Finite Group Databasebeta

← #29580642

Subgroups — #29580642

Order 15616.

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

normal subgroups only

This group has 492 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#21456594C211yesmaximal, characteristic
2#21455767C212yesmaximal
3#21444182C212yesmaximal
4#21443696C211yesmaximal, characteristic
5C61×#1818C211yesmaximal, characteristic
6C2×#14519756C2212yes—
7#16840103—24no—
8#16840098—22no—
9#16840097—22no—
10#16840092—22no—
11#16840003—22no—
12#16839920—22no—
13#16839805—22no—
14#16839770—22no—
15#16839726C2212yes—
16#16839487—24no—
17C2×#117×C61C2211yescharacteristic
18C2×C22⋊C8×C61C2211yescharacteristic
19C2×C22⋊C8×C61C2211yescharacteristic
20C61×#336—22no—
21C22×Dic122D412yes—
22C2×Dic244—22no—
23C2×#11758194—22no—
24#14519756—22no—
25#14519756—22no—
26#14519756—22no—
27#14519756—22no—
28C2×C4⋊Dic61D412yes—
29C2×#11758196—22no—
30C2×C22⋊Dic61—22no—
31#14519711—22no—
32#14519710—24no—
33#14519708—24no—
34#14519702—24no—
35#14519700—24no—
36#14519700—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
51C22×C4×C61—21no—
52C22×C4×C61—21no—
53C22×C4×C61—42no—
54C22×C4×C61C2×D412yes—
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C22×C4×C61C2×D412yes—
58C22×Dic61—22no—
59C22×Dic61—22no—
60C2×Dic122—22no—
61C2×Dic122—22no—
62C2×Dic122—44no—
63C2×C8×C61—22no—
64C2×C8×C61—42no—
65C2×C8×C61—42no—
66C2×C8×C61—41no—
67C4⋊C4×C61—22no—
68C4⋊C4×C61—22no—
69C22⋊C4×C61—42no—
70C42×C61—41no—
71C42×C61—41no—
72C22⋊Dic61—42no—
73C22⋊Dic61—42no—
74C4⋊Dic61—22no—
75C4⋊Dic61—22no—
76#11758196—42no—
77#11758196—42no—
78#11758194—44no—
79C2×#92418—24no—
80Dic244—82no—
81C23×C61—22no—
82C23×C61—41no—
83C23×C61—41no—
84C23×C61#12112yes—
85C23×C61#12111yescharacteristic
86C2×C4×C61—24no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61—41no—
93C2×C4×C61—42no—
94C2×C4×C61#12012yes—
95C2×C4×C61#12011yescharacteristic
96C2×C4×C61#12711yescharacteristic
97C2×Dic61—44no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—82no—
101Dic122—44no—
102Dic122—44no—
103C8×C61—42no—
104C8×C61—81no—
105#92418—44no—
106#9979—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—22no—
112C22×C61—82no—
113C22×C61#39211yescharacteristic
114C22×C61#47312yes—
115C4×C61—22no—
116C4×C61—21no—
117C4×C61—81no—
118C4×C61—81no—
119C4×C61#45812yes—
120Dic61—82no—
121Dic61—82no—
122#3189—611no—
123#3095—612no—
124#1818D6111yescharacteristic
125#1472—612no—
126#1293—611no—
127C2×C61—22no—
128C2×C61—42no—
129C2×C61#201711yescharacteristic
130C2×C61#202011yescharacteristic
131C2×C61#202211yescharacteristic
132C2×C22⋊Q8—612no—
133C2×#117C2×D6111yescharacteristic
134#485—1224no—
135#484—1222no—
136#484—1222no—
137#483—1222no—
138#467—1222no—
139#451—1222no—
140#428—1222no—
141#419—1222no—
142#407—612no—
143C2×C22⋊C8C2×D6111yescharacteristic
144C2×C22⋊C8C2×D6111yescharacteristic
145#336—22no—
146#324—1224no—
147C61#997911yescharacteristic, complemented, Sylow
148C22×Q8—612no—
149C23×C4C22×D6111yescharacteristic
150C2×Q16—1222no—
151C2×M16—1222no—
152C22×C8—21no—
153C22×C8C22⋊D6112yes—
154C22⋊Q8—1222no—
155C22⋊Q8—1222no—
156C22⋊Q8—1222no—
157C22⋊Q8—1222no—
158#117—22no—
159#117—22no—
160C2×C4⋊C4—612no—
161C2×C4⋊C4—1222no—
162C2×C4⋊C4D24411yescharacteristic
163C2×C4⋊C4D24411yescharacteristic
164C2×C22⋊C4—21no—
165C2×C22⋊C4—1222no—
166C2×C42—21no—
167#107—1224no—
168#107—1222no—
169#106—1224no—
170#103—1224no—
171#103—1224no—
172#103—1224no—
173C22⋊C8—22no—
174C22⋊C8—22no—
175C22⋊C8—614no—
176C22⋊C8—1222no—
177C24#1175822211yescharacteristic
178C2×Q8—1222no—
179C2×Q8—1222no—
180C2×Q8—2444no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—42no—
184C22×C4—1222no—
185C22×C4—1222no—
186C22×C4C2×D24411yescharacteristic
187C22×C4D4×D6112yes—
188C22×C4D4×D6112yes—
189C22×C4C2×C22⋊D6111yescharacteristic
190Q16—4882no—
191M16—2444no—
192C2×C8—22no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—41no—
196C2×C8—1224no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—1222no—
200C4⋊C4—1222no—
201C4⋊C4—2442no—
202C4⋊C4—2442no—
203C22⋊C4—42no—
204C22⋊C4—2442no—
205C22⋊C4—2442no—
206C42—41no—
207C42—41no—
208C23—22no—
209C23—41no—
210C23—41no—
211C23#1451975012yes—
212C23#1451975111yescharacteristic
213Q8—2444no—
214Q8—2444no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—4882no—
224C2×C4—2444no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4#1451974511yescharacteristic
228C2×C4#1451974712yes—
229C2×C4#1451977311yescharacteristic
230C8—42no—
231C8—81no—
232C8—2444no—
233C22—21no—
234C22—21no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—82no—
239C22#1683967111yescharacteristic
240C22#1684003712yes—
241C4—21no—
242C4—22no—
243C4—81no—
244C4—81no—
245C4—4882no—
246C4—4882no—
247C4#1683995112yes—
248C2—22no—
249C2—42no—
250C2#2144692311yescharacteristic
251C2#2144694011yescharacteristic
252C2#2144695011yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1818C2
socleC22×C61#392
prime radicalC24×C61#41
hypercenter#1818D61
hypocenterC61#9979
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
147. C61#9979semidirect

Maximal subgroups

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

subgroupindex
#214565942
#214557672
#214441822
#214436962
C61×#18182
#997961