Finite Group Databasebeta

← #15683051

Subgroups — #15683051

Order 2944.

460 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C22×#67275C211yesmaximal, characteristic, complemented
2C2×#10625078C211yesmaximal, characteristic
3#13092993C211yesmaximal, characteristic
4#13092991C211yesmaximal, characteristic
5#13092674C214yesmaximal, complemented
6#13092657C214yesmaximal, complemented
7#13092453C211yesmaximal, characteristic, complemented
8#13092427C211yesmaximal, characteristic, complemented
9C23×#419C211yesmaximal, characteristic, complemented
10C22×Q8×C23C2211yescharacteristic
11C2×#67288C2211yescharacteristic
12C22×Dic46C2211yescharacteristic
13C2×M16×C23C2211yescharacteristic
14C23×#117C2211yescharacteristic
15#10625118—21no—
16#10625117C2214yes—
17#10625115—21no—
18C2×#67275—24no—
19C2×#67275C2212yes—
20C2×#67275C2212yes—
21#10625100—22no—
22#10625097C2211yescharacteristic
23C22×C23⋊C8C2211yescharacteristic
24#10625078—24no—
25C2×#67262C2212yes—
26C2×C8×D23C2212yes—
27#10625068C2214yes—
28#10625057—22no—
29#10625046—21no—
30#10625040—21no—
31C23×#103C2214yes—
32#10624998C2214yes—
33#10624990C2212yes—
34#10624989C2212yes—
35C2×Q8×C23—21no—
36C2×Q8×C23—22no—
37C2×Q8×C23—22no—
38C2×Q8×C23C2312yes—
39C22×C4×C23—21no—
40C22×C4×C23C2311yescharacteristic
41C2×C22⋊D23D412yes—
42C22×Dic23—21no—
43#67288—22no—
44#67288—22no—
45C2×D92D411yescharacteristic
46C2×C4×D23C2312yes—
47C2×Dic46—22no—
48C2×Dic46—22no—
49C2×Dic46—21no—
50C2×Dic46D411yescharacteristic
51C2×Dic46C2312yes—
52M16×C23—22no—
53C2×C8×C23C2312yes—
54C4⋊C4×C23C2312yes—
55C22⋊C4×C23—21no—
56C42×C23—21no—
57C22⋊Dic23—21no—
58#67275—24no—
59#67275—24no—
60(C2×D23)⋊C4—24no—
61(C2×D23)⋊C4—24no—
62C4⋊Dic23—24no—
63C4⋊Dic23C2312yes—
64Dic23⋊C4—24no—
65C4×Dic23—21no—
66C2×C23⋊C8D414yes—
67C2×C23⋊C8C2311yescharacteristic
68C2×C23⋊C8C2311yescharacteristic
69#67262—24no—
70C8×D23—24no—
71C23×C23C2×D411yescharacteristic
72C22×D23C2×D412yes—
73Q8×C23—22no—
74Q8×C23—22no—
75Q8×C23—42no—
76C2×C4×C23—22no—
77C2×C4×C23—22no—
78C2×C4×C23—42no—
79C2×C4×C23C2×D411yescharacteristic
80C2×C4×C23C2×D412yes—
81C2×C4×C23#4112yes—
82C2×C4×C23C2411yescharacteristic
83C22⋊D23—24no—
84C2×Dic23—22no—
85C2×Dic23—22no—
86C2×Dic23—42no—
87C2×Dic23C2×D412yes—
88D92—22no—
89C4×D23—22no—
90C4×D23—22no—
91Dic46—22no—
92Dic46—22no—
93Dic46—22no—
94Dic46—42no—
95C8×C23—22no—
96C23⋊C8C2×D412yes—
97C23⋊C8C2×D412yes—
98#3059—231nomaximal, Sylow
99C22×C23—22no—
100C22×C23#12112yes—
101C22×C23C22×D411yescharacteristic
102C2×D23—22no—
103C2×D23—24no—
104C4×C23—42no—
105C4×C23—42no—
106C4×C23#12112yes—
107C4×C23C22×D411yescharacteristic
108C4×C23C2×#4111yescharacteristic
109Dic23—22no—
110Dic23—42no—
111Dic23—42no—
112C22×Q16—231no—
113C2×#131—231no—
114#536—231no—
115#536—231no—
116#470—234no—
117#467—234no—
118#427—231no—
119#419—231no—
120#419D2311yescharacteristic, complemented
121C2×C23—22no—
122C2×C23C2×#12111yescharacteristic
123C2×C23#57812yes—
124D23—42no—
125C2×#41—231no—
126C22×Q8—231no—
127C22×Q8C2×D2311yescharacteristic
128C2×Q16—232no—
129C2×Q16—232no—
130C2×Q16—464no—
131#131—464no—
132C2×M16—232no—
133C2×M16C2×D2311yescharacteristic
134C22×C8—231no—
135C22×C8—232no—
136C4⋊Q8—461no—
137C4⋊Q8—461no—
138#124—461no—
139#124—461no—
140#123—462no—
141#123—462no—
142C22⋊Q8—234no—
143C22⋊Q8—234no—
144#117—231no—
145#117C2×D2311yescharacteristic
146#107—232no—
147#106—232no—
148#103—234no—
149#103C2×D2314yes—
150C23#305911yescharacteristic, complemented, Sylow
151#41—462no—
152#41—462no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—231no—
157C2×Q8—232no—
158C2×Q8—461no—
159C2×Q8—462no—
160C2×Q8—462no—
161C2×Q8C22×D2312yes—
162C2×D4—232no—
163C2×D4—231no—
164C22×C4—21no—
165C22×C4—232no—
166C22×C4—461no—
167C22×C4C22×D2311yescharacteristic
168Q16—464no—
169Q16—464no—
170M16—22no—
171M16—464no—
172C2×C8—234no—
173C2×C8—231no—
174C2×C8—231no—
175C2×C8—464no—
176C2×C8C22×D2312yes—
177C4⋊C4—232no—
178C4⋊C4—464no—
179C4⋊C4—464no—
180C4⋊C4C22×D2312yes—
181C22⋊C4—21no—
182C22⋊C4—464no—
183C22⋊C4—464no—
184C22⋊C4—461no—
185C42—21no—
186C42—461no—
187C23—232no—
188C23D4×D2311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—462no—
193Q8—462no—
194Q8—462no—
195Q8—922no—
196D4—464no—
197D4—462no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—42no—
201C2×C4—232no—
202C2×C4—462no—
203C2×C4—462no—
204C2×C4—462no—
205C2×C4—462no—
206C2×C4—922no—
207C2×C4#6728812yes—
208C2×C4D4×D2311yescharacteristic
209C2×C4D4×D2312yes—
210C2×C4C23×D2311yescharacteristic
211C8—22no—
212C8—232no—
213C8—232no—
214C22—22no—
215C22—462no—
216C22—464no—
217C22#1062505512yes—
218C22C2×D4×D2311yescharacteristic
219C4—42no—
220C4—42no—
221C4—462no—
222C4—922no—
223C4—922no—
224C4#1062505512yes—
225C4C2×#6728811yescharacteristic
226C4C2×D4×D2311yescharacteristic
227C2—22no—
228C2—922no—
229C2C2×#1062505511yescharacteristic
230C2#1309323312yes—
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#419C2
socleC22×C23C22×D4
prime radicalC2×#67288C22
hypercenter#419D23
hypocenterC23#3059
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. C22×#67275C2semidirect
5. #13092674C2semidirect
6. #13092657C2semidirect
7. #13092453C2semidirect
8. #13092427C2semidirect
9. C23×#419C2semidirect
120. #419D23semidirect
150. C23#3059semidirect

Maximal subgroups

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

subgroupindex
C22×#672752
C2×#106250782
#130929932
#130929912
#130926742
#130926572
#130924532
#130924272
C23×#4192
#305923