Finite Group Databasebeta

← #18010787

Subgroups — #18010787

Order 4736.

324 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 72 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#14558475C211yesmaximal, characteristic
2C4×C22⋊#3866C211yesmaximal, characteristic
3#14558411C212yesmaximal
4#14558411C212yesmaximal
5C2×#11924514C211yesmaximal, characteristic
6C2×C4⋊#3866—21no—
7C2×C22⋊#3866C2212yes—
8C2×C22⋊#3866C2212yes—
9C2×C4×#3866—21no—
10(C2×#3866)⋊C4—21no—
11(C2×#3866)⋊C4—21no—
12C22×Dic74C411yescharacteristic, complemented
13C22×C4×D37C2211yescharacteristic
14#11924514—21no—
15#11924514—21no—
16#11924514—21no—
17#11924514—21no—
18C2×#10596936C411yescharacteristic, complemented
19C2×#10596936C411yescharacteristic, complemented
20C2×#10596938C2211yescharacteristic
21C2×#10596938C2211yescharacteristic
22C2×C4⋊C4×C37C411yescharacteristic, complemented
23C23×D37C2311yescharacteristic
24C22×#3866—22no—
25C22×#3866—22no—
26C22×C4×C37C2×C411yescharacteristic
27C22×C4×C37C2×C411yescharacteristic
28C22×C4×C37C2×C411yescharacteristic
29C22×Dic37C2×C411yescharacteristic
30C22×Dic37C2×C411yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C2×C4×D37—42no—
33C2×C4×D37D411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×Dic74—21no—
38C2×Dic74—21no—
39C2×Dic74—42no—
40C22⋊#3866—22no—
41C22⋊#3866—24no—
42C22⋊#3866Q814yescomplemented
43C4⋊#3866—42no—
44C4×#3866—42no—
45C4⋊C4×C37—21no—
46C4⋊C4×C37—21no—
47#10596938—21no—
48#10596938—21no—
49#10596938—21no—
50#10596938—21no—
51#10596936—21no—
52#10596936—21no—
53#10596936—21no—
54#10596936—21no—
55C23×C37C22×C411yescharacteristic
56C22×D37—41no—
57C22×D37—41no—
58C22×D37C2×D411yescharacteristic
59C22×D37C2×D411yescharacteristic
60C22×D37C2×Q812yes—
61C22×D37#4112yes—
62C2×#3866—24no—
63C2×#3866—42no—
64C2×#3866—42no—
65C2×#3866—42no—
66C2×#3866—42no—
67C2×#3866—42no—
68C2×C4×C37—21no—
69C2×C4×C37—21no—
70C2×C4×C37—41no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37C22⋊C411yescharacteristic
74C2×C4×C37C22⋊C411yescharacteristic
75C2×Dic37—22no—
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—41no—
79C2×Dic37—41no—
80C2×Dic37C22⋊C411yescharacteristic
81C2×Dic37C22⋊C411yescharacteristic
82C4×D37—22no—
83C4×D37—22no—
84C4×D37—41no—
85C4×D37—41no—
86Dic74—42no—
87Dic74—42no—
88C22×C37—21no—
89C22×C37—21no—
90C22×C37C2×C22⋊C411yescharacteristic
91C22×C37C4×Q812yes—
92C2×D37—21no—
93C2×D37—21no—
94C2×D37—21no—
95C2×D37—21no—
96C2×D37—42no—
97C2×D37—42no—
98C2×D37C22⋊Q812yes—
99C2×D37#12411yescharacteristic
100C2×D37C4⋊Q811yescharacteristic
101#3866—44no—
102#3866—82no—
103C4×C37—21no—
104C4×C37—21no—
105C4×C37—41no—
106C4×C37—41no—
107Dic37—21no—
108Dic37—41no—
109Dic37—41no—
110Dic37#9912yes—
111#1996—371nomaximal, Sylow
112C2×C37—22no—
113C2×C37#39111yescharacteristic
114C2×C37C2×#9911yescharacteristic
115C2×C37#41011yescharacteristic
116D37—22no—
117D37—21no—
118D37—21no—
119C2×C22⋊Q8—371no—
120#380—371no—
121C4×C22⋊C4—371no—
122#342—372no—
123#342—372no—
124C37#199611yescharacteristic, complemented, Sylow
125C22×Q8—371no—
126C23×C4—371no—
127C22⋊Q8—741no—
128C22⋊Q8—741no—
129C22⋊Q8—741no—
130C22⋊Q8—741no—
131C2×C4⋊C4—371no—
132C2×C4⋊C4—371no—
133C2×C4⋊C4—741no—
134C2×C4⋊C4#386611yescharacteristic, complemented
135C2×C22⋊C4—372no—
136C2×C22⋊C4—371no—
137C2×C22⋊C4—371no—
138C2×C22⋊C4—372no—
139C2×C42—741no—
140#95—741no—
141#95—741no—
142C24—371no—
143C2×Q8—741no—
144C2×Q8—741no—
145C2×Q8—1482no—
146C22×C4—371no—
147C22×C4—371no—
148C22×C4—371no—
149C22×C4—371no—
150C22×C4—371no—
151C22×C4—371no—
152C22×C4—371no—
153C22×C4—742no—
154C22×C4—742no—
155C22×C4—1482no—
156C22×C4C2×#386611yescharacteristic
157C22×C4C2×#386611yescharacteristic
158C22×C4C2×#386611yescharacteristic
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—741no—
162C4⋊C4—741no—
163C4⋊C4—741no—
164C4⋊C4—741no—
165C4⋊C4—1482no—
166C22⋊C4—374no—
167C22⋊C4—741no—
168C22⋊C4—741no—
169C22⋊C4—741no—
170C22⋊C4—741no—
171C22⋊C4—742no—
172C22⋊C4—744no—
173C42—1482no—
174C23—371no—
175C23—371no—
176C23—372no—
177C23—372no—
178C23—1481no—
179C23—1481no—
180C23C22×#386611yescharacteristic
181Q8—1482no—
182Q8—1482no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—371no—
189C2×C4—371no—
190C2×C4—742no—
191C2×C4—742no—
192C2×C4—742no—
193C2×C4—744no—
194C2×C4—741no—
195C2×C4—741no—
196C2×C4—1481no—
197C2×C4—1481no—
198C2×C4—1482no—
199C2×C4—1482no—
200C2×C4—1482no—
201C2×C4—1482no—
202C2×C4—1482no—
203C2×C4—1481no—
204C2×C4—1481no—
205C2×C4C22⋊#386611yescharacteristic
206C2×C4C22⋊#386611yescharacteristic
207C22—21no—
208C22—21no—
209C22—372no—
210C22—371no—
211C22—371no—
212C22—741no—
213C22—741no—
214C22—741no—
215C22—741no—
216C22—1482no—
217C22—1482no—
218C22C2×C22⋊#386611yescharacteristic
219C22Q8×#386612yes—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—372no—
225C4—2962no—
226C4—741no—
227C4—1484no—
228C4—1481no—
229C4—1481no—
230C2—22no—
231C2—741no—
232C2—742no—
233C2—741no—
234C2(C2×#3866)⋊Q811yescharacteristic
235C2D37⋊#9911yescharacteristic
236C2#1455851211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radical, cosocleC23×D37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1996
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
12. C22×Dic74C4semidirect
18. C2×#10596936C4semidirect
19. C2×#10596936C4semidirect
22. C2×C4⋊C4×C37C4semidirect
42. C22⋊#3866Q8semidirect
124. C37#1996semidirect
134. C2×C4⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
#145584752
C4×C22⋊#38662
#145584112
C2×#119245142
#199637