Finite Group Databasebeta

← #17993685

Subgroups — #17993685

Order 4736.

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

normal subgroups only

This group has 256 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#14557881C211yesmaximal, characteristic, complemented
2#14557728C211yesmaximal, characteristic, complemented
3#14557728C211yesmaximal, characteristic, complemented
4#14557279C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic, complemented
7C37×#547C211yesmaximal, characteristic, complemented
8C2×#10596939—21no—
9C2×#10596939—21no—
10#11924533C2211yescharacteristic
11C4⋊#64436C2211yescharacteristic
12C4⋊#64436C2211yescharacteristic
13#11924456—21no—
14#11924456—21no—
15#11924456—22no—
16C4×#64436C2211yescharacteristic
17C2×#41×C37—21no—
18C4⋊Q8×C37C2211yescharacteristic
19#123×C37—22no—
20C22⋊Q8×C37—21no—
21#121×C37—21no—
22C4×D4×C37C2211yescharacteristic
23C4×D4×C37C2211yescharacteristic
24C2×C4⋊C4×C37—21no—
25#41×C37—42no—
26#41×C37—42no—
27C2×Q8×C37—21no—
28C2×D4×C37—22no—
29C2×D4×C37D411yescharacteristic
30C2×D4×C37D411yescharacteristic
31C22×C4×C37—22no—
32C22×C4×C37—21no—
33C22×C4×C37—21no—
34C2×D148—21no—
35C2×D148—21no—
36C2×D148—21no—
37C4⋊C4×C37—22no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37D411yescharacteristic
40C4⋊C4×C37D411yescharacteristic
41C4⋊C4×C37D412yes—
42C22⋊C4×C37—22no—
43C22⋊C4×C37—21no—
44C22⋊C4×C37—21no—
45C42×C37C2311yescharacteristic
46#10596939—42no—
47#10596939—42no—
48C2×#64436—21no—
49C2×#64436—21no—
50C2×#64436—21no—
51C23×C37—21no—
52C23×C37—21no—
53C22×D37—41no—
54Q8×C37—41no—
55Q8×C37—41no—
56D4×C37—21no—
57D4×C37—21no—
58D4×C37—21no—
59D4×C37—44no—
60D4×C37D812yescomplemented
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—22no—
64C2×C4×C37—44no—
65C2×C4×C37—41no—
66C2×C4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37C2×D411yescharacteristic
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37C2×D411yescharacteristic
72D148—42no—
73D148—41no—
74D148—41no—
75D148—41no—
76D148—41no—
77#64436—41no—
78#64436—41no—
79#64436—41no—
80C22×C37—22no—
81C22×C37—41no—
82C22×C37—41no—
83C22×C37—41no—
84C22×C37—41no—
85C22×C37—41no—
86C22×C37#12011yescharacteristic
87C2×D37—81no—
88C2×D37—81no—
89C2×D37—81no—
90C4×C37—21no—
91C4×C37—41no—
92C4×C37—42no—
93C4×C37—41no—
94C4×C37C2×D811yescharacteristic
95C4×C37#13511yescharacteristic
96C4×C37AGL(1,ℤ/8)11yescharacteristic
97C4×C37AGL(1,ℤ/8)11yescharacteristic
98#1625—371nomaximal, Sylow
99C2×C37—42no—
100C2×C37—81no—
101C2×C37#44711yescharacteristic
102C2×C37#44911yescharacteristic
103C2×C37#45411yescharacteristic
104D37—161no—
105#547D3711yescharacteristic, complemented
106#486—371no—
107#459—371no—
108#459—371no—
109#332—371no—
110D4⋊C8—371no—
111D4⋊C8—371no—
112C37#162511yescharacteristic, complemented, Sylow
113C2×#41—21no—
114C2×D8—741no—
115C2×D8—741no—
116C4⋊Q8C2×D3711yescharacteristic
117#127—371no—
118#123—22no—
119C22⋊Q8—21no—
120#121—21no—
121C4×D4C2×D3711yescharacteristic
122C4×D4C2×D3711yescharacteristic
123C2×C4⋊C4—21no—
124C4⋊C8—371no—
125C4⋊C8—371no—
126#102—741no—
127#102—741no—
128#102—742no—
129C4×C8—371no—
130#41—42no—
131#41—42no—
132C2×Q8—21no—
133C2×D4—22no—
134C2×D4—741no—
135C2×D4—741no—
136C2×D4—741no—
137C2×D4C22⋊D3711yescharacteristic
138C2×D4C22⋊D3711yescharacteristic
139C22×C4—22no—
140C22×C4—21no—
141C22×C4—21no—
142D8—1482no—
143D8—1482no—
144C2×C8—741no—
145C2×C8—741no—
146C2×C8—741no—
147C4⋊C4—22no—
148C4⋊C4—21no—
149C4⋊C4C22⋊D3711yescharacteristic
150C4⋊C4C22⋊D3711yescharacteristic
151C4⋊C4C22⋊D3712yes—
152C22⋊C4—22no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C42C22×D3711yescharacteristic
156C23—21no—
157C23—21no—
158C23—1481no—
159Q8—41no—
160Q8—41no—
161D4—21no—
162D4—21no—
163D4—21no—
164D4—44no—
165D4—1482no—
166D4—1481no—
167D4—1481no—
168D4—1481no—
169D4—1481no—
170D4#1059693912yescomplemented
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—44no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4C2×C22⋊D3711yescharacteristic
180C2×C4C2×C22⋊D3711yescharacteristic
181C2×C4C2×C22⋊D3711yescharacteristic
182C8—1481no—
183C8—1481no—
184C8—1481no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—2961no—
192C22—2961no—
193C22—2961no—
194C22#1192450511yescharacteristic
195C4—21no—
196C4—41no—
197C4—42no—
198C4—41no—
199C4C2×#1059693911yescharacteristic
200C4#1192455611yescharacteristic
201C4#1192456111yescharacteristic
202C4#1192456211yescharacteristic
203C2—42no—
204C2—81no—
205C2—5921no—
206C2#1455766711yescharacteristic
207C2#1455767811yescharacteristic
208C2#1455770611yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#547C2
socleC22×C37#120
hypercenter#547D37
hypocenterC37#1625
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14557881C2semidirect
2. #14557728C2semidirect
3. #14557728C2semidirect
4. #14557279C2semidirect
5. D4⋊#64436C2semidirect
6. D4⋊#64436C2semidirect
7. C37×#547C2semidirect
60. D4×C37D8semidirect
105. #547D37semidirect
112. C37#1625semidirect
170. D4#10596939semidirect

Maximal subgroups

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

subgroupindex
#145578812
#145577282
#145572792
D4⋊#644362
C37×#5472
#162537