Finite Group Databasebeta

← #30601140

Subgroups — #30601140

Order 15616.

448 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462715C211yesmaximal, characteristic
2#21461348C212yesmaximal
3#21461082C211yesmaximal, characteristic
4#21460670C212yesmaximal
5#21451029C211yesmaximal, characteristic
6#16840813—24no—
7#16840782—21no—
8#16840782C2212yes—
9#16840782C2212yes—
10#16840778—21no—
11#16840621—24no—
12#16840607—21no—
13#16840607—21no—
14C2×#14519776C2211yescharacteristic
15C2×Q8×Dic61C2211yescharacteristic
16#16839683—21no—
17#16839683—21no—
18#16839669C411yescharacteristic
19#16839659—21no—
20#16839659—21no—
21#16839632C411yescharacteristic
22#16839631C411yescharacteristic
23C4×#11758196C2211yescharacteristic
24C61×#391C411yescharacteristic
25#14519844—22no—
26#14519844—22no—
27#14519844D414yes—
28C4⋊#92420—22no—
29C22⋊#92420—22no—
30C22⋊#92420—22no—
31#14519832—22no—
32#14519832—22no—
33#14519832—22no—
34C4×#92420—22no—
35C22×Dic122—21no—
36#14519776—22no—
37#14519776—22no—
38Q8×Dic61—22no—
39Q8×Dic61—22no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×C4⋊Dic61D411yescharacteristic
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×Q8×C61C2×C411yescharacteristic
58C2×C4⋊C4×C61C2×C411yescharacteristic
59C2×C42×C61C2×C411yescharacteristic
60#95×C61—21no—
61#95×C61—21no—
62C2×Q8×C61—22no—
63C2×Q8×C61—22no—
64C2×Q8×C61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22×C411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61C22⋊C411yescharacteristic
73C22×Dic61C22⋊C411yescharacteristic
74C22×Dic61C2×D411yescharacteristic
75C22×Dic61C2×D411yescharacteristic
76C2×Dic122—42no—
77C2×Dic122—81no—
78C2×Dic122—81no—
79C2×#92420—24no—
80C2×#92420—42no—
81C4⋊C4×C61—22no—
82C42×C61—41no—
83C4⋊Dic61—22no—
84C4⋊Dic61—22no—
85C4⋊Dic61—22no—
86C4⋊Dic61—22no—
87C4⋊Dic61—81no—
88C4⋊Dic61—81no—
89#11758196—24no—
90#11758196—41no—
91#11758196—41no—
92#11758196—81no—
93#11758196—81no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—41no—
99C4×Dic61C2×D412yes—
100C4×Dic61#4112yes—
101C23×C61C2×C22⋊C411yescharacteristic
102Q8×C61—44no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—22no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61#10112yes—
117C2×C4×C61C4×D412yes—
118C2×Dic61—22no—
119C2×Dic61—22no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61#12011yescharacteristic
131C2×Dic61#12112yes—
132C2×Dic61#12311yescharacteristic
133Dic122—84no—
134#92420—44no—
135#92420—82no—
136#9454—611nomaximal, Sylow
137C22×C61—21no—
138C22×C61—21no—
139C22×C61#38611yescharacteristic
140C22×C61C2×#10111yescharacteristic
141C22×C61#41311yescharacteristic
142C4×C61—22no—
143C4×C61—22no—
144C4×C61—42no—
145C4×C61—41no—
146C4×C61—81no—
147Dic61—21no—
148Dic61—22no—
149Dic61—42no—
150Dic61—41no—
151Dic61—41no—
152Dic61—81no—
153Dic61#45612yes—
154#2983—611no—
155#2567—611no—
156#1556—612no—
157#1467—611no—
158#1285—612no—
159C2×C61—21no—
160C2×C61—21no—
161C2×C61#188611yescharacteristic
162C2×C61#190111yescharacteristic
163C2×C61#191011yescharacteristic
164C2×C4⋊Q8—611no—
165C2×C4×Q8—611no—
166#446—1224no—
167#432—612no—
168#432—612no—
169#432—1221no—
170#431—1221no—
171#395—1221no—
172#395—1221no—
173#391—611no—
174#391#692311yescharacteristic
175#389—1221no—
176#389—1221no—
177#384—611no—
178#384—611no—
179C4×C4⋊C4—611no—
180#332—1224no—
181#324—1221no—
182#324—1221no—
183C61#945411yescharacteristic, complemented, Sylow
184C22×Q8—1221no—
185C22×Q8C2×#692311yescharacteristic
186C4⋊Q8—1222no—
187C4⋊Q8—1222no—
188C4×Q8—1222no—
189C4×Q8—1222no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—611no—
194C2×C4⋊C4—1221no—
195C2×C4⋊C4—1221no—
196C2×C4⋊C4—1221no—
197C2×C4⋊C4—1221no—
198C2×C4⋊C4—1221no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4C2×#692311yescharacteristic
201C2×C42—611no—
202C2×C42—611no—
203C2×C42—611no—
204C2×C42—611no—
205C2×C42C2×#692311yescharacteristic
206C4⋊C8—614no—
207C4⋊C8—1222no—
208C4⋊C8—1222no—
209C4⋊C8—1222no—
210C22⋊C8—1222no—
211C22⋊C8—1222no—
212#97—1222no—
213#97—1222no—
214#97—1222no—
215C4×C8—1222no—
216#95—21no—
217#95—21no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221C2×Q8—22no—
222C2×Q8—22no—
223C2×Q8—41no—
224C2×Q8—4881no—
225C2×Q8—4881no—
226C2×Q8—2442no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4C22⋊#692311yescharacteristic
236C22×C4C22⋊#692311yescharacteristic
237C22×C4C22×#692311yescharacteristic
238C2×C8—1224no—
239C2×C8—2442no—
240C4⋊C4—22no—
241C4⋊C4—1222no—
242C4⋊C4—1222no—
243C4⋊C4—1224no—
244C4⋊C4—1222no—
245C4⋊C4—1222no—
246C4⋊C4—4881no—
247C4⋊C4—4881no—
248C4⋊C4—4881no—
249C4⋊C4—4881no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C42—41no—
253C42—612no—
254C42—612no—
255C42—1221no—
256C42—1221no—
257C42—1221no—
258C42—1221no—
259C42—2441no—
260C23C2×C22⋊#692311yescharacteristic
261Q8—44no—
262Q8—4884no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—611no—
277C2×C4—612no—
278C2×C4—611no—
279C2×C4—1222no—
280C2×C4—1222no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4—2441no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4#1451983812yes—
292C2×C4D4×#692312yes—
293C8—4882no—
294C8—2444no—
295C22—21no—
296C22—21no—
297C22#1684071011yescharacteristic
298C22C2×#1451983811yescharacteristic
299C22#1684074911yescharacteristic
300C4—22no—
301C4—22no—
302C4—42no—
303C4—41no—
304C4—81no—
305C4—612no—
306C4—1221no—
307C4—1222no—
308C4—4881no—
309C4—2442no—
310C4—2441no—
311C4—2441no—
312C2—21no—
313C2—21no—
314C2#2146182511yescharacteristic
315C2#2146184611yescharacteristic
316C2#2146186311yescharacteristic
subgroupG/H
centerC22#16840710
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#9454
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
183. C61#9454semidirect

Maximal subgroups

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

subgroupindex
#214627152
#214613482
#214610822
#214606702
#214510292
#945461