Finite Group Databasebeta

← #15672587

Subgroups — #15672587

Order 2944.

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

normal subgroups only

This group has 250 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#13092694C211yesmaximal, characteristic, complemented
3#13092624C211yesmaximal, characteristic, complemented
4#13092161C211yesmaximal, characteristic, complemented
5#13092149C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×#486C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C23×C4⋊Q8C2211yescharacteristic
10C23×#127C2211yescharacteristic
11C2×#67275—21no—
12#10625111—21no—
13#10625110—22no—
14#10625109—21no—
15D4×Dic23—21no—
16C4×D92C2211yescharacteristic
17C4×Dic46C2211yescharacteristic
18C23×#102—22no—
19C4×C8×C23C2211yescharacteristic
20#10625017—21no—
21#10624991—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
37C2×C8×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23—21no—
40C42×C23C2311yescharacteristic
41C22⋊Dic23—22no—
42#67275—42no—
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—41no—
53Q8×C23—41no—
54D4×C23—42no—
55D4×C23—41no—
56D4×C23—41no—
57D4×C23—41no—
58D4×C23—41no—
59C2×C4×C23—41no—
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C2×C4×C23C2×D411yescharacteristic
63C22⋊D23—44no—
64C22⋊D23—82no—
65C2×Dic23—21no—
66C2×Dic23—21no—
67C2×Dic23—21no—
68C2×Dic23—44no—
69D92—21no—
70D92—21no—
71C4×D23—41no—
72C4×D23—41no—
73Dic46—21no—
74Dic46D812yes—
75C8×C23—41no—
76C23⋊C8—41no—
77C23⋊C8—41no—
78#1641—231nomaximal, Sylow
79C22×C23—42no—
80C22×C23—42no—
81C22×C23—42no—
82C22×C23#12011yescharacteristic
83C2×D23—41no—
84C2×D23—41no—
85C2×D23—41no—
86C4×C23—21no—
87C4×C23—81no—
88C4×C23C2×D811yescharacteristic
89C4×C23#13511yescharacteristic
90C4×C23AGL(1,ℤ/8)11yescharacteristic
91C4×C23#13711yescharacteristic
92Dic23—22no—
93Dic23—41no—
94Dic23—41no—
95#550—231no—
96#486D2311yescharacteristic, complemented
97#474—231no—
98#462—231no—
99#331—231no—
100Q8⋊C8—231no—
101D4⋊C8—231no—
102C2×C23—82no—
103C2×C23#44711yescharacteristic
104C2×C23#45211yescharacteristic
105C2×C23#45511yescharacteristic
106D23—81no—
107C2×#41—461no—
108C2×Q16—461no—
109C4⋊Q8C2×D2311yescharacteristic
110#127—461no—
111#127C2×D2311yescharacteristic
112#121—461no—
113#121—462no—
114C4×Q8—231no—
115C4×D4—231no—
116C4×D4—461no—
117#107—461no—
118C4⋊C8—231no—
119C4⋊C8—231no—
120#103—461no—
121#102—22no—
122#102—461no—
123C4×C8C2×D2311yescharacteristic
124C23#164111yescharacteristic, complemented, Sylow
125#41—922no—
126#41—922no—
127C2×Q8—21no—
128C2×Q8—231no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—231no—
132C2×D4—462no—
133C2×D4—462no—
134C2×D4C22⋊D2312yes—
135C22×C4—462no—
136C22×C4—461no—
137Q16—922no—
138C2×C8—21no—
139C2×C8—461no—
140C2×C8—461no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—231no—
144C4⋊C4—231no—
145C4⋊C4—461no—
146C22⋊C4—462no—
147C22⋊C4—461no—
148C42—461no—
149C42C22×D2311yescharacteristic
150C23—22no—
151C23—461no—
152Q8—41no—
153Q8—41no—
154Q8—232no—
155Q8—461no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—461no—
162D4—461no—
163D4—924no—
164D4—1842no—
165C2×C4—41no—
166C2×C4—461no—
167C2×C4—461no—
168C2×C4—461no—
169C2×C4—924no—
170C2×C4—921no—
171C2×C4—921no—
172C2×C4D4×D2311yescharacteristic
173C2×C4D4×D2311yescharacteristic
174C2×C4C2×C22⋊D2311yescharacteristic
175C8—41no—
176C8—921no—
177C8—921no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—921no—
182C22—921no—
183C22—921no—
184C22#1062510811yescharacteristic
185C4—21no—
186C4—81no—
187C4—462no—
188C4—921no—
189C4—921no—
190C4D8×D2311yescharacteristic
191C4#1062508211yescharacteristic
192C4#1062508611yescharacteristic
193C4#1062508711yescharacteristic
194C2—82no—
195C2—1841no—
196C2#1309254911yescharacteristic
197C2#1309257611yescharacteristic
198C2#1309259411yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#486C2
socleC22×C23#120
prime radical#13093087C2
hypercenter#486D23
hypocenterC23#1641
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #13092694C2semidirect
3. #13092624C2semidirect
4. #13092161C2semidirect
5. #13092149C2semidirect
6. #13092146C2semidirect
7. C23×#486C2semidirect
96. #486D23semidirect
124. C23#1641semidirect

Maximal subgroups

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

subgroupindex
#130930872
#130926942
#130926242
#130921612
#130921492
#130921462
C23×#4862
#164123