Finite Group Databasebeta

← #15675350

Subgroups — #15675350

Order 2944.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#13093217C211yesmaximal, characteristic
2#13092860C212yesmaximal, complemented
3#13092675C211yesmaximal, characteristic, complemented
4#13092228C212yesmaximal, complemented
5C23×#349C211yesmaximal, characteristic, complemented
6C2×#67288—21no—
7C2×M16×C23C2211yescharacteristic
8#10625095—21no—
9#10625080—22no—
10#10625079—22no—
11C2×Dic92C2211yescharacteristic, complemented
12#10625075—21no—
13#10625075C2212yes—
14C23×M32C2212yescomplemented
15#10624999C2211yescharacteristic, complemented
16#10624998—21no—
17Dic184—22no—
18#10624982—22no—
19C22×C4×C23D411yescharacteristic
20C2×C22⋊D23—41no—
21#67288—22no—
22#67288—22no—
23#67288—41no—
24#67288—41no—
25C2×D92—21no—
26C2×C4×D23—41no—
27C2×Dic46—21no—
28C2×Dic46—21no—
29M16×C23—22no—
30C2×C8×C23D411yescharacteristic
31C2×C8×C23C2311yescharacteristic
32C22⋊Dic23—41no—
33C4⋊Dic23—21no—
34Dic23⋊C4—41no—
35Dic92—21no—
36Dic92—22no—
37Dic92D412yes—
38D184—21no—
39D184D412yes—
40#67263—22no—
41#67263—22no—
42C16×C23—22no—
43C23×C23D811yescharacteristic
44C22×D23—41no—
45C2×C4×C23—21no—
46C2×C4×C23—21no—
47C2×C4×C23D811yescharacteristic
48C2×C4×C23C2×D411yescharacteristic
49C22⋊D23—42no—
50C22⋊D23—42no—
51C2×Dic23—41no—
52C2×Dic23—41no—
53C2×Dic23—41no—
54D92—22no—
55D92—41no—
56C4×D23—42no—
57C4×D23—42no—
58Dic46—22no—
59Dic46—41no—
60Dic46—41no—
61Dic46—41no—
62C8×C23—21no—
63C8×C23C2×D412yes—
64#2191—231nomaximal, Sylow
65C22×C23—21no—
66C22×C23—41no—
67C22×C23C2×D811yescharacteristic
68C2×D23—42no—
69C2×D23—82no—
70C4×C23—21no—
71C4×C23#12011yescharacteristic
72C4×C23AGL(1,ℤ/8)11yescharacteristic
73Dic23—42no—
74Dic23—81no—
75Dic23—81no—
76#575—231no—
77#510—232no—
78#470—231no—
79#360—232no—
80#349D2311yescharacteristic, complemented
81C2×C23—21no—
82C2×C23—41no—
83C2×C23#44711yescharacteristic
84D23—82no—
85C2×#41—461no—
86#137—462no—
87AGL(1,ℤ/8)—462no—
88#135—232no—
89#135—461no—
90C2×Q16—231no—
91C2×M16C2×D2311yescharacteristic
92C22⋊Q8—461no—
93Q32—462no—
94SD32—462no—
95M32C2×D2312yescomplemented
96#106—231no—
97#103—461no—
98C23#219111yescharacteristic, complemented, Sylow
99#41—462no—
100#41—462no—
101#41—921no—
102#41—921no—
103C2×Q8—461no—
104C2×Q8—461no—
105C2×D4—461no—
106C2×D4—921no—
107C22×C4—921no—
108C22×C4D9211yescharacteristic
109Q16—232no—
110Q16—461no—
111Q16—462no—
112SD16—462no—
113SD16—462no—
114D8—232no—
115D8—461no—
116M16—22no—
117C2×C8D9211yescharacteristic
118C2×C8C22×D2311yescharacteristic
119C4⋊C4—461no—
120C4⋊C4—921no—
121C22⋊C4—921no—
122C16—22no—
123C23—921no—
124C23D18411yescharacteristic
125Q8—462no—
126Q8—921no—
127Q8—921no—
128Q8—921no—
129D4—462no—
130D4—921no—
131D4—922no—
132D4—922no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—922no—
136C2×C4—921no—
137C2×C4—922no—
138C2×C4—921no—
139C2×C4—921no—
140C2×C4D18411yescharacteristic
141C2×C4C2×D9211yescharacteristic
142C8—21no—
143C8D4×D2312yes—
144C22—21no—
145C22—41no—
146C22—922no—
147C22—1842no—
148C22C2×D18411yescharacteristic
149C4—21no—
150C4—922no—
151C4—1841no—
152C4—1841no—
153C4#1062505311yescharacteristic
154C4#1062507911yescharacteristic
155C2—21no—
156C2—41no—
157C2—1842no—
158C2#1309255311yescharacteristic
subgroupG/H
centerC2#13092553
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#349C2
socleC2×C23#447
prime radical#13093217C2
hypercenter#349D23
hypocenterC23#2191
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #13092860C2semidirect
3. #13092675C2semidirect
4. #13092228C2semidirect
5. C23×#349C2semidirect
11. C2×Dic92C22semidirect
14. C23×M32C22semidirect
15. #10624999C22semidirect
80. #349D23semidirect
95. M32C2×D23semidirect
98. C23#2191semidirect

Maximal subgroups

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

subgroupindex
#130932172
#130928602
#130926752
#130922282
C23×#3492
#219123