Finite Group Databasebeta

← #29569245

Subgroups — #29569245

Order 15616.

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

normal subgroups only

This group has 410 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#21452851C211yesmaximal, characteristic
2#21447362C211yesmaximal, characteristic
3#21447297C212yesmaximal
4#21443641C212yesmaximal
5C61×#1272C211yesmaximal, characteristic
6C2×#14519775—21no—
7C2×#14519709—22no—
8C2×#14519708—21no—
9C2×#14519701—21no—
10#16839692—21no—
11#16839683—22no—
12#16839660C2212yes—
13#16839647—22no—
14#16839632C2211yescharacteristic
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#391C2211yescharacteristic
18C61×#336C2212yes—
19C22×Dic122—21no—
20C22×#92418—21no—
21#14519775—42no—
22#14519775—42no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—22no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61D412yes—
27C2×C4⋊Dic61D412yes—
28C2×#11758196—22no—
29C2×#11758196—22no—
30C2×C4×Dic61—21no—
31#14519709—44no—
32#14519708—42no—
33#14519701—42no—
34#14519684—22no—
35#14519684—21no—
36#14519684—22no—
37C22×Q8×C61D411yescharacteristic
38C22×C8×C61—22no—
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C42×C61C2311yescharacteristic
41#95×C61—22no—
42C2×Q8×C61—21no—
43C2×Q8×C61—41no—
44C2×Q8×C61—41no—
45C2×Q8×C61SD1612yes—
46C22×C4×C61—21no—
47C22×C4×C61—21no—
48C22×C4×C61C2×D411yescharacteristic
49C22×C4×C61C2×D412yes—
50C22×Dic61—22no—
51C22×Dic61—22no—
52C22×Dic61—41no—
53C2×Dic122—42no—
54C2×Dic122—81no—
55C2×Dic122—81no—
56C2×C8×C61—24no—
57C2×C8×C61—42no—
58C2×C8×C61—42no—
59C4⋊C4×C61—41no—
60C42×C61—41no—
61C4⋊Dic61—22no—
62C4⋊Dic61—42no—
63C4⋊Dic61—41no—
64C4⋊Dic61—41no—
65C4⋊Dic61—42no—
66C4⋊Dic61—42no—
67C4⋊Dic61—81no—
68C4⋊Dic61SD1614yes—
69#11758196—44no—
70#11758196—42no—
71#11758196—42no—
72C4×Dic61—42no—
73C2×#92418—22no—
74C2×#92418—41no—
75C2×#92418—41no—
76C23×C61#12011yescharacteristic
77Q8×C61—42no—
78Q8×C61—81no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—42no—
88C2×C4×C61C2×SD1612yes—
89C2×C4×C61C2×SD1611yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C2×C4×C61#13712yes—
92C2×Dic61—24no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—82no—
99C2×Dic61—81no—
100Dic122—84no—
101C8×C61—44no—
102#92418—42no—
103#7817—611nomaximal, Sylow
104C22×C61#44812yes—
105C22×C61#45011yescharacteristic
106C22×C61#45311yescharacteristic
107C22×C61#45612yes—
108C22×C61#45811yescharacteristic
109C4×C61—22no—
110C4×C61—22no—
111C4×C61—21no—
112C4×C61—21no—
113C4×C61—42no—
114C4×C61—81no—
115Dic61—44no—
116Dic61—82no—
117Dic61—161no—
118#2734—611no—
119#2096—611no—
120#2084—612no—
121#1272D6111yescharacteristic
122#1271—612no—
123C2×C61#161112yes—
124C2×C61#161311yescharacteristic
125C2×C61#162311yescharacteristic
126C2×C61#165112yes—
127C2×C61#166011yescharacteristic
128C2×C4⋊Q8—1221no—
129C2×#106—1222no—
130C2×#106—1221no—
131C2×#103—1221no—
132#398—1221no—
133#395—1222no—
134#391C2×D6111yescharacteristic
135#389—612no—
136#387—1222no—
137#384—611no—
138#340—1222no—
139#336—611no—
140#336C2×D6112yes—
141C61#781711yescharacteristic, complemented, Sylow
142C22×Q8—1221no—
143C22×Q8D24411yescharacteristic
144C22×C8—22no—
145C22×C8—1221no—
146C4⋊Q8—2442no—
147C4⋊Q8—2442no—
148C2×C4⋊C4—612no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4—1221no—
151C2×C4⋊C4—1222no—
152C2×C4⋊C4—1222no—
153C2×C4⋊C4—1221no—
154C2×C4⋊C4—1222no—
155C2×C4⋊C4D24411yescharacteristic
156C2×C42—1221no—
157C2×C42C22×D6111yescharacteristic
158#106—2442no—
159#106—2444no—
160#103—2442no—
161#95—22no—
162#95—1221no—
163#95—1222no—
164#95—1222no—
165C2×Q8—21no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—4881no—
169C2×Q8—4881no—
170C2×Q8—2442no—
171C2×Q8#1175819012yes—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—1222no—
175C22×C4—1222no—
176C22×C4—2441no—
177C22×C4C2×D24411yescharacteristic
178C22×C4D4×D6112yes—
179C2×C8—24no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—1222no—
183C2×C8—2441no—
184C2×C8—2441no—
185C4⋊C4—41no—
186C4⋊C4—614no—
187C4⋊C4—1222no—
188C4⋊C4—4881no—
189C4⋊C4—2441no—
190C4⋊C4—2441no—
191C4⋊C4—2442no—
192C4⋊C4—2444no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C4⋊C4—2442no—
196C4⋊C4—2442no—
197C42—41no—
198C42—2442no—
199C23#1451974711yescharacteristic
200Q8—42no—
201Q8—81no—
202Q8—4884no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—1224no—
213C2×C4—4882no—
214C2×C4—4881no—
215C2×C4—2442no—
216C2×C4—2442no—
217C2×C4—2442no—
218C2×C4—2442no—
219C2×C4—2442no—
220C2×C4SD16×D6112yes—
221C2×C4C2×#1175819011yescharacteristic
222C2×C4#1451980511yescharacteristic
223C2×C4#1451980912yes—
224C8—44no—
225C8—2442no—
226C22#1683990212yes—
227C22#1683991511yescharacteristic
228C22#1683993211yescharacteristic
229C22#1683994612yes—
230C22#1683995311yescharacteristic
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—42no—
236C4—81no—
237C4—9761no—
238C4—4882no—
239C4—2444no—
240C2#2144482812yes—
241C2#2144484111yescharacteristic
242C2#2144489811yescharacteristic
243C2#2144508512yes—
244C2#2144513111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61#120
hypercenter#1272D61
hypocenterC61#7817
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
141. C61#7817semidirect

Maximal subgroups

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

subgroupindex
#214528512
#214473622
#214472972
#214436412
C61×#12722
#781761