Finite Group Databasebeta

← #15672521

Subgroups — #15672521

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#13093087C211yesmaximal, characteristic
2#13092709C211yesmaximal, characteristic, complemented
3#13092704C211yesmaximal, characteristic, complemented
4#13092161C211yesmaximal, characteristic, complemented
5#13092149C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×#492C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C2×SD16×C23—22no—
10C23×C4⋊Q8C2211yescharacteristic
11C23×#127C2211yescharacteristic
12#10625111—21no—
13#10625110—22no—
14#10625109—21no—
15D4×Dic23—21no—
16C4×D92C2211yescharacteristic
17C4×Dic46C2211yescharacteristic
18C4×C8×C23C2211yescharacteristic
19#10624992—21no—
20#10624991—21no—
21#10624990—21no—
22#10624989—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×D4×C23—21no—
27C2×D4×C23—21no—
28C2×D4×C23D412yes—
29C2×C22⋊D23—22no—
30C2×C22⋊D23—22no—
31C22×Dic23—22no—
32#67290—42no—
33#67290—42no—
34C2×D92D411yescharacteristic
35C2×C4×D23—21no—
36C2×Dic46D411yescharacteristic
37SD16×C23—44no—
38C2×C8×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23—21no—
41C42×C23C2311yescharacteristic
42C22⋊Dic23—22no—
43(C2×D23)⋊C4—21no—
44C4⋊Dic23D411yescharacteristic
45C4⋊Dic23D411yescharacteristic
46Dic23⋊C4—21no—
47C4×Dic23—21no—
48C2×C23⋊C8—21no—
49C2×C23⋊C8—21no—
50C23×C23—22no—
51C22×D23—21no—
52Q8×C23—42no—
53D4×C23—42no—
54D4×C23—41no—
55D4×C23—41no—
56D4×C23—41no—
57D4×C23—41no—
58C2×C4×C23—41no—
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C22⋊D23—44no—
63C22⋊D23—82no—
64C2×Dic23—21no—
65C2×Dic23—21no—
66C2×Dic23—21no—
67C2×Dic23—44no—
68D92—21no—
69D92—21no—
70C4×D23—41no—
71C4×D23—41no—
72Dic46—21no—
73Dic46SD1612yescomplemented
74C8×C23—22no—
75C23⋊C8—41no—
76C23⋊C8—41no—
77#1631—231nomaximal, Sylow
78C22×C23—42no—
79C22×C23—42no—
80C22×C23—42no—
81C22×C23#12011yescharacteristic
82C2×D23—41no—
83C2×D23—41no—
84C2×D23—41no—
85C4×C23—21no—
86C4×C23—81no—
87C4×C23C2×SD1611yescharacteristic
88C4×C23#13511yescharacteristic
89C4×C23AGL(1,ℤ/8)11yescharacteristic
90C4×C23#13711yescharacteristic
91Dic23—22no—
92Dic23—41no—
93Dic23—41no—
94#550—231no—
95#492D2311yescharacteristic, complemented
96#477—231no—
97#476—231no—
98#331—231no—
99Q8⋊C8—231no—
100D4⋊C8—231no—
101C2×C23—82no—
102C2×C23#45011yescharacteristic
103C2×C23#45211yescharacteristic
104C2×C23#45311yescharacteristic
105D23—81no—
106C2×#41—461no—
107C2×SD16—22no—
108C4⋊Q8C2×D2311yescharacteristic
109#127—461no—
110#127C2×D2311yescharacteristic
111#121—461no—
112#121—462no—
113C4×Q8—231no—
114C4×D4—231no—
115C4×D4—461no—
116#107—461no—
117#106—461no—
118C4⋊C8—231no—
119C4⋊C8—231no—
120#103—461no—
121#102—461no—
122C4×C8C2×D2311yescharacteristic
123C23#163111yescharacteristic, complemented, Sylow
124#41—922no—
125#41—922no—
126C2×Q8—21no—
127C2×Q8—231no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—231no—
131C2×D4—462no—
132C2×D4—462no—
133C2×D4C22⋊D2312yes—
134C22×C4—462no—
135C22×C4—461no—
136SD16—44no—
137C2×C8—21no—
138C2×C8—461no—
139C2×C8—461no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—231no—
143C4⋊C4—231no—
144C4⋊C4—461no—
145C22⋊C4—462no—
146C22⋊C4—461no—
147C42—461no—
148C42C22×D2311yescharacteristic
149C23—22no—
150C23—461no—
151Q8—42no—
152Q8—232no—
153Q8—461no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—461no—
160D4—461no—
161D4—924no—
162D4—1842no—
163C2×C4—41no—
164C2×C4—461no—
165C2×C4—461no—
166C2×C4—461no—
167C2×C4—924no—
168C2×C4—921no—
169C2×C4—921no—
170C2×C4D4×D2311yescharacteristic
171C2×C4D4×D2311yescharacteristic
172C2×C4C2×C22⋊D2311yescharacteristic
173C8—22no—
174C8—921no—
175C8—921no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—921no—
180C22—921no—
181C22—921no—
182C22#1062510811yescharacteristic
183C4—21no—
184C4—81no—
185C4—462no—
186C4—921no—
187C4—921no—
188C4SD16×D2311yescharacteristic
189C4#1062508511yescharacteristic
190C4#1062508611yescharacteristic
191C4#1062508711yescharacteristic
192C2—82no—
193C2—1841no—
194C2#1309256611yescharacteristic
195C2#1309257611yescharacteristic
196C2#1309258411yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#492C2
socleC22×C23#120
prime radical#13093087C2
hypercenter#492D23
hypocenterC23#1631
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #13092709C2semidirect
3. #13092704C2semidirect
4. #13092161C2semidirect
5. #13092149C2semidirect
6. #13092146C2semidirect
7. C23×#492C2semidirect
73. Dic46SD16semidirect
95. #492D23semidirect
123. C23#1631semidirect

Maximal subgroups

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

subgroupindex
#130930872
#130927092
#130927042
#130921612
#130921492
#130921462
C23×#4922
#163123