Finite Group Databasebeta

← #17993890

Subgroups — #17993890

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#14557923C211yesmaximal, characteristic, complemented
3#14557922C211yesmaximal, characteristic, complemented
4#14557898C211yesmaximal, characteristic, complemented
5#14557274C211yesmaximal, characteristic, complemented
6#14557272C211yesmaximal, characteristic, complemented
7C37×#329C211yesmaximal, characteristic, complemented
8C2×#10596930—21no—
9C2×#10596941—21no—
10C2×D296—21no—
11C2×#10596939—21no—
12#11924533C2211yescharacteristic
13#11924528C2211yescharacteristic
14#11924524C2211yescharacteristic
15#11924520—21no—
16#11924518—21no—
17#11924513—21no—
18#11924512—21no—
19#11924509—21no—
20#11924508—21no—
21#11924458—21no—
22#11924458—21no—
23#11924447C2211yescharacteristic
24#124×C37C2211yescharacteristic
25#97×C37C2211yescharacteristic
26#97×C37C2211yescharacteristic
27C2×Q8×C37D411yescharacteristic
28C2×D4×C37D411yescharacteristic
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C22×Dic37—21no—
32C2×D148—21no—
33C2×D148—21no—
34C2×D148—21no—
35C2×D148D411yescharacteristic
36C2×C4×D37—21no—
37C2×Dic74D411yescharacteristic
38C2×C8×C37—21no—
39C2×C8×C37—21no—
40C22⋊C4×C37—21no—
41C22⋊C4×C37—21no—
42C42×C37C2311yescharacteristic
43C22⋊Dic37—21no—
44#10596941—42no—
45#10596939—42no—
46#10596938—21no—
47#10596938—21no—
48#10596938—21no—
49C4⋊Dic37—21no—
50C4⋊Dic37D411yescharacteristic
51C4⋊Dic37D411yescharacteristic
52#10596936—21no—
53#10596936—21no—
54#10596936—21no—
55C2×#64436—21no—
56D296—42no—
57#10596930—42no—
58C23×C37—21no—
59C22×D37—21no—
60C22×D37—41no—
61Q8×C37—41no—
62D4×C37—41no—
63C2×C4×C37—21no—
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67C22⋊D37—81no—
68C22⋊D37—81no—
69C2×Dic37—21no—
70C2×Dic37—21no—
71C2×Dic37—21no—
72C2×Dic37—81no—
73D148—41no—
74D148—41no—
75D148—41no—
76D148—41no—
77D148—41no—
78D148—42no—
79C4×D37—81no—
80Dic74—41no—
81C8×C37—22no—
82C8×C37—41no—
83#64436—22no—
84C22×C37—41no—
85C22×C37—41no—
86C22×C37—41no—
87C22×C37#12011yescharacteristic
88C2×D37—41no—
89C2×D37—41no—
90C2×D37—41no—
91C2×D37—81no—
92C2×D37—81no—
93C2×D37—81no—
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#45311yescharacteristic
104C2×C37#45311yescharacteristic
105C2×C37#45411yescharacteristic
106D37—81no—
107D37—161no—
108#562—371no—
109#496—371no—
110#496—371no—
111#490—371no—
112#330—371no—
113#329—371no—
114#329D3711yescharacteristic, complemented
115C37#165611yescharacteristic, complemented, Sylow
116C2×SD16—741no—
117C2×SD16—741no—
118C2×D8—741no—
119C2×D8—741no—
120#127—371no—
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#97C2×D3711yescharacteristic
134#97C2×D3711yescharacteristic
135C2×Q8—371no—
136C2×Q8D14811yescharacteristic
137C2×D4—371no—
138C2×D4—741no—
139C2×D4—741no—
140C2×D4—741no—
141C2×D4—741no—
142C2×D4—741no—
143C2×D4D14811yescharacteristic
144C22×C4—741no—
145C22×C4—741no—
146SD16—1482no—
147SD16—1482no—
148D8—1482no—
149D8—1482no—
150C2×C8—21no—
151C2×C8—21no—
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—741no—
168C23—1481no—
169Q8—41no—
170Q8—1481no—
171D4—41no—
172D4—2961no—
173D4—2961no—
174D4—1481no—
175D4—1481no—
176D4—1481no—
177D4—1481no—
178D4—1482no—
179D4—1481no—
180C2×C4—21no—
181C2×C4—2961no—
182C2×C4—2961no—
183C2×C4—741no—
184C2×C4—741no—
185C2×C4—741no—
186C2×C4C2×D14811yescharacteristic
187C2×C4D4×D3711yescharacteristic
188C2×C4D4×D3711yescharacteristic
189C8—22no—
190C8—41no—
191C8—742no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—2961no—
196C22—2961no—
197C22—2961no—
198C22—1481no—
199C22—1481no—
200C22—1481no—
201C22#1192450611yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—1481no—
207C4—1481no—
208C4—1481no—
209C2—81no—
210C2—2961no—
211C2—5921no—
212C2#1455770211yescharacteristic
213C2#1455770311yescharacteristic
214C2#1455770711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#329C2
socleC22×C37#120
hypercenter#329D37
hypocenterC37#1656
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #14558277C2semidirect
2. #14557923C2semidirect
3. #14557922C2semidirect
4. #14557898C2semidirect
5. #14557274C2semidirect
6. #14557272C2semidirect
7. C37×#329C2semidirect
114. #329D37semidirect
115. C37#1656semidirect

Maximal subgroups

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

subgroupindex
#145582772
#145579232
#145579222
#145578982
#145572742
#145572722
C37×#3292
#165637