Finite Group Databasebeta

← #30604108

Subgroups — #30604108

Order 15616.

670 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461070C212yesmaximal, complemented
2#21460748C214yesmaximal, complemented
3#21448399C211yesmaximal, characteristic
4#16840782—22no—
5#16840607C2214yescomplemented
6#16840605—22no—
7C23×D244C411yescharacteristic
8C2×#14519736C2211yescharacteristic
9#16839664C412yes—
10#16839664C2212yes—
11#16839663—22no—
12#16839617—22no—
13C2×#117×C61C411yescharacteristic
14#14519844—42no—
15C22⋊#92420—24no—
16#14519832—42no—
17C24×D61—21no—
18C22×D244—21no—
19C22×D244—24no—
20C22×D244—42no—
21C22×D244—42no—
22C22×D244C2×C412yes—
23#14519736—42no—
24C2×C4⋊Dic61C2×C411yescharacteristic
25C2×C4⋊Dic61C2311yescharacteristic
26C2×C22⋊Dic61D412yes—
27C2×#11758198—24no—
28C2×#11758198—24no—
29C2×C4×Dic61D412yes—
30C23×C4×C61C2×C411yescharacteristic
31#117×C61—42no—
32C2×C4⋊C4×C61—21no—
33C2×C22⋊C4×C61—21no—
34C2×C42×C61C2×C412yes—
35C24×C61C22⋊C411yescharacteristic
36C23×D61—22no—
37C23×D61—24no—
38C23×D61—42no—
39C23×D61—42no—
40C23×D61—82no—
41C23×D61—82no—
42C22×C4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61—22no—
45C22×C4×C61—22no—
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61C22⋊C412yes—
49C22×Dic61C2×D412yes—
50C2×D244—24no—
51C2×D244—22no—
52C2×D244—416no—
53C2×D244—42no—
54C2×D244—42no—
55C2×D244—42no—
56C2×D244—42no—
57C2×D244M1614yes—
58C2×#92420—44no—
59C4⋊C4×C61—42no—
60C22⋊C4×C61—42no—
61C42×C61—42no—
62C22⋊Dic61—42no—
63#11758198—84no—
64#11758198—84no—
65C4⋊Dic61—41no—
66C4⋊Dic61—41no—
67C4×Dic61—22no—
68C4×Dic61—22no—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61—41no—
72C23×C61—41no—
73C23×C61#10012yes—
74C23×C61C2×C22⋊C411yescharacteristic
75C22×D61—24no—
76C22×D61—44no—
77C22×D61—44no—
78C22×D61—48no—
79C22×D61—42no—
80C22×D61—42no—
81C22×D61—88no—
82C22×D61—88no—
83C22×D61—84no—
84C22×D61—84no—
85C2×C4×C61—28no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61#9912yes—
94C2×C4×C61C2×M1612yes—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99D244—44no—
100D244—48no—
101D244—44no—
102#92420—84no—
103#11509—611nomaximal, Sylow
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—22no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61—41no—
110C22×C61—41no—
111C22×C61#40711yescharacteristic
112C22×C61C2×#9911yescharacteristic
113C22×C61C2×#10011yescharacteristic
114C2×D61—48no—
115C2×D61—44no—
116C2×D61—84no—
117C2×D61—816no—
118C2×D61—82no—
119C2×D61—82no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—82no—
123Dic61—42no—
124Dic61—42no—
125#2309—611no—
126#1464—612no—
127#1318—614no—
128C2×C61—21no—
129C2×C61—21no—
130C2×C61—42no—
131C2×C61#146211yescharacteristic
132C2×C61#212811yescharacteristic
133C2×C61#213411yescharacteristic
134D61—84no—
135C23×D4—611no—
136C2×#117—611no—
137C2×#117#692311yescharacteristic
138#432—1222no—
139#390—612no—
140#390—612no—
141#390—1222no—
142#379—1222no—
143#324—614no—
144#323—1222no—
145C61#1150911yescharacteristic, complemented, Sylow
146C25—1221no—
147C22×D4—612no—
148C22×D4—1224no—
149C22×D4—1221no—
150C22×D4—2442no—
151C22×D4—2442no—
152C23×C4C2×#692311yescharacteristic
153#117—42no—
154#117—2442no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—611no—
157C2×C4⋊C4—611no—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—612no—
160C2×C22⋊C4—1224no—
161C2×C22⋊C4—1224no—
162C2×C42—612no—
163C2×C42C2×#692312yes—
164C4⋊C8—2442no—
165C22⋊C8—1224no—
166#97—2442no—
167C24—1224no—
168C24—1222no—
169C24—4882no—
170C24—4882no—
171C24—2442no—
172C24—2442no—
173C24C22⋊#692311yescharacteristic
174C2×D4—614no—
175C2×D4—1224no—
176C2×D4—1222no—
177C2×D4—2442no—
178C2×D4—2442no—
179C2×D4—24416no—
180C2×D4—2442no—
181C2×D4—2442no—
182C22×C4—22no—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—612no—
187C22×C4—612no—
188C22×C4C22⋊#692311yescharacteristic
189C22×C4C22×#692311yescharacteristic
190C2×C8—2444no—
191C4⋊C4—42no—
192C4⋊C4—2441no—
193C4⋊C4—2441no—
194C22⋊C4—42no—
195C22⋊C4—4884no—
196C22⋊C4—4884no—
197C22⋊C4—2442no—
198C42—42no—
199C42—1222no—
200C42—1222no—
201C23—21no—
202C23—21no—
203C23—41no—
204C23—41no—
205C23—1224no—
206C23—4888no—
207C23—4884no—
208C23—4884no—
209C23—4888no—
210C23—2444no—
211C23—2444no—
212C23—2448no—
213C23—2442no—
214C23—2442no—
215C23#1451983712yes—
216C23C2×C22⋊#692311yescharacteristic
217D4—2444no—
218D4—2448no—
219D4—2444no—
220C2×C4—28no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—2442no—
231C2×C4—2442no—
232C2×C4#1451983612yes—
233C2×C4D61⋊M1612yes—
234C8—4884no—
235C22—21no—
236C22—21no—
237C22—22no—
238C22—42no—
239C22—42no—
240C22—41no—
241C22—41no—
242C22—4884no—
243C22—48816no—
244C22—4882no—
245C22—4882no—
246C22—2448no—
247C22—2444no—
248C22#1684073411yescharacteristic
249C22C2×#1451983611yescharacteristic
250C22C2×#1451983711yescharacteristic
251C4—22no—
252C4—22no—
253C4—82no—
254C4—2442no—
255C4—2442no—
256C2—21no—
257C2—21no—
258C2—42no—
259C2—4884no—
260C2#2146106611yescharacteristic
261C2#2146210011yescharacteristic
262C2#2146212011yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC23×D244C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×#117#6923
hypocenterC61#11509
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21461070C2semidirect
2. #21460748C2semidirect
5. #16840607C22semidirect
145. C61#11509semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214607482
#214483992
#1150961