Finite Group Databasebeta

← #17993824

Subgroups — #17993824

Order 4736.

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

normal subgroups only

This group has 212 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#14557883C211yesmaximal, characteristic, complemented
2#14557813C211yesmaximal, characteristic, complemented
3#14557738C211yesmaximal, characteristic, complemented
4#14557282C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic, complemented
7C37×#555C211yesmaximal, characteristic
8C2×#10596940—21no—
9#11924536C2211yescharacteristic
10#11924469—21no—
11C4⋊#64436C2211yescharacteristic
12C4⋊#64436C2211yescharacteristic
13#11924460—22no—
14#11924459—21no—
15#11924457—21no—
16C4×#64436C2211yescharacteristic
17C4⋊Q8×C37C2211yescharacteristic
18#124×C37—22no—
19#121×C37—21no—
20#121×C37—21no—
21C4×D4×C37C2211yescharacteristic
22C4×D4×C37C2211yescharacteristic
23#117×C37—21no—
24#117×C37—21no—
25C2×Q8×C37D412yes—
26C2×D4×C37—22no—
27C2×D4×C37D411yescharacteristic
28C2×D4×C37D411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37—21no—
31C2×Dic74—21no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊C4×C37D411yescharacteristic
35C4⋊C4×C37D411yescharacteristic
36C22⋊C4×C37—22no—
37C22⋊C4×C37—22no—
38C22⋊C4×C37—21no—
39C22⋊C4×C37—21no—
40C42×C37—22no—
41C42×C37C2311yescharacteristic
42#10596940—42no—
43C4⋊Dic37—21no—
44C4⋊Dic37—21no—
45C2×#64436—21no—
46C2×#64436—21no—
47C2×#64436—21no—
48C23×C37—21no—
49C23×C37—21no—
50Q8×C37—42no—
51D4×C37—21no—
52D4×C37—21no—
53D4×C37—21no—
54D4×C37—21no—
55D4×C37—82no—
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37—22no—
59C2×C4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37—41no—
62C2×C4×C37—41no—
63C2×C4×C37C2×D411yescharacteristic
64C2×C4×C37C2×D411yescharacteristic
65C2×C4×C37C2×D411yescharacteristic
66C2×Dic37—41no—
67Dic74—41no—
68Dic74—41no—
69#64436—41no—
70#64436—41no—
71#64436—41no—
72C22×C37—41no—
73C22×C37—41no—
74C22×C37—41no—
75C22×C37—41no—
76C22×C37—41no—
77C22×C37—41no—
78C22×C37#12011yescharacteristic
79C4×C37—21no—
80C4×C37—41no—
81C4×C37—41no—
82C4×C37—42no—
83C4×C37#13511yescharacteristic
84C4×C37#13511yescharacteristic
85C4×C37AGL(1,ℤ/8)11yescharacteristic
86C4×C37#13711yescharacteristic
87Dic37—81no—
88#1646—371nomaximal, Sylow
89C2×C37—81no—
90C2×C37—81no—
91C2×C37#44911yescharacteristic
92C2×C37#45211yescharacteristic
93C2×C37#45511yescharacteristic
94#555D3711yescharacteristic
95#487—371no—
96#474—371no—
97#461—371no—
98#333—371no—
99D4⋊C8—371no—
100D4⋊C8—371no—
101C37#164611yescharacteristic, complemented, Sylow
102C2×SD16—741no—
103C4⋊Q8—371no—
104C4⋊Q8C2×D3711yescharacteristic
105#124—22no—
106#121—21no—
107#121—21no—
108C4×D4C2×D3711yescharacteristic
109C4×D4C2×D3711yescharacteristic
110#117—21no—
111#117—21no—
112#107—741no—
113C4⋊C8—371no—
114C4⋊C8—371no—
115#103—742no—
116#103—741no—
117#102—741no—
118C4×C8—371no—
119C2×Q8—741no—
120C2×Q8C22⋊D3712yes—
121C2×D4—22no—
122C2×D4C22⋊D3711yescharacteristic
123C2×D4C22⋊D3711yescharacteristic
124C22×C4—21no—
125C22×C4—21no—
126SD16—1482no—
127C2×C8—741no—
128C2×C8—741no—
129C2×C8—741no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—741no—
133C4⋊C4—741no—
134C4⋊C4C22⋊D3711yescharacteristic
135C4⋊C4C22⋊D3711yescharacteristic
136C22⋊C4—22no—
137C22⋊C4—22no—
138C22⋊C4—21no—
139C22⋊C4—21no—
140C42—22no—
141C42C22×D3711yescharacteristic
142C23—21no—
143C23—21no—
144Q8—42no—
145Q8—1481no—
146Q8—1481no—
147D4—21no—
148D4—21no—
149D4—21no—
150D4—21no—
151D4—82no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—1481no—
160C2×C4C2×C22⋊D3711yescharacteristic
161C2×C4C2×C22⋊D3711yescharacteristic
162C2×C4C2×C22⋊D3711yescharacteristic
163C8—1481no—
164C8—1481no—
165C8—1481no—
166C22—41no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22#1192450511yescharacteristic
173C4—21no—
174C4—42no—
175C4—41no—
176C4—41no—
177C4—2961no—
178C4#1192455611yescharacteristic
179C4#1192455611yescharacteristic
180C4#1192456111yescharacteristic
181C4#1192456611yescharacteristic
182C2—81no—
183C2—81no—
184C2#1455767811yescharacteristic
185C2#1455769511yescharacteristic
186C2#1455771111yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
Fitting, prime radicalC37×#555C2
socleC22×C37#120
hypercenter#555D37
hypocenterC37#1646
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #14557883C2semidirect
2. #14557813C2semidirect
3. #14557738C2semidirect
4. #14557282C2semidirect
5. D4⋊#64436C2semidirect
6. D4⋊#64436C2semidirect
101. C37#1646semidirect

Maximal subgroups

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

subgroupindex
#145578832
#145578132
#145577382
#145572822
D4⋊#644362
C37×#5552
#164637