Finite Group Databasebeta

← #17993537

Subgroups — #17993537

Order 4736.

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

normal subgroups only

This group has 266 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#14558162C211yesmaximal, characteristic, complemented
2#14557686C211yesmaximal, characteristic
3#14557683C211yesmaximal, characteristic
4#14557451C211yesmaximal, characteristic
5#14557269C211yesmaximal, characteristic, complemented
6#14557258C211yesmaximal, characteristic, complemented
7C37×#328C211yesmaximal, characteristic, complemented
8C22×D148C2211yescharacteristic
9C2×#10596930—21no—
10C2×#10596941—21no—
11#11924535—21no—
12#11924534—21no—
13#11924526—21no—
14#11924526—21no—
15#11924515C2211yescharacteristic
16#11924513—21no—
17#11924492—21no—
18C2×#10596936C2211yescharacteristic
19C2×#10596938—21no—
20C2×#10596938—21no—
21#11924458—21no—
22#11924456—21no—
23C22⋊#64436C2211yescharacteristic
24C22⋊Q8×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C23×D37—21no—
28C2×Q8×C37D411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C22×Dic37D411yescharacteristic
32C22×Dic37D411yescharacteristic
33C2×D148—21no—
34C2×D148—21no—
35C2×D148—42no—
36C2×Dic74—21no—
37C2×Dic74D411yescharacteristic
38C2×C8×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37D411yescharacteristic
41C22⋊C4×C37—21no—
42C22⋊Dic37—21no—
43#10596941—42no—
44#10596938—42no—
45#10596938—42no—
46C4⋊Dic37—21no—
47C4⋊Dic37D411yescharacteristic
48#10596936—21no—
49#10596936—21no—
50#10596936—21no—
51#10596936—21no—
52#10596936—21no—
53#10596936—21no—
54#10596936—21no—
55C4×Dic37—21no—
56C4×Dic37—21no—
57C2×#64436—21no—
58#10596930—42no—
59C23×C37C2×D411yescharacteristic
60C22×D37—22no—
61C22×D37—41no—
62C22×D37—41no—
63C22×D37—41no—
64C22×D37—41no—
65C22×D37—41no—
66C22×D37—41no—
67Q8×C37—41no—
68C2×C4×C37—21no—
69C2×C4×C37—21no—
70C2×C4×C37—41no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37—41no—
74C2×C4×C37C2×D411yescharacteristic
75C2×C4×C37C2×D411yescharacteristic
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—21no—
79C2×Dic37—21no—
80C2×Dic37—21no—
81C2×Dic37—41no—
82C2×Dic37SD1612yescomplemented
83D148—22no—
84D148—22no—
85D148—41no—
86D148—41no—
87Dic74—41no—
88Dic74—81no—
89C8×C37—41no—
90#64436—41no—
91C22×C37—21no—
92C22×C37—21no—
93C22×C37#12011yescharacteristic
94C22×C37C2×SD1611yescharacteristic
95C22×C37#13711yescharacteristic
96C2×D37—42no—
97C2×D37—42no—
98C2×D37—42no—
99C2×D37—81no—
100C2×D37—81no—
101C2×D37—81no—
102C2×D37—81no—
103C4×C37—21no—
104C4×C37—21no—
105C4×C37—41no—
106C4×C37—41no—
107C4×C37—81no—
108Dic37—22no—
109Dic37—41no—
110Dic37—41no—
111Dic37—41no—
112#1599—371nomaximal, Sylow
113C2×C37—21no—
114C2×C37—21no—
115C2×C37#44811yescharacteristic
116C2×C37#45411yescharacteristic
117C2×C37B(4,𝔽2)11yescharacteristic
118D37—82no—
119#544—371no—
120#450—371no—
121#450—371no—
122#394—371no—
123#328—371no—
124#328D3711yescharacteristic, complemented
125#324—371no—
126C37#159911yescharacteristic, complemented, Sylow
127C22×D4—371no—
128C2×SD16—741no—
129C2×SD16—741no—
130C4⋊Q8—741no—
131C4⋊Q8—741no—
132#125—741no—
133#125—741no—
134C22⋊Q8—371no—
135C22⋊Q8—741no—
136C22⋊Q8C2×D3711yescharacteristic
137#117—741no—
138C2×C4⋊C4—371no—
139C2×C22⋊C4—741no—
140C2×C22⋊C4—741no—
141#102—741no—
142#102—741no—
143C22⋊C8—371no—
144C22⋊C8C2×D3711yescharacteristic
145#95C2×D3711yescharacteristic
146C24—741no—
147C2×Q8—371no—
148C2×Q8—741no—
149C2×Q8D14811yescharacteristic
150C2×D4—741no—
151C2×D4—741no—
152C2×D4—1482no—
153C22×C4—21no—
154C22×C4—371no—
155C22×C4—371no—
156C22×C4C22×D3711yescharacteristic
157SD16—1482no—
158SD16—1482no—
159C2×C8—21no—
160C2×C8—741no—
161C4⋊C4—21no—
162C4⋊C4—371no—
163C4⋊C4—741no—
164C4⋊C4—741no—
165C4⋊C4—741no—
166C4⋊C4—741no—
167C4⋊C4—741no—
168C4⋊C4—741no—
169C4⋊C4—741no—
170C4⋊C4—741no—
171C4⋊C4D14811yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—741no—
174C22⋊C4—1482no—
175C22⋊C4—1482no—
176C42—741no—
177C42—741no—
178C23—742no—
179C23—1481no—
180C23—1481no—
181C23—1481no—
182C23—1481no—
183C23—1481no—
184C23—1481no—
185C23D4×D3711yescharacteristic
186Q8—41no—
187Q8—2961no—
188Q8—1481no—
189D4—742no—
190D4—742no—
191D4—1481no—
192D4—1481no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—372no—
200C2×C4—741no—
201C2×C4—741no—
202C2×C4—741no—
203C2×C4—741no—
204C2×C4—741no—
205C2×C4—1481no—
206C2×C4C2×D14811yescharacteristic
207C2×C4D4×D3711yescharacteristic
208C8—41no—
209C8—1481no—
210C22—21no—
211C22—21no—
212C22—2961no—
213C22—2961no—
214C22—2961no—
215C22—2961no—
216C22—1482no—
217C22—1482no—
218C22—1482no—
219C22#1192450611yescharacteristic
220C22SD16×D3711yescharacteristic
221C22#1192456811yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—742no—
228C4—1481no—
229C4—1481no—
230C4—1481no—
231C2—21no—
232C2—21no—
233C2—2962no—
234C2#1455767311yescharacteristic
235C2#1455770711yescharacteristic
236C2#1455772111yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#328C2
socleC22×C37#120
prime radicalC22×D148C22
hypercenter#328D37
hypocenterC37#1599
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
1. #14558162C2semidirect
5. #14557269C2semidirect
6. #14557258C2semidirect
7. C37×#328C2semidirect
82. C2×Dic37SD16semidirect
124. #328D37semidirect
126. C37#1599semidirect

Maximal subgroups

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

subgroupindex
#145581622
#145576862
#145576832
#145574512
#145572692
#145572582
C37×#3282
#159937