Finite Group Databasebeta

← #29572775

Subgroups — #29572775

Order 15616.

540 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 117 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#21448358C211yesmaximal, characteristic
2#21445673C212yesmaximal, complemented
3C2×#16839501C212yesmaximal
4#21443700C211yesmaximal, characteristic, complemented
5C61×#1295C211yesmaximal, characteristic, complemented
6C2×#14519765C2211yescharacteristic
7C2×#14519742C411yescharacteristic
8C2×#14519739C411yescharacteristic
9C2×#14519706—22no—
10C2×#14519688C2212yes—
11#16839667C411yescharacteristic
12#16839663C411yescharacteristic
13#16839651—22no—
14#16839609—22no—
15C42×Dic61C2211yescharacteristic
16#16839516—22no—
17#16839501—24no—
18C2×#97×C61C2212yes—
19C61×#382C2211yescharacteristic
20C22×Dic122C2×C411yescharacteristic
21C22×D244C2×C411yescharacteristic
22C22×C4×D61—21no—
23C22×#92418—22no—
24#14519765—22no—
25#14519765D412yes—
26#14519765Q812yes—
27#14519742—42no—
28#14519739—42no—
29C2×#11758196—21no—
30C2×#11758198—22no—
31C2×#11758198—21no—
32C2×#11758198—22no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61D412yes—
37C2×C4×Dic61D412yes—
38#14519706—28no—
39#14519688—22no—
40#14519688—22no—
41#14519684—22no—
42C22×C8×C61—22no—
43C2×C4⋊C4×C61C2×C411yescharacteristic
44C2×C4⋊C4×C61C2×C411yescharacteristic
45C2×C42×C61C2311yescharacteristic
46#97×C61—22no—
47#97×C61—22no—
48#95×C61—22no—
49C23×D61—21no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61C22×C411yescharacteristic
53C22×C4×C61C2×D412yes—
54C22×Dic61—21no—
55C22×Dic61C22⋊C412yes—
56C22×Dic61C22⋊C411yescharacteristic
57C22×Dic61C22⋊C411yescharacteristic
58C2×D244—21no—
59C2×D244—41no—
60C2×D244—41no—
61C2×D244C4⋊C412yes—
62C2×C4×D61—42no—
63C2×C4×D61—44no—
64C2×Dic122—21no—
65C2×Dic122—41no—
66C2×Dic122—41no—
67C2×Dic122C4⋊C412yes—
68C2×C8×C61—24no—
69C2×C8×C61—42no—
70C2×C8×C61—42no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C42×C61C2×D411yescharacteristic
74C42×C61C2×Q811yescharacteristic
75C42×C61#4112yes—
76#11758198—24no—
77#11758198—24no—
78#11758198—44no—
79#11758198—42no—
80#11758196—42no—
81C4×Dic61—22no—
82C4×Dic61—24no—
83C4×Dic61—41no—
84C4×Dic61—42no—
85C4×Dic61—42no—
86C2×#92418—24no—
87C2×#92418—42no—
88C2×#92418—42no—
89C23×C61C2×C22⋊C411yescharacteristic
90C22×D61—22no—
91C22×D61—41no—
92C22×D61—41no—
93C22×D61—42no—
94C22×D61—42no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61C2×C4⋊C411yescharacteristic
104C2×C4×C61#11711yescharacteristic
105C2×C4×C61#12112yes—
106C2×C4×C61C22⋊Q812yes—
107C2×Dic61—22no—
108C2×Dic61—21no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61#10012yes—
116C2×Dic61#10414yes—
117D244—42no—
118D244—42no—
119C4×D61—84no—
120Dic122—42no—
121Dic122—42no—
122C8×C61—44no—
123#92418—44no—
124#8579—611nomaximal, Sylow
125C22×C61#38011yescharacteristic
126C22×C61C2×#10011yescharacteristic
127C22×C61#41311yescharacteristic
128C22×C61C2×#10412yes—
129C22×C61#42112yes—
130C2×D61—42no—
131C2×D61—44no—
132C2×D61—81no—
133C2×D61—81no—
134C2×D61—82no—
135C4×C61—21no—
136C4×C61—21no—
137C4×C61—22no—
138C4×C61—22no—
139C4×C61—81no—
140C4×C61—81no—
141Dic61—41no—
142Dic61—42no—
143Dic61—42no—
144Dic61#32914yescomplemented
145C4×#124—611no—
146#1767—612no—
147C2×#329—612no—
148#1295—611no—
149#1295D6111yescharacteristic, complemented
150C2×C61C2×#32911yescharacteristic
151C2×C61#152912yes—
152C2×C61#153611yescharacteristic
153C2×C61#180011yescharacteristic
154C2×C61#180612yes—
155D61—82no—
156C2×#124—611no—
157C2×C4×Q8—611no—
158C2×C4×D4—611no—
159C2×C4⋊C8—1222no—
160C2×#97—612no—
161C2×#97C2×D6112yes—
162#391—611no—
163#390—611no—
164#388—1222no—
165#382C2×D6111yescharacteristic
166C4×C22⋊C4—1222no—
167C43—611no—
168#336—1222no—
169#329—1224no—
170C61#857911yescharacteristic, complemented, Sylow
171C22×Q8—611no—
172C22×D4—611no—
173C23×C4—1221no—
174C22×C8—22no—
175C22×C8—1222no—
176#124—612no—
177#124—612no—
178#124—1222no—
179C4×Q8—2442no—
180C4×D4—2442no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4C4×D6111yescharacteristic
183C2×C4⋊C4C4×D6111yescharacteristic
184C2×C22⋊C4—1222no—
185C2×C22⋊C4—1221no—
186C2×C22⋊C4—1222no—
187C2×C42—611no—
188C2×C42—612no—
189C2×C42—611no—
190C2×C42—612no—
191C2×C42—1221no—
192C2×C42C22×D6111yescharacteristic
193C4⋊C8—1228no—
194#97—22no—
195#97—22no—
196#97—1222no—
197#97—1222no—
198#95—22no—
199#95—1222no—
200C24—1221no—
201C2×Q8—612no—
202C2×Q8—1221no—
203C2×Q8—2441no—
204C2×Q8—2441no—
205C2×D4—612no—
206C2×D4—1221no—
207C2×D4—2441no—
208C2×D4—2441no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—611no—
212C22×C4—612no—
213C22×C4—611no—
214C22×C4—1221no—
215C22×C4—2442no—
216C22×C4—2444no—
217C22×C4C2×C4×D6111yescharacteristic
218C22×C4D4×D6112yes—
219C2×C8—24no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—1224no—
223C2×C8—2442no—
224C2×C8—2442no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—2442no—
228C22⋊C4—1224no—
229C22⋊C4—1224no—
230C22⋊C4—2442no—
231C22⋊C4—2444no—
232C42—1224no—
233C42—1222no—
234C42—2441no—
235C42—2442no—
236C42—2442no—
237C42#1175822212yes—
238C42D4×D6111yescharacteristic
239C42Q8×D6111yescharacteristic
240C23—1222no—
241C23—2441no—
242C23—2441no—
243C23—2442no—
244C23—2442no—
245C23C22⋊C4×D6111yescharacteristic
246Q8—2442no—
247Q8—2442no—
248D4—2442no—
249D4—2442no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—612no—
259C2×C4—614no—
260C2×C4—1221no—
261C2×C4—1222no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—4884no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4C4⋊C4×D6111yescharacteristic
270C2×C4#1451973411yescharacteristic
271C2×C4#1451975012yes—
272C2×C4#1451975512yes—
273C8—44no—
274C8—2444no—
275C22—4881no—
276C22—4882no—
277C22—4881no—
278C22—2442no—
279C22—2444no—
280C22#1683962111yescharacteristic
281C22#100×D6111yescharacteristic
282C22#1683974511yescharacteristic
283C22#104×D6112yes—
284C22#1683977712yes—
285C4—21no—
286C4—21no—
287C4—22no—
288C4—22no—
289C4—81no—
290C4—81no—
291C4—614no—
292C4—2442no—
293C4—2441no—
294C4—2442no—
295C2—4882no—
296C2#329×D6111yescharacteristic
297C2#2144442512yes—
298C2#2144445211yescharacteristic
299C2#2144581011yescharacteristic
300C2#2144583812yes—
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socleC23×C61C2×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1295D61
hypocenterC61#8579
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
2. #21445673C2semidirect
4. #21443700C2semidirect
5. C61×#1295C2semidirect
144. Dic61#329semidirect
149. #1295D61semidirect
170. C61#8579semidirect

Maximal subgroups

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

subgroupindex
#214483582
#214456732
C2×#168395012
#214437002
C61×#12952
#857961