Finite Group Databasebeta

← #37549750

Subgroups — #37549750

Order 23168.

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

normal subgroups only

This group has 304 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#26042357C211yesmaximal, characteristic
2#26042277C211yesmaximal, characteristic
3#26042272C211yesmaximal, characteristic, complemented
4D181⋊#101C211yesmaximal, characteristic, complemented
5#26042161C211yesmaximal, characteristic, complemented
6#26042148C211yesmaximal, characteristic, complemented
7C2×#19153845C211yesmaximal, characteristic
8#19153903—22no—
9#19153903—22no—
10D181⋊M16C2211yescharacteristic
11D181⋊M16C2211yescharacteristic
12D181⋊M16C2211yescharacteristic
13C2×#15668458—22no—
14#19153895C2211yescharacteristic
15#19153880—22no—
16#19153879—22no—
17#19153877—22no—
18C2×#15668448C2211yescharacteristic
19C2×Q8×D181C2211yescharacteristic
20#19153845—22no—
21#19153845—22no—
22C2×Dic724C411yescharacteristic, complemented
23C2×#15668439C411yescharacteristic, complemented
24C2×#15668437C411yescharacteristic, complemented
25C2×#15668432C2211yescharacteristic
26C2×SD16×C181C411yescharacteristic, complemented
27#15668459—21no—
28#15668459—21no—
29#15668459—21no—
30#15668458—24no—
31#15668458—21no—
32#15668458—21no—
33#15668458D412yes—
34D181⋊C8—21no—
35D181⋊C8—21no—
36D181⋊C8D412yes—
37C2×#13089685—24no—
38C4⋊#10624382—21no—
39C22⋊#10624382—21no—
40C4×#10624382—21no—
41#15668448—21no—
42#15668448—21no—
43#15668448D412yes—
44#15668448D412yes—
45C2×Dic362—21no—
46C2×Dic362C2×C411yescharacteristic
47C2×Dic362C2×C411yescharacteristic
48Q8×D181—21no—
49Q8×D181—21no—
50Q8×D181—21no—
51Q8×D181—21no—
52C2×C22⋊D181—21no—
53C22×Dic181—21no—
54C2×C4×D181—21no—
55C2×C4×D181C2311yescharacteristic
56Dic724—22no—
57#15668439—22no—
58#15668437—22no—
59#15668432—21no—
60#15668432—21no—
61C2×#13089678C2×C411yescharacteristic
62C2×Q8×C181C2×C411yescharacteristic
63C2×D4×C181C2×C411yescharacteristic
64SD16×C181—22no—
65C2×C8×C181C2×C411yescharacteristic
66C2×#10624382—41no—
67#13089685—22no—
68#13089685—22no—
69#13089685—41no—
70C22×D181#4111yescharacteristic
71Dic362—21no—
72Dic362—21no—
73Dic362—21no—
74Dic362—41no—
75Dic362—41no—
76Dic362C22⋊C412yes—
77C22⋊D181—22no—
78C22⋊D181—22no—
79C2×Dic181—21no—
80C2×Dic181—22no—
81C2×Dic181—22no—
82C2×Dic181—21no—
83C2×Dic181C2×D411yescharacteristic
84C4×D181—41no—
85C4×D181—41no—
86C4×D181C2×D411yescharacteristic
87C4×D181C2×D411yescharacteristic
88C4×D181C2×D411yescharacteristic
89C4×D181#4111yescharacteristic
90#13089678—21no—
91C23×C181—21no—
92Q8×C181—21no—
93Q8×C181—21no—
94D4×C181—21no—
95D4×C181C22⋊C412yes—
96C2×C4×C181—21no—
97C2×C4×C181C22×C411yescharacteristic
98C8×C181—21no—
99C22×C181—22no—
100C22×C181—81no—
101C22×C181C4×D411yescharacteristic
102C2×D181—41no—
103C2×D181#12111yescharacteristic
104C2×D181#12311yescharacteristic
105#10624382—81no—
106C4×C181—41no—
107C4×C181C2×C22⋊C411yescharacteristic
108C4×C181C4×D411yescharacteristic
109Dic181—22no—
110Dic181—41no—
111Dic181#12011yescharacteristic
112Dic181#12111yescharacteristic
113C2×C181—21no—
114C2×C181—42no—
115C2×C181#38611yescharacteristic
116D181—21no—
117D181—21no—
118C181#190211yescharacteristic, complemented, Sylow
119#1902—1811nomaximal, Sylow
120C2×#137—1811no—
121#568—1811no—
122#421—1811no—
123#419—1811no—
124C2×#101—1811no—
125#344—1811no—
126#338—1811no—
127C2×#41—1811no—
128C22×Q8—1811no—
129#137—3622no—
130#137—3622no—
131C2×Q16—1811no—
132C2×Q16—1811no—
133C2×SD16—1811no—
134C2×SD16#1062438211yescharacteristic, complemented
135#131—3622no—
136#131—3622no—
137C2×M16—3622no—
138C2×M16—1811no—
139C2×M16—1811no—
140C2×M16—1811no—
141C2×M16—1811no—
142#117—1811no—
143#104—3622no—
144#103—3622no—
145#101—3622no—
146#41—3621no—
147#41—3621no—
148#41—1812no—
149#41—1812no—
150C2×Q8—3621no—
151C2×Q8—3621no—
152C2×Q8—3621no—
153C2×Q8—3621no—
154C2×Q8—3621no—
155C2×Q8—1811no—
156C2×Q8—1811no—
157C2×Q8C2×#1062438211yescharacteristic
158C2×D4—3621no—
159C2×D4C2×#1062438211yescharacteristic
160C22×C4—3621no—
161C22×C4—3621no—
162C22×C4—1811no—
163Q16—3622no—
164Q16—3622no—
165SD16—22no—
166SD16—3622no—
167M16—3621no—
168M16—3621no—
169M16—3624no—
170M16—3621no—
171M16—3621no—
172M16—3621no—
173M16—3621no—
174M16—3621no—
175M16—1812no—
176C2×C8—3624no—
177C2×C8—3621no—
178C2×C8—3621no—
179C2×C8—1812no—
180C2×C8—1811no—
181C2×C8C2×#1062438211yescharacteristic
182C4⋊C4—3621no—
183C22⋊C4—3621no—
184C42—3621no—
185C23—21no—
186C23—1811no—
187Q8—21no—
188Q8—21no—
189Q8—3621no—
190Q8—3621no—
191Q8—3621no—
192Q8—1812no—
193Q8—7241no—
194Q8—7241no—
195D4—21no—
196D4—3622no—
197D4—3622no—
198D4C22⋊#1062438212yes—
199C2×C4—21no—
200C2×C4—3621no—
201C2×C4—3622no—
202C2×C4—3622no—
203C2×C4—3621no—
204C2×C4—1811no—
205C2×C4—1811no—
206C2×C4—1811no—
207C2×C4—1811no—
208C2×C4—1811no—
209C2×C4—7241no—
210C2×C4—7241no—
211C2×C4—7241no—
212C2×C4C22×#1062438211yescharacteristic
213C8—21no—
214C8—3622no—
215C8—3622no—
216C8—3621no—
217C8—7241no—
218C22—22no—
219C22—81no—
220C22—1811no—
221C22—1811no—
222C22—7241no—
223C22D4×#1062438211yescharacteristic
224C4—41no—
225C4—3622no—
226C4—14481no—
227C4—1811no—
228C4—1811no—
229C4—7241no—
230C4C2×C22⋊#1062438211yescharacteristic
231C4D4×#1062438211yescharacteristic
232C2—21no—
233C2—42no—
234C2—3621no—
235C2—3621no—
236C2#2604222711yescharacteristic
subgroupG/H
centerC2#26042227
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC2×SD16×C181C4
socleC2×C181#386
prime radicalC2×#15668448C22
cosocleC2×C4×D181C23
hypercenterC2×SD16#10624382
hypocenterC181#1902
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
3. #26042272C2semidirect
4. D181⋊#101C2semidirect
5. #26042161C2semidirect
6. #26042148C2semidirect
22. C2×Dic724C4semidirect
23. C2×#15668439C4semidirect
24. C2×#15668437C4semidirect
26. C2×SD16×C181C4semidirect
118. C181#1902semidirect
134. C2×SD16#10624382semidirect

Maximal subgroups

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

subgroupindex
#260423572
#260422772
#260422722
D181⋊#1012
#260421612
#260421482
C2×#191538452
#1902181