Finite Group Databasebeta

← #15672435

Subgroups — #15672435

Order 2944.

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

normal subgroups only

This group has 246 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#13092736C211yesmaximal, characteristic, complemented
3#13092733C211yesmaximal, characteristic, complemented
4#13092357C211yesmaximal, 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⋊Dic23C2211yescharacteristic
14C2×Dic23⋊C4C2211yescharacteristic
15#10625067—21no—
16#10625055—21no—
17#10625049—21no—
18C23×C22⋊C8C2211yescharacteristic
19C23×#95C2211yescharacteristic
20#10625014—21no—
21C23⋊#95—21no—
22C23⋊#95—21no—
23C22⋊(C23⋊C8)C2211yescharacteristic
24#10625003—21no—
25#10624999—21no—
26#10624990—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⋊Dic23D411yescharacteristic
52Dic23⋊C4—21no—
53Dic23⋊C4—21no—
54Dic23⋊C4—21no—
55C2×C23⋊C8—21no—
56C23×C23—21no—
57C23×C23C2×D411yescharacteristic
58C22×D23—21no—
59D4×C23—41no—
60D4×C23—41no—
61D4×C23—41no—
62C2×C4×C23—21no—
63C2×C4×C23—41no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23C2×D411yescharacteristic
69C22⋊D23—42no—
70C22⋊D23—41no—
71C22⋊D23—41no—
72C22⋊D23—81no—
73C2×Dic23—21no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—21no—
77C2×Dic23—42no—
78C2×Dic23—41no—
79C2×Dic23—42no—
80C2×Dic23—41no—
81C2×Dic23SD1612yes—
82D92—41no—
83C4×D23—42no—
84Dic46—42no—
85C8×C23—41no—
86C23⋊C8—41no—
87#1616—231nomaximal, Sylow
88C22×C23—21no—
89C22×C23—21no—
90C22×C23—41no—
91C22×C23—41no—
92C22×C23—41no—
93C22×C23#12011yescharacteristic
94C22×C23C2×SD1611yescharacteristic
95C22×C23AGL(1,ℤ/8)11yescharacteristic
96C2×D23—41no—
97C2×D23—41no—
98C2×D23—41no—
99C4×C23—21no—
100C4×C23—21no—
101C4×C23—41no—
102C4×C23—81no—
103Dic23—22no—
104Dic23—41no—
105Dic23—41no—
106Dic23—81no—
107#537—231no—
108#481—231no—
109#481—231no—
110#400—231no—
111#327—231no—
112#327D2311yescharacteristic, complemented
113#324—231no—
114C2×C23—21no—
115C2×C23—21no—
116C2×C23—81no—
117C2×C23#45011yescharacteristic
118C2×C23#45411yescharacteristic
119C2×C23#45811yescharacteristic
120D23—81no—
121C2×#41—461no—
122C22⋊Q8—461no—
123C22⋊Q8—461no—
124#121—231no—
125#121—461no—
126#121—461no—
127#121—461no—
128#121C2×D2311yescharacteristic
129C2×C4⋊C4—231no—
130C2×C4⋊C4—231no—
131#106—461no—
132#106—461no—
133#102—461no—
134#102—461no—
135C22⋊C8—231no—
136C22⋊C8C2×D2311yescharacteristic
137#95—461no—
138#95—461no—
139#95C2×D2311yescharacteristic
140C23#161611yescharacteristic, complemented, Sylow
141#41—922no—
142#41—922no—
143C2×Q8—461no—
144C2×D4—21no—
145C2×D4—231no—
146C2×D4—461no—
147C2×D4—461no—
148C2×D4—461no—
149C2×D4D9211yescharacteristic
150C22×C4—21no—
151C22×C4—231no—
152C22×C4—231no—
153C22×C4—461no—
154C22×C4—461no—
155C22×C4—461no—
156C22×C4C22×D2311yescharacteristic
157C2×C8—21no—
158C2×C8—461no—
159C4⋊C4—231no—
160C4⋊C4—461no—
161C4⋊C4—461no—
162C4⋊C4—461no—
163C4⋊C4—461no—
164C4⋊C4—461no—
165C4⋊C4D9211yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—461no—
168C22⋊C4—461no—
169C22⋊C4—461no—
170C23—21no—
171C23—461no—
172C23D4×D2311yescharacteristic
173Q8—922no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—921no—
178D4—922no—
179D4—921no—
180D4—921no—
181D4—1841no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—232no—
188C2×C4—461no—
189C2×C4—461no—
190C2×C4—461no—
191C2×C4—461no—
192C2×C4—922no—
193C2×C4—922no—
194C2×C4—921no—
195C2×C4—922no—
196C2×C4—921no—
197C2×C4C2×D9211yescharacteristic
198C2×C4D4×D2311yescharacteristic
199C8—41no—
200C8—921no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—921no—
207C22—921no—
208C22—921no—
209C22#1062505311yescharacteristic
210C22#1062508211yescharacteristic
211C22SD16×D2311yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—462no—
217C4—921no—
218C4—921no—
219C4—1841no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—1841no—
224C2#1309256911yescharacteristic
225C2#1309259111yescharacteristic
226C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#327C2
socleC22×C23#120
prime radical#13092994C2
hypercenter#327D23
hypocenterC23#1616
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. #13092736C2semidirect
3. #13092733C2semidirect
4. #13092357C2semidirect
5. #13092150C2semidirect
6. #13092142C2semidirect
7. C23×#327C2semidirect
112. #327D23semidirect
140. C23#1616semidirect

Maximal subgroups

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

subgroupindex
#130929942
#130927362
#130927332
#130923572
#130921502
#130921422
C23×#3272
#161623