Finite Group Databasebeta

← #30604179

Subgroups — #30604179

Order 15616.

596 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461075C212yesmaximal, complemented
2#21460762C212yesmaximal, complemented
3#21460748C212yesmaximal, complemented
4#21448383C211yesmaximal, characteristic
5#16840732—22no—
6#16840607C2214yes—
7#16840605—22no—
8C2×#14519773C411yescharacteristic
9C2×D4×Dic61C2211yescharacteristic
10C2×#14519739C411yescharacteristic
11C2×#14519737—22no—
12#16839664C2211yescharacteristic
13#16839662—22no—
14#16839631C2211yescharacteristic
15C42×Dic61C411yescharacteristic
16C61×#390C411yescharacteristic
17C2×#11758217—42no—
18C22⋊#92420—24no—
19C22⋊#92420—42no—
20C22×D244C2×C411yescharacteristic
21C22×C22⋊D61—22no—
22C23×Dic61D412yes—
23C22×C4×D61—21no—
24#14519773—22no—
25#14519773—22no—
26D4×Dic61—41no—
27D4×Dic61—41no—
28#14519739—41no—
29#14519739—41no—
30#14519737—48no—
31C2×C4⋊Dic61C2311yescharacteristic
32C2×#11758196—22no—
33C2×C22⋊Dic61D412yes—
34C2×#11758198—21no—
35C2×#11758198—22no—
36C2×C4×Dic61—21no—
37C2×C4×Dic61—21no—
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61C2×C411yescharacteristic
40C22×D4×C61C2×C411yescharacteristic
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C2×C22⋊C4×C61—22no—
43C2×C42×C61C2×C411yescharacteristic
44C24×C61C22⋊C412yes—
45C23×D61—21no—
46C2×D4×C61—21no—
47C2×D4×C61—21no—
48C2×D4×C61—41no—
49C2×D4×C61—41no—
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61C22×C411yescharacteristic
53C2×C22⋊D61—28no—
54C2×C22⋊D61—44no—
55C2×C22⋊D61—44no—
56C22×Dic61—21no—
57C22×Dic61—22no—
58C22×Dic61—22no—
59C22×Dic61—44no—
60C22×Dic61C22⋊C411yescharacteristic
61C22×Dic61C22⋊C411yescharacteristic
62C22×Dic61C2×D412yes—
63C2×D244—21no—
64C2×D244—41no—
65C2×D244—41no—
66C2×D244M1612yescomplemented
67C2×C4×D61—44no—
68C2×C4×D61—41no—
69C2×C4×D61—41no—
70#11758217—84no—
71C2×#92420—44no—
72C4⋊C4×C61—41no—
73C22⋊C4×C61—44no—
74C42×C61—41no—
75C22⋊Dic61—42no—
76#11758198—42no—
77#11758198—44no—
78C4⋊Dic61—41no—
79#11758196—44no—
80C4×Dic61—24no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83C4×Dic61—21no—
84C4×Dic61—42no—
85C4×Dic61M1612yescomplemented
86C23×C61—22no—
87C23×C61—22no—
88C23×C61—22no—
89C23×C61—42no—
90C23×C61—42no—
91C23×C61C2×C22⋊C411yescharacteristic
92C22×D61—22no—
93C22×D61—42no—
94C22×D61—42no—
95C22×D61—41no—
96C22×D61—41no—
97D4×C61—42no—
98D4×C61—42no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—22no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—42no—
105C2×C4×C61—41no—
106C2×C4×C61C2×M1611yescharacteristic
107C2×C4×C61C2×M1611yescharacteristic
108C22⋊D61—416no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—21no—
114C2×Dic61—22no—
115C2×Dic61—44no—
116C2×Dic61—41no—
117C2×Dic61—42no—
118C2×Dic61—82no—
119C2×Dic61#9911yescharacteristic
120C2×Dic61#9911yescharacteristic
121D244—42no—
122D244—42no—
123C4×D61—82no—
124C4×D61—82no—
125#92420—84no—
126#11529—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—44no—
130C22×C61—42no—
131C22×C61—42no—
132C22×C61—42no—
133C22×C61—82no—
134C22×C61#40711yescharacteristic
135C22×C61C2×#9911yescharacteristic
136C22×C61#41311yescharacteristic
137C2×D61—44no—
138C2×D61—42no—
139C2×D61—82no—
140C2×D61—81no—
141C2×D61—81no—
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—42no—
145C4×C61—81no—
146Dic61—24no—
147Dic61—21no—
148Dic61—42no—
149Dic61—41no—
150Dic61#35312yes—
151C4×#127—611no—
152#1465—612no—
153#1325—612no—
154#1318—612no—
155C2×C61—21no—
156C2×C61—21no—
157C2×C61—82no—
158C2×C61#146511yescharacteristic
159C2×C61C2×#35311yescharacteristic
160C2×C61#213211yescharacteristic
161D61—82no—
162C2×#127—611no—
163C2×C4×D4—611no—
164C2×C4×D4—611no—
165C2×C4×D4—1222no—
166#407—1222no—
167#390—611no—
168#390—1222no—
169#390#692311yescharacteristic
170#384—611no—
171C43—611no—
172#324—614no—
173#323—1222no—
174C61#1152911yescharacteristic, complemented, Sylow
175C22×D4—611no—
176C22×D4—1222no—
177C22×D4C2×#692311yescharacteristic
178C23×C4—612no—
179C23×C4—1221no—
180C2×M16—2442no—
181#127—1222no—
182#127—1222no—
183C4×D4—2448no—
184C4×D4—2441no—
185C4×D4—2441no—
186C4×D4—2441no—
187C4×D4—2441no—
188C2×C4⋊C4—611no—
189C2×C4⋊C4—1222no—
190C2×C4⋊C4C2×#692311yescharacteristic
191C2×C22⋊C4—22no—
192C2×C22⋊C4—612no—
193C2×C22⋊C4—1221no—
194C2×C22⋊C4—1222no—
195C2×C42—611no—
196C2×C42—611no—
197C2×C42—1221no—
198C2×C42—1221no—
199C2×C42C2×#692311yescharacteristic
200C22⋊C8—1224no—
201C22⋊C8—2442no—
202C24—1221no—
203C24C22⋊#692312yes—
204C2×D4—21no—
205C2×D4—21no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4—612no—
209C2×D4—1228no—
210C2×D4—1221no—
211C2×D4—2441no—
212C2×D4—2441no—
213C2×D4—2444no—
214C2×D4—2444no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—611no—
218C22×C4—612no—
219C22×C4—611no—
220C22×C4—1222no—
221C22×C4—1222no—
222C22×C4—1221no—
223C22×C4—2441no—
224C22×C4—2441no—
225C22×C4—2444no—
226C22×C4—2444no—
227C22×C4C22×#692311yescharacteristic
228M16—4884no—
229C2×C8—2444no—
230C4⋊C4—41no—
231C4⋊C4—2441no—
232C4⋊C4—2444no—
233C22⋊C4—44no—
234C22⋊C4—2444no—
235C22⋊C4—2442no—
236C22⋊C4—2442no—
237C42—41no—
238C42—612no—
239C42—1221no—
240C42—1221no—
241C42—1224no—
242C42—1221no—
243C42—2442no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—42no—
248C23—42no—
249C23—1222no—
250C23—2442no—
251C23—2442no—
252C23—2441no—
253C23—2441no—
254C23C2×C22⋊#692311yescharacteristic
255D4—42no—
256D4—42no—
257D4—2442no—
258D4—2442no—
259D4—24416no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—611no—
268C2×C4—611no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1221no—
274C2×C4—1222no—
275C2×C4—4882no—
276C2×C4—4882no—
277C2×C4—4882no—
278C2×C4—2444no—
279C2×C4—2441no—
280C2×C4—2442no—
281C2×C4D61⋊M1611yescharacteristic
282C2×C4D61⋊M1611yescharacteristic
283C8—4884no—
284C22—21no—
285C22—21no—
286C22—44no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—82no—
291C22—4882no—
292C22—4881no—
293C22—4881no—
294C22—2444no—
295C22—2442no—
296C22#1684073411yescharacteristic
297C22D61⋊#9911yescharacteristic
298C22#1684074911yescharacteristic
299C4—21no—
300C4—21no—
301C4—42no—
302C4—81no—
303C4—612no—
304C4—1224no—
305C4—1221no—
306C4—2442no—
307C4—2441no—
308C2—21no—
309C2—21no—
310C2—82no—
311C2—4882no—
312C2#2146107711yescharacteristic
313C2D61⋊#35311yescharacteristic
314C2#2146211311yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC22×C61C2×#99
prime radicalC2×#14519773C4
cosocleC2×C4⋊Dic61C23
hypercenter#390#6923
hypocenterC61#11529
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #21461075C2semidirect
2. #21460762C2semidirect
3. #21460748C2semidirect
66. C2×D244M16semidirect
85. C4×Dic61M16semidirect
174. C61#11529semidirect

Maximal subgroups

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

subgroupindex
#214610752
#214607622
#214607482
#214483832
#1152961