Finite Group Databasebeta

← #15672401

Subgroups — #15672401

Order 2944.

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

normal subgroups only

This group has 254 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#13092731C211yesmaximal, characteristic, complemented
3#13092728C211yesmaximal, characteristic, complemented
4#13092349C211yesmaximal, characteristic, complemented
5#13092150C211yesmaximal, characteristic, complemented
6#13092142C211yesmaximal, characteristic, complemented
7C23×#327C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C23×#121C2211yescharacteristic
10#10625110—21no—
11#10625110—21no—
12#10625101C2211yescharacteristic
13C2×C4⋊Dic23—21no—
14C2×C4⋊Dic23C2211yescharacteristic
15C2×Dic23⋊C4C2211yescharacteristic
16#10625067—21no—
17#10625055—21no—
18#10625049—21no—
19C23×C22⋊C8C2211yescharacteristic
20C23×#95C2211yescharacteristic
21#10625014—21no—
22C23⋊#95—21no—
23C22⋊(C23⋊C8)C2211yescharacteristic
24#10625003—21no—
25#10625000—21no—
26#10624989—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×C8×C23—21no—
44C4⋊C4×C23D411yescharacteristic
45C22⋊C4×C23—21no—
46C22⋊Dic23—21no—
47(C2×D23)⋊C4—21no—
48(C2×D23)⋊C4—21no—
49C4⋊Dic23—21no—
50C4⋊Dic23—21no—
51C4⋊Dic23—42no—
52C4⋊Dic23D411yescharacteristic
53Dic23⋊C4—21no—
54Dic23⋊C4—21no—
55Dic23⋊C4—21no—
56C2×C23⋊C8—21no—
57C23×C23—21no—
58C23×C23C2×D411yescharacteristic
59C22×D23—21no—
60D4×C23—41no—
61D4×C23—41no—
62D4×C23—41no—
63C2×C4×C23—22no—
64C2×C4×C23—21no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23C2×D411yescharacteristic
69C2×C4×C23C2×D411yescharacteristic
70C22⋊D23—42no—
71C22⋊D23—41no—
72C22⋊D23—41no—
73C22⋊D23—81no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—21no—
77C2×Dic23—21no—
78C2×Dic23—42no—
79C2×Dic23—41no—
80C2×Dic23—41no—
81C2×Dic23—41no—
82C2×Dic23—41no—
83C2×Dic23D812yes—
84D92—41no—
85C4×D23—42no—
86Dic46—42no—
87C8×C23—41no—
88C23⋊C8—41no—
89#1610—231nomaximal, Sylow
90C22×C23—21no—
91C22×C23—21no—
92C22×C23—41no—
93C22×C23—41no—
94C22×C23—41no—
95C22×C23#12011yescharacteristic
96C22×C23C2×D811yescharacteristic
97C22×C23AGL(1,ℤ/8)11yescharacteristic
98C2×D23—41no—
99C2×D23—41no—
100C2×D23—41no—
101C4×C23—21no—
102C4×C23—21no—
103C4×C23—42no—
104C4×C23—41no—
105Dic23—22no—
106Dic23—41no—
107Dic23—41no—
108Dic23—81no—
109#537—231no—
110#480—231no—
111#480—231no—
112#398—231no—
113#327—231no—
114#327D2311yescharacteristic, complemented
115#324—231no—
116C2×C23—21no—
117C2×C23—21no—
118C2×C23—81no—
119C2×C23#44711yescharacteristic
120C2×C23#45611yescharacteristic
121C2×C23#45811yescharacteristic
122D23—81no—
123C2×#41—461no—
124C22⋊Q8—461no—
125C22⋊Q8—461no—
126#121—231no—
127#121—461no—
128#121—461no—
129#121—461no—
130#121C2×D2311yescharacteristic
131C2×C4⋊C4—231no—
132C2×C4⋊C4—231no—
133C2×C4⋊C4—461no—
134#107—461no—
135#107—461no—
136#102—461no—
137#102—461no—
138C22⋊C8—231no—
139C22⋊C8C2×D2311yescharacteristic
140#95—461no—
141#95C2×D2311yescharacteristic
142C23#161011yescharacteristic, complemented, Sylow
143#41—922no—
144#41—922no—
145C2×Q8—461no—
146C2×D4—21no—
147C2×D4—231no—
148C2×D4—461no—
149C2×D4—461no—
150C2×D4—461no—
151C2×D4D9211yescharacteristic
152C22×C4—21no—
153C22×C4—231no—
154C22×C4—231no—
155C22×C4—461no—
156C22×C4—461no—
157C22×C4—461no—
158C22×C4C22×D2311yescharacteristic
159C2×C8—21no—
160C2×C8—461no—
161C4⋊C4—231no—
162C4⋊C4—461no—
163C4⋊C4—461no—
164C4⋊C4—461no—
165C4⋊C4—461no—
166C4⋊C4—461no—
167C4⋊C4—922no—
168C4⋊C4D9211yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—461no—
171C22⋊C4—461no—
172C22⋊C4—461no—
173C23—21no—
174C23—461no—
175C23D4×D2311yescharacteristic
176Q8—922no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—921no—
181D4—922no—
182D4—921no—
183D4—921no—
184D4—1841no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—232no—
191C2×C4—461no—
192C2×C4—461no—
193C2×C4—461no—
194C2×C4—461no—
195C2×C4—922no—
196C2×C4—922no—
197C2×C4—921no—
198C2×C4—921no—
199C2×C4—921no—
200C2×C4—921no—
201C2×C4C2×D9211yescharacteristic
202C2×C4D4×D2311yescharacteristic
203C8—41no—
204C8—921no—
205C22—21no—
206C22—21no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—921no—
211C22—921no—
212C22—921no—
213C22#1062505311yescharacteristic
214C22D8×D2311yescharacteristic
215C22#1062508511yescharacteristic
216C4—21no—
217C4—21no—
218C4—42no—
219C4—41no—
220C4—462no—
221C4—921no—
222C4—921no—
223C4—1841no—
224C2—21no—
225C2—21no—
226C2—81no—
227C2—1841no—
228C2#1309255211yescharacteristic
229C2#1309260111yescharacteristic
230C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#327C2
socleC22×C23#120
prime radical#13092994C2
hypercenter#327D23
hypocenterC23#1610
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. #13092731C2semidirect
3. #13092728C2semidirect
4. #13092349C2semidirect
5. #13092150C2semidirect
6. #13092142C2semidirect
7. C23×#327C2semidirect
114. #327D23semidirect
142. C23#1610semidirect

Maximal subgroups

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

subgroupindex
#130929942
#130927312
#130927282
#130923492
#130921502
#130921422
C23×#3272
#161023