Finite Group Databasebeta

← #29574681

Subgroups — #29574681

Order 15616.

510 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 119 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#21454904C211yesmaximal, characteristic
2C4×#14519775C211yesmaximal, characteristic
3#21444215C212yesmaximal
4#21443651C212yesmaximal
5C61×#1461C211yesmaximal, characteristic
6C2×#14519775C411yescharacteristic
7C2×C4×Dic122C2211yescharacteristic
8#16839893—24no—
9#16839819—22no—
10#16839815C2212yes—
11#16839669C411yescharacteristic
12#16839667C411yescharacteristic
13#16839657—22no—
14#16839631C411yescharacteristic
15C4×#11758196—22no—
16C42×Dic61C2211yescharacteristic
17#16839494—24no—
18C2×C4×Q8×C61C2211yescharacteristic
19C61×#431C2212yes—
20C61×#324—22no—
21C22×Dic122C2×C411yescharacteristic
22#14519775—22no—
23#14519775—22no—
24C4×Dic122—22no—
25C4×Dic122—22no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×#11758196—22no—
28C2×#11758196—22no—
29C2×#11758196—21no—
30C2×C4×Dic61—21no—
31C2×C4×Dic61—21no—
32C2×C4×Dic61—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61C2×C411yescharacteristic
35C4⋊#92418—24no—
36C4⋊#92418D414yes—
37C22⋊#92418—22no—
38#14519688—24no—
39C4×#92418—22no—
40#14519684—22no—
41#14519684—22no—
42C22×Q8×C61C2×C411yescharacteristic
43C4×Q8×C61—22no—
44C4×Q8×C61—22no—
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61D412yes—
47C2×C42×C61D412yes—
48C2×C42×C61C2311yescharacteristic
49C4⋊C8×C61—22no—
50C22⋊C8×C61—22no—
51C4×C8×C61—22no—
52C2×Q8×C61—22no—
53C2×Q8×C61—21no—
54C2×Q8×C61—21no—
55C2×Q8×C61—22no—
56C22×C4×C61C22⋊C412yes—
57C22×C4×C61C22⋊C412yes—
58C22×C4×C61C22×C411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—21no—
65C2×Dic122—22no—
66C2×Dic122—22no—
67C2×Dic122—21no—
68C2×Dic122M1612yes—
69C2×C8×C61—42no—
70C4⋊C4×C61—22no—
71C4⋊C4×C61—24no—
72C42×C61—22no—
73C42×C61—22no—
74C42×C61C2×D412yes—
75C42×C61#4112yes—
76C4⋊Dic61—22no—
77#11758196—28no—
78#11758196—44no—
79#11758196—42no—
80C4×Dic61—24no—
81C4×Dic61—21no—
82C4×Dic61—22no—
83C4×Dic61—42no—
84C4×Dic61—41no—
85C4×Dic61—41no—
86C4×Dic61M1612yes—
87C2×#92418—24no—
88C23×C61C2×C22⋊C411yescharacteristic
89Q8×C61—42no—
90Q8×C61—42no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—41no—
97C2×C4×C61—42no—
98C2×C4×C61C4×D412yes—
99C2×C4×C61#12011yescharacteristic
100C2×C4×C61#12112yes—
101C2×C4×C61#12311yescharacteristic
102C2×C4×C61C2×M1611yescharacteristic
103C2×C4×C61C2×M1611yescharacteristic
104C2×C4×C61#13112yes—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—42no—
115C2×Dic61—41no—
116Dic122—24no—
117Dic122—42no—
118C8×C61—82no—
119#92418—44no—
120#8962—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#38611yescharacteristic
124C22×C61#40711yescharacteristic
125C22×C61#40811yescharacteristic
126C4×C61—22no—
127C4×C61—21no—
128C4×C61—42no—
129C4×C61—42no—
130C4×C61#43512yes—
131C4×C61#43612yes—
132C4×C61#45612yes—
133Dic61—24no—
134Dic61—42no—
135Dic61—42no—
136Dic61—81no—
137#2983—611no—
138C4×C4⋊Q8—611no—
139#1479—612no—
140#1461D6111yescharacteristic
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×Q8C2×D6111yescharacteristic
150#446—1224no—
151#432—1222no—
152#431—612no—
153#431C2×D6112yes—
154#391—611no—
155#391—611no—
156#389—1222no—
157#384—611no—
158C4×C4⋊C4—1222no—
159C43—611no—
160Q8⋊C8—1224no—
161#324—22no—
162C61#896211yescharacteristic, complemented, Sylow
163C22×Q8—611no—
164C22×Q8C4×D6111yescharacteristic
165C4⋊Q8—1222no—
166C4⋊Q8—1222no—
167C4×Q8—22no—
168C4×Q8—22no—
169C4×Q8—1222no—
170C4×Q8—1222no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—1222no—
173C2×C4⋊C4—1222no—
174C2×C4⋊C4—1221no—
175C2×C4⋊C4C4×D6111yescharacteristic
176C2×C4⋊C4C22⋊D6112yes—
177C2×C42—611no—
178C2×C42—611no—
179C2×C42—1221no—
180C2×C42—1221no—
181C2×C42—1221no—
182C2×C42D24412yes—
183C2×C42C22×D6111yescharacteristic
184C4⋊C8—22no—
185C4⋊C8—614no—
186C4⋊C8—1224no—
187C22⋊C8—22no—
188C22⋊C8—1222no—
189#97—1224no—
190C4×C8—22no—
191C4×C8—1222no—
192#95—1222no—
193#95—1222no—
194C2×Q8—22no—
195C2×Q8—21no—
196C2×Q8—21no—
197C2×Q8—22no—
198C2×Q8—612no—
199C2×Q8—1221no—
200C2×Q8—1222no—
201C2×Q8—1222no—
202C22×C4—1221no—
203C22×C4—1221no—
204C22×C4—1221no—
205C22×C4—1221no—
206C22×C4#1175819812yes—
207C22×C4#1175819812yes—
208C22×C4C2×C4×D6111yescharacteristic
209C22×C4C2×D24411yescharacteristic
210C22×C4C2×C22⋊D6111yescharacteristic
211C2×C8—42no—
212C2×C8—1224no—
213C4⋊C4—22no—
214C4⋊C4—24no—
215C4⋊C4—1228no—
216C4⋊C4—1222no—
217C4⋊C4—2444no—
218C4⋊C4—2442no—
219C42—22no—
220C42—22no—
221C42—612no—
222C42—1224no—
223C42—1221no—
224C42—1222no—
225C42—2442no—
226C42—2441no—
227C42—2441no—
228C42D4×D6112yes—
229C42#1175822412yes—
230C23C2×#1175819811yescharacteristic
231Q8—42no—
232Q8—42no—
233Q8—1224no—
234Q8—2442no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—2442no—
248C2×C4—2441no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4#1451973712yes—
254C2×C4#1451974711yescharacteristic
255C2×C4#1451974912yes—
256C2×C4#1451976111yescharacteristic
257C2×C4M16×D6111yescharacteristic
258C2×C4M16×D6111yescharacteristic
259C2×C4#1451978312yes—
260C8—82no—
261C8—2444no—
262C22—21no—
263C22—21no—
264C22#1683963911yescharacteristic
265C22#1683972511yescharacteristic
266C22#1683972811yescharacteristic
267C4—22no—
268C4—21no—
269C4—42no—
270C4—42no—
271C4—1224no—
272C4—4881no—
273C4—2442no—
274C4—2442no—
275C4#1683983612yes—
276C4#1683983712yes—
277C4#1683994712yes—
278C2—21no—
279C2—21no—
280C2#2144611411yescharacteristic
281C2#2144620011yescharacteristic
282C2#2144621011yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1461C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1461D61
hypocenterC61#8962
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

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
#214549042
C4×#145197752
#214442152
#214436512
C61×#14612
#896261