Finite Group Databasebeta

← #15675373

Subgroups — #15675373

Order 2944.

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

normal subgroups only

This group has 206 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#13093234C211yesmaximal, characteristic
2#13092858C211yesmaximal, characteristic, complemented
3C2×#10625011C211yesmaximal, characteristic, complemented
4#13092232C211yesmaximal, characteristic, complemented
5#13092223C211yesmaximal, characteristic, complemented
6#13092201C211yesmaximal, characteristic, complemented
7C23×#473C211yesmaximal, characteristic, complemented
8#10625161—21no—
9C23×#137—21no—
10C2×Q16×C23C2211yescharacteristic
11C23×#131C2211yescharacteristic
12#10625080—21no—
13#10625080—22no—
14C2×Dic92—21no—
15C2×Dic92C2211yescharacteristic
16#10625075—21no—
17#10625075C2211yescharacteristic
18C23×#108C2211yescharacteristic
19C23×#101—21no—
20#10625011—22no—
21#10625011—21no—
22#10625010—21no—
23#10624994C2211yescharacteristic
24C2×C23⋊C16C2211yescharacteristic
25#41×C23D411yescharacteristic
26C2×Q8×C23—21no—
27Q8×D23—41no—
28#67290—42no—
29#67290—41no—
30#67288—22no—
31#67288—21no—
32C2×Dic46—22no—
33C2×Dic46—21no—
34Q16×C23—21no—
35Q16×C23—21no—
36Q16×C23—41no—
37SD16×C23—41no—
38M16×C23—21no—
39M16×C23—21no—
40M16×C23D411yescharacteristic
41C2×C8×C23—21no—
42C2×C8×C23C2311yescharacteristic
43Dic92—22no—
44Dic92—21no—
45Dic92D411yescharacteristic
46Dic92D412yes—
47D184D411yescharacteristic
48#67263—22no—
49#67263—21no—
50C23⋊C16—21no—
51C23⋊C16—21no—
52Q8×C23—41no—
53Q8×C23—41no—
54Q8×C23D811yescharacteristic
55D4×C23—21no—
56D4×C23D811yescharacteristic
57C2×C4×C23—21no—
58C2×C4×C23—41no—
59C2×C4×C23C2×D411yescharacteristic
60C22⋊D23—42no—
61C22⋊D23—41no—
62C2×Dic23—42no—
63C2×Dic23—41no—
64D92—21no—
65C4×D23—42no—
66C4×D23—41no—
67Dic46—22no—
68Dic46—21no—
69Dic46—42no—
70Dic46—41no—
71C8×C23—21no—
72C8×C23—41no—
73C8×C23C2×D411yescharacteristic
74C8×C23C2×D411yescharacteristic
75#2195—231nomaximal, Sylow
76C22×C23—21no—
77C22×C23AGL(1,ℤ/8)11yescharacteristic
78C2×D23—41no—
79C4×C23—21no—
80C4×C23—81no—
81C4×C23#12011yescharacteristic
82C4×C23C2×D811yescharacteristic
83Dic23—41no—
84Dic23—42no—
85#578—231no—
86#510—231no—
87C2×Q32—231no—
88#473D2311yescharacteristic, complemented
89#362—231no—
90#359—231no—
91#350—231no—
92C2×C23—21no—
93C2×C23—41no—
94C2×C23#44711yescharacteristic
95D23—81no—
962−1+4—461no—
97#137—21no—
98#137—462no—
99#137—461no—
100#135—231no—
101#135—461no—
102C2×Q16—231no—
103C2×Q16—461no—
104C2×Q16C2×D2311yescharacteristic
105#131C2×D2311yescharacteristic
106Q32—462no—
107Q32—461no—
108SD32—461no—
109M32—231no—
110C2×C16—231no—
111#108C2×D2311yescharacteristic
112#101—21no—
113C23#219511yescharacteristic, complemented, Sylow
114#41—462no—
115#41—461no—
116#41—922no—
117#41—921no—
118#41C22⋊D2311yescharacteristic
119C2×Q8—21no—
120C2×Q8—462no—
121C2×Q8—461no—
122C2×Q8—921no—
123Q16—21no—
124Q16—21no—
125Q16—41no—
126Q16—232no—
127Q16—231no—
128Q16—462no—
129Q16—461no—
130SD16—41no—
131SD16—462no—
132SD16—461no—
133D8—231no—
134M16—21no—
135M16—21no—
136M16C22⋊D2311yescharacteristic
137C2×C8—21no—
138C2×C8C22×D2311yescharacteristic
139C16—461no—
140C16—461no—
141Q8—41no—
142Q8—41no—
143Q8—462no—
144Q8—461no—
145Q8—922no—
146Q8—921no—
147Q8#6727211yescharacteristic
148D4—21no—
149D4—461no—
150D4—922no—
151D4—921no—
152D4#6727211yescharacteristic
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—922no—
156C2×C4—922no—
157C2×C4—921no—
158C2×C4—921no—
159C2×C4C2×C22⋊D2311yescharacteristic
160C8—21no—
161C8—41no—
162C8D4×D2311yescharacteristic
163C8D4×D2311yescharacteristic
164C22—21no—
165C22—921no—
166C22#1062512011yescharacteristic
167C4—21no—
168C4—81no—
169C4—922no—
170C4—921no—
171C4C2×#6727211yescharacteristic
172C4#1062510811yescharacteristic
173C2—21no—
174C2—41no—
175C2—1841no—
176C2#1309255011yescharacteristic
subgroupG/H
centerC2#13092550
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#473C2
socleC2×C23#447
prime radical#13093234C2
hypercenter#473D23
hypocenterC23#2195
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #473

Complements

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

NH ≅ G/Ntype
2. #13092858C2semidirect
3. C2×#10625011C2semidirect
4. #13092232C2semidirect
5. #13092223C2semidirect
6. #13092201C2semidirect
7. C23×#473C2semidirect
88. #473D23semidirect
113. C23#2195semidirect

Maximal subgroups

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

subgroupindex
#130932342
#130928582
C2×#106250112
#130922322
#130922232
#130922012
C23×#4732
#219523