Finite Group Databasebeta

← #15675345

Subgroups — #15675345

Order 2944.

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

normal subgroups only

This group has 226 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, complemented
2#13092855C212yesmaximal, complemented
3#13092670C211yesmaximal, characteristic, complemented
4#13092228C212yesmaximal, complemented
5C23×#349C211yesmaximal, characteristic, complemented
6C2×#67288—21no—
7C2×M16×C23C2211yescharacteristic
8#10625101—21no—
9#10625080—22no—
10#10625079—22no—
11#10625075—21no—
12#10625075C2212yes—
13C2×D184C2211yescharacteristic, complemented
14C23×M32C2212yescomplemented
15#10625003—21no—
16#10624999C2211yescharacteristic, complemented
17#10624982—22no—
18D368—22no—
19C22×C4×C23D411yescharacteristic
20C2×C22⋊D23—41no—
21C2×C22⋊D23—41no—
22#67288—22no—
23#67288—22no—
24#67288—41no—
25#67288—41no—
26C2×D92—21no—
27C2×D92—21no—
28C2×C4×D23—41no—
29C2×Dic46—21no—
30M16×C23—22no—
31C2×C8×C23D411yescharacteristic
32C2×C8×C23C2311yescharacteristic
33(C2×D23)⋊C4—41no—
34C4⋊Dic23—21no—
35Dic92—21no—
36Dic92D412yescomplemented
37D184—21no—
38D184—22no—
39D184D412yescomplemented
40#67263—22no—
41#67263—22no—
42C16×C23—22no—
43C23×C23D811yescharacteristic
44C22×D23—41no—
45C22×D23—41no—
46C2×C4×C23—21no—
47C2×C4×C23—21no—
48C2×C4×C23D811yescharacteristic
49C2×C4×C23C2×D411yescharacteristic
50C22⋊D23—42no—
51C22⋊D23—42no—
52C22⋊D23—82no—
53C2×Dic23—41no—
54C2×Dic23—41no—
55D92—22no—
56D92—41no—
57D92—41no—
58D92—41no—
59C4×D23—42no—
60C4×D23—42no—
61Dic46—22no—
62Dic46—41no—
63C8×C23—21no—
64C8×C23C2×D412yes—
65#2190—231nomaximal, Sylow
66C22×C23—21no—
67C22×C23—41no—
68C22×C23C2×D811yescharacteristic
69C2×D23—42no—
70C2×D23—82no—
71C2×D23—81no—
72C2×D23—81no—
73C2×D23—81no—
74C4×C23—21no—
75C4×C23#12011yescharacteristic
76C4×C23AGL(1,ℤ/8)11yescharacteristic
77Dic23—42no—
78Dic23—81no—
79#575—231no—
80#509—232no—
81#469—231no—
82#360—232no—
83#349D2311yescharacteristic, complemented
84C2×C23—21no—
85C2×C23—41no—
86C2×C23#44711yescharacteristic
87D23—82no—
88D23—161no—
89C2×#41—461no—
90#137—462no—
91AGL(1,ℤ/8)—462no—
92#135—232no—
93#135—461no—
94C2×D8—231no—
95C2×M16C2×D2311yescharacteristic
96#121—461no—
97SD32—462no—
98D16—462no—
99M32C2×D2312yescomplemented
100#106—231no—
101#102—461no—
102C23#219011yescharacteristic, complemented, Sylow
103#41—462no—
104#41—462no—
105#41—921no—
106#41—921no—
107C2×Q8—461no—
108C2×D4—461no—
109C2×D4—461no—
110C2×D4—921no—
111C2×D4—921no—
112C22×C4—921no—
113C22×C4D9211yescharacteristic
114Q16—232no—
115Q16—461no—
116SD16—462no—
117SD16—462no—
118D8—232no—
119D8—461no—
120D8—462no—
121M16—22no—
122C2×C8D9211yescharacteristic
123C2×C8C22×D2311yescharacteristic
124C4⋊C4—461no—
125C22⋊C4—921no—
126C16—22no—
127C23—921no—
128C23—921no—
129C23D18411yescharacteristic
130Q8—462no—
131Q8—921no—
132D4—462no—
133D4—921no—
134D4—922no—
135D4—922no—
136D4—921no—
137D4—921no—
138D4—1842no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—922no—
142C2×C4—921no—
143C2×C4—922no—
144C2×C4—921no—
145C2×C4D18411yescharacteristic
146C2×C4C2×D9211yescharacteristic
147C8—21no—
148C8D4×D2312yes—
149C22—21no—
150C22—41no—
151C22—922no—
152C22—1841no—
153C22—1841no—
154C22—1842no—
155C22—1841no—
156C22C2×D18411yescharacteristic
157C4—21no—
158C4—922no—
159C4—1841no—
160C4#1062505311yescharacteristic
161C4#1062507911yescharacteristic
162C2—21no—
163C2—41no—
164C2—3681no—
165C2—1842no—
166C2#1309255311yescharacteristic
subgroupG/H
centerC2#13092553
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#349C2
socleC2×C23#447
hypercenter#349D23
hypocenterC23#2190
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
1. #13093217C2semidirect
2. #13092855C2semidirect
3. #13092670C2semidirect
4. #13092228C2semidirect
5. C23×#349C2semidirect
13. C2×D184C22semidirect
14. C23×M32C22semidirect
16. #10624999C22semidirect
36. Dic92D4semidirect
39. D184D4semidirect
83. #349D23semidirect
99. M32C2×D23semidirect
102. C23#2190semidirect

Maximal subgroups

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

subgroupindex
#130932172
#130928552
#130926702
#130922282
C23×#3492
#219023