Finite Group Databasebeta

← #18010741

Subgroups — #18010741

Order 4736.

348 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C2×#11924604C211yesmaximal, characteristic, complemented
2C2×#11924599C211yesmaximal, characteristic, complemented
3C2×#11924598C211yesmaximal, characteristic
4C2×C8×#3866C211yesmaximal, characteristic, complemented
5(C2×#3866)⋊Q8C211yesmaximal, characteristic, complemented
6#14558485C211yesmaximal, characteristic
7C2×SD16×D37C211yesmaximal, characteristic
8C2×D37⋊C8C2211yescharacteristic
9C2×C4⋊#3866C2211yescharacteristic
10C2×C4⋊#3866C2211yescharacteristic
11C2×C22⋊#3866—22no—
12C2×C4×#3866C2211yescharacteristic
13#11924604—22no—
14#11924599—22no—
15#11924598—22no—
16C8×#3866—22no—
17(C2×#3866)⋊C4—22no—
18C2×Q8×D37C2211yescharacteristic
19C2×D4×D37C2211yescharacteristic
20C2×#10596930C411yescharacteristic, complemented
21C2×#10596940C411yescharacteristic, complemented
22C2×#10596941C411yescharacteristic, complemented
23SD16×D37—22no—
24SD16×D37—22no—
25C2×C8×D37C2211yescharacteristic
26C2×SD16×C37C411yescharacteristic, complemented
27C23×D37—21no—
28C22×#3866—21no—
29C22×#3866—21no—
30C22×#3866D412yes—
31C2×Q8×C37C2×C411yescharacteristic
32C2×D4×C37C2×C411yescharacteristic
33C2×C22⋊D37—21no—
34Q8×D37—21no—
35Q8×D37—21no—
36Q8×D37—21no—
37Q8×D37—21no—
38D4×D37—21no—
39D4×D37—21no—
40D4×D37—21no—
41D4×D37—21no—
42C2×D148C2×C411yescharacteristic
43C2×C4×D37—21no—
44C2×C4×D37C2311yescharacteristic
45C2×Dic74—21no—
46C2×Dic74C2×C411yescharacteristic
47C22⋊#3866—44no—
48C2×#64438—21no—
49C4⋊#3866—21no—
50C4⋊#3866—21no—
51C4⋊#3866—21no—
52C4⋊#3866—21no—
53C4×#3866—21no—
54C4×#3866—21no—
55D37⋊C8—21no—
56D37⋊C8D412yes—
57SD16×C37—22no—
58C2×C8×C37C2×C411yescharacteristic
59#10596941—22no—
60#10596940—22no—
61C2×#64436C2×C411yescharacteristic
62#10596930—22no—
63C8×D37D412yes—
64C8×D37D412yes—
65C23×C37—21no—
66C22×D37—21no—
67C22×D37—41no—
68C22×D37—41no—
69C22×D37—42no—
70C22×D37—42no—
71C22×D37C2×D411yescharacteristic
72C2×#3866—22no—
73C2×#3866—22no—
74C2×#3866—41no—
75C2×#3866—41no—
76C2×#3866—42no—
77C2×#3866—42no—
78C2×#3866SD1614yescomplemented
79Q8×C37—21no—
80Q8×C37—21no—
81D4×C37—21no—
82D4×C37—21no—
83C2×C4×C37—21no—
84C2×C4×C37C22×C411yescharacteristic
85C22⋊D37—41no—
86C22⋊D37—41no—
87C2×Dic37—21no—
88C2×Dic37#4111yescharacteristic
89D148—21no—
90D148—21no—
91C4×D37—41no—
92C4×D37—41no—
93C4×D37C2×D411yescharacteristic
94C4×D37C2×D411yescharacteristic
95C4×D37C2×D411yescharacteristic
96C4×D37#4111yescharacteristic
97Dic74—21no—
98Dic74—21no—
99Dic74—41no—
100Dic74—41no—
101#64438—22no—
102C8×C37C22⋊C412yescomplemented
103#64436C22⋊C412yescomplemented
104C22×C37—41no—
105C22×C37—42no—
106C22×C37C4×D411yescharacteristic
107C2×D37—41no—
108C2×D37—42no—
109C2×D37—82no—
110C2×D37—81no—
111C2×D37—81no—
112C2×D37#12111yescharacteristic
113C2×D37#12711yescharacteristic
114C2×D37C2×SD1612yes—
115C2×D37#13512yes—
116#3866—24no—
117#3866—81no—
118#3866—81no—
119C4×C37—41no—
120C4×C37C2×C22⋊C411yescharacteristic
121C4×C37C4×D411yescharacteristic
122Dic37—41no—
123Dic37#12111yescharacteristic
124Dic37#12411yescharacteristic
125#1968—371nomaximal, Sylow
126C2×C37—81no—
127C2×C37#39011yescharacteristic
128C2×C37C4×SD1612yes—
129D37—81no—
130D37#46512yes—
131D37#49211yescharacteristic
132D37#49511yescharacteristic
133C22×SD16—371no—
134C2×#106—371no—
135C2×#103—371no—
136C2×#102—371no—
137C2×C4×C8—371no—
138#391—371no—
139#390—371no—
140C37#196811yescharacteristic, complemented, Sylow
141C22×Q8—371no—
142C22×D4—371no—
143C2×SD16—371no—
144C2×SD16—371no—
145C2×SD16—371no—
146C2×SD16—742no—
147C2×SD16—742no—
148C2×SD16#386611yescharacteristic, complemented
149C22×C8—371no—
150C22×C8—371no—
151C2×C4⋊C4—371no—
152C2×C4⋊C4—371no—
153C2×C22⋊C4—742no—
154C2×C42—371no—
155#106—742no—
156#103—742no—
157#102—742no—
158C4×C8—742no—
159#95—742no—
160C24—741no—
161C2×Q8—371no—
162C2×Q8—741no—
163C2×Q8—741no—
164C2×Q8—741no—
165C2×Q8—741no—
166C2×Q8—741no—
167C2×Q8C2×#386611yescharacteristic
168C2×D4—371no—
169C2×D4—741no—
170C2×D4—741no—
171C2×D4—741no—
172C2×D4—741no—
173C2×D4—741no—
174C2×D4C2×#386611yescharacteristic
175C22×C4—371no—
176C22×C4—372no—
177C22×C4—741no—
178C22×C4—741no—
179C22×C4—741no—
180SD16—22no—
181SD16—742no—
182SD16—742no—
183SD16—742no—
184C2×C8—371no—
185C2×C8—372no—
186C2×C8—372no—
187C2×C8—372no—
188C2×C8—741no—
189C2×C8—741no—
190C2×C8C2×#386611yescharacteristic
191C4⋊C4—741no—
192C4⋊C4—741no—
193C4⋊C4—741no—
194C4⋊C4—741no—
195C22⋊C4—1484no—
196C42—741no—
197C42—741no—
198C23—21no—
199C23—371no—
200C23—741no—
201C23—1482no—
202C23—1481no—
203C23—1481no—
204C23—1482no—
205Q8—21no—
206Q8—21no—
207Q8—741no—
208Q8—741no—
209Q8—1481no—
210Q8—1481no—
211D4—21no—
212D4—21no—
213D4—741no—
214D4—741no—
215D4—1481no—
216D4—1481no—
217C2×C4—21no—
218C2×C4—371no—
219C2×C4—371no—
220C2×C4—371no—
221C2×C4—371no—
222C2×C4—371no—
223C2×C4—374no—
224C2×C4—742no—
225C2×C4—742no—
226C2×C4—741no—
227C2×C4—1481no—
228C2×C4—1481no—
229C2×C4—1482no—
230C2×C4—1481no—
231C2×C4—1481no—
232C2×C4—1482no—
233C2×C4C22×#386611yescharacteristic
234C8—372no—
235C8—742no—
236C8C22⋊#386612yescomplemented
237C22—41no—
238C22—42no—
239C22—371no—
240C22—371no—
241C22—372no—
242C22—372no—
243C22—2961no—
244C22—2961no—
245C22—2962no—
246C22—1481no—
247C22—1482no—
248C22D4×#386611yescharacteristic
249C4—41no—
250C4—371no—
251C4—371no—
252C4—2961no—
253C4—2961no—
254C4—744no—
255C4—1481no—
256C4C2×C22⋊#386611yescharacteristic
257C4D4×#386611yescharacteristic
258C2—81no—
259C2—371no—
260C2—371no—
261C2—372no—
262C2—2961no—
263C2#1455848511yescharacteristic
264C2SD16×#386612yes—
subgroupG/H
centerC22D4×#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×SD16×C37C4
socleC22×C37C4×D4
prime radicalC2×D4×D37C22
cosocleC2×C4×D37C23
hypercenterC2×SD16#3866
hypocenterC37#1968
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#11924604C2semidirect
2. C2×#11924599C2semidirect
4. C2×C8×#3866C2semidirect
5. (C2×#3866)⋊Q8C2semidirect
20. C2×#10596930C4semidirect
21. C2×#10596940C4semidirect
22. C2×#10596941C4semidirect
26. C2×SD16×C37C4semidirect
78. C2×#3866SD16semidirect
102. C8×C37C22⋊C4semidirect
103. #64436C22⋊C4semidirect
140. C37#1968semidirect
148. C2×SD16#3866semidirect
236. C8C22⋊#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119246042
C2×#119245992
C2×#119245982
C2×C8×#38662
(C2×#3866)⋊Q82
#145584852
C2×SD16×D372
#196837