Finite Group Databasebeta

← #30599298

Subgroups — #30599298

Order 15616.

522 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 112 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#21461052C212yesmaximal
2#21460647C212yesmaximal, complemented
3#21460643C212yesmaximal, complemented
4C4×#14519734C211yesmaximal, characteristic
5#16840778C2214yes—
6#16840608—22no—
7#16840606—22no—
8C2×#14519734C411yescharacteristic
9C2×#14519734C2211yescharacteristic
10C2×C42×D61C411yescharacteristic
11C4×#11758196—22no—
12C4×#11758198—22no—
13#16839608C411yescharacteristic
14#16839608C2211yescharacteristic
15C42×Dic61C2211yescharacteristic
16C43×C61C411yescharacteristic
17C4⋊#92420—24no—
18C22⋊#92420—24no—
19C4×#92420—24no—
20C22×C4×D61—21no—
21C22×C4×D61C2×C411yescharacteristic
22#14519734—22no—
23#14519734—22no—
24#14519734—22no—
25#14519734—22no—
26C2×#11758196—21no—
27C2×#11758196D412yes—
28C2×#11758198—21no—
29C2×#11758198D412yes—
30C2×C4×Dic61—21no—
31C2×C4×Dic61—22no—
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61C2311yescharacteristic
35C42×D61—22no—
36C42×D61C814yescomplemented
37#14519684—22no—
38#14519684—22no—
39C2×C42×C61—22no—
40C2×C42×C61C2×C411yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42C2×C42×C61C2×C411yescharacteristic
43C23×D61C22⋊C411yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C22⋊C412yes—
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61—21no—
49C22×Dic61—21no—
50C22×Dic61C22⋊C411yescharacteristic
51C22×Dic61C2×D412yes—
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—24no—
57C2×C4×D61—44no—
58C2×C4×D61C2×C812yes—
59C2×C4×D61M1612yes—
60C2×#92420—44no—
61C42×C61—21no—
62C42×C61—21no—
63C42×C61—21no—
64C42×C61—21no—
65C42×C61—44no—
66C42×C61C2×C812yes—
67C42×C61M1612yes—
68#11758198—24no—
69#11758198—24no—
70#11758196—24no—
71#11758196—24no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C4×Dic61—24no—
75C4×Dic61—44no—
76C4×Dic61C2×C812yes—
77C4×Dic61M1612yes—
78C4×Dic61#4112yes—
79C4×Dic61#4112yes—
80C23×C61C2×C22⋊C411yescharacteristic
81C22×D61—21no—
82C22×D61—21no—
83C22×D61—42no—
84C22×D61C22⋊C812yes—
85C2×C4×C61—24no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61#11711yescharacteristic
92C2×C4×C61#11711yescharacteristic
93C2×C4×C61C22×C811yescharacteristic
94C2×C4×C61C2×M1611yescharacteristic
95C2×C4×C61C2×M1611yescharacteristic
96C2×C4×C61C2×M1611yescharacteristic
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61C22⋊C812yes—
105C2×Dic61#12314yes—
106C4×D61—22no—
107C4×D61—22no—
108C4×D61—22no—
109C4×D61—22no—
110C4×D61—48no—
111#92420—84no—
112#8730—611nomaximal, Sylow
113C22×C61—22no—
114C22×C61#38111yescharacteristic
115C22×C61C2×C22⋊C811yescharacteristic
116C22×C61#40711yescharacteristic
117C2×D61—22no—
118C2×D61—42no—
119C2×D61—42no—
120C2×D61—42no—
121C4×C61—24no—
122C4×C61—42no—
123C4×C61—42no—
124C4×C61#43111yescharacteristic
125C4×C61#43111yescharacteristic
126C4×C61#43211yescharacteristic
127C4×C61#43211yescharacteristic
128Dic61—22no—
129Dic61—24no—
130Dic61—42no—
131Dic61—42no—
132C4×#117—611no—
133#1458—612no—
134#1276—612no—
135#1274—612no—
136C2×C61—21no—
137C2×C61—21no—
138C2×C61#181711yescharacteristic
139C2×C61#182712yes—
140D61—42no—
141C2×#117—611no—
142C2×#117—611no—
143C22×C42—611no—
144#431—614no—
145C4×C4⋊C4—1222no—
146C4×C22⋊C4—1222no—
147#376—611no—
148#376—611no—
149C43—611no—
150C43#692311yescharacteristic
151#324—1222no—
152#323—1222no—
153C61#873011yescharacteristic, complemented, Sylow
154C23×C4—611no—
155C23×C4—1221no—
156#117—1222no—
157#117—1222no—
158#117—1222no—
159#117—1222no—
160C2×C4⋊C4—612no—
161C2×C4⋊C4—1221no—
162C2×C22⋊C4—612no—
163C2×C22⋊C4—1221no—
164C2×C42—22no—
165C2×C42—611no—
166C2×C42—611no—
167C2×C42—611no—
168C2×C42—614no—
169C2×C42—1222no—
170C2×C42—1221no—
171C2×C42—1222no—
172C2×C42C2×#692311yescharacteristic
173C2×C42C2×#692311yescharacteristic
174C2×C42C2×#692311yescharacteristic
175C4⋊C8—1224no—
176C22⋊C8—1224no—
177C4×C8—1224no—
178#95—1222no—
179#95—1222no—
180C24—611no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—611no—
184C22×C4—612no—
185C22×C4—612no—
186C22×C4—612no—
187C22×C4—1224no—
188C22×C4—1221no—
189C22×C4—1221no—
190C22×C4—1221no—
191C22×C4—1221no—
192C22×C4—1221no—
193C22×C4—1221no—
194C22×C4—2444no—
195C22×C4C22⋊#692312yes—
196C22×C4C22×#692311yescharacteristic
197C2×C8—2444no—
198C4⋊C4—1224no—
199C4⋊C4—1224no—
200C22⋊C4—1224no—
201C22⋊C4—1224no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—44no—
207C42—612no—
208C42—612no—
209C42—612no—
210C42—612no—
211C42—1224no—
212C42—1221no—
213C42—1221no—
214C42—2444no—
215C42D61⋊C812yes—
216C42#1175821312yes—
217C23—612no—
218C23—1221no—
219C23—1221no—
220C23—2442no—
221C23C2×C22⋊#692311yescharacteristic
222C2×C4—24no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—614no—
229C2×C4—612no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—2448no—
239C2×C4—2442no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4#1451985611yescharacteristic
243C2×C4#1451985611yescharacteristic
244C2×C4C2×D61⋊C811yescharacteristic
245C2×C4D61⋊M1611yescharacteristic
246C2×C4D61⋊M1611yescharacteristic
247C2×C4C2×#1175821311yescharacteristic
248C8—4884no—
249C22—22no—
250C22—1222no—
251C22—2442no—
252C22—2442no—
253C22—2442no—
254C22#1684070511yescharacteristic
255C22D61⋊(C22⋊C8)11yescharacteristic
256C22#1684073311yescharacteristic
257C4—24no—
258C4—42no—
259C4—42no—
260C4—1222no—
261C4—1224no—
262C4—2442no—
263C4—2442no—
264C4#1684078011yescharacteristic
265C4#1684078111yescharacteristic
266C4#1684078411yescharacteristic
267C4#1684078511yescharacteristic
268C2—21no—
269C2—21no—
270C2—2442no—
271C2#2146171111yescharacteristic
272C2#2146172812yes—
subgroupG/H
centerC2×C4#14519856
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC43×C61C4
socleC22×C61#381
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC43#6923
hypocenterC61#8730
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
2. #21460647C2semidirect
3. #21460643C2semidirect
36. C42×D61C8semidirect
153. C61#8730semidirect

Maximal subgroups

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

subgroupindex
#214610522
#214606472
#214606432
C4×#145197342
#873061