Finite Group Databasebeta

← #17993554

Subgroups — #17993554

Order 4736.

256 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 51 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#14558158C211yesmaximal, characteristic
2#14557691C211yesmaximal, characteristic, complemented
3#14557688C211yesmaximal, characteristic, complemented
4#14557446C211yesmaximal, characteristic
5#14557269C211yesmaximal, characteristic, complemented
6#14557256C211yesmaximal, characteristic
7C37×#328C211yesmaximal, characteristic, complemented
8C22×Dic74C2211yescharacteristic
9C2×Dic148—21no—
10C2×#10596942—21no—
11#11924516—21no—
12#11924515C2211yescharacteristic
13#11924514—21no—
14#11924514—21no—
15#11924513—21no—
16#11924512—21no—
17C2×#10596938—21no—
18C2×#10596938C2211yescharacteristic
19C22⋊C4×D37—21no—
20#11924461—21no—
21#11924459—21no—
22C22⋊#64436C2211yescharacteristic
23#11924443—21no—
24C22⋊Q8×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C23×D37D411yescharacteristic
28C2×Q8×C37D411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C22×Dic37—21no—
32C22×Dic37D411yescharacteristic
33C2×C4×D37—21no—
34C2×C4×D37—21no—
35C2×Dic74—21no—
36C2×Dic74—21no—
37C2×Dic74—21no—
38C2×Dic74—42no—
39C2×Dic74D411yescharacteristic
40C2×C8×C37—21no—
41C4⋊C4×C37—21no—
42C4⋊C4×C37D411yescharacteristic
43C22⋊C4×C37—21no—
44C22⋊Dic37—21no—
45#10596942—42no—
46#10596938—21no—
47#10596938—21no—
48#10596938—21no—
49#10596938—21no—
50#10596938—42no—
51C4⋊Dic37—21no—
52C4⋊Dic37D411yescharacteristic
53#10596936—21no—
54#10596936—21no—
55#10596936—21no—
56C2×#64436—21no—
57Dic148—42no—
58C23×C37C2×D411yescharacteristic
59C22×D37—21no—
60C22×D37—21no—
61C22×D37—41no—
62C22×D37—41no—
63C22×D37Q1612yescomplemented
64Q8×C37—41no—
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37—41no—
70C2×C4×C37—41no—
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×Dic37—22no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—41no—
78C2×Dic37—41no—
79C2×Dic37—41no—
80C4×D37—81no—
81C4×D37—81no—
82Dic74—22no—
83Dic74—22no—
84Dic74—41no—
85Dic74—41no—
86Dic74—41no—
87Dic74—81no—
88C8×C37—41no—
89#64436—41no—
90C22×C37—21no—
91C22×C37—21no—
92C22×C37#12011yescharacteristic
93C22×C37C2×Q1611yescharacteristic
94C22×C37#13711yescharacteristic
95C2×D37—22no—
96C2×D37—41no—
97C2×D37—41no—
98C2×D37—42no—
99C2×D37—81no—
100C4×C37—21no—
101C4×C37—21no—
102C4×C37—41no—
103C4×C37—41no—
104C4×C37—81no—
105Dic37—41no—
106Dic37—41no—
107Dic37—42no—
108Dic37—41no—
109#1602—371nomaximal, Sylow
110C2×C37—21no—
111C2×C37—21no—
112C2×C37#45111yescharacteristic
113C2×C37#45511yescharacteristic
114C2×C37B(4,𝔽2)11yescharacteristic
115D37—42no—
116#543—371no—
117#451—371no—
118#451—371no—
119#393—371no—
120#328—371no—
121#328D3711yescharacteristic, complemented
122#323—371no—
123C37#160211yescharacteristic, complemented, Sylow
124C22×Q8—371no—
125C2×Q16—741no—
126C2×Q16—741no—
127C22⋊Q8—371no—
128C22⋊Q8—741no—
129C22⋊Q8—741no—
130C22⋊Q8—741no—
131C22⋊Q8—741no—
132C22⋊Q8—741no—
133C22⋊Q8C2×D3711yescharacteristic
134C2×C22⋊C4—371no—
135C2×C22⋊C4—741no—
136C2×C22⋊C4—741no—
137#103—741no—
138#103—741no—
139C22⋊C8—371no—
140C22⋊C8C2×D3711yescharacteristic
141#95—741no—
142#95C2×D3711yescharacteristic
143C24—371no—
144C2×Q8—371no—
145C2×Q8—741no—
146C2×Q8—741no—
147C2×Q8—741no—
148C2×Q8—1482no—
149C2×Q8D14811yescharacteristic
150C22×C4—21no—
151C22×C4—371no—
152C22×C4—741no—
153C22×C4—741no—
154C22×C4—741no—
155C22×C4C22×D3711yescharacteristic
156Q16—1482no—
157Q16—1482no—
158C2×C8—21no—
159C2×C8—741no—
160C4⋊C4—21no—
161C4⋊C4—371no—
162C4⋊C4—741no—
163C4⋊C4—741no—
164C4⋊C4—741no—
165C4⋊C4—741no—
166C4⋊C4D14811yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—741no—
169C22⋊C4—741no—
170C22⋊C4—741no—
171C22⋊C4—741no—
172C22⋊C4—741no—
173C22⋊C4—1482no—
174C23—372no—
175C23—741no—
176C23—741no—
177C23—1481no—
178C23—1481no—
179C23D4×D3711yescharacteristic
180Q8—41no—
181Q8—2961no—
182Q8—742no—
183Q8—742no—
184Q8—1481no—
185Q8—1481no—
186Q8—1481no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—2961no—
194C2×C4—2961no—
195C2×C4—742no—
196C2×C4—741no—
197C2×C4—741no—
198C2×C4—741no—
199C2×C4—1481no—
200C2×C4—1481no—
201C2×C4—1481no—
202C2×C4C2×D14811yescharacteristic
203C2×C4D4×D3711yescharacteristic
204C8—41no—
205C8—1481no—
206C22—21no—
207C22—21no—
208C22—2961no—
209C22—742no—
210C22—1482no—
211C22—1481no—
212C22—1481no—
213C22#1192450611yescharacteristic
214C22Q16×D3711yescharacteristic
215C22#1192456511yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—41no—
220C4—81no—
221C4—1481no—
222C4—1481no—
223C4—1481no—
224C4—1482no—
225C2—21no—
226C2—21no—
227C2—1482no—
228C2#1455769011yescharacteristic
229C2#1455771211yescharacteristic
230C2#1455772111yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#328C2
socleC22×C37#120
prime radicalC23×D37D4
hypercenter#328D37
hypocenterC37#1602
LCSG ▷ C22×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #14557691C2semidirect
3. #14557688C2semidirect
5. #14557269C2semidirect
7. C37×#328C2semidirect
63. C22×D37Q16semidirect
121. #328D37semidirect
123. C37#1602semidirect

Maximal subgroups

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

subgroupindex
#145581582
#145576912
#145576882
#145574462
#145572692
#145572562
C37×#3282
#160237