Finite Group Databasebeta

← #29568339

Subgroups — #29568339

Order 15616.

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

normal subgroups only

This group has 456 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#21448388C211yesmaximal, characteristic
2#21445934C212yesmaximal
3#21443645C211yesmaximal, characteristic
4#21443644C212yesmaximal
5C61×#1272C211yesmaximal, characteristic
6C2×#14519775C411yescharacteristic
7C2×Q8×Dic61C411yescharacteristic
8C2×#14519742C411yescharacteristic
9C2×#14519706—22no—
10#16839668C2211yescharacteristic
11#16839659—22no—
12#16839631C411yescharacteristic
13#16839613—22no—
14C42×Dic61C2211yescharacteristic
15#16839517C2212yes—
16#16839516—22no—
17C61×#391C2211yescharacteristic
18C61×#336C2212yes—
19C22×Dic122C2×C411yescharacteristic
20C22×#92418—22no—
21#14519775—22no—
22#14519775—22no—
23Q8×Dic61—42no—
24#14519742—42no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×#11758196—22no—
28C2×#11758196—21no—
29C2×#11758196—22no—
30C2×C4×Dic61—21no—
31C2×C4×Dic61—21no—
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61D412yes—
35C2×C4×Dic61D412yes—
36#14519706—44no—
37#14519684—22no—
38C22×Q8×C61C2×C411yescharacteristic
39C22×C8×C61—22no—
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C42×C61C2311yescharacteristic
42#95×C61—22no—
43C2×Q8×C61—21no—
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C2×Q8×C61M1612yes—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C22×C411yescharacteristic
50C22×C4×C61C2×D412yes—
51C22×Dic61—21no—
52C22×Dic61—21no—
53C22×Dic61C22⋊C411yescharacteristic
54C22×Dic61C22⋊C412yes—
55C22×Dic61C22⋊C411yescharacteristic
56C2×Dic122—21no—
57C2×Dic122—41no—
58C2×Dic122—41no—
59C2×Dic122M1612yes—
60C2×C8×C61—42no—
61C2×C8×C61—42no—
62C2×C8×C61—42no—
63C4⋊C4×C61—41no—
64C42×C61—41no—
65C4⋊Dic61—42no—
66C4⋊Dic61—41no—
67#11758196—28no—
68#11758196—44no—
69#11758196—42no—
70C4×Dic61—21no—
71C4×Dic61—21no—
72C4×Dic61—22no—
73C4×Dic61—42no—
74C4×Dic61—42no—
75C4×Dic61—42no—
76C4×Dic61SD1614yes—
77C4×Dic61Q1614yes—
78C2×#92418—42no—
79C2×#92418—42no—
80C2×#92418—42no—
81C23×C61C2×C22⋊C411yescharacteristic
82Q8×C61—42no—
83Q8×C61—42no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—42no—
93C2×C4×C61C2×M1611yescharacteristic
94C2×C4×C61C2×M1611yescharacteristic
95C2×C4×C61C2×SD1612yes—
96C2×C4×C61C2×Q1612yes—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—42no—
106C2×Dic61#10012yes—
107C2×Dic61#10314yes—
108C2×Dic61#10314yes—
109Dic122—42no—
110Dic122—42no—
111C8×C61—82no—
112#92418—82no—
113#7653—611nomaximal, Sylow
114C22×C61#40711yescharacteristic
115C22×C61#41011yescharacteristic
116C22×C61C2×#10011yescharacteristic
117C22×C61C2×#10312yes—
118C22×C61#42112yes—
119C4×C61—21no—
120C4×C61—21no—
121C4×C61—22no—
122C4×C61—22no—
123C4×C61—42no—
124C4×C61—81no—
125Dic61—24no—
126Dic61—41no—
127Dic61—42no—
128Dic61—81no—
129Dic61#33314yes—
130C4×C4⋊Q8—611no—
131#1831—612no—
132#1272—611no—
133#1272—612no—
134#1272D6111yescharacteristic
135C2×C61#146611yescharacteristic
136C2×C61#148712yes—
137C2×C61#151812yes—
138C2×C61#153611yescharacteristic
139C2×C61C2×#33311yescharacteristic
140C2×C4⋊Q8—611no—
141C2×C4×Q8—611no—
142C2×C4×Q8—611no—
143C2×C4⋊C8—1222no—
144#391—611no—
145#391C2×D6111yescharacteristic
146#389—1222no—
147#384—611no—
148C4×C4⋊C4—1222no—
149C43—611no—
150#336—612no—
151#336—1222no—
152#336C2×D6112yes—
153C61#765311yescharacteristic, complemented, Sylow
154C22×Q8—611no—
155C22×Q8C4×D6111yescharacteristic
156C22×C8—22no—
157C22×C8—1222no—
158C4⋊Q8—1222no—
159C4⋊Q8—1222no—
160C4×Q8—2442no—
161C4×Q8—2442no—
162C2×C4⋊C4—611no—
163C2×C4⋊C4—1222no—
164C2×C4⋊C4—1221no—
165C2×C4⋊C4—1221no—
166C2×C4⋊C4—1222no—
167C2×C4⋊C4C4×D6111yescharacteristic
168C2×C42—612no—
169C2×C42—611no—
170C2×C42—611no—
171C2×C42—612no—
172C2×C42—1221no—
173C2×C42—1221no—
174C2×C42C22×D6111yescharacteristic
175C4⋊C8—2444no—
176#95—22no—
177#95—1222no—
178C2×Q8—21no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—612no—
182C2×Q8—1221no—
183C2×Q8—2441no—
184C2×Q8—2441no—
185C2×Q8#1175818912yes—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—611no—
189C22×C4—612no—
190C22×C4—611no—
191C22×C4—1221no—
192C22×C4—1221no—
193C22×C4C2×C4×D6111yescharacteristic
194C22×C4D4×D6112yes—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—2442no—
199C2×C8—2442no—
200C2×C8—2442no—
201C4⋊C4—41no—
202C4⋊C4—1228no—
203C4⋊C4—2441no—
204C4⋊C4—2444no—
205C4⋊C4—2442no—
206C4⋊C4—2442no—
207C42—41no—
208C42—614no—
209C42—614no—
210C42—1222no—
211C42—1221no—
212C42—1221no—
213C42—2442no—
214C42—2442no—
215C42—2442no—
216C23C22⋊C4×D6111yescharacteristic
217Q8—42no—
218Q8—42no—
219Q8—2442no—
220Q8—2442no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—612no—
231C2×C4—614no—
232C2×C4—614no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1221no—
237C2×C4—1222no—
238C2×C4—2441no—
239C2×C4—2442no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4M16×D6111yescharacteristic
243C2×C4C2×#1175818911yescharacteristic
244C2×C4SD16×D6112yes—
245C2×C4Q16×D6112yes—
246C8—82no—
247C8—4882no—
248C22#1683972411yescharacteristic
249C22#1683973411yescharacteristic
250C22#100×D6111yescharacteristic
251C22#103×D6112yes—
252C22#1683977712yes—
253C4—22no—
254C4—22no—
255C4—21no—
256C4—21no—
257C4—42no—
258C4—81no—
259C4—614no—
260C4—1224no—
261C4—4881no—
262C4—2442no—
263C4—2441no—
264C2#2144415811yescharacteristic
265C2#2144424612yes—
266C2#2144438112yes—
267C2#2144445211yescharacteristic
268C2#333×D6111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1272D61
hypocenterC61#7653
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
153. C61#7653semidirect

Maximal subgroups

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

subgroupindex
#214483882
#214459342
#214436452
#214436442
C61×#12722
#765361