Finite Group Databasebeta

← #29580631

Subgroups — #29580631

Order 15616.

544 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 85 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#21456570C211yesmaximal, characteristic
2#21455760C212yesmaximal, complemented
3#21445888C211yesmaximal, characteristic, complemented
4#21444180C212yesmaximal, complemented
5C61×#1293C211yesmaximal, characteristic, complemented
6C2×#14519751C2212yes—
7C2×#14519736C2211yescharacteristic
8#16840087—24no—
9#16840081—22no—
10#16840076—22no—
11#16840076—22no—
12#16839998—22no—
13#16839898—22no—
14#16839804—22no—
15#16839768—22no—
16C2×C22⋊#92418C2211yescharacteristic
17#16839516—22no—
18#16839485—24no—
19C61×#407C2212yes—
20C2×C22⋊C8×C61C2211yescharacteristic
21C22×D244D412yes—
22C22×C22⋊D61—22no—
23C2×D488—22no—
24C22×#92418—21no—
25#14519751—22no—
26#14519751—22no—
27#14519751—22no—
28#14519751—22no—
29#14519736—22no—
30#14519736—22no—
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×C4⋊Dic61D412yes—
34C2×C22⋊Dic61—21no—
35C2×#11758198—22no—
36C2×C4×Dic61—21no—
37#14519711—22no—
38#14519711—24no—
39#14519709—24no—
40#14519699—24no—
41#14519699—24no—
42#14519699—24no—
43C22⋊#92418—22no—
44C23×C4×C61C2311yescharacteristic
45C2×M16×C61—22no—
46C22×C8×C61D412yes—
47C22⋊C8×C61—22no—
48C22⋊C8×C61—22no—
49C22⋊C8×C61D414yes—
50C24×C61#4111yescharacteristic
51C23×D61—22no—
52C22×C4×C61—42no—
53C22×C4×C61C2×D412yes—
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D412yes—
57C2×C22⋊D61—42no—
58C2×C22⋊D61—42no—
59C2×C22⋊D61—84no—
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61—22no—
63C2×D244—22no—
64C2×D244—22no—
65C2×D244—44no—
66M16×C61—44no—
67C2×C8×C61—22no—
68C2×C8×C61—24no—
69C2×C8×C61—42no—
70C22⋊Dic61—42no—
71#11758198—42no—
72#11758198—42no—
73C4⋊Dic61—22no—
74C4⋊Dic61—22no—
75C4⋊Dic61—22no—
76C4⋊Dic61—22no—
77C4×Dic61—41no—
78C4×Dic61—41no—
79C2×#92418—42no—
80C2×#92418—41no—
81D488—82no—
82C23×C61—22no—
83C23×C61—41no—
84C23×C61—41no—
85C23×C61#12112yes—
86C23×C61#12111yescharacteristic
87C22×D61—42no—
88C22×D61—44no—
89C22×D61—82no—
90C22×D61—82no—
91C2×C4×C61—22no—
92C2×C4×C61—24no—
93C2×C4×C61—42no—
94C2×C4×C61—41no—
95C2×C4×C61#12012yes—
96C2×C4×C61#12011yescharacteristic
97C2×C4×C61#12711yescharacteristic
98C22⋊D61—84no—
99C22⋊D61—84no—
100C2×Dic61—42no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—82no—
106D244—44no—
107D244—44no—
108C8×C61—44no—
109C8×C61—42no—
110#92418—81no—
111#9977—611nomaximal, Sylow
112C22×C61—21no—
113C22×C61—21no—
114C22×C61—22no—
115C22×C61—22no—
116C22×C61—22no—
117C22×C61—82no—
118C22×C61#39211yescharacteristic
119C22×C61#47212yes—
120C2×D61—82no—
121C2×D61—82no—
122C2×D61—82no—
123C2×D61—164no—
124C4×C61—21no—
125C4×C61—22no—
126C4×C61#45812yes—
127Dic61—81no—
128Dic61—81no—
129Dic61—82no—
130#3186—611no—
131#3094—612no—
132#1818—611no—
133#1471—612no—
134#1293D6111yescharacteristic, complemented
135C2×C61—22no—
136C2×C61—42no—
137C2×C61#201711yescharacteristic
138C2×C61#201811yescharacteristic
139C2×C61#202211yescharacteristic
140D61—162no—
141C2×#121—612no—
142C2×#117—611no—
143#482—1224no—
144#481—1222no—
145#480—1222no—
146#480—1222no—
147#466—1222no—
148#447—1222no—
149#428—1222no—
150#418—1222no—
151#407C2×D6112yes—
152C2×C22⋊C8—611no—
153C2×C22⋊C8C2×D6111yescharacteristic
154#336—1222no—
155#323—1224no—
156C61#997711yescharacteristic, complemented, Sylow
157C22×D4—612no—
158C22×D4—1222no—
159C23×C4C22×D6111yescharacteristic
160C2×D8—1222no—
161C2×M16—22no—
162C22×C8—1221no—
163C22×C8D24412yes—
164#121—1222no—
165#121—1222no—
166#121—1222no—
167#121—1222no—
168#117—1222no—
169#117—1222no—
170C2×C4⋊C4—611no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—612no—
173C2×C22⋊C4—1221no—
174C2×C22⋊C4—1222no—
175C2×C42—1221no—
176#107—1224no—
177#107—1222no—
178#106—1224no—
179#102—1224no—
180#102—1224no—
181#102—1224no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184C22⋊C8—1222no—
185C22⋊C8D24414yes—
186C24—1222no—
187C24#1175822611yescharacteristic
188C2×D4—1222no—
189C2×D4—1222no—
190C2×D4—4884no—
191C2×D4—2444no—
192C2×D4—2442no—
193C2×D4—2442no—
194C22×C4—42no—
195C22×C4—1222no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4C2×D24411yescharacteristic
199C22×C4C2×D24412yes—
200C22×C4D4×D6112yes—
201C22×C4D4×D6111yescharacteristic
202D8—4882no—
203M16—44no—
204C2×C8—22no—
205C2×C8—24no—
206C2×C8—42no—
207C2×C8—2442no—
208C2×C8—2441no—
209C4⋊C4—1222no—
210C4⋊C4—1222no—
211C4⋊C4—1222no—
212C4⋊C4—1222no—
213C22⋊C4—2442no—
214C22⋊C4—2442no—
215C22⋊C4—2442no—
216C42—2441no—
217C42—2441no—
218C23—22no—
219C23—41no—
220C23—41no—
221C23—4882no—
222C23—4882no—
223C23—2444no—
224C23—2442no—
225C23#1451975212yes—
226C23#1451975211yescharacteristic
227D4—4884no—
228D4—4884no—
229D4—2444no—
230D4—2444no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—4882no—
236C2×C4—2442no—
237C2×C4—2442no—
238C2×C4—2441no—
239C2×C4—2441no—
240C2×C4—2442no—
241C2×C4#1451974712yes—
242C2×C4#1451974711yescharacteristic
243C2×C4#1451977411yescharacteristic
244C8—44no—
245C8—42no—
246C8—4881no—
247C22—21no—
248C22—21no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—82no—
253C22—9764no—
254C22—4882no—
255C22—4882no—
256C22—4882no—
257C22#1683967211yescharacteristic
258C22#1684003312yes—
259C4—22no—
260C4—21no—
261C4—4881no—
262C4—4882no—
263C4—4881no—
264C4#1683995312yes—
265C2—22no—
266C2—42no—
267C2—9762no—
268C2#2144692411yescharacteristic
269C2#2144692911yescharacteristic
270C2#2144695111yescharacteristic
subgroupG/H
centerC22#16839672
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1293C2
socleC22×C61#392
prime radical#21456570C2
hypercenter#1293D61
hypocenterC61#9977
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1293

Complements

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

NH ≅ G/Ntype
2. #21455760C2semidirect
3. #21445888C2semidirect
4. #21444180C2semidirect
5. C61×#1293C2semidirect
134. #1293D61semidirect
156. C61#9977semidirect

Maximal subgroups

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

subgroupindex
#214565702
#214557602
#214458882
#214441802
C61×#12932
#997761