Finite Group Databasebeta

← #18010556

Subgroups — #18010556

Order 4736.

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

normal subgroups only

This group has 286 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#14558477C211yesmaximal, 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⋊#3866C2211yescharacteristic
16C2×C4⋊#3866C2211yescharacteristic
17#11924605—21no—
18#11924604—21no—
19#11924599—21no—
20#11924598—21no—
21(C2×#3866)⋊C4—22no—
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⋊#3866D411yescharacteristic
53C4⋊#3866D411yescharacteristic
54C4×#3866—22no—
55C4×#3866—21no—
56#10596953—21no—
57D37⋊C8—21no—
58M16×C37C2×C411yescharacteristic, complemented
59C42×C37C2×C411yescharacteristic, complemented
60C4×Dic37—21no—
61C4×Dic37C2×C411yescharacteristic, complemented
62#10596934C2×C411yescharacteristic, complemented
63#10596929—21no—
64C8×D37—21no—
65C22×D37—21no—
66C22×D37C2×D411yescharacteristic
67C2×#3866—21no—
68C2×#3866—22no—
69C2×#3866—21no—
70C2×#3866—42no—
71C2×#3866—42no—
72C2×#3866—41no—
73C2×#3866—82no—
74Q8×C37C4⋊C411yescharacteristic
75D4×C37—21no—
76D4×C37C4⋊C411yescharacteristic
77C2×C4×C37—21no—
78C2×C4×C37—21no—
79C2×C4×C37C22×C411yescharacteristic
80C22⋊D37—21no—
81C22⋊D37—21no—
82C22⋊D37—21no—
83C2×Dic37—21no—
84C2×Dic37—21no—
85C2×Dic37#4111yescharacteristic
86D148—21no—
87D148C4⋊C411yescharacteristic
88C4×D37—21no—
89C4×D37—21no—
90C4×D37—21no—
91C4×D37—41no—
92C4×D37—41no—
93C4×D37C2×D411yescharacteristic
94C4×D37C2×D411yescharacteristic
95C4×D37C2×Q811yescharacteristic
96C4×D37#4111yescharacteristic
97Dic74—21no—
98Dic74C4⋊C411yescharacteristic
99#64438—41no—
100C8×C37—21no—
101#64436—21no—
102C22×C37—21no—
103C22×C37C4×D411yescharacteristic
104C2×D37—21no—
105C2×D37—21no—
106C2×D37—21no—
107C2×D37—41no—
108C2×D37—41no—
109C2×D37#12011yescharacteristic
110C2×D37C22⋊Q811yescharacteristic
111#3866—41no—
112#3866—42no—
113#3866—41no—
114#3866—81no—
115C4×C37—21no—
116C4×C37—41no—
117C4×C37C2×C4⋊C411yescharacteristic
118C4×C37C4×D411yescharacteristic
119Dic37—21no—
120Dic37—41no—
121Dic37C22⋊Q811yescharacteristic
122Dic37#12311yescharacteristic
123#1860—371nomaximal, Sylow
124C2×C37—21no—
125C2×C37—41no—
126C2×C37#38511yescharacteristic
127D37—21no—
128D37—41no—
129D37#45411yescharacteristic
130D37#45511yescharacteristic
131#520—371no—
132#428—371no—
133C2×#104—371no—
134#417—371no—
135#382—371no—
136#343—371no—
137#339—371no—
138C37#186011yescharacteristic, complemented, Sylow
139C2×#41—371no—
140C2×M16—371no—
141C2×M16—371no—
142C4×Q8—741no—
143C4×D4—742no—
144C4×D4—741no—
145#117—371no—
146#117—741no—
147C2×C4⋊C4—371no—
148C2×C4⋊C4—371no—
149C2×C4⋊C4—741no—
150C2×C42—371no—
151#107—741no—
152#106—741no—
153#104—371no—
154#104—371no—
155#104—371no—
156#104#386611yescharacteristic, complemented
157#103—741no—
158#102—741no—
159#95—742no—
160#41—371no—
161#41—371no—
162#41—371no—
163#41—741no—
164#41—741no—
165#41C2×#386611yescharacteristic
166C2×Q8—371no—
167C2×D4—371no—
168C2×D4—741no—
169C22×C4—371no—
170C22×C4—372no—
171C22×C4—741no—
172C22×C4—741no—
173C22×C4—742no—
174C22×C4—741no—
175M16—371no—
176M16—741no—
177M16—741no—
178M16—741no—
179M16C2×#386611yescharacteristic, complemented
180C2×C8—741no—
181C2×C8—741no—
182C4⋊C4—371no—
183C4⋊C4—371no—
184C4⋊C4—741no—
185C4⋊C4—741no—
186C4⋊C4—741no—
187C4⋊C4—741no—
188C4⋊C4—742no—
189C22⋊C4—741no—
190C22⋊C4—742no—
191C42—371no—
192C42—741no—
193C42—741no—
194C42—742no—
195C42C2×#386611yescharacteristic, complemented
196C23—371no—
197C23—741no—
198Q8—371no—
199Q8—741no—
200Q8C4⋊#386611yescharacteristic
201D4—21no—
202D4—371no—
203D4—741no—
204D4—741no—
205D4—741no—
206D4—741no—
207D4C4⋊#386611yescharacteristic
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—371no—
211C2×C4—371no—
212C2×C4—371no—
213C2×C4—371no—
214C2×C4—371no—
215C2×C4—2962no—
216C2×C4—741no—
217C2×C4—741no—
218C2×C4—741no—
219C2×C4—741no—
220C2×C4—741no—
221C2×C4—741no—
222C2×C4—742no—
223C2×C4—741no—
224C2×C4—1481no—
225C2×C4—1481no—
226C2×C4—1481no—
227C2×C4—1482no—
228C2×C4—1482no—
229C2×C4C22×#386611yescharacteristic
230C8—21no—
231C8—741no—
232C8—1481no—
233C22—21no—
234C22—371no—
235C22—371no—
236C22—741no—
237C22—741no—
238C22—741no—
239C22—1481no—
240C22—1481no—
241C22D4×#386611yescharacteristic
242C4—21no—
243C4—41no—
244C4—371no—
245C4—371no—
246C4—2961no—
247C4—741no—
248C4—1481no—
249C4—1481no—
250C4—1482no—
251C4—1481no—
252C4C2×C4⋊#386611yescharacteristic
253C4D4×#386611yescharacteristic
254C2—21no—
255C2—41no—
256C2—371no—
257C2—371no—
258C2—741no—
259C2—1481no—
260C2#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#1860
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. #14558477C2semidirect
5. #14558412C2semidirect
6. #14558404C2semidirect
25. #11924464C4semidirect
26. #11924463C4semidirect
27. #11924462C4semidirect
28. #104×C37C4semidirect
58. M16×C37C2×C4semidirect
59. C42×C37C2×C4semidirect
61. C4×Dic37C2×C4semidirect
62. #10596934C2×C4semidirect
138. C37#1860semidirect
156. #104#3866semidirect
179. M16C2×#3866semidirect
195. C42C2×#3866semidirect

Maximal subgroups

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

subgroupindex
#145586022
#145585442
#145585242
#145584772
#145584122
#145584042
#104×D372
#186037