Finite Group Databasebeta

← #15672389

Subgroups — #15672389

Order 2944.

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

normal subgroups only

This group has 228 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#13093042C211yesmaximal, characteristic
2#13092748C211yesmaximal, characteristic, complemented
3#13092745C211yesmaximal, characteristic, complemented
4#13092344C211yesmaximal, characteristic
5#13092153C211yesmaximal, characteristic, complemented
6#13092140C211yesmaximal, characteristic
7C23×#328C211yesmaximal, characteristic, complemented
8C23×C22⋊Q8C2211yescharacteristic
9#10625117—21no—
10C2×(C2×D23)⋊C4—21no—
11C2×(C2×D23)⋊C4C2211yescharacteristic
12C2×C4⋊Dic23C2211yescharacteristic
13#10625095C2211yescharacteristic
14#10625068—21no—
15#10625067—21no—
16#10625067—21no—
17C22⋊C4×D23—21no—
18#10625049—21no—
19C23×C22⋊C8C2211yescharacteristic
20C23×#95C2211yescharacteristic
21#10625017—21no—
22C23⋊#95—21no—
23C22⋊(C23⋊C8)C2211yescharacteristic
24#10624999—21no—
25#10624998—21no—
26#10624990—21no—
27C23×D23D411yescharacteristic
28C2×Q8×C23D411yescharacteristic
29C22×C4×C23—21no—
30C22×C4×C23C2311yescharacteristic
31C22×Dic23—21no—
32C22×Dic23D411yescharacteristic
33C2×C4×D23—21no—
34C2×C4×D23—21no—
35C2×Dic46—21no—
36C2×Dic46D411yescharacteristic
37C2×C8×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23D411yescharacteristic
40C22⋊C4×C23—21no—
41C22⋊Dic23—21no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45(C2×D23)⋊C4—21no—
46(C2×D23)⋊C4—42no—
47C4⋊Dic23—21no—
48C4⋊Dic23—21no—
49C4⋊Dic23—21no—
50C4⋊Dic23D411yescharacteristic
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53Dic23⋊C4—21no—
54C2×C23⋊C8—21no—
55C23×C23C2×D411yescharacteristic
56C22×D23—21no—
57C22×D23—21no—
58C22×D23—41no—
59C22×D23—41no—
60C22×D23SD1612yes—
61Q8×C23—41no—
62C2×C4×C23—21no—
63C2×C4×C23—21no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23C2×D411yescharacteristic
69C2×C4×C23C2×D411yescharacteristic
70C2×Dic23—21no—
71C2×Dic23—21no—
72C2×Dic23—21no—
73C2×Dic23—41no—
74C2×Dic23—41no—
75C2×Dic23—41no—
76C2×Dic23—41no—
77C4×D23—81no—
78C4×D23—81no—
79Dic46—41no—
80Dic46—81no—
81C8×C23—41no—
82C23⋊C8—41no—
83#1608—231nomaximal, Sylow
84C22×C23—21no—
85C22×C23—21no—
86C22×C23#12011yescharacteristic
87C22×C23C2×SD1611yescharacteristic
88C22×C23#13711yescharacteristic
89C2×D23—22no—
90C2×D23—41no—
91C2×D23—41no—
92C2×D23—42no—
93C2×D23—81no—
94C4×C23—21no—
95C4×C23—21no—
96C4×C23—41no—
97C4×C23—41no—
98C4×C23—81no—
99Dic23—41no—
100Dic23—41no—
101Dic23—41no—
102Dic23—81no—
103#543—231no—
104#483—231no—
105#483—231no—
106#397—231no—
107#328—231no—
108#328D2311yescharacteristic, complemented
109#323—231no—
110C2×C23—21no—
111C2×C23—21no—
112C2×C23#44811yescharacteristic
113C2×C23#45511yescharacteristic
114C2×C23#45811yescharacteristic
115D23—42no—
116C22⋊Q8—231no—
117C22⋊Q8—461no—
118C22⋊Q8—461no—
119C22⋊Q8—461no—
120C22⋊Q8—461no—
121C22⋊Q8—461no—
122C22⋊Q8C2×D2311yescharacteristic
123C2×C4⋊C4—231no—
124C2×C22⋊C4—231no—
125C2×C22⋊C4—461no—
126C2×C22⋊C4—461no—
127#106—461no—
128#106—461no—
129#103—461no—
130#103—461no—
131C22⋊C8—231no—
132C22⋊C8C2×D2311yescharacteristic
133#95—461no—
134#95C2×D2311yescharacteristic
135C23#160811yescharacteristic, complemented, Sylow
136C24—231no—
137C2×Q8—231no—
138C2×Q8—461no—
139C2×Q8D9211yescharacteristic
140C22×C4—21no—
141C22×C4—231no—
142C22×C4—461no—
143C22×C4—461no—
144C22×C4—461no—
145C22×C4C22×D2311yescharacteristic
146C2×C8—21no—
147C2×C8—461no—
148C4⋊C4—21no—
149C4⋊C4—231no—
150C4⋊C4—461no—
151C4⋊C4—461no—
152C4⋊C4—461no—
153C4⋊C4—461no—
154C4⋊C4—461no—
155C4⋊C4—461no—
156C4⋊C4D9211yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—461no—
159C22⋊C4—461no—
160C22⋊C4—461no—
161C22⋊C4—461no—
162C22⋊C4—461no—
163C22⋊C4—922no—
164C23—232no—
165C23—461no—
166C23—461no—
167C23—921no—
168C23—921no—
169C23D4×D2311yescharacteristic
170Q8—41no—
171Q8—921no—
172Q8—1841no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—461no—
180C2×C4—461no—
181C2×C4—461no—
182C2×C4—921no—
183C2×C4—921no—
184C2×C4—921no—
185C2×C4—921no—
186C2×C4—1841no—
187C2×C4—1841no—
188C2×C4C2×D9211yescharacteristic
189C2×C4D4×D2311yescharacteristic
190C8—41no—
191C8—921no—
192C22—21no—
193C22—21no—
194C22—462no—
195C22—922no—
196C22—921no—
197C22—921no—
198C22—1841no—
199C22#1062505311yescharacteristic
200C22SD16×D2311yescharacteristic
201C22#1062508911yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—921no—
208C4—921no—
209C4—921no—
210C4—1841no—
211C2—21no—
212C2—21no—
213C2—922no—
214C2#1309255711yescharacteristic
215C2#1309259611yescharacteristic
216C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23#120
prime radicalC23×D23D4
hypercenter#328D23
hypocenterC23#1608
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #13092748C2semidirect
3. #13092745C2semidirect
5. #13092153C2semidirect
7. C23×#328C2semidirect
108. #328D23semidirect
135. C23#1608semidirect

Maximal subgroups

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

subgroupindex
#130930422
#130927482
#130927452
#130923442
#130921532
#130921402
C23×#3282
#160823