Finite Group Databasebeta

← #15672459

Subgroups — #15672459

Order 2944.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#13093087C211yesmaximal, characteristic, complemented
2#13092614C211yesmaximal, characteristic, complemented
3#13092609C211yesmaximal, characteristic, complemented
4#13092161C211yesmaximal, characteristic, complemented
5#13092149C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×#493C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C2×D8×C23—22no—
10C23×#127C2211yescharacteristic
11C23×#127C2211yescharacteristic
12#10625111—21no—
13#10625110—22no—
14#10625109—21no—
15D4×Dic23—21no—
16C2×#67273—21no—
17C2×#67272—21no—
18C4×D92C2211yescharacteristic
19C4×Dic46C2211yescharacteristic
20C4×C8×C23C2211yescharacteristic
21#10625014—21no—
22#10625014—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×D4×C23—21no—
26C2×D4×C23—21no—
27C2×D4×C23—21no—
28C2×D4×C23—21no—
29C2×D4×C23—21no—
30C2×D4×C23D412yes—
31C2×C22⋊D23—22no—
32C2×C22⋊D23—22no—
33C22×Dic23—22no—
34#67290—42no—
35#67290—42no—
36C2×D92D411yescharacteristic
37C2×C4×D23—21no—
38C2×Dic46D411yescharacteristic
39D8×C23—44no—
40C2×C8×C23—21no—
41C42×C23C2311yescharacteristic
42C22⋊Dic23—22no—
43#67273—42no—
44#67272—42no—
45(C2×D23)⋊C4—21no—
46C4⋊Dic23D411yescharacteristic
47C4⋊Dic23D411yescharacteristic
48Dic23⋊C4—21no—
49C4×Dic23—21no—
50C2×C23⋊C8—21no—
51C2×C23⋊C8—21no—
52C23×C23—22no—
53C23×C23—41no—
54C22×D23—21no—
55D4×C23—42no—
56D4×C23—42no—
57D4×C23—41no—
58D4×C23—41no—
59D4×C23—41no—
60D4×C23—41no—
61D4×C23—41no—
62D4×C23—41no—
63D4×C23—41no—
64D4×C23—41no—
65C2×C4×C23C2×D411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C22⋊D23—44no—
69C22⋊D23—82no—
70C2×Dic23—21no—
71C2×Dic23—21no—
72C2×Dic23—21no—
73C2×Dic23—44no—
74D92—21no—
75D92—21no—
76C4×D23—41no—
77C4×D23—41no—
78Dic46—21no—
79Dic46D812yescomplemented
80C8×C23—22no—
81C23⋊C8—41no—
82C23⋊C8—41no—
83#1621—231nomaximal, Sylow
84C22×C23—42no—
85C22×C23—42no—
86C22×C23—42no—
87C22×C23—81no—
88C22×C23—81no—
89C22×C23—81no—
90C22×C23#12011yescharacteristic
91C2×D23—41no—
92C2×D23—41no—
93C2×D23—41no—
94C4×C23—21no—
95C4×C23C2×D811yescharacteristic
96C4×C23#13511yescharacteristic
97C4×C23AGL(1,ℤ/8)11yescharacteristic
98C4×C23AGL(1,ℤ/8)11yescharacteristic
99Dic23—22no—
100Dic23—41no—
101Dic23—41no—
102#550—231no—
103#493D2311yescharacteristic, complemented
104#460—231no—
105#459—231no—
106#331—231no—
107Q8⋊C8—231no—
108D4⋊C8—231no—
109C2×C23—82no—
110C2×C23—161no—
111C2×C23#44711yescharacteristic
112C2×C23#44911yescharacteristic
113C2×C23#45311yescharacteristic
114D23—81no—
115C2×#41—461no—
116C2×SD16—461no—
117C2×D8—22no—
118C2×D8—461no—
119#127—461no—
120#127C2×D2311yescharacteristic
121#127C2×D2311yescharacteristic
122#121—461no—
123#121—462no—
124C4×Q8—231no—
125C4×D4—231no—
126C4×D4—461no—
127C4⋊C8—231no—
128C4⋊C8—231no—
129#102—461no—
130#102—461no—
131C4×C8C2×D2311yescharacteristic
132C23#162111yescharacteristic, complemented, Sylow
133#41—922no—
134#41—922no—
135C2×Q8—231no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—231no—
142C2×D4—462no—
143C2×D4—462no—
144C2×D4C22⋊D2312yes—
145C22×C4—462no—
146C22×C4—461no—
147SD16—922no—
148D8—44no—
149D8—922no—
150C2×C8—21no—
151C2×C8—461no—
152C2×C8—461no—
153C4⋊C4—231no—
154C4⋊C4—231no—
155C4⋊C4—461no—
156C22⋊C4—462no—
157C22⋊C4—461no—
158C42—461no—
159C42C22×D2311yescharacteristic
160C23—22no—
161C23—41no—
162C23—461no—
163Q8—232no—
164Q8—461no—
165D4—42no—
166D4—42no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—461no—
176D4—461no—
177D4—924no—
178D4—1842no—
179C2×C4—461no—
180C2×C4—461no—
181C2×C4—461no—
182C2×C4—924no—
183C2×C4—921no—
184C2×C4—921no—
185C2×C4D4×D2311yescharacteristic
186C2×C4D4×D2311yescharacteristic
187C2×C4C2×C22⋊D2311yescharacteristic
188C8—22no—
189C8—921no—
190C8—921no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—921no—
198C22—921no—
199C22—921no—
200C22#1062510811yescharacteristic
201C4—21no—
202C4—462no—
203C4—921no—
204C4—921no—
205C4D8×D2311yescharacteristic
206C4#1062508211yescharacteristic
207C4#1062508211yescharacteristic
208C4#1062508311yescharacteristic
209C2—82no—
210C2—161no—
211C2—1841no—
212C2#1309254911yescharacteristic
213C2#1309255911yescharacteristic
214C2#1309258411yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#493C2
socleC22×C23#120
hypercenter#493D23
hypocenterC23#1621
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #13093087C2semidirect
2. #13092614C2semidirect
3. #13092609C2semidirect
4. #13092161C2semidirect
5. #13092149C2semidirect
6. #13092146C2semidirect
7. C23×#493C2semidirect
79. Dic46D8semidirect
103. #493D23semidirect
132. C23#1621semidirect

Maximal subgroups

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

subgroupindex
#130930872
#130926142
#130926092
#130921612
#130921492
#130921462
C23×#4932
#162123