Finite Group Databasebeta

← #29580957

Subgroups — #29580957

Order 15616.

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

normal subgroups only

This group has 512 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#21457129C211yesmaximal, characteristic
2#21455941C212yesmaximal, complemented
3#21444429C212yesmaximal, complemented
4#21443689C211yesmaximal, characteristic, complemented
5C61×#1985C211yesmaximal, characteristic, complemented
6#16840312C2212yes—
7#16840075—22no—
8#16840057—22no—
9#16840043—22no—
10#16839998—22no—
11#16839962—22no—
12#16839958—22no—
13#16839901—22no—
14#16839860—24no—
15#16839819C2212yes—
16#16839501—24no—
17C2×C4×Q8×C61C2211yescharacteristic
18C2×C4⋊C8×C61C2211yescharacteristic
19C2×#97×C61C2211yescharacteristic
20C61×#336—22no—
21C2×#11758222—22no—
22C2×#11758201—24no—
23C2×D488—22no—
24#14519777D412yes—
25#14519774D412yes—
26#14519765—22no—
27#14519751—22no—
28#14519751—22no—
29C4×D244—22no—
30C4×D244—22no—
31#14519711—22no—
32#14519710—24no—
33C4⋊#92418—22no—
34#14519701—24no—
35#14519699—24no—
36#14519697—24no—
37C22⋊#92418—22no—
38#14519688D414yes—
39C22×Q8×C61D411yescharacteristic
40C22×C8×C61—21no—
41C22×C8×C61D412yes—
42C4×Q8×C61—22no—
43C4×Q8×C61—22no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C42×C61—21no—
47C2×C42×C61C2311yescharacteristic
48C4⋊C8×C61—22no—
49#97×C61—22no—
50C2×Q8×C61—22no—
51C2×Q8×C61—42no—
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C2×D411yescharacteristic
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61#4111yescharacteristic
57C2×C22⋊D61—42no—
58#11758222—84no—
59C2×D244—22no—
60C2×D244—22no—
61C2×D244—22no—
62C2×C4×D61—42no—
63C2×Dic122—22no—
64C2×C8×C61—22no—
65C2×C8×C61—22no—
66C2×C8×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61—42no—
69C4⋊C4×C61—22no—
70C4⋊C4×C61—42no—
71C42×C61—41no—
72C42×C61—41no—
73C42×C61C2×D412yes—
74C42×C61C2×D412yes—
75#11758201—48no—
76#11758198—42no—
77#11758198—42no—
78C4⋊Dic61—22no—
79C4⋊Dic61—22no—
80C2×#92418—24no—
81D488—82no—
82C23×C61#12111yescharacteristic
83C22×D61—42no—
84Q8×C61—24no—
85Q8×C61—42no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—42no—
95C2×C4×C61#12012yes—
96C2×C4×C61#12011yescharacteristic
97C2×C4×C61#12112yes—
98C2×C4×C61#12711yescharacteristic
99C22⋊D61—84no—
100C2×Dic61—42no—
101D244—44no—
102D244—42no—
103D244—42no—
104D244—82no—
105C4×D61—84no—
106Dic122—82no—
107C8×C61—42no—
108C8×C61—42no—
109#92418—44no—
110#10028—611nomaximal, Sylow
111C22×C61—21no—
112C22×C61—21no—
113C22×C61#39211yescharacteristic
114C22×C61#47212yes—
115C2×D61—82no—
116C2×D61—82no—
117C2×D61—82no—
118C4×C61—21no—
119C4×C61—22no—
120C4×C61—22no—
121C4×C61—42no—
122C4×C61—81no—
123C4×C61#45511yescharacteristic
124C4×C61#45611yescharacteristic
125Dic61—82no—
126#3245—611no—
127#3112—612no—
128#1985D6111yescharacteristic, complemented
129#1530—612no—
130#1290—611no—
131C2×C61—22no—
132C2×C61#200711yescharacteristic
133C2×C61#201011yescharacteristic
134C2×C61#201811yescharacteristic
135D61—162no—
136#532—612no—
137C2×C4×Q8C2×D6111yescharacteristic
138#480—1222no—
139#477—1222no—
140#474—1222no—
141#466—1222no—
142#460—1222no—
143#459—1222no—
144#448—1222no—
145#440—1224no—
146#432—612no—
147C2×C4⋊C8C2×D6111yescharacteristic
148C2×#97C2×D6111yescharacteristic
149#336—22no—
150#329—1224no—
151C61#1002811yescharacteristic, complemented, Sylow
152C2×#41—1222no—
153C22×Q8D24411yescharacteristic
154C2×SD16—1224no—
155C2×D8—1222no—
156C22×C8—21no—
157C22×C8C22⋊D6112yes—
158C4⋊Q8—612no—
159#127—612no—
160#124—1222no—
161#121—1222no—
162#121—1222no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×D4—1222no—
166C4×D4—1222no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4D24411yescharacteristic
169C2×C42—21no—
170C2×C42C22×D6111yescharacteristic
171#107—1224no—
172#107—1222no—
173C4⋊C8—22no—
174C4⋊C8—1222no—
175#103—1224no—
176#102—1224no—
177#102—1224no—
178C22⋊C8—1222no—
179#97—22no—
180#97—614no—
181#41—4884no—
182C2×Q8—22no—
183C2×Q8—42no—
184C2×Q8—1222no—
185C2×D4—1222no—
186C2×D4—1222no—
187C2×D4—1222no—
188C2×D4—2442no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—2442no—
192C22×C4C2×D24411yescharacteristic
193C22×C4#1175822211yescharacteristic
194C22×C4C2×C22⋊D6111yescharacteristic
195SD16—2448no—
196D8—4882no—
197C2×C8—22no—
198C2×C8—22no—
199C2×C8—41no—
200C2×C8—41no—
201C2×C8—42no—
202C2×C8—1224no—
203C4⋊C4—22no—
204C4⋊C4—42no—
205C4⋊C4—1222no—
206C4⋊C4—1222no—
207C22⋊C4—2442no—
208C22⋊C4—2442no—
209C42—41no—
210C42—41no—
211C42D4×D6112yes—
212C42D4×D6112yes—
213C23—2442no—
214C23#1451975111yescharacteristic
215Q8—24no—
216Q8—42no—
217Q8—4882no—
218D4—4882no—
219D4—4884no—
220D4—2444no—
221D4—2442no—
222D4—2442no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—4884no—
233C2×C4—2442no—
234C2×C4#1451974511yescharacteristic
235C2×C4#1451974712yes—
236C2×C4#1451975012yes—
237C2×C4#1451977311yescharacteristic
238C8—42no—
239C8—42no—
240C8—2444no—
241C22—21no—
242C22—21no—
243C22—4882no—
244C22—4882no—
245C22—4882no—
246C22#1683967111yescharacteristic
247C22#1684003212yes—
248C4—22no—
249C4—21no—
250C4—22no—
251C4—42no—
252C4—81no—
253C4—4882no—
254C4#1683993911yescharacteristic
255C4#1683994411yescharacteristic
256C2—22no—
257C2—9762no—
258C2#2144686511yescharacteristic
259C2#2144688611yescharacteristic
260C2#2144692811yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1985C2
socleC22×C61#392
prime radical#21457129C2
hypercenter#1985D61
hypocenterC61#10028
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. #21455941C2semidirect
3. #21444429C2semidirect
4. #21443689C2semidirect
5. C61×#1985C2semidirect
128. #1985D61semidirect
151. C61#10028semidirect

Maximal subgroups

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

subgroupindex
#214571292
#214559412
#214444292
#214436892
C61×#19852
#1002861