Finite Group Databasebeta

← #17993730

Subgroups — #17993730

Order 4736.

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

normal subgroups only

This group has 214 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#14557912C211yesmaximal, characteristic, complemented
2#14557828C211yesmaximal, characteristic, complemented
3#14557823C211yesmaximal, characteristic
4#14557282C211yesmaximal, characteristic, complemented
5Q8⋊#64436C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic
7C37×#554C211yesmaximal, characteristic
8C2×#10596942—22no—
9#11924536C2211yescharacteristic
10#11924469—21no—
11#11924467—21no—
12C4⋊#64436C2211yescharacteristic
13C4⋊#64436C2211yescharacteristic
14#11924460—21no—
15#11924457—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×Dic74—21no—
31C4⋊C4×C37—22no—
32C4⋊C4×C37—22no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37D411yescharacteristic
37C4⋊C4×C37D411yescharacteristic
38C22⋊C4×C37—22no—
39C22⋊C4×C37—21no—
40C42×C37—21no—
41C42×C37C2311yescharacteristic
42#10596942—44no—
43C4⋊Dic37—21no—
44C4⋊Dic37—21no—
45C2×#64436—21no—
46C2×#64436—21no—
47C2×#64436—21no—
48C23×C37—21no—
49Q8×C37—21no—
50Q8×C37—21no—
51Q8×C37—42no—
52D4×C37—21no—
53D4×C37Q1612yescomplemented
54C2×C4×C37—21no—
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37—22no—
58C2×C4×C37—41no—
59C2×C4×C37—41no—
60C2×C4×C37—82no—
61C2×C4×C37C2×D411yescharacteristic
62C2×C4×C37C2×D411yescharacteristic
63C2×C4×C37C2×D411yescharacteristic
64C2×Dic37—41no—
65Dic74—42no—
66#64436—22no—
67#64436—41no—
68#64436—41no—
69C22×C37—22no—
70C22×C37—41no—
71C22×C37—41no—
72C22×C37#12011yescharacteristic
73C4×C37—21no—
74C4×C37—41no—
75C4×C37—41no—
76C4×C37—41no—
77C4×C37—42no—
78C4×C37C2×Q1611yescharacteristic
79C4×C37#13511yescharacteristic
80C4×C37#13711yescharacteristic
81C4×C37#13711yescharacteristic
82Dic37—81no—
83#1632—371nomaximal, Sylow
84C2×C37—42no—
85C2×C37#45111yescharacteristic
86C2×C37#45211yescharacteristic
87C2×C37#45311yescharacteristic
88#554D3711yescharacteristic
89#494—371no—
90#477—371no—
91#476—371no—
92#333—371no—
93Q8⋊C8—371no—
94D4⋊C8—371no—
95C37#163211yescharacteristic, complemented, Sylow
96C2×Q16—742no—
97C4⋊Q8—371no—
98C4⋊Q8C2×D3711yescharacteristic
99#125—21no—
100C22⋊Q8—21no—
101C22⋊Q8—22no—
102C4×Q8C2×D3711yescharacteristic
103C4×D4—21no—
104C4×D4C2×D3711yescharacteristic
105C2×C4⋊C4—21no—
106#107—741no—
107#106—741no—
108C4⋊C8—371no—
109C4⋊C8—371no—
110#103—741no—
111#102—741no—
112C4×C8—371no—
113C2×Q8—741no—
114C2×Q8C22⋊D3711yescharacteristic
115C2×Q8C22⋊D3712yes—
116C2×D4C22⋊D3711yescharacteristic
117C22×C4—22no—
118C22×C4—21no—
119Q16—1484no—
120C2×C8—741no—
121C2×C8—741no—
122C2×C8—741no—
123C4⋊C4—22no—
124C4⋊C4—22no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4C22⋊D3711yescharacteristic
131C4⋊C4C22⋊D3711yescharacteristic
132C22⋊C4—22no—
133C22⋊C4—21no—
134C42—21no—
135C42C22×D3711yescharacteristic
136C23—21no—
137Q8—21no—
138Q8—21no—
139Q8—42no—
140Q8—1482no—
141D4—21no—
142D4#1059694212yescomplemented
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—82no—
150C2×C4—1481no—
151C2×C4C2×C22⋊D3711yescharacteristic
152C2×C4C2×C22⋊D3711yescharacteristic
153C2×C4C2×C22⋊D3711yescharacteristic
154C8—742no—
155C8—1481no—
156C8—1481no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1192450511yescharacteristic
161C4—21no—
162C4—41no—
163C4—42no—
164C4—41no—
165C4—41no—
166C4—2961no—
167C4C2×#1059694211yescharacteristic
168C4#1192455611yescharacteristic
169C4#1192456611yescharacteristic
170C4#1192456711yescharacteristic
171C2—42no—
172C2#1455768911yescharacteristic
173C2#1455769511yescharacteristic
174C2#1455770111yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#554C2
socleC22×C37#120
prime radicalC2×D4×C37D4
hypercenter#554D37
hypocenterC37#1632
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. #14557912C2semidirect
2. #14557828C2semidirect
4. #14557282C2semidirect
5. Q8⋊#64436C2semidirect
53. D4×C37Q16semidirect
95. C37#1632semidirect
142. D4#10596942semidirect

Maximal subgroups

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

subgroupindex
#145579122
#145578282
#145578232
#145572822
Q8⋊#644362
D4⋊#644362
C37×#5542
#163237