Finite Group Databasebeta

← #30605415

Subgroups — #30605415

Order 15616.

408 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461686C211yesmaximal, characteristic
2#21461063C211yesmaximal, characteristic
3#21460804C212yesmaximal
4#21460803C212yesmaximal
5#21450803C211yesmaximal, characteristic
6#16840778—21no—
7#16840765—21no—
8C2×#14519838—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519776—21no—
13C2×#14519776C411yescharacteristic
14C2×#14519742C2211yescharacteristic
15#16839694C2211yescharacteristic
16#16839693C2211yescharacteristic
17#16839692C411yescharacteristic
18#16839666—21no—
19#16839659—21no—
20#16839657—21no—
21#16839613C411yescharacteristic
22C61×#398C411yescharacteristic
23C2×#11758217—22no—
24#14519844—41no—
25C4⋊#92420—41no—
26C4⋊#92420—41no—
27#14519838—42no—
28C22⋊#92420—22no—
29C4×#92420—41no—
30C22×Dic122—21no—
31C22×Dic122D411yescharacteristic
32#14519776—41no—
33#14519776—41no—
34#14519776—42no—
35#14519776—42no—
36#14519742—41no—
37#14519742—41no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196D411yescharacteristic
45C2×#11758196C2311yescharacteristic
46C2×C4×Dic61—21no—
47C2×C4×Dic61C2×C411yescharacteristic
48C2×C4×Dic61D411yescharacteristic
49C2×C4×Dic61D411yescharacteristic
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684C2×C411yescharacteristic
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61C2×C411yescharacteristic
56C2×C4⋊C4×C61C2×C411yescharacteristic
57#95×C61—21no—
58#95×C61C2×C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×Dic122—41no—
71C2×Dic122—41no—
72C2×Dic122—42no—
73C2×Dic122—42no—
74C2×Dic122—42no—
75C2×Dic122D812yes—
76C2×Dic122SD1612yes—
77#11758217—42no—
78#11758217—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—42no—
84C4⋊Dic61—41no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87#11758196—24no—
88#11758196—41no—
89#11758196—41no—
90#11758196—42no—
91#11758196—41no—
92#11758196—41no—
93#11758196—41no—
94#11758196—41no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C4×Dic61—21no—
100C4×Dic61—21no—
101C4×Dic61—42no—
102C23×C61C2×C22⋊C411yescharacteristic
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—22no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61#10212yes—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—22no—
121C2×Dic61—22no—
122C2×Dic61—21no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61#9911yescharacteristic
130C2×Dic61#9911yescharacteristic
131C2×Dic61#10212yes—
132C2×Dic61C2×D811yescharacteristic
133C2×Dic61C2×SD1611yescharacteristic
134Dic122—42no—
135Dic122—42no—
136Dic122—84no—
137#92420—82no—
138#92420—82no—
139#11883—611nomaximal, Sylow
140C22×C61—21no—
141C22×C61—21no—
142C22×C61C2×#9911yescharacteristic
143C22×C61C2×#10211yescharacteristic
144C22×C61#42111yescharacteristic
145C4×C61—22no—
146C4×C61—42no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—81no—
150Dic61—21no—
151Dic61—21no—
152Dic61—22no—
153Dic61—21no—
154Dic61—42no—
155Dic61—41no—
156Dic61—81no—
157Dic61#35612yes—
158#2546—611no—
159#1801—611no—
160#1461—611no—
161#1346—612no—
162#1346—612no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61#151911yescharacteristic
166C2×C61#212311yescharacteristic
167C2×C61C2×#35611yescharacteristic
168C2×C4⋊Q8—611no—
169C2×C4⋊Q8—1221no—
170C2×C4×Q8—611no—
171#431—1221no—
172#423—1221no—
173C2×#101—1221no—
174#398—611no—
175#398—611no—
176#398—611no—
177#398#692311yescharacteristic
178#391—1221no—
179#389—1221no—
180#389—1221no—
181C4×C4⋊C4—611no—
182#343—612no—
183#324—612no—
184#324—1221no—
185C61#1188311yescharacteristic, complemented, Sylow
186C22×Q8—611no—
187C22×Q8—1221no—
188C2×M16—1222no—
189C4⋊Q8—2441no—
190C4⋊Q8—2441no—
191C4⋊Q8—2442no—
192C4⋊Q8—2442no—
193C4×Q8—2441no—
194C4×Q8—2441no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—1221no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—1221no—
202C2×C4⋊C4—1221no—
203C2×C4⋊C4—1221no—
204C2×C4⋊C4C2×#692311yescharacteristic
205C2×C4⋊C4C2×#692311yescharacteristic
206C2×C42—611no—
207C2×C42—611no—
208C2×C42—611no—
209C2×C42—1221no—
210C4⋊C8—2441no—
211C4⋊C8—2441no—
212C4⋊C8—2441no—
213#101—2442no—
214C22⋊C8—1222no—
215C4×C8—2441no—
216#95—21no—
217#95—611no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95C2×#692311yescharacteristic
222C2×Q8—612no—
223C2×Q8—612no—
224C2×Q8—2441no—
225C2×Q8—2441no—
226C2×Q8—2442no—
227C2×Q8—2442no—
228C2×Q8—2442no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—611no—
232C22×C4—611no—
233C22×C4—611no—
234C22×C4—611no—
235C22×C4—1221no—
236C22×C4—1221no—
237C22×C4C22⋊#692311yescharacteristic
238C22×C4C22⋊#692311yescharacteristic
239C22×C4C22×#692311yescharacteristic
240M16—2442no—
241M16—2442no—
242C2×C8—2442no—
243C2×C8—2442no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—42no—
247C4⋊C4—1224no—
248C4⋊C4—2441no—
249C4⋊C4—2441no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4—2442no—
258C42—1221no—
259C42—1221no—
260C42—1221no—
261C42—1221no—
262C42—1221no—
263C42—1221no—
264C42—2442no—
265C23C2×C22⋊#692311yescharacteristic
266Q8—4884no—
267Q8—2442no—
268Q8—2442no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—611no—
282C2×C4—611no—
283C2×C4—612no—
284C2×C4—611no—
285C2×C4—611no—
286C2×C4—1222no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—1221no—
291C2×C4—1222no—
292C2×C4—1221no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4#1451983912yes—
300C8—4882no—
301C8—4882no—
302C22—21no—
303C22—21no—
304C22D61⋊#9911yescharacteristic
305C22C2×#1451983911yescharacteristic
306C22#1684075911yescharacteristic
307C4—22no—
308C4—42no—
309C4—41no—
310C4—41no—
311C4—81no—
312C4—612no—
313C4—1221no—
314C4—1222no—
315C4—1221no—
316C4—1221no—
317C4—4881no—
318C4—2442no—
319C4—2441no—
320C2—21no—
321C2—21no—
322C2#2146125411yescharacteristic
323C2#2146208211yescharacteristic
324C2D61⋊#35611yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#398C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×#11758196C23
hypercenter#398#6923
hypocenterC61#11883
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #398

Complements

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

NH ≅ G/Ntype
185. C61#11883semidirect

Maximal subgroups

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

subgroupindex
#214616862
#214610632
#214608042
#214608032
#214508032
#1188361