Finite Group Databasebeta

← #29571448

Subgroups — #29571448

Order 15616.

812 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 147 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#21444210C214yesmaximal, complemented
2#21444133C212yesmaximal, complemented
3C2×C61×#540C211yesmaximal, characteristic
4#16839815C2214yes—
5D4⋊#92418—28no—
6#16839488—22no—
7#16839486—22no—
8C61×#540—28no—
9C2×#127×C61C411yescharacteristic
10C2×#125×C61C411yescharacteristic
11C2×#123×C61—22no—
12C2×#121×C61—22no—
13C2×#121×C61C412yes—
14C2×C4×D4×C61C2212yes—
15C2×#117×C61C2211yescharacteristic
16C4⋊#92418—24no—
17C22⋊#92418—24no—
18C4×#92418—24no—
19C22×D4×C61—22no—
20C22×D4×C61—22no—
21C22×D4×C61C2×C412yes—
22C23×C4×C61—22no—
23C23×C4×C61C2×C411yescharacteristic
24#127×C61—24no—
25#125×C61—24no—
26#123×C61—216no—
27#121×C61—216no—
28#121×C61—24no—
29#121×C61—24no—
30C4×D4×C61—24no—
31C4×D4×C61D418yes—
32#117×C61—24no—
33C2×C4⋊C4×C61—22no—
34C2×C4⋊C4×C61C2×C412yes—
35C2×C4⋊C4×C61D412yes—
36C2×C22⋊C4×C61—22no—
37C2×C22⋊C4×C61—22no—
38C2×C22⋊C4×C61D412yes—
39C2×C42×C61C2×C411yescharacteristic
40C2×C42×C61C2311yescharacteristic
41C24×C61—22no—
42C24×C61C22⋊C411yescharacteristic
43C2×D4×C61—28no—
44C2×D4×C61—28no—
45C2×D4×C61—22no—
46C2×D4×C61—28no—
47C2×D4×C61—84no—
48C2×D4×C61—84no—
49C2×D4×C61C22⋊C414yes—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—24no—
53C22×C4×C61—28no—
54C22×C4×C61—84no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C412yes—
57C22×C4×C61C22×C411yescharacteristic
58C22×C4×C61C2×D412yes—
59C4⋊C4×C61—28no—
60C4⋊C4×C61—22no—
61C4⋊C4×C61—24no—
62C4⋊C4×C61C22⋊C414yes—
63C22⋊C4×C61—28no—
64C22⋊C4×C61—28no—
65C22⋊C4×C61—24no—
66C42×C61—22no—
67C42×C61C2×D414yes—
68C2×#92418—44no—
69C23×C61—21no—
70C23×C61—24no—
71C23×C61—22no—
72C23×C61—44no—
73C23×C61—44no—
74C23×C61—42no—
75C23×C61—44no—
76C23×C61C2×C22⋊C411yescharacteristic
77D4×C61—28no—
78D4×C61—44no—
79D4×C61—88no—
80D4×C61—88no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—24no—
84C2×C4×C61—22no—
85C2×C4×C61—42no—
86C2×C4×C61—44no—
87C2×C4×C61—44no—
88C2×C4×C61—42no—
89C2×C4×C61—88no—
90C2×C4×C61C2×C22⋊C412yes—
91C2×C4×C61#12014yes—
92C2×C4×C61#13114yes—
93#92418—84no—
94#8326—611nomaximal, Sylow
95C22×C61—22no—
96C22×C61—44no—
97C22×C61—42no—
98C22×C61—44no—
99C22×C61—41no—
100C22×C61—44no—
101C22×C61—82no—
102C22×C61—88no—
103C22×C61#37911yescharacteristic
104C22×C61#40812yes—
105C4×C61—24no—
106C4×C61—44no—
107C4×C61—42no—
108C4×C61—41no—
109C4×C61#40814yes—
110C2×#540D6111yescharacteristic
111#1478—614no—
112#1458—612no—
113C2×C61—22no—
114C2×C61—81no—
115C2×C61—84no—
116C2×C61#178011yescharacteristic
117C2×C61#179512yes—
118#540—28no—
119C2×#127Dic6111yescharacteristic
120C2×#125Dic6111yescharacteristic
121C2×#123—22no—
122C2×#121—22no—
123C2×#121Dic6112yes—
124C2×C4×D4C2×D6112yes—
125C2×#117C2×D6111yescharacteristic
126#431—614no—
127D4⋊C8—1228no—
128#324—1222no—
129#323—1222no—
130C61#832611yescharacteristic, complemented, Sylow
131C22×D4—22no—
132C22×D4—22no—
133C22×D4C2×Dic6112yes—
134C23×C4—22no—
135C23×C4C2×Dic6111yescharacteristic
136#127—24no—
137#125—24no—
138#123—216no—
139#121—216no—
140#121—24no—
141#121—24no—
142C4×D4—24no—
143C4×D4C22⋊D6118yes—
144#117—24no—
145C2×C4⋊C4—22no—
146C2×C4⋊C4C2×Dic6112yes—
147C2×C4⋊C4C22⋊D6112yes—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4C22⋊D6112yes—
151C2×C42C2×Dic6111yescharacteristic
152C2×C42C22×D6111yescharacteristic
153C4⋊C8—1224no—
154C22⋊C8—1224no—
155C4×C8—1224no—
156C24—22no—
157C24C22⋊Dic6111yescharacteristic
158C2×D4—28no—
159C2×D4—28no—
160C2×D4—22no—
161C2×D4—28no—
162C2×D4—84no—
163C2×D4—84no—
164C2×D4C22⋊Dic6114yes—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—24no—
168C22×C4—28no—
169C22×C4—84no—
170C22×C4C22⋊Dic6111yescharacteristic
171C22×C4C22⋊Dic6112yes—
172C22×C4C22×Dic6111yescharacteristic
173C22×C4C2×C22⋊D6112yes—
174C2×C8—2444no—
175C4⋊C4—28no—
176C4⋊C4—22no—
177C4⋊C4—24no—
178C4⋊C4C22⋊Dic6114yes—
179C22⋊C4—28no—
180C22⋊C4—28no—
181C22⋊C4—24no—
182C42—22no—
183C42C2×C22⋊D6114yes—
184C23—21no—
185C23—24no—
186C23—22no—
187C23—44no—
188C23—44no—
189C23—42no—
190C23—44no—
191C23C2×C22⋊Dic6111yescharacteristic
192D4—28no—
193D4—44no—
194D4—88no—
195D4—88no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—24no—
200C2×C4—42no—
201C2×C4—44no—
202C2×C4—44no—
203C2×C4—42no—
204C2×C4—88no—
205C2×C4C2×C22⋊Dic6112yes—
206C2×C4#1451974614yes—
207C2×C4#1451978414yes—
208C8—4884no—
209C22—22no—
210C22—41no—
211C22—44no—
212C22—44no—
213C22—42no—
214C22—44no—
215C22—82no—
216C22—88no—
217C22#1683961811yescharacteristic
218C22#1683972912yes—
219C4—24no—
220C4—41no—
221C4—44no—
222C4—42no—
223C4#1683972914yes—
224C2—22no—
225C2—84no—
226C2—81no—
227C2#2144573111yescharacteristic
228C2#2144578912yes—
subgroupG/H
centerC22#16839618
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
Fitting, prime radicalC2×C61×#540C2
socleC22×C61#379
cosocleC2×C42×C61C23
hypercenterC2×#540D61
hypocenterC61#8326
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. #21444210C2semidirect
2. #21444133C2semidirect
130. C61#8326semidirect

Maximal subgroups

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

subgroupindex
#214442102
#214441332
C2×C61×#5402
#832661