Finite Group Databasebeta

← #15671938

Subgroups — #15671938

Order 2944.

286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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
2#13092381C211yesmaximal, characteristic, complemented
3#13092153C212yesmaximal, complemented
4#13092150C212yesmaximal, complemented
5C23×#380C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C2×#67288C411yescharacteristic, complemented
8C2×C4⋊C4×C23—21no—
9C2×C22⋊C4×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
19C2×#67267—21no—
20C23×#95C2212yes—
21C22⋊(C23⋊C8)—21no—
22C22⋊(C23⋊C8)C2212yes—
23C24×C23D411yescharacteristic
24C22×C4×C23—22no—
25C22×C4×C23—42no—
26C22×C4×C23C2×C411yescharacteristic
27C22×C4×C23C2×C411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23D411yescharacteristic
30C22×C4×C23D411yescharacteristic
31C22×C4×C23C2311yescharacteristic
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C2×C22⋊D23—21no—
35#67288—42no—
36C2×D92C2×C411yescharacteristic
37C2×C4×D23—21no—
38C2×Dic46C2×C411yescharacteristic
39C4⋊C4×C23—42no—
40C22⋊C4×C23—42no—
41C22⋊Dic23—21no—
42C22⋊Dic23—21no—
43C22⋊Dic23—21no—
44(C2×D23)⋊C4—21no—
45(C2×D23)⋊C4—21no—
46C4⋊Dic23C2×C411yescharacteristic
47C4⋊Dic23C2×C411yescharacteristic
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50C4×Dic23—21no—
51#67267—42no—
52C2×C23⋊C8—22no—
53C23×C23—21no—
54C23×C23—21no—
55C23×C23—41no—
56C23×C23—41no—
57C23×C23C22⋊C411yescharacteristic
58C23×C23C22⋊C411yescharacteristic
59C23×C23C2×D411yescharacteristic
60C22×D23—21no—
61C2×C4×C23—22no—
62C2×C4×C23—22no—
63C2×C4×C23—22no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—42no—
68C2×C4×C23—42no—
69C2×C4×C23—42no—
70C2×C4×C23C22⋊C411yescharacteristic
71C2×C4×C23C22⋊C411yescharacteristic
72C2×C4×C23C22×C411yescharacteristic
73C2×C4×C23C2×D411yescharacteristic
74C22⋊D23—42no—
75C22⋊D23—42no—
76C22⋊D23—41no—
77C22⋊D23—41no—
78C2×Dic23—21no—
79C2×Dic23—21no—
80C2×Dic23—21no—
81D92—41no—
82C4×D23—42no—
83Dic46—41no—
84C23⋊C8—42no—
85#1513—231nomaximal, Sylow
86C22×C23—21no—
87C22×C23—21no—
88C22×C23—21no—
89C22×C23—21no—
90C22×C23—21no—
91C22×C23—21no—
92C22×C23—21no—
93C22×C23—21no—
94C22×C23—42no—
95C22×C23—42no—
96C22×C23C2×C22⋊C411yescharacteristic
97C22×C23AGL(1,ℤ/8)11yescharacteristic
98C22×C23#13711yescharacteristic
99C2×D23—41no—
100C2×D23—41no—
101C2×D23—41no—
102C4×C23—21no—
103C4×C23—21no—
104C4×C23—21no—
105C4×C23—82no—
106C4×C23#9912yes—
107Dic23—41no—
108Dic23—41no—
109Dic23—41no—
110#525—231no—
111#407—231no—
112#380D2311yescharacteristic, complemented
113#328—232no—
114#327—232no—
115C2×C23—21no—
116C2×C23—21no—
117C2×C23—41no—
118C2×C23—41no—
119C2×C23C2×#9911yescharacteristic
120C2×C23#41711yescharacteristic
121C2×C23#42111yescharacteristic
122D23—81no—
123C2×#41—231no—
124C23×C4C2×D2311yescharacteristic
125C2×M16—461no—
126#123—461no—
127C22⋊Q8—231no—
128C22⋊Q8—231no—
129#121—231no—
130#121—231no—
131#120—461no—
132C4×D4—461no—
133C4×D4—461no—
134#117—231no—
135C2×C4⋊C4—21no—
136C2×C22⋊C4—21no—
137C22⋊C8—232no—
138C22⋊C8—461no—
139#95C2×D2312yes—
140C23#151311yescharacteristic, complemented, Sylow
141C24C22⋊D2311yescharacteristic
142#41—922no—
143C2×Q8—231no—
144C2×D4—231no—
145C2×D4—461no—
146C2×D4—461no—
147C2×D4—461no—
148C22×C4—22no—
149C22×C4—42no—
150C22×C4—461no—
151C22×C4C4×D2311yescharacteristic
152C22×C4C4×D2311yescharacteristic
153C22×C4D9211yescharacteristic
154C22×C4D9211yescharacteristic
155C22×C4C22⋊D2311yescharacteristic
156C22×C4C22×D2311yescharacteristic
157M16—922no—
158C2×C8—462no—
159C4⋊C4—42no—
160C4⋊C4—231no—
161C4⋊C4—231no—
162C4⋊C4—461no—
163C4⋊C4—461no—
164C22⋊C4—42no—
165C22⋊C4—461no—
166C22⋊C4—461no—
167C22⋊C4—461no—
168C22⋊C4—461no—
169C22⋊C4—461no—
170C42—461no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23—461no—
176C23(C2×D23)⋊C411yescharacteristic
177C23(C2×D23)⋊C411yescharacteristic
178C23C2×C22⋊D2311yescharacteristic
179Q8—921no—
180D4—921no—
181D4—922no—
182D4—922no—
183D4—921no—
184D4—921no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—461no—
195C2×C4—461no—
196C2×C4—461no—
197C2×C4—922no—
198C2×C4(C2×D23)⋊C411yescharacteristic
199C2×C4(C2×D23)⋊C411yescharacteristic
200C2×C4C2×C4×D2311yescharacteristic
201C2×C4C2×D9211yescharacteristic
202C8—922no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—921no—
214C22—921no—
215C22—921no—
216C22C2×(C2×D23)⋊C411yescharacteristic
217C22#1062510311yescharacteristic
218C22#1062511311yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—82no—
223C4—921no—
224C4—921no—
225C4—921no—
226C4#1062498812yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—1841no—
232C2C2×#1062498811yescharacteristic
233C2#1309241611yescharacteristic
234C2#1309243511yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#380C2
socleC22×C23C2×C22⋊C4
prime radical#13092928C2
cosocleC22×C4×C23C23
hypercenter#380D23
hypocenterC23#1513
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
2. #13092381C2semidirect
3. #13092153C2semidirect
4. #13092150C2semidirect
5. C23×#380C2semidirect
7. C2×#67288C4semidirect
11. #10625101C4semidirect
16. #10625097C4semidirect
17. #10625095C4semidirect
112. #380D23semidirect
140. C23#1513semidirect

Maximal subgroups

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

subgroupindex
#130929282
#130923812
#130921532
#130921502
C23×#3802
#151323