Finite Group Databasebeta

← #30599303

Subgroups — #30599303

Order 15616.

404 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 88 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#21461050C211yesmaximal, characteristic
2#21461050C211yesmaximal, characteristic
3#21460647C212yesmaximal, complemented
4#21460643C212yesmaximal, complemented
5#21448315C211yesmaximal, characteristic
6#16840778C2212yes—
7#16840778C2212yes—
8#16840607—21no—
9#16840607—21no—
10#16840605—21no—
11#16840605—21no—
12C2×#14519736C2211yescharacteristic
13#16839656—21no—
14#16839650—21no—
15#16839647—21no—
16#16839645—21no—
17C4×#11758196C411yescharacteristic
18C4×#11758196C411yescharacteristic
19C4×C22⋊Dic61C411yescharacteristic
20#16839608C2211yescharacteristic
21C42×Dic61C2211yescharacteristic
22C4×C22⋊C4×C61C411yescharacteristic
23C4⋊#92420—22no—
24C4⋊#92420—22no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C4×#92420—22no—
28C4×#92420—22no—
29#14519736—22no—
30#14519736—22no—
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61D411yescharacteristic
37C2×C22⋊Dic61D411yescharacteristic
38C2×C4×Dic61—21no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61C2×C411yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61C2311yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C23×C4×C61C2×C411yescharacteristic
50C2×C22⋊C4×C61—21no—
51C2×C42×C61C2×C411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53#95×C61—21no—
54C24×C61C22⋊C411yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—22no—
59C22×C4×C61—22no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×#92420—42no—
70C2×#92420—42no—
71C22⋊C4×C61—42no—
72C42×C61—22no—
73C42×C61—22no—
74C22⋊Dic61—22no—
75C22⋊Dic61—22no—
76C22⋊Dic61—42no—
77C4⋊Dic61—22no—
78C4⋊Dic61—22no—
79#11758196—42no—
80#11758196—42no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C4×Dic61—42no—
86C4×Dic61—42no—
87C4×Dic61#4112yes—
88C4×Dic61#4112yes—
89C23×C61—21no—
90C23×C61—21no—
91C23×C61—21no—
92C23×C61—41no—
93C23×C61—41no—
94C23×C61C2×C22⋊C411yescharacteristic
95C2×C4×C61—22no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61#11711yescharacteristic
107C2×C4×C61#11711yescharacteristic
108C2×C4×C61#13112yes—
109C2×C4×C61#13112yes—
110C2×Dic61—22no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61#12312yes—
123C2×Dic61#12312yes—
124#92420—82no—
125#92420—82no—
126#8732—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—41no—
130C22×C61—41no—
131C22×C61—41no—
132C22×C61—81no—
133C22×C61—81no—
134C22×C61#38111yescharacteristic
135C22×C61#40811yescharacteristic
136C22×C61#40811yescharacteristic
137C4×C61—42no—
138C4×C61—41no—
139C4×C61—81no—
140C4×C61#43312yes—
141C4×C61#43312yes—
142Dic61—22no—
143Dic61—22no—
144Dic61—42no—
145Dic61—41no—
146Dic61—41no—
147Dic61—81no—
148#2298—611no—
149#1458—611no—
150#1458—611no—
151#1276—612no—
152#1274—612no—
153C2×C61—21no—
154C2×C61—21no—
155C2×C61—81no—
156C2×C61#181811yescharacteristic
157C2×C61#182711yescharacteristic
158C2×C61#182711yescharacteristic
159C2×#117—611no—
160#431—612no—
161#431—612no—
162#388—1221no—
163#388—1221no—
164#387—1221no—
165#387—1221no—
166C4×C4⋊C4—611no—
167C4×C4⋊C4—611no—
168C4×C22⋊C4—611no—
169C4×C22⋊C4#692311yescharacteristic
170#376—611no—
171C43—611no—
172#324—1221no—
173#324—1221no—
174#323—1221no—
175#323—1221no—
176C61#873211yescharacteristic, complemented, Sylow
177C23×C4C2×#692311yescharacteristic
178#117—1222no—
179#117—1222no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4—1221no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—611no—
186C2×C22⋊C4—611no—
187C2×C22⋊C4—1221no—
188C2×C42—611no—
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42—1221no—
193C2×C42—1221no—
194C2×C42C2×#692311yescharacteristic
195C2×C42C2×#692311yescharacteristic
196C4⋊C8—1222no—
197C4⋊C8—1222no—
198C22⋊C8—1222no—
199C22⋊C8—1222no—
200C4×C8—1222no—
201C4×C8—1222no—
202#95—21no—
203#95—1221no—
204#95—1221no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208C24C22⋊#692311yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—21no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—1221no—
220C22×C4—1221no—
221C22×C4C22⋊#692311yescharacteristic
222C22×C4C22×#692311yescharacteristic
223C2×C8—2442no—
224C2×C8—2442no—
225C4⋊C4—1222no—
226C4⋊C4—1222no—
227C4⋊C4—2442no—
228C4⋊C4—2442no—
229C22⋊C4—42no—
230C22⋊C4—1222no—
231C22⋊C4—1222no—
232C22⋊C4—2442no—
233C42—22no—
234C42—22no—
235C42—612no—
236C42—612no—
237C42—1221no—
238C42—1221no—
239C42—1222no—
240C42—1222no—
241C42—2442no—
242C42—2442no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23C2×C22⋊#692311yescharacteristic
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—612no—
261C2×C4—612no—
262C2×C4—1222no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4—2441no—
269C2×C4—2441no—
270C2×C4—2441no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4#1451985611yescharacteristic
275C2×C4#1451985611yescharacteristic
276C2×C4#1451986412yes—
277C2×C4#1451986412yes—
278C8—4882no—
279C8—4882no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22—81no—
286C22—81no—
287C22#1684070511yescharacteristic
288C22#1684073511yescharacteristic
289C22#1684073511yescharacteristic
290C4—42no—
291C4—41no—
292C4—81no—
293C4—1222no—
294C4—1222no—
295C4—4881no—
296C4—2442no—
297C4—2441no—
298C4—2441no—
299C4#1684078612yes—
300C4#1684078612yes—
301C2—21no—
302C2—21no—
303C2—81no—
304C2#2146171211yescharacteristic
305C2#2146172811yescharacteristic
306C2#2146172911yescharacteristic
subgroupG/H
centerC2×C4#14519856
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8732
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460647C2semidirect
4. #21460643C2semidirect
176. C61#8732semidirect

Maximal subgroups

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

subgroupindex
#214610502
#214606472
#214606432
#214483152
#873261