Finite Group Databasebeta

← #30607260

Subgroups — #30607260

Order 15616.

642 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 642 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461655C212yesmaximal
2#21460916C214yesmaximal, complemented
3#21448309C211yesmaximal, characteristic
4C2×#14519838C2214yes—
5C2×#14519837—22no—
6#16840734—22no—
7C22×#11758222C2211yescharacteristic
8C2×#14519736C411yescharacteristic
9#16839668C2212yes—
10#16839664C412yes—
11#16839641—22no—
12C4×#11758198—22no—
13C22×C42×C61C411yescharacteristic
14C2×#11758217—24no—
15#14519838—28no—
16#14519837—44no—
17#14519834—44no—
18C2×#11758222—24no—
19C2×#11758222—42no—
20C2×#11758222—42no—
21C22×Dic122C2311yescharacteristic
22C22×D244C2×C411yescharacteristic
23C22×C22⋊D61D412yes—
24C22×C4×D61D412yes—
25#14519736—42no—
26C2×C4⋊Dic61C2×C412yes—
27C2×C22⋊Dic61—21no—
28C2×#11758198—24no—
29C2×C4×Dic61—21no—
30#14519684—24no—
31C23×C4×C61—21no—
32C23×C4×C61C2×C411yescharacteristic
33C2×C42×C61—21no—
34C2×C42×C61—42no—
35C2×C42×C61C2×C412yes—
36C24×C61C22⋊C411yescharacteristic
37C23×D61C22⋊C412yes—
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61—22no—
41C22×C4×C61—22no—
42C22×C4×C61—44no—
43C22×C4×C61—42no—
44C22×C4×C61C22⋊C411yescharacteristic
45C22×C4×C61C22×C411yescharacteristic
46C2×C22⋊D61—24no—
47C2×C22⋊D61—24no—
48C2×C22⋊D61—42no—
49C22×Dic61—22no—
50C22×Dic61C2×D412yes—
51#11758222—416no—
52C2×D244—22no—
53C2×D244—41no—
54C2×D244—41no—
55C2×C4×D61—24no—
56C2×C4×D61—24no—
57C2×C4×D61—42no—
58C2×Dic122—41no—
59C2×Dic122—41no—
60C2×Dic122#4114yes—
61#11758217—44no—
62#11758217—44no—
63C2×#92420—44no—
64C42×C61—42no—
65C42×C61—42no—
66C22⋊Dic61—42no—
67#11758198—48no—
68C4⋊Dic61—42no—
69C4×Dic61—42no—
70C23×C61—21no—
71C23×C61—21no—
72C23×C61—42no—
73C23×C61#9912yes—
74C23×C61C2×C22⋊C411yescharacteristic
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—44no—
79C2×C4×C61—28no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—24no—
85C2×C4×C61—42no—
86C2×C4×C61—48no—
87C2×C4×C61—42no—
88C2×C4×C61#9912yes—
89C2×C4×C61#11712yes—
90C22⋊D61—48no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—44no—
94C2×Dic61—42no—
95C2×Dic61#12314yes—
96D244—44no—
97C4×D61—48no—
98Dic122—44no—
99#92420—84no—
100#12861—611nomaximal, Sylow
101C22×C61—22no—
102C22×C61—22no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61#38111yescharacteristic
107C22×C61C2×#9911yescharacteristic
108C22×C61C2×#9911yescharacteristic
109C2×D61—44no—
110C2×D61—42no—
111C2×D61—44no—
112C2×D61—82no—
113C4×C61—22no—
114C4×C61—22no—
115C4×C61—44no—
116Dic61—24no—
117Dic61—82no—
118#2297—611no—
119#1785—612no—
120#1394—614no—
121C2×C61—21no—
122C2×C61—21no—
123C2×C61—42no—
124C2×C61#181911yescharacteristic
125C2×C61#213212yes—
126D61—82no—
127C22×#41—611no—
128C2×#117—611no—
129C22×C42#692311yescharacteristic
130C2×#101—614no—
131C2×#100—1222no—
132#407—1222no—
133#391—612no—
134#390—612no—
135#386—1222no—
136C4×C22⋊C4—1222no—
137C61#1286111yescharacteristic, complemented, Sylow
138C2×#41—1224no—
139C2×#41—2442no—
140C2×#41—2442no—
141C22×Q8—611no—
142C22×D4—612no—
143C22×D4—611no—
144C23×C4—21no—
145C23×C4—612no—
146C23×C4C2×#692311yescharacteristic
147C2×M16—1224no—
148#117—2442no—
149C2×C4⋊C4—612no—
150C2×C22⋊C4—1224no—
151C2×C22⋊C4—1221no—
152C2×C42—21no—
153C2×C42—42no—
154C2×C42—1221no—
155C2×C42C2×#692312yes—
156#101—1228no—
157#100—2444no—
158C22⋊C8—2444no—
159#95—1224no—
160C24—612no—
161C24C22⋊#692311yescharacteristic
162#41—24416no—
163C2×Q8—614no—
164C2×Q8—2441no—
165C2×Q8—2441no—
166C2×D4—1224no—
167C2×D4—1224no—
168C2×D4—1222no—
169C2×D4—2441no—
170C2×D4—2441no—
171C2×D4—2442no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—44no—
177C22×C4—42no—
178C22×C4—612no—
179C22×C4—1224no—
180C22×C4—1224no—
181C22×C4—1222no—
182C22×C4—2442no—
183C22×C4C22⋊#692311yescharacteristic
184C22×C4C22×#692311yescharacteristic
185M16—2444no—
186M16—2444no—
187C2×C8—2444no—
188C4⋊C4—2442no—
189C22⋊C4—2448no—
190C22⋊C4—2442no—
191C42—42no—
192C42—42no—
193C42—2442no—
194C23—21no—
195C23—21no—
196C23—42no—
197C23—1222no—
198C23—1222no—
199C23—1222no—
200C23—2444no—
201C23#1451983512yes—
202C23C2×C22⋊#692311yescharacteristic
203Q8—2444no—
204D4—2444no—
205D4—2448no—
206C2×C4—28no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—24no—
212C2×C4—42no—
213C2×C4—48no—
214C2×C4—42no—
215C2×C4—614no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—2448no—
219C2×C4—2444no—
220C2×C4—2442no—
221C2×C4#1451983612yes—
222C2×C4#1451985612yes—
223C8—4884no—
224C22—22no—
225C22—22no—
226C22—42no—
227C22—42no—
228C22—42no—
229C22—4882no—
230C22—2444no—
231C22—2444no—
232C22—2442no—
233C22#1684070511yescharacteristic
234C22C2×#1451983511yescharacteristic
235C22C2×#1451983611yescharacteristic
236C4—22no—
237C4—22no—
238C4—44no—
239C4—1224no—
240C4—4882no—
241C2—21no—
242C2—21no—
243C2—42no—
244C2—4882no—
245C2#2146171411yescharacteristic
246C2#2146211212yes—
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C42×C61C4
socleC22×C61C2×#99
prime radicalC22×#11758222C22
cosocleC22×Dic122C23
hypercenterC22×C42#6923
hypocenterC61#12861
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
2. #21460916C2semidirect
137. C61#12861semidirect

Maximal subgroups

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

subgroupindex
#214616552
#214609162
#214483092
#1286161