Finite Group Databasebeta

← #17993775

Subgroups — #17993775

Order 4736.

308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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#14557879C211yesmaximal, characteristic, complemented
2#14557813C211yesmaximal, characteristic, complemented
3#14557738C211yesmaximal, characteristic, complemented
4#14557277C211yesmaximal, characteristic, complemented
5D4⋊#64436C211yesmaximal, characteristic, complemented
6D4⋊#64436C211yesmaximal, characteristic, complemented
7D42×C37C211yesmaximal, characteristic
8C2×#10596940—21no—
9#11924536C2211yescharacteristic, complemented
10#11924469—21no—
11C4⋊#64436C2211yescharacteristic, complemented
12C4⋊#64436C2211yescharacteristic, complemented
13#11924459—21no—
14#11924457—21no—
15#11924457—22no—
16C4×#64436C2211yescharacteristic, complemented
17C22×D4×C37—21no—
18C22×D4×C37—21no—
19#127×C37C2211yescharacteristic
20#121×C37—21no—
21#121×C37—21no—
22#120×C37—22no—
23C4×D4×C37C2211yescharacteristic
24C4×D4×C37C2211yescharacteristic
25C24×C37—22no—
26C2×D4×C37—22no—
27C2×D4×C37—22no—
28C2×D4×C37—21no—
29C2×D4×C37—21no—
30C2×D4×C37—42no—
31C2×D4×C37—42no—
32C2×D4×C37—42no—
33C2×D4×C37—42no—
34C2×D4×C37D411yescharacteristic
35C2×D4×C37D411yescharacteristic
36C2×D4×C37D412yes—
37C22×C4×C37—21no—
38C22×C4×C37—21no—
39C2×Dic74—21no—
40C4⋊C4×C37D411yescharacteristic
41C4⋊C4×C37D411yescharacteristic
42C22⋊C4×C37—22no—
43C22⋊C4×C37—21no—
44C22⋊C4×C37—21no—
45C42×C37C2311yescharacteristic
46#10596940—42no—
47C4⋊Dic37—21no—
48C4⋊Dic37—21no—
49C2×#64436—21no—
50C2×#64436—21no—
51C2×#64436—21no—
52C23×C37—21no—
53C23×C37—21no—
54C23×C37—22no—
55C23×C37—44no—
56C23×C37—44no—
57C23×C37—82no—
58D4×C37—21no—
59D4×C37—21no—
60D4×C37—42no—
61D4×C37—44no—
62D4×C37—44no—
63D4×C37—41no—
64D4×C37—41no—
65D4×C37—41no—
66D4×C37—41no—
67D4×C37D812yes—
68D4×C37SD1612yescomplemented
69C2×C4×C37—21no—
70C2×C4×C37—21no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37—41no—
74C2×C4×C37—41no—
75C2×C4×C37C2×D411yescharacteristic
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×Dic37—41no—
79Dic74—41no—
80Dic74—41no—
81#64436—41no—
82#64436—41no—
83#64436—41no—
84C22×C37—22no—
85C22×C37—22no—
86C22×C37—41no—
87C22×C37—41no—
88C22×C37—41no—
89C22×C37—41no—
90C22×C37—42no—
91C22×C37—42no—
92C22×C37—42no—
93C22×C37—88no—
94C22×C37#12011yescharacteristic
95C4×C37—21no—
96C4×C37—41no—
97C4×C37—41no—
98C4×C37C2×D811yescharacteristic
99C4×C37C2×SD1611yescharacteristic
100C4×C37AGL(1,ℤ/8)11yescharacteristic
101C4×C37AGL(1,ℤ/8)11yescharacteristic
102Dic37—81no—
103#1639—371nomaximal, Sylow
104C2×C37—42no—
105C2×C37—42no—
106C2×C37—82no—
107C2×C37#44711yescharacteristic
108C2×C37#45011yescharacteristic
109C2×C37#45511yescharacteristic
110D42D3711yescharacteristic
111#486—371no—
112#474—371no—
113#461—371no—
114#331—371no—
115D4⋊C8—371no—
116D4⋊C8—371no—
117C37#163911yescharacteristic, complemented, Sylow
118C22×D4—21no—
119C22×D4—21no—
120C2×SD16—741no—
121C4⋊Q8—371no—
122#127C2×D3711yescharacteristic
123#121—21no—
124#121—21no—
125#120—22no—
126C4×D4C2×D3711yescharacteristic
127C4×D4C2×D3711yescharacteristic
128#107—741no—
129C4⋊C8—371no—
130C4⋊C8—371no—
131#103—741no—
132#102—741no—
133#102—742no—
134C4×C8—371no—
135C24—22no—
136C2×Q8—741no—
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—42no—
142C2×D4—42no—
143C2×D4—42no—
144C2×D4—42no—
145C2×D4C22⋊D3711yescharacteristic
146C2×D4C22⋊D3711yescharacteristic
147C2×D4C22⋊D3712yes—
148C22×C4—21no—
149C22×C4—21no—
150SD16—1482no—
151C2×C8—741no—
152C2×C8—741no—
153C2×C8—741no—
154C4⋊C4—741no—
155C4⋊C4—741no—
156C4⋊C4C22⋊D3711yescharacteristic
157C4⋊C4C22⋊D3711yescharacteristic
158C22⋊C4—22no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C42C22×D3711yescharacteristic
162C23—21no—
163C23—21no—
164C23—22no—
165C23—44no—
166C23—44no—
167C23—82no—
168Q8—1481no—
169Q8—1481no—
170D4—21no—
171D4—21no—
172D4—42no—
173D4—44no—
174D4—44no—
175D4—41no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4#1059693912yes—
180D4#1059694012yescomplemented
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—1481no—
188C2×C4C2×C22⋊D3711yescharacteristic
189C2×C4C2×C22⋊D3711yescharacteristic
190C2×C4C2×C22⋊D3711yescharacteristic
191C8—1481no—
192C8—1481no—
193C8—1481no—
194C22—22no—
195C22—22no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—41no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—88no—
204C22#1192450511yescharacteristic
205C4—21no—
206C4—41no—
207C4—41no—
208C4—2961no—
209C4C2×#1059693911yescharacteristic
210C4C2×#1059694011yescharacteristic
211C4#1192456211yescharacteristic
212C4#1192456211yescharacteristic
213C2—42no—
214C2—42no—
215C2—82no—
216C2#1455766711yescharacteristic
217C2#1455768411yescharacteristic
218C2#1455771111yescharacteristic
subgroupG/H
centerC22#11924505
commutator, cosocleC42×C37C23
FrattiniC42C22×D37
Fitting, prime radicalD42×C37C2
socleC22×C37#120
hypercenterD42D37
hypocenterC37#1639
LCSG ▷ C42×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #14557879C2semidirect
2. #14557813C2semidirect
3. #14557738C2semidirect
4. #14557277C2semidirect
5. D4⋊#64436C2semidirect
6. D4⋊#64436C2semidirect
9. #11924536C22semidirect
11. C4⋊#64436C22semidirect
12. C4⋊#64436C22semidirect
16. C4×#64436C22semidirect
68. D4×C37SD16semidirect
117. C37#1639semidirect
180. D4#10596940semidirect

Maximal subgroups

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

subgroupindex
#145578792
#145578132
#145577382
#145572772
D4⋊#644362
D42×C372
#163937