Finite Group Databasebeta

← #17993662

Subgroups — #17993662

Order 4736.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#14558203C211yesmaximal, characteristic, complemented
2#14557909C211yesmaximal, characteristic, complemented
3#14557734C211yesmaximal, characteristic, complemented
4#14557729C211yesmaximal, characteristic, complemented
5#14557263C211yesmaximal, characteristic, complemented
6#14557260C211yesmaximal, characteristic, complemented
7C37×#331C211yesmaximal, characteristic, complemented
8C2×#10596964—21no—
9C2×#10596930—21no—
10C2×D296—21no—
11C2×#10596939—22no—
12#11924533C2211yescharacteristic
13#11924532—21no—
14#11924508—22no—
15#11924507—21no—
16C4×Dic74C2211yescharacteristic
17C4×D148C2211yescharacteristic
18D4×Dic37—21no—
19#11924458—21no—
20#11924458—21no—
21C4×#64436C2211yescharacteristic
22#127×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4⋊C8×C37C2211yescharacteristic
25C2×D4×C37—21no—
26C2×D4×C37—21no—
27C2×D4×C37D412yes—
28C2×C22⋊D37—22no—
29C2×C22⋊D37—22no—
30C22×Dic37—22no—
31#10596964—42no—
32#10596964—42no—
33C2×D148—21no—
34C2×D148—21no—
35C2×D148—21no—
36C2×D148D411yescharacteristic
37C2×C4×D37—21no—
38C2×Dic74D411yescharacteristic
39C2×C8×C37—21no—
40C2×C8×C37—21no—
41C42×C37C2311yescharacteristic
42C22⋊Dic37—22no—
43#10596939—44no—
44#10596938—21no—
45C4⋊Dic37D411yescharacteristic
46C4⋊Dic37D411yescharacteristic
47#10596936—21no—
48C4×Dic37—21no—
49C2×#64436—21no—
50D296—42no—
51#10596930—42no—
52C23×C37—22no—
53C22×D37—21no—
54C22×D37—41no—
55D4×C37—42no—
56D4×C37—41no—
57D4×C37—41no—
58D4×C37—41no—
59D4×C37—41no—
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C22⋊D37—44no—
64C22⋊D37—82no—
65C2×Dic37—21no—
66C2×Dic37—21no—
67C2×Dic37—21no—
68C2×Dic37—44no—
69D148—21no—
70D148—21no—
71D148—42no—
72D148—41no—
73D148—41no—
74D148—41no—
75D148—41no—
76C4×D37—41no—
77C4×D37—41no—
78Dic74—21no—
79Dic74D812yescomplemented
80C8×C37—41no—
81C8×C37—41no—
82#64436—22no—
83C22×C37—42no—
84C22×C37—42no—
85C22×C37—42no—
86C22×C37#12011yescharacteristic
87C2×D37—41no—
88C2×D37—41no—
89C2×D37—41no—
90C2×D37—81no—
91C2×D37—81no—
92C2×D37—81no—
93C4×C37—21no—
94C4×C37C2×D811yescharacteristic
95C4×C37#13511yescharacteristic
96C4×C37AGL(1,ℤ/8)11yescharacteristic
97C4×C37AGL(1,ℤ/8)11yescharacteristic
98Dic37—22no—
99Dic37—41no—
100Dic37—41no—
101#1621—371nomaximal, Sylow
102C2×C37—82no—
103C2×C37#44711yescharacteristic
104C2×C37#44911yescharacteristic
105C2×C37#45311yescharacteristic
106D37—81no—
107D37—161no—
108#550—371no—
109#493—371no—
110#460—371no—
111#459—371no—
112#331D3711yescharacteristic, complemented
113Q8⋊C8—371no—
114D4⋊C8—371no—
115C37#162111yescharacteristic, complemented, Sylow
116C2×#41—741no—
117C2×SD16—741no—
118C2×D8—741no—
119C2×D8—742no—
120#127—371no—
121#127—741no—
122#127C2×D3711yescharacteristic
123#121—741no—
124#121—742no—
125C4×Q8—371no—
126C4×D4—371no—
127C4×D4—741no—
128C4⋊C8C2×D3711yescharacteristic
129C4⋊C8C2×D3711yescharacteristic
130#102—741no—
131#102—741no—
132C4×C8—371no—
133#41—1482no—
134#41—1482no—
135C2×Q8—371no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—371no—
139C2×D4—742no—
140C2×D4—742no—
141C2×D4—741no—
142C2×D4—741no—
143C2×D4—741no—
144C2×D4D14812yes—
145C22×C4—742no—
146C22×C4—741no—
147SD16—1482no—
148D8—1482no—
149D8—1484no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—741no—
153C4⋊C4—371no—
154C4⋊C4—371no—
155C4⋊C4—741no—
156C22⋊C4—742no—
157C22⋊C4—741no—
158C42—741no—
159C42C22×D3711yescharacteristic
160C23—22no—
161C23—741no—
162C23—1481no—
163Q8—372no—
164Q8—741no—
165D4—42no—
166D4—41no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—2962no—
171D4—741no—
172D4—741no—
173D4—1482no—
174D4—1484no—
175D4—1481no—
176D4—1481no—
177D4—1481no—
178D4—1481no—
179C2×C4—741no—
180C2×C4—741no—
181C2×C4—741no—
182C2×C4—1484no—
183C2×C4—1481no—
184C2×C4—1481no—
185C2×C4C2×D14811yescharacteristic
186C2×C4D4×D3711yescharacteristic
187C2×C4D4×D3711yescharacteristic
188C8—41no—
189C8—41no—
190C8—742no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—2961no—
195C22—2961no—
196C22—2961no—
197C22—1481no—
198C22—1481no—
199C22—1481no—
200C22#1192450611yescharacteristic
201C4—21no—
202C4—742no—
203C4—1481no—
204C4—1481no—
205C4D8×D3711yescharacteristic
206C4#1192455711yescharacteristic
207C4#1192456011yescharacteristic
208C4#1192456311yescharacteristic
209C2—82no—
210C2—2961no—
211C2—5921no—
212C2#1455766811yescharacteristic
213C2#1455767911yescharacteristic
214C2#1455770311yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#331C2
socleC22×C37#120
hypercenter#331D37
hypocenterC37#1621
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #14558203C2semidirect
2. #14557909C2semidirect
3. #14557734C2semidirect
4. #14557729C2semidirect
5. #14557263C2semidirect
6. #14557260C2semidirect
7. C37×#331C2semidirect
79. Dic74D8semidirect
112. #331D37semidirect
115. C37#1621semidirect

Maximal subgroups

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

subgroupindex
#145582032
#145579092
#145577342
#145577292
#145572632
#145572602
C37×#3312
#162137