Finite Group Databasebeta

← #18010854

Subgroups — #18010854

Order 4736.

280 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 52 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, complemented
2D37⋊#99C211yesmaximal, characteristic, complemented
3#14558435C212yesmaximal, complemented
4#14558434C212yesmaximal, complemented
5#14558094C211yesmaximal, characteristic
6D37⋊M16—21no—
7C2×C22⋊#3866—21no—
8#11924596—21no—
9#11924596C2212yes—
10#11924595—21no—
11#11924594C2212yes—
12C22×D148C411yescharacteristic, complemented
13C2×D4×D37C2211yescharacteristic
14#11924521—21no—
15#11924519C2211yescharacteristic
16#11924511—21no—
17#11924509—21no—
18#11924506—21no—
19#11924506C2211yescharacteristic
20#11924504C411yescharacteristic, complemented
21C22⋊C4×D37C411yescharacteristic, complemented
22#123×C37C411yescharacteristic, complemented
23C23×D37C2×C411yescharacteristic
24C23×D37C2×C411yescharacteristic, complemented
25C23×D37D411yescharacteristic
26C22×#3866—41no—
27C2×D4×C37C2×C411yescharacteristic
28C22×C4×C37C2×C411yescharacteristic, complemented
29C2×C22⋊D37—21no—
30C2×C22⋊D37D411yescharacteristic
31C2×C22⋊D37C2311yescharacteristic
32D4×D37—41no—
33D4×D37—41no—
34C2×D148—21no—
35C2×D148—21no—
36C2×D148—21no—
37C2×D148—41no—
38C2×D148—41no—
39C2×D148D411yescharacteristic
40C2×C4×D37—21no—
41C2×C4×D37D411yescharacteristic
42C22⋊#3866—22no—
43C22⋊#3866—41no—
44#10596957—22no—
45#10596953—41no—
46D37⋊C8—41no—
47C4⋊C4×C37—21no—
48C22⋊C4×C37—21no—
49C22⋊C4×C37C2×C411yescharacteristic, complemented
50C22⋊Dic37C2×C411yescharacteristic, complemented
51#10596938—21no—
52#10596938—21no—
53#10596938—21no—
54#10596938—21no—
55#10596936—21no—
56C23×C37C22⋊C411yescharacteristic
57C23×C37C22×C411yescharacteristic
58C22×D37—21no—
59C22×D37—21no—
60C22×D37—21no—
61C22×D37—21no—
62C22×D37—21no—
63C22×D37—41no—
64C22×D37—81no—
65C22×D37—81no—
66C22×D37—81no—
67C22×D37C22⋊C411yescharacteristic
68C22×D37C22⋊C411yescharacteristic
69C22×D37C2×D411yescharacteristic
70C2×#3866—42no—
71C2×#3866—82no—
72D4×C37—41no—
73C2×C4×C37—21no—
74C2×C4×C37—21no—
75C2×C4×C37—41no—
76C2×C4×C37C22⋊C411yescharacteristic
77C22⋊D37—41no—
78C22⋊D37—41no—
79C22⋊D37—81no—
80C2×Dic37—21no—
81C2×Dic37C2×D411yescharacteristic
82D148—41no—
83D148—42no—
84D148—41no—
85D148—41no—
86D148—81no—
87C4×D37—21no—
88C4×D37—21no—
89C4×D37—81no—
90#64438—42no—
91C22×C37—21no—
92C22×C37—21no—
93C22×C37—41no—
94C22×C37—41no—
95C22×C37C2×C22⋊C411yescharacteristic
96C2×D37—21no—
97C2×D37—21no—
98C2×D37—41no—
99C2×D37—42no—
100C2×D37—41no—
101C2×D37—41no—
102C2×D37—41no—
103C2×D37—41no—
104C2×D37—41no—
105C2×D37—81no—
106C2×D37—81no—
107C2×D37—81no—
108C2×D37—82no—
109C2×D37#9911yescharacteristic
110C2×D37#9911yescharacteristic
111#3866—82no—
112C4×C37—21no—
113C4×C37—41no—
114C4×C37—41no—
115Dic37—21no—
116Dic37—41no—
117#2121—371nomaximal, Sylow
118C2×C37—21no—
119C2×C37—41no—
120C2×C37—41no—
121C2×C37C2×#9911yescharacteristic
122D37—21no—
123D37—21no—
124D37—41no—
125D37—41no—
126D37—81no—
127#534—371no—
128C2×#100—371no—
129C2×#99—371no—
130#352—372no—
131AΣL(1,𝔽16)—372no—
132C37#212111yescharacteristic, complemented, Sylow
133C22×D4—371no—
134C22×D4—371no—
135C2×M16—741no—
136#123—371no—
137#123—741no—
138#123#386611yescharacteristic, complemented
139#121—741no—
140#121—741no—
141#120—371no—
142#120—371no—
143#120—741no—
144C2×C22⋊C4—371no—
145C2×C22⋊C4—741no—
146#100—372no—
147#100—741no—
148#99—372no—
149#99—741no—
150C24—371no—
151C24—371no—
152C24—371no—
153C2×D4—371no—
154C2×D4—371no—
155C2×D4—371no—
156C2×D4—741no—
157C2×D4—741no—
158C2×D4—741no—
159C2×D4—741no—
160C2×D4—1481no—
161C2×D4—1481no—
162C2×D4—1481no—
163C2×D4—1481no—
164C2×D4C2×#386611yescharacteristic
165C22×C4—371no—
166C22×C4—741no—
167C22×C4—1481no—
168C22×C4C2×#386611yescharacteristic, complemented
169M16—742no—
170M16—1481no—
171C2×C8—1481no—
172C4⋊C4—21no—
173C4⋊C4—741no—
174C22⋊C4—21no—
175C22⋊C4—371no—
176C22⋊C4—741no—
177C22⋊C4—741no—
178C22⋊C4—741no—
179C22⋊C4—741no—
180C22⋊C4—742no—
181C22⋊C4—1481no—
182C22⋊C4C2×#386611yescharacteristic, complemented
183C23—371no—
184C23—371no—
185C23—371no—
186C23—2961no—
187C23—2961no—
188C23—2961no—
189C23—741no—
190C23—741no—
191C23—741no—
192C23—741no—
193C23—741no—
194C23—1481no—
195C23C22⋊#386611yescharacteristic
196C23C22×#386611yescharacteristic
197D4—41no—
198D4—2961no—
199D4—2961no—
200D4—1481no—
201D4—1481no—
202D4—1481no—
203D4—1482no—
204D4—1481no—
205D4—1481no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—371no—
210C2×C4—2961no—
211C2×C4—2962no—
212C2×C4—741no—
213C2×C4—741no—
214C2×C4—741no—
215C2×C4—1482no—
216C2×C4C22⋊#386611yescharacteristic
217C8—1482no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—371no—
223C22—371no—
224C22—2962no—
225C22—2961no—
226C22—2961no—
227C22—2961no—
228C22—741no—
229C22—741no—
230C22—1481no—
231C22—1481no—
232C22—1481no—
233C22—1481no—
234C22—1481no—
235C22—1482no—
236C22—1481no—
237C22C2×C22⋊#386611yescharacteristic
238C4—21no—
239C4—41no—
240C4—41no—
241C4—2962no—
242C4—741no—
243C4—1481no—
244C2—21no—
245C2—41no—
246C2—41no—
247C2—2961no—
248C2—741no—
249C2—741no—
250C2—1481no—
251C2—1481no—
252C2D37⋊#9911yescharacteristic
subgroupG/H
centerC2D37⋊#99
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#123×C37C4
socleC2×C37C2×#99
prime radical#14558094C2
cosocleC2×C22⋊D37C23
hypercenter#123#3866
hypocenterC37#2121
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
1. D37⋊#100C2semidirect
2. D37⋊#99C2semidirect
3. #14558435C2semidirect
4. #14558434C2semidirect
12. C22×D148C4semidirect
20. #11924504C4semidirect
21. C22⋊C4×D37C4semidirect
22. #123×C37C4semidirect
24. C23×D37C2×C4semidirect
28. C22×C4×C37C2×C4semidirect
49. C22⋊C4×C37C2×C4semidirect
50. C22⋊Dic37C2×C4semidirect
132. C37#2121semidirect
138. #123#3866semidirect
168. C22×C4C2×#3866semidirect
182. 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
#145584352
#145584342
#145580942
#212137