Finite Group Databasebeta

← #17993913

Subgroups — #17993913

Order 4736.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#14557943C211yesmaximal, characteristic, complemented
2#14557928C211yesmaximal, characteristic, complemented
3#14557892C211yesmaximal, characteristic, complemented
4#14557275C211yesmaximal, characteristic, complemented
5#14557273C211yesmaximal, characteristic, complemented
6#14557273C211yesmaximal, characteristic, complemented
7C37×#562C211yesmaximal, characteristic
8C2×#10596942—21no—
9C2×#10596940—21no—
10#11924536C2211yescharacteristic
11#11924469—21no—
12#11924467—21no—
13#11924460—21no—
14#11924457—21no—
15#11924447C2211yescharacteristic
16#11924447C2211yescharacteristic
17#11924447C2211yescharacteristic
18#125×C37C2211yescharacteristic
19#124×C37C2211yescharacteristic
20#124×C37C2211yescharacteristic
21#123×C37—21no—
22#123×C37—21no—
23C22⋊Q8×C37—21no—
24C22⋊Q8×C37—21no—
25#121×C37—21no—
26#121×C37—21no—
27C2×Q8×C37D411yescharacteristic
28C2×Q8×C37D411yescharacteristic
29C2×D4×C37—21no—
30C2×D4×C37—21no—
31C2×D4×C37D411yescharacteristic
32C2×D4×C37D411yescharacteristic
33C22×C4×C37—21no—
34C22×C4×C37—21no—
35C2×Dic74—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37—21no—
40C4⋊C4×C37D411yescharacteristic
41C4⋊C4×C37D411yescharacteristic
42C22⋊C4×C37—21no—
43C22⋊C4×C37—21no—
44C22⋊C4×C37—21no—
45C22⋊C4×C37—21no—
46C22⋊C4×C37—21no—
47C22⋊C4×C37—21no—
48C42×C37C2311yescharacteristic
49#10596942—42no—
50#10596940—42no—
51C4⋊Dic37—21no—
52C4⋊Dic37—21no—
53C2×#64436—21no—
54C2×#64436—21no—
55C2×#64436—21no—
56C23×C37—21no—
57C23×C37—21no—
58Q8×C37—41no—
59Q8×C37—41no—
60D4×C37—41no—
61D4×C37—41no—
62D4×C37—81no—
63D4×C37—81no—
64C2×C4×C37—21no—
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—81no—
69C2×C4×C37—81no—
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×Dic37—41no—
74Dic74—41no—
75Dic74—41no—
76#64436—22no—
77#64436—22no—
78#64436—41no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37—41no—
82C22×C37—41no—
83C22×C37—41no—
84C22×C37—41no—
85C22×C37#12011yescharacteristic
86C4×C37—21no—
87C4×C37—21no—
88C4×C37—21no—
89C4×C37—41no—
90C4×C37—41no—
91C4×C37—41no—
92C4×C37—41no—
93Dic37—81no—
94#1661—371nomaximal, Sylow
95C2×C37—81no—
96C2×C37—81no—
97C2×C37#45311yescharacteristic
98C2×C37#45511yescharacteristic
99C2×C37#45611yescharacteristic
100#562D3711yescharacteristic
101#501—371no—
102#497—371no—
103#489—371no—
104#330—371no—
105#329—371no—
106#329—371no—
107C37#166111yescharacteristic, complemented, Sylow
108C2×Q16—741no—
109C2×SD16—741no—
110C4⋊Q8—371no—
111#125C2×D3711yescharacteristic
112#124C2×D3711yescharacteristic
113#124C2×D3711yescharacteristic
114#123—21no—
115#123—21no—
116C22⋊Q8—21no—
117C22⋊Q8—21no—
118#121—21no—
119#121—21no—
120#107—741no—
121#106—741no—
122#103—741no—
123#102—741no—
124#97—371no—
125#97—371no—
126#97—371no—
127C2×Q8—741no—
128C2×Q8C22⋊D3711yescharacteristic
129C2×Q8C22⋊D3711yescharacteristic
130C2×D4—21no—
131C2×D4—21no—
132C2×D4C22⋊D3711yescharacteristic
133C2×D4C22⋊D3711yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136Q16—1482no—
137SD16—1482no—
138C2×C8—741no—
139C2×C8—741no—
140C2×C8—741no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—741no—
146C4⋊C4—741no—
147C4⋊C4C22⋊D3711yescharacteristic
148C4⋊C4C22⋊D3711yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C42C22×D3711yescharacteristic
156C23—21no—
157C23—21no—
158Q8—41no—
159Q8—41no—
160Q8—1481no—
161Q8—1481no—
162D4—41no—
163D4—41no—
164D4—81no—
165D4—81no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4—1481no—
173C2×C4C2×C22⋊D3711yescharacteristic
174C2×C4C2×C22⋊D3711yescharacteristic
175C2×C4C2×C22⋊D3711yescharacteristic
176C8—742no—
177C8—742no—
178C8—1481no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22#1192450511yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—41no—
192C4—41no—
193C4—2961no—
194C2—81no—
195C2—81no—
196C2#1455770111yescharacteristic
197C2#1455771111yescharacteristic
198C2#1455771611yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
Fitting, prime radicalC37×#562C2
socleC22×C37#120
hypercenter#562D37
hypocenterC37#1661
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #14557943C2semidirect
2. #14557928C2semidirect
3. #14557892C2semidirect
4. #14557275C2semidirect
5. #14557273C2semidirect
6. #14557273C2semidirect
107. C37#1661semidirect

Maximal subgroups

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

subgroupindex
#145579432
#145579282
#145578922
#145572752
#145572732
C37×#5622
#166137