Finite Group Databasebeta

← #29589310

Subgroups — #29589310

Order 15616.

392 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 87 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#21448536C211yesmaximal, characteristic
2#21444141C212yesmaximal
3#21443763C211yesmaximal, characteristic
4#21443752C212yesmaximal
5C61×#1324C211yesmaximal, characteristic
6C2×#14519777C411yescharacteristic
7C2×#14519742C411yescharacteristic
8C2×#14519742C2211yescharacteristic
9#16839812—22no—
10#16839667C411yescharacteristic
11#16839667C2211yescharacteristic
12#16839645—22no—
13#16839645—22no—
14#16839608C411yescharacteristic
15#16839488C2212yes—
16#16839487—22no—
17C61×#382C2211yescharacteristic
18C61×#324C2212yes—
19C22×Dic122C2×C411yescharacteristic
20C22×Dic122C2×C411yescharacteristic
21#14519777—22no—
22#14519777C814yescomplemented
23#14519742—42no—
24#14519742—42no—
25C2×C4⋊Dic61—22no—
26C2×#11758196—21no—
27C2×#11758196D412yes—
28C2×C4×Dic61—21no—
29C2×C4×Dic61C2×C411yescharacteristic
30C2×C4×Dic61C2×C411yescharacteristic
31C2×C4×Dic61D412yes—
32#14519706—42no—
33C22⋊#92418—22no—
34C8×Dic61—42no—
35#14519684—22no—
36#14519684—21no—
37#14519684—21no—
38#14519684—22no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2311yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42C22⋊C8×C61—22no—
43#95×C61—22no—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C22×C411yescharacteristic
47C22×C4×C61C2×D412yes—
48C22×Dic61—21no—
49C22×Dic61—21no—
50C22×Dic61C22⋊C412yes—
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C22⋊C411yescharacteristic
53C2×Dic122—21no—
54C2×Dic122—41no—
55C2×Dic122—41no—
56C2×Dic122—41no—
57C2×Dic122—41no—
58C2×Dic122C2×C812yes—
59C2×Dic122C2×C812yes—
60C2×Dic122M1612yes—
61C2×C8×C61—42no—
62C4⋊C4×C61—41no—
63C4⋊C4×C61—41no—
64C42×C61—21no—
65C42×C61C2×C812yes—
66C4⋊Dic61—28no—
67#11758196—42no—
68#11758196—42no—
69C4×Dic61—22no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61—42no—
73C4×Dic61—41no—
74C2×#92418—42no—
75C23×C61C2×C22⋊C411yescharacteristic
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61—41no—
85C2×C4×C61C22×C811yescharacteristic
86C2×C4×C61C2×M1611yescharacteristic
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—21no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—41no—
95C2×Dic61—41no—
96C2×Dic61—41no—
97C2×Dic61—41no—
98C2×Dic61C22⋊C814yes—
99C2×Dic61#9912yes—
100Dic122—42no—
101Dic122—42no—
102Dic122—42no—
103Dic122—42no—
104C8×C61—82no—
105#92418—82no—
106#11482—611nomaximal, Sylow
107C22×C61—21no—
108C22×C61—21no—
109C22×C61C2×C22⋊C811yescharacteristic
110C22×C61C2×#9911yescharacteristic
111C22×C61#41311yescharacteristic
112C4×C61—21no—
113C4×C61—21no—
114C4×C61—42no—
115C4×C61—42no—
116C4×C61—81no—
117Dic61—22no—
118Dic61—24no—
119Dic61—41no—
120Dic61—42no—
121Dic61—81no—
122#2327—611no—
123#1461—612no—
124#1324—611no—
125#1324D6111yescharacteristic
126#1319—612no—
127C2×C61—21no—
128C2×C61—21no—
129C2×C61#145911yescharacteristic
130C2×C61#212911yescharacteristic
131C2×C61#213311yescharacteristic
132C2×C4⋊Q8—611no—
133C2×C4×Q8—611no—
134C2×C4×Q8—611no—
135#431—1222no—
136#391—611no—
137#391—611no—
138#387—1222no—
139#387—1222no—
140#382C2×D6111yescharacteristic
141#376—611no—
142#324—612no—
143#324—1222no—
144#324C2×D6112yes—
145C61#1148211yescharacteristic, complemented, Sylow
146C22×Q8—611no—
147C22×Q8—611no—
148C4⋊Q8—614no—
149C4⋊Q8—1222no—
150C4×Q8—2442no—
151C4×Q8—2442no—
152C2×C4⋊C4—612no—
153C2×C4⋊C4—1222no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4C4×D6111yescharacteristic
156C2×C4⋊C4C22×D6111yescharacteristic
157C2×C42—611no—
158C2×C42—612no—
159C2×C42—611no—
160C2×C42—1221no—
161C2×C42C4×D6111yescharacteristic
162C4⋊C8—2442no—
163C22⋊C8—22no—
164C22⋊C8—1222no—
165C4×C8—2442no—
166#95—22no—
167#95—1221no—
168#95—1221no—
169#95—1222no—
170#95—1222no—
171C2×Q8—612no—
172C2×Q8—612no—
173C2×Q8—612no—
174C2×Q8—1221no—
175C2×Q8—2441no—
176C2×Q8—2441no—
177C2×Q8—2441no—
178C2×Q8—2441no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—612no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—1221no—
185C22×C4—1221no—
186C22×C4C2×C4×D6111yescharacteristic
187C22×C4D4×D6112yes—
188C2×C8—42no—
189C2×C8—2442no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—1228no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C42—21no—
196C42—1222no—
197C42—1222no—
198C42—1222no—
199C42—2441no—
200C42—2442no—
201C42C8×D6112yes—
202C23C22⋊C4×D6111yescharacteristic
203Q8—2442no—
204Q8—2442no—
205Q8—2442no—
206Q8—2442no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—41no—
216C2×C4—614no—
217C2×C4—612no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1221no—
222C2×C4—2441no—
223C2×C4—2441no—
224C2×C4—2441no—
225C2×C4—2441no—
226C2×C4—2441no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4C2×C8×D6111yescharacteristic
230C2×C4M16×D6111yescharacteristic
231C8—82no—
232C8—4882no—
233C22—21no—
234C22—21no—
235C22C22⋊C8×D6111yescharacteristic
236C22#99×D6111yescharacteristic
237C22#1683974511yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—81no—
243C4—1224no—
244C4—1222no—
245C4—4881no—
246C4—2442no—
247C4—2441no—
248C2—21no—
249C2—21no—
250C2#2144413611yescharacteristic
251C2#2144749211yescharacteristic
252C2#2144750511yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1324C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1324D61
hypocenterC61#11482
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1324

Complements

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

NH ≅ G/Ntype
22. #14519777C8semidirect
145. C61#11482semidirect

Maximal subgroups

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

subgroupindex
#214485362
#214441412
#214437632
#214437522
C61×#13242
#1148261