Finite Group Databasebeta

← #29568842

Subgroups — #29568842

Order 15616.

468 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 87 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#21452851C211yesmaximal, characteristic
2#21447148C212yesmaximal
3#21446918C211yesmaximal, characteristic
4#21443641C212yesmaximal
5C61×#1272C211yesmaximal, characteristic
6C22×#11758202—21no—
7C2×#14519777C2211yescharacteristic
8C2×#14519775—21no—
9C2×#14519711—22no—
10C2×#14519700—21no—
11#16839692—21no—
12#16839683—22no—
13#16839660C2212yes—
14#16839647—22no—
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#391C2211yescharacteristic
18C61×#336C2212yes—
19C22×Dic122—21no—
20C22×Dic122—21no—
21C2×#11758202—42no—
22C2×#11758202—42no—
23C2×#11758202—42no—
24C22×#92418—21no—
25#14519777—42no—
26#14519775—42no—
27#14519775—42no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61D412yes—
31C2×C4⋊Dic61D412yes—
32C2×#11758196—22no—
33C2×#11758196—22no—
34C2×C4×Dic61—21no—
35#14519711—44no—
36#14519700—42no—
37#14519684—22no—
38#14519684—21no—
39#14519684—22no—
40C22×Q8×C61D411yescharacteristic
41C22×C8×C61—22no—
42C2×C4⋊C4×C61D411yescharacteristic
43C2×C42×C61C2311yescharacteristic
44#95×C61—22no—
45C2×Q8×C61—21no—
46C2×Q8×C61—41no—
47C2×Q8×C61—41no—
48C2×Q8×C61D812yes—
49C22×C4×C61—21no—
50C22×C4×C61—21no—
51C22×C4×C61C2×D411yescharacteristic
52C22×C4×C61C2×D412yes—
53C22×Dic61—22no—
54C22×Dic61—22no—
55C22×Dic61—41no—
56C2×Dic122—22no—
57C2×Dic122—41no—
58C2×Dic122—41no—
59C2×Dic122—41no—
60C2×Dic122—41no—
61C2×Dic122—42no—
62C2×Dic122—41no—
63C2×Dic122—81no—
64C2×Dic122—81no—
65C2×C8×C61—24no—
66C2×C8×C61—42no—
67C2×C8×C61—42no—
68C4⋊C4×C61—41no—
69C42×C61—41no—
70#11758202—48no—
71C4⋊Dic61—22no—
72C4⋊Dic61—24no—
73C4⋊Dic61—42no—
74C4⋊Dic61—42no—
75C4⋊Dic61—81no—
76C4⋊Dic61Q1614yescomplemented
77#11758196—44no—
78#11758196—42no—
79#11758196—42no—
80C4×Dic61—42no—
81C2×#92418—22no—
82C2×#92418—41no—
83C2×#92418—41no—
84C23×C61#12011yescharacteristic
85Q8×C61—42no—
86Q8×C61—81no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—42no—
96C2×C4×C61C2×D811yescharacteristic
97C2×C4×C61C2×Q1612yes—
98C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
99C2×C4×C61#13712yes—
100C2×Dic61—24no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61—42no—
106C2×Dic61—42no—
107C2×Dic61—81no—
108C2×Dic61—81no—
109Dic122—42no—
110Dic122—42no—
111Dic122—81no—
112Dic122—81no—
113Dic122—84no—
114C8×C61—44no—
115#92418—42no—
116#7757—611nomaximal, Sylow
117C22×C61#44711yescharacteristic
118C22×C61#45112yes—
119C22×C61#45311yescharacteristic
120C22×C61#45612yes—
121C22×C61B(4,𝔽2)11yescharacteristic
122C4×C61—21no—
123C4×C61—21no—
124C4×C61—22no—
125C4×C61—22no—
126C4×C61—42no—
127C4×C61—81no—
128Dic61—44no—
129Dic61—82no—
130Dic61—82no—
131#2734—611no—
132#2057—612no—
133#2016—611no—
134#1272D6111yescharacteristic
135#1271—612no—
136C2×C61#159511yescharacteristic
137C2×C61#160512yes—
138C2×C61#163311yescharacteristic
139C2×C61#164912yes—
140C2×C61#166011yescharacteristic
141C22×Q16—1221no—
142C2×C4⋊Q8—611no—
143C2×C4⋊Q8—1221no—
144C2×#107—1222no—
145C2×#103—1221no—
146#398—1221no—
147#395—1222no—
148#391C2×D6111yescharacteristic
149#389—612no—
150#387—1222no—
151#340—1222no—
152#336—611no—
153#336C2×D6112yes—
154C61#775711yescharacteristic, complemented, Sylow
155C22×Q8—1221no—
156C22×Q8—1221no—
157C22×Q8D24411yescharacteristic
158C2×Q16—2442no—
159C2×Q16—2442no—
160C2×Q16—2442no—
161C22×C8—22no—
162C22×C8—1221no—
163C4⋊Q8—2442no—
164C4⋊Q8—2442no—
165C4⋊Q8—2442no—
166C2×C4⋊C4—612no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—1222no—
169C2×C4⋊C4—1221no—
170C2×C4⋊C4—1222no—
171C2×C4⋊C4—1222no—
172C2×C4⋊C4D24411yescharacteristic
173C2×C42—1221no—
174C2×C42C22×D6111yescharacteristic
175#107—2444no—
176#103—2442no—
177#95—22no—
178#95—1221no—
179#95—1222no—
180#95—1222no—
181C2×Q8—21no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—1222no—
185C2×Q8—4881no—
186C2×Q8—4881no—
187C2×Q8—2441no—
188C2×Q8—2441no—
189C2×Q8—2441no—
190C2×Q8—2442no—
191C2×Q8—2441no—
192C2×Q8—2441no—
193C2×Q8D48812yes—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—1222no—
197C22×C4—1222no—
198C22×C4—2441no—
199C22×C4C2×D24411yescharacteristic
200C22×C4D4×D6112yes—
201Q16—2448no—
202C2×C8—24no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—1222no—
206C2×C8—2441no—
207C2×C8—2441no—
208C4⋊C4—41no—
209C4⋊C4—614no—
210C4⋊C4—1224no—
211C4⋊C4—1222no—
212C4⋊C4—4881no—
213C4⋊C4—2442no—
214C4⋊C4—2444no—
215C4⋊C4—2442no—
216C4⋊C4—2442no—
217C4⋊C4—2442no—
218C42—41no—
219C42—2442no—
220C23#1451974711yescharacteristic
221Q8—42no—
222Q8—81no—
223Q8—4881no—
224Q8—4881no—
225Q8—4884no—
226Q8—2442no—
227Q8—2442no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—1224no—
238C2×C4—4881no—
239C2×C4—4881no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4—2442no—
244C2×C4—2442no—
245C2×C4—2442no—
246C2×C4C2×D48811yescharacteristic
247C2×C4Q16×D6112yes—
248C2×C4#1451980511yescharacteristic
249C2×C4#1451980612yes—
250C8—44no—
251C8—2442no—
252C22#1683989811yescharacteristic
253C22#1683991912yes—
254C22#1683993211yescharacteristic
255C22#1683994612yes—
256C22#1683995011yescharacteristic
257C4—21no—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—81no—
263C4—4882no—
264C4—4882no—
265C4—2444no—
266C2#2144473911yescharacteristic
267C2#2144479412yes—
268C2#2144496011yescharacteristic
269C2#2144507012yes—
270C2#2144513111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61#120
hypercenter#1272D61
hypocenterC61#7757
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
76. C4⋊Dic61Q16semidirect
154. C61#7757semidirect

Maximal subgroups

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

subgroupindex
#214528512
#214471482
#214469182
#214436412
C61×#12722
#775761