Finite Group Databasebeta

← #17993588

Subgroups — #17993588

Order 4736.

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

normal subgroups only

This group has 228 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#14557864C211yesmaximal, characteristic, complemented
3#14557861C211yesmaximal, characteristic, complemented
4#14557460C211yesmaximal, characteristic
5#14557269C211yesmaximal, characteristic, complemented
6#14557256C211yesmaximal, characteristic
7C37×#328C211yesmaximal, characteristic, complemented
8#11924516—21no—
9#11924515C2211yescharacteristic
10#11924514—21no—
11#11924514—21no—
12#11924513—21no—
13#11924512—21no—
14C2×C4⋊Dic37C2211yescharacteristic
15C2×#10596938—21no—
16C2×#10596938C2211yescharacteristic
17C22⋊C4×D37—21no—
18#11924468—21no—
19#11924467—21no—
20#11924461—21no—
21#11924460—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×Dic74D411yescharacteristic
37C2×C8×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37D411yescharacteristic
40C22⋊C4×C37—21no—
41C22⋊Dic37—21no—
42#10596938—21no—
43#10596938—21no—
44#10596938—21no—
45#10596938—21no—
46#10596938—42no—
47C4⋊Dic37—21no—
48C4⋊Dic37—21no—
49C4⋊Dic37—21no—
50C4⋊Dic37D411yescharacteristic
51#10596936—21no—
52#10596936—21no—
53#10596936—21no—
54C2×#64436—21no—
55C23×C37C2×D411yescharacteristic
56C22×D37—21no—
57C22×D37—21no—
58C22×D37—41no—
59C22×D37—41no—
60C22×D37SD1612yes—
61Q8×C37—41no—
62C2×C4×C37—21no—
63C2×C4×C37—21no—
64C2×C4×C37—41no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37C2×D411yescharacteristic
69C2×C4×C37C2×D411yescharacteristic
70C2×Dic37—21no—
71C2×Dic37—21no—
72C2×Dic37—21no—
73C2×Dic37—41no—
74C2×Dic37—41no—
75C2×Dic37—41no—
76C2×Dic37—41no—
77C4×D37—81no—
78C4×D37—81no—
79Dic74—41no—
80Dic74—81no—
81C8×C37—41no—
82#64436—41no—
83C22×C37—21no—
84C22×C37—21no—
85C22×C37#12011yescharacteristic
86C22×C37C2×SD1611yescharacteristic
87C22×C37#13711yescharacteristic
88C2×D37—22no—
89C2×D37—41no—
90C2×D37—41no—
91C2×D37—42no—
92C2×D37—81no—
93C4×C37—21no—
94C4×C37—21no—
95C4×C37—41no—
96C4×C37—41no—
97C4×C37—81no—
98Dic37—41no—
99Dic37—41no—
100Dic37—41no—
101Dic37—81no—
102#1608—371nomaximal, Sylow
103C2×C37—21no—
104C2×C37—21no—
105C2×C37#44811yescharacteristic
106C2×C37#45511yescharacteristic
107C2×C37#45811yescharacteristic
108D37—42no—
109#543—371no—
110#483—371no—
111#483—371no—
112#397—371no—
113#328—371no—
114#328D3711yescharacteristic, complemented
115#323—371no—
116C37#160811yescharacteristic, complemented, Sylow
117C22⋊Q8—371no—
118C22⋊Q8—741no—
119C22⋊Q8—741no—
120C22⋊Q8—741no—
121C22⋊Q8—741no—
122C22⋊Q8—741no—
123C22⋊Q8C2×D3711yescharacteristic
124C2×C4⋊C4—371no—
125C2×C22⋊C4—371no—
126C2×C22⋊C4—741no—
127C2×C22⋊C4—741no—
128#106—741no—
129#106—741no—
130#103—741no—
131#103—741no—
132C22⋊C8—371no—
133C22⋊C8C2×D3711yescharacteristic
134#95—741no—
135#95C2×D3711yescharacteristic
136C24—371no—
137C2×Q8—371no—
138C2×Q8—741no—
139C2×Q8D14811yescharacteristic
140C22×C4—21no—
141C22×C4—371no—
142C22×C4—741no—
143C22×C4—741no—
144C22×C4—741no—
145C22×C4C22×D3711yescharacteristic
146C2×C8—21no—
147C2×C8—741no—
148C4⋊C4—21no—
149C4⋊C4—371no—
150C4⋊C4—741no—
151C4⋊C4—741no—
152C4⋊C4—741no—
153C4⋊C4—741no—
154C4⋊C4—741no—
155C4⋊C4—741no—
156C4⋊C4D14811yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—741no—
159C22⋊C4—741no—
160C22⋊C4—741no—
161C22⋊C4—741no—
162C22⋊C4—741no—
163C22⋊C4—1482no—
164C23—372no—
165C23—741no—
166C23—741no—
167C23—1481no—
168C23—1481no—
169C23D4×D3711yescharacteristic
170Q8—41no—
171Q8—2961no—
172Q8—1481no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—2961no—
180C2×C4—2961no—
181C2×C4—741no—
182C2×C4—741no—
183C2×C4—741no—
184C2×C4—1481no—
185C2×C4—1481no—
186C2×C4—1481no—
187C2×C4—1481no—
188C2×C4C2×D14811yescharacteristic
189C2×C4D4×D3711yescharacteristic
190C8—41no—
191C8—1481no—
192C22—21no—
193C22—21no—
194C22—2961no—
195C22—742no—
196C22—1482no—
197C22—1481no—
198C22—1481no—
199C22#1192450611yescharacteristic
200C22SD16×D3711yescharacteristic
201C22#1192456811yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—2961no—
208C4—1481no—
209C4—1481no—
210C4—1481no—
211C2—21no—
212C2—21no—
213C2—1482no—
214C2#1455767311yescharacteristic
215C2#1455771211yescharacteristic
216C2#1455772411yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#328C2
socleC22×C37#120
prime radicalC23×D37D4
hypercenter#328D37
hypocenterC37#1608
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. #14557864C2semidirect
3. #14557861C2semidirect
5. #14557269C2semidirect
7. C37×#328C2semidirect
114. #328D37semidirect
116. C37#1608semidirect

Maximal subgroups

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

subgroupindex
#145581582
#145578642
#145578612
#145574602
#145572692
#145572562
C37×#3282
#160837