Finite Group Databasebeta

← #15672448

Subgroups — #15672448

Order 2944.

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

normal subgroups only

This group has 240 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#13093007C211yesmaximal, characteristic
2#13092750C211yesmaximal, characteristic, complemented
3#13092736C211yesmaximal, characteristic, complemented
4#13092354C211yesmaximal, characteristic, complemented
5#13092150C211yesmaximal, characteristic, complemented
6#13092140C211yesmaximal, characteristic, complemented
7C23×#328C211yesmaximal, characteristic, complemented
8C23×C22⋊Q8C2211yescharacteristic
9#10625118—21no—
10#10625101C2211yescharacteristic
11C2×(C2×D23)⋊C4—21no—
12C2×(C2×D23)⋊C4C2211yescharacteristic
13C2×C4⋊Dic23—21no—
14C2×C4⋊Dic23C2211yescharacteristic
15#10625069—21no—
16#10625066—21no—
17#10625065—21no—
18#10625053—21no—
19(C22⋊D23)⋊C4—21no—
20C23×C22⋊C8C2211yescharacteristic
21C23×#95C2211yescharacteristic
22#10625017—21no—
23C22⋊(C23⋊C8)C2211yescharacteristic
24#10625003—21no—
25#10624999—21no—
26#10624989—21no—
27C23×D23D411yescharacteristic
28C2×Q8×C23D411yescharacteristic
29C22×C4×C23—21no—
30C22×C4×C23C2311yescharacteristic
31C2×C22⋊D23—21no—
32C22×Dic23—21no—
33C22×Dic23D411yescharacteristic
34C2×D92—21no—
35C2×D92—21no—
36C2×D92D411yescharacteristic
37C2×C4×D23—21no—
38C2×C8×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23D411yescharacteristic
41C22⋊C4×C23—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—21no—
47(C2×D23)⋊C4—21no—
48(C2×D23)⋊C4—42no—
49C4⋊Dic23—21no—
50C4⋊Dic23—21no—
51C4⋊Dic23—42no—
52C4⋊Dic23D411yescharacteristic
53Dic23⋊C4—21no—
54C4×Dic23—21no—
55C2×C23⋊C8—21no—
56C23×C23C2×D411yescharacteristic
57C22×D23—21no—
58C22×D23—21no—
59C22×D23—21no—
60C22×D23—21no—
61C22×D23—41no—
62C22×D23—41no—
63Q8×C23—41no—
64C2×C4×C23—22no—
65C2×C4×C23—21no—
66C2×C4×C23—21no—
67C2×C4×C23—41no—
68C2×C4×C23—41no—
69C2×C4×C23—41no—
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C22⋊D23—41no—
73C22⋊D23—41no—
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—41no—
77C2×Dic23—41no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80D92—41no—
81D92—81no—
82D92—81no—
83C4×D23—81no—
84C8×C23—41no—
85C23⋊C8—41no—
86#1618—231nomaximal, Sylow
87C22×C23—21no—
88C22×C23—21no—
89C22×C23#12011yescharacteristic
90C22×C23#13511yescharacteristic
91C22×C23#13711yescharacteristic
92C2×D23—42no—
93C2×D23—41no—
94C2×D23—41no—
95C2×D23—41no—
96C2×D23—41no—
97C2×D23—41no—
98C2×D23—41no—
99C2×D23—81no—
100C4×C23—21no—
101C4×C23—21no—
102C4×C23—42no—
103C4×C23—41no—
104C4×C23—41no—
105Dic23—41no—
106Dic23—41no—
107Dic23—81no—
108#538—231no—
109#484—231no—
110#481—231no—
111#399—231no—
112#328D2311yescharacteristic, complemented
113#327—231no—
114#323—231no—
115C2×C23—21no—
116C2×C23—21no—
117C2×C23#45211yescharacteristic
118C2×C23#45311yescharacteristic
119C2×C23#45811yescharacteristic
120D23—81no—
121D23—81no—
122#126—461no—
123#124—461no—
124#123—461no—
125C22⋊Q8C2×D2311yescharacteristic
126#121—231no—
127#121—461no—
128#120—461no—
129C4×D4—461no—
130C2×C4⋊C4—231no—
131C2×C4⋊C4—461no—
132C2×C22⋊C4—231no—
133C2×C22⋊C4—461no—
134#107—461no—
135#106—461no—
136#103—461no—
137#102—461no—
138C22⋊C8—231no—
139C22⋊C8C2×D2311yescharacteristic
140#95C2×D2311yescharacteristic
141C23#161811yescharacteristic, complemented, Sylow
142C24—231no—
143C2×Q8D9211yescharacteristic
144C2×D4—231no—
145C2×D4—461no—
146C2×D4—461no—
147C2×D4—461no—
148C22×C4—21no—
149C22×C4—231no—
150C22×C4—461no—
151C22×C4—461no—
152C22×C4C22×D2311yescharacteristic
153C2×C8—21no—
154C2×C8—461no—
155C4⋊C4—21no—
156C4⋊C4—231no—
157C4⋊C4—461no—
158C4⋊C4—461no—
159C4⋊C4—461no—
160C4⋊C4—922no—
161C4⋊C4D9211yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—461no—
164C22⋊C4—461no—
165C22⋊C4—461no—
166C22⋊C4—461no—
167C22⋊C4—461no—
168C22⋊C4—461no—
169C22⋊C4—922no—
170C42—461no—
171C23—461no—
172C23—461no—
173C23—461no—
174C23—461no—
175C23—921no—
176C23—921no—
177C23D4×D2311yescharacteristic
178Q8—41no—
179D4—921no—
180D4—921no—
181D4—921no—
182D4—1841no—
183D4—1841no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—461no—
191C2×C4—461no—
192C2×C4—921no—
193C2×C4—921no—
194C2×C4—921no—
195C2×C4—921no—
196C2×C4—1841no—
197C2×C4C2×D9211yescharacteristic
198C2×C4D4×D2311yescharacteristic
199C8—41no—
200C8—921no—
201C22—21no—
202C22—21no—
203C22—922no—
204C22—921no—
205C22—921no—
206C22—921no—
207C22—921no—
208C22—921no—
209C22—921no—
210C22—1841no—
211C22#1062505311yescharacteristic
212C22#1062508711yescharacteristic
213C22#1062508911yescharacteristic
214C4—21no—
215C4—21no—
216C4—42no—
217C4—41no—
218C4—41no—
219C4—921no—
220C4—921no—
221C4—1841no—
222C2—21no—
223C2—21no—
224C2—1841no—
225C2—1841no—
226C2#1309258211yescharacteristic
227C2#1309258611yescharacteristic
228C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23#120
prime radical#13093007C2
hypercenter#328D23
hypocenterC23#1618
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. #13092750C2semidirect
3. #13092736C2semidirect
4. #13092354C2semidirect
5. #13092150C2semidirect
6. #13092140C2semidirect
7. C23×#328C2semidirect
112. #328D23semidirect
141. C23#1618semidirect

Maximal subgroups

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

subgroupindex
#130930072
#130927502
#130927362
#130923542
#130921502
#130921402
C23×#3282
#161823