Finite Group Databasebeta

← #18010647

Subgroups — #18010647

Order 4736.

340 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 66 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#14558611C211yesmaximal, characteristic, complemented
2#14558520C211yesmaximal, characteristic, complemented
3C2×#11924596C212yesmaximal, complemented
4#14558414C212yesmaximal, complemented
5#14558098C211yesmaximal, characteristic
6#11924623—24no—
7D37⋊M16—21no—
8C2×#10596957—21no—
9C2×#10596957C2212yes—
10C2×#10596957C2212yes—
11#11924597—21no—
12#11924596—21no—
13#11924596—24no—
14C2×#10596964C2211yescharacteristic
15C22×C22⋊D37C2211yescharacteristic
16#11924532—21no—
17#11924522—21no—
18#11924509—21no—
19#11924508—21no—
20#11924506C411yescharacteristic
21#11924505C411yescharacteristic
22#11924504C411yescharacteristic
23#11924492C2211yescharacteristic
24#120×C37C411yescharacteristic
25C24×C37C2×C411yescharacteristic
26C23×D37C2×C411yescharacteristic
27C2×D4×C37—21no—
28C2×D4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32C2×C22⋊D37—21no—
33C2×C22⋊D37—22no—
34C2×C22⋊D37—22no—
35C2×C22⋊D37C2×C411yescharacteristic
36C2×C22⋊D37D411yescharacteristic
37C22×Dic37D411yescharacteristic
38C22×Dic37C2311yescharacteristic
39#10596964—22no—
40#10596964—22no—
41C2×D148—21no—
42C2×C4×D37D411yescharacteristic
43C2×Dic74D411yescharacteristic
44#10596957—22no—
45#10596957—22no—
46#10596957—22no—
47#10596957—22no—
48#10596957D414yescomplemented
49C2×#64438—22no—
50C2×#64438—22no—
51C2×#64438—22no—
52#10596953—22no—
53D37⋊C8—22no—
54C22⋊C4×C37—21no—
55C22⋊C4×C37C2×C411yescharacteristic
56C22⋊Dic37—21no—
57C22⋊Dic37C2×C411yescharacteristic
58#10596938—21no—
59#10596938—21no—
60#10596936—21no—
61C4×Dic37—21no—
62C23×C37—21no—
63C23×C37—22no—
64C23×C37—81no—
65C23×C37C22⋊C411yescharacteristic
66C23×C37C22×C411yescharacteristic
67C22×D37—21no—
68C22×D37—22no—
69C22×D37—81no—
70C22×D37C22⋊C411yescharacteristic
71D4×C37—22no—
72D4×C37—81no—
73C2×C4×C37—21no—
74C2×C4×C37C22⋊C411yescharacteristic
75C22⋊D37—22no—
76C22⋊D37—22no—
77C22⋊D37—41no—
78C22⋊D37—42no—
79C22⋊D37—41no—
80C22⋊D37—81no—
81C22⋊D37—81no—
82C2×Dic37—21no—
83C2×Dic37—21no—
84C2×Dic37—21no—
85C2×Dic37C22⋊C411yescharacteristic
86C2×Dic37C2×D412yes—
87C2×Dic37C2×D411yescharacteristic
88C2×Dic37C2×D411yescharacteristic
89C2×Dic37#4112yes—
90D148—81no—
91C4×D37—21no—
92C4×D37—21no—
93Dic74—22no—
94#64438—24no—
95#64438—42no—
96C22×C37—21no—
97C22×C37—41no—
98C22×C37—41no—
99C22×C37—41no—
100C22×C37—41no—
101C22×C37—41no—
102C22×C37—82no—
103C22×C37C2×C22⋊C411yescharacteristic
104C22×C37C4×D412yes—
105C2×D37—21no—
106C2×D37—41no—
107C2×D37—41no—
108C2×D37—41no—
109C2×D37—41no—
110C2×D37—82no—
111C4×C37—21no—
112C4×C37—41no—
113Dic37—21no—
114Dic37—41no—
115Dic37#12011yescharacteristic
116Dic37#12112yes—
117Dic37#12311yescharacteristic
118#1914—371nomaximal, Sylow
119C2×C37—21no—
120C2×C37—22no—
121C2×C37—41no—
122C2×C37—81no—
123C2×C37#38611yescharacteristic
124D37—41no—
125D37—81no—
126#568—371no—
127#535—371no—
128#413—371no—
129C2×#100—372no—
130#344—372no—
131C37#191411yescharacteristic, complemented, Sylow
132C2×#41—371no—
133C22×D4—371no—
134#131—744no—
135C2×M16—372no—
136C2×M16—372no—
137C2×M16—741no—
138C2×M16—741no—
139#127—741no—
140#124—741no—
141#121—741no—
142#121—741no—
143#120—371no—
144#120—371no—
145#120—371no—
146#120#386611yescharacteristic
147#117—371no—
148#101—741no—
149#100—744no—
150#100—741no—
151C24—371no—
152C24C2×#386611yescharacteristic
153#41—742no—
154#41—742no—
155C2×Q8—371no—
156C2×D4—21no—
157C2×D4—371no—
158C2×D4—371no—
159C2×D4—741no—
160C2×D4—742no—
161C2×D4—741no—
162C2×D4—741no—
163C2×D4—742no—
164C2×D4—741no—
165C2×D4—741no—
166C2×D4C2×#386611yescharacteristic
167C22×C4—371no—
168C22×C4—371no—
169C22×C4—371no—
170M16—374no—
171M16—742no—
172M16—742no—
173M16—742no—
174M16—742no—
175M16—742no—
176C2×C8—742no—
177C2×C8—742no—
178C2×C8—742no—
179C2×C8—742no—
180C4⋊C4—741no—
181C22⋊C4—21no—
182C22⋊C4—371no—
183C22⋊C4—741no—
184C22⋊C4—741no—
185C22⋊C4—741no—
186C22⋊C4C2×#386611yescharacteristic
187C42—741no—
188C23—21no—
189C23—22no—
190C23—81no—
191C23—371no—
192C23—2961no—
193C23—742no—
194C23—741no—
195C23C22⋊#386611yescharacteristic
196C23C22×#386611yescharacteristic
197Q8—742no—
198D4—22no—
199D4—81no—
200D4—2961no—
201D4—2961no—
202D4—2961no—
203D4—742no—
204D4—742no—
205D4—1481no—
206D4—1482no—
207D4—1481no—
208C2×C4—21no—
209C2×C4—371no—
210C2×C4—371no—
211C2×C4—372no—
212C2×C4—372no—
213C2×C4—371no—
214C2×C4—741no—
215C2×C4—741no—
216C2×C4—741no—
217C2×C4—741no—
218C2×C4—741no—
219C2×C4C22⋊#386611yescharacteristic
220C8—744no—
221C8—1482no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—82no—
229C22—2962no—
230C22—741no—
231C22—1481no—
232C22—1481no—
233C22—1481no—
234C22—1481no—
235C22C2×C22⋊#386611yescharacteristic
236C22D4×#386612yes—
237C4—21no—
238C4—41no—
239C4—371no—
240C4—372no—
241C4—371no—
242C4—741no—
243C4—1481no—
244C2—21no—
245C2—22no—
246C2—41no—
247C2—81no—
248C2—2961no—
249C2—1481no—
250C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#120×C37C4
socleC2×C37#386
prime radical#14558098C2
cosocleC22×Dic37C23
hypercenter#120#3866
hypocenterC37#1914
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #14558611C2semidirect
2. #14558520C2semidirect
3. C2×#11924596C2semidirect
4. #14558414C2semidirect
48. #10596957D4semidirect
131. C37#1914semidirect

Maximal subgroups

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

subgroupindex
#145586112
#145585202
C2×#119245962
#145584142
#145580982
#191437