Finite Group Databasebeta

← #29593562

Subgroups — #29593562

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#21458824C211yesmaximal, characteristic
2#21448071C211yesmaximal, characteristic
3#21445186C211yesmaximal, characteristic
4#21443869C211yesmaximal, characteristic
5#21443797C211yesmaximal, characteristic
6#21443783C211yesmaximal, characteristic
7C61×#2209C211yesmaximal, characteristic
8#16840490—21no—
9C2×#14519723—22no—
10#16840142C2211yescharacteristic
11#16840140—21no—
12#16840044—21no—
13#16839972—21no—
14#16839971—22no—
15C8×Dic122C2211yescharacteristic
16#16839856—21no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839508—21no—
20C2×Q32×C61—21no—
21C61×#494C2211yescharacteristic
22C4×Q16×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#358—21no—
25C2×Dic244—21no—
26C2×Dic244D412yes—
27C2×#11758202—22no—
28#14519777—21no—
29#14519775—22no—
30#14519769—41no—
31#14519767—42no—
32C4×Dic122—41no—
33C4×Dic122D411yescharacteristic
34#14519742—22no—
35#14519723—44no—
36C2×#11758185—21no—
37#14519708—41no—
38C4⋊#92418—21no—
39C4⋊#92418D411yescharacteristic
40#14519706—21no—
41#14519700—22no—
42#14519700—41no—
43C8×Dic61—21no—
44C2×Q16×C61—21no—
45C2×Q16×C61—21no—
46C2×Q16×C61D411yescharacteristic
47C4⋊Q8×C61—21no—
48C4×Q8×C61—21no—
49Q32×C61—42no—
50C2×C16×C61—21no—
51#107×C61D411yescharacteristic
52#103×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—21no—
55C2×Q8×C61—41no—
56C2×Dic122—22no—
57C2×Dic122D811yescharacteristic
58Q16×C61—21no—
59Q16×C61—21no—
60Q16×C61—42no—
61Q16×C61—41no—
62Q16×C61—41no—
63C2×C8×C61C2×D411yescharacteristic
64C2×C8×C61C2×D411yescharacteristic
65C4⋊C4×C61—21no—
66C4⋊C4×C61—41no—
67C4⋊C4×C61—41no—
68C4⋊C4×C61—41no—
69C42×C61—41no—
70C42×C61C2×D411yescharacteristic
71#11758202—82no—
72C4⋊Dic61—41no—
73C4⋊Dic61—41no—
74C4⋊Dic61D811yescharacteristic
75#11758196—21no—
76#11758196—42no—
77#11758196—42no—
78#11758196—42no—
79C4×Dic61—21no—
80C4×Dic61—42no—
81C2×#92418—21no—
82C2×#92418—41no—
83Dic244—42no—
84Dic244—41no—
85Dic244—41no—
86C16×C61—41no—
87#11758185—22no—
88Q8×C61—41no—
89Q8×C61—41no—
90Q8×C61—81no—
91Q8×C61—81no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—81no—
95C2×C4×C61#12011yescharacteristic
96C2×C4×C61C2×D811yescharacteristic
97C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—42no—
101Dic122—21no—
102Dic122—42no—
103Dic122—42no—
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—81no—
114C4×C61—81no—
115C4×C61—161no—
116C4×C61#44911yescharacteristic
117C4×C61#45311yescharacteristic
118C4×C61C2×Q3211yescharacteristic
119C4×C61#51011yescharacteristic
120Dic61—22no—
121Dic61—41no—
122Dic61—82no—
123#3395—611no—
124#2247—611no—
125#2209D6111yescharacteristic
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—21no—
135C2×Q32—1222no—
136#494—611no—
137#494—1221no—
138#494C2×D6111yescharacteristic
139#475—1221no—
140#462—1222no—
141#462—1221no—
142C8×Q8—611no—
143C4×Q16—1221no—
144C4×Q16C2×D6111yescharacteristic
145C4⋊C16C2×D6111yescharacteristic
146#358—21no—
147C4×C16—611no—
148#335—611no—
149#332—1221no—
150C61#1233411yescharacteristic, complemented, Sylow
151C2×Q16—21no—
152C2×Q16—21no—
153C2×Q16—612no—
154C2×Q16—1222no—
155C2×Q16—1221no—
156C2×Q16C22⋊D6111yescharacteristic
157C4⋊Q8—21no—
158C4⋊Q8—1222no—
159C4⋊Q8—1221no—
160#125—2441no—
161#125—2442no—
162C4×Q8—21no—
163C4×Q8—611no—
164C4×Q8—1222no—
165C4×Q8—2441no—
166Q32—42no—
167Q32—2444no—
168C2×C16—21no—
169C2×C16—1221no—
170#107C22⋊D6111yescharacteristic
171#106—2441no—
172C4⋊C8—611no—
173C4⋊C8—1221no—
174C4⋊C8—1221no—
175#103—21no—
176#103—1222no—
177#103—2441no—
178C4×C8—1221no—
179C4×C8C22×D6111yescharacteristic
180C2×Q8—21no—
181C2×Q8—41no—
182C2×Q8—611no—
183C2×Q8—1222no—
184Q16—21no—
185Q16—21no—
186Q16—42no—
187Q16—41no—
188Q16—41no—
189Q16—4882no—
190Q16—2442no—
191Q16—2441no—
192Q16—2441no—
193C2×C8—1221no—
194C2×C8—2441no—
195C2×C8D4×D6111yescharacteristic
196C2×C8C2×C22⋊D6111yescharacteristic
197C4⋊C4—21no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—611no—
202C4⋊C4—1221no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C4⋊C4—2442no—
206C4⋊C4—2441no—
207C4⋊C4—2441no—
208C42—41no—
209C42—1221no—
210C42—2442no—
211C42D4×D6111yescharacteristic
212C16—41no—
213C16—1222no—
214Q8—41no—
215Q8—41no—
216Q8—81no—
217Q8—81no—
218Q8—612no—
219Q8—1221no—
220Q8—2442no—
221Q8—2442no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—81no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—2442no—
228C2×C4#1451974511yescharacteristic
229C2×C4D8×D6111yescharacteristic
230C2×C4#1451980111yescharacteristic
231C8—21no—
232C8—4881no—
233C8—2441no—
234C8#1451979711yescharacteristic
235C8#1451980311yescharacteristic
236C22#1683989411yescharacteristic
237C4—21no—
238C4—81no—
239C4—81no—
240C4—161no—
241C4—1222no—
242C4—4882no—
243C4—2441no—
244C4#1683990511yescharacteristic
245C4#1683992811yescharacteristic
246C4Q32×D6111yescharacteristic
247C4#1684020411yescharacteristic
248C2#2144488311yescharacteristic
249C2#2144775111yescharacteristic
250C2#2144779411yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2209C2
socle, prime radicalC22×C61#447
hypercenter#2209D61
hypocenterC61#12334
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2209

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
#214588242
#214480712
#214451862
#214438692
#214437972
#214437832
C61×#22092
#1233461