Finite Group Databasebeta

← #29593565

Subgroups — #29593565

Order 15616.

306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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#21458825C211yesmaximal, characteristic
2#21448072C211yesmaximal, characteristic
3#21447870C211yesmaximal, characteristic
4#21445189C211yesmaximal, characteristic
5#21443869C211yesmaximal, characteristic
6#21443784C211yesmaximal, characteristic
7C61×Q8⋊C16C211yesmaximal, characteristic
8#16840491—21no—
9C2×Dic488—22no—
10C2×Dic488—21no—
11#16840142—21no—
12#16840142C2211yescharacteristic
13#16840142C2211yescharacteristic
14#16840047—21no—
15#16839973—22no—
16#16839973—21no—
17C4×Dic244—21no—
18C4×Dic244C2211yescharacteristic
19#16839567—21no—
20#16839515C2211yescharacteristic
21#16839509—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—21no—
27C2×Dic244—21no—
28C2×Dic244—22no—
29C2×Dic244D411yescharacteristic
30C2×Dic244D412yes—
31#14519777—22no—
32#14519777—21no—
33#14519777—21no—
34#14519768—42no—
35#14519768—41no—
36Q8×Dic61—41no—
37C4×Dic122—22no—
38C4×Dic122—21no—
39Dic488—44no—
40Dic488—42no—
41#14519711D411yescharacteristic
42#14519708—41no—
43C4⋊#92418—21no—
44#14519702—22no—
45#14519702—21no—
46#14519701—41no—
47C4×Q8×C61D411yescharacteristic
48C2×C16×C61—21no—
49C2×C16×C61—21no—
50C4⋊C8×C61—21no—
51C4⋊C8×C61D411yescharacteristic
52C4×C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61D811yescharacteristic
55C2×Dic122—21no—
56C2×Dic122—22no—
57C2×Dic122—41no—
58C2×C8×C61—21no—
59C2×C8×C61C2×D411yescharacteristic
60C2×C8×C61C2×D411yescharacteristic
61C4⋊C4×C61—21no—
62C4⋊C4×C61D811yescharacteristic
63C42×C61—21no—
64C42×C61C2×D411yescharacteristic
65C4⋊Dic61—21no—
66C4⋊Dic61—42no—
67C4⋊Dic61—42no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70C4⋊Dic61—41no—
71C4⋊Dic61—41no—
72#11758196—42no—
73#11758196—41no—
74C4×Dic61—42no—
75C4×Dic61—41no—
76C2×#92418—41no—
77Dic244—21no—
78Dic244—21no—
79Dic244—42no—
80Dic244—42no—
81Dic244—41no—
82Dic244—41no—
83Dic244—41no—
84Dic244—41no—
85Dic244—82no—
86C16×C61—22no—
87C16×C61—41no—
88Q8×C61—21no—
89Q8×C61Q3212yescomplemented
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61#12011yescharacteristic
93C2×C4×C61C2×D811yescharacteristic
94C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
95C2×Dic61—41no—
96C2×Dic61—42no—
97C2×Dic61—41no—
98C2×Dic61—81no—
99Dic122—41no—
100Dic122—42no—
101Dic122—42no—
102Dic122—41no—
103Dic122—81no—
104Dic122—81no—
105C8×C61—21no—
106C8×C61—41no—
107C8×C61#13511yescharacteristic
108C8×C61AGL(1,ℤ/8)11yescharacteristic
109#92418—81no—
110#12334—611nomaximal, Sylow
111C22×C61#44711yescharacteristic
112C4×C61—22no—
113C4×C61—21no—
114C4×C61—41no—
115C4×C61#44911yescharacteristic
116C4×C61#45311yescharacteristic
117C4×C61C2×Q3211yescharacteristic
118C4×C61#51011yescharacteristic
119Dic61—81no—
120Dic61—82no—
121Dic61—81no—
122Dic61—161no—
123#3395—611no—
124#2247—611no—
125#2209—611no—
126#1670—611no—
127#1362—611no—
128Q8⋊C16D6111yescharacteristic
129#1332—611no—
130C2×C61#162111yescharacteristic
131C2×C61#218811yescharacteristic
132C2×C61#219511yescharacteristic
133#557—1221no—
134C2×Q32—1221no—
135C2×Q32—1222no—
136#494—611no—
137#494—611no—
138#494—1221no—
139#475—1221no—
140#462—1222no—
141#462—1221no—
142C8×Q8C2×D6111yescharacteristic
143C4×Q16—611no—
144C4×Q16—1221no—
145C4⋊C16C2×D6111yescharacteristic
146#358—1221no—
147C4×C16C2×D6111yescharacteristic
148#335—611no—
149#332—1221no—
150C61#1233411yescharacteristic, complemented, Sylow
151C2×Q16—611no—
152C2×Q16—612no—
153C2×Q16—1222no—
154C2×Q16—1221no—
155C2×Q16—1221no—
156C2×Q16—1221no—
157C4⋊Q8—1222no—
158C4⋊Q8—1221no—
159C4⋊Q8—1221no—
160#125—2442no—
161#125—2441no—
162C4×Q8—1222no—
163C4×Q8—1221no—
164C4×Q8—2441no—
165C4×Q8D24411yescharacteristic
166Q32—2444no—
167Q32—2442no—
168C2×C16—21no—
169C2×C16—21no—
170#107—611no—
171#106—2441no—
172C4⋊C8—21no—
173C4⋊C8—1221no—
174C4⋊C8D24411yescharacteristic
175#103—1222no—
176#103—1221no—
177#103—2441no—
178C4×C8—21no—
179C4×C8C22×D6111yescharacteristic
180C2×Q8—1221no—
181C2×Q8—1222no—
182C2×Q8—2441no—
183C2×Q8D48811yescharacteristic
184Q16—1221no—
185Q16—1221no—
186Q16—4882no—
187Q16—2442no—
188Q16—2442no—
189Q16—2441no—
190Q16—2441no—
191Q16—2441no—
192Q16—2441no—
193C2×C8—21no—
194C2×C8—2441no—
195C2×C8D4×D6111yescharacteristic
196C2×C8D4×D6111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—1221no—
199C4⋊C4—2442no—
200C4⋊C4—2442no—
201C4⋊C4—2442no—
202C4⋊C4—2441no—
203C4⋊C4—2441no—
204C4⋊C4—2441no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C4⋊C4D48811yescharacteristic
208C42—21no—
209C42—2442no—
210C42—2441no—
211C42C2×D24411yescharacteristic
212C16—22no—
213C16—41no—
214Q8—21no—
215Q8—4881no—
216Q8—4881no—
217Q8—2441no—
218Q8—2442no—
219Q8—2441no—
220Q8—2442no—
221Q8Dic48812yescomplemented
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—4881no—
225C2×C4—2441no—
226C2×C4—2442no—
227C2×C4—2441no—
228C2×C4#1451974711yescharacteristic
229C2×C4C2×D48811yescharacteristic
230C2×C4#1451980511yescharacteristic
231C8—21no—
232C8—41no—
233C8—4881no—
234C8#1451980011yescharacteristic
235C8#1451980411yescharacteristic
236C22#1683989811yescharacteristic
237C4—22no—
238C4—21no—
239C4—41no—
240C4—9761no—
241C4—4881no—
242C4—4882no—
243C4—4881no—
244C4#1683991011yescharacteristic
245C4#1683993111yescharacteristic
246C4C2×Dic48811yescharacteristic
247C4#1684020511yescharacteristic
248C2#2144488611yescharacteristic
249C2#2144775511yescharacteristic
250C2#2144779911yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×Q8⋊C16C2
socle, prime radicalC22×C61#447
hypercenterQ8⋊C16D61
hypocenterC61#12334
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
89. Q8×C61Q32semidirect
150. C61#12334semidirect
221. Q8Dic488semidirect

Maximal subgroups

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

subgroupindex
#214588252
#214480722
#214478702
#214451892
#214438692
#214437842
C61×Q8⋊C162
#1233461