Finite Group Databasebeta

← #29592475

Subgroups — #29592475

Order 15616.

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

normal subgroups only

This group has 354 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#21457164C211yesmaximal, characteristic
2#21447753C212yesmaximal
3#21443830C212yesmaximal
4#21443759C211yesmaximal, characteristic
5C61×#2056C211yesmaximal, characteristic
6#16840319—21no—
7C2×#14519723—22no—
8#16840058—22no—
9#16840003—21no—
10#16840003C2212yes—
11#16839973—22no—
12#16839566—22no—
13C22⋊#11758185C2212yes—
14C22×Q16×C61C2211yescharacteristic
15C2×C4⋊C8×C61C2211yescharacteristic
16C2×#103×C61—21no—
17C61×#391—21no—
18C61×#340C2211yescharacteristic
19C2×Dic244—21no—
20C2×Dic244D412yes—
21#14519777—21no—
22#14519777—21no—
23#14519769—41no—
24#14519756—22no—
25#14519756—41no—
26C4×Dic122—22no—
27C4×Dic122—41no—
28#14519736—41no—
29#14519723—44no—
30C2×#11758185—22no—
31#14519711—21no—
32#14519711D412yes—
33#14519702—22no—
34#14519702—22no—
35C22×Q8×C61—21no—
36C2×Q16×C61—22no—
37C2×Q16×C61—42no—
38C22×C8×C61D411yescharacteristic
39C22×C8×C61C2311yescharacteristic
40C2×C4⋊C4×C61—21no—
41C2×C42×C61D411yescharacteristic
42C4⋊C8×C61—22no—
43#103×C61—42no—
44#95×C61—41no—
45#95×C61—41no—
46C2×Q8×C61—22no—
47C2×Q8×C61—41no—
48C2×Q8×C61—41no—
49C2×Q8×C61—41no—
50C2×Q8×C61—41no—
51C2×Q8×C61—41no—
52C22×C4×C61—41no—
53C22×C4×C61—41no—
54C22×C4×C61D811yescharacteristic
55C22×C4×C61D811yescharacteristic
56C22×C4×C61C2×D411yescharacteristic
57C2×Dic122—22no—
58C2×Dic122—41no—
59Q16×C61—24no—
60Q16×C61—42no—
61C2×C8×C61—21no—
62C2×C8×C61—41no—
63C2×C8×C61—41no—
64C2×C8×C61C2×D412yes—
65C4⋊C4×C61—41no—
66C4⋊C4×C61—41no—
67C42×C61—21no—
68C42×C61—21no—
69C22⋊Dic61—42no—
70C4⋊Dic61—22no—
71C4⋊Dic61—41no—
72C4⋊Dic61—41no—
73C4⋊Dic61—41no—
74#11758196—42no—
75#11758196—42no—
76C4×Dic61—42no—
77Dic244—42no—
78Dic244—81no—
79#11758185—42no—
80C23×C61C2×D811yescharacteristic
81Q8×C61—42no—
82Q8×C61—42no—
83Q8×C61—81no—
84Q8×C61—81no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61—42no—
92C2×C4×C61—81no—
93C2×C4×C61—81no—
94C2×C4×C61—81no—
95C2×C4×C61—81no—
96C2×C4×C61—81no—
97C2×C4×C61Q3212yescomplemented
98C2×C4×C61#12011yescharacteristic
99C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
100C2×Dic61—42no—
101C2×Dic61—42no—
102Dic122—42no—
103Dic122—42no—
104Dic122—82no—
105C8×C61—22no—
106C8×C61—41no—
107#12162—611nomaximal, Sylow
108C22×C61—21no—
109C22×C61—21no—
110C22×C61#44711yescharacteristic
111C22×C61C2×Q3211yescharacteristic
112C22×C61#51011yescharacteristic
113C4×C61—21no—
114C4×C61—22no—
115C4×C61—41no—
116C4×C61—82no—
117C4×C61—161no—
118C4×C61#45411yescharacteristic
119C4×C61B(4,𝔽2)11yescharacteristic
120Dic61—82no—
121Dic61—82no—
122#3249—611no—
123#2188—612no—
124#2056D6111yescharacteristic
125#1348—612no—
126#1322—611no—
127C2×C61—21no—
128C2×C61—21no—
129C2×C61#159811yescharacteristic
130C2×C61#218811yescharacteristic
131C2×C61#219111yescharacteristic
132C22×Q16C2×D6111yescharacteristic
133#533—1221no—
134C2×Q32—1222no—
135#477—1222no—
136#467—612no—
137#467—1221no—
138#462—1222no—
139C2×C4⋊C8C2×D6111yescharacteristic
140C2×#103—21no—
141#391—21no—
142#358—1222no—
143C22⋊C16—612no—
144#340C2×D6111yescharacteristic
145C61#1216211yescharacteristic, complemented, Sylow
146C22×Q8—21no—
147C2×Q16—22no—
148C2×Q16—42no—
149C2×Q16—612no—
150C2×Q16—1221no—
151C22×C8C22⋊D6111yescharacteristic
152C22×C8C22×D6111yescharacteristic
153C4⋊Q8—1221no—
154C4⋊Q8—1221no—
155#125—2441no—
156C22⋊Q8—1222no—
157C22⋊Q8—2441no—
158C4×Q8—1222no—
159C4×Q8—2441no—
160#117—2441no—
161C2×C4⋊C4—21no—
162C2×C42C22⋊D6111yescharacteristic
163Q32—2444no—
164C2×C16—1222no—
165#107—612no—
166#107—1221no—
167C4⋊C8—22no—
168#103—42no—
169#103—1222no—
170#103—1222no—
171#95—41no—
172#95—41no—
173C2×Q8—22no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—1222no—
180C2×Q8—2441no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4#1175819911yescharacteristic
184C22×C4#1175819911yescharacteristic
185C22×C4C2×C22⋊D6111yescharacteristic
186Q16—24no—
187Q16—42no—
188Q16—4881no—
189Q16—2442no—
190C2×C8—21no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8D4×D6112yes—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—1222no—
197C4⋊C4—2442no—
198C4⋊C4—2441no—
199C4⋊C4—2441no—
200C4⋊C4—2441no—
201C4⋊C4—2442no—
202C22⋊C4—2442no—
203C42—21no—
204C42—21no—
205C42—2442no—
206C16—2442no—
207C23C2×#1175819911yescharacteristic
208Q8—42no—
209Q8—42no—
210Q8—81no—
211Q8—81no—
212Q8—4882no—
213Q8—2442no—
214Q8—2442no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—41no—
221C2×C4—42no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—81no—
225C2×C4—81no—
226C2×C4—81no—
227C2×C4—2442no—
228C2×C4—2442no—
229C2×C4#1451972312yescomplemented
230C2×C4#1451974511yescharacteristic
231C2×C4#1451980211yescharacteristic
232C8—22no—
233C8—41no—
234C22—21no—
235C22—21no—
236C22#1683989511yescharacteristic
237C22C2×#1451972311yescharacteristic
238C22#1684020211yescharacteristic
239C4—22no—
240C4—21no—
241C4—41no—
242C4—82no—
243C4—161no—
244C4—4882no—
245C4—4882no—
246C4#1683993411yescharacteristic
247C4#1683994811yescharacteristic
248C2—21no—
249C2—21no—
250C2#2144475311yescharacteristic
251C2#2144775211yescharacteristic
252C2#2144776911yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2056C2
socleC22×C61#447
prime radicalC23×C61C2×D8
hypercenter#2056D61
hypocenterC61#12162
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2056

Complements

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

NH ≅ G/Ntype
97. C2×C4×C61Q32semidirect
145. C61#12162semidirect
229. C2×C4#14519723semidirect

Maximal subgroups

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

subgroupindex
#214571642
#214477532
#214438302
#214437592
C61×#20562
#1216261