Finite Group Databasebeta

← #18010555

Subgroups — #18010555

Order 4736.

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

normal subgroups only

This group has 302 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
1#14558602C211yesmaximal, characteristic
2#14558544C211yesmaximal, characteristic, complemented
3#14558524C211yesmaximal, characteristic
4#14558479C211yesmaximal, characteristic, complemented
5#14558412C211yesmaximal, characteristic, complemented
6#14558404C211yesmaximal, characteristic, complemented
7#104×D37C211yesmaximal, characteristic
8D37⋊M16C2211yescharacteristic
9Q8×#3866—21no—
10D4×#3866—22no—
11D4×#3866—21no—
12#11924615—21no—
13#11924615C2211yescharacteristic
14C2×C4⋊#3866—21no—
15C2×C4⋊#3866—22no—
16C2×C4⋊#3866C2211yescharacteristic
17C2×C4⋊#3866C2211yescharacteristic
18#11924605—21no—
19#11924604—21no—
20#11924599—21no—
21#11924598—21no—
22#41×D37C2211yescharacteristic
23M16×D37C2211yescharacteristic
24C42×D37C2211yescharacteristic
25#11924464C411yescharacteristic, complemented
26#11924463C411yescharacteristic, complemented
27#11924462C411yescharacteristic, complemented
28#104×C37C411yescharacteristic, complemented
29C22×#3866—22no—
30C22×#3866—21no—
31C22×#3866D412yes—
32#41×C37C2×C411yescharacteristic
33#10596966Q811yescharacteristic
34Q8×D37D411yescharacteristic
35#10596964—21no—
36#10596964Q811yescharacteristic
37D4×D37—21no—
38D4×D37D411yescharacteristic
39#10596962—21no—
40#10596962C2×C411yescharacteristic
41C2×C4×D37—21no—
42C2×C4×D37—21no—
43C2×C4×D37C2311yescharacteristic
44C22⋊#3866—22no—
45C22⋊#3866—21no—
46#10596957—21no—
47C4⋊#3866—22no—
48C4⋊#3866—21no—
49C4⋊#3866—21no—
50C4⋊#3866—21no—
51C4⋊#3866—21no—
52C4⋊#3866—44no—
53C4⋊#3866D411yescharacteristic
54C4⋊#3866D411yescharacteristic
55C4×#3866—22no—
56C4×#3866—21no—
57#10596953—21no—
58D37⋊C8—21no—
59M16×C37C2×C411yescharacteristic, complemented
60C42×C37C2×C411yescharacteristic, complemented
61C4×Dic37—21no—
62C4×Dic37C2×C411yescharacteristic, complemented
63#10596934C2×C411yescharacteristic, complemented
64#10596929—21no—
65C8×D37—21no—
66C22×D37—21no—
67C22×D37C2×D411yescharacteristic
68C2×#3866—21no—
69C2×#3866—22no—
70C2×#3866—21no—
71C2×#3866—42no—
72C2×#3866—42no—
73C2×#3866—41no—
74C2×#3866—82no—
75Q8×C37C4⋊C411yescharacteristic, complemented
76D4×C37—21no—
77D4×C37C4⋊C411yescharacteristic, complemented
78C2×C4×C37—21no—
79C2×C4×C37—21no—
80C2×C4×C37C22×C411yescharacteristic
81C22⋊D37—21no—
82C22⋊D37—21no—
83C22⋊D37—21no—
84C2×Dic37—21no—
85C2×Dic37—21no—
86C2×Dic37#4111yescharacteristic
87D148—21no—
88D148C4⋊C411yescharacteristic, complemented
89C4×D37—22no—
90C4×D37—22no—
91C4×D37—21no—
92C4×D37—21no—
93C4×D37—21no—
94C4×D37C2×D411yescharacteristic
95C4×D37C2×D411yescharacteristic
96C4×D37C2×Q811yescharacteristic
97C4×D37#4111yescharacteristic
98Dic74—21no—
99Dic74C4⋊C411yescharacteristic, complemented
100#64438—41no—
101C8×C37—21no—
102#64436—21no—
103C22×C37—21no—
104C22×C37C4×D411yescharacteristic
105C2×D37—21no—
106C2×D37—21no—
107C2×D37—21no—
108C2×D37—41no—
109C2×D37—41no—
110C2×D37#12011yescharacteristic
111C2×D37C22⋊Q811yescharacteristic
112#3866—42no—
113#3866—41no—
114#3866—41no—
115#3866—81no—
116C4×C37—22no—
117C4×C37—21no—
118C4×C37C2×C4⋊C411yescharacteristic
119C4×C37C4×D411yescharacteristic
120Dic37—22no—
121Dic37—21no—
122Dic37C22⋊Q811yescharacteristic
123Dic37#12311yescharacteristic
124#1859—371nomaximal, Sylow
125C2×C37—21no—
126C2×C37—41no—
127C2×C37#38511yescharacteristic
128D37—21no—
129D37—41no—
130D37#45311yescharacteristic
131D37#45611yescharacteristic
132#520—371no—
133#428—371no—
134C2×#104—371no—
135#417—371no—
136#384—371no—
137#343—371no—
138#339—371no—
139C37#185911yescharacteristic, complemented, Sylow
140C2×#41—371no—
141C2×M16—371no—
142C2×M16—371no—
143C4×Q8—741no—
144C4×D4—742no—
145C4×D4—741no—
146#117—371no—
147#117—741no—
148C2×C4⋊C4—371no—
149C2×C4⋊C4—371no—
150C2×C4⋊C4—741no—
151C2×C4⋊C4—742no—
152C2×C42—371no—
153#107—741no—
154#106—741no—
155#104—371no—
156#104—371no—
157#104—371no—
158#104#386611yescharacteristic, complemented
159#103—741no—
160#102—741no—
161#41—371no—
162#41—371no—
163#41—371no—
164#41—741no—
165#41—741no—
166#41C2×#386611yescharacteristic
167C2×Q8—371no—
168C2×D4—371no—
169C2×D4—741no—
170C22×C4—371no—
171C22×C4—372no—
172C22×C4—741no—
173C22×C4—741no—
174C22×C4—742no—
175C22×C4—741no—
176M16—371no—
177M16—741no—
178M16—741no—
179M16—741no—
180M16C2×#386611yescharacteristic, complemented
181C2×C8—741no—
182C2×C8—741no—
183C4⋊C4—371no—
184C4⋊C4—371no—
185C4⋊C4—741no—
186C4⋊C4—741no—
187C4⋊C4—741no—
188C4⋊C4—741no—
189C4⋊C4—742no—
190C4⋊C4—1484no—
191C22⋊C4—741no—
192C22⋊C4—742no—
193C42—371no—
194C42—741no—
195C42—741no—
196C42—742no—
197C42C2×#386611yescharacteristic, complemented
198C23—371no—
199C23—741no—
200Q8—371no—
201Q8—741no—
202Q8C4⋊#386611yescharacteristic, complemented
203D4—21no—
204D4—371no—
205D4—741no—
206D4—741no—
207D4—741no—
208D4—741no—
209D4C4⋊#386611yescharacteristic, complemented
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—371no—
213C2×C4—371no—
214C2×C4—371no—
215C2×C4—371no—
216C2×C4—371no—
217C2×C4—2962no—
218C2×C4—741no—
219C2×C4—741no—
220C2×C4—742no—
221C2×C4—742no—
222C2×C4—741no—
223C2×C4—741no—
224C2×C4—741no—
225C2×C4—741no—
226C2×C4—741no—
227C2×C4—742no—
228C2×C4—1481no—
229C2×C4—1482no—
230C2×C4—1482no—
231C2×C4C22×#386611yescharacteristic
232C8—21no—
233C8—741no—
234C8—1481no—
235C22—21no—
236C22—371no—
237C22—371no—
238C22—741no—
239C22—741no—
240C22—741no—
241C22—1481no—
242C22—1481no—
243C22D4×#386611yescharacteristic
244C4—22no—
245C4—21no—
246C4—371no—
247C4—371no—
248C4—2961no—
249C4—742no—
250C4—741no—
251C4—1481no—
252C4—1482no—
253C4—1481no—
254C4C2×C4⋊#386611yescharacteristic
255C4D4×#386611yescharacteristic
256C2—21no—
257C2—41no—
258C2—371no—
259C2—371no—
260C2—741no—
261C2—1481no—
262C2#1455848011yescharacteristic
subgroupG/H
centerC2#14558480
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#104×C37C4
socleC2×C37#385
prime radical#41×D37C22
cosocleC2×C4×D37C23
hypercenter#104#3866
hypocenterC37#1859
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #14558544C2semidirect
4. #14558479C2semidirect
5. #14558412C2semidirect
6. #14558404C2semidirect
25. #11924464C4semidirect
26. #11924463C4semidirect
27. #11924462C4semidirect
28. #104×C37C4semidirect
59. M16×C37C2×C4semidirect
60. C42×C37C2×C4semidirect
62. C4×Dic37C2×C4semidirect
63. #10596934C2×C4semidirect
75. Q8×C37C4⋊C4semidirect
77. D4×C37C4⋊C4semidirect
88. D148C4⋊C4semidirect
99. Dic74C4⋊C4semidirect
139. C37#1859semidirect
158. #104#3866semidirect
180. M16C2×#3866semidirect
197. C42C2×#3866semidirect
202. Q8C4⋊#3866semidirect
209. D4C4⋊#3866semidirect

Maximal subgroups

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

subgroupindex
#145586022
#145585442
#145585242
#145584792
#145584122
#145584042
#104×D372
#185937