Finite Group Databasebeta

← #15675346

Subgroups — #15675346

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#13092858C211yesmaximal, characteristic, complemented
3#13092672C211yesmaximal, characteristic, complemented
4#13092228C211yesmaximal, characteristic, complemented
5#13092227C211yesmaximal, characteristic, complemented
6#13092198C211yesmaximal, characteristic, complemented
7C23×#510C211yesmaximal, characteristic, complemented
8#41×D23—21no—
9C23×#135C2211yescharacteristic
10C2×Q16×C23C2211yescharacteristic, complemented
11#10625121—21no—
12#10625117—21no—
13#10625089—21no—
14#10625086—21no—
15#10625085—21no—
16#10625082—21no—
17#10625075C2211yescharacteristic
18C2×#67262C2211yescharacteristic
19C23×Q32—21no—
20C23×SD32—21no—
21C23×M32C2211yescharacteristic, complemented
22#10625017—21no—
23#10625011—21no—
24#10625010—21no—
25#10624999C2211yescharacteristic, complemented
26#10624994C2211yescharacteristic, complemented
27#41×C23—21no—
28C2×Q8×C23—21no—
29#67292—21no—
30Q8×D23—21no—
31#67290—21no—
32#67290—41no—
33D4×D23—21no—
34D4×D23—41no—
35#67288—21no—
36#67288—41no—
37C2×C4×D23—41no—
38C2×C4×D23D411yescharacteristic
39Q16×C23—21no—
40Q16×C23—21no—
41Q16×C23D411yescharacteristic
42SD16×C23—21no—
43D8×C23D411yescharacteristic
44C2×C8×C23C2311yescharacteristic
45#67275—21no—
46#67274—21no—
47#67273—21no—
48#67272—21no—
49(C2×D23)⋊C4—41no—
50C4⋊Dic23—21no—
51Dic23⋊C4—41no—
52C2×C23⋊C8D411yescharacteristic
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—
63Q8×C23—41no—
64Q8×C23—41no—
65D4×C23—21no—
66D4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23—41no—
69C2×C4×C23C2×D411yescharacteristic
70C22⋊D23—41no—
71C22⋊D23—41no—
72C22⋊D23—41no—
73C2×Dic23—41no—
74C2×Dic23—41no—
75C2×Dic23D811yescharacteristic
76D92—21no—
77D92—41no—
78C4×D23—21no—
79C4×D23—21no—
80C4×D23—41no—
81C4×D23—41no—
82C4×D23—41no—
83Dic46—21no—
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#510D2311yescharacteristic, complemented
105#470—231no—
106#360—231no—
107#360—231no—
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×Q16C2×D2311yescharacteristic, complemented
123C2×M16—231no—
124C22⋊Q8—461no—
125Q32—21no—
126Q32—461no—
127SD32—21no—
128SD32—461no—
129M32—231no—
130M32C2×D2311yescharacteristic, complemented
131#106—231no—
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—21no—
141C2×Q8—461no—
142C2×D4—461no—
143C2×D4—921no—
144C22×C4—231no—
145C22×C4—921no—
146Q16—21no—
147Q16—21no—
148Q16—231no—
149Q16—461no—
150Q16C22⋊D2311yescharacteristic
151SD16—21no—
152SD16—461no—
153SD16—461no—
154SD16—461no—
155D8—231no—
156D8—461no—
157D8C22⋊D2311yescharacteristic
158M16—461no—
159M16—461no—
160C2×C8—231no—
161C2×C8C22×D2311yescharacteristic
162C4⋊C4—461no—
163C4⋊C4—921no—
164C22⋊C4—921no—
165C16—21no—
166C16—461no—
167C23—231no—
168C23—921no—
169Q8—21no—
170Q8—41no—
171Q8—41no—
172Q8—461no—
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—
193C8D4×D2311yescharacteristic
194C8C2×C22⋊D2311yescharacteristic
195C22—41no—
196C22—461no—
197C22—921no—
198C22—921no—
199C22—1842no—
200C22D8×D2311yescharacteristic
201C4—41no—
202C4—81no—
203C4—461no—
204C4—921no—
205C4—1841no—
206C4#1062508211yescharacteristic
207C4#1062510811yescharacteristic
208C2—21no—
209C2—81no—
210C2—921no—
211C2—1841no—
212C2#1309254911yescharacteristic
subgroupG/H
centerC2#13092549
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#510C2
socleC2×C23#447
prime radical#13093214C2
hypercenter#510D23
hypocenterC23#2191
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #13092858C2semidirect
3. #13092672C2semidirect
4. #13092228C2semidirect
5. #13092227C2semidirect
6. #13092198C2semidirect
7. C23×#510C2semidirect
10. C2×Q16×C23C22semidirect
21. C23×M32C22semidirect
25. #10624999C22semidirect
26. #10624994C22semidirect
104. #510D23semidirect
122. C2×Q16C2×D23semidirect
130. M32C2×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
#130928582
#130926722
#130922282
#130922272
#130921982
C23×#5102
#219123