Finite Group Databasebeta

← #30599306

Subgroups — #30599306

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#21461052C211yesmaximal, characteristic
2#21461052C211yesmaximal, characteristic
3#21460647C212yesmaximal, complemented
4#21460643C212yesmaximal, complemented
5#21448312C211yesmaximal, characteristic
6#16840778C2212yes—
7#16840778C2212yes—
8#16840608—21no—
9#16840608—21no—
10#16840606—21no—
11#16840606—21no—
12C2×#14519734C2211yescharacteristic
13#16839654—21no—
14#16839652—21no—
15#16839649—21no—
16#16839643—21no—
17C4×C4⋊Dic61C411yescharacteristic
18C4×#11758198C411yescharacteristic
19C4×#11758198C411yescharacteristic
20#16839608C2211yescharacteristic
21C42×Dic61C2211yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic
23C4⋊#92420—22no—
24C4⋊#92420—22no—
25C22⋊#92420—22no—
26C22⋊#92420—22no—
27C4×#92420—22no—
28C4×#92420—22no—
29C22×C4×D61C2×C411yescharacteristic
30#14519734—22no—
31#14519734—22no—
32C2×C4⋊Dic61—21no—
33C2×#11758196D411yescharacteristic
34C2×#11758196D411yescharacteristic
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198D411yescharacteristic
38C2×#11758198D411yescharacteristic
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
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—
49C2×C4⋊C4×C61—21no—
50C2×C42×C61C2×C411yescharacteristic
51C2×C42×C61C2×C411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53#95×C61—21no—
54C23×D61C22⋊C411yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C2×D411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—22no—
68C2×C4×D61—22no—
69C2×#92420—42no—
70C2×#92420—42no—
71C4⋊C4×C61—42no—
72C42×C61—21no—
73C42×C61—21no—
74C42×C61—22no—
75C42×C61—22no—
76#11758198—22no—
77#11758198—22no—
78#11758198—42no—
79#11758198—42no—
80C4⋊Dic61—42no—
81#11758196—22no—
82#11758196—22no—
83C4×Dic61—22no—
84C4×Dic61—22no—
85C4×Dic61—42no—
86C4×Dic61—42no—
87C4×Dic61#4112yes—
88C4×Dic61#4112yes—
89C23×C61C2×C22⋊C411yescharacteristic
90C22×D61—21no—
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—41no—
94C22×D61—41no—
95C2×C4×C61—22no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61#11711yescharacteristic
106C2×C4×C61#11711yescharacteristic
107C2×C4×C61#13112yes—
108C2×C4×C61#13112yes—
109C2×Dic61—22no—
110C2×Dic61—21no—
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#12312yes—
121C2×Dic61#12312yes—
122C4×D61—42no—
123C4×D61—42no—
124#92420—82no—
125#92420—82no—
126#8733—611nomaximal, Sylow
127C22×C61—21no—
128C22×C61—21no—
129C22×C61#38111yescharacteristic
130C22×C61#40811yescharacteristic
131C22×C61#40811yescharacteristic
132C2×D61—41no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—81no—
136C2×D61—81no—
137C4×C61—42no—
138C4×C61—41no—
139C4×C61—41no—
140C4×C61—81no—
141C4×C61#43312yes—
142C4×C61#43312yes—
143Dic61—22no—
144Dic61—22no—
145Dic61—42no—
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#181811yescharacteristic
156C2×C61#182711yescharacteristic
157C2×C61#182711yescharacteristic
158D61—81no—
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#692311yescharacteristic
168C4×C22⋊C4—611no—
169C4×C22⋊C4—611no—
170#376—611no—
171C43—611no—
172#324—1221no—
173#324—1221no—
174#323—1221no—
175#323—1221no—
176C61#873311yescharacteristic, complemented, Sylow
177C23×C4—611no—
178#117—1222no—
179#117—1222no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—611no—
183C2×C4⋊C4—1221no—
184C2×C22⋊C4—611no—
185C2×C22⋊C4—611no—
186C2×C22⋊C4—1221no—
187C2×C22⋊C4—1221no—
188C2×C42—611no—
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—1221no—
192C2×C42—1221no—
193C2×C42C2×#692311yescharacteristic
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—
208C24—611no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—1221no—
215C22×C4—1221no—
216C22×C4—1221no—
217C22×C4—1222no—
218C22×C4—1222no—
219C22×C4—1221no—
220C22×C4C22⋊#692311yescharacteristic
221C22×C4C22⋊#692311yescharacteristic
222C22×C4C22×#692311yescharacteristic
223C2×C8—2442no—
224C2×C8—2442no—
225C4⋊C4—42no—
226C4⋊C4—1222no—
227C4⋊C4—1222no—
228C4⋊C4—2442no—
229C22⋊C4—1222no—
230C22⋊C4—1222no—
231C22⋊C4—2442no—
232C22⋊C4—2442no—
233C42—21no—
234C42—21no—
235C42—22no—
236C42—22no—
237C42—612no—
238C42—612no—
239C42—1222no—
240C42—1222no—
241C42—2442no—
242C42—2442no—
243C23—1221no—
244C23—1221no—
245C23—1221no—
246C23—2441no—
247C23—2441no—
248C23C2×C22⋊#692311yescharacteristic
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—612no—
260C2×C4—612no—
261C2×C4—1222no—
262C2×C4—1221no—
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—2442no—
273C2×C4—2442no—
274C2×C4#1451985611yescharacteristic
275C2×C4#1451985611yescharacteristic
276C2×C4#1451986412yes—
277C2×C4#1451986512yes—
278C8—4882no—
279C8—4882no—
280C22—21no—
281C22—21no—
282C22—4881no—
283C22—4881no—
284C22—2441no—
285C22—2441no—
286C22—2441no—
287C22#1684070511yescharacteristic
288C22#1684073611yescharacteristic
289C22#1684073711yescharacteristic
290C4—42no—
291C4—41no—
292C4—41no—
293C4—81no—
294C4—1222no—
295C4—1222no—
296C4—4881no—
297C4—2442no—
298C4—2441no—
299C4#1684078712yes—
300C4#1684078712yes—
301C2—21no—
302C2—21no—
303C2—4881no—
304C2#2146171311yescharacteristic
305C2#2146172811yescharacteristic
306C2#2146172911yescharacteristic
subgroupG/H
centerC2×C4#14519856
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC22×C61#381
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8733
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460647C2semidirect
4. #21460643C2semidirect
176. C61#8733semidirect

Maximal subgroups

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

subgroupindex
#214610522
#214606472
#214606432
#214483122
#873361