Finite Group Databasebeta

← #15675372

Subgroups — #15675372

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#13093231C211yesmaximal, characteristic
2C2×#10625011C211yesmaximal, characteristic, complemented
3#13092689C211yesmaximal, characteristic, complemented
4#13092234C211yesmaximal, characteristic, complemented
5#13092224C211yesmaximal, characteristic, complemented
6#13092202C211yesmaximal, characteristic, complemented
7C23×#510C211yesmaximal, characteristic, complemented
8#10625161—21no—
9C23×#135C2211yescharacteristic
10C2×Q16×C23C2211yescharacteristic
11#10625122—21no—
12#10625113—21no—
13Q16×D23—21no—
14#10625086—22no—
15#10625083—21no—
16C2×Dic92C2211yescharacteristic
17#10625072C2211yescharacteristic
18C23×Q32—21no—
19C23×SD32—21no—
20C23×M32C2211yescharacteristic
21#10625018—21no—
22#10625011—22no—
23#10625001C2211yescharacteristic
24C2×C23⋊C16C2211yescharacteristic
25#41×C23—21no—
26C2×Q8×C23—21no—
27Q8×D23—22no—
28#67290—22no—
29#67290—42no—
30#67288—41no—
31#67288D411yescharacteristic
32C2×Dic46—21no—
33C2×Dic46—41no—
34Q16×C23—21no—
35Q16×C23—21no—
36Q16×C23D411yescharacteristic
37SD16×C23—21no—
38D8×C23D411yescharacteristic
39C2×C8×C23C2311yescharacteristic
40#67275—22no—
41#67275—41no—
42#67274—41no—
43#67273—22no—
44#67267—21no—
45#67267D411yescharacteristic
46Dic92—21no—
47Dic92D412yes—
48#67262—21no—
49C8×D23—21no—
50C16×C23—21no—
51C23⋊C16—21no—
52Q8×C23—21no—
53Q8×C23—41no—
54Q8×C23—41no—
55D4×C23—21no—
56D4×C23—41no—
57C2×C4×C23—41no—
58C2×C4×C23—41no—
59C2×C4×C23C2×D411yescharacteristic
60C22⋊D23—21no—
61C22⋊D23—42no—
62C2×Dic23—42no—
63C2×Dic23—41no—
64D92D811yescharacteristic
65C4×D23—21no—
66C4×D23—42no—
67Dic46—22no—
68Dic46—42no—
69Dic46—41no—
70Dic46D811yescharacteristic
71C8×C23C2×D411yescharacteristic
72C8×C23C2×D411yescharacteristic
73C23⋊C8—21no—
74C23⋊C8—41no—
75#2195—231nomaximal, Sylow
76C22×C23—41no—
77C22×C23AGL(1,ℤ/8)11yescharacteristic
78C2×D23—21no—
79C4×C23—41no—
80C4×C23—81no—
81C4×C23#12011yescharacteristic
82C4×C23C2×D811yescharacteristic
83Dic23—21no—
84Dic23—42no—
85#578—231no—
86#510D2311yescharacteristic, complemented
87C2×Q32—231no—
88#473—231no—
89#362—231no—
90#359—231no—
91#350—231no—
92C2×C23—21no—
93C2×C23—81no—
94C2×C23#44711yescharacteristic
95D23—41no—
962−1+4—461no—
97#137—461no—
98#137—462no—
99#137—461no—
100#135—461no—
101#135C2×D2311yescharacteristic
102C2×Q16—231no—
103C2×Q16—461no—
104C2×Q16C2×D2311yescharacteristic
105#131—231no—
106Q32—21no—
107Q32—462no—
108SD32—21no—
109M32C2×D2311yescharacteristic
110C2×C16—231no—
111#108—231no—
112#101—461no—
113C23#219511yescharacteristic, complemented, Sylow
114#41—21no—
115#41—231no—
116#41—462no—
117#41—921no—
118#41—922no—
119C2×Q8—21no—
120C2×Q8—462no—
121C2×Q8—461no—
122C2×Q8—921no—
123Q16—21no—
124Q16—21no—
125Q16—232no—
126Q16—462no—
127Q16—461no—
128Q16—921no—
129Q16C22⋊D2311yescharacteristic
130SD16—21no—
131SD16—462no—
132SD16—921no—
133D8C22⋊D2311yescharacteristic
134M16—231no—
135M16—461no—
136M16—461no—
137C2×C8—461no—
138C2×C8C22×D2311yescharacteristic
139C16—21no—
140C16—461no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—231no—
145Q8—462no—
146Q8—922no—
147Q8—921no—
148D4—21no—
149D4—41no—
150D4—231no—
151D4—461no—
152D4—922no—
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—41no—
165C22—461no—
166C22#1062508211yescharacteristic
167C4—41no—
168C4—81no—
169C4—461no—
170C4—922no—
171C4D8×D2311yescharacteristic
172C4#1062510811yescharacteristic
173C2—21no—
174C2—81no—
175C2—921no—
176C2#1309254911yescharacteristic
subgroupG/H
centerC2#13092549
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#510C2
socleC2×C23#447
prime radical#13093231C2
hypercenter#510D23
hypocenterC23#2195
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C2×#10625011C2semidirect
3. #13092689C2semidirect
4. #13092234C2semidirect
5. #13092224C2semidirect
6. #13092202C2semidirect
7. C23×#510C2semidirect
86. #510D23semidirect
113. C23#2195semidirect

Maximal subgroups

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

subgroupindex
#130932312
C2×#106250112
#130926892
#130922342
#130922242
#130922022
C23×#5102
#219523