Finite Group Databasebeta

← #15672485

Subgroups — #15672485

Order 2944.

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

normal subgroups only

This group has 256 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#13093072C211yesmaximal, characteristic, complemented
2#13092763C211yesmaximal, characteristic, complemented
3#13092609C211yesmaximal, characteristic, complemented
4#13092162C211yesmaximal, characteristic, complemented
5D4⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic, complemented
7C23×#459C211yesmaximal, characteristic, complemented
8C2×#67288—21no—
9C2×D8×C23—21no—
10C23×#127C2211yescharacteristic
11C4×D4×C23C2211yescharacteristic
12#10625109—21no—
13C2×#67272—21no—
14#10625095—21no—
15C4⋊C4×D23—21no—
16#10625054—22no—
17C4×D92C2211yescharacteristic
18#10625040C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20C23×#102—21no—
21#10625014—21no—
22#10625014—22no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4×C23⋊C8C2211yescharacteristic
25C2×D4×C23—21no—
26C2×D4×C23—21no—
27C2×D4×C23—21no—
28C2×D4×C23D411yescharacteristic
29C22×C4×C23—21no—
30C2×C22⋊D23—22no—
31#67288—42no—
32#67288—42no—
33C2×D92D411yescharacteristic
34C2×C4×D23—22no—
35C2×C4×D23—21no—
36C2×Dic46—21no—
37D8×C23—42no—
38C2×C8×C23—21no—
39C4⋊C4×C23D411yescharacteristic
40C22⋊C4×C23—21no—
41C42×C23C2311yescharacteristic
42C22⋊Dic23—22no—
43#67272—42no—
44(C2×D23)⋊C4—21no—
45C4⋊Dic23—21no—
46C4⋊Dic23D412yes—
47C4⋊Dic23D411yescharacteristic
48Dic23⋊C4—22no—
49C2×C23⋊C8—21no—
50C2×C23⋊C8—21no—
51C23×C23—21no—
52C23×C23—41no—
53C22×D23—21no—
54D4×C23—21no—
55D4×C23—21no—
56D4×C23—42no—
57D4×C23—41no—
58D4×C23—41no—
59D4×C23—41no—
60D4×C23—41no—
61C2×C4×C23—21no—
62C2×C4×C23—41no—
63C2×C4×C23—41no—
64C2×C4×C23C2×D411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C22⋊D23—44no—
68C2×Dic23—21no—
69C2×Dic23—22no—
70D92—21no—
71D92D812yescomplemented
72C4×D23—44no—
73C4×D23—41no—
74C4×D23—41no—
75Dic46—41no—
76Dic46—41no—
77C8×C23—41no—
78C23⋊C8—41no—
79C23⋊C8—41no—
80#1625—231nomaximal, Sylow
81C22×C23—41no—
82C22×C23—41no—
83C22×C23—41no—
84C22×C23—81no—
85C22×C23—81no—
86C22×C23—81no—
87C22×C23#12011yescharacteristic
88C2×D23—22no—
89C2×D23—41no—
90C2×D23—41no—
91C4×C23—21no—
92C4×C23—41no—
93C4×C23C2×D811yescharacteristic
94C4×C23#13511yescharacteristic
95C4×C23AGL(1,ℤ/8)11yescharacteristic
96C4×C23AGL(1,ℤ/8)11yescharacteristic
97Dic23—42no—
98Dic23—41no—
99#547—231no—
100#486—231no—
101#459—231no—
102#459D2311yescharacteristic, complemented
103#332—231no—
104D4⋊C8—231no—
105D4⋊C8—231no—
106C2×C23—81no—
107C2×C23—161no—
108C2×C23#44711yescharacteristic
109C2×C23#44911yescharacteristic
110C2×C23#45411yescharacteristic
111D23—42no—
112C2×#41—461no—
113C2×D8—21no—
114C2×D8—461no—
115C4⋊Q8—231no—
116#127C2×D2311yescharacteristic
117#123—462no—
118C22⋊Q8—461no—
119#121—461no—
120C4×D4—231no—
121C4×D4C2×D2311yescharacteristic
122C2×C4⋊C4—461no—
123C4⋊C8—231no—
124C4⋊C8C2×D2311yescharacteristic
125#102—21no—
126#102—461no—
127#102—462no—
128C4×C8—231no—
129C23#162511yescharacteristic, complemented, Sylow
130#41—922no—
131#41—922no—
132C2×Q8—461no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4—231no—
137C2×D4—462no—
138C2×D4C22⋊D2311yescharacteristic
139C22×C4—21no—
140C22×C4—462no—
141C22×C4—461no—
142D8—42no—
143D8—922no—
144C2×C8—21no—
145C2×C8—461no—
146C2×C8—461no—
147C4⋊C4—231no—
148C4⋊C4—232no—
149C4⋊C4—462no—
150C4⋊C4—461no—
151C4⋊C4C22⋊D2311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—462no—
154C22⋊C4—461no—
155C42C22×D2311yescharacteristic
156C23—21no—
157C23—41no—
158C23—461no—
159Q8—921no—
160Q8—921no—
161D4—21no—
162D4—21no—
163D4—42no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—232no—
169D4—461no—
170D4—924no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—461no—
175C2×C4—462no—
176C2×C4—924no—
177C2×C4—921no—
178C2×C4—921no—
179C2×C4D4×D2311yescharacteristic
180C2×C4D4×D2311yescharacteristic
181C2×C4C2×C22⋊D2311yescharacteristic
182C8—41no—
183C8—921no—
184C8—921no—
185C22—41no—
186C22—41no—
187C22—41no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—462no—
192C22—921no—
193C22—921no—
194C22#1062510811yescharacteristic
195C4—21no—
196C4—41no—
197C4—922no—
198C4—921no—
199C4D8×D2311yescharacteristic
200C4#1062508211yescharacteristic
201C4#1062510311yescharacteristic
202C4#1062512111yescharacteristic
203C2—81no—
204C2—161no—
205C2—922no—
206C2#1309254911yescharacteristic
207C2#1309256011yescharacteristic
208C2#1309258811yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#459C2
socleC22×C23#120
hypercenter#459D23
hypocenterC23#1625
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #13093072C2semidirect
2. #13092763C2semidirect
3. #13092609C2semidirect
4. #13092162C2semidirect
5. D4⋊(C23⋊C8)C2semidirect
6. #13092144C2semidirect
7. C23×#459C2semidirect
71. D92D8semidirect
102. #459D23semidirect
129. C23#1625semidirect

Maximal subgroups

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

subgroupindex
#130930722
#130927632
#130926092
#130921622
D4⋊(C23⋊C8)2
#130921442
C23×#4592
#162523