Finite Group Databasebeta

← #17996539

Subgroups — #17996539

Order 4736.

220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C2×#11924559C211yesmaximal, characteristic
2C2×#11924482C211yesmaximal, characteristic, complemented
3C2×#11924481C211yesmaximal, characteristic, complemented
4#14557775C211yesmaximal, characteristic, complemented
5#14557333C211yesmaximal, characteristic, complemented
6#14557312C211yesmaximal, characteristic, complemented
7C37×#358C211yesmaximal, characteristic, complemented
8C2×#10596966—21no—
9#11924559—22no—
10#11924559—22no—
11C2×Dic148C2211yescharacteristic
12C2×#10596941—21no—
13C2×D296C2211yescharacteristic
14C2×C8×D37C2211yescharacteristic
15#11924516—21no—
16#11924482—22no—
17#11924481—22no—
18C2×#10596925C2211yescharacteristic
19#11924459—21no—
20C2×Q16×C37C2211yescharacteristic
21C2×C16×C37C2211yescharacteristic
22#107×C37C2211yescharacteristic
23C2×Q8×C37—21no—
24#10596966—24no—
25#10596966—42no—
26C2×D148—21no—
27C2×D148—41no—
28C2×C4×D37—41no—
29C2×C4×D37D411yescharacteristic
30C2×Dic74—21no—
31Q16×C37—21no—
32Q16×C37D412yes—
33C2×C8×C37C2311yescharacteristic
34C4⋊C4×C37—21no—
35#10596941—24no—
36#10596938—41no—
37C4⋊Dic37—41no—
38C2×#64436D411yescharacteristic
39Dic148—21no—
40Dic148—21no—
41D296—21no—
42D296D412yes—
43C8×D37—21no—
44C8×D37—21no—
45C16×C37—21no—
46#10596925—21no—
47C22×D37—41no—
48C22×D37D811yescharacteristic
49Q8×C37—22no—
50Q8×C37—41no—
51C2×C4×C37—41no—
52C2×C4×C37—41no—
53C2×C4×C37C2×D411yescharacteristic
54C2×Dic37—41no—
55C2×Dic37D811yescharacteristic
56D148—22no—
57D148—44no—
58D148—41no—
59C4×D37—21no—
60C4×D37—21no—
61C4×D37—44no—
62Dic74—41no—
63Dic74—41no—
64C8×C37C2×D411yescharacteristic
65C8×C37C2×D411yescharacteristic
66#64436—21no—
67C22×C37C2×D811yescharacteristic
68C2×D37—21no—
69C2×D37—21no—
70C2×D37—21no—
71C2×D37—42no—
72C2×D37—81no—
73C2×D37—81no—
74C4×C37—42no—
75C4×C37—81no—
76C4×C37#12011yescharacteristic
77C4×C37AGL(1,ℤ/8)11yescharacteristic
78Dic37—21no—
79Dic37—81no—
80#2189—371nomaximal, Sylow
81C2×C37#44711yescharacteristic
82C2×C37#50811yescharacteristic
83C2×C37#51011yescharacteristic
84D37—41no—
85D37—82no—
86C2×#135—371no—
87C2×Q32—371no—
88C2×SD32—371no—
89#467—371no—
90#358D3711yescharacteristic, complemented
91#357—371no—
92C22⋊C16—371no—
93C37#218911yescharacteristic, complemented, Sylow
94C2×#41—741no—
95#135—742no—
96#135—742no—
97C2×Q16—371no—
98C2×Q16C2×D3711yescharacteristic
99C2×SD16—741no—
100C2×D8—371no—
101C22×C8—371no—
102C22⋊Q8—741no—
103Q32—742no—
104SD32—742no—
105C2×C16—371no—
106C2×C16C2×D3711yescharacteristic
107#107C2×D3711yescharacteristic
108#103—741no—
109#41—744no—
110#41—1482no—
111C2×Q8—21no—
112C2×Q8—741no—
113C2×D4—741no—
114C2×D4—1481no—
115C22×C4—371no—
116C22×C4—1481no—
117Q16—21no—
118Q16—741no—
119Q16—741no—
120Q16D14812yes—
121SD16—744no—
122D8—372no—
123D8—741no—
124C2×C8—371no—
125C2×C8—741no—
126C2×C8—741no—
127C2×C8C22×D3711yescharacteristic
128C4⋊C4—21no—
129C4⋊C4—1481no—
130C22⋊C4—1481no—
131C16—21no—
132C16—741no—
133C23—371no—
134C23—1481no—
135Q8—22no—
136Q8—41no—
137Q8—1481no—
138Q8—1481no—
139D4—742no—
140D4—1484no—
141D4—1481no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—371no—
145C2×C4—741no—
146C2×C4—741no—
147C2×C4—1484no—
148C2×C4—1481no—
149C2×C4D4×D3711yescharacteristic
150C8—741no—
151C8C2×D14811yescharacteristic
152C8D4×D3711yescharacteristic
153C22—2961no—
154C22—2961no—
155C22—741no—
156C22—741no—
157C22—741no—
158C22—1482no—
159C22D8×D3711yescharacteristic
160C4—42no—
161C4—81no—
162C4—2961no—
163C4—741no—
164C4#1192450611yescharacteristic
165C4#1192456311yescharacteristic
166C2—2962no—
167C2—1481no—
168C2#1455766811yescharacteristic
169C2#1455796411yescharacteristic
170C2#1455797511yescharacteristic
subgroupG/H
centerC22D8×D37
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#358C2
socleC22×C37C2×D8
prime radicalC2×#11924559C2
hypercenter#358D37
hypocenterC37#2189
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
2. C2×#11924482C2semidirect
3. C2×#11924481C2semidirect
4. #14557775C2semidirect
5. #14557333C2semidirect
6. #14557312C2semidirect
7. C37×#358C2semidirect
90. #358D37semidirect
93. C37#2189semidirect

Maximal subgroups

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

subgroupindex
C2×#119245592
C2×#119244822
C2×#119244812
#145577752
#145573332
#145573122
C37×#3582
#218937