Finite Group Databasebeta

← C4×#16840620 #30597797

Subgroups — C4×#16840620 #30597797

Order 15616.

708 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 162 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
1C4×#14519844C212yesmaximal, complemented
2C2×#16840620C212yesmaximal
3#21460697C212yesmaximal, complemented
4C4×#14519773C211yesmaximal, characteristic
5C2×#14519844C2214yes—
6C2×C4×#92420—22no—
7#16840628—22no—
8#16840620C418yesdirect product factor
9C2×#14519773C2211yescharacteristic
10C2×C4×D244C411yescharacteristic
11C2×C4×C22⋊D61—22no—
12#16839665C411yescharacteristic
13#16839663C411yescharacteristic
14#16839662—22no—
15#16839631C2211yescharacteristic
16C42×Dic61C2211yescharacteristic
17C2×C4×D4×C61C411yescharacteristic
18C22×#92420—24no—
19#14519844—24no—
20#14519844C2×C418yescomplemented
21C4×#92420—44no—
22C22×D244C2×C411yescharacteristic
23C22×C22⋊D61—22no—
24C22×C4×D61—21no—
25#14519773—22no—
26#14519773C2×C414yes—
27C4×D244—42no—
28C4×C22⋊D61—44no—
29C4×C22⋊D61—44no—
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—22no—
32C2×C22⋊Dic61—22no—
33C2×#11758198—21no—
34C2×#11758198—22no—
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61D412yes—
37C2×C4×Dic61D412yes—
38C2×C4×Dic61C2311yescharacteristic
39C22×D4×C61C2×C411yescharacteristic
40C23×C4×C61—21no—
41C4×D4×C61—42no—
42C2×C4⋊C4×C61C2×C411yescharacteristic
43C2×C22⋊C4×C61—21no—
44C2×C42×C61C2×C411yescharacteristic
45C24×C61—21no—
46C23×D61—21no—
47C2×D4×C61—21no—
48C2×D4×C61—41no—
49C2×D4×C61—41no—
50C2×D4×C61C4212yes—
51C22×C4×C61—21no—
52C22×C4×C61—42no—
53C22×C4×C61—44no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C2×C22⋊D61—28no—
58C2×C22⋊D61—42no—
59C2×C22⋊D61—42no—
60C2×C22⋊D61—44no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C412yes—
63C22×Dic61C2×D412yes—
64C2×D244—21no—
65C2×D244—41no—
66C2×D244—41no—
67C2×D244C4212yes—
68C2×C4×D61—42no—
69C2×C4×D61—44no—
70C2×#92420—28no—
71C2×#92420—44no—
72C2×#92420—44no—
73C4⋊C4×C61—41no—
74C22⋊C4×C61—42no—
75C42×C61—22no—
76C22⋊Dic61—44no—
77#11758198—42no—
78#11758198—44no—
79C4⋊Dic61—41no—
80#11758196—42no—
81#11758196—42no—
82C4×Dic61—24no—
83C4×Dic61—41no—
84C4×Dic61D814yes—
85C4×Dic61SD1614yes—
86C4×Dic61C22×C412yes—
87C4×Dic61#4112yes—
88C23×C61—22no—
89C23×C61—41no—
90C23×C61—41no—
91C23×C61—42no—
92C23×C61—42no—
93C23×C61C2×C22⋊C411yescharacteristic
94C22×D61—22no—
95C22×D61—41no—
96C22×D61—41no—
97C22×D61—42no—
98C22×D61—42no—
99D4×C61—42no—
100D4×C61—42no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—22no—
105C2×C4×C61—41no—
106C2×C4×C61—42no—
107C2×C4×C61—84no—
108C2×C4×C61#10012yes—
109C2×C4×C61#10214yes—
110C2×C4×C61C2×C4211yescharacteristic
111C2×C4×C61#11711yescharacteristic
112C22⋊D61—48no—
113C22⋊D61—48no—
114C2×Dic61—22no—
115C2×Dic61—22no—
116C2×Dic61—41no—
117C2×Dic61—42no—
118C2×Dic61#10214yes—
119C2×Dic61C4×D414yes—
120C2×Dic61C2×D812yes—
121C2×Dic61C2×SD1612yes—
122C2×Dic61#13514yes—
123D244—42no—
124D244—42no—
125C4×D61—84no—
126#92420—48no—
127C4×#331—611nomaximal, Sylow
128C22×C61—42no—
129C22×C61—44no—
130C22×C61—81no—
131C22×C61—82no—
132C22×C61—81no—
133C22×C61C4×C22⋊C411yescharacteristic
134C22×C61C2×#10011yescharacteristic
135C22×C61#41311yescharacteristic
136C22×C61C2×#10212yes—
137C22×C61#41612yes—
138C2×D61—42no—
139C2×D61—44no—
140C2×D61—81no—
141C2×D61—82no—
142C2×D61—81no—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—41no—
146C4×C61—81no—
147C4×C61#33114yescomplemented
148Dic61—24no—
149Dic61—81no—
150Dic61C4×D814yes—
151Dic61C4×SD1614yes—
152C4×#127—611no—
153C4×C4⋊C8—612no—
154C2×#331—612no—
155#1296—612no—
156C2×C61—82no—
157C2×C61C2×#33111yescharacteristic
158C2×C61#154012yes—
159C2×C61#154311yescharacteristic
160C2×C61C4×#10011yescharacteristic
161C2×C61C4×#10212yes—
162D61—82no—
163C2×#127—611no—
164C2×C4×D4—611no—
165C2×C4×D4—1222no—
166C2×C4×D4#692311yescharacteristic
167C2×C4⋊C8—614no—
168C2×C4×C8—1222no—
169#390—611no—
170#390—611no—
171#390—1222no—
172#384—611no—
173C43—611no—
174#336—1222no—
175#331—618no—
176C61C4×#33111yescharacteristic, complemented, Sylow
177C22×D4—611no—
178C22×D4—1222no—
179C22×D4C2×#692311yescharacteristic
180C23×C4—21no—
181C23×C4—1221no—
182C22×C8—1224no—
183#127—614no—
184#127—1222no—
185C4×D4—42no—
186C4×D4—2442no—
187C4×D4—2444no—
188C4×D4—2444no—
189C2×C4⋊C4—611no—
190C2×C4⋊C4—1222no—
191C2×C4⋊C4C2×#692311yescharacteristic
192C2×C22⋊C4—21no—
193C2×C22⋊C4—1222no—
194C2×C22⋊C4—1222no—
195C2×C22⋊C4—1221no—
196C2×C42—612no—
197C2×C42—611no—
198C2×C42—612no—
199C2×C42—611no—
200C2×C42C2×#692311yescharacteristic
201C4⋊C8—618no—
202C4⋊C8—1224no—
203C4×C8—2444no—
204C24—21no—
205C24—1221no—
206C2×D4—21no—
207C2×D4—41no—
208C2×D4—41no—
209C2×D4—612no—
210C2×D4—1228no—
211C2×D4—1221no—
212C2×D4—2441no—
213C2×D4—2441no—
214C2×D4—2442no—
215C2×D4—2442no—
216C2×D4—2444no—
217C2×D4C4×#692312yes—
218C22×C4—21no—
219C22×C4—42no—
220C22×C4—44no—
221C22×C4—612no—
222C22×C4—612no—
223C22×C4—1221no—
224C22×C4—2442no—
225C22×C4—2444no—
226C22×C4C22⋊#692311yescharacteristic
227C22×C4C22⋊#692311yescharacteristic
228C22×C4C22×#692311yescharacteristic
229C2×C8—1228no—
230C2×C8—2444no—
231C2×C8—2444no—
232C4⋊C4—41no—
233C4⋊C4—2441no—
234C4⋊C4—2442no—
235C4⋊C4—2442no—
236C22⋊C4—42no—
237C22⋊C4—2442no—
238C22⋊C4—2444no—
239C22⋊C4—2444no—
240C42—22no—
241C42—614no—
242C42—614no—
243C42—612no—
244C42—612no—
245C42—1224no—
246C42—2441no—
247C23—22no—
248C23—41no—
249C23—41no—
250C23—42no—
251C23—42no—
252C23—1222no—
253C23—2441no—
254C23—2441no—
255C23—2442no—
256C23—2442no—
257C23C2×C22⋊#692311yescharacteristic
258D4—42no—
259D4—42no—
260D4—2442no—
261D4—2442no—
262D4—2448no—
263D4—2448no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—84no—
271C2×C4—612no—
272C2×C4—612no—
273C2×C4—614no—
274C2×C4—614no—
275C2×C4—614no—
276C2×C4—1222no—
277C2×C4—1222no—
278C2×C4—4884no—
279C2×C4—2441no—
280C2×C4—2442no—
281C2×C4#1451983712yes—
282C2×C4#1451983914yes—
283C2×C4C2×C4×#692311yescharacteristic
284C2×C4#1451985611yescharacteristic
285C8—2448no—
286C22—42no—
287C22—44no—
288C22—81no—
289C22—82no—
290C22—81no—
291C22—4881no—
292C22—4882no—
293C22—4881no—
294C22—2442no—
295C22—2444no—
296C22C4×C22⋊#692311yescharacteristic
297C22C2×#1451983711yescharacteristic
298C22#1684074811yescharacteristic
299C22C2×#1451983912yes—
300C22#1684075212yes—
301C4—21no—
302C4—21no—
303C4—41no—
304C4—81no—
305C4—614no—
306C4—614no—
307C4—1224no—
308C4—4881no—
309C4#1684062014yesdirect product factor
310C2—82no—
311C2—4882no—
312C2C2×#1684062011yescharacteristic
313C2#2146131612yes—
314C2#2146132211yescharacteristic
315C2C4×#1451983711yescharacteristic
316C2C4×#1451983912yes—
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519773C22
cosocleC2×C4×Dic61C23
hypercenterC2×C4×D4#6923
hypocenterC61C4×#331
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C4×#14519844C2semidirect
3. #21460697C2semidirect
8. #16840620C4direct (N × H)
20. #14519844C2×C4semidirect
147. C4×C61#331semidirect
176. C61C4×#331semidirect
309. C4#16840620direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#145198442
C2×#168406202
#214606972
C4×#145197732
C4×#33161