Finite Group Databasebeta

← #18005251

Subgroups — #18005251

Order 4736.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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#14558141C212yesmaximal
2#14557934C211yesmaximal, characteristic, complemented
3#14557911C211yesmaximal, characteristic, complemented
4#14557900C212yesmaximal, complemented
5#14557790C212yesmaximal
6#14557775C211yesmaximal, characteristic
7#14557771C211yesmaximal, characteristic
8#14557638C212yesmaximal, complemented
9C4×Dic148C211yesmaximal, characteristic, complemented
10#14557487C211yesmaximal, characteristic
11C4×Q16×C37C211yesmaximal, characteristic, complemented
12C2×Dic148C2211yescharacteristic
13C2×#10596942C2212yes—
14C2×#10596929C2211yescharacteristic
15C2×C8×D37C2211yescharacteristic
16#11924534C2212yes—
17#11924531—22no—
18#11924530—22no—
19#11924528—22no—
20#11924527C2212yes—
21#11924526—22no—
22#11924516C2212yes—
23#11924512C2212yes—
24C4×Dic74C2212yes—
25#11924493C2211yescharacteristic
26#11924470C2211yescharacteristic
27#11924467C2212yes—
28#11924461C2212yes—
29#11924460C2212yes—
30#11924459C2212yes—
31#11924447C2211yescharacteristic
32#11924446C2211yescharacteristic
33C8×Dic37C2211yescharacteristic
34C2×Q16×C37C2211yescharacteristic
35C4×Q8×C37C2212yes—
36#107×C37C2211yescharacteristic
37#103×C37C2212yes—
38C4×C8×C37C2211yescharacteristic
39C2×Q8×C37C2312yes—
40C2×C4×D37C2311yescharacteristic
41C2×Dic74C2312yes—
42Q16×C37—22no—
43C2×C8×C37C2311yescharacteristic
44C2×C8×C37C2311yescharacteristic
45C4⋊C4×C37—22no—
46C4⋊C4×C37C2312yes—
47C42×C37—22no—
48C42×C37C2311yescharacteristic
49#10596942—24no—
50#10596938—22no—
51#10596938—22no—
52#10596938D411yescharacteristic
53#10596938D411yescharacteristic
54C4⋊Dic37—22no—
55C4⋊Dic37—22no—
56C4⋊Dic37C2312yes—
57#10596936—22no—
58#10596936—22no—
59#10596936—22no—
60#10596936—22no—
61#10596936—22no—
62#10596936D411yescharacteristic
63#10596936D411yescharacteristic
64C4×Dic37—22no—
65C4×Dic37C2311yescharacteristic
66C2×#64436C2311yescharacteristic
67C2×#64436C2311yescharacteristic
68Dic148—22no—
69#10596929—22no—
70C8×D37—22no—
71C22×D37C2×D411yescharacteristic
72Q8×C37—22no—
73Q8×C37—22no—
74C2×C4×C37—22no—
75C2×C4×C37—22no—
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2411yescharacteristic
79C2×Dic37—22no—
80C2×Dic37—22no—
81C2×Dic37C2×D411yescharacteristic
82C2×Dic37C2×D411yescharacteristic
83C2×Dic37C2×D411yescharacteristic
84C4×D37—21no—
85C4×D37—21no—
86Dic74—22no—
87Dic74—22no—
88C8×C37—21no—
89C8×C37#4112yes—
90#64436—21no—
91#64436#4112yes—
92C22×C37C22×D411yescharacteristic
93C2×D37—21no—
94C2×D37—21no—
95C2×D37—21no—
96C4×C37—21no—
97C4×C37—21no—
98C4×C37—42no—
99C4×C37—42no—
100C4×C37C2×#4111yescharacteristic
101C4×C37C2×#4111yescharacteristic
102Dic37—21no—
103Dic37—21no—
104Dic37—21no—
105Dic37—42no—
106Dic37—42no—
107#3177—371nomaximal, Sylow
108C2×C37#53211yescharacteristic
109C2×C37#57811yescharacteristic
110C2×C37#57811yescharacteristic
111D37—41no—
112#541—372no—
113#499—371no—
114#494—371no—
115#491—372no—
116#470—372no—
117#467—371no—
118#467—371no—
119#441—372no—
120C4×Q16—371no—
121C4×Q16D3711yescharacteristic, complemented
122#405—371no—
123C37#317711yescharacteristic, complemented, Sylow
124C2×Q16—372no—
125C2×Q16—371no—
126C2×Q16C2×D3711yescharacteristic
127C2×M16—371no—
128C22×C8—371no—
129C4⋊Q8—372no—
130#126—742no—
131#126—742no—
132#125—372no—
133#125—742no—
134#125—742no—
135C22⋊Q8—372no—
136C22⋊Q8—372no—
137C4×Q8—372no—
138C4×Q8C2×D3712yes—
139#117—371no—
140#107—371no—
141#107C2×D3711yescharacteristic
142#106—372no—
143#103—372no—
144#103—372no—
145#103—372no—
146#103C2×D3712yes—
147#97—371no—
148#97—371no—
149C4×C8—371no—
150C4×C8C2×D3711yescharacteristic
151C2×Q8—372no—
152C2×Q8C22×D3712yes—
153C22×C4—371no—
154Q16—22no—
155Q16—744no—
156Q16—742no—
157M16—742no—
158C2×C8—371no—
159C2×C8—371no—
160C2×C8—742no—
161C2×C8C22×D3711yescharacteristic
162C2×C8C22×D3711yescharacteristic
163C4⋊C4—22no—
164C4⋊C4—371no—
165C4⋊C4—371no—
166C4⋊C4—372no—
167C4⋊C4—742no—
168C4⋊C4—742no—
169C4⋊C4—742no—
170C4⋊C4—742no—
171C4⋊C4—742no—
172C4⋊C4—742no—
173C4⋊C4—742no—
174C4⋊C4C22×D3712yes—
175C22⋊C4—371no—
176C22⋊C4—371no—
177C22⋊C4—742no—
178C22⋊C4—742no—
179C42—22no—
180C42—371no—
181C42—742no—
182C42C22×D3711yescharacteristic
183C23—371no—
184Q8—22no—
185Q8—22no—
186Q8—742no—
187Q8—742no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—371no—
191C2×C4—371no—
192C2×C4—371no—
193C2×C4—741no—
194C2×C4—741no—
195C2×C4—742no—
196C2×C4—742no—
197C2×C4D4×D3711yescharacteristic
198C2×C4D4×D3711yescharacteristic
199C2×C4C23×D3711yescharacteristic
200C8—21no—
201C8—372no—
202C8—741no—
203C8#1059696212yes—
204C22—741no—
205C22—741no—
206C22—741no—
207C22C2×D4×D3711yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—42no—
212C4—741no—
213C4—741no—
214C4—741no—
215C4—1482no—
216C4—1482no—
217C4#41×D3711yescharacteristic
218C4C2×#1059696211yescharacteristic
219C2—1481no—
220C2#1455808011yescharacteristic
221C2#1455834611yescharacteristic
222C2#1455834711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC4×Q16×C37C2
socleC22×C37C22×D4
prime radicalC22×D37C2×D4
hypercenterC4×Q16D37
hypocenterC37#3177
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. #14557934C2semidirect
3. #14557911C2semidirect
4. #14557900C2semidirect
8. #14557638C2semidirect
9. C4×Dic148C2semidirect
11. C4×Q16×C37C2semidirect
121. C4×Q16D37semidirect
123. C37#3177semidirect

Maximal subgroups

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

subgroupindex
#145581412
#145579342
#145579112
#145579002
#145577902
#145577752
#145577712
#145576382
C4×Dic1482
#145574872
C4×Q16×C372
#317737