Finite Group Databasebeta

← #29589253

Subgroups — #29589253

Order 15616.

386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 87 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#21454512C211yesmaximal, characteristic
2#21447428C212yesmaximal, complemented
3#21443761C211yesmaximal, characteristic, complemented
4#21443744C212yesmaximal, complemented
5C61×#1323C211yesmaximal, characteristic, complemented
6C2×#14519785C411yescharacteristic
7C22×C8×D61C2211yescharacteristic
8#16840274C411yescharacteristic
9C2×#14519716—22no—
10#16839832—22no—
11#16839827—22no—
12#16839728C2211yescharacteristic
13#16839725C411yescharacteristic
14#16839718C411yescharacteristic
15C22⋊#11758185C2212yes—
16#16839541—22no—
17C61×#424C2211yescharacteristic
18C61×C22⋊C16C2212yes—
19C2×#11758222C2×C411yescharacteristic
20C22×C4×D61C2×C411yescharacteristic
21#14519785—42no—
22C2×#11758194C2×C411yescharacteristic
23C2×#11758189—21no—
24C22×#92418C2×C411yescharacteristic
25C2×C8×D61—21no—
26C2×C8×D61—42no—
27C2×C8×D61D412yes—
28C2×C8×D61D412yes—
29#14519761—21no—
30#14519757C812yes—
31#14519752C812yes—
32#14519747—21no—
33C4×D244—22no—
34#14519716—44no—
35C2×#11758185—22no—
36#14519689—22no—
37#14519689—22no—
38#14519688—21no—
39C4×#92418—21no—
40C2×M16×C61C2×C411yescharacteristic
41C22×C8×C61C2311yescharacteristic
42#117×C61C2×C411yescharacteristic
43C2×C16×C61—22no—
44C4⋊C8×C61—22no—
45C23×D61M1611yescharacteristic
46C22×C4×C61C22×C411yescharacteristic
47C2×C22⋊D61—21no—
48C22×Dic61M1611yescharacteristic
49#11758222—41no—
50#11758222—41no—
51C2×D244—22no—
52C2×D244C2×C811yescharacteristic
53C2×C4×D61—21no—
54C2×C4×D61—41no—
55C2×C4×D61—41no—
56C2×C4×D61C22⋊C412yes—
57C2×C4×D61C2×C812yes—
58C2×Dic122C2×C811yescharacteristic
59M16×C61—41no—
60C2×C8×C61—21no—
61C2×C8×C61—41no—
62C2×C8×C61C2×D412yes—
63C4⋊C4×C61C2×C812yes—
64C22⋊C4×C61—21no—
65C42×C61—21no—
66#11758198—22no—
67#11758198—22no—
68C4⋊Dic61—22no—
69#11758194—41no—
70C2×#92418—22no—
71C2×#92418—21no—
72C2×#92418C22⋊C411yescharacteristic
73C2×#92418C22⋊C411yescharacteristic
74#11758189—42no—
75C8×D61—24no—
76C8×D61—42no—
77C8×D61—42no—
78C16×C61—42no—
79#11758185—42no—
80C23×C61C2×M1611yescharacteristic
81C22×D61—21no—
82C22×D61—41no—
83C22×D61—42no—
84C22×D61C22⋊C812yes—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61C2×C22⋊C411yescharacteristic
89C2×C4×C61C22×C811yescharacteristic
90C22⋊D61—42no—
91C2×Dic61—21no—
92C2×Dic61—41no—
93C2×Dic61C22⋊C812yes—
94D244—41no—
95D244—44no—
96C4×D61—22no—
97C4×D61—22no—
98C4×D61—42no—
99C4×D61—41no—
100C4×D61—41no—
101Dic122—41no—
102C8×C61—22no—
103C8×C61—41no—
104#92418—21no—
105#92418—41no—
106#92418#9912yes—
107#11469—611nomaximal, Sylow
108C22×C61—22no—
109C22×C61—21no—
110C22×C61C2×C22⋊C811yescharacteristic
111C2×D61—22no—
112C2×D61—22no—
113C2×D61—22no—
114C2×D61—44no—
115C2×D61—42no—
116C2×D61—41no—
117C4×C61—21no—
118C4×C61—42no—
119C4×C61C2×#9911yescharacteristic
120C4×C61#41311yescharacteristic
121Dic61—22no—
122Dic61—41no—
123#2929—611no—
124#2112—612no—
125#1323—611no—
126#1323D6111yescharacteristic, complemented
127#1315—612no—
128C2×C61—41no—
129C2×C61#145911yescharacteristic
130C2×C61#211712yes—
131D61—42no—
132D61—81no—
133C2×#131—611no—
134C23×C8—611no—
135#525—611no—
136C2×M32—1222no—
137#435—1222no—
138C8×D4—1222no—
139#424C2×D6111yescharacteristic
140#408—611no—
141#407—611no—
142#405—611no—
143C22⋊C16—612no—
144C22⋊C16—1222no—
145C22⋊C16C2×D6112yes—
146C61#1146911yescharacteristic, complemented, Sylow
147C2×#41—611no—
148C23×C4—611no—
149#131—2442no—
150C2×M16—611no—
151C2×M16—1221no—
152C2×M16C4×D6111yescharacteristic
153C22×C8—611no—
154C22×C8—612no—
155C22×C8—612no—
156C22×C8—1221no—
157C22×C8—2442no—
158C22×C8C22×D6111yescharacteristic
159#123—1221no—
160C22⋊Q8—612no—
161#121—612no—
162#120—1221no—
163C4×D4—1222no—
164#117C4×D6111yescharacteristic
165M32—2444no—
166C2×C16—22no—
167C2×C16—1222no—
168C4⋊C8—22no—
169C22⋊C8—1222no—
170C22⋊C8—1222no—
171#97—1221no—
172C4×C8—1221no—
173C24—611no—
174#41—2441no—
175#41—2441no—
176C2×Q8—611no—
177C2×D4—611no—
178C2×D4—1222no—
179C2×D4—1221no—
180C22×C4—611no—
181C22×C4—612no—
182C22×C4—612no—
183C22×C4—1221no—
184C22×C4—2441no—
185C22×C4—2441no—
186C22×C4C2×C4×D6111yescharacteristic
187M16—41no—
188M16—2442no—
189M16—2441no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—611no—
193C2×C8—611no—
194C2×C8—1224no—
195C2×C8—1222no—
196C2×C8—1221no—
197C2×C8—2442no—
198C2×C8—2442no—
199C2×C8D4×D6112yes—
200C4⋊C4—1222no—
201C4⋊C4C8×D6112yes—
202C22⋊C4—21no—
203C22⋊C4—1222no—
204C22⋊C4—1222no—
205C42—21no—
206C16—42no—
207C16—2442no—
208C23—612no—
209C23—1221no—
210C23—2441no—
211C23—2442no—
212C23M16×D6111yescharacteristic
213Q8—2441no—
214D4—2441no—
215D4—2444no—
216D4—2442no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—612no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1221no—
224C2×C4—2442no—
225C2×C4—2441no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4C22⋊C4×D6111yescharacteristic
229C2×C4C2×C8×D6111yescharacteristic
230C8—22no—
231C8—41no—
232C8—612no—
233C8—1221no—
234C8—2441no—
235C22—22no—
236C22—21no—
237C22—1222no—
238C22—1222no—
239C22—1222no—
240C22—2444no—
241C22—2442no—
242C22—2441no—
243C22C22⋊C8×D6111yescharacteristic
244C4—21no—
245C4—42no—
246C4—1222no—
247C4—2441no—
248C4#99×D6111yescharacteristic
249C4#1683974511yescharacteristic
250C2—41no—
251C2—4881no—
252C2—2442no—
253C2#2144413611yescharacteristic
254C2#2144744512yes—
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#1323C2
socleC22×C61C2×C22⋊C8
prime radical#16840274C4
cosocleC22×C8×C61C23
hypercenter#1323D61
hypocenterC61#11469
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #21447428C2semidirect
3. #21443761C2semidirect
4. #21443744C2semidirect
5. C61×#1323C2semidirect
126. #1323D61semidirect
146. C61#11469semidirect

Maximal subgroups

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

subgroupindex
#214545122
#214474282
#214437612
#214437442
C61×#13232
#1146961