Finite Group Databasebeta

← #17993887

Subgroups — #17993887

Order 4736.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#14558277C211yesmaximal, characteristic, complemented
2#14557920C211yesmaximal, characteristic, complemented
3#14557897C211yesmaximal, characteristic, complemented
4#14557274C211yesmaximal, characteristic, complemented
5#14557273C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic, complemented
7C37×#496C211yesmaximal, characteristic, complemented
8C2×#10596940—21no—
9C2×#10596939—21no—
10#11924528C2211yescharacteristic
11#11924524C2211yescharacteristic
12#11924520—21no—
13#11924518—21no—
14#11924513—21no—
15#11924512—21no—
16#11924509—21no—
17#11924508—21no—
18#11924457—21no—
19#11924457—21no—
20#11924447C2211yescharacteristic
21#11924447C2211yescharacteristic
22C2×SD16×C37—21no—
23C2×D8×C37—21no—
24#127×C37C2211yescharacteristic
25#124×C37C2211yescharacteristic
26#97×C37C2211yescharacteristic
27C2×Q8×C37D411yescharacteristic
28C2×D4×C37—21no—
29C2×D4×C37—21no—
30C2×D4×C37—21no—
31C2×D4×C37D411yescharacteristic
32C2×C22⋊D37—21no—
33C2×C22⋊D37—21no—
34C22×Dic37—21no—
35C2×D148D411yescharacteristic
36C2×C4×D37—21no—
37C2×Dic74D411yescharacteristic
38SD16×C37—42no—
39D8×C37—42no—
40C2×C8×C37—21no—
41C22⋊C4×C37—21no—
42C22⋊C4×C37—21no—
43C42×C37C2311yescharacteristic
44C22⋊Dic37—21no—
45#10596940—42no—
46#10596939—42no—
47#10596938—21no—
48#10596938—21no—
49#10596938—21no—
50C4⋊Dic37—21no—
51C4⋊Dic37D411yescharacteristic
52C4⋊Dic37D411yescharacteristic
53#10596936—21no—
54#10596936—21no—
55#10596936—21no—
56C2×#64436—21no—
57C2×#64436—21no—
58C23×C37—21no—
59C23×C37—41no—
60C22×D37—21no—
61Q8×C37—41no—
62D4×C37—41no—
63D4×C37—41no—
64D4×C37—41no—
65D4×C37—41no—
66D4×C37—41no—
67D4×C37—42no—
68C2×C4×C37—21no—
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C22⋊D37—81no—
73C22⋊D37—81no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—81no—
78D148—41no—
79C4×D37—81no—
80Dic74—41no—
81C8×C37—22no—
82#64436—22no—
83#64436—41no—
84C22×C37—41no—
85C22×C37—41no—
86C22×C37—41no—
87C22×C37—81no—
88C22×C37—81no—
89C22×C37—81no—
90C22×C37#12011yescharacteristic
91C2×D37—41no—
92C2×D37—41no—
93C2×D37—41no—
94C4×C37—21no—
95C4×C37—21no—
96C4×C37—21no—
97C4×C37—41no—
98Dic37—41no—
99Dic37—41no—
100Dic37—41no—
101#1656—371nomaximal, Sylow
102C2×C37—81no—
103C2×C37—161no—
104C2×C37#45311yescharacteristic
105C2×C37#45311yescharacteristic
106C2×C37#45411yescharacteristic
107D37—81no—
108#562—371no—
109#496—371no—
110#496D3711yescharacteristic, complemented
111#490—371no—
112#330—371no—
113#329—371no—
114#329—371no—
115C37#165611yescharacteristic, complemented, Sylow
116C2×SD16—21no—
117C2×SD16—741no—
118C2×D8—21no—
119C2×D8—741no—
120#127C2×D3711yescharacteristic
121#125—371no—
122#124—371no—
123#124C2×D3711yescharacteristic
124#123—741no—
125#123—741no—
126C22⋊Q8—741no—
127C22⋊Q8—741no—
128#121—741no—
129#121—741no—
130#102—741no—
131#102—741no—
132#97—371no—
133#97—371no—
134#97C2×D3711yescharacteristic
135C2×Q8—371no—
136C2×Q8C22⋊D3711yescharacteristic
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—371no—
141C2×D4—741no—
142C2×D4—741no—
143C2×D4C22⋊D3711yescharacteristic
144C22×C4—741no—
145C22×C4—741no—
146SD16—42no—
147SD16—1482no—
148D8—42no—
149D8—1482no—
150C2×C8—21no—
151C2×C8—741no—
152C2×C8—741no—
153C4⋊C4—371no—
154C4⋊C4—371no—
155C4⋊C4—741no—
156C4⋊C4—741no—
157C4⋊C4—741no—
158C4⋊C4—741no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—741no—
162C22⋊C4—741no—
163C22⋊C4—741no—
164C22⋊C4—741no—
165C42C22×D3711yescharacteristic
166C23—21no—
167C23—41no—
168C23—741no—
169Q8—41no—
170Q8—1481no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—41no—
176D4—42no—
177D4—2961no—
178D4—2961no—
179D4—1481no—
180C2×C4—21no—
181C2×C4—2961no—
182C2×C4—2961no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4—741no—
186C2×C4D4×D3711yescharacteristic
187C2×C4D4×D3711yescharacteristic
188C2×C4C2×C22⋊D3711yescharacteristic
189C8—22no—
190C8—742no—
191C8—1481no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—81no—
196C22—81no—
197C22—81no—
198C22—1481no—
199C22—1481no—
200C22—1481no—
201C22#1192450411yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—1481no—
207C4—1481no—
208C4—1481no—
209C2—81no—
210C2—161no—
211C2—2961no—
212C2#1455769911yescharacteristic
213C2#1455770011yescharacteristic
214C2#1455770411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#496C2
socleC22×C37#120
hypercenter#496D37
hypocenterC37#1656
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #14558277C2semidirect
2. #14557920C2semidirect
3. #14557897C2semidirect
4. #14557274C2semidirect
5. #14557273C2semidirect
6. #14557272C2semidirect
7. C37×#496C2semidirect
110. #496D37semidirect
115. C37#1656semidirect

Maximal subgroups

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

subgroupindex
#145582772
#145579202
#145578972
#145572742
#145572732
#145572722
C37×#4962
#165637