Finite Group Databasebeta

← #15672479

Subgroups — #15672479

Order 2944.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#13093132C211yesmaximal, characteristic, complemented
2#13092789C211yesmaximal, characteristic, complemented
3#13092609C211yesmaximal, characteristic, complemented
4#13092165C211yesmaximal, characteristic, complemented
5D4⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic, complemented
7C23×#459C211yesmaximal, characteristic, complemented
8C2×D8×C23—21no—
9C23×#127C2211yescharacteristic
10C4×D4×C23C2211yescharacteristic
11#10625109—21no—
12C2×#67273—22no—
13C2×#67272—21no—
14#10625101—21no—
15#10625097—21no—
16#10625063—21no—
17#10625056—22no—
18C4×D92C2211yescharacteristic
19#10625040C2211yescharacteristic
20C23×C4⋊C8C2211yescharacteristic
21C23×#102—21no—
22#10625014—21no—
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—
31C2×D92D411yescharacteristic
32C2×C4×D23—21no—
33C2×Dic46D412yes—
34D8×C23—42no—
35C2×C8×C23—21no—
36C4⋊C4×C23D411yescharacteristic
37C22⋊C4×C23—21no—
38C42×C23C2311yescharacteristic
39C22⋊Dic23—22no—
40#67273—44no—
41#67272—42no—
42(C2×D23)⋊C4—22no—
43(C2×D23)⋊C4—21no—
44C4⋊Dic23—21no—
45C4⋊Dic23—21no—
46C4⋊Dic23D411yescharacteristic
47C4×Dic23—22no—
48C2×C23⋊C8—21no—
49C2×C23⋊C8—21no—
50C23×C23—21no—
51C23×C23—41no—
52C22×D23—21no—
53D4×C23—21no—
54D4×C23—21no—
55D4×C23—42no—
56D4×C23—41no—
57D4×C23—41no—
58D4×C23—41no—
59D4×C23—41no—
60C2×C4×C23—21no—
61C2×C4×C23—41no—
62C2×C4×C23—41no—
63C2×C4×C23C2×D411yescharacteristic
64C2×C4×C23C2×D411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C22⋊D23—82no—
67C2×Dic23—21no—
68C2×Dic23—22no—
69D92—21no—
70D92—21no—
71C4×D23—41no—
72C4×D23—41no—
73Dic46—42no—
74C8×C23—41no—
75C23⋊C8—22no—
76C23⋊C8—41no—
77#1624—231nomaximal, Sylow
78C22×C23—41no—
79C22×C23—41no—
80C22×C23—41no—
81C22×C23—81no—
82C22×C23—81no—
83C22×C23—81no—
84C22×C23#12011yescharacteristic
85C2×D23—41no—
86C2×D23—41no—
87C2×D23—41no—
88C4×C23—21no—
89C4×C23—41no—
90C4×C23#13511yescharacteristic
91C4×C23#13511yescharacteristic
92C4×C23AGL(1,ℤ/8)11yescharacteristic
93C4×C23AGL(1,ℤ/8)11yescharacteristic
94Dic23—41no—
95Dic23—42no—
96#555—231no—
97#492—231no—
98#459—231no—
99#459D2311yescharacteristic, complemented
100#333—231no—
101D4⋊C8—231no—
102D4⋊C8—231no—
103C2×C23—81no—
104C2×C23—161no—
105C2×C23#44911yescharacteristic
106C2×C23#44911yescharacteristic
107C2×C23#45311yescharacteristic
108D23—81no—
109C2×SD16—462no—
110C2×D8—21no—
111C2×D8—461no—
112C4⋊Q8—231no—
113#127C2×D2311yescharacteristic
114#124—462no—
115#121—461no—
116#121—461no—
117C4×D4—231no—
118C4×D4C2×D2311yescharacteristic
119#117—461no—
120#117—461no—
121C4⋊C8—231no—
122C4⋊C8C2×D2311yescharacteristic
123#102—21no—
124#102—461no—
125C4×C8—231no—
126C23#162411yescharacteristic, complemented, Sylow
127C2×Q8—232no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—231no—
132C2×D4—462no—
133C2×D4C22⋊D2311yescharacteristic
134C22×C4—21no—
135C22×C4—461no—
136SD16—924no—
137D8—42no—
138D8—922no—
139C2×C8—21no—
140C2×C8—461no—
141C2×C8—461no—
142C4⋊C4—231no—
143C4⋊C4—461no—
144C4⋊C4—461no—
145C4⋊C4C22⋊D2311yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—462no—
148C22⋊C4—462no—
149C22⋊C4—461no—
150C42—462no—
151C42C22×D2311yescharacteristic
152C23—21no—
153C23—41no—
154C23—461no—
155Q8—922no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—461no—
164D4—461no—
165D4—1842no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—461no—
170C2×C4—462no—
171C2×C4—921no—
172C2×C4—921no—
173C2×C4D4×D2311yescharacteristic
174C2×C4D4×D2311yescharacteristic
175C2×C4C2×C22⋊D2311yescharacteristic
176C8—41no—
177C8—462no—
178C8—921no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—921no—
186C22—921no—
187C22—921no—
188C22#1062510811yescharacteristic
189C4—21no—
190C4—41no—
191C4—921no—
192C4—922no—
193C4#1062508211yescharacteristic
194C4#1062508311yescharacteristic
195C4#1062510311yescharacteristic
196C4#1062512111yescharacteristic
197C2—81no—
198C2—161no—
199C2—1841no—
200C2#1309255911yescharacteristic
201C2#1309256011yescharacteristic
202C2#1309258311yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#459C2
socleC22×C23#120
hypercenter#459D23
hypocenterC23#1624
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. #13093132C2semidirect
2. #13092789C2semidirect
3. #13092609C2semidirect
4. #13092165C2semidirect
5. D4⋊(C23⋊C8)C2semidirect
6. #13092144C2semidirect
7. C23×#459C2semidirect
99. #459D23semidirect
126. C23#1624semidirect

Maximal subgroups

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

subgroupindex
#130931322
#130927892
#130926092
#130921652
D4⋊(C23⋊C8)2
#130921442
C23×#4592
#162423