Finite Group Databasebeta

← #37534735

Subgroups — #37534735

Order 23168.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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×#19153841C211yesmaximal, characteristic, complemented
2#26041843C211yesmaximal, characteristic, complemented
3C2×#19153813C211yesmaximal, characteristic, complemented
4#26041285C211yesmaximal, characteristic, complemented
5C2×#19153732C211yesmaximal, characteristic, complemented
6#26041039C211yesmaximal, characteristic, complemented
7C2×#104×C181C211yesmaximal, characteristic, complemented
8C22×D724—22no—
9C22×D724C2211yescharacteristic
10C22×D724C2211yescharacteristic
11#19153841—22no—
12#19153841—22no—
13C2×#15668436—21no—
14C2×#15668434—21no—
15C2×#15668433C2211yescharacteristic
16#19153813—22no—
17#19153813—22no—
18#19153812—21no—
19#19153805—21no—
20#19153790—22no—
21#19153784—22no—
22#19153775C2211yescharacteristic
23#19153738—22no—
24#19153732—22no—
25C2×#41×C181C2211yescharacteristic
26C2×M16×C181C2211yescharacteristic
27C2×C42×C181C2211yescharacteristic
28#104×C181—22no—
29C23×D181—21no—
30C23×D181D412yes—
31C2×D724—28no—
32C2×D724—21no—
33C2×D724—21no—
34C2×D724—21no—
35C2×D724—21no—
36C2×D724—21no—
37C2×D724—21no—
38C2×D724—21no—
39C2×D724—21no—
40C2×D724—21no—
41C2×D724—21no—
42C2×D724—21no—
43C2×D724—48no—
44C2×D724D412yescomplemented
45C2×C22⋊D181—24no—
46#15668436—24no—
47#15668434—24no—
48#15668433—21no—
49#15668433D412yescomplemented
50C2×#13089678—21no—
51C4⋊Dic181D412yescomplemented
52C22⋊Dic181—21no—
53#15668426—24no—
54C4×Dic181—21no—
55#41×C181—21no—
56#41×C181—21no—
57#41×C181—21no—
58#41×C181—21no—
59C2×Q8×C181D411yescharacteristic, complemented
60C2×D4×C181—21no—
61C2×D4×C181D411yescharacteristic, complemented
62C22×C4×C181—21no—
63C22×C4×C181—21no—
64C22×C4×C181C2311yescharacteristic
65M16×C181—21no—
66M16×C181—21no—
67C2×C8×C181—21no—
68C42×C181—21no—
69C42×C181D412yescomplemented
70C22×D181—22no—
71C22×D181—22no—
72C22×D181—22no—
73C22×D181—22no—
74C22×D181—44no—
75C22×D181—44no—
76C22×D181—41no—
77C22×D181—41no—
78D724—22no—
79D724—22no—
80D724—416no—
81D724—41no—
82D724—41no—
83D724—41no—
84D724—41no—
85D724—41no—
86D724—41no—
87C22⋊D181—84no—
88C2×Dic181—22no—
89#13089678—22no—
90C23×C181—21no—
91C23×C181C2×D411yescharacteristic
92Q8×C181—21no—
93Q8×C181—21no—
94D4×C181—21no—
95D4×C181—21no—
96D4×C181—41no—
97D4×C181—41no—
98C2×C4×C181—24no—
99C2×C4×C181—22no—
100C2×C4×C181—21no—
101C2×C4×C181—41no—
102C2×C4×C181—41no—
103C2×C4×C181C2×D411yescharacteristic
104C2×C4×C181C2×D411yescharacteristic
105C2×C4×C181C2×D411yescharacteristic
106C2×C4×C181C2×D411yescharacteristic
107C2×C4×C181C2×D411yescharacteristic
108C2×C4×C181#4111yescharacteristic
109C8×C181—41no—
110C22×C181—22no—
111C22×C181—41no—
112C22×C181—42no—
113C22×C181#12011yescharacteristic
114C22×C181#12011yescharacteristic
115C22×C181#12111yescharacteristic
116C2×D181—44no—
117C2×D181—44no—
118C2×D181—42no—
119C2×D181—42no—
120C2×D181—44no—
121C2×D181—82no—
122C2×D181—82no—
123C2×D181—82no—
124C4×C181—24no—
125C4×C181—41no—
126C4×C181#12011yescharacteristic
127C4×C181#12111yescharacteristic
128C4×C181#12111yescharacteristic
129C4×C181#12711yescharacteristic
130Dic181—42no—
131C2×C181—21no—
132C2×C181—21no—
133C2×C181—81no—
134C2×C181#39211yescharacteristic
135C2×C181#45312yes—
136D181—82no—
137D181—82no—
138C181#200211yescharacteristic, complemented, Sylow
139#2002—1811nomaximal, Sylow
140C2×AGL(1,ℤ/8)—1811no—
141#535—1811no—
142C2×#127—1811no—
143C2×#104D18111yescharacteristic, complemented
144#418—1811no—
145C2×#100—1811no—
146#339—1811no—
147C2×#41C2×D18111yescharacteristic
148C22×D4—3622no—
149C22×D4—1811no—
150C22×D4—1811no—
151AGL(1,ℤ/8)—3622no—
152AGL(1,ℤ/8)—3622no—
153C2×SD16—3621no—
154C2×D8—3621no—
155C2×M16—1811no—
156C2×M16C2×D18111yescharacteristic
157#127—3622no—
158#127—3621no—
159#127—3622no—
160#124—3621no—
161#121—3622no—
162#120—3622no—
163#117—1811no—
164C2×C42C2×D18111yescharacteristic
165#104—22no—
166#102—3622no—
167#100—3622no—
168C24—3621no—
169C24—1812no—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8D72411yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—3628no—
177C2×D4—3624no—
178C2×D4—3621no—
179C2×D4—3621no—
180C2×D4—3621no—
181C2×D4—3621no—
182C2×D4—3621no—
183C2×D4—3621no—
184C2×D4—3621no—
185C2×D4—3621no—
186C2×D4—3621no—
187C2×D4—3621no—
188C2×D4—3621no—
189C2×D4—1812no—
190C2×D4—7248no—
191C2×D4D72411yescharacteristic, complemented
192C22×C4—21no—
193C22×C4—21no—
194C22×C4C22×D18111yescharacteristic
195SD16—3624no—
196D8—3624no—
197M16—21no—
198M16—21no—
199M16—3621no—
200M16—1812no—
201C2×C8—21no—
202C2×C8—3621no—
203C4⋊C4—1812no—
204C22⋊C4—3624no—
205C22⋊C4—3621no—
206C42—21no—
207C42—3621no—
208C42C22⋊D18112yescomplemented
209C23—21no—
210C23—3622no—
211C23—3622no—
212C23—3622no—
213C23—3622no—
214C23—7244no—
215C23—7244no—
216C23—7241no—
217C23—7241no—
218C23D4×D18111yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—21no—
223D4—41no—
224D4—41no—
225D4—3622no—
226D4—3622no—
227D4—14484no—
228D4—72416no—
229D4—7241no—
230D4—7241no—
231D4—7241no—
232D4—7241no—
233D4—7241no—
234D4—7241no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—3622no—
241C2×C4D4×D18111yescharacteristic
242C2×C4D4×D18111yescharacteristic
243C2×C4D4×D18111yescharacteristic
244C2×C4C2×C22⋊D18111yescharacteristic
245C2×C4C2×D72411yescharacteristic
246C2×C4#1566844911yescharacteristic
247C8—41no—
248C8—3622no—
249C22—22no—
250C22—41no—
251C22—42no—
252C22—14482no—
253C22—14482no—
254C22—14482no—
255C22—7244no—
256C22—7244no—
257C22—7242no—
258C22—7242no—
259C22—7244no—
260C22#1915378411yescharacteristic
261C22#1915378611yescharacteristic
262C22#1915378911yescharacteristic
263C4—24no—
264C4—41no—
265C4—7242no—
266C4#1915378611yescharacteristic
267C4#1915378911yescharacteristic
268C4#1915379011yescharacteristic
269C4#1915381211yescharacteristic
270C2—21no—
271C2—21no—
272C2—81no—
273C2—14482no—
274C2—14482no—
275C2#2604118811yescharacteristic
276C2#2604144812yes—
subgroupG/H
centerC22#19153786
commutator, cosocleC22×C4×C181C23
FrattiniC22×C4C22×D181
FittingC2×#104×C181C2
socleC22×C181#120
hypercenterC2×#104D181
hypocenterC181#2002
LCSG ▷ C22×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#19153841C2semidirect
2. #26041843C2semidirect
3. C2×#19153813C2semidirect
4. #26041285C2semidirect
5. C2×#19153732C2semidirect
6. #26041039C2semidirect
7. C2×#104×C181C2semidirect
44. C2×D724D4semidirect
49. #15668433D4semidirect
51. C4⋊Dic181D4semidirect
59. C2×Q8×C181D4semidirect
61. C2×D4×C181D4semidirect
69. C42×C181D4semidirect
138. C181#2002semidirect
143. C2×#104D181semidirect
174. C2×Q8D724semidirect
191. C2×D4D724semidirect
208. C42C22⋊D181semidirect

Maximal subgroups

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

subgroupindex
C2×#191538412
#260418432
C2×#191538132
#260412852
C2×#191537322
#260410392
C2×#104×C1812
#2002181