Finite Group Databasebeta

← #29589284

Subgroups — #29589284

Order 15616.

460 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 89 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#21448366C211yesmaximal, characteristic
2#21444141C212yesmaximal, complemented
3#21443762C212yesmaximal, complemented
4#21443751C211yesmaximal, characteristic
5C61×#1318C211yesmaximal, characteristic
6C2×#14519764C411yescharacteristic
7C2×#14519742C2211yescharacteristic
8C2×D4×Dic61C411yescharacteristic
9#16839812—22no—
10#16839668C411yescharacteristic
11#16839650—22no—
12#16839627C2211yescharacteristic
13C22⋊C4×Dic61—22no—
14C42×Dic61C411yescharacteristic
15#16839488C2212yes—
16#16839487—22no—
17C61×#390C2211yescharacteristic
18C61×#324C2212yes—
19C22×Dic122C2×C411yescharacteristic
20C23×Dic61—21no—
21#14519764—22no—
22#14519764C814yescomplemented
23#14519742—41no—
24#14519742—41no—
25D4×Dic61—41no—
26D4×Dic61—41no—
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196D412yes—
29C2×C22⋊Dic61—22no—
30C2×C22⋊Dic61—21no—
31C2×C4×Dic61—21no—
32C2×C4×Dic61—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61D412yes—
36#14519706—42no—
37C22⋊#92418—22no—
38C8×Dic61—42no—
39#14519684—22no—
40#14519684—22no—
41C22×D4×C61C2×C411yescharacteristic
42C2×C4⋊C4×C61C2311yescharacteristic
43C2×C22⋊C4×C61—22no—
44C2×C42×C61C2×C411yescharacteristic
45C22⋊C8×C61—22no—
46C24×C61—21no—
47C2×D4×C61—21no—
48C2×D4×C61—41no—
49C2×D4×C61—41no—
50C2×D4×C61C2×C812yes—
51C22×C4×C61—21no—
52C22×C4×C61C22×C411yescharacteristic
53C22×C4×C61C2×D412yes—
54C22×Dic61—21no—
55C22×Dic61—21no—
56C22×Dic61—44no—
57C22×Dic61—41no—
58C22×Dic61—41no—
59C22×Dic61C22⋊C412yes—
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C22⋊C411yescharacteristic
62C2×Dic122—41no—
63C2×Dic122—41no—
64C2×Dic122C2×C812yes—
65C2×Dic122M1612yes—
66C2×C8×C61—42no—
67C4⋊C4×C61—41no—
68C22⋊C4×C61—44no—
69C42×C61—41no—
70C22⋊Dic61—28no—
71C22⋊Dic61—42no—
72C4⋊Dic61—41no—
73#11758196—42no—
74C4×Dic61—21no—
75C4×Dic61—22no—
76C4×Dic61—22no—
77C4×Dic61—21no—
78C4×Dic61—21no—
79C4×Dic61—42no—
80C4×Dic61—42no—
81C4×Dic61C2×C812yes—
82C2×#92418—42no—
83C23×C61—22no—
84C23×C61—42no—
85C23×C61—42no—
86C23×C61—41no—
87C23×C61—41no—
88C23×C61C2×C22⋊C411yescharacteristic
89D4×C61—42no—
90D4×C61—42no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—42no—
98C2×C4×C61C22×C811yescharacteristic
99C2×C4×C61C2×M1611yescharacteristic
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—21no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—42no—
109C2×Dic61—41no—
110C2×Dic61—82no—
111C2×Dic61—82no—
112C2×Dic61C22⋊C814yes—
113C2×Dic61#9911yescharacteristic
114C2×Dic61#9911yescharacteristic
115Dic122—42no—
116Dic122—42no—
117C8×C61—82no—
118#92418—82no—
119#11476—611nomaximal, Sylow
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—44no—
123C22×C61—42no—
124C22×C61—82no—
125C22×C61—81no—
126C22×C61—81no—
127C22×C61C2×C22⋊C811yescharacteristic
128C22×C61C2×#9911yescharacteristic
129C22×C61#41311yescharacteristic
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—42no—
133C4×C61—42no—
134Dic61—21no—
135Dic61—24no—
136Dic61—42no—
137Dic61—41no—
138Dic61—81no—
139Dic61#35512yes—
140C4×#124—611no—
141#1461—612no—
142#1324—612no—
143#1318—611no—
144#1318D6111yescharacteristic
145C2×C61—21no—
146C2×C61—21no—
147C2×C61—82no—
148C2×C61#145911yescharacteristic
149C2×C61#212611yescharacteristic
150C2×C61C2×#35511yescharacteristic
151C2×#124—611no—
152C2×C4×Q8—611no—
153C2×C4×D4—611no—
154#431—1222no—
155#391—611no—
156#390C2×D6111yescharacteristic
157#388—1222no—
158#382—611no—
159C4×C22⋊C4—1222no—
160C43—611no—
161#324—612no—
162#324—1222no—
163#324C2×D6112yes—
164C61#1147611yescharacteristic, complemented, Sylow
165C22×Q8—611no—
166C22×D4C4×D6111yescharacteristic
167C23×C4—1221no—
168#124—614no—
169#124—1222no—
170C4×Q8—2441no—
171C4×Q8—2441no—
172C4×D4—2441no—
173C4×D4—2441no—
174C2×C4⋊C4—612no—
175C2×C4⋊C4—611no—
176C2×C4⋊C4C22×D6111yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—1222no—
179C2×C22⋊C4—1221no—
180C2×C42—611no—
181C2×C42—611no—
182C2×C42—612no—
183C2×C42—1221no—
184C2×C42—1221no—
185C2×C42C4×D6111yescharacteristic
186C4⋊C8—2442no—
187C22⋊C8—22no—
188C22⋊C8—1222no—
189C4×C8—2442no—
190#95—1222no—
191#95—1222no—
192C24—21no—
193C2×Q8—612no—
194C2×Q8—612no—
195C2×Q8—2441no—
196C2×Q8—2441no—
197C2×D4—21no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4C8×D6112yes—
201C22×C4—21no—
202C22×C4—612no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—1221no—
206C22×C4—1221no—
207C22×C4—2441no—
208C22×C4—2441no—
209C22×C4—2444no—
210C22×C4C2×C4×D6111yescharacteristic
211C22×C4D4×D6112yes—
212C2×C8—42no—
213C2×C8—2442no—
214C4⋊C4—41no—
215C4⋊C4—2442no—
216C4⋊C4—2441no—
217C22⋊C4—44no—
218C22⋊C4—1228no—
219C22⋊C4—2442no—
220C42—41no—
221C42—612no—
222C42—1222no—
223C42—1222no—
224C42—1221no—
225C42—1221no—
226C42—1221no—
227C42—2442no—
228C42—2442no—
229C23—22no—
230C23—42no—
231C23—42no—
232C23—41no—
233C23—41no—
234C23C22⋊C4×D6111yescharacteristic
235Q8—2442no—
236Q8—2442no—
237D4—42no—
238D4—42no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—611no—
247C2×C4—614no—
248C2×C4—611no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1221no—
254C2×C4—4882no—
255C2×C4—4882no—
256C2×C4—2442no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4C2×C8×D6111yescharacteristic
262C2×C4M16×D6111yescharacteristic
263C8—82no—
264C8—4882no—
265C22—21no—
266C22—21no—
267C22—44no—
268C22—42no—
269C22—82no—
270C22—81no—
271C22—81no—
272C22C22⋊C8×D6111yescharacteristic
273C22#99×D6111yescharacteristic
274C22#1683974311yescharacteristic
275C4—21no—
276C4—21no—
277C4—42no—
278C4—42no—
279C4—612no—
280C4—1224no—
281C4—1221no—
282C4—4881no—
283C4—2442no—
284C4—2441no—
285C2—21no—
286C2—21no—
287C2—82no—
288C2#2144413411yescharacteristic
289C2#2144748111yescharacteristic
290C2#355×D6111yescharacteristic
subgroupG/H
centerC22#99×D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1318C2
socleC22×C61C2×#99
prime radicalC22×D4×C61C2×C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1318D61
hypocenterC61#11476
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1318

Complements

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

NH ≅ G/Ntype
2. #21444141C2semidirect
3. #21443762C2semidirect
22. #14519764C8semidirect
164. C61#11476semidirect

Maximal subgroups

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

subgroupindex
#214483662
#214441412
#214437622
#214437512
C61×#13182
#1147661