Finite Group Databasebeta

← #37546394

Subgroups — #37546394

Order 23168.

336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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
1Q8×Dic362C211yesmaximal, characteristic
2#26042004C211yesmaximal, characteristic
3#26041629C211yesmaximal, characteristic
4#26041628C212yesmaximal
5#26041575C211yesmaximal, characteristic
6#26041572C212yesmaximal
7#26041487C212yesmaximal
8#26041403C211yesmaximal, characteristic
9Q16×Dic181C212yesmaximal
10C4×#15668439C211yesmaximal, characteristic
11#462×C181C211yesmaximal, characteristic
12C2×#15668439C2211yescharacteristic
13#19153816—21no—
14#19153816C2211yescharacteristic
15#19153815—22no—
16#19153815C2212yes—
17#19153814C2212yes—
18#19153807—21no—
19#19153806—22no—
20Q8×Dic181C2212yes—
21Q8×Dic181C2212yes—
22C4×Dic362—21no—
23C4×Dic362C2211yescharacteristic
24C4×Dic362C2211yescharacteristic
25#19153781—21no—
26#19153750C2212yes—
27#19153749C2211yescharacteristic
28#19153745C2212yes—
29#19153741C2212yes—
30#19153740C2211yescharacteristic
31#19153740C2212yes—
32#19153740C2212yes—
33#19153739C2211yescharacteristic
34C4×#13089678C2211yescharacteristic
35C8×Dic181C2212yes—
36C2×Q16×C181C2212yes—
37C4⋊Q8×C181C2211yescharacteristic
38C4×Q8×C181C2211yescharacteristic
39C4⋊C8×C181C2211yescharacteristic
40#103×C181C2212yes—
41C2×Dic362—22no—
42C2×Dic362—21no—
43C2×Dic362D411yescharacteristic
44C2×Dic362C2311yescharacteristic
45#15668439—22no—
46C2×#13089678C2311yescharacteristic
47C2×#13089678C2311yescharacteristic
48C4⋊Dic181—22no—
49C4⋊Dic181—22no—
50C4⋊Dic181—21no—
51C4⋊Dic181D411yescharacteristic
52C4⋊Dic181C2312yes—
53C4⋊Dic181C2311yescharacteristic
54#15668428—22no—
55#15668428—22no—
56#15668428—22no—
57#15668428—21no—
58#15668428D412yes—
59C4×Dic181—22no—
60C4×Dic181—22no—
61C4×Dic181—21no—
62C4×Dic181C2312yes—
63C2×Q8×C181C2312yes—
64C2×Q8×C181C2311yescharacteristic
65Q16×C181—24no—
66C2×C8×C181C2312yes—
67C4⋊C4×C181—21no—
68C4⋊C4×C181—21no—
69C4⋊C4×C181—21no—
70C4⋊C4×C181C2311yescharacteristic
71C42×C181—21no—
72C42×C181C2311yescharacteristic
73Dic362—21no—
74Dic362—21no—
75Dic362—82no—
76Dic362—81no—
77Dic362Q1614yescomplemented
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—22no—
87Q8×C181—22no—
88Q8×C181#4112yes—
89C2×C4×C181—21no—
90C2×C4×C181—21no—
91C2×C4×C181—22no—
92C2×C4×C181C2×D411yescharacteristic
93C2×C4×C181C2×D411yescharacteristic
94C2×C4×C181C2411yescharacteristic
95C8×C181—22no—
96C22×C181C22×D411yescharacteristic
97C4×C181—22no—
98C4×C181—21no—
99C4×C181—42no—
100C4×C181—41no—
101C4×C181C2×Q1612yes—
102C4×C181C2×#4111yescharacteristic
103C4×C1812−1+411yescharacteristic
104Dic181—22no—
105Dic181—41no—
106Dic181—41no—
107Dic181—42no—
108Dic181C2×Q1614yes—
109C2×C181#54811yescharacteristic
110C2×C181C22×Q1611yescharacteristic
111C2×C181#57711yescharacteristic
112C181#336311yescharacteristic, complemented, Sylow
113#3363—1811nomaximal, Sylow
114Q82—1811no—
115#557—1811no—
116#487—1811no—
117#487—1812no—
118#477—1811no—
119#477—1812no—
120#462—1812no—
121#462D18111yescharacteristic
122C8×Q8—1811no—
123C4×Q16—1812no—
124C4×Q16—1811no—
125C2×Q16—1811no—
126C2×Q16C2×D18112yes—
127C4⋊Q8—3621no—
128C4⋊Q8—3622no—
129C4⋊Q8—1812no—
130C4⋊Q8—1812no—
131C4⋊Q8—1811no—
132C4⋊Q8C2×D18111yescharacteristic
133#125—3622no—
134#125—3621no—
135C4×Q8—3621no—
136C4×Q8—3621no—
137C4×Q8—1812no—
138C4×Q8—1812no—
139C4×Q8—1811no—
140C4×Q8—1811no—
141C4×Q8C2×D18111yescharacteristic
142#107—1812no—
143#107—1811no—
144C4⋊C8—1812no—
145C4⋊C8C2×D18111yescharacteristic
146#103—1811no—
147#103—1812no—
148#103—1812no—
149#103—1812no—
150#103—1811no—
151#103C2×D18112yes—
152C4×C8—1812no—
153C4×C8—1811no—
154C2×Q8—3622no—
155C2×Q8—3621no—
156C2×Q8—1811no—
157C2×Q8—1811no—
158C2×Q8C22×D18112yes—
159C2×Q8C22×D18111yescharacteristic
160Q16—24no—
161Q16—3622no—
162C2×C8—1811no—
163C2×C8—1811no—
164C2×C8C22×D18112yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—3622no—
169C4⋊C4—3622no—
170C4⋊C4—3622no—
171C4⋊C4—3622no—
172C4⋊C4—3622no—
173C4⋊C4—3621no—
174C4⋊C4—3621no—
175C4⋊C4—1812no—
176C4⋊C4—1811no—
177C4⋊C4—1812no—
178C4⋊C4—1811no—
179C4⋊C4C22×D18111yescharacteristic
180C42—21no—
181C42—3622no—
182C42—3622no—
183C42—3621no—
184C42—1812no—
185C42C22×D18111yescharacteristic
186Q8—21no—
187Q8—22no—
188Q8—22no—
189Q8—3621no—
190Q8—3621no—
191Q8—14481no—
192Q8—14482no—
193Q8—1814no—
194Q8#1566844812yes—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—3621no—
199C2×C4—3621no—
200C2×C4—3622no—
201C2×C4—1812no—
202C2×C4—1812no—
203C2×C4D4×D18111yescharacteristic
204C2×C4D4×D18111yescharacteristic
205C2×C4C23×D18111yescharacteristic
206C8—22no—
207C8—3621no—
208C8—3621no—
209C22C2×D4×D18111yescharacteristic
210C4—22no—
211C4—21no—
212C4—42no—
213C4—41no—
214C4—3622no—
215C4—1814no—
216C4—7241no—
217C4—7242no—
218C4—7241no—
219C4Q16×D18112yes—
220C4C2×#1566844811yescharacteristic
221C4#1915386311yescharacteristic
222C2#2604193511yescharacteristic
223C2C2×Q16×D18111yescharacteristic
224C2#2604208811yescharacteristic
subgroupG/H
centerC22C2×D4×D181
commutator, cosocleC2×C4×C181C24
FrattiniC2×C4C23×D181
Fitting#462×C181C2
socle, prime radicalC22×C181C22×D4
hypercenter#462D181
hypocenterC181#3363
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
77. Dic362Q16semidirect
112. C181#3363semidirect

Maximal subgroups

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

subgroupindex
Q8×Dic3622
#260420042
#260416292
#260416282
#260415752
#260415722
#260414872
#260414032
Q16×Dic1812
C4×#156684392
#462×C1812
#3363181