Finite Group Databasebeta

← #17993706

Subgroups — #17993706

Order 4736.

216 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 57 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#14557881C211yesmaximal, characteristic, complemented
2#14557733C211yesmaximal, characteristic, complemented
3#14557728C211yesmaximal, characteristic
4#14557279C211yesmaximal, characteristic, complemented
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic, complemented
7C37×#556C211yesmaximal, characteristic, complemented
8C2×#10596941—21no—
9C2×#10596939—21no—
10#11924533C2211yescharacteristic
11C4⋊#64436C2211yescharacteristic
12C4⋊#64436C2211yescharacteristic
13#11924456—21no—
14#11924456—21no—
15#11924456—22no—
16C4×#64436C2211yescharacteristic
17C4⋊Q8×C37C2211yescharacteristic
18#126×C37—22no—
19#124×C37—21no—
20C22⋊Q8×C37—21no—
21C4×Q8×C37—21no—
22C4×Q8×C37C2211yescharacteristic
23C4×D4×C37C2211yescharacteristic
24#117×C37—21no—
25C2×Q8×C37—21no—
26C2×Q8×C37D411yescharacteristic
27C2×D4×C37D411yescharacteristic
28C22×C4×C37—21no—
29C2×D148—21no—
30C2×D148—21no—
31C2×D148—21no—
32C4⋊C4×C37—22no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37D411yescharacteristic
36C4⋊C4×C37D411yescharacteristic
37C4⋊C4×C37D412yes—
38C22⋊C4×C37—22no—
39C22⋊C4×C37—22no—
40C22⋊C4×C37—21no—
41C42×C37—22no—
42C42×C37—21no—
43C42×C37C2311yescharacteristic
44#10596941—42no—
45#10596939—42no—
46C2×#64436—21no—
47C2×#64436—21no—
48C2×#64436—21no—
49C23×C37—21no—
50C22×D37—41no—
51Q8×C37—21no—
52Q8×C37—21no—
53Q8×C37—41no—
54Q8×C37—41no—
55D4×C37—21no—
56D4×C37—21no—
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×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66D148—42no—
67D148—41no—
68D148—41no—
69D148—41no—
70D148—41no—
71#64436—41no—
72#64436—41no—
73#64436—41no—
74C22×C37—41no—
75C22×C37—41no—
76C22×C37—41no—
77C22×C37#12011yescharacteristic
78C2×D37—81no—
79C2×D37—81no—
80C2×D37—81no—
81C4×C37—21no—
82C4×C37—41no—
83C4×C37—41no—
84C4×C37—42no—
85C4×C37—41no—
86C4×C37#13511yescharacteristic
87C4×C37#13511yescharacteristic
88C4×C37AGL(1,ℤ/8)11yescharacteristic
89C4×C37AGL(1,ℤ/8)11yescharacteristic
90#1628—371nomaximal, Sylow
91C2×C37—81no—
92C2×C37#44911yescharacteristic
93C2×C37#44911yescharacteristic
94C2×C37#45411yescharacteristic
95D37—161no—
96#556D3711yescharacteristic, complemented
97#486—371no—
98#460—371no—
99#459—371no—
100#332—371no—
101Q8⋊C8—371no—
102D4⋊C8—371no—
103C37#162811yescharacteristic, complemented, Sylow
104C2×SD16—741no—
105C2×D8—741no—
106C4⋊Q8C2×D3711yescharacteristic
107#127—371no—
108#126—22no—
109#124—21no—
110C22⋊Q8—21no—
111C4×Q8—21no—
112C4×Q8C2×D3711yescharacteristic
113C4×D4C2×D3711yescharacteristic
114#117—21no—
115C4⋊C8—371no—
116C4⋊C8—371no—
117#102—741no—
118#102—741no—
119#102—742no—
120C4×C8—371no—
121C2×Q8—21no—
122C2×Q8C22⋊D3711yescharacteristic
123C2×D4—741no—
124C2×D4—741no—
125C2×D4—741no—
126C2×D4C22⋊D3711yescharacteristic
127C22×C4—21no—
128SD16—1482no—
129D8—1482no—
130C2×C8—741no—
131C2×C8—741no—
132C2×C8—741no—
133C4⋊C4—22no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4C22⋊D3711yescharacteristic
137C4⋊C4C22⋊D3711yescharacteristic
138C4⋊C4C22⋊D3712yes—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—21no—
142C42—22no—
143C42—21no—
144C42C22×D3711yescharacteristic
145C23—21no—
146C23—1481no—
147Q8—21no—
148Q8—21no—
149Q8—41no—
150Q8—41no—
151D4—21no—
152D4—21no—
153D4—1482no—
154D4—1481no—
155D4—1481no—
156D4—1481no—
157D4—1481no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4C2×C22⋊D3711yescharacteristic
165C2×C4C2×C22⋊D3711yescharacteristic
166C2×C4C2×C22⋊D3711yescharacteristic
167C8—1481no—
168C8—1481no—
169C8—1481no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—2961no—
174C22—2961no—
175C22—2961no—
176C22#1192450511yescharacteristic
177C4—21no—
178C4—41no—
179C4—41no—
180C4—41no—
181C4—42no—
182C4#1192455611yescharacteristic
183C4#1192455611yescharacteristic
184C4#1192456111yescharacteristic
185C4#1192456111yescharacteristic
186C2—81no—
187C2—5921no—
188C2#1455767811yescharacteristic
189C2#1455767811yescharacteristic
190C2#1455770611yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#556C2
socleC22×C37#120
prime radical#14557728C2
hypercenter#556D37
hypocenterC37#1628
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #14557881C2semidirect
2. #14557733C2semidirect
4. #14557279C2semidirect
5. Q8⋊#64436C2semidirect
6. D4⋊#64436C2semidirect
7. C37×#556C2semidirect
96. #556D37semidirect
103. C37#1628semidirect

Maximal subgroups

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

subgroupindex
#145578812
#145577332
#145577282
#145572792
Q8⋊#644362
D4⋊#644362
C37×#5562
#162837