Finite Group Databasebeta

← #29582369

Subgroups — #29582369

Order 15616.

560 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C2×#16840058C212yesmaximal
2#21451192C211yesmaximal, characteristic
3#21446620C211yesmaximal, characteristic
4C2×#16839492C212yesmaximal
5C61×#1296C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7C2×C4×Dic122C2212yes—
8#16840058—24no—
9#16840058—24no—
10C2×#14519711—22no—
11C2×#14519702—22no—
12C2×#14519700—22no—
13C2×C4×#92418C2211yescharacteristic
14#16839692—22no—
15#16839667—22no—
16#16839661—22no—
17#16839492—24no—
18C2×C4⋊C8×C61C2212yes—
19C61×#384C2211yescharacteristic
20C22×Dic122—21no—
21C22×Dic122D412yes—
22C22×#92418—21no—
23#14519777—22no—
24#14519777—21no—
25#14519777D412yes—
26C4×Dic122—22no—
27C4×Dic122—22no—
28C4×Dic122—22no—
29C4×Dic122—22no—
30C2×C4⋊Dic61—22no—
31C2×C4⋊Dic61—22no—
32C2×C4⋊Dic61D412yes—
33C2×#11758196—22no—
34C2×C4×Dic61—22no—
35#14519711—28no—
36#14519702—28no—
37#14519700—44no—
38C4×#92418—22no—
39#14519684—24no—
40#14519684—22no—
41C22×C8×C61—22no—
42C2×C4⋊C4×C61—22no—
43C2×C4⋊C4×C61D412yes—
44C2×C42×C61C2311yescharacteristic
45C4⋊C8×C61—22no—
46C4⋊C8×C61D414yes—
47C22×C4×C61—22no—
48C22×C4×C61C2×D411yescharacteristic
49C22×C4×C61C2×D412yes—
50C22×Dic61—22no—
51C22×Dic61—22no—
52C22×Dic61—41no—
53C2×Dic122—22no—
54C2×Dic122—22no—
55C2×Dic122—22no—
56C2×Dic122—22no—
57C2×Dic122—22no—
58C2×Dic122—22no—
59C2×Dic122—42no—
60C2×Dic122—42no—
61C2×Dic122—41no—
62C2×Dic122Q1614yes—
63C2×C8×C61—24no—
64C2×C8×C61—42no—
65C2×C8×C61—42no—
66C4⋊C4×C61—42no—
67C4⋊C4×C61—42no—
68C4⋊C4×C61—42no—
69C42×C61C2×D411yescharacteristic
70C42×C61C2×D412yes—
71C42×C61#4111yescharacteristic
72C4⋊Dic61—24no—
73C4⋊Dic61—22no—
74C4⋊Dic61—22no—
75C4⋊Dic61—42no—
76C4⋊Dic61—82no—
77#11758196—42no—
78#11758196—42no—
79C4×Dic61—42no—
80C4×Dic61—42no—
81C2×#92418—22no—
82C2×#92418—41no—
83C2×#92418—41no—
84C23×C61#12011yescharacteristic
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—44no—
88C2×C4×C61—42no—
89C2×C4×C61#12012yes—
90C2×C4×C61#12111yescharacteristic
91C2×C4×C61#12112yes—
92C2×C4×C61#12711yescharacteristic
93C2×C4×C61C2×Q1612yes—
94C2×C4×C61#13512yes—
95C2×C4×C61#13712yes—
96C2×C4×C61#13712yes—
97C2×Dic61—24no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61—81no—
105C2×Dic61—81no—
106Dic122—24no—
107Dic122—24no—
108Dic122—42no—
109Dic122—42no—
110Dic122—44no—
111Dic122—82no—
112C8×C61—44no—
113#92418—42no—
114#10237—611nomaximal, Sylow
115C22×C61#39211yescharacteristic
116C22×C61#45112yes—
117C22×C61#45212yes—
118C22×C61#45311yescharacteristic
119C22×C61#45411yescharacteristic
120C4×C61—21no—
121C4×C61—21no—
122C4×C61—82no—
123C4×C61#45112yes—
124C4×C61#45212yes—
125C4×C61#46712yes—
126C4×C61#47012yes—
127Dic61—44no—
128Dic61—82no—
129Dic61—82no—
130C2×#477—612no—
131#2582—611no—
132#1956—611no—
133C2×Q8⋊C8—612no—
134#1296D6111yescharacteristic
135C2×C61#163011yescharacteristic
136C2×C61#163311yescharacteristic
137C2×C61#163612yes—
138C2×C61#200112yes—
139C2×C61#200611yescharacteristic
140C2×C4⋊Q8—611no—
141C2×C4×Q8—612no—
142#477—1224no—
143#477—1224no—
144C2×#107—1222no—
145C2×C4⋊C8C2×D6112yes—
146C2×#103—1222no—
147C2×#103—1222no—
148C2×C4×C8—611no—
149#398—1222no—
150#391—1222no—
151#389—1222no—
152#384C2×D6111yescharacteristic
153Q8⋊C8—1224no—
154C61#1023711yescharacteristic, complemented, Sylow
155C22×Q8—612no—
156C22×Q8—1221no—
157C22×C8—22no—
158C22×C8—1221no—
159C4⋊Q8—612no—
160C4⋊Q8—1222no—
161C4⋊Q8—1221no—
162C4×Q8—1222no—
163C4×Q8—1222no—
164C4×Q8—1222no—
165C4×Q8—1222no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—1222no—
169C2×C4⋊C4—1222no—
170C2×C4⋊C4—1222no—
171C2×C4⋊C4D24412yes—
172C2×C42—1222no—
173C2×C42C22×D6111yescharacteristic
174#107—1228no—
175C4⋊C8—22no—
176C4⋊C8D24414yes—
177#103—1228no—
178#103—2444no—
179C4×C8—1222no—
180#95—1224no—
181#95—1222no—
182C2×Q8—614no—
183C2×Q8—1222no—
184C2×Q8—1222no—
185C2×Q8—1222no—
186C2×Q8—1222no—
187C2×Q8—1222no—
188C2×Q8—1222no—
189C2×Q8—2442no—
190C2×Q8—2442no—
191C2×Q8—2441no—
192C22×C4—22no—
193C22×C4—1222no—
194C22×C4—1222no—
195C22×C4—2441no—
196C22×C4C2×D24411yescharacteristic
197C22×C4D4×D6112yes—
198C2×C8—24no—
199C2×C8—42no—
200C2×C8—42no—
201C2×C8—1222no—
202C2×C8—2441no—
203C2×C8—2441no—
204C4⋊C4—42no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—1224no—
208C4⋊C4—1222no—
209C4⋊C4—1222no—
210C4⋊C4—4882no—
211C4⋊C4—2442no—
212C4⋊C4—2442no—
213C4⋊C4—2442no—
214C42—2442no—
215C42—2442no—
216C42C2×D24412yes—
217C42D4×D6111yescharacteristic
218C42#1175822611yescharacteristic
219C23#1451974711yescharacteristic
220Q8—1224no—
221Q8—1224no—
222Q8—4882no—
223Q8—2444no—
224Q8—2442no—
225Q8—2442no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—44no—
229C2×C4—42no—
230C2×C4—1224no—
231C2×C4—4881no—
232C2×C4—4881no—
233C2×C4—2442no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4—2442no—
238C2×C4—2442no—
239C2×C4#1451974712yes—
240C2×C4#1451975211yescharacteristic
241C2×C4#1451975212yes—
242C2×C4#1451977411yescharacteristic
243C2×C4Q16×D6112yes—
244C2×C4#1451979612yes—
245C2×C4#1451980612yes—
246C2×C4#1451980612yes—
247C8—44no—
248C8—2442no—
249C22#1683967211yescharacteristic
250C22#1683991912yes—
251C22#1683992512yes—
252C22#1683993211yescharacteristic
253C22#1683993711yescharacteristic
254C4—21no—
255C4—21no—
256C4—82no—
257C4—4882no—
258C4—4882no—
259C4—2444no—
260C4#1683991912yes—
261C4#1683992512yes—
262C4#1684000412yes—
263C4#1684002112yes—
264C2#2144494111yescharacteristic
265C2#2144496011yescharacteristic
266C2#2144497812yes—
267C2#2144683012yes—
268C2#2144686311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socle, prime radicalC23×C61#120
hypercenter#1296D61
hypocenterC61#10237
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
154. C61#10237semidirect

Maximal subgroups

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

subgroupindex
C2×#168400582
#214511922
#214466202
C2×#168394922
C61×#12962
#1023761