Finite Group Databasebeta

← #18010756

Subgroups — #18010756

Order 4736.

296 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 68 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⋊#108C211yesmaximal, characteristic, complemented
2#14558526C211yesmaximal, characteristic, complemented
3#14558525C211yesmaximal, characteristic
4D37⋊#101C211yesmaximal, characteristic, complemented
5D37⋊#100C211yesmaximal, characteristic
6#14558496C211yesmaximal, characteristic, complemented
7C2×SD16×D37C211yesmaximal, characteristic
8D37⋊M16C2211yescharacteristic
9D37⋊M16C2211yescharacteristic
10D37⋊M16C2211yescharacteristic
11#11924615C2211yescharacteristic
12#11924607—21no—
13#11924606—21no—
14#11924599—22no—
15#11924598—22no—
16#11924597—22no—
17#11924596—22no—
18#11924590—21no—
19C8×#3866—21no—
20C2×Q8×D37C2211yescharacteristic
21C2×D4×D37C2211yescharacteristic
22C2×#10596930C411yescharacteristic, complemented
23C2×#10596940C411yescharacteristic, complemented
24C2×#10596941C411yescharacteristic, complemented
25SD16×D37—21no—
26SD16×D37—21no—
27SD16×D37—21no—
28SD16×D37—21no—
29C2×C8×D37C2211yescharacteristic
30C2×SD16×C37C411yescharacteristic, complemented
31C23×D37—21no—
32C2×Q8×C37C2×C411yescharacteristic
33C2×D4×C37C2×C411yescharacteristic
34C2×C22⋊D37—21no—
35Q8×D37—21no—
36Q8×D37—21no—
37Q8×D37—21no—
38Q8×D37—21no—
39D4×D37—21no—
40D4×D37—21no—
41D4×D37—21no—
42D4×D37—21no—
43C2×D148C2×C411yescharacteristic
44C2×C4×D37—21no—
45C2×C4×D37C2311yescharacteristic
46C2×Dic74—21no—
47C2×Dic74C2×C411yescharacteristic
48C22⋊#3866—21no—
49#10596957—21no—
50#10596957—21no—
51#10596957D412yes—
52C4⋊#3866D412yes—
53C4×#3866—21no—
54#10596953—21no—
55#10596953—21no—
56#10596953—21no—
57D37⋊C8—21no—
58D37⋊C8—21no—
59D37⋊C8—21no—
60SD16×C37—21no—
61SD16×C37—21no—
62C2×C8×C37C2×C411yescharacteristic
63#10596941—21no—
64#10596941—21no—
65#10596940—21no—
66#10596940—21no—
67C2×#64436C2×C411yescharacteristic
68#10596930—21no—
69#10596930—21no—
70C8×D37D411yescharacteristic
71C8×D37D411yescharacteristic
72C8×D37D411yescharacteristic
73C8×D37D411yescharacteristic
74C23×C37—21no—
75C22×D37—21no—
76C22×D37—41no—
77C22×D37—41no—
78C22×D37—82no—
79C22×D37#4111yescharacteristic
80C2×#3866—22no—
81Q8×C37—21no—
82Q8×C37—21no—
83D4×C37—21no—
84D4×C37—21no—
85C2×C4×C37—21no—
86C2×C4×C37C22×C411yescharacteristic
87C22⋊D37—41no—
88C22⋊D37—41no—
89C2×Dic37—21no—
90C2×Dic37C2×D411yescharacteristic
91D148—21no—
92D148—21no—
93C4×D37—41no—
94C4×D37—41no—
95C4×D37C2×D411yescharacteristic
96C4×D37C2×D411yescharacteristic
97C4×D37C2×D411yescharacteristic
98C4×D37#4111yescharacteristic
99Dic74—21no—
100Dic74—21no—
101Dic74—41no—
102Dic74—41no—
103#64438—22no—
104#64438—41no—
105#64438—41no—
106C8×C37C22⋊C411yescharacteristic
107C8×C37C22⋊C411yescharacteristic
108#64436C22⋊C411yescharacteristic
109#64436C22⋊C411yescharacteristic
110C22×C37—41no—
111C22×C37—81no—
112C22×C37C4×D411yescharacteristic
113C2×D37—22no—
114C2×D37—41no—
115C2×D37—82no—
116C2×D37—82no—
117C2×D37—81no—
118C2×D37#12111yescharacteristic
119C2×D37#12411yescharacteristic
120#3866—42no—
121C4×C37—41no—
122C4×C37C2×C22⋊C411yescharacteristic
123C4×C37C4×D411yescharacteristic
124Dic37—41no—
125Dic37#12111yescharacteristic
126Dic37#12711yescharacteristic
127#1977—371nomaximal, Sylow
128C2×C37—21no—
129C2×C37—81no—
130C2×C37#39011yescharacteristic
131D37—21no—
132D37—81no—
133D37#47112yes—
134C22×SD16—371no—
135C2×#108—371no—
136#419—371no—
137#418—371no—
138C2×#101—371no—
139C2×#100—371no—
140#405—371no—
141C37#197711yescharacteristic, complemented, Sylow
142C22×Q8—371no—
143C22×D4—371no—
144C2×SD16—371no—
145C2×SD16—371no—
146C2×SD16—371no—
147C2×SD16—741no—
148C2×SD16—741no—
149C2×SD16—741no—
150C2×SD16—741no—
151C2×SD16#386611yescharacteristic, complemented
152C2×M16—371no—
153C2×M16—371no—
154C2×M16—371no—
155C22×C8—371no—
156#117—371no—
157#108—741no—
158#108—741no—
159#103—742no—
160#102—742no—
161#101—742no—
162#100—742no—
163#97—741no—
164C4×C8—741no—
165C24—741no—
166C2×Q8—371no—
167C2×Q8—741no—
168C2×Q8—741no—
169C2×Q8—741no—
170C2×Q8—741no—
171C2×Q8—741no—
172C2×Q8C2×#386611yescharacteristic
173C2×D4—371no—
174C2×D4—741no—
175C2×D4—741no—
176C2×D4—741no—
177C2×D4—741no—
178C2×D4—741no—
179C2×D4C2×#386611yescharacteristic
180C22×C4—371no—
181C22×C4—741no—
182SD16—21no—
183SD16—21no—
184SD16—741no—
185SD16—741no—
186SD16—741no—
187SD16—741no—
188SD16—741no—
189SD16—741no—
190M16—372no—
191M16—741no—
192M16—741no—
193M16—741no—
194M16—741no—
195M16—741no—
196C2×C8—371no—
197C2×C8—371no—
198C2×C8—371no—
199C2×C8—371no—
200C2×C8—371no—
201C2×C8—741no—
202C2×C8—741no—
203C2×C8—741no—
204C2×C8C2×#386611yescharacteristic
205C4⋊C4—372no—
206C22⋊C4—741no—
207C42—741no—
208C23—21no—
209C23—371no—
210C23—2962no—
211C23—741no—
212C23—1481no—
213C23—1481no—
214Q8—21no—
215Q8—21no—
216Q8—741no—
217Q8—741no—
218Q8—1481no—
219Q8—1481no—
220D4—21no—
221D4—21no—
222D4—741no—
223D4—741no—
224D4—1481no—
225D4—1481no—
226C2×C4—21no—
227C2×C4—371no—
228C2×C4—371no—
229C2×C4—371no—
230C2×C4—371no—
231C2×C4—371no—
232C2×C4—742no—
233C2×C4—741no—
234C2×C4—1481no—
235C2×C4—1481no—
236C2×C4C22×#386611yescharacteristic
237C8—371no—
238C8—371no—
239C8—742no—
240C8—1481no—
241C8—1481no—
242C8C22⋊#386611yescharacteristic
243C8C22⋊#386611yescharacteristic
244C22—41no—
245C22—81no—
246C22—371no—
247C22—371no—
248C22—2961no—
249C22—2962no—
250C22—2962no—
251C22—742no—
252C22—1481no—
253C22D4×#386611yescharacteristic
254C4—41no—
255C4—371no—
256C4—371no—
257C4—1482no—
258C4—1481no—
259C4C2×C22⋊#386611yescharacteristic
260C4D4×#386611yescharacteristic
261C2—21no—
262C2—81no—
263C2—372no—
264C2—2961no—
265C2—741no—
266C2#1455848511yescharacteristic
subgroupG/H
centerC2#14558485
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×SD16×C37C4
socleC2×C37#390
prime radicalC2×D4×D37C22
cosocleC2×C4×D37C23
hypercenterC2×SD16#3866
hypocenterC37#1977
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. D37⋊#108C2semidirect
2. #14558526C2semidirect
4. D37⋊#101C2semidirect
6. #14558496C2semidirect
22. C2×#10596930C4semidirect
23. C2×#10596940C4semidirect
24. C2×#10596941C4semidirect
30. C2×SD16×C37C4semidirect
141. C37#1977semidirect
151. C2×SD16#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#1082
#145585262
#145585252
D37⋊#1012
D37⋊#1002
#145584962
C2×SD16×D372
#197737