Finite Group Databasebeta

← #17993639

Subgroups — #17993639

Order 4736.

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

normal subgroups only

This group has 202 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
2#14557869C211yesmaximal, characteristic
3#14557866C211yesmaximal, characteristic
4#14557473C211yesmaximal, characteristic
5#14557269C211yesmaximal, characteristic
6#14557258C211yesmaximal, characteristic
7C37×#328C211yesmaximal, characteristic
8#11924535—21no—
9#11924534—21no—
10#11924526—21no—
11#11924526—21no—
12#11924515C2211yescharacteristic
13#11924513—21no—
14#11924492—21no—
15C2×C4⋊Dic37C2211yescharacteristic
16C2×#10596936C2211yescharacteristic
17#11924470—21no—
18#11924469—21no—
19#11924461—21no—
20#11924460—21no—
21C22⋊#64436C2211yescharacteristic
22#11924443—21no—
23#11924443—21no—
24C22⋊Q8×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C2×Q8×C37D411yescharacteristic
28C22×C4×C37—21no—
29C22×C4×C37C2311yescharacteristic
30C22×Dic37—21no—
31C22×Dic37D411yescharacteristic
32C22×Dic37D411yescharacteristic
33C2×Dic74—21no—
34C2×Dic74D411yescharacteristic
35C2×C8×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37D411yescharacteristic
38C22⋊C4×C37—21no—
39C22⋊Dic37—21no—
40C4⋊Dic37—21no—
41C4⋊Dic37—21no—
42C4⋊Dic37—21no—
43C4⋊Dic37D411yescharacteristic
44#10596936—21no—
45#10596936—21no—
46#10596936—21no—
47#10596936—21no—
48#10596936—21no—
49#10596936—21no—
50#10596936—21no—
51C4×Dic37—21no—
52C4×Dic37—21no—
53C2×#64436—21no—
54C23×C37C2×D411yescharacteristic
55Q8×C37—41no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37—41no—
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×Dic37—21no—
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37—21no—
68C2×Dic37—21no—
69C2×Dic37—41no—
70C2×Dic37—42no—
71C2×Dic37—41no—
72C2×Dic37Q1612yes—
73Dic74—41no—
74Dic74—81no—
75C8×C37—41no—
76#64436—41no—
77C22×C37—21no—
78C22×C37—21no—
79C22×C37#12011yescharacteristic
80C22×C37C2×Q1611yescharacteristic
81C22×C37#13711yescharacteristic
82C4×C37—21no—
83C4×C37—21no—
84C4×C37—41no—
85C4×C37—41no—
86C4×C37—81no—
87Dic37—22no—
88Dic37—41no—
89Dic37—41no—
90Dic37—41no—
91Dic37—81no—
92#1617—371nomaximal, Sylow
93C2×C37—21no—
94C2×C37—21no—
95C2×C37#45111yescharacteristic
96C2×C37#45411yescharacteristic
97C2×C37#45811yescharacteristic
98#544—371no—
99#484—371no—
100#484—371no—
101#400—371no—
102#328—371no—
103#328D3711yescharacteristic
104#324—371no—
105C37#161711yescharacteristic, complemented, Sylow
106C4⋊Q8—741no—
107C4⋊Q8—741no—
108#125—741no—
109#125—741no—
110C22⋊Q8—371no—
111C22⋊Q8—741no—
112C22⋊Q8C2×D3711yescharacteristic
113#117—741no—
114C2×C4⋊C4—371no—
115C2×C4⋊C4—371no—
116#107—741no—
117#107—741no—
118#103—741no—
119#103—741no—
120C22⋊C8—371no—
121C22⋊C8C2×D3711yescharacteristic
122#95—741no—
123#95—741no—
124#95C2×D3711yescharacteristic
125C2×Q8—371no—
126C2×Q8—741no—
127C2×Q8D14811yescharacteristic
128C22×C4—21no—
129C22×C4—371no—
130C22×C4—371no—
131C22×C4—741no—
132C22×C4C22×D3711yescharacteristic
133C2×C8—21no—
134C2×C8—741no—
135C4⋊C4—21no—
136C4⋊C4—371no—
137C4⋊C4—741no—
138C4⋊C4—741no—
139C4⋊C4—741no—
140C4⋊C4—741no—
141C4⋊C4—741no—
142C4⋊C4—741no—
143C4⋊C4—741no—
144C4⋊C4—741no—
145C4⋊C4—741no—
146C4⋊C4—741no—
147C4⋊C4D14811yescharacteristic
148C22⋊C4—21no—
149C22⋊C4—741no—
150C42—741no—
151C42—741no—
152C23D4×D3711yescharacteristic
153Q8—41no—
154Q8—2961no—
155Q8—1481no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—372no—
163C2×C4—741no—
164C2×C4—741no—
165C2×C4—741no—
166C2×C4—741no—
167C2×C4—741no—
168C2×C4—1482no—
169C2×C4—1481no—
170C2×C4—1481no—
171C2×C4C2×D14811yescharacteristic
172C2×C4D4×D3711yescharacteristic
173C8—41no—
174C8—1481no—
175C22—21no—
176C22—21no—
177C22#1192450611yescharacteristic
178C22Q16×D3711yescharacteristic
179C22#1192456511yescharacteristic
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—81no—
185C4—2961no—
186C4—742no—
187C4—1481no—
188C4—1481no—
189C4—1481no—
190C2—21no—
191C2—21no—
192C2#1455769011yescharacteristic
193C2#1455770711yescharacteristic
194C2#1455772411yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#328C2
socleC22×C37#120
prime radicalC23×C37C2×D4
hypercenter#328D37
hypocenterC37#1617
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
105. C37#1617semidirect

Maximal subgroups

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

subgroupindex
#145581622
#145578692
#145578662
#145574732
#145572692
#145572582
C37×#3282
#161737