Finite Group Databasebeta

← #18010648

Subgroups — #18010648

Order 4736.

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

normal subgroups only

This group has 308 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
2#14558520C211yesmaximal, characteristic
3C2×#11924597C212yesmaximal, complemented
4#14558414C212yesmaximal, complemented
5#14558105C211yesmaximal, characteristic
6#11924623—24no—
7D37⋊M16—21no—
8C2×#10596957—21no—
9C2×#10596957C2212yes—
10C2×#10596957C2212yes—
11#11924597—21no—
12#11924597—24no—
13#11924596—21no—
14C2×#10596964C2211yescharacteristic
15C22×Dic74C2211yescharacteristic
16#11924535—21no—
17#11924522—21no—
18#11924520C411yescharacteristic
19#11924519C411yescharacteristic
20#11924517C411yescharacteristic
21#11924514—21no—
22#11924513—21no—
23#11924492C2211yescharacteristic
24#123×C37C411yescharacteristic
25C2×D4×C37C2×C411yescharacteristic
26C22×C4×C37C2×C411yescharacteristic
27C2×C22⋊D37C2×C411yescharacteristic
28C2×C22⋊D37D411yescharacteristic
29C22×Dic37C2×C411yescharacteristic
30C22×Dic37D411yescharacteristic
31C22×Dic37C2311yescharacteristic
32#10596964—22no—
33#10596964—22no—
34C2×C4×D37D411yescharacteristic
35C2×Dic74—21no—
36C2×Dic74—21no—
37C2×Dic74—22no—
38C2×Dic74—22no—
39C2×Dic74D411yescharacteristic
40#10596957—22no—
41#10596957—22no—
42#10596957—22no—
43#10596957—22no—
44#10596957D414yes—
45C2×#64438—22no—
46C2×#64438—22no—
47C2×#64438—22no—
48#10596953—22no—
49D37⋊C8—22no—
50C4⋊C4×C37—21no—
51C22⋊C4×C37—21no—
52C22⋊C4×C37C2×C411yescharacteristic
53C22⋊Dic37—21no—
54C22⋊Dic37C2×C411yescharacteristic
55#10596938—21no—
56#10596938—21no—
57C4⋊Dic37—21no—
58#10596936—21no—
59#10596936—21no—
60#10596936—21no—
61C4×Dic37—21no—
62C23×C37C22⋊C411yescharacteristic
63C23×C37C22×C411yescharacteristic
64C22×D37C22⋊C411yescharacteristic
65D4×C37—22no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—22no—
69C2×C4×C37C22⋊C411yescharacteristic
70C22⋊D37—22no—
71C22⋊D37—22no—
72C2×Dic37—21no—
73C2×Dic37—21no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—22no—
77C2×Dic37C22⋊C411yescharacteristic
78C2×Dic37C2×D412yes—
79C2×Dic37C2×D411yescharacteristic
80C2×Dic37C2×D411yescharacteristic
81C2×Dic37#4112yes—
82C4×D37—21no—
83C4×D37—21no—
84Dic74—22no—
85Dic74—41no—
86Dic74—42no—
87Dic74—41no—
88#64438—24no—
89#64438—42no—
90C22×C37—21no—
91C22×C37—41no—
92C22×C37—41no—
93C22×C37C2×C22⋊C411yescharacteristic
94C22×C37C4×D412yes—
95C2×D37—21no—
96C2×D37—41no—
97C4×C37—21no—
98C4×C37—41no—
99C4×C37—41no—
100Dic37—21no—
101Dic37—41no—
102Dic37—41no—
103Dic37#12011yescharacteristic
104Dic37#12112yes—
105Dic37#12311yescharacteristic
106#1915—371nomaximal, Sylow
107C2×C37—21no—
108C2×C37—22no—
109C2×C37—41no—
110C2×C37#38611yescharacteristic
111D37—41no—
112#568—371no—
113#536—371no—
114#413—371no—
115C2×#101—372no—
116#344—372no—
117C37#191511yescharacteristic, complemented, Sylow
118C2×#41—371no—
119C22×Q8—371no—
120#131—744no—
121C2×M16—372no—
122C2×M16—372no—
123C2×M16—741no—
124C2×M16—741no—
125C4⋊Q8—741no—
126#124—741no—
127#123—371no—
128#123—371no—
129#123—371no—
130#123#386611yescharacteristic
131C22⋊Q8—741no—
132C22⋊Q8—741no—
133#117—371no—
134#101—744no—
135#101—741no—
136#100—741no—
137#41—742no—
138#41—742no—
139C2×Q8—371no—
140C2×Q8—742no—
141C2×Q8—741no—
142C2×Q8—741no—
143C2×Q8—742no—
144C2×D4—371no—
145C2×D4—371no—
146C2×D4C2×#386611yescharacteristic
147C22×C4—371no—
148C22×C4—371no—
149C22×C4—371no—
150C22×C4—371no—
151C22×C4C2×#386611yescharacteristic
152M16—374no—
153M16—742no—
154M16—742no—
155M16—742no—
156M16—742no—
157M16—742no—
158C2×C8—742no—
159C2×C8—742no—
160C2×C8—742no—
161C2×C8—742no—
162C4⋊C4—21no—
163C4⋊C4—741no—
164C4⋊C4—741no—
165C4⋊C4—741no—
166C4⋊C4—741no—
167C22⋊C4—21no—
168C22⋊C4—371no—
169C22⋊C4—741no—
170C22⋊C4—741no—
171C22⋊C4—741no—
172C22⋊C4C2×#386611yescharacteristic
173C42—741no—
174C23—371no—
175C23C22⋊#386611yescharacteristic
176C23C22×#386611yescharacteristic
177Q8—742no—
178Q8—1481no—
179Q8—1482no—
180Q8—1481no—
181D4—22no—
182D4—742no—
183D4—742no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—371no—
188C2×C4—371no—
189C2×C4—372no—
190C2×C4—372no—
191C2×C4—371no—
192C2×C4—741no—
193C2×C4—741no—
194C2×C4—741no—
195C2×C4—741no—
196C2×C4—741no—
197C2×C4—741no—
198C2×C4—742no—
199C2×C4C22⋊#386611yescharacteristic
200C8—744no—
201C8—1482no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—741no—
206C22—1481no—
207C22C2×C22⋊#386611yescharacteristic
208C22D4×#386612yes—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—371no—
213C4—372no—
214C4—371no—
215C4—741no—
216C4—1481no—
217C4—1481no—
218C2—21no—
219C2—22no—
220C2—41no—
221C2—1481no—
222C2#1455848111yescharacteristic
subgroupG/H
centerC2#14558481
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
Fitting#123×C37C4
socleC2×C37#386
prime radicalC2×#10596964C22
cosocleC22×Dic37C23
hypercenter#123#3866
hypocenterC37#1915
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C23 ◁ #123

Complements

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

NH ≅ G/Ntype
3. C2×#11924597C2semidirect
4. #14558414C2semidirect
117. C37#1915semidirect

Maximal subgroups

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

subgroupindex
#145586112
#145585202
C2×#119245972
#145584142
#145581052
#191537