Finite Group Databasebeta

← #15672361

Subgroups — #15672361

Order 2944.

244 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 49 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#13093012C211yesmaximal, characteristic
2#13092575C211yesmaximal, characteristic, complemented
3#13092555C211yesmaximal, characteristic
4#13092338C211yesmaximal, characteristic, complemented
5#13092153C211yesmaximal, characteristic, complemented
6#13092142C211yesmaximal, characteristic, complemented
7C23×#327C211yesmaximal, characteristic
8C22×Dic46C2211yescharacteristic
9C23×#121C2211yescharacteristic
10#10625106—21no—
11#10625106—21no—
12D4×Dic23—21no—
13C2×#67273—21no—
14C2×C4⋊Dic23—21no—
15#10625095C2211yescharacteristic
16C2×Dic23⋊C4C2211yescharacteristic
17C2×Dic92—21no—
18#10625060—21no—
19#10625050—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
31C22×Dic23—21no—
32C22×Dic23—21no—
33C22×Dic23D411yescharacteristic
34C22×Dic23D411yescharacteristic
35C2×Dic46—21no—
36C2×Dic46—21no—
37C2×Dic46—42no—
38C2×Dic46D411yescharacteristic
39C2×C8×C23—21no—
40C4⋊C4×C23D411yescharacteristic
41C22⋊C4×C23—21no—
42C22⋊Dic23—21no—
43C22⋊Dic23—21no—
44C22⋊Dic23—21no—
45C22⋊Dic23—21no—
46#67273—42no—
47C4⋊Dic23—21no—
48C4⋊Dic23—42no—
49C4⋊Dic23D411yescharacteristic
50Dic23⋊C4—21no—
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53Dic23⋊C4—21no—
54Dic23⋊C4—21no—
55C4×Dic23—21no—
56C2×C23⋊C8—21no—
57Dic92—42no—
58C23×C23—21no—
59C23×C23C2×D411yescharacteristic
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
70C2×Dic23—22no—
71C2×Dic23—21no—
72C2×Dic23—21no—
73C2×Dic23—21no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—21no—
77C2×Dic23—41no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80C2×Dic23—81no—
81Dic46—22no—
82Dic46—22no—
83Dic46—41no—
84Dic46—41no—
85Dic46—41no—
86C8×C23—41no—
87C23⋊C8—41no—
88#1603—231nomaximal, Sylow
89C22×C23—21no—
90C22×C23—21no—
91C22×C23—41no—
92C22×C23—41no—
93C22×C23—41no—
94C22×C23#12011yescharacteristic
95C22×C23#13511yescharacteristic
96C22×C23#13711yescharacteristic
97C4×C23—21no—
98C4×C23—21no—
99C4×C23—42no—
100C4×C23—41no—
101Dic23—41no—
102Dic23—41no—
103Dic23—42no—
104Dic23—41no—
105Dic23—41no—
106#539—231no—
107#451—231no—
108#448—231no—
109#395—231no—
110#328—231no—
111#327D2311yescharacteristic
112#324—231no—
113C2×C23—21no—
114C2×C23—21no—
115C2×C23—81no—
116C2×C23#45211yescharacteristic
117C2×C23#45611yescharacteristic
118C2×C23B(4,𝔽2)11yescharacteristic
119C22×Q8—231no—
120C2×Q16—461no—
121C2×SD16—461no—
122#126—461no—
123#125—461no—
124#123—461no—
125#123—461no—
126C22⋊Q8—231no—
127C22⋊Q8—461no—
128#121C2×D2311yescharacteristic
129C4×D4—461no—
130C2×C4⋊C4—231no—
131C2×C4⋊C4—461no—
132#103—461no—
133#103—461no—
134C22⋊C8—231no—
135C22⋊C8C2×D2311yescharacteristic
136#95—461no—
137#95C2×D2311yescharacteristic
138C23#160311yescharacteristic, complemented, Sylow
139C2×Q8—231no—
140C2×Q8—461no—
141C2×Q8—461no—
142C2×Q8—922no—
143C2×D4—21no—
144C2×D4D9211yescharacteristic
145C22×C4—21no—
146C22×C4—231no—
147C22×C4—231no—
148C22×C4—461no—
149C22×C4—461no—
150C22×C4C22×D2311yescharacteristic
151Q16—922no—
152SD16—922no—
153C2×C8—21no—
154C2×C8—461no—
155C4⋊C4—231no—
156C4⋊C4—461no—
157C4⋊C4—461no—
158C4⋊C4—461no—
159C4⋊C4—461no—
160C4⋊C4—461no—
161C4⋊C4—461no—
162C4⋊C4—922no—
163C4⋊C4D9211yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—461no—
166C22⋊C4—461no—
167C22⋊C4—461no—
168C22⋊C4—461no—
169C42—461no—
170C23—21no—
171C23D4×D2311yescharacteristic
172Q8—462no—
173Q8—462no—
174Q8—921no—
175Q8—921no—
176Q8—921no—
177D4—41no—
178D4—41no—
179D4—41no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—462no—
186C2×C4—461no—
187C2×C4—461no—
188C2×C4—461no—
189C2×C4—461no—
190C2×C4—461no—
191C2×C4—461no—
192C2×C4—921no—
193C2×C4—921no—
194C2×C4—921no—
195C2×C4—1841no—
196C2×C4C2×D9211yescharacteristic
197C2×C4D4×D2311yescharacteristic
198C8—41no—
199C8—921no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22#1062505311yescharacteristic
206C22#1062508311yescharacteristic
207C22#1062508611yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—41no—
212C4—921no—
213C4—921no—
214C4—922no—
215C4—921no—
216C4—921no—
217C2—21no—
218C2—21no—
219C2—81no—
220C2#1309258011yescharacteristic
221C2#1309260111yescharacteristic
222C2#1309260511yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#327C2
socleC22×C23#120
prime radicalC23×#121C22
hypercenter#327D23
hypocenterC23#1603
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. #13092575C2semidirect
4. #13092338C2semidirect
5. #13092153C2semidirect
6. #13092142C2semidirect
138. C23#1603semidirect

Maximal subgroups

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

subgroupindex
#130930122
#130925752
#130925552
#130923382
#130921532
#130921422
C23×#3272
#160323