Finite Group Databasebeta

← #29568852

Subgroups — #29568852

Order 15616.

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

normal subgroups only

This group has 456 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#21453812C211yesmaximal, characteristic
2#21446961C212yesmaximal
3#21446918C211yesmaximal, characteristic
4#21443644C212yesmaximal
5C61×#1272C211yesmaximal, characteristic
6C22×#11758202—21no—
7C2×#14519777C2211yescharacteristic
8C2×#14519702—22no—
9C2×#14519700—21no—
10#16839683—22no—
11#16839682—21no—
12#16839669—21no—
13#16839668C2212yes—
14#16839666—22no—
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#391C2211yescharacteristic
18C61×#336C2212yes—
19C22×Dic122—21no—
20C22×Dic122—21no—
21C22×Dic122D412yes—
22C2×#11758202—42no—
23C2×#11758202—42no—
24C2×#11758202—42no—
25C22×#92418—21no—
26#14519777—42no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61D412yes—
30C2×#11758196—22no—
31C2×C4×Dic61—21no—
32#14519702—44no—
33#14519700—42no—
34#14519684—21no—
35#14519684—22no—
36#14519684—22no—
37#14519684—22no—
38C22×Q8×C61D411yescharacteristic
39C22×C8×C61—22no—
40C2×C4⋊C4×C61D411yescharacteristic
41C2×C42×C61C2311yescharacteristic
42#95×C61—22no—
43C2×Q8×C61—21no—
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C2×Q8×C61SD1612yes—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C2×D411yescharacteristic
50C22×C4×C61C2×D412yes—
51C22×Dic61—22no—
52C22×Dic61—22no—
53C22×Dic61—41no—
54C2×Dic122—22no—
55C2×Dic122—22no—
56C2×Dic122—42no—
57C2×Dic122—42no—
58C2×Dic122—41no—
59C2×Dic122—41no—
60C2×Dic122—41no—
61C2×Dic122—41no—
62C2×Dic122—41no—
63C2×Dic122—81no—
64C2×Dic122—82no—
65C2×Dic122Q1614yescomplemented
66C2×C8×C61—42no—
67C2×C8×C61—42no—
68C2×C8×C61—42no—
69C4⋊C4×C61—41no—
70C42×C61—41no—
71#11758202—48no—
72C4⋊Dic61—24no—
73C4⋊Dic61—42no—
74C4⋊Dic61—42no—
75C4⋊Dic61—81no—
76#11758196—82no—
77C4×Dic61—81no—
78C2×#92418—22no—
79C2×#92418—41no—
80C2×#92418—41no—
81C23×C61#12011yescharacteristic
82Q8×C61—42no—
83Q8×C61—81no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×C4×C61—42no—
93C2×C4×C61C2×SD1611yescharacteristic
94C2×C4×C61C2×Q1612yes—
95C2×C4×C61#13711yescharacteristic
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—44no—
107Dic122—42no—
108Dic122—42no—
109Dic122—82no—
110Dic122—81no—
111Dic122—81no—
112Dic122—84no—
113C8×C61—82no—
114#92418—42no—
115#7759—611nomaximal, Sylow
116C22×C61#44811yescharacteristic
117C22×C61#45112yes—
118C22×C61#45311yescharacteristic
119C22×C61#45512yes—
120C22×C61B(4,𝔽2)11yescharacteristic
121C4×C61—21no—
122C4×C61—21no—
123C4×C61—22no—
124C4×C61—22no—
125C4×C61—42no—
126C4×C61—81no—
127Dic61—44no—
128Dic61—82no—
129Dic61—82no—
130#2811—611no—
131#2024—612no—
132#2016—611no—
133#1272—612no—
134#1272D6111yescharacteristic
135C2×C61#159611yescharacteristic
136C2×C61#160212yes—
137C2×C61#163311yescharacteristic
138C2×C61#164512yes—
139C2×C61#165911yescharacteristic
140C22×Q16—1221no—
141C2×C4⋊Q8—611no—
142C2×#103—1222no—
143C2×#103—1221no—
144#395—1222no—
145#395—1221no—
146#391—612no—
147#391—1222no—
148#391—1221no—
149#391C2×D6111yescharacteristic
150#340—1222no—
151#336—611no—
152#336C2×D6112yes—
153C61#775911yescharacteristic, complemented, Sylow
154C22×Q8—612no—
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—
164C2×C4⋊C4—612no—
165C2×C4⋊C4—1222no—
166C2×C4⋊C4—1222no—
167C2×C4⋊C4—1221no—
168C2×C4⋊C4D24411yescharacteristic
169C2×C42—1221no—
170C2×C42C22×D6111yescharacteristic
171#103—2442no—
172#103—2444no—
173#95—22no—
174#95—1222no—
175#95—1221no—
176#95—1222no—
177#95—1222no—
178C2×Q8—21no—
179C2×Q8—41no—
180C2×Q8—41no—
181C2×Q8—614no—
182C2×Q8—1222no—
183C2×Q8—1222no—
184C2×Q8—4882no—
185C2×Q8—4881no—
186C2×Q8—2441no—
187C2×Q8—2441no—
188C2×Q8—2441no—
189C2×Q8—2442no—
190C2×Q8—2442no—
191C2×Q8—2441no—
192C2×Q8—2441no—
193C2×Q8#1175819012yes—
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—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—1222no—
206C2×C8—2441no—
207C2×C8—2441no—
208C4⋊C4—41no—
209C4⋊C4—1224no—
210C4⋊C4—4882no—
211C4⋊C4—4881no—
212C4⋊C4—2442no—
213C4⋊C4—2442no—
214C42—41no—
215C42—4881no—
216C23#1451974711yescharacteristic
217Q8—42no—
218Q8—81no—
219Q8—4881no—
220Q8—4881no—
221Q8—4882no—
222Q8—4884no—
223Q8—2442no—
224Q8—2442no—
225Q8—2444no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—1224no—
236C2×C4—4881no—
237C2×C4—4881no—
238C2×C4—2442no—
239C2×C4—2442no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4—2442no—
244C2×C4C2×#1175819011yescharacteristic
245C2×C4Q16×D6112yes—
246C2×C4#1451980612yes—
247C2×C4#1451981011yescharacteristic
248C8—82no—
249C8—2442no—
250C22#1683990311yescharacteristic
251C22#1683991912yes—
252C22#1683993211yescharacteristic
253C22#1683994112yes—
254C22#1683995011yescharacteristic
255C4—21no—
256C4—21no—
257C4—22no—
258C4—22no—
259C4—42no—
260C4—81no—
261C4—4882no—
262C4—4882no—
263C4—2444no—
264C2#2144474411yescharacteristic
265C2#2144477712yes—
266C2#2144496011yescharacteristic
267C2#2144504212yes—
268C2#2144512611yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61#120
hypercenter#1272D61
hypocenterC61#7759
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
65. C2×Dic122Q16semidirect
153. C61#7759semidirect

Maximal subgroups

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

subgroupindex
#214538122
#214469612
#214469182
#214436442
C61×#12722
#775961