Finite Group Databasebeta

← #29580882

Subgroups — #29580882

Order 15616.

528 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 103 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#21455854C212yesmaximal
2#21449112C211yesmaximal, characteristic
3#21444247C212yesmaximal
4#21443648C211yesmaximal, characteristic
5C61×#1995C211yesmaximal, characteristic
6C2×C4×Dic122C2212yes—
7#16840095—22no—
8#16840054—22no—
9#16839969—22no—
10#16839917—22no—
11C4×#11758202—24no—
12#16839815C2212yes—
13#16839694—22no—
14#16839683—22no—
15C4×C4⋊Dic61—22no—
16#16839492—24no—
17C61×#533C2211yescharacteristic
18C61×#423C2211yescharacteristic
19C61×#376C2211yescharacteristic
20C61×#339—22no—
21C22×Dic122D412yes—
22C2×#11758202—24no—
23C4×Dic122—22no—
24C4×Dic122—22no—
25C4×Dic122—22no—
26C4×Dic122—22no—
27C2×C4⋊Dic61—24no—
28C2×C4⋊Dic61D412yes—
29C2×#11758196—22no—
30C2×C4×Dic61—22no—
31#14519710—24no—
32C4⋊#92418—22no—
33#14519701—24no—
34#14519700—24no—
35C22⋊#92418—22no—
36C4×#92418D414yes—
37#14519684—22no—
38#14519684—22no—
39C2×M16×C61—21no—
40C4⋊Q8×C61D412yes—
41#125×C61—21no—
42C22⋊Q8×C61—22no—
43C4×Q8×C61—22no—
44#117×C61—21no—
45C2×C42×C61D412yes—
46C2×C42×C61C2311yescharacteristic
47C4⋊C8×C61—22no—
48#95×C61—22no—
49C2×Q8×C61—22no—
50C22×C4×C61—22no—
51C22×C4×C61C2×D412yes—
52C22×C4×C61C2×D411yescharacteristic
53C22×Dic61—22no—
54C22×Dic61—22no—
55C2×Dic122—22no—
56C2×Dic122—22no—
57C2×Dic122—44no—
58M16×C61—42no—
59C2×C8×C61—41no—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—22no—
62C4⋊C4×C61—42no—
63C22⋊C4×C61—41no—
64C42×C61—22no—
65C42×C61—41no—
66C42×C61Q1614yescomplemented
67C42×C61C2×D411yescharacteristic
68C42×C61C2×D412yes—
69C42×C61#4111yescharacteristic
70#11758202—48no—
71C4⋊Dic61—22no—
72C4⋊Dic61—22no—
73C4⋊Dic61—48no—
74#11758196—42no—
75#11758196—42no—
76C4×Dic61—42no—
77C4×Dic61—42no—
78C2×#92418—24no—
79C23×C61#12011yescharacteristic
80Q8×C61—44no—
81C2×C4×C61—24no—
82C2×C4×C61—42no—
83C2×C4×C61—44no—
84C2×C4×C61—42no—
85C2×C4×C61#12012yes—
86C2×C4×C61#12112yes—
87C2×C4×C61#12111yescharacteristic
88C2×C4×C61#12711yescharacteristic
89C2×C4×C61C2×Q1612yes—
90C2×C4×C61#13712yes—
91C2×Dic61—24no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—44no—
95C2×Dic61—42no—
96Dic122—24no—
97Dic122—24no—
98Dic122—42no—
99Dic122—42no—
100C8×C61—81no—
101#92418—44no—
102#10017—611nomaximal, Sylow
103C22×C61—22no—
104C22×C61#39211yescharacteristic
105C22×C61#45112yes—
106C4×C61—22no—
107C4×C61—22no—
108C4×C61—44no—
109C4×C61—82no—
110C4×C61#46212yes—
111C4×C61#49411yescharacteristic
112C4×C61#49711yescharacteristic
113Dic61—44no—
114Dic61—82no—
115#3104—612no—
116#2399—611no—
117#1995D6111yescharacteristic
118#1487—612no—
119#1274—611no—
120C2×C61—22no—
121C2×C61#201012yes—
122C2×C61#201611yescharacteristic
123#533C2×D6111yescharacteristic
124C2×C4×Q8—612no—
125#484—1222no—
126#477—1222no—
127#462—1222no—
128#451—1222no—
129C4×Q16—1224no—
130#431—612no—
131#423C2×D6111yescharacteristic
132#398—1222no—
133#395—1222no—
134C4×C4⋊C4—1222no—
135#376C2×D6111yescharacteristic
136#339—22no—
137Q8⋊C8—1224no—
138C61#1001711yescharacteristic, complemented, Sylow
139C22×Q8—612no—
140C2×Q16—1224no—
141C2×M16—21no—
142C4⋊Q8D24412yes—
143#125—21no—
144C22⋊Q8—22no—
145C4×Q8—22no—
146C4×Q8—1222no—
147C4×Q8—1222no—
148C4×Q8—1222no—
149C4×Q8—1222no—
150#117—21no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4—1224no—
153C2×C4⋊C4—1222no—
154C2×C42—1222no—
155C2×C42C22⋊D6112yes—
156C2×C42C22×D6111yescharacteristic
157#107—1224no—
158C4⋊C8—22no—
159C4⋊C8—1222no—
160#103—1224no—
161#103—1224no—
162C22⋊C8—1222no—
163C4×C8—614no—
164#95—22no—
165#95—1222no—
166#95—1222no—
167C2×Q8—22no—
168C2×Q8—1222no—
169C2×Q8—1222no—
170C2×Q8—2444no—
171C22×C4—22no—
172C22×C4—1222no—
173C22×C4—1222no—
174C22×C4D4×D6112yes—
175C22×C4C2×C22⋊D6111yescharacteristic
176Q16—2448no—
177M16—42no—
178C2×C8—41no—
179C2×C8—1224no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—42no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C4⋊C4—2448no—
186C4⋊C4—2442no—
187C4⋊C4—2442no—
188C22⋊C4—41no—
189C42—22no—
190C42—41no—
191C42—2442no—
192C42—2442no—
193C42#1175820214yescomplemented
194C42C2×D24411yescharacteristic
195C42#1175822211yescharacteristic
196C42D4×D6112yes—
197C23#1451974511yescharacteristic
198Q8—44no—
199Q8—1224no—
200Q8—1224no—
201Q8—2442no—
202Q8—2442no—
203C2×C4—24no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4—1224no—
208C2×C4—2444no—
209C2×C4—2442no—
210C2×C4—2442no—
211C2×C4—2442no—
212C2×C4#1451974712yes—
213C2×C4#1451975012yes—
214C2×C4#1451975111yescharacteristic
215C2×C4#1451977311yescharacteristic
216C2×C4C2×#1175820212yes—
217C2×C4#1451980712yes—
218C8—81no—
219C8—2444no—
220C22—22no—
221C22#1683967111yescharacteristic
222C22#1683991712yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—82no—
227C4—4882no—
228C4—2444no—
229C4#1683997212yes—
230C4#1684014111yescharacteristic
231C4#1684015711yescharacteristic
232C2—22no—
233C2#2144688512yes—
234C2#2144691811yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1995C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#1995D61
hypocenterC61#10017
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
66. C42×C61Q16semidirect
138. C61#10017semidirect
193. C42#11758202semidirect

Maximal subgroups

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

subgroupindex
#214558542
#214491122
#214442472
#214436482
C61×#19952
#1001761