Finite Group Databasebeta

← #15675349

Subgroups — #15675349

Order 2944.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#13093214C211yesmaximal, characteristic
2#13092860C211yesmaximal, characteristic, complemented
3#13092857C211yesmaximal, characteristic, complemented
4#13092676C211yesmaximal, characteristic, complemented
5#13092226C211yesmaximal, characteristic, complemented
6#13092198C211yesmaximal, characteristic, complemented
7C23×#360C211yesmaximal, characteristic, complemented
8#41×D23—21no—
9C23×#135C2211yescharacteristic
10#10625121—21no—
11#10625089—21no—
12#10625086—21no—
13#10625085—21no—
14#10625082—21no—
15C2×Dic92C2211yescharacteristic, complemented
16#10625075C2211yescharacteristic
17C2×#67262C2211yescharacteristic
18#10625068—21no—
19C23×M32C2211yescharacteristic, complemented
20C23×#106C2211yescharacteristic, complemented
21#10625011—21no—
22#10625009—21no—
23#10624994C2211yescharacteristic, complemented
24#10624992—21no—
25Dic184—21no—
26#10624982—21no—
27#41×C23—21no—
28#67292—21no—
29Q8×D23—21no—
30#67290—21no—
31#67290—41no—
32D4×D23—21no—
33D4×D23—41no—
34#67288—21no—
35#67288—41no—
36C2×C4×D23—41no—
37C2×C4×D23D411yescharacteristic
38C2×Dic46—21no—
39Q16×C23D411yescharacteristic
40SD16×C23—21no—
41D8×C23D411yescharacteristic
42C2×C8×C23C2311yescharacteristic
43C4⋊C4×C23—21no—
44#67275—21no—
45#67274—21no—
46#67273—21no—
47#67272—21no—
48(C2×D23)⋊C4—41no—
49C4⋊Dic23—41no—
50C2×C23⋊C8D411yescharacteristic
51Dic92—21no—
52Dic92—21no—
53Dic92D411yescharacteristic
54D184D411yescharacteristic
55#67263—21no—
56#67262—21no—
57#67262—21no—
58C16×C23—21no—
59C23⋊C16—21no—
60C22×D23—41no—
61C22×D23D811yescharacteristic
62Q8×C23—21no—
63D4×C23—21no—
64D4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23C2×D411yescharacteristic
68C22⋊D23—41no—
69C22⋊D23—41no—
70C22⋊D23—41no—
71C2×Dic23—41no—
72C2×Dic23—41no—
73C2×Dic23D811yescharacteristic
74D92—21no—
75D92—41no—
76C4×D23—21no—
77C4×D23—21no—
78C4×D23—41no—
79C4×D23—41no—
80C4×D23—41no—
81Dic46—21no—
82Dic46—41no—
83Dic46—41no—
84Dic46—41no—
85C8×C23C2×D411yescharacteristic
86C8×C23C2×D411yescharacteristic
87C23⋊C8—21no—
88#2191—231nomaximal, Sylow
89C22×C23—41no—
90C22×C23C2×D811yescharacteristic
91C2×D23—21no—
92C2×D23—41no—
93C2×D23—41no—
94C2×D23—82no—
95C4×C23—41no—
96C4×C23—81no—
97C4×C23#12011yescharacteristic
98C4×C23AGL(1,ℤ/8)11yescharacteristic
99Dic23—21no—
100Dic23—41no—
101Dic23—81no—
102#575—231no—
103#510—231no—
104#510—231no—
105#470—231no—
106#360—231no—
107#360D2311yescharacteristic, complemented
108#349—231no—
109C2×C23—21no—
110C2×C23—81no—
111C2×C23#44711yescharacteristic
112D23—41no—
113D23—81no—
114C2×#41—461no—
115#137—461no—
116#137—461no—
117AGL(1,ℤ/8)—461no—
118AGL(1,ℤ/8)—461no—
119#135—231no—
120#135—461no—
121#135C2×D2311yescharacteristic
122C2×Q16—231no—
123C2×M16—231no—
124C22⋊Q8—461no—
125Q32—461no—
126Q32—461no—
127SD32—461no—
128SD32—461no—
129M32—231no—
130M32C2×D2311yescharacteristic, complemented
131#106C2×D2311yescharacteristic, complemented
132#103—461no—
133C23#219111yescharacteristic, complemented, Sylow
134#41—21no—
135#41—461no—
136#41—461no—
137#41—461no—
138#41—921no—
139#41—921no—
140C2×Q8—461no—
141C2×Q8—461no—
142C2×D4—461no—
143C2×D4—921no—
144C22×C4—231no—
145C22×C4—921no—
146Q16—231no—
147Q16—461no—
148Q16—461no—
149Q16—461no—
150Q16D9211yescharacteristic
151SD16—21no—
152SD16—461no—
153SD16—461no—
154SD16—461no—
155D8—231no—
156D8—461no—
157D8D9211yescharacteristic
158M16—461no—
159M16—461no—
160C2×C8—231no—
161C2×C8C22×D2311yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—921no—
164C22⋊C4—921no—
165C16—21no—
166C16—461no—
167C23—231no—
168C23—921no—
169Q8—21no—
170Q8—461no—
171Q8—921no—
172Q8—921no—
173Q8—921no—
174D4—21no—
175D4—41no—
176D4—461no—
177D4—921no—
178D4—921no—
179D4—921no—
180D4—921no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—231no—
184C2×C4—461no—
185C2×C4—461no—
186C2×C4—921no—
187C2×C4—921no—
188C2×C4—921no—
189C2×C4—921no—
190C2×C4—921no—
191C2×C4D4×D2311yescharacteristic
192C8—461no—
193C8C2×D9211yescharacteristic
194C8D4×D2311yescharacteristic
195C22—41no—
196C22—461no—
197C22—921no—
198C22—921no—
199C22—1842no—
200C22D8×D2311yescharacteristic
201C4—41no—
202C4—81no—
203C4—461no—
204C4—921no—
205C4—1841no—
206C4#1062505311yescharacteristic
207C4#1062508511yescharacteristic
208C2—21no—
209C2—81no—
210C2—921no—
211C2—1841no—
212C2#1309255211yescharacteristic
subgroupG/H
centerC2#13092552
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#360C2
socleC2×C23#447
prime radical#13093214C2
hypercenter#360D23
hypocenterC23#2191
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #13092860C2semidirect
3. #13092857C2semidirect
4. #13092676C2semidirect
5. #13092226C2semidirect
6. #13092198C2semidirect
7. C23×#360C2semidirect
15. C2×Dic92C22semidirect
19. C23×M32C22semidirect
20. C23×#106C22semidirect
23. #10624994C22semidirect
107. #360D23semidirect
130. M32C2×D23semidirect
131. #106C2×D23semidirect
133. C23#2191semidirect

Maximal subgroups

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

subgroupindex
#130932142
#130928602
#130928572
#130926762
#130922262
#130921982
C23×#3602
#219123