Finite Group Databasebeta

← #29589490

Subgroups — #29589490

Order 15616.

412 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 77 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#21444161C212yesmaximal
3#21443764C212yesmaximal
4#21443753C211yesmaximal, characteristic
5C61×#1319C211yesmaximal, characteristic
6C2×#14519775C411yescharacteristic
7C2×Q8×Dic61C411yescharacteristic
8C2×#14519742C2211yescharacteristic
9#16839816—22no—
10#16839668C411yescharacteristic
11#16839659—22no—
12#16839631C2211yescharacteristic
13#16839613—22no—
14C42×Dic61C411yescharacteristic
15#16839488C2212yes—
16#16839487—22no—
17C61×#391C2211yescharacteristic
18C61×#324C2212yes—
19C22×Dic122C2×C411yescharacteristic
20#14519775—22no—
21#14519775—22no—
22Q8×Dic61—41no—
23Q8×Dic61—41no—
24#14519742—41no—
25#14519742—41no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—22no—
29C2×#11758196—22no—
30C2×#11758196D412yes—
31C2×C4×Dic61—21no—
32C2×C4×Dic61—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61D412yes—
37#14519706—42no—
38C22⋊#92418—22no—
39#14519687—42no—
40#14519684—22no—
41C22×Q8×C61C2×C411yescharacteristic
42C2×C4⋊C4×C61C2311yescharacteristic
43C2×C42×C61C2×C411yescharacteristic
44C22⋊C8×C61—22no—
45#95×C61—22no—
46C2×Q8×C61—21no—
47C2×Q8×C61—41no—
48C2×Q8×C61—41no—
49C2×Q8×C61M1612yes—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61C22×C411yescharacteristic
53C22×C4×C61C2×D412yes—
54C22×Dic61—21no—
55C22×Dic61—21no—
56C22×Dic61C22⋊C412yes—
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C22⋊C411yescharacteristic
59C2×Dic122—21no—
60C2×Dic122—21no—
61C2×Dic122—41no—
62C2×Dic122—41no—
63C2×C8×C61—42no—
64C4⋊C4×C61—41no—
65C42×C61—41no—
66C4⋊Dic61—42no—
67C4⋊Dic61—41no—
68#11758196—28no—
69#11758196—42no—
70#11758196—44no—
71C4×Dic61—24no—
72C4×Dic61—21no—
73C4×Dic61—22no—
74C4×Dic61—22no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61—42no—
78C4×Dic61—41no—
79C4×Dic61—41no—
80C4×Dic61M1612yes—
81C2×#92418—42no—
82C23×C61C2×C22⋊C411yescharacteristic
83Q8×C61—42no—
84Q8×C61—42no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—42no—
95C2×C4×C61C2×M1611yescharacteristic
96C2×C4×C61C2×M1611yescharacteristic
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—21no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—41no—
106C2×Dic61—42no—
107C2×Dic61—41no—
108C2×Dic61#9911yescharacteristic
109C2×Dic61#9911yescharacteristic
110Dic122—42no—
111Dic122—42no—
112C8×C61—82no—
113#92418—82no—
114#11532—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61#40711yescharacteristic
118C22×C61C2×#9911yescharacteristic
119C22×C61#41311yescharacteristic
120C4×C61—21no—
121C4×C61—21no—
122C4×C61—42no—
123C4×C61—42no—
124C4×C61—42no—
125Dic61—24no—
126Dic61—21no—
127Dic61—41no—
128Dic61—42no—
129Dic61—81no—
130Dic61#35612yes—
131C4×C4⋊Q8—611no—
132#1467—612no—
133#1325—612no—
134#1319—611no—
135#1319D6111yescharacteristic
136C2×C61—21no—
137C2×C61—21no—
138C2×C61#146511yescharacteristic
139C2×C61#212611yescharacteristic
140C2×C61C2×#35611yescharacteristic
141C2×C4⋊Q8—611no—
142C2×C4×Q8—611no—
143C2×C4×Q8—611no—
144#432—1222no—
145#391—611no—
146#391C2×D6111yescharacteristic
147#389—1222no—
148#384—611no—
149C4×C4⋊C4—1222no—
150C43—611no—
151#324—612no—
152#324—1222no—
153#324C2×D6112yes—
154C61#1153211yescharacteristic, complemented, Sylow
155C22×Q8—611no—
156C22×Q8C4×D6111yescharacteristic
157C4⋊Q8—1222no—
158C4⋊Q8—1222no—
159C4×Q8—2441no—
160C4×Q8—2441no—
161C4×Q8—2441no—
162C4×Q8—2441no—
163C2×C4⋊C4—612no—
164C2×C4⋊C4—611no—
165C2×C4⋊C4—1222no—
166C2×C4⋊C4—1221no—
167C2×C4⋊C4—1222no—
168C2×C4⋊C4C22×D6111yescharacteristic
169C2×C42—611no—
170C2×C42—611no—
171C2×C42—612no—
172C2×C42—1221no—
173C2×C42—1221no—
174C2×C42—1221no—
175C2×C42C4×D6111yescharacteristic
176C4⋊C8—2442no—
177C22⋊C8—22no—
178C22⋊C8—1222no—
179#97—2442no—
180#95—22no—
181#95—1222no—
182C2×Q8—21no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—1221no—
186C2×Q8—1221no—
187C2×Q8—2441no—
188C2×Q8—2441no—
189C2×Q8#1175818912yes—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—611no—
193C22×C4—612no—
194C22×C4—611no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4C2×C4×D6111yescharacteristic
198C22×C4D4×D6112yes—
199C2×C8—42no—
200C2×C8—2442no—
201C4⋊C4—41no—
202C4⋊C4—1228no—
203C4⋊C4—2442no—
204C4⋊C4—2441no—
205C4⋊C4—2444no—
206C4⋊C4—2442no—
207C42—41no—
208C42—612no—
209C42—1222no—
210C42—1222no—
211C42—1221no—
212C42—1221no—
213C42—1224no—
214C42—1221no—
215C42—2441no—
216C42—2441no—
217C42—2442no—
218C23C22⋊C4×D6111yescharacteristic
219Q8—42no—
220Q8—42no—
221Q8—2442no—
222Q8—2442no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1221no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—2442no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4M16×D6111yescharacteristic
247C2×C4C2×#1175818911yescharacteristic
248C8—82no—
249C8—4882no—
250C22—21no—
251C22—21no—
252C22#1683972411yescharacteristic
253C22#99×D6111yescharacteristic
254C22#1683974311yescharacteristic
255C4—21no—
256C4—21no—
257C4—42no—
258C4—42no—
259C4—42no—
260C4—612no—
261C4—1224no—
262C4—1221no—
263C4—4881no—
264C4—2442no—
265C4—2441no—
266C2—21no—
267C2—21no—
268C2#2144415411yescharacteristic
269C2#2144748311yescharacteristic
270C2#356×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1319C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1319D61
hypocenterC61#11532
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
154. C61#11532semidirect

Maximal subgroups

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

subgroupindex
#214483882
#214441612
#214437642
#214437532
C61×#13192
#1153261