Finite Group Databasebeta

← #29593560

Subgroups — #29593560

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#21447866C211yesmaximal, characteristic
3#21445186C211yesmaximal, characteristic
4#21443868C211yesmaximal, characteristic
5#21443799C211yesmaximal, characteristic
6#21443784C211yesmaximal, characteristic
7C61×#2247C211yesmaximal, characteristic
8#16840487—21no—
9C2×#14519723—21no—
10#16840140—21no—
11#16840044—21no—
12#16839970—22no—
13#16839969—21no—
14C8×Dic122C2211yescharacteristic
15C4×Dic244C2211yescharacteristic
16Q16×Dic61—21no—
17C4⋊#11758185C2211yescharacteristic
18#16839566—21no—
19#16839515C2211yescharacteristic
20#16839508—21no—
21C2×Q32×C61—22no—
22C61×#494C2211yescharacteristic
23C61×#494C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Dic244D411yescharacteristic
26C2×#11758202—22no—
27#14519775—22no—
28#14519768—41no—
29#14519767—42no—
30Q8×Dic61—22no—
31C4×Dic122—21no—
32C4×Dic122D411yescharacteristic
33#14519742—41no—
34#14519723—42no—
35C2×#11758185—21no—
36#14519711D411yescharacteristic
37#14519708—41no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519702—21no—
42#14519701—22no—
43#14519700—41no—
44C8×Dic61—21no—
45C2×Q16×C61—21no—
46C2×Q16×C61—21no—
47C2×Q16×C61—21no—
48C2×Q16×C61D412yes—
49C4⋊Q8×C61—21no—
50C4⋊Q8×C61—21no—
51Q32×C61—44no—
52C2×C16×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—22no—
55C2×Q8×C61—41no—
56C2×Dic122—21no—
57C2×Dic122D811yescharacteristic
58Q16×C61—42no—
59Q16×C61—42no—
60Q16×C61—41no—
61Q16×C61—41no—
62Q16×C61—41no—
63Q16×C61—41no—
64C2×C8×C61C2×D411yescharacteristic
65C2×C8×C61C2×D411yescharacteristic
66C4⋊C4×C61—41no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C4⋊C4×C61—41no—
70C42×C61C2×D411yescharacteristic
71#11758202—82no—
72C4⋊Dic61—21no—
73C4⋊Dic61—42no—
74C4⋊Dic61D811yescharacteristic
75#11758196—21no—
76#11758196—42no—
77#11758196—42no—
78#11758196—41no—
79C4×Dic61—21no—
80C4×Dic61—42no—
81C4×Dic61—41no—
82C2×#92418—21no—
83C2×#92418—41no—
84Dic244—21no—
85Dic244—21no—
86C16×C61—22no—
87#11758185—41no—
88Q8×C61—42no—
89Q8×C61—42no—
90Q8×C61—81no—
91Q8×C61—81no—
92C2×C4×C61—42no—
93C2×C4×C61—81no—
94C2×C4×C61#12011yescharacteristic
95C2×C4×C61C2×D811yescharacteristic
96C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101Dic122—21no—
102Dic122—41no—
103Dic122—41no—
104Dic122Q3212yescomplemented
105C8×C61—21no—
106C8×C61#13511yescharacteristic
107C8×C61AGL(1,ℤ/8)11yescharacteristic
108#92418—41no—
109#92418—81no—
110#12334—611nomaximal, Sylow
111C22×C61#44711yescharacteristic
112C4×C61—21no—
113C4×C61—82no—
114C4×C61—161no—
115C4×C61#44911yescharacteristic
116C4×C61#45311yescharacteristic
117C4×C61C2×Q3211yescharacteristic
118C4×C61#51011yescharacteristic
119Dic61—22no—
120Dic61—41no—
121Dic61—81no—
122Dic61—81no—
123#3395—611no—
124#2247D6111yescharacteristic
125#2209—611no—
126#1670—611no—
127#1362—611no—
128Q8⋊C16—611no—
129#1332—611no—
130C2×C61#162111yescharacteristic
131C2×C61#218811yescharacteristic
132C2×C61#219511yescharacteristic
133#557—1221no—
134C2×Q32—22no—
135C2×Q32—1221no—
136#494—1221no—
137#494C2×D6111yescharacteristic
138#494C2×D6111yescharacteristic
139#475—1221no—
140#462—1221no—
141#462—1222no—
142C8×Q8—611no—
143C4×Q16—611no—
144C4×Q16—1221no—
145C4⋊C16—611no—
146#358—1221no—
147C4×C16C2×D6111yescharacteristic
148#335—611no—
149#332—1221no—
150C61#1233411yescharacteristic, complemented, Sylow
151C2×Q16—21no—
152C2×Q16—21no—
153C2×Q16—21no—
154C2×Q16—611no—
155C2×Q16—1222no—
156C2×Q16C22⋊D6112yes—
157C4⋊Q8—21no—
158C4⋊Q8—21no—
159C4⋊Q8—1222no—
160#125—2441no—
161#125—2442no—
162C4×Q8—611no—
163C4×Q8—1222no—
164C4×Q8—1221no—
165C4×Q8—2441no—
166Q32—44no—
167Q32—2442no—
168C2×C16—21no—
169C2×C16—1221no—
170#107—611no—
171#106—2441no—
172C4⋊C8—611no—
173C4⋊C8—1221no—
174C4⋊C8—1221no—
175#103—1222no—
176#103—1221no—
177#103—2441no—
178C4×C8—1221no—
179C4×C8C22×D6111yescharacteristic
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—611no—
183C2×Q8—1221no—
184Q16—42no—
185Q16—42no—
186Q16—41no—
187Q16—41no—
188Q16—41no—
189Q16—41no—
190Q16—1221no—
191Q16—1221no—
192Q16—4882no—
193C2×C8—1221no—
194C2×C8—2441no—
195C2×C8D4×D6111yescharacteristic
196C2×C8C2×C22⋊D6111yescharacteristic
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—611no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4—2442no—
205C4⋊C4—2442no—
206C4⋊C4—2442no—
207C4⋊C4—2441no—
208C42—1221no—
209C42—2442no—
210C42—2441no—
211C42D4×D6111yescharacteristic
212C16—22no—
213C16—2441no—
214Q8—42no—
215Q8—42no—
216Q8—81no—
217Q8—81no—
218Q8—612no—
219Q8—1221no—
220Q8—2441no—
221Q8—2441no—
222C2×C4—42no—
223C2×C4—81no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4#1451974511yescharacteristic
229C2×C4D8×D6111yescharacteristic
230C2×C4#1451980111yescharacteristic
231C8—21no—
232C8—4881no—
233C8—2441no—
234C8#1451979611yescharacteristic
235C8#1451980111yescharacteristic
236C22#1683989411yescharacteristic
237C4—21no—
238C4—82no—
239C4—161no—
240C4—1222no—
241C4—4881no—
242C4—4881no—
243C4—2441no—
244C4#1683990411yescharacteristic
245C4#1683992911yescharacteristic
246C4Q32×D6111yescharacteristic
247C4#1684020411yescharacteristic
248C2#2144488111yescharacteristic
249C2#2144775111yescharacteristic
250C2#2144779611yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2247C2
socle, prime radicalC22×C61#447
hypercenter#2247D61
hypocenterC61#12334
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2247

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
#214478662
#214451862
#214438682
#214437992
#214437842
C61×#22472
#1233461