Finite Group Databasebeta

← #17996561

Subgroups — #17996561

Order 4736.

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

normal subgroups only

This group has 210 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#14558347C211yesmaximal, characteristic, complemented
2#14557968C211yesmaximal, characteristic, complemented
3C2×#11924481C211yesmaximal, characteristic, complemented
4#14557804C211yesmaximal, characteristic, complemented
5#14557348C211yesmaximal, characteristic, complemented
6#14557316C211yesmaximal, characteristic, complemented
7C37×#359C211yesmaximal, characteristic, complemented
8#11924583—21no—
9#11924566—21no—
10#11924565—22no—
11#11924564—21no—
12#11924555—21no—
13C2×Dic148C2211yescharacteristic
14Q16×D37—21no—
15C2×D296C2211yescharacteristic
16#11924542C2211yescharacteristic
17#11924481—22no—
18#11924479—21no—
19#11924477—21no—
20#11924476C2211yescharacteristic
21#11924452—21no—
22#135×C37C2211yescharacteristic
23C2×C16×C37C2211yescharacteristic
24#108×C37C2211yescharacteristic
25#41×C37—21no—
26Q8×D37—22no—
27#10596964—22no—
28#10596964—42no—
29#10596962—41no—
30#10596962D411yescharacteristic
31C2×D148—21no—
32C2×Dic74—21no—
33C2×Dic74—41no—
34Q16×C37D411yescharacteristic
35SD16×C37—21no—
36D8×C37D411yescharacteristic
37M16×C37—21no—
38C2×C8×C37C2311yescharacteristic
39#10596942—22no—
40#10596940—22no—
41#10596934D411yescharacteristic
42Dic148—21no—
43Dic148D412yes—
44D296—21no—
45D296—21no—
46D296—41no—
47#10596930—41no—
48#10596929—21no—
49C8×D37—21no—
50C16×C37—21no—
51#10596925—21no—
52C22×D37—41no—
53Q8×C37—21no—
54D4×C37—21no—
55D4×C37—41no—
56C2×C4×C37—41no—
57C2×C4×C37C2×D411yescharacteristic
58C22⋊D37—21no—
59C22⋊D37—42no—
60C2×Dic37—42no—
61C2×Dic37—41no—
62D148—41no—
63D148—41no—
64D148D811yescharacteristic
65C4×D37—21no—
66C4×D37—42no—
67Dic74—22no—
68Dic74—42no—
69Dic74—41no—
70Dic74D811yescharacteristic
71C8×C37—41no—
72C8×C37C2×D411yescharacteristic
73C8×C37C2×D411yescharacteristic
74#64436—21no—
75C22×C37—41no—
76C22×C37AGL(1,ℤ/8)11yescharacteristic
77C2×D37—21no—
78C2×D37—81no—
79C2×D37—161no—
80C4×C37—41no—
81C4×C37#12011yescharacteristic
82C4×C37C2×D811yescharacteristic
83Dic37—21no—
84Dic37—42no—
85#2193—371nomaximal, Sylow
86C2×C37—21no—
87C2×C37—81no—
88C2×C37#44711yescharacteristic
89D37—41no—
90D37—161no—
91#578—371no—
92#509—371no—
93C2×SD32—371no—
94#472—371no—
95#362—371no—
96#359D3711yescharacteristic, complemented
97#350—371no—
98C37#219311yescharacteristic, complemented, Sylow
992−1+4—741no—
100#137—741no—
101#137—742no—
102AGL(1,ℤ/8)—741no—
103#135—741no—
104#135C2×D3711yescharacteristic
105C2×Q16—371no—
106C2×Q16—741no—
107C2×D8—371no—
108#131—371no—
109SD32—742no—
110SD32—741no—
111D16—741no—
112M32—371no—
113C2×C16C2×D3711yescharacteristic
114#108C2×D3711yescharacteristic
115#100—741no—
116#41—21no—
117#41—371no—
118#41—742no—
119#41—1481no—
120#41—1482no—
121C2×Q8—742no—
122C2×Q8—741no—
123C2×Q8—1481no—
124C2×D4—741no—
125Q16—372no—
126Q16—742no—
127Q16—741no—
128Q16D14811yescharacteristic
129SD16—21no—
130SD16—742no—
131SD16—1481no—
132D8—741no—
133D8—741no—
134D8—1481no—
135D8D14811yescharacteristic
136M16—21no—
137M16—371no—
138M16—741no—
139C2×C8—741no—
140C2×C8C22×D3711yescharacteristic
141C16—21no—
142C16—741no—
143C23—1481no—
144Q8—21no—
145Q8—371no—
146Q8—742no—
147Q8—1482no—
148Q8—1481no—
149D4—21no—
150D4—41no—
151D4—371no—
152D4—741no—
153D4—1482no—
154D4—1481no—
155D4—1481no—
156C2×C4—41no—
157C2×C4—741no—
158C2×C4—1482no—
159C2×C4—1482no—
160C2×C4—1481no—
161C2×C4D4×D3711yescharacteristic
162C8—41no—
163C8—741no—
164C8C2×D14811yescharacteristic
165C8D4×D3711yescharacteristic
166C22—41no—
167C22—2961no—
168C22—741no—
169C22—5921no—
170C22#1192456311yescharacteristic
171C4—41no—
172C4—741no—
173C4—1482no—
174C4#1192450611yescharacteristic
175C4D8×D3711yescharacteristic
176C2—21no—
177C2—81no—
178C2—5921no—
179C2—1481no—
180C2#1455766811yescharacteristic
subgroupG/H
centerC2#14557668
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#359C2
socleC2×C37#447
hypercenter#359D37
hypocenterC37#2193
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #359

Complements

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

NH ≅ G/Ntype
1. #14558347C2semidirect
2. #14557968C2semidirect
3. C2×#11924481C2semidirect
4. #14557804C2semidirect
5. #14557348C2semidirect
6. #14557316C2semidirect
7. C37×#359C2semidirect
96. #359D37semidirect
98. C37#2193semidirect

Maximal subgroups

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

subgroupindex
#145583472
#145579682
C2×#119244812
#145578042
#145573482
#145573162
C37×#3592
#219337