Finite Group Databasebeta

← #37549592

Subgroups — #37549592

Order 23168.

292 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 84 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
1D181⋊(C4⋊C8)C211yesmaximal, characteristic
2C2×#19153879C212yesmaximal
3#26042223C211yesmaximal, characteristic
4#26042152C212yesmaximal
5C4×Q8×D181C211yesmaximal, characteristic
6C2×D181⋊C8C2212yes—
7C2×C4⋊#10624382C2212yes—
8#19153883—21no—
9C4⋊#13089685—21no—
10#19153879—24no—
11(C2×#10624382)⋊C4—21no—
12(C2×#10624382)⋊C4—21no—
13C2×Q8×D181C2211yescharacteristic
14Q8×Dic181C411yescharacteristic, complemented
15C4×Dic362—21no—
16C4×Dic362C411yescharacteristic, complemented
17#19153781—21no—
18#19153781C411yescharacteristic, complemented
19C4⋊C4×D181—21no—
20C4⋊C4×D181C2211yescharacteristic
21C42×D181—21no—
22C42×D181C2211yescharacteristic
23C4×Q8×C181C411yescharacteristic, complemented
24C22×#10624382—22no—
25D181⋊C8—22no—
26D181⋊C8—22no—
27C2×#13089685—22no—
28C4⋊#10624382—22no—
29C4⋊#10624382—22no—
30C2×Dic362—21no—
31C2×Dic362C2×C411yescharacteristic
32Q8×D181—21no—
33Q8×D181—21no—
34Q8×D181D412yes—
35Q8×D181Q812yes—
36C2×C4×D181—21no—
37C2×C4×D181—21no—
38C2×C4×D181D411yescharacteristic
39C2×C4×D181D411yescharacteristic
40C2×C4×D181C2311yescharacteristic
41C4⋊Dic181—21no—
42C4⋊Dic181C2×C411yescharacteristic
43#15668428—21no—
44#15668428—21no—
45#15668428—21no—
46C4×Dic181—21no—
47C4×Dic181—21no—
48C4×Dic181—21no—
49C4×Dic181C2×C411yescharacteristic
50C4×Dic181D411yescharacteristic
51C4×Dic181D411yescharacteristic
52C2×Q8×C181C2×C411yescharacteristic
53C4⋊C4×C181—21no—
54C4⋊C4×C181C2×C411yescharacteristic
55C42×C181—21no—
56C42×C181C2×C411yescharacteristic
57C2×#10624382—42no—
58C2×#10624382—42no—
59C2×#10624382—42no—
60#13089685—42no—
61C22×D181C2×D411yescharacteristic
62Dic362—21no—
63Dic362—22no—
64Dic362—22no—
65Dic362C4⋊C412yes—
66C2×Dic181—21no—
67C2×Dic181—21no—
68C2×Dic181C22⋊C411yescharacteristic
69C2×Dic181C22⋊C411yescharacteristic
70C2×Dic181C2×D411yescharacteristic
71C4×D181—22no—
72C4×D181—22no—
73C4×D181—22no—
74C4×D181—22no—
75C4×D181—42no—
76C4×D181C2×D411yescharacteristic
77C4×D181C2×Q811yescharacteristic
78C4×D181#4111yescharacteristic
79C4×D181#4111yescharacteristic
80Q8×C181—21no—
81Q8×C181C4⋊C412yes—
82C2×C4×C181—21no—
83C2×C4×C181—21no—
84C2×C4×C181C22⋊C411yescharacteristic
85C2×C4×C181C22⋊C411yescharacteristic
86C2×C4×C181C22×C411yescharacteristic
87C22×C181C2×C22⋊C411yescharacteristic
88C2×D181#12111yescharacteristic
89C2×D181C22⋊Q811yescharacteristic
90C2×D181#13512yes—
91C2×D181#13712yes—
92#10624382—82no—
93C4×C181—22no—
94C4×C181—21no—
95C4×C181—21no—
96C4×C181—41no—
97C4×C181C2×C4⋊C411yescharacteristic
98C4×C181#11711yescharacteristic
99Dic181—22no—
100Dic181—21no—
101Dic181—21no—
102Dic181—41no—
103Dic181#12111yescharacteristic
104Dic181C22⋊Q811yescharacteristic
105C2×C181#38011yescharacteristic
106C2×C181#41611yescharacteristic
107C2×C181#41911yescharacteristic
108D181#46412yes—
109D181#47912yes—
110C181#180511yescharacteristic, complemented, Sylow
111#1805—1811nomaximal, Sylow
112C2×C4×Q8—1811no—
113C2×C4⋊C8—1811no—
114C2×#103—1812no—
115#382—1811no—
116#340—1812no—
117C22×Q8—1811no—
118C22×C8—1812no—
119C4×Q8—3621no—
120C4×Q8—3621no—
121C4×Q8—1811no—
122C4×Q8—1811no—
123C4×Q8—1811no—
124C4×Q8#1062438211yescharacteristic, complemented
125C2×C4⋊C4—3621no—
126C2×C4⋊C4—1812no—
127C2×C4⋊C4—1811no—
128C2×C42—3621no—
129C2×C42—1811no—
130C4⋊C8—3621no—
131C4⋊C8—3621no—
132#103—3624no—
133#95—3621no—
134#95—3621no—
135C2×Q8—3621no—
136C2×Q8—3621no—
137C2×Q8—3621no—
138C2×Q8—1812no—
139C2×Q8—1812no—
140C2×Q8—1811no—
141C2×Q8C2×#1062438211yescharacteristic
142C22×C4—3621no—
143C22×C4—3621no—
144C22×C4—3622no—
145C22×C4—1811no—
146C22×C4—1811no—
147C22×C4—1811no—
148C2×C8—3622no—
149C2×C8—3622no—
150C2×C8—3622no—
151C4⋊C4—21no—
152C4⋊C4—3621no—
153C4⋊C4—3621no—
154C4⋊C4—3621no—
155C4⋊C4—3621no—
156C4⋊C4—3622no—
157C4⋊C4—3622no—
158C4⋊C4—1811no—
159C4⋊C4C2×#1062438211yescharacteristic
160C42—21no—
161C42—3621no—
162C42—3621no—
163C42—3621no—
164C42—1811no—
165C42—1811no—
166C42—1811no—
167C42C2×#1062438211yescharacteristic
168C23—1811no—
169Q8—21no—
170Q8—3622no—
171Q8—3622no—
172Q8—3621no—
173Q8—1812no—
174Q8C4⋊#1062438212yes—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—3622no—
178C2×C4—3622no—
179C2×C4—3622no—
180C2×C4—3622no—
181C2×C4—3621no—
182C2×C4—3621no—
183C2×C4—1811no—
184C2×C4—1811no—
185C2×C4—1811no—
186C2×C4—1811no—
187C2×C4—1811no—
188C2×C4—1811no—
189C2×C4—1811no—
190C2×C4—7242no—
191C2×C4—7242no—
192C2×C4—7242no—
193C2×C4—7242no—
194C2×C4C22⋊#1062438211yescharacteristic
195C2×C4C22⋊#1062438211yescharacteristic
196C2×C4C22×#1062438211yescharacteristic
197C8—7242no—
198C22—1811no—
199C22—1811no—
200C22—1812no—
201C22—1812no—
202C22C2×C22⋊#1062438211yescharacteristic
203C4—22no—
204C4—21no—
205C4—21no—
206C4—41no—
207C4—3622no—
208C4—3621no—
209C4—3621no—
210C4—14482no—
211C4—1811no—
212C4—1811no—
213C4—7241no—
214C4C2×C4⋊#1062438211yescharacteristic
215C4#1915389511yescharacteristic
216C2—1812no—
217C2—1812no—
218C2#2604222111yescharacteristic
219C2#2604226911yescharacteristic
220C2#2604227211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10624382
commutatorC2×C4×C181C22×C4
FrattiniC2×C4C22×#10624382
FittingC4×Q8×C181C4
socleC22×C181C2×C22⋊C4
prime radicalC22×D181C2×D4
cosocleC2×C4×D181C23
hypercenterC4×Q8#10624382
hypocenterC181#1805
LCSG ▷ C2×C4×C181 ▷ C2×C181 ▷ C181
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
14. Q8×Dic181C4semidirect
16. C4×Dic362C4semidirect
18. #19153781C4semidirect
23. C4×Q8×C181C4semidirect
110. C181#1805semidirect
124. C4×Q8#10624382semidirect

Maximal subgroups

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

subgroupindex
D181⋊(C4⋊C8)2
C2×#191538792
#260422232
#260421522
C4×Q8×D1812
#1805181