2212yes—
17#19153808—21no—
18#19153807C2212yes—
19#19153806—22no—
20#19153806—22no—
21Q8×Dic181—21no—
22C4×Dic362—21no—
23C4×Dic362C2211yescharacteristic
24C4×Dic362C2211yescharacteristic
25#19153781C2212yes—
26#19153781C2212yes—
27#19153749C2211yescharacteristic
28#19153745C2212yes—
29#19153741C2212yes—
30#19153740C2211yescharacteristic
31#19153739C2211yescharacteristic
32#19153739C2212yes—
33#19153739C2212yes—
34#19153726C2212yes—
35C4×#13089678C2211yescharacteristic
36C4⋊Q8×C181C2211yescharacteristic
37C4×Q8×C181C2211yescharacteristic
38#106×C181C2212yes—
39C4⋊C8×C181C2211yescharacteristic
40#103×C181C2212yes—
41C2×Dic362D411yescharacteristic
42C2×Dic362C2312yes—
43C2×Dic362C2311yescharacteristic
44Dic724—24no—
45#15668439—22no—
46C2×#13089678C2311yescharacteristic
47C2×#13089678C2311yescharacteristic
48C4⋊Dic181—22no—
49C4⋊Dic181—21no—
50C4⋊Dic181—21no—
51C4⋊Dic181D411yescharacteristic
52C4⋊Dic181C2311yescharacteristic
53#15668428—22no—
54#15668428—22no—
55#15668428—22no—
56#15668428—22no—
57#15668428—22no—
58#15668428—21no—
59#15668428D412yes—
60C4×Dic181—22no—
61C4×Dic181—22no—
62C4×Dic181—21no—
63C4×Dic181C2312yes—
64C2×Q8×C181—21no—
65C2×Q8×C181C2311yescharacteristic
66C2×C8×C181C2312yes—
67C4⋊C4×C181—21no—
68C4⋊C4×C181—21no—
69C4⋊C4×C181C2312yes—
70C4⋊C4×C181C2311yescharacteristic
71C42×C181—21no—
72C42×C181C2311yescharacteristic
73Dic362—22no—
74Dic362—21no—
75Dic362—22no—
76Dic362—22no—
77Dic362#4112yes—
78C2×Dic181—21no—
79C2×Dic181—21no—
80C2×Dic181—22no—
81C2×Dic181C2×D412yes—
82C2×Dic181C2×D412yes—
83#13089678—21no—
84#13089678—21no—
85Q8×C181—21no—
86Q8×C181—21no—
87Q8×C181—42no—
88C2×C4×C181—21no—
89C2×C4×C181—21no—
90C2×C4×C181—22no—
91C2×C4×C181C2×D411yescharacteristic
92C2×C4×C181C2×D411yescharacteristic
93C2×C4×C181C2411yescharacteristic
94C8×C181—22no—
95C22×C181C22×D411yescharacteristic
96C4×C181—21no—
97C4×C181—41no—
98C4×C181—42no—
99C4×C181—41no—
100C4×C181#13712yes—
101C4×C181C2×#4111yescharacteristic
102C4×C1812−1+411yescharacteristic
103Dic181—22no—
104Dic181—22no—
105Dic181—22no—
106Dic181—42no—
107Dic181—41no—
108C2×C181#54811yescharacteristic
109C2×C181C2×#13711yescharacteristic
110C2×C181#57811yescharacteristic
111C181#337411yescharacteristic, complemented, Sylow
112#3374—1811nomaximal, Sylow
113#557—1811no—
114#557—1811no—
115#491—1812no—
116#487—1811no—
117#479—1812no—
118#475D18111yescharacteristic
119#462—1811no—
120#462—1812no—
121#446—1811no—
122#441—1812no—
123C4×Q16—1811no—
124C2×Q16—1811no—
125C2×Q16—1812no—
126C4⋊Q8—3621no—
127C4⋊Q8—1812no—
128C4⋊Q8—1811no—
129C4⋊Q8C2×D18111yescharacteristic
130#125—3621no—
131#125—3622no—
132#125—3622no—
133#125—1812no—
134C4×Q8—3621no—
135C4×Q8—3621no—
136C4×Q8—1812no—
137C4×Q8—1812no—
138C4×Q8—1811no—
139C4×Q8—1811no—
140C4×Q8C2×D18111yescharacteristic
141#107—1811no—
142#106C2×D18112yes—
143C4⋊C8—1812no—
144C4⋊C8C2×D18111yescharacteristic
145#103—1811no—
146#103—1812no—
147#103—1811no—
148#103—1812no—
149#103—1812no—
150#103C2×D18112yes—
151#97—1812no—
152C4×C8—1811no—
153C2×Q8—21no—
154C2×Q8—1812no—
155C2×Q8—1811no—
156C2×Q8—1811no—
157C2×Q8C22×D18111yescharacteristic
158Q16—3624no—
159Q16—3622no—
160C2×C8—1811no—
161C2×C8—1811no—
162C2×C8C22×D18112yes—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—3622no—
166C4⋊C4—3622no—
167C4⋊C4—3622no—
168C4⋊C4—3622no—
169C4⋊C4—3622no—
170C4⋊C4—3622no—
171C4⋊C4—3621no—
172C4⋊C4—3621no—
173C4⋊C4—3621no—
174C4⋊C4—1811no—
175C4⋊C4—1811no—
176C4⋊C4—1812no—
177C4⋊C4C22×D18112yes—
178C4⋊C4C22×D18111yescharacteristic
179C42—21no—
180C42—3622no—
181C42—3622no—
182C42—3621no—
183C42—1812no—
184C42C22×D18111yescharacteristic
185Q8—21no—
186Q8—21no—
187Q8—42no—
188Q8—3622no—
189Q8—3621no—
190Q8—3622no—
191Q8—3622no—
192Q8—1812no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—3621no—
197C2×C4—3621no—
198C2×C4—3622no—
199C2×C4—1812no—
200C2×C4—1812no—
201C2×C4D4×D18111yescharacteristic
202C2×C4D4×D18111yescharacteristic
203C2×C4C23×D18111yescharacteristic
204C8—22no—
205C8—3621no—
206C8—3621no—
207C22C2×D4×D18111yescharacteristic
208C4—21no—
209C4—41no—
210C4—42no—
211C4—41no—
212C4—3622no—
213C4—3622no—
214C4—3622no—
215C4—7242no—
216C4—7241no—
217C4#1915384512yes—
218C4#41×D18111yescharacteristic
219C4#1915386411yescharacteristic
220C2#2604193911yescharacteristic
221C2C2×#1915384511yescharacteristic
222C2#2604209511yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#475×C181C2
socle, prime radicalC22×C181C22×D4
hypercenter#475D181
hypocenterC181#3374
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
111. C181#3374semidirect

Maximal subgroups

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

subgroupindex
#260420072
#260420042
#260416462
#260416312
#260415892
#260414902
#260414882
#260414062
#260413852
C4×#156684392
#475×C1812
#3374181