Finite Group Databasebeta

← #354×D37 #17996255

Subgroups — #354×D37 #17996255

Order 4736.

284 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D37C211yesmaximal, characteristic
2#99×D37C212yesmaximal
3#14557328C211yesmaximal, characteristic, complemented
4#14557327C212yesmaximal, complemented
5C37×#354C211yesmaximal, characteristic, complemented
6C2×Q8×D37C411yescharacteristic, complemented
7C2×D4×D37C2211yescharacteristic
8#11924525C411yescharacteristic, complemented
9#11924524C411yescharacteristic, complemented
10#11924523C2211yescharacteristic
11#11924522—22no—
12C22⋊C4×D37—22no—
13C22⋊C4×D37—22no—
14C42×D37C411yescharacteristic, complemented
15#11924451C2212yes—
16#11924450—22no—
17#124×C37C2211yescharacteristic
18#99×C37C2212yes—
19C23×D37D412yes—
20C2×Q8×C37C2×C411yescharacteristic, complemented
21C2×D4×C37C2311yescharacteristic
22C2×C22⋊D37D412yes—
23Q8×D37—41no—
24Q8×D37—41no—
25D4×D37—41no—
26D4×D37—41no—
27C2×D148C2×C411yescharacteristic
28C2×C4×D37—21no—
29C2×C4×D37—21no—
30C2×C4×D37—42no—
31C2×C4×D37C2×C411yescharacteristic
32C2×Dic74—21no—
33C2×Dic74C2×C411yescharacteristic, complemented
34C22⋊C4×C37—22no—
35C22⋊C4×C37—22no—
36C42×C37C2×C411yescharacteristic, complemented
37C22⋊Dic37—22no—
38C22⋊Dic37—22no—
39#10596938—22no—
40#10596938—22no—
41#10596938—42no—
42C4×Dic37—21no—
43C4×Dic37C2×C411yescharacteristic, complemented
44C23×C37C2×D412yes—
45C22×D37—22no—
46C22×D37—22no—
47C22×D37—44no—
48C22×D37C22⋊C411yescharacteristic
49C22×D37C22⋊C412yes—
50Q8×C37—41no—
51D4×C37—41no—
52C2×C4×C37—21no—
53C2×C4×C37—21no—
54C2×C4×C37—42no—
55C2×C4×C37C22×C411yescharacteristic
56C22⋊D37—42no—
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37—42no—
60C2×Dic37C22⋊C411yescharacteristic
61D148—41no—
62C4×D37—21no—
63C4×D37—21no—
64C4×D37—42no—
65C4×D37—41no—
66C4×D37—41no—
67C4×D37—84no—
68Dic74—42no—
69Dic74—41no—
70C22×C37—22no—
71C22×C37—42no—
72C22×C37C2×C22⋊C411yescharacteristic
73C2×D37—22no—
74C2×D37—22no—
75C2×D37—44no—
76C2×D37—42no—
77C2×D37—82no—
78C2×D37#9911yescharacteristic
79C2×D37#9911yescharacteristic
80C4×C37—21no—
81C4×C37—41no—
82C4×C37—41no—
83C4×C37—82no—
84Dic37—21no—
85Dic37—41no—
86Dic37—41no—
87Dic37—82no—
88C2×#354—371nomaximal, Sylow
89C2×C37—21no—
90C2×C37—42no—
91C2×C37C2×#9911yescharacteristic
92D37—21no—
93D37—42no—
94D37#35412yesdirect product factor
95C2×#124—371no—
96C2×#99—372no—
97#354—371no—
98#354—372no—
99#354D3711yescharacteristic, direct product factor
100C37C2×#35411yescharacteristic, complemented, Sylow
101C22×Q8—371no—
102C22×D4—371no—
103#124—371no—
104#124—371no—
105#124—371no—
106#124—742no—
107#124C2×D3711yescharacteristic
108C2×C22⋊C4—742no—
109C2×C22⋊C4—742no—
110C2×C42—371no—
111#99—372no—
112#99—742no—
113#99C2×D3712yes—
114C24—372no—
115C2×Q8—371no—
116C2×Q8—741no—
117C2×Q8—1481no—
118C2×Q8—1481no—
119C2×Q8C4×D3711yescharacteristic, complemented
120C2×D4—372no—
121C2×D4—371no—
122C2×D4—1481no—
123C2×D4—1481no—
124C2×D4C22×D3711yescharacteristic
125C22×C4—371no—
126C22×C4—741no—
127C22×C4—741no—
128C22×C4—1482no—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C22⋊C4—742no—
132C22⋊C4—742no—
133C22⋊C4—742no—
134C22⋊C4—742no—
135C22⋊C4—1482no—
136C42—371no—
137C42—741no—
138C42C4×D3711yescharacteristic, complemented
139C23—371no—
140C23—372no—
141C23—742no—
142C23—742no—
143C23—1484no—
144C23D4×D3712yes—
145Q8—41no—
146Q8—1481no—
147Q8—1482no—
148D4—41no—
149D4—1481no—
150D4—1482no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—371no—
155C2×C4—2964no—
156C2×C4—741no—
157C2×C4—741no—
158C2×C4—741no—
159C2×C4—741no—
160C2×C4—1481no—
161C2×C4—1481no—
162C2×C4—1482no—
163C2×C4—1482no—
164C2×C4C2×C4×D3711yescharacteristic
165C22—22no—
166C22—42no—
167C22—371no—
168C22—371no—
169C22—2962no—
170C22—742no—
171C22—742no—
172C22—1482no—
173C22—1484no—
174C22C22⋊C4×D3711yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—82no—
179C4—2962no—
180C4—741no—
181C4—1481no—
182C4—1481no—
183C2—21no—
184C2—42no—
185C2—372no—
186C2—741no—
187C2—1482no—
188C2#99×D3711yescharacteristic
subgroupG/H
centerC2#99×D37
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#354C2
socleC2×C37C2×#99
prime radicalC2×D4×D37C22
cosocleC2×D4×C37C23
hypercenter#354D37
hypocenterC37C2×#354
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
6. C2×Q8×D37C4semidirect
8. #11924525C4semidirect
9. #11924524C4semidirect
14. C42×D37C4semidirect
20. C2×Q8×C37C2×C4semidirect
33. C2×Dic74C2×C4semidirect
36. C42×C37C2×C4semidirect
43. C4×Dic37C2×C4semidirect
94. D37#354direct (N × H)
99. #354D37direct (N × H)
100. C37C2×#354semidirect
119. C2×Q8C4×D37semidirect
138. C42C4×D37semidirect

Maximal subgroups

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

subgroupindex
#124×D372
#99×D372
#145573282
#145573272
C37×#3542
C2×#35437