Finite Group Databasebeta

← #15671902

Subgroups — #15671902

Order 2944.

334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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#13092928C211yesmaximal, characteristic
2C2×C23⋊#95C211yesmaximal, characteristic, complemented
3#13092155C212yesmaximal, complemented
4#13092152C212yesmaximal, complemented
5C23×#407C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C23×Dic23—21no—
8C2×#67288C411yescharacteristic, complemented
9C2×M16×C23—21no—
10#10625124—21no—
11#10625101C411yescharacteristic, complemented
12#10625101C2211yescharacteristic
13#10625100—21no—
14C4×C22⋊D23—21no—
15C4×C22⋊D23—21no—
16#10625097C411yescharacteristic, complemented
17#10625095C411yescharacteristic, complemented
18#10625095C2211yescharacteristic
19C23×C22⋊C8—21no—
20C23×C22⋊C8C2212yes—
21C23⋊#95—21no—
22C23⋊#95C2212yes—
23C24×C23D411yescharacteristic
24C22×C4×C23—42no—
25C22×C4×C23C2×C411yescharacteristic
26C22×C4×C23C2×C411yescharacteristic
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23D411yescharacteristic
30C22×C4×C23C2311yescharacteristic
31C2×C22⋊D23—21no—
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C22×Dic23—24no—
35C22×Dic23—22no—
36C22×Dic23—42no—
37C22×Dic23—42no—
38#67288—42no—
39C2×D92C2×C411yescharacteristic, complemented
40C2×C4×D23—21no—
41C2×Dic46C2×C411yescharacteristic, complemented
42M16×C23—42no—
43C2×C8×C23—22no—
44C22⋊Dic23—21no—
45C22⋊Dic23—21no—
46C22⋊Dic23—21no—
47(C2×D23)⋊C4—21no—
48(C2×D23)⋊C4—21no—
49C4⋊Dic23C2×C411yescharacteristic, complemented
50C4⋊Dic23C2×C411yescharacteristic, complemented
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53C4×Dic23—21no—
54C23×C23—22no—
55C23×C23—22no—
56C23×C23—21no—
57C23×C23—21no—
58C23×C23C22⋊C411yescharacteristic
59C23×C23C22⋊C411yescharacteristic
60C23×C23C2×D411yescharacteristic
61C22×D23—21no—
62C2×C4×C23—22no—
63C2×C4×C23—22no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23C22⋊C411yescharacteristic
69C2×C4×C23C22⋊C411yescharacteristic
70C2×C4×C23C22×C411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C22⋊D23—42no—
73C22⋊D23—42no—
74C22⋊D23—41no—
75C22⋊D23—41no—
76C2×Dic23—24no—
77C2×Dic23—21no—
78C2×Dic23—21no—
79C2×Dic23—21no—
80C2×Dic23—48no—
81C2×Dic23—42no—
82C2×Dic23—42no—
83D92—41no—
84C4×D23—42no—
85Dic46—41no—
86C8×C23—42no—
87#1504—231nomaximal, Sylow
88C22×C23—24no—
89C22×C23—24no—
90C22×C23—21no—
91C22×C23—21no—
92C22×C23—21no—
93C22×C23—21no—
94C22×C23—21no—
95C22×C23—21no—
96C22×C23#9912yes—
97C22×C23#10412yes—
98C22×C23C2×C22⋊C411yescharacteristic
99C22×C23AGL(1,ℤ/8)11yescharacteristic
100C22×C23#13711yescharacteristic
101C2×D23—41no—
102C2×D23—41no—
103C2×D23—41no—
104C4×C23—21no—
105C4×C23—21no—
106C4×C23—21no—
107C4×C23—21no—
108Dic23—44no—
109Dic23—41no—
110Dic23—41no—
111Dic23—41no—
112#525—231no—
113#407D2311yescharacteristic, complemented
114C2×#95—231no—
115#328—232no—
116#327—232no—
117C2×C23—21no—
118C2×C23—22no—
119C2×C23—22no—
120C2×C23—21no—
121C2×C23C2×#9911yescharacteristic
122C2×C23#41711yescharacteristic
123C2×C23C2×#10411yescharacteristic
124D23—81no—
125C2×#41—231no—
126C23×C4—461no—
127C23×C4C2×D2311yescharacteristic
128C2×M16—21no—
129#123—461no—
130C22⋊Q8—231no—
131C22⋊Q8—231no—
132#121—231no—
133#121—231no—
134#120—461no—
135C4×D4—461no—
136C4×D4—461no—
137#117—231no—
138C22⋊C8—21no—
139C22⋊C8C2×D2312yes—
140#95—232no—
141#95—461no—
142C23#150411yescharacteristic, complemented, Sylow
143C24D9211yescharacteristic
144#41—922no—
145C2×Q8—231no—
146C2×D4—231no—
147C2×D4—461no—
148C2×D4—461no—
149C2×D4—461no—
150C22×C4—42no—
151C22×C4—464no—
152C22×C4—462no—
153C22×C4—461no—
154C22×C4—922no—
155C22×C4—922no—
156C22×C4C4×D2311yescharacteristic
157C22×C4C4×D2311yescharacteristic
158C22×C4D9211yescharacteristic
159C22×C4C22⋊D2311yescharacteristic
160C22×C4C22⋊D2311yescharacteristic
161C22×C4C22×D2311yescharacteristic
162M16—42no—
163C2×C8—22no—
164C4⋊C4—231no—
165C4⋊C4—231no—
166C4⋊C4—461no—
167C4⋊C4—461no—
168C22⋊C4—461no—
169C22⋊C4—461no—
170C22⋊C4—461no—
171C22⋊C4—461no—
172C22⋊C4—461no—
173C42—461no—
174C23—21no—
175C23—21no—
176C23—22no—
177C23—22no—
178C23—461no—
179C23(C2×D23)⋊C411yescharacteristic
180C23(C2×D23)⋊C411yescharacteristic
181C23C2×D9211yescharacteristic
182Q8—921no—
183D4—921no—
184D4—921no—
185D4—921no—
186D4—922no—
187D4—922no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—464no—
195C2×C4—461no—
196C2×C4—461no—
197C2×C4—461no—
198C2×C4—922no—
199C2×C4—928no—
200C2×C4—922no—
201C2×C4—922no—
202C2×C4(C2×D23)⋊C411yescharacteristic
203C2×C4(C2×D23)⋊C411yescharacteristic
204C2×C4C2×C4×D2311yescharacteristic
205C2×C4C2×C22⋊D2311yescharacteristic
206C8—42no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—921no—
216C22—921no—
217C22—921no—
218C22#1062498812yes—
219C22#1062500712yes—
220C22#1062507911yescharacteristic
221C22#1062508011yescharacteristic
222C22C2×(C2×D23)⋊C411yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—924no—
228C4—921no—
229C4—921no—
230C4—921no—
231C2—21no—
232C2—21no—
233C2—22no—
234C2—22no—
235C2—1841no—
236C2C2×#1062498811yescharacteristic
237C2#1309241911yescharacteristic
238C2C2×#1062500711yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#407C2
socleC22×C23C2×C22⋊C4
prime radical#13092928C2
cosocleC22×C4×C23C23
hypercenter#407D23
hypocenterC23#1504
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. C2×C23⋊#95C2semidirect
3. #13092155C2semidirect
4. #13092152C2semidirect
5. C23×#407C2semidirect
8. C2×#67288C4semidirect
11. #10625101C4semidirect
16. #10625097C4semidirect
17. #10625095C4semidirect
39. C2×D92C2×C4semidirect
41. C2×Dic46C2×C4semidirect
49. C4⋊Dic23C2×C4semidirect
50. C4⋊Dic23C2×C4semidirect
113. #407D23semidirect
142. C23#1504semidirect

Maximal subgroups

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

subgroupindex
#130929282
C2×C23⋊#952
#130921552
#130921522
C23×#4072
#150423