Finite Group Databasebeta

← #15672630

Subgroups — #15672630

Order 2944.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#13093071C211yesmaximal, characteristic
2#13092820C211yesmaximal, characteristic, complemented
3#13092694C211yesmaximal, characteristic, complemented
4#13092164C211yesmaximal, characteristic, complemented
5D4⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic, complemented
7C23×#461C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C2×SD16×C23—21no—
10C23×C4⋊Q8C2211yescharacteristic
11C4×D4×C23C2211yescharacteristic
12#10625101—21no—
13C2×C4⋊Dic23—21no—
14#10625068—21no—
15#10625057—22no—
16C4×D92C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×C4⋊C8C2211yescharacteristic
19C23×#103—21no—
20#10624991—21no—
21#10624989—21no—
22#10624989—22no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×D4×C23D411yescharacteristic
27C22×C4×C23—21no—
28C2×C22⋊D23—22no—
29C22×Dic23—22no—
30#67290—42no—
31#67290—42no—
32C2×D92D411yescharacteristic
33C2×C4×D23—21no—
34C2×Dic46—21no—
35SD16×C23—42no—
36C2×C8×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23D411yescharacteristic
40C22⋊C4×C23—21no—
41C42×C23C2311yescharacteristic
42(C2×D23)⋊C4—22no—
43(C2×D23)⋊C4—21no—
44C4⋊Dic23—22no—
45C4⋊Dic23—21no—
46C4⋊Dic23D412yes—
47C4⋊Dic23D411yescharacteristic
48C2×C23⋊C8—21no—
49C2×C23⋊C8—21no—
50C23×C23—21no—
51C22×D23—21no—
52Q8×C23—41no—
53Q8×C23—41no—
54D4×C23—21no—
55D4×C23D812yes—
56C2×C4×C23—21no—
57C2×C4×C23—41no—
58C2×C4×C23—41no—
59C2×C4×C23—41no—
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C2×C4×C23C2×D411yescharacteristic
63C22⋊D23—44no—
64C2×Dic23—22no—
65C2×Dic23—21no—
66C2×Dic23—44no—
67D92—21no—
68D92—21no—
69C4×D23—41no—
70C4×D23—41no—
71Dic46—41no—
72Dic46—41no—
73C8×C23—41no—
74C23⋊C8—22no—
75C23⋊C8—41no—
76#1647—231nomaximal, Sylow
77C22×C23—22no—
78C22×C23—41no—
79C22×C23—41no—
80C22×C23#12011yescharacteristic
81C2×D23—41no—
82C2×D23—41no—
83C2×D23—41no—
84C4×C23—21no—
85C4×C23—41no—
86C4×C23—81no—
87C4×C23C2×D811yescharacteristic
88C4×C23#13511yescharacteristic
89C4×C23AGL(1,ℤ/8)11yescharacteristic
90C4×C23#13711yescharacteristic
91Dic23—42no—
92Dic23—41no—
93#547—231no—
94#500—231no—
95#474—231no—
96#461D2311yescharacteristic, complemented
97#332—231no—
98D4⋊C8—231no—
99D4⋊C8—231no—
100C2×C23—42no—
101C2×C23#44711yescharacteristic
102C2×C23#45211yescharacteristic
103C2×C23#45611yescharacteristic
104D23—81no—
105C2×#41—461no—
106C2×SD16—21no—
107C4⋊Q8—231no—
108C4⋊Q8C2×D2311yescharacteristic
109#123—462no—
110C22⋊Q8—461no—
111#121—461no—
112C4×D4—231no—
113C4×D4C2×D2311yescharacteristic
114C2×C4⋊C4—461no—
115#107—461no—
116#107—462no—
117C4⋊C8—231no—
118C4⋊C8C2×D2311yescharacteristic
119#103—21no—
120#102—461no—
121C4×C8—231no—
122C23#164711yescharacteristic, complemented, Sylow
123#41—922no—
124#41—922no—
125C2×Q8—21no—
126C2×Q8—461no—
127C2×D4—231no—
128C2×D4—462no—
129C2×D4C22⋊D2311yescharacteristic
130C22×C4—21no—
131C22×C4—462no—
132C22×C4—461no—
133SD16—42no—
134C2×C8—21no—
135C2×C8—461no—
136C2×C8—461no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—231no—
140C4⋊C4—232no—
141C4⋊C4—462no—
142C4⋊C4—461no—
143C4⋊C4C22⋊D2311yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—462no—
146C22⋊C4—461no—
147C42C22×D2311yescharacteristic
148C23—21no—
149C23—461no—
150Q8—41no—
151Q8—41no—
152Q8—921no—
153Q8—921no—
154D4—21no—
155D4—461no—
156D4—461no—
157D4—924no—
158D4#6727212yes—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—461no—
164C2×C4—462no—
165C2×C4—924no—
166C2×C4—921no—
167C2×C4—921no—
168C2×C4D4×D2311yescharacteristic
169C2×C4D4×D2311yescharacteristic
170C2×C4C2×C22⋊D2311yescharacteristic
171C8—41no—
172C8—462no—
173C8—921no—
174C22—22no—
175C22—41no—
176C22—41no—
177C22—921no—
178C22—921no—
179C22—921no—
180C22#1062510811yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—921no—
185C4—922no—
186C4#1062508611yescharacteristic
187C4#1062508711yescharacteristic
188C4C2×#6727211yescharacteristic
189C4#1062512011yescharacteristic
190C2—42no—
191C2—1841no—
192C2#1309255011yescharacteristic
193C2#1309257611yescharacteristic
194C2#1309259811yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#461C2
socleC22×C23#120
prime radical#13093071C2
hypercenter#461D23
hypocenterC23#1647
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #13092820C2semidirect
3. #13092694C2semidirect
4. #13092164C2semidirect
5. D4⋊(C23⋊C8)C2semidirect
6. #13092144C2semidirect
7. C23×#461C2semidirect
96. #461D23semidirect
122. C23#1647semidirect

Maximal subgroups

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

subgroupindex
#130930712
#130928202
#130926942
#130921642
D4⋊(C23⋊C8)2
#130921442
C23×#4612
#164723