Finite Group Databasebeta

← #37549755

Subgroups — #37549755

Order 23168.

346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 66 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#26042346C211yesmaximal, characteristic, complemented
2#26042277C211yesmaximal, characteristic, complemented
3#26042271C211yesmaximal, characteristic, complemented
4#26042259C211yesmaximal, characteristic, complemented
5#26042161C211yesmaximal, characteristic, complemented
6#26042147C211yesmaximal, characteristic, complemented
7C2×#19153840C211yesmaximal, characteristic
8D181⋊M16C2211yescharacteristic
9D4×#10624382—22no—
10D4×#10624382—22no—
11#19153895C2211yescharacteristic
12#19153895C2211yescharacteristic
13#19153895C2211yescharacteristic
14C2×C22⋊#10624382—22no—
15#19153880—22no—
16#19153878—22no—
17#19153874—22no—
18C2×#15668448C2211yescharacteristic
19C2×D4×D181C2211yescharacteristic
20#19153840—22no—
21#19153840—22no—
22C2×#15668438C411yescharacteristic, complemented
23C2×#15668437C411yescharacteristic, complemented
24C2×#15668434C411yescharacteristic, complemented
25C2×#15668432C2211yescharacteristic
26C2×D8×C181C411yescharacteristic, complemented
27C22×#10624382—24no—
28#15668459—21no—
29#15668458—21no—
30D181⋊C8—21no—
31C4⋊#10624382—21no—
32C4⋊#10624382—21no—
33C4⋊#10624382—21no—
34C22⋊#10624382—24no—
35C22⋊#10624382—21no—
36C22⋊#10624382—21no—
37C22⋊#10624382D412yes—
38C4×#10624382—21no—
39C4×#10624382—21no—
40C4×#10624382D412yes—
41C23×D181—21no—
42#15668448—21no—
43#15668448—21no—
44#15668448—21no—
45#15668448—21no—
46C2×Dic362C2×C411yescharacteristic, complemented
47C2×D724C2×C411yescharacteristic
48C2×C22⋊D181—21no—
49C2×C22⋊D181—21no—
50D4×D181—21no—
51D4×D181—21no—
52D4×D181D412yes—
53D4×D181D412yes—
54C22×Dic181—21no—
55C2×C4×D181C2311yescharacteristic
56#15668438—22no—
57#15668437—22no—
58#15668434—22no—
59#15668432—21no—
60#15668432—21no—
61C2×#13089678C2×C411yescharacteristic, complemented
62C2×D4×C181C2×C411yescharacteristic
63C2×D4×C181C2×C411yescharacteristic, complemented
64D8×C181—22no—
65C2×C8×C181C2×C411yescharacteristic, complemented
66C2×#10624382—22no—
67C2×#10624382—22no—
68C2×#10624382—41no—
69C2×#10624382—84no—
70#13089685—41no—
71C22×D181—21no—
72C22×D181—22no—
73C22×D181—22no—
74C22×D181—82no—
75C22×D181C2×D411yescharacteristic
76Dic362—21no—
77Dic362—21no—
78D724—21no—
79D724C22⋊C412yes—
80C22⋊D181—22no—
81C22⋊D181—22no—
82C22⋊D181—41no—
83C22⋊D181—41no—
84C2×Dic181—21no—
85C2×Dic181—41no—
86C2×Dic181—41no—
87C2×Dic181#4111yescharacteristic
88C4×D181C2×D411yescharacteristic
89C4×D181C2×D411yescharacteristic
90C4×D181C2×D411yescharacteristic
91C4×D181#4111yescharacteristic
92#13089678—21no—
93C23×C181—21no—
94C23×C181—21no—
95D4×C181—21no—
96D4×C181—21no—
97D4×C181—21no—
98D4×C181C22⋊C412yes—
99C2×C4×C181C22×C411yescharacteristic
100C8×C181—21no—
101C22×C181—22no—
102C22×C181—41no—
103C22×C181—81no—
104C22×C181—81no—
105C22×C181C4×D411yescharacteristic
106C2×D181—22no—
107C2×D181—41no—
108C2×D181—44no—
109C2×D181—82no—
110C2×D181—81no—
111C2×D181#12011yescharacteristic
112C2×D181#12111yescharacteristic
113#10624382—42no—
114#10624382—42no—
115#10624382—81no—
116C4×C181C2×C22⋊C411yescharacteristic
117C4×C181C4×D411yescharacteristic
118Dic181—41no—
119Dic181#12111yescharacteristic
120Dic181#12311yescharacteristic
121C2×C181—21no—
122C2×C181—42no—
123C2×C181—81no—
124C2×C181#38611yescharacteristic
125D181—21no—
126D181—21no—
127D181—42no—
128C181#190411yescharacteristic, complemented, Sylow
129#1904—1811nomaximal, Sylow
130C2×AGL(1,ℤ/8)—1811no—
131#518—1811no—
132#421—1811no—
133#418—1811no—
134#410—1811no—
135#344—1811no—
136H(3,ℤ/4)—1811no—
137C2×#41—1811no—
138C22×D4—1811no—
139AGL(1,ℤ/8)—3622no—
140AGL(1,ℤ/8)—3622no—
141C2×SD16—1811no—
142C2×SD16—1811no—
143C2×D8—1811no—
144C2×D8#1062438211yescharacteristic, complemented
145C2×M16—1811no—
146C2×M16—1811no—
147C4×D4—3622no—
148C4×D4—3622no—
149#117—1811no—
150#117—1811no—
151#117—1811no—
152C2×C22⋊C4—3622no—
153#104—3622no—
154#102—3622no—
155#99—3622no—
156C24—3621no—
157#41—3621no—
158#41—3621no—
159#41—3621no—
160#41—3621no—
161C2×Q8—1811no—
162C2×D4—3621no—
163C2×D4—3621no—
164C2×D4—3621no—
165C2×D4—3621no—
166C2×D4—1812no—
167C2×D4—1812no—
168C2×D4—1811no—
169C2×D4C2×#1062438211yescharacteristic
170C2×D4C2×#1062438211yescharacteristic, complemented
171C22×C4—3624no—
172C22×C4—3621no—
173C22×C4—1811no—
174SD16—3622no—
175SD16—3622no—
176D8—22no—
177D8—3622no—
178M16—3621no—
179M16—3621no—
180M16—3621no—
181M16—3621no—
182C2×C8—3621no—
183C2×C8—1811no—
184C2×C8C2×#1062438211yescharacteristic, complemented
185C4⋊C4—3621no—
186C4⋊C4—3621no—
187C4⋊C4—3621no—
188C22⋊C4—3624no—
189C22⋊C4—3621no—
190C22⋊C4—3621no—
191C22⋊C4—1812no—
192C42—3621no—
193C42—3621no—
194C42—1812no—
195C23—21no—
196C23—21no—
197C23—3622no—
198C23—3622no—
199C23—3621no—
200C23—14482no—
201C23—1811no—
202Q8—3621no—
203Q8—3621no—
204D4—21no—
205D4—21no—
206D4—21no—
207D4—3622no—
208D4—3622no—
209D4—3621no—
210D4—1812no—
211D4—7241no—
212D4—7241no—
213D4C22⋊#1062438212yes—
214C2×C4—3622no—
215C2×C4—3622no—
216C2×C4—3621no—
217C2×C4—14484no—
218C2×C4—1811no—
219C2×C4—1811no—
220C2×C4—1811no—
221C2×C4—1811no—
222C2×C4—1811no—
223C2×C4—7241no—
224C2×C4—7241no—
225C2×C4—7241no—
226C2×C4C22×#1062438211yescharacteristic
227C8—21no—
228C8—3621no—
229C8—7241no—
230C22—22no—
231C22—41no—
232C22—81no—
233C22—81no—
234C22—3622no—
235C22—14481no—
236C22—14482no—
237C22—1811no—
238C22—1811no—
239C22—7241no—
240C22—7244no—
241C22D4×#1062438211yescharacteristic
242C4—14481no—
243C4—1811no—
244C4—1811no—
245C4—7242no—
246C4—7242no—
247C4—7241no—
248C4C2×C22⋊#1062438211yescharacteristic
249C4D4×#1062438211yescharacteristic
250C2—21no—
251C2—42no—
252C2—81no—
253C2—3621no—
254C2—3621no—
255C2—7242no—
256C2#2604222711yescharacteristic
subgroupG/H
centerC2#26042227
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×D8×C181C4
socleC2×C181#386
prime radicalC2×#19153840C2
cosocleC2×C4×D181C23
hypercenterC2×D8#10624382
hypocenterC181#1904
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #26042346C2semidirect
2. #26042277C2semidirect
3. #26042271C2semidirect
4. #26042259C2semidirect
5. #26042161C2semidirect
6. #26042147C2semidirect
22. C2×#15668438C4semidirect
23. C2×#15668437C4semidirect
24. C2×#15668434C4semidirect
26. C2×D8×C181C4semidirect
46. C2×Dic362C2×C4semidirect
61. C2×#13089678C2×C4semidirect
63. C2×D4×C181C2×C4semidirect
65. C2×C8×C181C2×C4semidirect
128. C181#1904semidirect
144. C2×D8#10624382semidirect
170. C2×D4C2×#10624382semidirect
184. C2×C8C2×#10624382semidirect

Maximal subgroups

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

subgroupindex
#260423462
#260422772
#260422712
#260422592
#260421612
#260421472
C2×#191538402
#1904181