Finite Group Databasebeta

← #17993844

Subgroups — #17993844

Order 4736.

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

normal subgroups only

This group has 234 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
1D4×Dic74C211yesmaximal, characteristic
2#14557936C211yesmaximal, characteristic, complemented
3#14557740C211yesmaximal, characteristic, complemented
4#14557278C211yesmaximal, characteristic, complemented
5#14557263C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic
7C37×#474C211yesmaximal, characteristic
8C22×Dic74—21no—
9C2×#10596942—21no—
10#11924536C2211yescharacteristic
11#11924535—21no—
12#11924515—21no—
13#11924513—22no—
14C4×Dic74C2211yescharacteristic
15D4×Dic37—21no—
16#11924469—22no—
17C4⋊#64436C2211yescharacteristic
18#11924460—21no—
19C4×#64436C2211yescharacteristic
20C4⋊Q8×C37C2211yescharacteristic
21C4×D4×C37C2211yescharacteristic
22#107×C37—21no—
23C4⋊C8×C37C2211yescharacteristic
24#102×C37—21no—
25C2×Q8×C37—21no—
26C2×D4×C37D411yescharacteristic
27C22×C4×C37—21no—
28C22×Dic37—22no—
29C2×Dic74—22no—
30C2×Dic74—21no—
31C2×Dic74—42no—
32C2×Dic74—42no—
33C2×Dic74D411yescharacteristic
34C2×C8×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37—21no—
37C4⋊C4×C37D411yescharacteristic
38C22⋊C4×C37—21no—
39C42×C37C2311yescharacteristic
40C22⋊Dic37—22no—
41#10596942—42no—
42C4⋊Dic37—21no—
43C4⋊Dic37D411yescharacteristic
44C4⋊Dic37D412yes—
45#10596936—22no—
46#10596936—21no—
47C4×Dic37—21no—
48C2×#64436—21no—
49C2×#64436—21no—
50C23×C37—21no—
51Q8×C37—41no—
52Q8×C37—41no—
53D4×C37—21no—
54D4×C37Q1612yescomplemented
55C2×C4×C37—21no—
56C2×C4×C37—41no—
57C2×C4×C37—41no—
58C2×C4×C37—41no—
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×C4×C37C2×D411yescharacteristic
62C2×Dic37—21no—
63C2×Dic37—21no—
64C2×Dic37—22no—
65C2×Dic37—44no—
66Dic74—21no—
67Dic74—44no—
68Dic74—41no—
69Dic74—41no—
70Dic74D812yes—
71C8×C37—41no—
72#64436—22no—
73#64436—41no—
74C22×C37—22no—
75C22×C37—41no—
76C22×C37—41no—
77C22×C37#12011yescharacteristic
78C4×C37—21no—
79C4×C37—41no—
80C4×C37—81no—
81C4×C37C2×D811yescharacteristic
82C4×C37C2×Q1611yescharacteristic
83C4×C37AGL(1,ℤ/8)11yescharacteristic
84C4×C37#13711yescharacteristic
85Dic37—22no—
86Dic37—42no—
87Dic37—41no—
88#1649—371nomaximal, Sylow
89C2×C37—42no—
90C2×C37#44711yescharacteristic
91C2×C37#45111yescharacteristic
92C2×C37#45611yescharacteristic
93D4×Q8—371no—
94#500—371no—
95#474D3711yescharacteristic
96#462—371no—
97#332—371no—
98Q8⋊C8—371no—
99D4⋊C8—371no—
100C37#164911yescharacteristic, complemented, Sylow
101C22×Q8—741no—
102C2×Q16—741no—
103C4⋊Q8—371no—
104C4⋊Q8—741no—
105C4⋊Q8C2×D3711yescharacteristic
106C22⋊Q8—742no—
107C22⋊Q8—741no—
108C4×Q8—371no—
109C4×D4—741no—
110C4×D4C2×D3711yescharacteristic
111#107—21no—
112#107—742no—
113C4⋊C8—371no—
114C4⋊C8C2×D3711yescharacteristic
115#103—741no—
116#102—21no—
117C4×C8—371no—
118C2×Q8—21no—
119C2×Q8—371no—
120C2×Q8—742no—
121C2×Q8—741no—
122C2×Q8—1482no—
123C2×Q8—1482no—
124C2×D4C22⋊D3711yescharacteristic
125C22×C4—21no—
126C22×C4—742no—
127Q16—1482no—
128C2×C8—21no—
129C2×C8—741no—
130C2×C8—741no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—371no—
134C4⋊C4—372no—
135C4⋊C4—742no—
136C4⋊C4—741no—
137C4⋊C4—741no—
138C4⋊C4C22⋊D3711yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—742no—
141C42—741no—
142C42C22×D3711yescharacteristic
143C23—21no—
144Q8—41no—
145Q8—41no—
146Q8—372no—
147Q8—741no—
148Q8—1484no—
149Q8—1481no—
150Q8—1481no—
151D4—21no—
152D4#1059694212yescomplemented
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—741no—
158C2×C4—741no—
159C2×C4—742no—
160C2×C4—1484no—
161C2×C4D4×D3711yescharacteristic
162C2×C4D4×D3711yescharacteristic
163C2×C4C2×C22⋊D3711yescharacteristic
164C8—41no—
165C8—742no—
166C8—1481no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#1192450411yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—742no—
175C4—1481no—
176C4—1482no—
177C4D8×D3711yescharacteristic
178C4C2×#1059694211yescharacteristic
179C4#1192456011yescharacteristic
180C4#1192456611yescharacteristic
181C2—42no—
182C2#1455766511yescharacteristic
183C2#1455768811yescharacteristic
184C2#1455771411yescharacteristic
subgroupG/H
centerC22#11924504
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
FittingC37×#474C2
socleC22×C37#120
prime radicalC2×D4×C37D4
hypercenter#474D37
hypocenterC37#1649
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #14557936C2semidirect
3. #14557740C2semidirect
4. #14557278C2semidirect
5. #14557263C2semidirect
54. D4×C37Q16semidirect
100. C37#1649semidirect
152. D4#10596942semidirect

Maximal subgroups

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

subgroupindex
D4×Dic742
#145579362
#145577402
#145572782
#145572632
D4⋊#644362
C37×#4742
#164937