Finite Group Databasebeta

← #30597828

Subgroups — #30597828

Order 15616.

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

normal subgroups only

This group has 534 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
1C8×C22⋊#6923C212yesmaximal, complemented
2#21461196C212yesmaximal
3#21460701C211yesmaximal, characteristic, complemented
4#21460699C211yesmaximal, characteristic, complemented
5#21454512C211yesmaximal, characteristic
6D61⋊(C22⋊C8)C2212yes—
7C2×C8×#6923—22no—
8C4×C22⋊#6923C2212yes—
9(C2×#6923)⋊C8—22no—
10#16840615C414yescomplemented
11#16840614C414yescomplemented
12C2×#14519785C411yescharacteristic, complemented
13C22×C8×D61C2211yescharacteristic
14#16840274C2211yescharacteristic
15#16839832—22no—
16#16839827—22no—
17#16839728C411yescharacteristic, complemented
18#16839725C2211yescharacteristic
19#16839718C411yescharacteristic, complemented
20C61×#424C411yescharacteristic, complemented
21C2×D61⋊C8—22no—
22C2×C22⋊#6923—22no—
23C2×C4×#6923—22no—
24#14519834C2×C414yes—
25C22⋊#92420—22no—
26C8×#6923—44no—
27(C2×#6923)⋊C4C2×C414yes—
28C2×#11758222C2×C411yescharacteristic
29C22×C4×D61C2311yescharacteristic
30#14519785—42no—
31C2×#11758194C2×C411yescharacteristic
32C2×#11758189—21no—
33C22×#92418C2×C411yescharacteristic
34C2×C8×D61—21no—
35C2×C8×D61—42no—
36C2×C8×D61D412yes—
37C2×C8×D61D412yes—
38#14519761—21no—
39#14519757C2×C412yes—
40#14519752C2×C412yes—
41#14519747—21no—
42C4×D244—22no—
43#14519689—22no—
44#14519689—22no—
45#14519688—21no—
46C4×#92418—21no—
47C2×M16×C61C2×C411yescharacteristic
48C22×C8×C61C2×C411yescharacteristic
49#117×C61C2×C411yescharacteristic
50C4⋊C8×C61—22no—
51C23×D61#4111yescharacteristic
52C22×#6923—24no—
53C22×C4×C61C22×C411yescharacteristic
54C2×C22⋊D61—21no—
55C22×Dic61#4111yescharacteristic
56#11758222—41no—
57#11758222—41no—
58C2×D244—22no—
59C2×D244C4211yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61—41no—
62C2×C4×D61—41no—
63C2×C4×D61C22×C412yes—
64C2×C4×D61C2×D412yes—
65C2×Dic122C4211yescharacteristic
66C22⋊#6923—28no—
67C2×#92420—24no—
68C4×#6923—42no—
69C4×#6923—42no—
70D61⋊C8—42no—
71D61⋊C8—42no—
72M16×C61—41no—
73C2×C8×C61—21no—
74C2×C8×C61—41no—
75C2×C8×C61C22⋊C412yes—
76C4⋊C4×C61C4212yes—
77C22⋊C4×C61—21no—
78C42×C61—21no—
79#11758198—22no—
80#11758198—22no—
81C4⋊Dic61—22no—
82#11758194—41no—
83C2×#92418—22no—
84C2×#92418—21no—
85C2×#92418C22⋊C411yescharacteristic
86C2×#92418C22⋊C411yescharacteristic
87#11758189—42no—
88C8×D61—24no—
89C8×D61—42no—
90C8×D61—42no—
91C23×C61#11711yescharacteristic
92C22×D61—24no—
93C22×D61—21no—
94C22×D61—41no—
95C22×D61C4×D412yes—
96C2×#6923—28no—
97C2×#6923—44no—
98C2×#6923—44no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61C2×C4211yescharacteristic
103C2×C4×C61C2×C22⋊C411yescharacteristic
104C22⋊D61—42no—
105C2×Dic61—21no—
106C2×Dic61—41no—
107C2×Dic61C4×D412yes—
108D244—41no—
109D244—44no—
110C4×D61—22no—
111C4×D61—22no—
112C4×D61—42no—
113C4×D61—41no—
114C4×D61—41no—
115Dic122—41no—
116#92420—44no—
117C8×C61—22no—
118C8×C61—41no—
119#92418—21no—
120#92418—41no—
121#92418#9912yes—
122#8238—611nomaximal, Sylow
123C22×C61—21no—
124C22×C61—22no—
125C22×C61C4×C22⋊C411yescharacteristic
126C2×D61—22no—
127C2×D61—22no—
128C2×D61—44no—
129C2×D61—41no—
130C2×D61—42no—
131C2×D61#44314yes—
132#6923—48no—
133C4×C61—21no—
134C4×C61—42no—
135C4×C61C2×#9911yescharacteristic
136C4×C61#41011yescharacteristic
137Dic61—22no—
138Dic61—41no—
139#2929—611no—
140C8×C22⋊C4—612no—
141#1501—612no—
142#1298—611no—
143#1297—611no—
144C2×C61—41no—
145C2×C61C4×#9911yescharacteristic
146C2×C61#176412yes—
147D61—24no—
148D61—81no—
149C2×#131—611no—
150C23×C8—611no—
151#525—611no—
152#435—1222no—
153C8×D4—1222no—
154#424#692311yescharacteristic, complemented
155#408—611no—
156#407—611no—
157C2×C22⋊C8—612no—
158#405—611no—
159C2×C4×C8—1222no—
160C4×C22⋊C4—612no—
161#336—1222no—
162#328—614no—
163#327—614no—
164C61#823811yescharacteristic, complemented, Sylow
165C2×#41—611no—
166C23×C4—611no—
167#131—2442no—
168C2×M16—611no—
169C2×M16—1221no—
170C2×M16C2×#692311yescharacteristic
171C22×C8—611no—
172C22×C8—612no—
173C22×C8—612no—
174C22×C8—1221no—
175C22×C8—1222no—
176C22×C8—2442no—
177C22×C8C2×#692311yescharacteristic
178#123—1221no—
179C22⋊Q8—612no—
180#121—612no—
181#120—1221no—
182C4×D4—1222no—
183#117C2×#692311yescharacteristic
184C2×C22⋊C4—1222no—
185C2×C42—1222no—
186C4⋊C8—22no—
187C22⋊C8—614no—
188C22⋊C8—1222no—
189C22⋊C8—1222no—
190C22⋊C8—1222no—
191#97—1221no—
192C4×C8—1221no—
193C4×C8—2444no—
194#95—614no—
195C24—611no—
196#41—2441no—
197#41—2441no—
198C2×Q8—611no—
199C2×D4—611no—
200C2×D4—1222no—
201C2×D4—1221no—
202C22×C4—611no—
203C22×C4—612no—
204C22×C4—612no—
205C22×C4—1224no—
206C22×C4—1221no—
207C22×C4—2441no—
208C22×C4—2441no—
209C22×C4C22×#692311yescharacteristic
210M16—41no—
211M16—2442no—
212M16—2441no—
213C2×C8—21no—
214C2×C8—41no—
215C2×C8—611no—
216C2×C8—611no—
217C2×C8—1224no—
218C2×C8—1222no—
219C2×C8—1224no—
220C2×C8—1221no—
221C2×C8—2442no—
222C2×C8—2442no—
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8C22⋊#692312yes—
226C4⋊C4—1222no—
227C4⋊C4C4×#692312yes—
228C22⋊C4—21no—
229C22⋊C4—1222no—
230C22⋊C4—1222no—
231C22⋊C4—1228no—
232C42—21no—
233C42—2442no—
234C42—2442no—
235C23—612no—
236C23—1224no—
237C23—1221no—
238C23—2441no—
239C23#1451985611yescharacteristic
240Q8—2441no—
241D4—2441no—
242D4—2444no—
243D4—2442no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—612no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1228no—
251C2×C4—1221no—
252C2×C4—2442no—
253C2×C4—2441no—
254C2×C4—2444no—
255C2×C4—2444no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4C2×C4×#692311yescharacteristic
259C2×C4C2×C22⋊#692311yescharacteristic
260C8—22no—
261C8—41no—
262C8—612no—
263C8—1221no—
264C8—2444no—
265C8—2441no—
266C22—21no—
267C22—22no—
268C22—614no—
269C22—1222no—
270C22—1222no—
271C22—2444no—
272C22—2441no—
273C22—2442no—
274C22C4×C22⋊#692311yescharacteristic
275C4—21no—
276C4—42no—
277C4—1222no—
278C4—2448no—
279C4—2441no—
280C4D61⋊#9911yescharacteristic
281C4#1684074311yescharacteristic
282C2—41no—
283C2—1224no—
284C2—4881no—
285C2#2146156411yescharacteristic
286C2#2146159312yes—
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#424C4
socleC22×C61C4×C22⋊C4
prime radical#16840274C22
cosocleC22×C4×D61C23
hypercenter#424#6923
hypocenterC61#8238
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
1. C8×C22⋊#6923C2semidirect
3. #21460701C2semidirect
4. #21460699C2semidirect
10. #16840615C4semidirect
11. #16840614C4semidirect
12. C2×#14519785C4semidirect
17. #16839728C4semidirect
19. #16839718C4semidirect
20. C61×#424C4semidirect
154. #424#6923semidirect
164. C61#8238semidirect

Maximal subgroups

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

subgroupindex
C8×C22⋊#69232
#214611962
#214607012
#214606992
#214545122
#823861