Finite Group Databasebeta

← #37546529

Subgroups — #37546529

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#26042004C211yesmaximal, characteristic
2#26042004C211yesmaximal, characteristic
3#26041646C212yesmaximal
4#26041588C212yesmaximal
5#26041561C211yesmaximal, characteristic
6#26041488C212yesmaximal
7#26041486C211yesmaximal, characteristic
8#26041409C211yesmaximal, characteristic
9#26041383C212yesmaximal
10C4×Dic724C211yesmaximal, characteristic
11#487×C181C211yesmaximal, characteristic
12C2×Dic724C2211yescharacteristic
13C2×#15668439C2212yes—
14#19153814—21no—
15#19153814C2212yes—
16#19153807—21no—
17#19153807C2212yes—
18#19153806—22no—
19#19153806—22no—
20Q8×Dic181—21no—
21Q8×Dic181C2212yes—
22C4×Dic362C2211yescharacteristic
23C4×Dic362C2211yescharacteristic
24C4×Dic362C2211yescharacteristic
25#19153781—21no—
26#19153781C2212yes—
27#19153750C2211yescharacteristic
28#19153747C2212yes—
29C4⋊#13089678C2211yescharacteristic
30#19153745C2212yes—
31#19153741C2211yescharacteristic
32#19153741C2211yescharacteristic
33#19153740C2212yes—
34#19153739C2212yes—
35#19153726C2212yes—
36C4⋊Q8×C181C2211yescharacteristic
37C4⋊Q8×C181C2211yescharacteristic
38#103×C181C2212yes—
39#103×C181C2212yes—
40C4×C8×C181C2211yescharacteristic
41C2×Dic362D411yescharacteristic
42C2×Dic362C2311yescharacteristic
43C2×Dic362C2311yescharacteristic
44Dic724—22no—
45#15668439—24no—
46C2×#13089678C2312yes—
47C4⋊Dic181—22no—
48C4⋊Dic181—22no—
49C4⋊Dic181D411yescharacteristic
50C4⋊Dic181C2311yescharacteristic
51C4⋊Dic181C2311yescharacteristic
52#15668428—22no—
53#15668428—22no—
54#15668428—22no—
55#15668428—22no—
56#15668428—21no—
57#15668428—21no—
58#15668428D412yes—
59C4×Dic181—22no—
60C4×Dic181—22no—
61C4×Dic181—21no—
62C4×Dic181—21no—
63C4×Dic181C2312yes—
64C2×Q8×C181—21no—
65C2×Q8×C181C2312yes—
66C2×C8×C181C2311yescharacteristic
67C2×C8×C181C2311yescharacteristic
68C4⋊C4×C181—21no—
69C4⋊C4×C181—21no—
70C4⋊C4×C181—21no—
71C4⋊C4×C181C2312yes—
72C42×C181C2311yescharacteristic
73Dic362—22no—
74Dic362—21no—
75Dic362—21no—
76Dic362—21no—
77Dic362#4112yes—
78C2×Dic181—21no—
79C2×Dic181—21no—
80C2×Dic181—21no—
81C2×Dic181—21no—
82C2×Dic181C2×D412yes—
83C2×Dic181C2×D412yes—
84#13089678—22no—
85Q8×C181—22no—
86Q8×C181—22no—
87Q8×C181—42no—
88C2×C4×C181—22no—
89C2×C4×C181—22no—
90C2×C4×C181C2×D411yescharacteristic
91C2×C4×C181C2×D411yescharacteristic
92C2×C4×C181C2411yescharacteristic
93C8×C181—21no—
94C8×C181—21no—
95C22×C181C22×D411yescharacteristic
96C4×C181—21no—
97C4×C181—42no—
98C4×C181—42no—
99C4×C181#13712yes—
100C4×C181C2×#4111yescharacteristic
101C4×C1812−1+411yescharacteristic
102Dic181—22no—
103Dic181—22no—
104Dic181—22no—
105Dic181—41no—
106Dic181—41no—
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#487D18111yescharacteristic
117#479—1812no—
118#475—1811no—
119#462—1811no—
120#462—1812no—
121#446—1811no—
122#441—1812no—
123C4×Q16—1811no—
124C2×Q16—1812no—
125C2×Q16—1811no—
126C4⋊Q8—3621no—
127C4⋊Q8—1812no—
128C4⋊Q8C2×D18111yescharacteristic
129C4⋊Q8C2×D18111yescharacteristic
130#125—3622no—
131#125—3622no—
132#125—3621no—
133#125—1812no—
134C4×Q8—3621no—
135C4×Q8—3621no—
136C4×Q8—1812no—
137C4×Q8—1812no—
138C4×Q8—1811no—
139C4×Q8—1811no—
140C4×Q8—1811no—
141#107—1811no—
142#106—1812no—
143C4⋊C8—1812no—
144C4⋊C8—1811no—
145#103—1812no—
146#103—1811no—
147#103—1811no—
148#103—1812no—
149#103C2×D18112yes—
150#103C2×D18112yes—
151#97—1812no—
152C4×C8C2×D18111yescharacteristic
153C2×Q8—21no—
154C2×Q8—1811no—
155C2×Q8—1811no—
156C2×Q8—1811no—
157C2×Q8C22×D18112yes—
158Q16—3622no—
159Q16—3624no—
160C2×C8—1812no—
161C2×C8C22×D18111yescharacteristic
162C2×C8C22×D18111yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—3622no—
167C4⋊C4—3622no—
168C4⋊C4—3622no—
169C4⋊C4—3622no—
170C4⋊C4—3622no—
171C4⋊C4—3622no—
172C4⋊C4—3621no—
173C4⋊C4—3621no—
174C4⋊C4—1811no—
175C4⋊C4—1811no—
176C4⋊C4—1811no—
177C4⋊C4—1812no—
178C4⋊C4C22×D18112yes—
179C42—3622no—
180C42—3622no—
181C42—3621no—
182C42—3621no—
183C42—1812no—
184C42C22×D18111yescharacteristic
185Q8—22no—
186Q8—22no—
187Q8—42no—
188Q8—3622no—
189Q8—3621no—
190Q8—3621no—
191Q8—3621no—
192Q8—1812no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—3621no—
196C2×C4—3621no—
197C2×C4—3621no—
198C2×C4—3621no—
199C2×C4—1812no—
200C2×C4—1812no—
201C2×C4D4×D18111yescharacteristic
202C2×C4D4×D18111yescharacteristic
203C2×C4C23×D18111yescharacteristic
204C8—21no—
205C8—21no—
206C8—3622no—
207C22C2×D4×D18111yescharacteristic
208C4—21no—
209C4—42no—
210C4—42no—
211C4—3622no—
212C4—3622no—
213C4—3622no—
214C4—7241no—
215C4—7241no—
216C4—7241no—
217C4#1915384512yes—
218C4#41×D18111yescharacteristic
219C4#1915386311yescharacteristic
220C2#2604193711yescharacteristic
221C2C2×#1915384511yescharacteristic
222C2#2604209211yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#487×C181C2
socle, prime radicalC22×C181C22×D4
hypercenter#487D181
hypocenterC181#3374
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #487

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
#260420042
#260416462
#260415882
#260415612
#260414882
#260414862
#260414092
#260413832
C4×Dic7242
#487×C1812
#3374181