Finite Group Databasebeta

← #30607266

Subgroups — #30607266

Order 15616.

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

normal subgroups only

This group has 614 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#21448407C211yesmaximal, characteristic
4C2×#14519838C2214yes—
5C2×#14519837—22no—
6#16840734—22no—
7C22×#11758222C2211yescharacteristic
8C22×C4⋊Dic61C411yescharacteristic
9#16839668C2212yes—
10#16839664C412yes—
11#16839639—22no—
12#16839619—22no—
13C2×#117×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—
24C23×Dic61—21no—
25C22×C4×D61D412yes—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—42no—
28C2×C4⋊Dic61C2×C412yes—
29C2×#11758198—24no—
30#14519684—24no—
31C23×C4×C61C2×C411yescharacteristic
32#117×C61—42no—
33C2×C4⋊C4×C61—21no—
34C2×C22⋊C4×C61—21no—
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×C61C22⋊C411yescharacteristic
43C22×C4×C61C22×C411yescharacteristic
44C2×C22⋊D61—24no—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—42no—
47C22×Dic61—22no—
48C22×Dic61—42no—
49C22×Dic61—82no—
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—
64C4⋊C4×C61—42no—
65C22⋊C4×C61—42no—
66C42×C61—42no—
67#11758198—84no—
68C4⋊Dic61—42no—
69C4⋊Dic61—42no—
70C23×C61—21no—
71C23×C61—21no—
72C23×C61—41no—
73C23×C61—41no—
74C23×C61#9912yes—
75C23×C61C2×C22⋊C411yescharacteristic
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—42no—
80C22×D61—42no—
81C2×C4×C61—28no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—42no—
89C2×C4×C61#9912yes—
90C2×C4×C61#11712yes—
91C22⋊D61—48no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—44no—
95C2×Dic61—42no—
96C2×Dic61—84no—
97C2×Dic61#12314yes—
98D244—44no—
99C4×D61—48no—
100Dic122—44no—
101#92420—84no—
102#12863—611nomaximal, Sylow
103C22×C61—21no—
104C22×C61—21no—
105C22×C61—22no—
106C22×C61—42no—
107C22×C61—42no—
108C22×C61—41no—
109C22×C61—41no—
110C22×C61#38111yescharacteristic
111C22×C61C2×#9911yescharacteristic
112C22×C61C2×#9911yescharacteristic
113C2×D61—44no—
114C2×D61—42no—
115C2×D61—42no—
116C2×D61—42no—
117C2×D61—82no—
118C4×C61—22no—
119C4×C61—22no—
120C4×C61—82no—
121Dic61—24no—
122Dic61—82no—
123#2311—611no—
124#1785—612no—
125#1394—614no—
126C2×C61—21no—
127C2×C61—21no—
128C2×C61—42no—
129C2×C61#181911yescharacteristic
130C2×C61#213411yescharacteristic
131C2×C61#213511yescharacteristic
132D61—82no—
133C22×#41—611no—
134C2×#117#692311yescharacteristic
135C22×C4⋊C4—611no—
136C2×#101—614no—
137C2×#100—1222no—
138#407—1222no—
139#391—612no—
140#390—612no—
141#386—1222no—
142#380—1222no—
143C61#1286311yescharacteristic, complemented, Sylow
144C2×#41—1224no—
145C2×#41—2442no—
146C2×#41—2442no—
147C22×Q8—611no—
148C22×D4—612no—
149C22×D4—611no—
150C23×C4—612no—
151C23×C4—1221no—
152C23×C4C2×#692311yescharacteristic
153C2×M16—1224no—
154#117—42no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4—2442no—
159C2×C22⋊C4—21no—
160C2×C22⋊C4—1224no—
161C2×C42C2×#692312yes—
162#101—1228no—
163#100—2444no—
164C22⋊C8—2444no—
165#95—1224no—
166C24—612no—
167C24C22⋊#692311yescharacteristic
168#41—24416no—
169C2×Q8—614no—
170C2×Q8—2441no—
171C2×Q8—2441no—
172C2×D4—1224no—
173C2×D4—1224no—
174C2×D4—1222no—
175C2×D4—2441no—
176C2×D4—2441no—
177C2×D4—2442no—
178C22×C4—22no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—612no—
183C22×C4—1224no—
184C22×C4—1224no—
185C22×C4—1222no—
186C22×C4—4882no—
187C22×C4—2442no—
188C22×C4—2442no—
189C22×C4C22⋊#692311yescharacteristic
190C22×C4C22×#692311yescharacteristic
191M16—2444no—
192M16—2444no—
193C2×C8—2444no—
194C4⋊C4—42no—
195C4⋊C4—2442no—
196C4⋊C4—2442no—
197C22⋊C4—42no—
198C22⋊C4—4884no—
199C42—42no—
200C23—21no—
201C23—21no—
202C23—41no—
203C23—41no—
204C23—1222no—
205C23—1222no—
206C23—1222no—
207C23—2442no—
208C23—2442no—
209C23#1451983512yes—
210C23C2×C22⋊#692311yescharacteristic
211Q8—2444no—
212D4—2444no—
213D4—2448no—
214C2×C4—28no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—614no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—4884no—
226C2×C4—2448no—
227C2×C4—2444no—
228C2×C4—2442no—
229C2×C4#1451983612yes—
230C2×C4#1451985612yes—
231C8—4884no—
232C22—21no—
233C22—21no—
234C22—22no—
235C22—42no—
236C22—42no—
237C22—41no—
238C22—41no—
239C22—4882no—
240C22—2444no—
241C22—2442no—
242C22—2442no—
243C22—2442no—
244C22#1684070511yescharacteristic
245C22C2×#1451983511yescharacteristic
246C22C2×#1451983611yescharacteristic
247C4—22no—
248C4—22no—
249C4—82no—
250C4—1224no—
251C4—4882no—
252C2—21no—
253C2—21no—
254C2—42no—
255C2—4882no—
256C2#2146171411yescharacteristic
257C2#2146212011yescharacteristic
258C2#2146212311yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC22×#11758222C22
cosocleC22×Dic122C23
hypercenterC2×#117#6923
hypocenterC61#12863
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460916C2semidirect
143. C61#12863semidirect

Maximal subgroups

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

subgroupindex
#214616552
#214609162
#214484072
#1286361