Finite Group Databasebeta

← #30594497

Subgroups — #30594497

Order 15616.

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#21462047C211yesmaximal, characteristic
2#21461695C211yesmaximal, characteristic
3#21445843C211yesmaximal, characteristic
4C2×#14519852C412yescomplemented
5C2×#14519845—21no—
6#16840704—21no—
7#16840657—21no—
8C22⋊#11758187—21no—
9#16840636C412yescomplemented
10C22×C8×D61C2211yescharacteristic
11C2×#14519708—21no—
12#16839619—21no—
13#16839525C411yescharacteristic, complemented
14C61×#340C411yescharacteristic, complemented
15C2×C4⋊#6923—22no—
16C2×C22⋊#6923—41no—
17#14519852—42no—
18C2×#11758187—22no—
19#14519845—42no—
20(C2×#6923)⋊C4—41no—
21C22×C4×D61D411yescharacteristic
22C22×#92418D411yescharacteristic
23C2×C8×D61—42no—
24C2×C8×D61C2×C411yescharacteristic
25C2×C8×D61C2×C411yescharacteristic
26C2×C8×D61D411yescharacteristic
27C2×C8×D61Q811yescharacteristic
28C2×C4⋊Dic61—21no—
29C2×#11758198—41no—
30#14519708—42no—
31#14519684—41no—
32C22×C8×C61C2×C411yescharacteristic
33C2×C4⋊C4×C61—21no—
34C23×D61D811yescharacteristic
35C22×#6923—42no—
36C22×C4×C61—41no—
37C22×C4×C61C22⋊C411yescharacteristic
38C22×Dic61—41no—
39C22×Dic61SD1611yescharacteristic
40C2×C4×D61—41no—
41C2×C4×D61—41no—
42C2×C4×D61C22⋊C411yescharacteristic
43C2×C4×D61C4⋊C411yescharacteristic
44C2×C4×D61SD1611yescharacteristic
45C2×C4×D61Q1611yescharacteristic
46C22⋊#6923—81no—
47C22⋊#6923—81no—
48C4⋊#6923—42no—
49C4⋊#6923—42no—
50C2×C8×C61—41no—
51C2×C8×C61C4211yescharacteristic
52C2×C8×C61C4⋊C411yescharacteristic
53C4⋊C4×C61—41no—
54C4⋊C4×C61—41no—
55#11758198—82no—
56C4⋊Dic61—41no—
57C4⋊Dic61—41no—
58C2×#92418—22no—
59C2×#92418C22⋊C411yescharacteristic
60C2×#92418C4⋊C411yescharacteristic
61C8×D61—22no—
62C8×D61—22no—
63C8×D61—41no—
64C8×D61—41no—
65#11758187—42no—
66C23×C61#10211yescharacteristic
67C22×D61—21no—
68C22×D61—21no—
69C22×D61—22no—
70C22×D61—41no—
71C22×D61#10211yescharacteristic
72C22×D61#10711yescharacteristic
73C2×#6923—82no—
74C2×#6923—82no—
75C2×#6923—82no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—81no—
79C2×C4×C61—81no—
80C2×C4×C61—81no—
81C2×C4×C61#9511yescharacteristic
82C2×C4×C61#10311yescharacteristic
83C2×Dic61—41no—
84C2×Dic61—81no—
85C2×Dic61—81no—
86C2×Dic61—81no—
87C2×Dic61#10311yescharacteristic
88C2×Dic61#10611yescharacteristic
89C4×D61—21no—
90C4×D61—21no—
91C4×D61—21no—
92C4×D61—21no—
93C4×D61—41no—
94C4×D61—41no—
95C8×C61—21no—
96C8×C61—21no—
97#92418—21no—
98#92418#9912yes—
99#7233—611nomaximal, Sylow
100C22×C61—21no—
101C22×C61—21no—
102C22×C61#34011yescharacteristic
103C22×C61#36011yescharacteristic
104C22×C61#36011yescharacteristic
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—21no—
109C2×D61—21no—
110C2×D61—42no—
111C2×D61—42no—
112C2×D61#36012yes—
113#6923—162no—
114C4×C61—21no—
115C4×C61—161no—
116C4×C61H(3,ℤ/4)11yescharacteristic
117C4×C61#34211yescharacteristic
118Dic61—21no—
119Dic61—21no—
120Dic61—161no—
121#2112—611no—
122#1807—611no—
123#1807—611no—
124C2×C61—21no—
125C2×C61—21no—
126C2×C61#128911yescharacteristic
127C2×C61#138611yescharacteristic
128C2×C61#138611yescharacteristic
129D61—22no—
130D61—41no—
131C23×C8—611no—
132C2×M32—612no—
133C2×#106—1221no—
134C2×#106—1221no—
135#380—1221no—
136#380—1221no—
137C22⋊C16—1221no—
138C22⋊C16—1221no—
139#340—612no—
140#340—611no—
141#340#692311yescharacteristic, complemented
142C61#723311yescharacteristic, complemented, Sylow
143C23×C4—611no—
144C22×C8—611no—
145C22×C8—611no—
146C22×C8—611no—
147C22×C8—611no—
148C22×C8—611no—
149C22×C8—2442no—
150C22×C8C2×#692311yescharacteristic
151C2×C4⋊C4—21no—
152C2×C4⋊C4—1222no—
153C2×C4⋊C4—1221no—
154C2×C22⋊C4—2441no—
155C2×C22⋊C4—2441no—
156M32—2442no—
157C2×C16—1222no—
158#106—2442no—
159#106—2442no—
160#95—2441no—
161#95—2441no—
162C24—611no—
163C22×C4—41no—
164C22×C4—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—2441no—
170C22×C4—2441no—
171C22×C4—2442no—
172C22×C4—2441no—
173C22×C4C22⋊#692311yescharacteristic
174C2×C8—41no—
175C2×C8—611no—
176C2×C8—611no—
177C2×C8—1222no—
178C2×C8—1222no—
179C2×C8—1222no—
180C2×C8—2441no—
181C2×C8—2441no—
182C2×C8C4×#692311yescharacteristic
183C2×C8C4⋊#692311yescharacteristic
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—2441no—
187C4⋊C4—2441no—
188C4⋊C4—2442no—
189C4⋊C4—2442no—
190C22⋊C4—4882no—
191C22⋊C4—4881no—
192C22⋊C4—4881no—
193C16—2442no—
194C23—611no—
195C23—611no—
196C23—1222no—
197C23—1221no—
198C23—1221no—
199C23—2441no—
200C23#1451983911yescharacteristic
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—81no—
204C2×C4—81no—
205C2×C4—81no—
206C2×C4—611no—
207C2×C4—611no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—4881no—
213C2×C4—4881no—
214C2×C4—4882no—
215C2×C4—4882no—
216C2×C4—4882no—
217C2×C4—4881no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4(C2×#6923)⋊C411yescharacteristic
222C2×C4#1451984011yescharacteristic
223C8—21no—
224C8—21no—
225C8—612no—
226C8—1221no—
227C22—21no—
228C22—21no—
229C22—612no—
230C22—1221no—
231C22—1221no—
232C22—1221no—
233C22—1221no—
234C22—1221no—
235C22—2442no—
236C22—2442no—
237C22#1684063511yescharacteristic
238C22#1684067811yescharacteristic
239C22#1684067911yescharacteristic
240C4—21no—
241C4—161no—
242C4—1221no—
243C4—1221no—
244C4—9761no—
245C4—9762no—
246C4#1684062911yescharacteristic
247C4#1684063911yescharacteristic
248C2—21no—
249C2—21no—
250C2—1222no—
251C2—2441no—
252C2#2146068111yescharacteristic
253C2#2146089011yescharacteristic
254C2#2146089211yescharacteristic
subgroupG/H
centerC22#16840635
commutatorC2×C8×C61C42
FrattiniC22×C8C2×#6923
FittingC61×#340C4
socleC22×C61#340
prime radicalC23×D61D8
cosocleC22×C8×D61C22
hypercenter#340#6923
hypocenterC61#7233
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
4. C2×#14519852C4semidirect
9. #16840636C4semidirect
13. #16839525C4semidirect
14. C61×#340C4semidirect
141. #340#6923semidirect
142. C61#7233semidirect

Maximal subgroups

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

subgroupindex
#214620472
#214616952
#214458432
#723361