Finite Group Databasebeta

← #29593283

Subgroups — #29593283

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#21448017C212yesmaximal
3#21447307C211yesmaximal, characteristic
4#21443832C212yesmaximal
5C61×#1322C211yesmaximal, characteristic
6#16840319—21no—
7#16840058—22no—
8#16840003—21no—
9#16840003C2212yes—
10#16839973—22no—
11C2×#14519711C2211yescharacteristic
12#16839660—21no—
13#16839590—22no—
14#16839567—22no—
15#16839525—21no—
16#16839525C2211yescharacteristic
17C2×C4⋊C8×C61C2211yescharacteristic
18C61×C22⋊C16C2212yes—
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×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×#11758196—41no—
32#14519711—21no—
33#14519711—22no—
34#14519711D412yes—
35#14519702—22no—
36#14519702—22no—
37#14519684—41no—
38C22×C8×C61D411yescharacteristic
39C22×C8×C61C2311yescharacteristic
40C2×C42×C61D411yescharacteristic
41C2×C16×C61—22no—
42C4⋊C8×C61—22no—
43C22×C4×C61D811yescharacteristic
44C22×C4×C61D811yescharacteristic
45C22×C4×C61C2×D411yescharacteristic
46C22×Dic61—41no—
47C22×Dic61—41no—
48C2×Dic122—22no—
49C2×Dic122—41no—
50C2×C8×C61—21no—
51C2×C8×C61—41no—
52C2×C8×C61—41no—
53C2×C8×C61C2×D412yes—
54C42×C61—21no—
55C42×C61—21no—
56C22⋊Dic61—42no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61—41no—
60C4⋊Dic61—41no—
61C4⋊Dic61—41no—
62C4⋊Dic61—41no—
63C4⋊Dic61—41no—
64C4⋊Dic61—41no—
65#11758196—42no—
66#11758196—42no—
67#11758196—82no—
68C4×Dic61—42no—
69Dic244—42no—
70Dic244—81no—
71C16×C61—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×C61SD3212yes—
80C2×C4×C61#12011yescharacteristic
81C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—81no—
86C2×Dic61—81no—
87C2×Dic61—81no—
88C2×Dic61—81no—
89C2×Dic61—81no—
90Dic122—42no—
91Dic122—42no—
92Dic122—82no—
93C8×C61—22no—
94C8×C61—41no—
95#12289—611nomaximal, Sylow
96C22×C61—21no—
97C22×C61—21no—
98C22×C61#44711yescharacteristic
99C22×C61C2×SD3211yescharacteristic
100C22×C61#51011yescharacteristic
101C4×C61—21no—
102C4×C61—22no—
103C4×C61—41no—
104C4×C61#45611yescharacteristic
105C4×C61#45811yescharacteristic
106Dic61—82no—
107Dic61—82no—
108Dic61—82no—
109Dic61—161no—
110#3249—611no—
111#2235—612no—
112#2086—611no—
113#1348—612no—
114#1322D6111yescharacteristic
115C2×C61—21no—
116C2×C61—21no—
117C2×C61#161011yescharacteristic
118C2×C61#218511yescharacteristic
119C2×C61#219111yescharacteristic
120#533—1221no—
121#477—1222no—
122#467—612no—
123#467—1221no—
124#462—1222no—
125C2×#107—611no—
126C2×C4⋊C8C2×D6111yescharacteristic
127#389—1221no—
128#367—1222no—
129#358—1222no—
130C22⋊C16C2×D6112yes—
131#340—611no—
132#340—1221no—
133C61#1228911yescharacteristic, complemented, Sylow
134C2×Q16—612no—
135C2×Q16—1221no—
136C22×C8D24411yescharacteristic
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—1221no—
147C2×C4⋊C4—1221no—
148C2×C4⋊C4—2441no—
149C2×C42D24411yescharacteristic
150C2×C16—22no—
151#107—612no—
152#107—1221no—
153#107—1222no—
154C4⋊C8—22no—
155#103—1222no—
156#103—1222no—
157#95—2441no—
158C2×Q8—1222no—
159C2×Q8—2441no—
160C22×C4—2441no—
161C22×C4—2441no—
162C22×C4D48811yescharacteristic
163C22×C4D48811yescharacteristic
164C22×C4C2×D24411yescharacteristic
165Q16—4881no—
166Q16—2442no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8D4×D6112yes—
171C4⋊C4—1222no—
172C4⋊C4—1222no—
173C4⋊C4—4882no—
174C4⋊C4—2441no—
175C4⋊C4—2442no—
176C4⋊C4—2441no—
177C4⋊C4—2441no—
178C4⋊C4—2441no—
179C4⋊C4—2441no—
180C4⋊C4—2441no—
181C4⋊C4—2442no—
182C22⋊C4—2442no—
183C42—21no—
184C42—21no—
185C42—2442no—
186C16—42no—
187C23C2×D48811yescharacteristic
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—4881no—
198C2×C4—4881no—
199C2×C4—4881no—
200C2×C4—4881no—
201C2×C4—4881no—
202C2×C4—2442no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4#1451972212yes—
206C2×C4#1451974711yescharacteristic
207C2×C4#1451980511yescharacteristic
208C8—22no—
209C8—41no—
210C22—21no—
211C22—21no—
212C22#1683989811yescharacteristic
213C22C2×#1451972211yescharacteristic
214C22#1684020511yescharacteristic
215C4—22no—
216C4—21no—
217C4—41no—
218C4—9761no—
219C4—4882no—
220C4—4882no—
221C4—4882no—
222C4#1683994711yescharacteristic
223C4#1683995311yescharacteristic
224C2—21no—
225C2—21no—
226C2#2144482411yescharacteristic
227C2#2144773811yescharacteristic
228C2#2144777211yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC22×C8×C61C23
FrattiniC22×C8C22×D61
FittingC61×#1322C2
socleC22×C61#447
prime radicalC23×C61C2×D8
hypercenter#1322D61
hypocenterC61#12289
LCSG ▷ C22×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
133. C61#12289semidirect

Maximal subgroups

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

subgroupindex
#214571642
#214480172
#214473072
#214438322
C61×#13222
#1228961