Finite Group Databasebeta

← C2×#21461083 #30609966

Subgroups — C2×#21461083 #30609966

Order 15616.

1218 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 1218 conjugacy classes of subgroups — too many to draw. Only its 264 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
1C2×#16840782C212yesmaximal
2#21461083C218yesmaximal, direct product factor
3C2×#16840608C214yesmaximal
4C22×#14519742C211yesmaximal, characteristic
5#16840782—24no—
6#16840782C2218yes—
7C2×#14519844—22no—
8C2×C22⋊#92420C2214yes—
9C2×#14519832—22no—
10#16840608C22116yes—
11C23×Dic122C411yescharacteristic
12C2×#14519742—22no—
13C2×#14519742—22no—
14C2×#14519742—24no—
15C2×#14519742C414yes—
16C2×#14519742C2214yes—
17C22×#11758196C2212yes—
18C22×C4×Dic61C412yes—
19C22×C4×Dic61C2211yescharacteristic
20C22×C4⋊C4×C61C411yescharacteristic
21C22×#92420—24no—
22#14519844—28no—
23C22⋊#92420—24no—
24C22⋊#92420C2318yes—
25#14519832—28no—
26C22×Dic122—22no—
27C22×Dic122—22no—
28C22×Dic122—28no—
29C22×Dic122C2×C414yes—
30C23×Dic61C2×C411yescharacteristic
31C23×Dic61C2×C412yes—
32C23×Dic61C2311yescharacteristic
33#14519742—28no—
34#14519742—28no—
35#14519742—28no—
36#14519742—28no—
37C2×#11758196—24no—
38C2×#11758196—24no—
39C2×#11758196C2×C414yes—
40C2×#11758196C2314yes—
41C2×C4×Dic61—24no—
42C2×C4×Dic61—22no—
43C2×C4×Dic61—22no—
44C2×C4×Dic61C2×C418yes—
45C2×C4×Dic61C2×C412yes—
46C2×C4×Dic61D412yes—
47C2×C4×Dic61D412yes—
48C2×C4×Dic61D414yes—
49C2×C4×Dic61C2312yes—
50C23×C4×C61C2×C412yes—
51C23×C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61—22no—
53C2×C4⋊C4×C61—22no—
54C2×C4⋊C4×C61C2×C414yes—
55C24×C61C22×C411yescharacteristic
56C22×C4×C61—24no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61—44no—
60C22×C4×C61C22⋊C412yes—
61C22×C4×C61C22⋊C412yes—
62C22×C4×C61C22×C412yes—
63C22×C4×C61C22×C414yes—
64C22×Dic61—22no—
65C22×Dic61—22no—
66C22×Dic61—24no—
67C22×Dic61—24no—
68C22×Dic61—42no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C412yes—
71C22×Dic61C22⋊C411yescharacteristic
72C22×Dic61M1618yes—
73C22×Dic61C22×C412yes—
74C22×Dic61C22×C414yes—
75C22×Dic61C22×C411yescharacteristic
76C22×Dic61C2×D412yes—
77C22×Dic61C2×D412yes—
78C22×Dic61C2411yescharacteristic
79C2×Dic122—216no—
80C2×Dic122—216no—
81C2×Dic122—28no—
82C2×Dic122—216no—
83C2×#92420—28no—
84C2×#92420—48no—
85C4⋊C4×C61—28no—
86#11758196—28no—
87#11758196—28no—
88C4×Dic61—28no—
89C4×Dic61—28no—
90C4×Dic61C22⋊C414yes—
91C4×Dic61C22⋊C414yes—
92C4×Dic61C2×D414yes—
93C4×Dic61C2×D414yes—
94C23×C61—22no—
95C23×C61—22no—
96C23×C61C2×C22⋊C411yescharacteristic
97C23×C61C2×C22⋊C411yescharacteristic
98C23×C61C2×M1614yes—
99C23×C61C23×C411yescharacteristic
100C2×C4×C61—24no—
101C2×C4×C61—24no—
102C2×C4×C61—24no—
103C2×C4×C61—24no—
104C2×C4×C61—44no—
105C2×C4×C61—44no—
106C2×C4×C61—44no—
107C2×C4×C61C2×C22⋊C414yes—
108C2×Dic61—24no—
109C2×Dic61—24no—
110C2×Dic61—28no—
111C2×Dic61—28no—
112C2×Dic61—24no—
113C2×Dic61—22no—
114C2×Dic61—24no—
115C2×Dic61—24no—
116C2×Dic61—41no—
117C2×Dic61—42no—
118C2×Dic61—41no—
119C2×Dic61#10114yes—
120C2×Dic61C2×C22⋊C412yes—
121C2×Dic61C2×C22⋊C412yes—
122C2×Dic61C2×C22⋊C412yes—
123C2×Dic61C2×M1618yes—
124C2×Dic61C22×D412yes—
125Dic122—232no—
126#92420—48no—
127C2×#1467—611nomaximal, Sylow
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—28no—
133C22×C61#40712yes—
134C22×C61#40712yes—
135C22×C61#41012yes—
136C22×C61C2×#10112yes—
137C22×C61C22×C22⋊C411yescharacteristic
138C22×C61C22×M1612yes—
139C4×C61—24no—
140C4×C61—44no—
141Dic61—28no—
142Dic61—22no—
143Dic61—22no—
144Dic61—22no—
145Dic61C2×#10114yes—
146C22×C4×Q8—611no—
147C2×#432—612no—
148#1467—618no—
149C2×#324—614no—
150C2×C61—22no—
151C2×C61—22no—
152C2×C61#146714yescomplemented
153C2×C61C2×#40711yescharacteristic
154C2×C61C2×#41011yescharacteristic
155C2×C61C22×#10111yescharacteristic
156C23×Q8—611no—
157C2×C4×Q8—614no—
158C2×C4×Q8—614no—
159C2×C4×Q8—1222no—
160C2×C4×Q8—1222no—
161C2×C4×Q8—1224no—
162C22×C4⋊C4—612no—
163C22×C4⋊C4#692311yescharacteristic
164C22×C42—611no—
165C22×C42—612no—
166#432—618no—
167#432—1224no—
168C2×C4⋊C8—1222no—
169C2×C22⋊C8—614no—
170C2×#97—1222no—
171#324—6116no—
172C61C2×#146711yescharacteristic, complemented, Sylow
173C22×Q8—614no—
174C22×Q8—1228no—
175C22×Q8—1222no—
176C22×Q8—1222no—
177C23×C4—612no—
178C23×C4—611no—
179C23×C4—611no—
180C23×C4C2×#692312yes—
181C23×C4C2×#692311yescharacteristic
182C22×C8—1224no—
183C4×Q8—1228no—
184C4×Q8—1228no—
185C4×Q8—1228no—
186C4×Q8—1228no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—614no—
190C2×C4⋊C4—614no—
191C2×C4⋊C4—1224no—
192C2×C4⋊C4—1224no—
193C2×C4⋊C4C2×#692314yes—
194C2×C42—612no—
195C2×C42—612no—
196C2×C42—614no—
197C2×C42—612no—
198C2×C42—612no—
199C2×C42—618no—
200C2×C42—1224no—
201C2×C42—1222no—
202C2×C42—1222no—
203C4⋊C8—1228no—
204C22⋊C8—618no—
205C22⋊C8—1224no—
206#97—1228no—
207C24C22×#692311yescharacteristic
208C2×Q8—12216no—
209C2×Q8—12216no—
210C2×Q8—12216no—
211C2×Q8—1228no—
212C22×C4—24no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—44no—
216C22×C4—611no—
217C22×C4—612no—
218C22×C4—611no—
219C22×C4—612no—
220C22×C4—618no—
221C22×C4—612no—
222C22×C4—614no—
223C22×C4—612no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—1224no—
227C22×C4—1222no—
228C22×C4—1222no—
229C22×C4—1224no—
230C22×C4—2442no—
231C22×C4C22⋊#692312yes—
232C22×C4C22⋊#692312yes—
233C22×C4C22×#692312yes—
234C22×C4C22×#692314yes—
235C2×C8—1228no—
236C2×C8—2448no—
237C4⋊C4—28no—
238C4⋊C4—1228no—
239C4⋊C4—1228no—
240C42—614no—
241C42—614no—
242C42—614no—
243C42—614no—
244C42—1228no—
245C42—1228no—
246C23—22no—
247C23—22no—
248C23C2×C22⋊#692311yescharacteristic
249C23C2×C22⋊#692311yescharacteristic
250C23D61⋊M1614yes—
251C23C23×#692311yescharacteristic
252Q8—12232no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—24no—
256C2×C4—24no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—614no—
261C2×C4—612no—
262C2×C4—612no—
263C2×C4—612no—
264C2×C4—612no—
265C2×C4—618no—
266C2×C4—1224no—
267C2×C4—1224no—
268C2×C4—1228no—
269C2×C4—1228no—
270C2×C4—1224no—
271C2×C4—1222no—
272C2×C4—1224no—
273C2×C4—1224no—
274C2×C4—2441no—
275C2×C4—2442no—
276C2×C4—2441no—
277C2×C4C2×C22⋊#692314yes—
278C8—2448no—
279C22—28no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22#1684073412yes—
285C22#1684073412yes—
286C22#1684074212yes—
287C22D61⋊#10112yes—
288C22C22×C22⋊#692311yescharacteristic
289C22C2×D61⋊M1612yes—
290C4—24no—
291C4—44no—
292C4—614no—
293C4—1228no—
294C4—1222no—
295C4—1222no—
296C4—1222no—
297C2—22no—
298C2—22no—
299C2#2146108314yesdirect product factor
300C2C2×#1684073411yescharacteristic
301C2C2×#1684074211yescharacteristic
302C2C2×D61⋊#10111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC22×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1467
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #21461083C2direct (N × H)
152. C2×C61#1467semidirect
172. C61C2×#1467semidirect
299. C2#21461083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168407822
#214610832
C2×#168406082
C22×#145197422
C2×#146761