Finite Group Databasebeta

← #17993701

Subgroups — #17993701

Order 4736.

250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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
1Q8×D148C211yesmaximal, characteristic, complemented
2#14557880C211yesmaximal, characteristic, complemented
3#14557733C211yesmaximal, characteristic, complemented
4#14557729C211yesmaximal, characteristic
5#14557278C211yesmaximal, characteristic, complemented
6#14557262C211yesmaximal, characteristic, complemented
7C37×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×Q8×D37—21no—
9C2×#10596941—21no—
10C2×D296—21no—
11#11924536—21no—
12#11924536C2211yescharacteristic
13#11924533C2211yescharacteristic
14#11924516—21no—
15#11924516—22no—
16C4×D148—21no—
17C4×D148C2211yescharacteristic
18C4⋊#64436C2211yescharacteristic
19#11924458—21no—
20#11924458—22no—
21#11924456—21no—
22C4×Q8×C37C2211yescharacteristic
23C4⋊C8×C37C2211yescharacteristic
24C4×C8×C37C2211yescharacteristic
25C2×Q8×C37D411yescharacteristic
26Q8×D37—42no—
27Q8×D37—42no—
28C2×D148—21no—
29C2×D148—21no—
30C2×D148—21no—
31C2×D148D411yescharacteristic
32C2×C4×D37—22no—
33C2×C4×D37—21no—
34C2×Dic74—22no—
35C2×Dic74—21no—
36C2×C8×C37—21no—
37C2×C8×C37—21no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37D411yescharacteristic
40C42×C37—21no—
41C42×C37C2311yescharacteristic
42#10596941—42no—
43#10596938—22no—
44#10596938—21no—
45C4⋊Dic37—22no—
46C4⋊Dic37—21no—
47C4⋊Dic37D411yescharacteristic
48C4⋊Dic37D412yes—
49C2×#64436—21no—
50D296—42no—
51C22×D37—21no—
52C22×D37—41no—
53Q8×C37—21no—
54Q8×C37D812yescomplemented
55C2×C4×C37—21no—
56C2×C4×C37—21no—
57C2×C4×C37C2×D411yescharacteristic
58C2×C4×C37C2×D411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C2×Dic37—21no—
61C2×Dic37—22no—
62D148—21no—
63D148—42no—
64D148—41no—
65D148—41no—
66D148—41no—
67D148—41no—
68D148SD1612yescomplemented
69C4×D37—44no—
70C4×D37—41no—
71C4×D37—41no—
72Dic74—44no—
73Dic74—41no—
74Dic74—41no—
75C8×C37—41no—
76C8×C37—41no—
77#64436—41no—
78C22×C37#12011yescharacteristic
79C2×D37—22no—
80C2×D37—41no—
81C2×D37—41no—
82C2×D37—81no—
83C2×D37—81no—
84C2×D37—81no—
85C4×C37—22no—
86C4×C37—21no—
87C4×C37—41no—
88C4×C37C2×D811yescharacteristic
89C4×C37C2×SD1611yescharacteristic
90C4×C37AGL(1,ℤ/8)11yescharacteristic
91C4×C37#13711yescharacteristic
92Dic37—41no—
93Dic37—42no—
94#1627—371nomaximal, Sylow
95C2×C37#44711yescharacteristic
96C2×C37#44811yescharacteristic
97C2×C37#45411yescharacteristic
98D37—42no—
99D37—161no—
100D4×Q8—371no—
101#486—371no—
102#460—371no—
103#459—371no—
104#332—371no—
105Q8⋊C8D3711yescharacteristic, complemented
106D4⋊C8—371no—
107C37#162711yescharacteristic, complemented, Sylow
108C22×Q8—741no—
109C2×SD16—741no—
110C2×D8—741no—
111C4⋊Q8—371no—
112C4⋊Q8—741no—
113#127—371no—
114C22⋊Q8—742no—
115C22⋊Q8—741no—
116C4×Q8C2×D3711yescharacteristic
117C4×D4—371no—
118C4×D4—741no—
119C4⋊C8—371no—
120C4⋊C8C2×D3711yescharacteristic
121#102—741no—
122#102—742no—
123#102—741no—
124C4×C8C2×D3711yescharacteristic
125C2×Q8—742no—
126C2×Q8—741no—
127C2×Q8—1482no—
128C2×Q8—1482no—
129C2×Q8D14811yescharacteristic
130C2×D4—371no—
131C2×D4—741no—
132C2×D4—741no—
133C2×D4—741no—
134C22×C4—742no—
135C22×C4—741no—
136SD16—1482no—
137D8—1482no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—741no—
141C4⋊C4—21no—
142C4⋊C4—371no—
143C4⋊C4—372no—
144C4⋊C4—742no—
145C4⋊C4—741no—
146C4⋊C4D14811yescharacteristic
147C22⋊C4—742no—
148C22⋊C4—741no—
149C42—21no—
150C42C22×D3711yescharacteristic
151C23—741no—
152C23—1481no—
153Q8—21no—
154Q8—1484no—
155Q8—1481no—
156Q8—1481no—
157Q8D29612yescomplemented
158D4—372no—
159D4—741no—
160D4—1482no—
161D4—1481no—
162D4—1481no—
163D4—1481no—
164D4—1481no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—742no—
168C2×C4—741no—
169C2×C4—1484no—
170C2×C4—1481no—
171C2×C4—1481no—
172C2×C4C2×D14811yescharacteristic
173C2×C4D4×D3711yescharacteristic
174C2×C4D4×D3711yescharacteristic
175C8—41no—
176C8—41no—
177C8—1481no—
178C22—2961no—
179C22—2961no—
180C22—2961no—
181C22—742no—
182C22—1481no—
183C22—1481no—
184C22#1192450611yescharacteristic
185C4—21no—
186C4—22no—
187C4—41no—
188C4—1482no—
189C4—1481no—
190C4C2×D29611yescharacteristic
191C4SD16×D3711yescharacteristic
192C4#1192456411yescharacteristic
193C4#1192456811yescharacteristic
194C2—5921no—
195C2—1482no—
196C2#1455766911yescharacteristic
197C2#1455767311yescharacteristic
198C2#1455770711yescharacteristic
subgroupG/H
centerC22#11924506
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×Q8⋊C8C2
socleC22×C37#120
prime radical#14557729C2
hypercenterQ8⋊C8D37
hypocenterC37#1627
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. Q8×D148C2semidirect
2. #14557880C2semidirect
3. #14557733C2semidirect
5. #14557278C2semidirect
6. #14557262C2semidirect
7. C37×Q8⋊C8C2semidirect
54. Q8×C37D8semidirect
68. D148SD16semidirect
105. Q8⋊C8D37semidirect
107. C37#1627semidirect
157. Q8D296semidirect

Maximal subgroups

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

subgroupindex
Q8×D1482
#145578802
#145577332
#145577292
#145572782
#145572622
C37×Q8⋊C82
#162737