Finite Group Databasebeta

← #29580630

Subgroups — #29580630

Order 15616.

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

normal subgroups only

This group has 544 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#21456570C211yesmaximal, characteristic
2#21455759C212yesmaximal, complemented
3#21444178C212yesmaximal, complemented
4#21443696C211yesmaximal, characteristic, complemented
5C61×#1818C211yesmaximal, characteristic, complemented
6C2×#14519751C2212yes—
7#16840086—24no—
8#16840080—22no—
9#16840076—22no—
10#16840075—22no—
11#16839998—22no—
12#16839898—22no—
13#16839805—22no—
14#16839766—22no—
15#16839726C2212yes—
16#16839485—24no—
17C2×#117×C61C2211yescharacteristic
18C2×C22⋊C8×C61C2211yescharacteristic
19C2×C22⋊C8×C61C2211yescharacteristic
20C61×#336—22no—
21C22×D244D412yes—
22C22×C22⋊D61—22no—
23C2×D488—22no—
24C2×#11758194—22no—
25#14519751—22no—
26#14519751—22no—
27#14519751—22no—
28#14519751—22no—
29C2×C4⋊Dic61D412yes—
30C2×#11758198—22no—
31#14519711—22no—
32#14519710—24no—
33#14519708—24no—
34#14519699—24no—
35#14519697—24no—
36#14519697—24no—
37C22⋊#92418—22no—
38C22⋊#92418D414yes—
39C23×C4×C61C2311yescharacteristic
40C22×C8×C61—21no—
41C22×C8×C61D412yes—
42#117×C61—22no—
43#117×C61—22no—
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C22⋊C4×C61—21no—
47C2×C42×C61—21no—
48C22⋊C8×C61—22no—
49C22⋊C8×C61—22no—
50C24×C61#4111yescharacteristic
51C23×D61—22no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61—42no—
55C22×C4×C61C2×D412yes—
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D411yescharacteristic
58C22×C4×C61C2×D412yes—
59C2×C22⋊D61—42no—
60C2×C22⋊D61—42no—
61C2×C22⋊D61—84no—
62C22×Dic61—22no—
63C2×D244—22no—
64C2×D244—22no—
65C2×D244—44no—
66C2×C8×C61—22no—
67C2×C8×C61—42no—
68C2×C8×C61—42no—
69C2×C8×C61—41no—
70C4⋊C4×C61—22no—
71C4⋊C4×C61—22no—
72C22⋊C4×C61—42no—
73C42×C61—41no—
74C42×C61—41no—
75#11758198—42no—
76#11758198—42no—
77C4⋊Dic61—22no—
78C4⋊Dic61—22no—
79#11758194—44no—
80C2×#92418—24no—
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—24no—
92C2×C4×C61—22no—
93C2×C4×C61—41no—
94C2×C4×C61—42no—
95C2×C4×C61—42no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—42no—
99C2×C4×C61#12012yes—
100C2×C4×C61#12011yescharacteristic
101C2×C4×C61#12711yescharacteristic
102C22⋊D61—84no—
103C22⋊D61—84no—
104C2×Dic61—42no—
105C2×Dic61—82no—
106D244—44no—
107D244—44no—
108C8×C61—42no—
109C8×C61—81no—
110#92418—44no—
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—22no—
125C4×C61—21no—
126C4×C61—81no—
127C4×C61—81no—
128C4×C61#45812yes—
129Dic61—82no—
130#3186—611no—
131#3094—612no—
132#1818D6111yescharacteristic, complemented
133#1471—612no—
134#1293—611no—
135C2×C61—22no—
136C2×C61—42no—
137C2×C61#201711yescharacteristic
138C2×C61#201811yescharacteristic
139C2×C61#202211yescharacteristic
140D61—162no—
141C2×#121—612no—
142C2×#117C2×D6111yescharacteristic
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#407—612no—
152C2×C22⋊C8C2×D6111yescharacteristic
153C2×C22⋊C8C2×D6111yescharacteristic
154#336—22no—
155#323—1224no—
156C61#997711yescharacteristic, complemented, Sylow
157C22×D4—612no—
158C22×D4—1222no—
159C23×C4C22×D6111yescharacteristic
160C2×D8—1222no—
161C2×M16—1222no—
162C22×C8—21no—
163C22×C8C22⋊D6112yes—
164#121—1222no—
165#121—1222no—
166#121—1222no—
167#121—1222no—
168#117—22no—
169#117—22no—
170C2×C4⋊C4—612no—
171C2×C4⋊C4D24411yescharacteristic
172C2×C4⋊C4D24411yescharacteristic
173C2×C22⋊C4—21no—
174C2×C22⋊C4—1222no—
175C2×C42—21no—
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—614no—
185C22⋊C8—1222no—
186C24—1222no—
187C24#1175822211yescharacteristic
188C2×D4—1222no—
189C2×D4—1222no—
190C2×D4—4884no—
191C2×D4—2444no—
192C2×D4—2442no—
193C2×D4—2442no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—42no—
197C22×C4—1222no—
198C22×C4C2×D24411yescharacteristic
199C22×C4D4×D6112yes—
200C22×C4D4×D6112yes—
201C22×C4C2×C22⋊D6111yescharacteristic
202D8—4882no—
203M16—2444no—
204C2×C8—22no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—41no—
208C2×C8—1224no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—1222no—
212C4⋊C4—1222no—
213C22⋊C4—42no—
214C22⋊C4—2442no—
215C22⋊C4—2442no—
216C42—41no—
217C42—41no—
218C23—22no—
219C23—41no—
220C23—41no—
221C23—4882no—
222C23—4882no—
223C23—2444no—
224C23—2442no—
225C23#1451975012yes—
226C23#1451975111yescharacteristic
227D4—4884no—
228D4—4884no—
229D4—2444no—
230D4—2444no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—4882no—
240C2×C4—2442no—
241C2×C4#1451974511yescharacteristic
242C2×C4#1451974712yes—
243C2×C4#1451977311yescharacteristic
244C8—42no—
245C8—81no—
246C8—2444no—
247C22—21no—
248C22—21no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—82no—
253C22—9764no—
254C22—4882no—
255C22—4882no—
256C22—4882no—
257C22#1683967111yescharacteristic
258C22#1684003212yes—
259C4—21no—
260C4—22no—
261C4—81no—
262C4—81no—
263C4—4882no—
264C4#1683995112yes—
265C2—22no—
266C2—42no—
267C2—9762no—
268C2#2144692311yescharacteristic
269C2#2144692811yescharacteristic
270C2#2144695011yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1818C2
socleC22×C61#392
prime radical#21456570C2
hypercenter#1818D61
hypocenterC61#9977
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
2. #21455759C2semidirect
3. #21444178C2semidirect
4. #21443696C2semidirect
5. C61×#1818C2semidirect
132. #1818D61semidirect
156. C61#9977semidirect

Maximal subgroups

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

subgroupindex
#214565702
#214557592
#214441782
#214436962
C61×#18182
#997761