Finite Group Databasebeta

← #15675374

Subgroups — #15675374

Order 2944.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#13093230C211yesmaximal, characteristic
2#13092858C211yesmaximal, characteristic, complemented
3#13092689C211yesmaximal, characteristic, complemented
4#13092233C211yesmaximal, characteristic, complemented
5#13092225C211yesmaximal, characteristic, complemented
6#13092200C211yesmaximal, characteristic, complemented
7C2×C23×Q32C211yesmaximal, characteristic, complemented
8#10625158—21no—
9C2×Q16×C23C2211yescharacteristic
10C2×Q16×C23C2211yescharacteristic
11#10625113—21no—
12#10625113—21no—
13#10625090—21no—
14#10625089—22no—
15Q16×D23—21no—
16#10625075C2211yescharacteristic
17#10625072C2211yescharacteristic
18C23×Q32—22no—
19C2×C16×C23C2211yescharacteristic
20#10625018—21no—
21#10625011—21no—
22#10625010—21no—
23#10625001C2211yescharacteristic
24#10624994C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×Q8×C23—21no—
27#67292—22no—
28#67292—41no—
29Q8×D23—22no—
30Q8×D23—41no—
31#67288—21no—
32#67288—42no—
33#67288D411yescharacteristic
34Q16×C23—21no—
35Q16×C23—21no—
36Q16×C23—21no—
37Q16×C23D412yes—
38C2×C8×C23C2311yescharacteristic
39#67275—22no—
40#67275—41no—
41#67274—22no—
42#67274—41no—
43#67267—21no—
44#67267D411yescharacteristic
45Dic92D411yescharacteristic
46D184D411yescharacteristic
47#67263—21no—
48#67262—21no—
49C8×D23—21no—
50C16×C23—21no—
51C23⋊C16—21no—
52Q8×C23—22no—
53Q8×C23—41no—
54Q8×C23—41no—
55Q8×C23—41no—
56C2×C4×C23—41no—
57C2×C4×C23—41no—
58C2×C4×C23C2×D411yescharacteristic
59C22⋊D23—21no—
60C22⋊D23—41no—
61D92—21no—
62D92—42no—
63D92D811yescharacteristic
64C4×D23—21no—
65C4×D23—42no—
66C4×D23—42no—
67C4×D23—41no—
68Dic46—21no—
69Dic46—42no—
70Dic46D811yescharacteristic
71C8×C23C2×D411yescharacteristic
72C8×C23C2×D411yescharacteristic
73C23⋊C8—21no—
74C23⋊C8—41no—
75#2195—231nomaximal, Sylow
76C22×C23AGL(1,ℤ/8)11yescharacteristic
77C2×D23—21no—
78C2×D23—41no—
79C4×C23—42no—
80C4×C23—81no—
81C4×C23#12011yescharacteristic
82C4×C23C2×D811yescharacteristic
83Dic23—21no—
84Dic23—41no—
85#578—231no—
86#510—231no—
87C2×Q32D2311yescharacteristic, complemented
88#473—231no—
89#362—231no—
90#359—231no—
91#350—231no—
92C2×C23—21no—
93C2×C23#44711yescharacteristic
94D23—41no—
95D23—81no—
962−1+4—461no—
97#137—461no—
98#137—462no—
99#137—461no—
100#135—231no—
101#135—461no—
102C2×Q16—461no—
103C2×Q16C2×D2311yescharacteristic
104C2×Q16C2×D2311yescharacteristic
105#131—231no—
106Q32—22no—
107Q32—461no—
108SD32—461no—
109M32—231no—
110C2×C16C2×D2311yescharacteristic
111#108—231no—
112#101—461no—
113C23#219511yescharacteristic, complemented, Sylow
114#41—231no—
115#41—462no—
116#41—461no—
117#41—922no—
118#41—921no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—462no—
122C2×Q8—921no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—231no—
127Q16—462no—
128Q16—921no—
129Q16C22⋊D2312yes—
130SD16—462no—
131SD16—461no—
132SD16—921no—
133D8—231no—
134M16—231no—
135M16—461no—
136M16—461no—
137C2×C8—461no—
138C2×C8C22×D2311yescharacteristic
139C16—21no—
140C16—461no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—231no—
146Q8—461no—
147Q8—922no—
148D4—231no—
149D4—461no—
150D4—461no—
151D4—922no—
152D4—921no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—461no—
156C2×C4—922no—
157C2×C4—922no—
158C2×C4—921no—
159C2×C4D4×D2311yescharacteristic
160C8—461no—
161C8—921no—
162C8D4×D2311yescharacteristic
163C8C2×C22⋊D2311yescharacteristic
164C22—461no—
165C22—921no—
166C22#1062508211yescharacteristic
167C4—42no—
168C4—81no—
169C4—461no—
170C4—921no—
171C4D8×D2311yescharacteristic
172C4#1062510811yescharacteristic
173C2—21no—
174C2—921no—
175C2—1841no—
176C2#1309254911yescharacteristic
subgroupG/H
centerC2#13092549
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC2×C23×Q32C2
socleC2×C23#447
prime radical#13093230C2
hypercenterC2×Q32D23
hypocenterC23#2195
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #13092858C2semidirect
3. #13092689C2semidirect
4. #13092233C2semidirect
5. #13092225C2semidirect
6. #13092200C2semidirect
7. C2×C23×Q32C2semidirect
87. C2×Q32D23semidirect
113. C23#2195semidirect

Maximal subgroups

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

subgroupindex
#130932302
#130928582
#130926892
#130922332
#130922252
#130922002
C2×C23×Q322
#219523