Finite Group Databasebeta

← #29593564

Subgroups — #29593564

Order 15616.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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#21458823C211yesmaximal, characteristic
2#21448071C211yesmaximal, characteristic
3#21447870C211yesmaximal, characteristic
4#21445190C211yesmaximal, characteristic
5#21443797C211yesmaximal, characteristic
6#21443782C211yesmaximal, characteristic
7C61×#1362C211yesmaximal, characteristic
8#16840487—21no—
9C2×Dic488—21no—
10C2×#14519723—22no—
11#16840142C2211yescharacteristic
12#16840140—21no—
13#16840048—21no—
14#16839970—22no—
15#16839969—21no—
16C8×Dic122C2211yescharacteristic
17C4×Dic244C2211yescharacteristic
18Q16×Dic61—21no—
19#16839567—21no—
20C4×#11758185C2211yescharacteristic
21#16839507—21no—
22C61×#494C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#335C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—21no—
27C2×Dic244D411yescharacteristic
28C2×#11758202—22no—
29#14519777—21no—
30#14519775—22no—
31#14519768—41no—
32#14519767—42no—
33Q8×Dic61—22no—
34C4×Dic122—21no—
35C4×Dic122D411yescharacteristic
36#14519742—41no—
37Dic488—42no—
38#14519723—44no—
39C2×#11758185—21no—
40#14519711D411yescharacteristic
41#14519709—41no—
42C4⋊#92418D411yescharacteristic
43#14519706—21no—
44#14519702—21no—
45#14519702—41no—
46#14519701—22no—
47C8×Dic61—21no—
48C2×Q16×C61—21no—
49C2×Q16×C61D412yes—
50C4⋊Q8×C61—21no—
51C2×C16×C61—21no—
52C4⋊C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—22no—
55C2×Dic122—21no—
56C2×Dic122—41no—
57C2×Dic122D811yescharacteristic
58Q16×C61—42no—
59Q16×C61—41no—
60Q16×C61—41no—
61C2×C8×C61—41no—
62C2×C8×C61C2×D411yescharacteristic
63C2×C8×C61C2×D411yescharacteristic
64C4⋊C4×C61—41no—
65C4⋊C4×C61—41no—
66C42×C61C2×D411yescharacteristic
67#11758202—82no—
68C4⋊Dic61—21no—
69C4⋊Dic61—42no—
70C4⋊Dic61—41no—
71C4⋊Dic61—41no—
72C4⋊Dic61D811yescharacteristic
73#11758196—21no—
74#11758196—42no—
75#11758196—42no—
76#11758196—41no—
77C4×Dic61—21no—
78C4×Dic61—42no—
79C4×Dic61—41no—
80C2×#92418—21no—
81Dic244—21no—
82Dic244—21no—
83Dic244—42no—
84Dic244—41no—
85Dic244—41no—
86C16×C61—41no—
87#11758185—22no—
88Q8×C61—42no—
89Q8×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61#12011yescharacteristic
92C2×C4×C61C2×D811yescharacteristic
93C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—41no—
97C2×Dic61—41no—
98C2×Dic61—81no—
99Dic122—21no—
100Dic122—41no—
101Dic122—41no—
102Dic122—81no—
103Dic122—81no—
104Dic122Q3212yescomplemented
105C8×C61—21no—
106C8×C61—81no—
107C8×C61#13511yescharacteristic
108C8×C61AGL(1,ℤ/8)11yescharacteristic
109#92418—41no—
110#12334—611nomaximal, Sylow
111C22×C61#44711yescharacteristic
112C4×C61—21no—
113C4×C61—82no—
114C4×C61#44911yescharacteristic
115C4×C61#45311yescharacteristic
116C4×C61C2×Q3211yescharacteristic
117C4×C61#51011yescharacteristic
118Dic61—22no—
119Dic61—41no—
120Dic61—81no—
121Dic61—81no—
122Dic61—161no—
123#3395—611no—
124#2247—611no—
125#2209—611no—
126#1670—611no—
127#1362D6111yescharacteristic
128Q8⋊C16—611no—
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—1221no—
138#494C2×D6111yescharacteristic
139#475—1221no—
140#462—1221no—
141#462—1222no—
142C8×Q8—611no—
143C4×Q16—611no—
144C4×Q16—1221no—
145C4⋊C16C2×D6111yescharacteristic
146#358—1221no—
147C4×C16—611no—
148#335C2×D6111yescharacteristic
149#332—1221no—
150C61#1233411yescharacteristic, complemented, Sylow
151C2×Q16—21no—
152C2×Q16—611no—
153C2×Q16—1222no—
154C2×Q16—1221no—
155C2×Q16—1221no—
156C2×Q16D24412yes—
157C4⋊Q8—21no—
158C4⋊Q8—1222no—
159C4⋊Q8—1221no—
160#125—2441no—
161#125—2442no—
162C4×Q8—611no—
163C4×Q8—1222no—
164C4×Q8—1221no—
165C4×Q8—2441no—
166Q32—2442no—
167Q32—2444no—
168C2×C16—21no—
169C2×C16—1221no—
170#107—611no—
171#106—2441no—
172C4⋊C8—21no—
173C4⋊C8—611no—
174C4⋊C8—1221no—
175#103—1222no—
176#103—1221no—
177#103—2441no—
178C4×C8—1221no—
179C4×C8C22×D6111yescharacteristic
180C2×Q8—22no—
181C2×Q8—611no—
182C2×Q8—1221no—
183C2×Q8—2441no—
184Q16—42no—
185Q16—41no—
186Q16—41no—
187Q16—1221no—
188Q16—1221no—
189Q16—4882no—
190Q16—2442no—
191Q16—2441no—
192Q16—2441no—
193C2×C8—41no—
194C2×C8—1221no—
195C2×C8C2×D24411yescharacteristic
196C2×C8D4×D6111yescharacteristic
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—611no—
200C4⋊C4—1221no—
201C4⋊C4—1221no—
202C4⋊C4—2442no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C4⋊C4—2441no—
208C42—1221no—
209C42—2442no—
210C42—2441no—
211C42D4×D6111yescharacteristic
212C16—41no—
213C16—1222no—
214Q8—42no—
215Q8—42no—
216Q8—612no—
217Q8—1221no—
218Q8—4881no—
219Q8—4881no—
220Q8—2441no—
221Q8—2441no—
222C2×C4—42no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—4881no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4#1451974711yescharacteristic
229C2×C4D8×D6111yescharacteristic
230C2×C4#1451980411yescharacteristic
231C8—21no—
232C8—81no—
233C8—2441no—
234C8#1451979811yescharacteristic
235C8#1451980111yescharacteristic
236C22#1683989711yescharacteristic
237C4—21no—
238C4—82no—
239C4—1222no—
240C4—9761no—
241C4—4881no—
242C4—4881no—
243C4—2441no—
244C4#1683990811yescharacteristic
245C4#1683993211yescharacteristic
246C4Q32×D6111yescharacteristic
247C4#1684020111yescharacteristic
248C2#2144488511yescharacteristic
249C2#2144775411yescharacteristic
250C2#2144780011yescharacteristic
subgroupG/H
centerC22#16839897
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socle, prime radicalC22×C61#447
hypercenter#1362D61
hypocenterC61#12334
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
104. Dic122Q32semidirect
150. C61#12334semidirect

Maximal subgroups

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

subgroupindex
#214588232
#214480712
#214478702
#214451902
#214437972
#214437822
C61×#13622
#1233461