Finite Group Databasebeta

← #29569330

Subgroups — #29569330

Order 15616.

438 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 83 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#21453765C211yesmaximal, characteristic
2#21447358C212yesmaximal, complemented
3#21443644C212yesmaximal, complemented
4#21443640C211yesmaximal, characteristic
5C61×#2094C211yesmaximal, characteristic
6C2×#14519710—22no—
7C2×#14519700—22no—
8#16839701—21no—
9#16839674—22no—
10#16839668C2212yes—
11#16839642—21no—
12#16839637—22no—
13#16839517C2212yes—
14C2×#106×C61—21no—
15C2×#102×C61—21no—
16C61×#390C2211yescharacteristic
17C61×#384C2211yescharacteristic
18C61×#336C2211yescharacteristic
19C22×Dic122D412yes—
20C23×Dic61—21no—
21C22×#92418—22no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61D412yes—
24C2×C22⋊Dic61—22no—
25C2×C22⋊Dic61—21no—
26#14519710—44no—
27#14519700—44no—
28#14519684—22no—
29#14519684—21no—
30#14519684—22no—
31#14519684—22no—
32C22×D4×C61D411yescharacteristic
33C22×C8×C61—21no—
34C2×C4⋊C4×C61—22no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61D411yescharacteristic
37C2×C22⋊C4×C61—22no—
38C2×C42×C61C2311yescharacteristic
39#106×C61—42no—
40#102×C61—42no—
41C24×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—41no—
44C2×D4×C61—41no—
45C2×D4×C61Q1612yes—
46C22×C4×C61—21no—
47C22×C4×C61—41no—
48C22×C4×C61C2×D411yescharacteristic
49C22×C4×C61C2×D412yes—
50C22×Dic61—22no—
51C22×Dic61—22no—
52C22×Dic61—82no—
53C22×Dic61—81no—
54C2×Dic122—22no—
55C2×Dic122—22no—
56C2×Dic122—42no—
57C2×Dic122—42no—
58C2×C8×C61—22no—
59C2×C8×C61—41no—
60C2×C8×C61—41no—
61C4⋊C4×C61—41no—
62C4⋊C4×C61—41no—
63C4⋊C4×C61—41no—
64C4⋊C4×C61—42no—
65C4⋊C4×C61—42no—
66C22⋊C4×C61—42no—
67C22⋊C4×C61—42no—
68C42×C61—41no—
69C22⋊Dic61—82no—
70C22⋊Dic61—81no—
71C4⋊Dic61—42no—
72C4⋊Dic61—81no—
73C2×#92418—24no—
74C2×#92418—42no—
75C2×#92418—42no—
76C23×C61—22no—
77C23×C61—42no—
78C23×C61—42no—
79C23×C61—41no—
80C23×C61—41no—
81C23×C61#12011yescharacteristic
82D4×C61—42no—
83D4×C61—81no—
84C2×C4×C61—22no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—42no—
89C2×C4×C61—41no—
90C2×C4×C61—82no—
91C2×C4×C61—81no—
92C2×C4×C61C2×Q1611yescharacteristic
93C2×C4×C61#13512yes—
94C2×C4×C61#13712yes—
95C2×C4×C61#13711yescharacteristic
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—84no—
103Dic122—44no—
104Dic122—82no—
105C8×C61—42no—
106#92418—44no—
107#7833—611nomaximal, Sylow
108C22×C61—42no—
109C22×C61—44no—
110C22×C61—82no—
111C22×C61—81no—
112C22×C61—81no—
113C22×C61#45111yescharacteristic
114C22×C61#45212yes—
115C22×C61#45312yes—
116C22×C61#45311yescharacteristic
117C22×C61#45811yescharacteristic
118C4×C61—21no—
119C4×C61—21no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—81no—
123C4×C61—161no—
124Dic61—82no—
125Dic61—82no—
126#2804—611no—
127#2095—612no—
128#2094D6111yescharacteristic
129#1272—612no—
130#1270—611no—
131C2×C61—82no—
132C2×C61#161411yescharacteristic
133C2×C61#161812yes—
134C2×C61#163011yescharacteristic
135C2×C61#163212yes—
136C2×C61#165511yescharacteristic
137C2×#107—1222no—
138C2×#106—21no—
139C2×#103—1222no—
140C2×#102—21no—
141#400—1221no—
142#393—1222no—
143#391—612no—
144#390C2×D6111yescharacteristic
145#386—1221no—
146#385—1222no—
147#384C2×D6111yescharacteristic
148#336—612no—
149#336C2×D6111yescharacteristic
150C61#783311yescharacteristic, complemented, Sylow
151C22×Q8—612no—
152C22×D4C22⋊D6111yescharacteristic
153C23×C4—1221no—
154C22×C8—21no—
155C22×C8—1222no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—612no—
159C2×C4⋊C4—1221no—
160C2×C4⋊C4C22⋊D6111yescharacteristic
161C2×C22⋊C4—22no—
162C2×C22⋊C4—1222no—
163C2×C22⋊C4—1221no—
164C2×C42C22×D6111yescharacteristic
165#107—2444no—
166#106—42no—
167#103—2444no—
168#102—42no—
169#95—1222no—
170#95—1221no—
171#95—1222no—
172#95—1222no—
173C24—21no—
174C2×Q8—1222no—
175C2×Q8—1222no—
176C2×Q8—2442no—
177C2×Q8—2442no—
178C2×D4—21no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4#1175820212yes—
182C22×C4—21no—
183C22×C4—41no—
184C22×C4—1222no—
185C22×C4—1222no—
186C22×C4—4882no—
187C22×C4—4881no—
188C22×C4D4×D6112yes—
189C22×C4C2×C22⋊D6111yescharacteristic
190C2×C8—22no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—1224no—
194C2×C8—2442no—
195C2×C8—2442no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—42no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—4881no—
202C4⋊C4—2442no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C22⋊C4—4881no—
206C22⋊C4—4882no—
207C42—41no—
208C23—22no—
209C23—41no—
210C23—42no—
211C23—42no—
212C23—41no—
213C23#1451974511yescharacteristic
214Q8—4882no—
215Q8—2444no—
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—82no—
225C2×C4—81no—
226C2×C4—4884no—
227C2×C4—2442no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4—2442no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4C2×#1175820211yescharacteristic
234C2×C4#1451979812yes—
235C2×C4#1451980612yes—
236C2×C4#1451980711yescharacteristic
237C8—42no—
238C8—2444no—
239C22—44no—
240C22—42no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22#1683991711yescharacteristic
245C22#1683992112yes—
246C22#1683992812yes—
247C22#1683992911yescharacteristic
248C22#1683995111yescharacteristic
249C4—22no—
250C4—22no—
251C4—21no—
252C4—21no—
253C4—81no—
254C4—161no—
255C4—4882no—
256C4—4882no—
257C2—82no—
258C2#2144484311yescharacteristic
259C2#2144486412yes—
260C2#2144493811yescharacteristic
261C2#2144495112yes—
262C2#2144510711yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2094C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#2094D61
hypocenterC61#7833
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2094

Complements

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

NH ≅ G/Ntype
2. #21447358C2semidirect
3. #21443644C2semidirect
150. C61#7833semidirect

Maximal subgroups

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

subgroupindex
#214537652
#214473582
#214436442
#214436402
C61×#20942
#783361