Finite Group Databasebeta

← #30599908

Subgroups — #30599908

Order 15616.

510 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 100 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#21462717C211yesmaximal, characteristic
2#21461123C212yesmaximal
3#21461063C211yesmaximal, characteristic
4#21460647C212yesmaximal
5#21448386C211yesmaximal, characteristic
6#16840812—24no—
7#16840783—22no—
8#16840778C2212yes—
9#16840778C2212yes—
10#16840612—24no—
11#16840608—22no—
12C2×#14519777C411yescharacteristic
13C2×#14519742C2211yescharacteristic
14C2×#14519742C2211yescharacteristic
15#16839667C411yescharacteristic
16#16839667C411yescharacteristic
17#16839658—22no—
18C4⋊C4×Dic61—22no—
19C42×Dic61C2211yescharacteristic
20C61×#384C411yescharacteristic
21C4⋊#92420—24no—
22C4⋊#92420—22no—
23C4⋊#92420D414yes—
24C22⋊#92420—22no—
25C22⋊#92420—22no—
26#14519832—24no—
27C4×#92420—22no—
28C4×#92420—22no—
29C22×Dic122C2×C411yescharacteristic
30C22×Dic122C2×C411yescharacteristic
31#14519777—22no—
32#14519777—22no—
33#14519742—22no—
34#14519742—22no—
35#14519742—22no—
36#14519742—22no—
37C2×C4⋊Dic61—22no—
38C2×#11758196—21no—
39C2×#11758196D412yes—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C2×C4×Dic61C2×C411yescharacteristic
44C2×C4×Dic61D412yes—
45C2×C4×Dic61C2311yescharacteristic
46#14519684—22no—
47#14519684—22no—
48C2×C4⋊C4×C61—22no—
49C2×C4⋊C4×C61C2×C411yescharacteristic
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C42×C61C2×C411yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C22⋊C412yes—
55C22×C4×C61C22×C411yescharacteristic
56C22×Dic61—21no—
57C22×Dic61—21no—
58C22×Dic61C22⋊C412yes—
59C22×Dic61C2×D411yescharacteristic
60C22×Dic61C2×D411yescharacteristic
61C2×Dic122—22no—
62C2×Dic122—22no—
63C2×Dic122—22no—
64C2×Dic122—21no—
65C2×Dic122—21no—
66C2×Dic122—21no—
67C2×Dic122—22no—
68C2×Dic122M1612yes—
69C2×#92420—24no—
70C2×#92420—42no—
71C4⋊C4×C61—22no—
72C4⋊C4×C61—22no—
73C4⋊C4×C61—44no—
74C42×C61—21no—
75C42×C61M1612yes—
76C4⋊Dic61—28no—
77#11758196—24no—
78#11758196—42no—
79C4×Dic61—24no—
80C4×Dic61—22no—
81C4×Dic61—22no—
82C4×Dic61—22no—
83C4×Dic61—42no—
84C4×Dic61—41no—
85C4×Dic61—41no—
86C4×Dic61C2×D412yes—
87C4×Dic61#4112yes—
88C23×C61C2×C22⋊C411yescharacteristic
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61—41no—
96C2×C4×C61C4×D412yes—
97C2×C4×C61C2×M1611yescharacteristic
98C2×C4×C61C2×M1611yescharacteristic
99C2×C4×C61#13112yes—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61#12011yescharacteristic
112C2×Dic61#12112yes—
113C2×Dic61#12311yescharacteristic
114Dic122—24no—
115Dic122—42no—
116Dic122—42no—
117Dic122—42no—
118#92420—44no—
119#92420—82no—
120#8962—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#38611yescharacteristic
124C22×C61#40711yescharacteristic
125C22×C61#40811yescharacteristic
126C4×C61—24no—
127C4×C61—42no—
128C4×C61—81no—
129C4×C61#43512yes—
130C4×C61#43612yes—
131Dic61—22no—
132Dic61—21no—
133Dic61—42no—
134Dic61—42no—
135Dic61—42no—
136Dic61#45612yes—
137#2983—611no—
138C4×C4⋊Q8—611no—
139#1479—612no—
140#1461—611no—
141#1276—612no—
142C2×C61—21no—
143C2×C61—21no—
144C2×C61#187011yescharacteristic
145C2×C61#188411yescharacteristic
146C2×C61#188611yescharacteristic
147C2×C4⋊Q8—611no—
148C2×C4×Q8—611no—
149C2×C4×Q8—611no—
150#446—1224no—
151#432—1222no—
152#431—612no—
153#431—612no—
154#391—611no—
155#391—611no—
156#389—1222no—
157#384#692311yescharacteristic
158C4×C4⋊C4—1222no—
159C43—611no—
160Q8⋊C8—1224no—
161#324—1222no—
162C61#896211yescharacteristic, complemented, Sylow
163C22×Q8—611no—
164C22×Q8—611no—
165C4⋊Q8—1222no—
166C4⋊Q8—1222no—
167C4×Q8—1222no—
168C4×Q8—1222no—
169C4×Q8—1222no—
170C4×Q8—1222no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—612no—
173C2×C4⋊C4—1222no—
174C2×C4⋊C4—1221no—
175C2×C4⋊C4C2×#692311yescharacteristic
176C2×C4⋊C4C2×#692311yescharacteristic
177C2×C42—611no—
178C2×C42—612no—
179C2×C42—611no—
180C2×C42—1221no—
181C2×C42—1221no—
182C2×C42—1221no—
183C2×C42C2×#692311yescharacteristic
184C4⋊C8—614no—
185C4⋊C8—1222no—
186C4⋊C8—1224no—
187C22⋊C8—1222no—
188C22⋊C8—1222no—
189#97—1224no—
190C4×C8—1222no—
191C4×C8—1222no—
192#95—1222no—
193#95—1222no—
194C2×Q8—612no—
195C2×Q8—1222no—
196C2×Q8—1221no—
197C2×Q8—1221no—
198C2×Q8—1221no—
199C2×Q8—1222no—
200C2×Q8—1222no—
201C2×Q8—1222no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—612no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4C22⋊#692312yes—
210C22×C4C22×#692311yescharacteristic
211C2×C8—1224no—
212C2×C8—2442no—
213C4⋊C4—22no—
214C4⋊C4—22no—
215C4⋊C4—44no—
216C4⋊C4—1224no—
217C4⋊C4—1228no—
218C4⋊C4—2442no—
219C42—21no—
220C42—612no—
221C42—612no—
222C42—1222no—
223C42—1222no—
224C42—1224no—
225C42—1222no—
226C42—2442no—
227C42—2441no—
228C42—2441no—
229C42#1175821312yes—
230C23C2×C22⋊#692311yescharacteristic
231Q8—1224no—
232Q8—2442no—
233Q8—2442no—
234Q8—2442no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—611no—
243C2×C4—612no—
244C2×C4—611no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4D4×#692312yes—
257C2×C4D61⋊M1611yescharacteristic
258C2×C4C2×#1175821311yescharacteristic
259C2×C4#1451986512yes—
260C8—4882no—
261C8—2444no—
262C22—21no—
263C22—21no—
264C22#1684071011yescharacteristic
265C22#1684073311yescharacteristic
266C22#1684073711yescharacteristic
267C4—24no—
268C4—42no—
269C4—81no—
270C4—612no—
271C4—1222no—
272C4—1221no—
273C4—2442no—
274C4—2442no—
275C4—2442no—
276C4#1684079212yes—
277C4#1684079612yes—
278C2—21no—
279C2—21no—
280C2#2146179911yescharacteristic
281C2#2146182211yescharacteristic
282C2#2146182511yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#8962
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
162. C61#8962semidirect

Maximal subgroups

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

subgroupindex
#214627172
#214611232
#214610632
#214606472
#214483862
#896261