Finite Group Databasebeta

← #18005126

Subgroups — #18005126

Order 4736.

340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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#14558164C211yesmaximal, characteristic
2#14558161C211yesmaximal, characteristic
3#14557941C212yesmaximal, complemented
4#14557940C212yesmaximal, complemented
5#14557934C212yesmaximal, complemented
6#14557930C212yesmaximal, complemented
7#14557575C211yesmaximal, characteristic
8#14557569C211yesmaximal, characteristic
9C2×#11924467C211yesmaximal, characteristic
10#14557491C211yesmaximal, characteristic
11C37×#428C211yesmaximal, characteristic
12C22×#64436C2211yescharacteristic
13#11924536—21no—
14#11924535—21no—
15#11924535C2212yes—
16#11924535C2212yes—
17#11924528—21no—
18#11924527—21no—
19#11924527C2212yes—
20#11924527C2212yes—
21#11924515—22no—
22#11924513—22no—
23#11924495C2211yescharacteristic
24#11924495C2211yescharacteristic
25C2×C4⋊Dic37C2211yescharacteristic
26#11924470C2212yes—
27#11924469C2211yescharacteristic
28#11924469C2211yescharacteristic
29#11924468C2212yes—
30#11924467C2212yes—
31#11924467C2212yes—
32#11924467C2211yescharacteristic
33#11924467C2211yescharacteristic
34#11924446C2212yes—
35C8×Dic37C2212yes—
36C2×M16×C37C2211yescharacteristic
37#117×C37C2211yescharacteristic
38C2×C4⋊C4×C37C2211yescharacteristic
39#107×C37C2212yes—
40#106×C37C2212yes—
41C22×C4×C37—21no—
42C22×C4×C37C2311yescharacteristic
43C22×Dic37—21no—
44C2×Dic74—22no—
45C2×Dic74—22no—
46M16×C37Q814yescomplemented
47C2×C8×C37C2312yes—
48C4⋊C4×C37—21no—
49C4⋊C4×C37C2311yescharacteristic
50C4⋊C4×C37C2312yes—
51C4⋊C4×C37C2311yescharacteristic
52C22⋊C4×C37—21no—
53C42×C37—21no—
54C22⋊Dic37—21no—
55C22⋊Dic37D412yes—
56C4⋊Dic37—21no—
57C4⋊Dic37—22no—
58C4⋊Dic37—22no—
59C4⋊Dic37D411yescharacteristic
60C4⋊Dic37D411yescharacteristic
61C4⋊Dic37C2312yes—
62C4⋊Dic37C2311yescharacteristic
63C4⋊Dic37C2311yescharacteristic
64#10596936—22no—
65#10596936—22no—
66#10596936—22no—
67#10596936—22no—
68C4×Dic37—21no—
69C4×Dic37C2312yes—
70C2×#64436Q814yescomplemented
71C2×#64436C2311yescharacteristic
72C2×#64436C2311yescharacteristic
73C23×C37C2×D411yescharacteristic
74C2×C4×C37—21no—
75C2×C4×C37—22no—
76C2×C4×C37—21no—
77C2×C4×C37—81no—
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×Q812yes—
80C2×C4×C37C2×Q812yes—
81C2×C4×C37C2411yescharacteristic
82C2×Dic37—21no—
83C2×Dic37—21no—
84C2×Dic37—22no—
85C2×Dic37—81no—
86C2×Dic37C2×D412yes—
87C2×Dic37C2×D412yes—
88Dic74—82no—
89Dic74—82no—
90C8×C37C2×Q814yes—
91#64436C2×Q812yes—
92#64436C2×Q812yes—
93C22×C37—21no—
94C22×C37—21no—
95C22×C37C4⋊Q812yes—
96C22×C37C22×D411yescharacteristic
97C4×C37—41no—
98C4×C37—42no—
99C4×C37—41no—
100C4×C37C4⋊Q812yes—
101C4×C37C22×Q811yescharacteristic
102C4×C37C22×Q811yescharacteristic
103Dic37—22no—
104Dic37—22no—
105Dic37—41no—
106Dic37—42no—
107Dic37—41no—
108#3163—371nomaximal, Sylow
109C2×C37—22no—
110C2×C37C2×C4⋊Q811yescharacteristic
111C2×C37#57711yescharacteristic
112C2×C37#57711yescharacteristic
113#544—371no—
114#544—371no—
115#501—372no—
116#501—372no—
117#499—372no—
118#498—372no—
119#428—371no—
120#428D3711yescharacteristic
121#427—371no—
122C2×#106—371no—
123#405—371no—
124C37#316311yescharacteristic, complemented, Sylow
125C2×M16C2×D3711yescharacteristic
126C22×C8—371no—
127C4⋊Q8—372no—
128C4⋊Q8—372no—
129C4⋊Q8—741no—
130C4⋊Q8—741no—
131#125—372no—
132#125—372no—
133#125—741no—
134#125—741no—
135C22⋊Q8—742no—
136C22⋊Q8—742no—
137#117—371no—
138#117—371no—
139#117C2×D3711yescharacteristic
140C2×C4⋊C4—371no—
141C2×C4⋊C4C2×D3711yescharacteristic
142#107—372no—
143#107—371no—
144#107—371no—
145#107C2×D3712yes—
146#106—372no—
147#106—372no—
148#106—372no—
149#106—371no—
150#106—371no—
151#106C2×D3712yes—
152#97—372no—
153C4×C8—372no—
154C2×Q8—742no—
155C2×Q8—742no—
156C22×C4—21no—
157C22×C4—741no—
158C22×C4C22×D3711yescharacteristic
159M16Dic7414yescomplemented
160C2×C8—374no—
161C2×C8—371no—
162C2×C8—371no—
163C2×C8C22×D3712yes—
164C4⋊C4—21no—
165C4⋊C4—371no—
166C4⋊C4—371no—
167C4⋊C4—372no—
168C4⋊C4—371no—
169C4⋊C4—371no—
170C4⋊C4—742no—
171C4⋊C4—742no—
172C4⋊C4—742no—
173C4⋊C4—742no—
174C4⋊C4—742no—
175C4⋊C4—742no—
176C4⋊C4—741no—
177C4⋊C4C22×D3712yes—
178C4⋊C4C22×D3711yescharacteristic
179C4⋊C4C22×D3711yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—372no—
182C22⋊C4—741no—
183C42—21no—
184C42—372no—
185C42—741no—
186C23D4×D3711yescharacteristic
187Q8—2962no—
188Q8—2962no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—81no—
193C2×C4—372no—
194C2×C4—372no—
195C2×C4—2961no—
196C2×C4—741no—
197C2×C4—741no—
198C2×C4—742no—
199C2×C4C2×Dic7412yes—
200C2×C4D4×D3711yescharacteristic
201C2×C4Q8×D3712yes—
202C2×C4C23×D3711yescharacteristic
203C8—372no—
204C8—372no—
205C8C2×Dic7414yes—
206C22—21no—
207C22—21no—
208C22#1192453512yes—
209C22C2×D4×D3711yescharacteristic
210C4—41no—
211C4—42no—
212C4—41no—
213C4—742no—
214C4—742no—
215C4—1482no—
216C4—1481no—
217C4—1481no—
218C4#1192453512yes—
219C4C2×Q8×D3711yescharacteristic
220C4C22×Dic7411yescharacteristic
221C2—22no—
222C2C2×#1192453511yescharacteristic
223C2#1455834211yescharacteristic
224C2#1455834311yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#428C2
socleC22×C37C22×D4
prime radicalC23×C37C2×D4
hypercenter#428D37
hypocenterC37#3163
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #14557941C2semidirect
4. #14557940C2semidirect
5. #14557934C2semidirect
6. #14557930C2semidirect
46. M16×C37Q8semidirect
70. C2×#64436Q8semidirect
124. C37#3163semidirect
159. M16Dic74semidirect

Maximal subgroups

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

subgroupindex
#145581642
#145581612
#145579412
#145579402
#145579342
#145579302
#145575752
#145575692
C2×#119244672
#145574912
C37×#4282
#316337