Finite Group Databasebeta

← C2×#21460818 #30604828

Subgroups — C2×#21460818 #30604828

Order 15616.

500 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 104 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×#16840642C211yesmaximal, characteristic
2C2×#16840608C211yesmaximal, characteristic
3#21460818C214yesmaximal, direct product factor
4C2×#16839700C211yesmaximal, characteristic
5C22×#11758217—21no—
6C2×C22⋊#92420—21no—
7#16840642—21no—
8#16840642C2212yes—
9#16840608—21no—
10#16840608C2212yes—
11C22×#11758196C2211yescharacteristic
12#16839700—21no—
13#16839700—21no—
14#16839700C412yes—
15#16839700C2212yes—
16C2×#14519684—21no—
17C2×#14519684—21no—
18C2×#14519684C411yescharacteristic
19C22×C4⋊C4×C61C411yescharacteristic
20C2×#11758217—24no—
21C2×#11758217—22no—
22C2×#11758217—41no—
23C2×#11758217—42no—
24C22×#92420—41no—
25C22×#92420—41no—
26C22⋊#92420—22no—
27C22⋊#92420—41no—
28C23×Dic61—21no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C2×#11758196—41no—
32C2×#11758196—41no—
33C2×#11758196C2×C411yescharacteristic
34C2×#11758196D411yescharacteristic
35C2×#11758196D411yescharacteristic
36C2×#11758196C2311yescharacteristic
37#14519684—21no—
38#14519684—22no—
39#14519684—22no—
40#14519684—22no—
41#14519684—22no—
42#14519684C2×C412yes—
43C23×C4×C61—21no—
44C23×C4×C61C2×C411yescharacteristic
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—41no—
47C2×C4⋊C4×C61—41no—
48C2×C4⋊C4×C61C2×C412yes—
49C24×C61C22⋊C411yescharacteristic
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—22no—
53C22×C4×C61—42no—
54C22×C4×C61—44no—
55C22×C4×C61—41no—
56C22×C4×C61—41no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22×C411yescharacteristic
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61—22no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—22no—
65C22×Dic61—42no—
66C22×Dic61—42no—
67C22×Dic61—42no—
68C22×Dic61—42no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C22⋊C411yescharacteristic
71C22×Dic61SD1612yes—
72C22×Dic61Q1612yes—
73C22×Dic61C2×D411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75#11758217—24no—
76#11758217—44no—
77#11758217—42no—
78C2×#92420—44no—
79C2×#92420—42no—
80C2×#92420—42no—
81C2×#92420—82no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—42no—
84#11758196—41no—
85#11758196—41no—
86#11758196—41no—
87#11758196—41no—
88C23×C61—22no—
89C23×C61—22no—
90C23×C61#9911yescharacteristic
91C23×C61#9911yescharacteristic
92C23×C61#10312yes—
93C23×C61#10412yes—
94C23×C61C2×C22⋊C411yescharacteristic
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—44no—
102C2×C4×C61—42no—
103C2×C4×C61—82no—
104C2×C4×C61—82no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—42no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—42no—
119C2×Dic61—42no—
120C2×Dic61—42no—
121C2×Dic61—81no—
122C2×Dic61—84no—
123C2×Dic61#10312yes—
124C2×Dic61C2×SD1611yescharacteristic
125C2×Dic61C2×Q1611yescharacteristic
126#92420—44no—
127#92420—82no—
128C2×#1353—611nomaximal, Sylow
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—24no—
132C22×C61—24no—
133C22×C61—21no—
134C22×C61—21no—
135C22×C61#32812yes—
136C22×C61#32812yes—
137C22×C61#35212yes—
138C22×C61#35512yes—
139C22×C61C2×#9911yescharacteristic
140C22×C61C2×#10311yescharacteristic
141C22×C61C2×#10411yescharacteristic
142C4×C61—41no—
143C4×C61—41no—
144C4×C61—82no—
145Dic61—21no—
146Dic61—22no—
147Dic61—21no—
148Dic61—41no—
149Dic61—41no—
150Dic61—82no—
151C2×#400—611no—
152C2×#343—611no—
153C2×#324—611no—
154#1353—614no—
155C2×C61—21no—
156C2×C61—22no—
157C2×C61—21no—
158C2×C61#135314yescomplemented
159C2×C61C2×#32811yescharacteristic
160C2×C61C2×#35211yescharacteristic
161C2×C61C2×#35511yescharacteristic
162C22×M16—1221no—
163C22×C4⋊C4—611no—
164C22×C4⋊C4#692311yescharacteristic
165C2×C22⋊C8—1221no—
166#400—612no—
167#400—612no—
168#400—1221no—
169#400—1221no—
170C2×#95—611no—
171C2×#95—1221no—
172C2×#95—1221no—
173#343—612no—
174#343—1221no—
175#324—612no—
176#324—1221no—
177C61C2×#135311yescharacteristic, complemented, Sylow
178C23×C4—21no—
179C23×C4—611no—
180C23×C4—611no—
181C23×C4—1221no—
182C23×C4C2×#692311yescharacteristic
183C2×M16—1222no—
184C2×M16—1224no—
185C2×M16—2442no—
186C2×M16—2441no—
187C22×C8—2441no—
188C22×C8—2441no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4—41no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—611no—
195C2×C4⋊C4—611no—
196C2×C4⋊C4—2441no—
197C2×C4⋊C4—2441no—
198C2×C4⋊C4C2×#692312yes—
199C22⋊C8—1222no—
200C22⋊C8—2441no—
201#95—612no—
202#95—1222no—
203#95—1222no—
204#95—1222no—
205#95—1222no—
206#95—1221no—
207C24C22⋊#692311yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—44no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—612no—
216C22×C4—612no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4—1222no—
224C22×C4—1221no—
225C22×C4—1221no—
226C22×C4—1222no—
227C22×C4—2442no—
228C22×C4—2442no—
229C22×C4—2442no—
230C22×C4—2442no—
231C22×C4C22⋊#692311yescharacteristic
232C22×C4C22×#692311yescharacteristic
233M16—1224no—
234M16—2442no—
235M16—2444no—
236C2×C8—4882no—
237C2×C8—2442no—
238C2×C8—2442no—
239C2×C8—2444no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—2441no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C23—22no—
247C23—22no—
248C23#1451983511yescharacteristic
249C23#1451983511yescharacteristic
250C23#1451984012yes—
251C23#1451984212yes—
252C23C2×C22⋊#692311yescharacteristic
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—612no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—4884no—
277C2×C4—4881no—
278C2×C4—2442no—
279C2×C4—2442no—
280C2×C4—2442no—
281C2×C4—2442no—
282C2×C4—2441no—
283C2×C4—2441no—
284C8—4882no—
285C8—2444no—
286C22—21no—
287C22—21no—
288C22—24no—
289C22—24no—
290C22—21no—
291C22—21no—
292C22#1684061612yes—
293C22#1684061612yes—
294C22#1684066412yes—
295C22#1684067012yes—
296C22C2×#1451983511yescharacteristic
297C22C2×#1451984011yescharacteristic
298C22C2×#1451984211yescharacteristic
299C4—41no—
300C4—41no—
301C4—82no—
302C4—1221no—
303C4—1222no—
304C4—1221no—
305C4—4882no—
306C4—2441no—
307C4—2441no—
308C2—21no—
309C2—21no—
310C2—22no—
311C2#2146081814yesdirect product factor
312C2C2×#1684061611yescharacteristic
313C2C2×#1684066411yescharacteristic
314C2C2×#1684067011yescharacteristic
subgroupG/H
centerC23#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61#99
prime radicalC24×C61C22⋊C4
cosocleC2×#11758196C23
hypercenterC22×C4⋊C4#6923
hypocenterC61C2×#1353
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460818C2direct (N × H)
158. C2×C61#1353semidirect
177. C61C2×#1353semidirect
311. C2#21460818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168406422
C2×#168406082
#214608182
C2×#168397002
C2×#135361