Finite Group Databasebeta

← #30598206

Subgroups — #30598206

Order 15616.

812 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 108 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#21461118C214yesmaximal, complemented
2#21461052C212yesmaximal, complemented
3C2×#16840366C211yesmaximal, characteristic
4#16840778C2214yes—
5D4⋊#92420—28no—
6#16840608—22no—
7#16840606—22no—
8#16840366—28no—
9C2×#14519769C411yescharacteristic
10C2×#14519758—22no—
11C2×#14519749—22no—
12C2×#14519748C412yes—
13C2×D4×Dic61C2212yes—
14C2×#14519734C2211yescharacteristic
15C2×#127×C61C411yescharacteristic
16C4⋊#92420—24no—
17C22⋊#92420—24no—
18C4×#92420—24no—
19C22×C22⋊D61—22no—
20C23×Dic61—22no—
21C22×C4×D61C2×C411yescharacteristic
22#14519769—24no—
23#14519758—216no—
24#14519749—216no—
25#14519748—24no—
26#14519748—24no—
27D4×Dic61—24no—
28D4×Dic61D418yes—
29#14519734—24no—
30C2×C4⋊Dic61C2×C412yes—
31C2×#11758196—22no—
32C2×#11758196D412yes—
33C2×C22⋊Dic61—22no—
34C2×C22⋊Dic61—22no—
35C2×#11758198D412yes—
36C2×C4×Dic61C2311yescharacteristic
37C22×D4×C61—22no—
38C22×D4×C61C2×C412yes—
39#127×C61—24no—
40C2×C42×C61C2×C411yescharacteristic
41C24×C61—22no—
42C23×D61C22⋊C411yescharacteristic
43C2×D4×C61—28no—
44C2×D4×C61—22no—
45C2×D4×C61—28no—
46C2×D4×C61—84no—
47C2×D4×C61C22⋊C414yes—
48C22×C4×C61C22⋊C412yes—
49C22×C4×C61C22×C411yescharacteristic
50C2×C22⋊D61—28no—
51C2×C22⋊D61—84no—
52C22×Dic61—22no—
53C22×Dic61—28no—
54C22×Dic61—84no—
55C22×Dic61C22⋊C411yescharacteristic
56C22×Dic61C2×D412yes—
57C2×C4×D61—22no—
58C2×C4×D61—24no—
59C2×#92420—44no—
60C42×C61—22no—
61C22⋊Dic61—28no—
62C22⋊Dic61—28no—
63#11758198—24no—
64C4⋊Dic61—22no—
65C4⋊Dic61C22⋊C414yes—
66#11758196—28no—
67#11758196—24no—
68C4×Dic61C2×D414yes—
69C23×C61—24no—
70C23×C61—44no—
71C23×C61—44no—
72C23×C61—44no—
73C23×C61C2×C22⋊C411yescharacteristic
74C22×D61—21no—
75C22×D61—22no—
76C22×D61—42no—
77D4×C61—28no—
78D4×C61—44no—
79D4×C61—88no—
80C2×C4×C61—22no—
81C2×C4×C61—42no—
82C2×C4×C61C2×C22⋊C412yes—
83C2×C4×C61#13114yes—
84C22⋊D61—88no—
85C2×Dic61—24no—
86C2×Dic61—21no—
87C2×Dic61—22no—
88C2×Dic61—42no—
89C2×Dic61—44no—
90C2×Dic61—88no—
91C2×Dic61#12014yes—
92C4×D61—44no—
93#92420—84no—
94#8326—611nomaximal, Sylow
95C22×C61—22no—
96C22×C61—44no—
97C22×C61—44no—
98C22×C61—44no—
99C22×C61—88no—
100C22×C61#37911yescharacteristic
101C22×C61#40812yes—
102C2×D61—42no—
103C2×D61—41no—
104C2×D61—82no—
105C4×C61—42no—
106C4×C61#40814yes—
107Dic61—24no—
108Dic61—44no—
109Dic61—41no—
110C2×#540—611no—
111#1478—614no—
112#1458—612no—
113C2×C61—22no—
114C2×C61—84no—
115C2×C61#178011yescharacteristic
116C2×C61#179512yes—
117D61—81no—
118#540—1228no—
119C2×#127#692311yescharacteristic
120C2×#125—611no—
121C2×#123—1222no—
122C2×#121—612no—
123C2×#121—1222no—
124C2×C4×D4—612no—
125C2×#117—611no—
126#431—614no—
127D4⋊C8—1228no—
128#324—1222no—
129#323—1222no—
130C61#832611yescharacteristic, complemented, Sylow
131C22×D4—22no—
132C22×D4—1222no—
133C22×D4C2×#692312yes—
134C23×C4—611no—
135C23×C4—1222no—
136#127—24no—
137#125—1224no—
138#123—12216no—
139#121—1224no—
140#121—12216no—
141#121—1224no—
142C4×D4—618no—
143C4×D4—1224no—
144#117—1224no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—1222no—
148C2×C22⋊C4—612no—
149C2×C22⋊C4—1222no—
150C2×C22⋊C4—1222no—
151C2×C42—611no—
152C2×C42C2×#692311yescharacteristic
153C4⋊C8—1224no—
154C22⋊C8—1224no—
155C4×C8—1224no—
156C24—22no—
157C24—611no—
158C2×D4—28no—
159C2×D4—22no—
160C2×D4—28no—
161C2×D4—84no—
162C2×D4—1228no—
163C2×D4—4884no—
164C2×D4C22⋊#692314yes—
165C22×C4—612no—
166C22×C4—611no—
167C22×C4—1228no—
168C22×C4—1222no—
169C22×C4—1222no—
170C22×C4—1224no—
171C22×C4—4884no—
172C22×C4C22⋊#692312yes—
173C22×C4C22×#692311yescharacteristic
174C2×C8—2444no—
175C4⋊C4—614no—
176C4⋊C4—1224no—
177C4⋊C4—1228no—
178C4⋊C4—1222no—
179C22⋊C4—1224no—
180C22⋊C4—1228no—
181C22⋊C4—1228no—
182C42—22no—
183C42—614no—
184C23—24no—
185C23—44no—
186C23—44no—
187C23—44no—
188C23—1222no—
189C23—1221no—
190C23—2442no—
191C23C2×C22⋊#692311yescharacteristic
192D4—28no—
193D4—44no—
194D4—88no—
195D4—4888no—
196C2×C4—22no—
197C2×C4—42no—
198C2×C4—614no—
199C2×C4—1222no—
200C2×C4—1221no—
201C2×C4—1224no—
202C2×C4—4888no—
203C2×C4—2442no—
204C2×C4—2444no—
205C2×C4—2444no—
206C2×C4C2×C22⋊#692312yes—
207C2×C4#1451986414yes—
208C8—4884no—
209C22—22no—
210C22—44no—
211C22—44no—
212C22—44no—
213C22—88no—
214C22—4882no—
215C22—2441no—
216C22—2442no—
217C22#1684070311yescharacteristic
218C22#1684073612yes—
219C4—42no—
220C4—1224no—
221C4—2441no—
222C4—2444no—
223C4#1684073514yes—
224C2—22no—
225C2—84no—
226C2—4881no—
227C2#2146164311yescharacteristic
228C2#2146166912yes—
subgroupG/H
centerC22#16840703
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#127×C61C4
socleC22×C61#379
prime radicalC2×#16840366C2
cosocleC2×C4×Dic61C23
hypercenterC2×#127#6923
hypocenterC61#8326
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #21461118C2semidirect
2. #21461052C2semidirect
130. C61#8326semidirect

Maximal subgroups

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

subgroupindex
#214611182
#214610522
C2×#168403662
#832661