Finite Group Databasebeta

← #17993668

Subgroups — #17993668

Order 4736.

236 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 61 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#14557907C211yesmaximal, characteristic, complemented
2#14557733C211yesmaximal, characteristic, complemented
3#14557728C211yesmaximal, characteristic
4#14557282C211yesmaximal, characteristic, complemented
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic, complemented
7C37×#554C211yesmaximal, characteristic, complemented
8C2×#10596941—21no—
9C2×#10596941—22no—
10C2×#10596939—21no—
11#11924533C2211yescharacteristic
12C4⋊#64436C2211yescharacteristic
13C4⋊#64436C2211yescharacteristic
14#11924456—21no—
15#11924456—21no—
16C4×#64436C2211yescharacteristic
17C4⋊Q8×C37C2211yescharacteristic
18#125×C37—21no—
19C22⋊Q8×C37—21no—
20C22⋊Q8×C37—22no—
21C4×Q8×C37C2211yescharacteristic
22C4×D4×C37—21no—
23C4×D4×C37C2211yescharacteristic
24C2×C4⋊C4×C37—21no—
25C2×Q8×C37D411yescharacteristic
26C2×Q8×C37D412yes—
27C2×D4×C37D411yescharacteristic
28C22×C4×C37—22no—
29C22×C4×C37—21no—
30C2×D148—21no—
31C2×D148—21no—
32C2×D148—21no—
33C4⋊C4×C37—22no—
34C4⋊C4×C37—22no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37D411yescharacteristic
39C4⋊C4×C37D411yescharacteristic
40C22⋊C4×C37—22no—
41C22⋊C4×C37—21no—
42C42×C37—21no—
43C42×C37C2311yescharacteristic
44#10596941—44no—
45#10596941—42no—
46#10596939—42no—
47C2×#64436—21no—
48C2×#64436—21no—
49C2×#64436—21no—
50C23×C37—21no—
51C22×D37—41no—
52Q8×C37—21no—
53Q8×C37—21no—
54Q8×C37—42no—
55D4×C37—21no—
56D4×C37SD1612yescomplemented
57C2×C4×C37—21no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—22no—
61C2×C4×C37—41no—
62C2×C4×C37—41no—
63C2×C4×C37—82no—
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×C4×C37C2×D411yescharacteristic
67D148—42no—
68D148—41no—
69D148—41no—
70D148—41no—
71D148—41no—
72#64436—22no—
73#64436—41no—
74#64436—41no—
75C22×C37—22no—
76C22×C37—41no—
77C22×C37—41no—
78C22×C37#12011yescharacteristic
79C2×D37—81no—
80C2×D37—81no—
81C2×D37—81no—
82C4×C37—21no—
83C4×C37—41no—
84C4×C37—41no—
85C4×C37—41no—
86C4×C37—42no—
87C4×C37C2×SD1611yescharacteristic
88C4×C37#13511yescharacteristic
89C4×C37AGL(1,ℤ/8)11yescharacteristic
90C4×C37#13711yescharacteristic
91#1622—371nomaximal, Sylow
92C2×C37—42no—
93C2×C37#44811yescharacteristic
94C2×C37#44911yescharacteristic
95C2×C37#45311yescharacteristic
96D37—161no—
97#554D3711yescharacteristic, complemented
98#492—371no—
99#460—371no—
100#459—371no—
101#333—371no—
102Q8⋊C8—371no—
103D4⋊C8—371no—
104C37#162211yescharacteristic, complemented, Sylow
105C2×SD16—741no—
106C2×SD16—742no—
107C2×D8—741no—
108C4⋊Q8C2×D3711yescharacteristic
109#127—371no—
110#125—21no—
111C22⋊Q8—21no—
112C22⋊Q8—22no—
113C4×Q8C2×D3711yescharacteristic
114C4×D4—21no—
115C4×D4C2×D3711yescharacteristic
116C2×C4⋊C4—21no—
117C4⋊C8—371no—
118C4⋊C8—371no—
119#102—741no—
120#102—741no—
121C4×C8—371no—
122C2×Q8C22⋊D3711yescharacteristic
123C2×Q8C22⋊D3712yes—
124C2×D4—741no—
125C2×D4—741no—
126C2×D4—741no—
127C2×D4C22⋊D3711yescharacteristic
128C22×C4—22no—
129C22×C4—21no—
130SD16—1484no—
131SD16—1482no—
132D8—1482no—
133C2×C8—741no—
134C2×C8—741no—
135C2×C8—741no—
136C4⋊C4—22no—
137C4⋊C4—22no—
138C4⋊C4—21no—
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4C22⋊D3711yescharacteristic
142C4⋊C4C22⋊D3711yescharacteristic
143C22⋊C4—22no—
144C22⋊C4—21no—
145C42—21no—
146C42C22×D3711yescharacteristic
147C23—21no—
148C23—1481no—
149Q8—21no—
150Q8—21no—
151Q8—42no—
152D4—21no—
153D4—1482no—
154D4—1481no—
155D4—1481no—
156D4—1481no—
157D4—1481no—
158D4#1059694112yescomplemented
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—22no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—82no—
166C2×C4C2×C22⋊D3711yescharacteristic
167C2×C4C2×C22⋊D3711yescharacteristic
168C2×C4C2×C22⋊D3711yescharacteristic
169C8—742no—
170C8—1481no—
171C8—1481no—
172C22—22no—
173C22—41no—
174C22—41no—
175C22—2961no—
176C22—2961no—
177C22—2961no—
178C22#1192450511yescharacteristic
179C4—21no—
180C4—41no—
181C4—42no—
182C4—41no—
183C4—41no—
184C4C2×#1059694111yescharacteristic
185C4#1192455611yescharacteristic
186C4#1192456111yescharacteristic
187C4#1192456711yescharacteristic
188C2—42no—
189C2—5921no—
190C2#1455767211yescharacteristic
191C2#1455767811yescharacteristic
192C2#1455770111yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#554C2
socleC22×C37#120
prime radical#14557728C2
hypercenter#554D37
hypocenterC37#1622
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #14557907C2semidirect
2. #14557733C2semidirect
4. #14557282C2semidirect
5. Q8⋊#64436C2semidirect
6. D4⋊#64436C2semidirect
7. C37×#554C2semidirect
56. D4×C37SD16semidirect
97. #554D37semidirect
104. C37#1622semidirect
158. D4#10596941semidirect

Maximal subgroups

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

subgroupindex
#145579072
#145577332
#145577282
#145572822
Q8⋊#644362
D4⋊#644362
C37×#5542
#162237