Finite Group Databasebeta

← #17996269

Subgroups — #17996269

Order 4736.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558103C211yesmaximal, characteristic
2#14557505C212yesmaximal
3#14557328C211yesmaximal, characteristic, complemented
4#14557327C212yesmaximal, complemented
5C37×#354C211yesmaximal, characteristic, complemented
6C2×#10596964C2211yescharacteristic
7C2×Q8×D37C411yescharacteristic, complemented
8#11924536C411yescharacteristic, complemented
9#11924534C411yescharacteristic, complemented
10#11924523C2211yescharacteristic
11#11924518—22no—
12#11924513—22no—
13#11924493C411yescharacteristic, complemented
14#11924492—22no—
15#11924451C2212yes—
16#11924450—22no—
17#124×C37C2211yescharacteristic
18#99×C37C2212yes—
19C2×Q8×C37C2×C411yescharacteristic
20C2×D4×C37C2311yescharacteristic
21C2×C22⋊D37D412yes—
22C22×Dic37D412yes—
23Q8×D37—42no—
24#10596964—42no—
25C2×C4×D37—21no—
26C2×C4×D37C2×C411yescharacteristic
27C2×Dic74—21no—
28C2×Dic74C2×C411yescharacteristic
29C2×Dic74C2×C411yescharacteristic
30C22⋊C4×C37—22no—
31C22⋊C4×C37—22no—
32C42×C37C2×C411yescharacteristic
33C22⋊Dic37—22no—
34C22⋊Dic37—22no—
35#10596938—21no—
36C4⋊Dic37—22no—
37#10596936—21no—
38#10596936—22no—
39#10596936—42no—
40C4×Dic37—42no—
41C4×Dic37C2×C411yescharacteristic
42C23×C37C2×D412yes—
43C22×D37C22⋊C411yescharacteristic
44Q8×C37—41no—
45D4×C37—41no—
46C2×C4×C37—21no—
47C2×C4×C37—21no—
48C2×C4×C37—42no—
49C2×C4×C37C22×C411yescharacteristic
50C22⋊D37—42no—
51C2×Dic37—22no—
52C2×Dic37—22no—
53C2×Dic37—21no—
54C2×Dic37—21no—
55C2×Dic37—42no—
56C2×Dic37C22⋊C412yes—
57C2×Dic37C22⋊C411yescharacteristic
58C4×D37—22no—
59C4×D37—42no—
60Dic74—41no—
61Dic74—42no—
62Dic74—41no—
63C22×C37—22no—
64C22×C37—42no—
65C22×C37C2×C22⋊C411yescharacteristic
66C2×D37—21no—
67C2×D37—41no—
68C4×C37—21no—
69C4×C37—41no—
70C4×C37—41no—
71C4×C37—82no—
72Dic37—22no—
73Dic37—41no—
74Dic37—41no—
75Dic37—82no—
76Dic37#9912yes—
77#2129—371nomaximal, Sylow
78C2×C37—21no—
79C2×C37—42no—
80C2×C37C2×#9911yescharacteristic
81D37—41no—
82#536—371no—
83#410—372no—
84#354—371no—
85#354—372no—
86#354D3711yescharacteristic, complemented
87C37#212911yescharacteristic, complemented, Sylow
88C2×#41—371no—
89C22×Q8—371no—
90C4⋊Q8—371no—
91C4⋊Q8—371no—
92#124—371no—
93#124C2×D3711yescharacteristic
94#123—742no—
95C22⋊Q8—742no—
96#117—371no—
97#117—742no—
98#99—372no—
99#99—742no—
100#99C2×D3712yes—
101#41—1482no—
102C2×Q8—371no—
103C2×Q8—371no—
104C2×Q8—741no—
105C2×Q8—1482no—
106C2×Q8C4×D3711yescharacteristic
107C2×D4—372no—
108C2×D4C22×D3711yescharacteristic
109C22×C4—372no—
110C22×C4—371no—
111C22×C4—741no—
112C4⋊C4—741no—
113C4⋊C4—742no—
114C4⋊C4—742no—
115C4⋊C4—1482no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—741no—
119C22⋊C4—742no—
120C22⋊C4—742no—
121C42—371no—
122C42—1482no—
123C42C4×D3711yescharacteristic
124C23—371no—
125C23D4×D3712yes—
126Q8—41no—
127Q8—1481no—
128Q8—1481no—
129Q8—1482no—
130D4—41no—
131D4—1482no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—371no—
136C2×C4—372no—
137C2×C4—742no—
138C2×C4—742no—
139C2×C4—742no—
140C2×C4—741no—
141C2×C4—741no—
142C2×C4—1482no—
143C2×C4—1482no—
144C2×C4C2×C4×D3711yescharacteristic
145C22—22no—
146C22—42no—
147C22—741no—
148C22—1481no—
149C22C22⋊C4×D3711yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—372no—
155C4—2962no—
156C4—742no—
157C4—1481no—
158C4—1481no—
159C2—21no—
160C2—42no—
161C2—1481no—
162C2#99×D3711yescharacteristic
subgroupG/H
centerC2#99×D37
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#354C2
socleC2×C37C2×#99
prime radicalC2×#10596964C22
cosocleC2×D4×C37C23
hypercenter#354D37
hypocenterC37#2129
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #14557328C2semidirect
4. #14557327C2semidirect
5. C37×#354C2semidirect
7. C2×Q8×D37C4semidirect
8. #11924536C4semidirect
9. #11924534C4semidirect
13. #11924493C4semidirect
86. #354D37semidirect
87. C37#2129semidirect

Maximal subgroups

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

subgroupindex
#145581032
#145575052
#145573282
#145573272
C37×#3542
#212937