Finite Group Databasebeta

← D37⋊#352 #18010845

Subgroups — D37⋊#352 #18010845

Order 4736.

278 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D37⋊#100C211yesmaximal, characteristic
2D37⋊#99C211yesmaximal, characteristic
3#14558436C212yesmaximal, complemented
4#14558435C212yesmaximal, complemented
5#123×D37C211yesmaximal, characteristic
6D37⋊M16—21no—
7C2×C22⋊#3866—21no—
8#11924596—21no—
9#11924596C2212yes—
10#11924595—21no—
11#11924594C2212yes—
12C2×D4×D37C2211yescharacteristic
13C22×C4×D37C411yescharacteristic, complemented
14#11924521—21no—
15#11924520C2211yescharacteristic
16#11924519C2211yescharacteristic
17#11924518—21no—
18#11924517C411yescharacteristic, complemented
19C4⋊C4×D37—21no—
20C22⋊C4×D37—21no—
21C22⋊C4×D37C411yescharacteristic, complemented
22#123×C37C411yescharacteristic, complemented
23C23×D37C2×C411yescharacteristic
24C23×D37D411yescharacteristic
25C22×#3866—41no—
26C2×D4×C37C2×C411yescharacteristic
27C22×C4×C37C2×C411yescharacteristic, complemented
28C2×C22⋊D37D411yescharacteristic
29C2×C22⋊D37C2311yescharacteristic
30C22×Dic37C2×C411yescharacteristic, complemented
31D4×D37—41no—
32D4×D37—41no—
33C2×D148D411yescharacteristic
34C2×C4×D37—21no—
35C2×C4×D37—21no—
36C2×C4×D37—21no—
37C2×C4×D37—41no—
38C2×C4×D37—41no—
39C2×C4×D37D411yescharacteristic
40C22⋊#3866—22no—
41C22⋊#3866—41no—
42#10596957—22no—
43#10596953—41no—
44D37⋊C8—41no—
45C4⋊C4×C37—21no—
46C22⋊C4×C37—21no—
47C22⋊C4×C37C2×C411yescharacteristic, complemented
48C22⋊Dic37—21no—
49C22⋊Dic37C2×C411yescharacteristic, complemented
50#10596938—21no—
51#10596938—21no—
52#10596938—21no—
53C4⋊Dic37—21no—
54#10596936—21no—
55#10596936—21no—
56C23×C37C22⋊C411yescharacteristic
57C23×C37C22×C411yescharacteristic
58C22×D37—21no—
59C22×D37—21no—
60C22×D37—21no—
61C22×D37—21no—
62C22×D37—42no—
63C22×D37—42no—
64C22×D37C22⋊C411yescharacteristic
65C22×D37C22⋊C411yescharacteristic
66C22×D37C2×D411yescharacteristic
67C2×#3866—42no—
68C2×#3866—82no—
69D4×C37—41no—
70C2×C4×C37—21no—
71C2×C4×C37—21no—
72C2×C4×C37—41no—
73C2×C4×C37C22⋊C411yescharacteristic
74C22⋊D37—41no—
75C22⋊D37—41no—
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—41no—
79C2×Dic37C2×D411yescharacteristic
80D148—41no—
81C4×D37—21no—
82C4×D37—21no—
83C4×D37—42no—
84C4×D37—42no—
85C4×D37—41no—
86C4×D37—41no—
87#64438—42no—
88C22×C37—21no—
89C22×C37—21no—
90C22×C37—41no—
91C22×C37—41no—
92C22×C37C2×C22⋊C411yescharacteristic
93C2×D37—22no—
94C2×D37—21no—
95C2×D37—21no—
96C2×D37—42no—
97C2×D37—42no—
98C2×D37—42no—
99C2×D37—41no—
100C2×D37—41no—
101C2×D37—81no—
102C2×D37#9911yescharacteristic
103C2×D37#9911yescharacteristic
104#3866—82no—
105C4×C37—21no—
106C4×C37—41no—
107C4×C37—41no—
108Dic37—21no—
109Dic37—41no—
110Dic37—41no—
111C2×#352—371nomaximal, Sylow
112C2×C37—21no—
113C2×C37—41no—
114C2×C37—41no—
115C2×C37C2×#9911yescharacteristic
116D37—21no—
117D37—41no—
118D37—41no—
119D37#35212yescomplemented
120C2×#123—371no—
121C2×#100—371no—
122C2×#99—371no—
123#352—372no—
124#352—372no—
125C37C2×#35211yescharacteristic, complemented, Sylow
126C22×D4—371no—
127C23×C4—371no—
128C2×M16—741no—
129#123—371no—
130#123—371no—
131#123—371no—
132#123—741no—
133#123—741no—
134#123#386611yescharacteristic, complemented
135C2×C4⋊C4—741no—
136C2×C22⋊C4—371no—
137C2×C22⋊C4—741no—
138C2×C22⋊C4—741no—
139#100—372no—
140#100—741no—
141#99—372no—
142#99—741no—
143C24—371no—
144C24—371no—
145C2×D4—371no—
146C2×D4—371no—
147C2×D4—371no—
148C2×D4—1481no—
149C2×D4—1481no—
150C2×D4C2×#386611yescharacteristic
151C22×C4—371no—
152C22×C4—371no—
153C22×C4—741no—
154C22×C4—741no—
155C22×C4—741no—
156C22×C4—1481no—
157C22×C4—1481no—
158C22×C4—1481no—
159C22×C4C2×#386611yescharacteristic, complemented
160M16—742no—
161M16—1481no—
162C2×C8—1481no—
163C4⋊C4—21no—
164C4⋊C4—741no—
165C4⋊C4—741no—
166C4⋊C4—741no—
167C22⋊C4—21no—
168C22⋊C4—371no—
169C22⋊C4—741no—
170C22⋊C4—741no—
171C22⋊C4—741no—
172C22⋊C4—741no—
173C22⋊C4—742no—
174C22⋊C4—1481no—
175C22⋊C4C2×#386611yescharacteristic, complemented
176C23—371no—
177C23—371no—
178C23—371no—
179C23—741no—
180C23—741no—
181C23—741no—
182C23—741no—
183C23—1482no—
184C23—1482no—
185C23C22⋊#386611yescharacteristic
186C23C22×#386611yescharacteristic
187D4—41no—
188D4—1481no—
189D4—1481no—
190D4—1481no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—371no—
195C2×C4—2962no—
196C2×C4—741no—
197C2×C4—741no—
198C2×C4—741no—
199C2×C4—741no—
200C2×C4—1481no—
201C2×C4—1481no—
202C2×C4—1482no—
203C2×C4—1482no—
204C2×C4—1482no—
205C2×C4—1481no—
206C2×C4C22⋊#386611yescharacteristic
207C8—1482no—
208C22—21no—
209C22—21no—
210C22—41no—
211C22—41no—
212C22—371no—
213C22—371no—
214C22—2961no—
215C22—742no—
216C22—741no—
217C22—741no—
218C22—1481no—
219C22—1481no—
220C22—1482no—
221C22—1482no—
222C22—1482no—
223C22C2×C22⋊#386611yescharacteristic
224C4—21no—
225C4—41no—
226C4—41no—
227C4—2962no—
228C4—741no—
229C4—1481no—
230C4—1481no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—372no—
235C2—741no—
236C2—1481no—
237C2—1481no—
238C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#123×C37C4
socleC2×C37C2×#99
prime radicalC2×D4×D37C22
cosocleC2×C22⋊D37C23
hypercenter#123#3866
hypocenterC37C2×#352
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #14558436C2semidirect
4. #14558435C2semidirect
13. C22×C4×D37C4semidirect
18. #11924517C4semidirect
21. C22⋊C4×D37C4semidirect
22. #123×C37C4semidirect
27. C22×C4×C37C2×C4semidirect
30. C22×Dic37C2×C4semidirect
47. C22⋊C4×C37C2×C4semidirect
49. C22⋊Dic37C2×C4semidirect
119. D37#352semidirect
125. C37C2×#352semidirect
134. #123#3866semidirect
159. C22×C4C2×#3866semidirect
175. C22⋊C4C2×#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#1002
D37⋊#992
#145584362
#145584352
#123×D372
C2×#35237