Finite Group Databasebeta

← #15672367

Subgroups — #15672367

Order 2944.

282 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 51 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#13092994C211yesmaximal, characteristic
2#13092558C211yesmaximal, characteristic, complemented
3#13092555C211yesmaximal, characteristic, complemented
4#13092338C211yesmaximal, characteristic, complemented
5#13092150C211yesmaximal, characteristic, complemented
6#13092142C211yesmaximal, characteristic, complemented
7C23×#327C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C22×Dic46C2211yescharacteristic
10C23×#121C2211yescharacteristic
11#10625110—21no—
12#10625110—21no—
13C2×#67273—21no—
14#10625101C2211yescharacteristic
15C2×C4⋊Dic23—21no—
16C2×Dic23⋊C4C2211yescharacteristic
17C2×#67263—21no—
18#10625067—21no—
19#10625055—21no—
20#10625049—21no—
21C23×C22⋊C8C2211yescharacteristic
22C23×#95C2211yescharacteristic
23C23⋊#95—21no—
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10624998—21no—
26#10624992—21no—
27C2×D4×C23—21no—
28C2×D4×C23D411yescharacteristic
29C22×C4×C23—21no—
30C22×C4×C23C2311yescharacteristic
31C2×C22⋊D23—21no—
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C22×Dic23—21no—
35C22×Dic23—21no—
36C22×Dic23D411yescharacteristic
37C22×Dic23D411yescharacteristic
38#67290—42no—
39#67290—42no—
40C2×D92D411yescharacteristic
41C2×C4×D23—21no—
42C2×Dic46—21no—
43C2×Dic46—21no—
44C2×Dic46—21no—
45C2×Dic46—42no—
46C2×C8×C23—21no—
47C4⋊C4×C23D411yescharacteristic
48C22⋊C4×C23—21no—
49C22⋊Dic23—21no—
50#67273—42no—
51(C2×D23)⋊C4—21no—
52(C2×D23)⋊C4—21no—
53C4⋊Dic23—42no—
54C4⋊Dic23D411yescharacteristic
55Dic23⋊C4—21no—
56Dic23⋊C4—21no—
57Dic23⋊C4—21no—
58C2×C23⋊C8—21no—
59#67263—42no—
60C23×C23—21no—
61C23×C23C2×D411yescharacteristic
62C22×D23—21no—
63D4×C23—41no—
64D4×C23—41no—
65D4×C23—41no—
66C2×C4×C23—22no—
67C2×C4×C23—21no—
68C2×C4×C23—41no—
69C2×C4×C23—41no—
70C2×C4×C23—41no—
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C22⋊D23—42no—
74C22⋊D23—41no—
75C22⋊D23—41no—
76C22⋊D23—81no—
77C2×Dic23—21no—
78C2×Dic23—21no—
79C2×Dic23—22no—
80C2×Dic23—21no—
81C2×Dic23—21no—
82C2×Dic23—42no—
83C2×Dic23—41no—
84C2×Dic23—41no—
85C2×Dic23—41no—
86C2×Dic23SD1612yescomplemented
87D92—41no—
88C4×D23—42no—
89Dic46—22no—
90Dic46—22no—
91Dic46—42no—
92Dic46—41no—
93Dic46—41no—
94C8×C23—41no—
95C23⋊C8—41no—
96#1604—231nomaximal, Sylow
97C22×C23—21no—
98C22×C23—21no—
99C22×C23—41no—
100C22×C23—41no—
101C22×C23—41no—
102C22×C23#12011yescharacteristic
103C22×C23C2×SD1611yescharacteristic
104C22×C23AGL(1,ℤ/8)11yescharacteristic
105C2×D23—41no—
106C2×D23—41no—
107C2×D23—41no—
108C4×C23—21no—
109C4×C23—21no—
110C4×C23—42no—
111C4×C23—41no—
112Dic23—22no—
113Dic23—41no—
114Dic23—42no—
115Dic23—41no—
116#537—231no—
117#448—231no—
118#448—231no—
119#395—231no—
120#327—231no—
121#327D2311yescharacteristic, complemented
122#324—231no—
123C2×C23—21no—
124C2×C23—21no—
125C2×C23—81no—
126C2×C23#45011yescharacteristic
127C2×C23#45611yescharacteristic
128C2×C23B(4,𝔽2)11yescharacteristic
129D23—81no—
130C2×#41—461no—
131C22×Q8—231no—
132C2×SD16—461no—
133C2×SD16—461no—
134C22⋊Q8—461no—
135C22⋊Q8—461no—
136#121—231no—
137#121—461no—
138#121—461no—
139#121—461no—
140#121C2×D2311yescharacteristic
141C2×C4⋊C4—231no—
142C2×C4⋊C4—461no—
143#103—461no—
144#103—461no—
145C22⋊C8—231no—
146C22⋊C8C2×D2311yescharacteristic
147#95—461no—
148#95C2×D2311yescharacteristic
149C23#160411yescharacteristic, complemented, Sylow
150#41—922no—
151#41—922no—
152C2×Q8—461no—
153C2×Q8—461no—
154C2×Q8—461no—
155C2×Q8—922no—
156C2×D4—21no—
157C2×D4—231no—
158C2×D4—461no—
159C2×D4—461no—
160C2×D4—461no—
161C2×D4D9211yescharacteristic
162C22×C4—21no—
163C22×C4—231no—
164C22×C4—231no—
165C22×C4—461no—
166C22×C4—461no—
167C22×C4—461no—
168C22×C4C22×D2311yescharacteristic
169SD16—922no—
170SD16—922no—
171C2×C8—21no—
172C2×C8—461no—
173C4⋊C4—231no—
174C4⋊C4—461no—
175C4⋊C4—461no—
176C4⋊C4—461no—
177C4⋊C4—922no—
178C4⋊C4D9211yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—461no—
181C22⋊C4—461no—
182C22⋊C4—461no—
183C23—21no—
184C23—461no—
185C23D4×D2311yescharacteristic
186Q8—462no—
187Q8—462no—
188Q8—921no—
189Q8—921no—
190Q8—922no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—921no—
195D4—922no—
196D4—921no—
197D4—921no—
198D4—1841no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—232no—
205C2×C4—461no—
206C2×C4—461no—
207C2×C4—462no—
208C2×C4—461no—
209C2×C4—461no—
210C2×C4—922no—
211C2×C4—922no—
212C2×C4—921no—
213C2×C4—921no—
214C2×C4—921no—
215C2×C4C2×D9211yescharacteristic
216C2×C4D4×D2311yescharacteristic
217C8—41no—
218C8—921no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—921no—
225C22—921no—
226C22—921no—
227C22#1062505311yescharacteristic
228C22#1062508211yescharacteristic
229C22SD16×D2311yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—41no—
234C4—462no—
235C4—921no—
236C4—922no—
237C4—921no—
238C2—21no—
239C2—21no—
240C2—81no—
241C2—1841no—
242C2#1309256911yescharacteristic
243C2#1309260111yescharacteristic
244C2#1309260511yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#327C2
socleC22×C23#120
prime radical#13092994C2
hypercenter#327D23
hypocenterC23#1604
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #13092558C2semidirect
3. #13092555C2semidirect
4. #13092338C2semidirect
5. #13092150C2semidirect
6. #13092142C2semidirect
7. C23×#327C2semidirect
86. C2×Dic23SD16semidirect
121. #327D23semidirect
149. C23#1604semidirect

Maximal subgroups

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

subgroupindex
#130929942
#130925582
#130925552
#130923382
#130921502
#130921422
C23×#3272
#160423