Finite Group Databasebeta

← #29593297

Subgroups — #29593297

Order 15616.

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

normal subgroups only

This group has 310 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#21448021C212yesmaximal
3#21443830C212yesmaximal
4#21443759C211yesmaximal, characteristic
5C61×#2087C211yesmaximal, characteristic
6#16840319—21no—
7#16840058—22no—
8#16840003—21no—
9#16840003C2212yes—
10#16839973—22no—
11#16839587—22no—
12#16839565—22no—
13C22⋊#11758185C2212yes—
14C2×#107×C61C2211yescharacteristic
15C2×C4⋊C8×C61C2211yescharacteristic
16C61×#389—21no—
17C61×#340—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—
29C2×#11758185—22no—
30#14519711—21no—
31#14519711D412yes—
32#14519702—22no—
33#14519702—22no—
34C22×C8×C61D411yescharacteristic
35C22×C8×C61C2311yescharacteristic
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—41no—
39C2×C42×C61D411yescharacteristic
40#107×C61—22no—
41C4⋊C8×C61—22no—
42#95×C61—41no—
43C22×C4×C61—41no—
44C22×C4×C61—41no—
45C22×C4×C61D811yescharacteristic
46C22×C4×C61D811yescharacteristic
47C22×C4×C61C2×D411yescharacteristic
48C2×Dic122—22no—
49C2×Dic122—41no—
50C2×C8×C61—21no—
51C2×C8×C61—41no—
52C2×C8×C61—41no—
53C2×C8×C61C2×D412yes—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—41no—
56C4⋊C4×C61—41no—
57C4⋊C4×C61—41no—
58C4⋊C4×C61—82no—
59C42×C61—21no—
60C42×C61—21no—
61C22⋊Dic61—42no—
62C4⋊Dic61—22no—
63C4⋊Dic61—41no—
64C4⋊Dic61—41no—
65C4⋊Dic61—41no—
66#11758196—42no—
67#11758196—42no—
68C4×Dic61—42no—
69Dic244—42no—
70Dic244—81no—
71#11758185—42no—
72C23×C61C2×D811yescharacteristic
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—41no—
79C2×C4×C61—42no—
80C2×C4×C61—81no—
81C2×C4×C61—81no—
82C2×C4×C61—81no—
83C2×C4×C61—81no—
84C2×C4×C61—81no—
85C2×C4×C61Q3212yes—
86C2×C4×C61#12011yescharacteristic
87C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
88C2×Dic61—42no—
89C2×Dic61—42no—
90Dic122—42no—
91Dic122—42no—
92Dic122—82no—
93C8×C61—22no—
94C8×C61—41no—
95#12292—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—21no—
98C22×C61#44711yescharacteristic
99C22×C61C2×Q3211yescharacteristic
100C22×C61#51011yescharacteristic
101C4×C61—21no—
102C4×C61—22no—
103C4×C61—41no—
104C4×C61—82no—
105C4×C61—161no—
106C4×C61#45611yescharacteristic
107C4×C61#45811yescharacteristic
108Dic61—82no—
109Dic61—82no—
110#3249—611no—
111#2236—612no—
112#2087D6111yescharacteristic
113#1348—612no—
114#1322—611no—
115C2×C61—21no—
116C2×C61—21no—
117C2×C61#161011yescharacteristic
118C2×C61#218811yescharacteristic
119C2×C61#219011yescharacteristic
120#533—1221no—
121#477—1222no—
122#467—612no—
123#467—1221no—
124#462—1222no—
125C2×#107C2×D6111yescharacteristic
126C2×C4⋊C8C2×D6111yescharacteristic
127#389—21no—
128#366—1222no—
129#358—1222no—
130C22⋊C16—612no—
131#340—21no—
132#340C2×D6111yescharacteristic
133C61#1229211yescharacteristic, complemented, Sylow
134C2×Q16—612no—
135C2×Q16—1221no—
136C22×C8C22⋊D6111yescharacteristic
137C22×C8C22×D6111yescharacteristic
138C4⋊Q8—1221no—
139C4⋊Q8—1221no—
140#125—2441no—
141C22⋊Q8—1222no—
142C22⋊Q8—2441no—
143C4×Q8—1222no—
144C4×Q8—2441no—
145#117—2441no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—41no—
149C2×C42C22⋊D6111yescharacteristic
150C2×C16—1222no—
151#107—22no—
152#107—612no—
153#107—1221no—
154C4⋊C8—22no—
155#103—1222no—
156#103—1222no—
157#95—41no—
158C2×Q8—1222no—
159C2×Q8—2441no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4#1175819911yescharacteristic
163C22×C4#1175819911yescharacteristic
164C22×C4C2×C22⋊D6111yescharacteristic
165Q16—4881no—
166Q16—2442no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8D4×D6112yes—
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—82no—
176C4⋊C4—1222no—
177C4⋊C4—2442no—
178C4⋊C4—2441no—
179C4⋊C4—2441no—
180C4⋊C4—2441no—
181C4⋊C4—2442no—
182C22⋊C4—2442no—
183C42—21no—
184C42—21no—
185C42—2442no—
186C16—2442no—
187C23C2×#1175819911yescharacteristic
188Q8—4882no—
189Q8—2442no—
190Q8—2442no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—81no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4#1451972312yes—
206C2×C4#1451974511yescharacteristic
207C2×C4#1451980211yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1683989511yescharacteristic
213C22C2×#1451972311yescharacteristic
214C22#1684020211yescharacteristic
215C4—22no—
216C4—21no—
217C4—41no—
218C4—82no—
219C4—161no—
220C4—4882no—
221C4—4882no—
222C4#1683994411yescharacteristic
223C4#1683995111yescharacteristic
224C2—21no—
225C2—21no—
226C2#2144482111yescharacteristic
227C2#2144775211yescharacteristic
228C2#2144776411yescharacteristic
subgroupG/H
centerC22#16839895
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#2087C2
socleC22×C61#447
prime radicalC23×C61C2×D8
hypercenter#2087D61
hypocenterC61#12292
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #2087

Complements

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

NH ≅ G/Ntype
133. C61#12292semidirect

Maximal subgroups

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

subgroupindex
#214571642
#214480212
#214438302
#214437592
C61×#20872
#1229261