Finite Group Databasebeta

← #30605302

Subgroups — #30605302

Order 15616.

396 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461719C211yesmaximal, characteristic
2D61⋊#324C211yesmaximal, characteristic
3#21460817C212yesmaximal, complemented
4#21460803C212yesmaximal, complemented
5#21450101C211yesmaximal, characteristic
6#16840734—21no—
7D61⋊(C22⋊C8)—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C2×#14519735C411yescharacteristic
13C2×C4⋊C4×D61C2211yescharacteristic
14#16839702C2211yescharacteristic
15#16839701C411yescharacteristic
16#16839693C2211yescharacteristic
17#16839648—21no—
18#16839644—21no—
19#16839633—21no—
20#16839624—21no—
21#16839624C411yescharacteristic
22C61×#398C411yescharacteristic
23C2×#11758217—22no—
24C2×D61⋊C8—41no—
25#14519834—41no—
26#14519834—41no—
27#14519834—41no—
28C22⋊#92420—22no—
29C22×C4×D61C2×C411yescharacteristic
30C22×C4×D61D411yescharacteristic
31C22×C4×D61D411yescharacteristic
32#14519735—41no—
33#14519735—41no—
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196D411yescharacteristic
38C2×#11758196C2311yescharacteristic
39C4⋊C4×D61—41no—
40C4⋊C4×D61—41no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×C4×Dic61—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684C2×C411yescharacteristic
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54#95×C61—21no—
55#95×C61C2×C411yescharacteristic
56C23×D61C22⋊C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C2×C4×D61—21no—
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×C4×D61—22no—
73C2×C4×D61—21no—
74C2×C4×D61—41no—
75C2×C4×D61—42no—
76C2×C4×D61—42no—
77#11758217—42no—
78#11758217—42no—
79C2×#92420—42no—
80C2×#92420—42no—
81D61⋊C8—82no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—41no—
85#11758198—42no—
86#11758198—41no—
87#11758198—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90#11758196—41no—
91#11758196—41no—
92#11758196—42no—
93C4×Dic61—42no—
94C23×C61C2×C22⋊C411yescharacteristic
95C22×D61—21no—
96C22×D61—21no—
97C22×D61—22no—
98C22×D61—41no—
99C22×D61#9911yescharacteristic
100C22×D61#9911yescharacteristic
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
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×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—42no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61#13512yes—
126C4×D61—42no—
127C4×D61—42no—
128C4×D61—42no—
129C4×D61—42no—
130C4×D61—42no—
131C4×D61—81no—
132#92420—82no—
133#92420—82no—
134#11850—611nomaximal, Sylow
135C22×C61—21no—
136C22×C61—21no—
137C22×C61C2×#9911yescharacteristic
138C22×C61#41611yescharacteristic
139C22×C61#42111yescharacteristic
140C2×D61—21no—
141C2×D61—21no—
142C2×D61—21no—
143C2×D61—21no—
144C2×D61—21no—
145C2×D61—42no—
146C2×D61—42no—
147C2×D61#35212yes—
148C4×C61—41no—
149C4×C61—41no—
150C4×C61—41no—
151C4×C61—81no—
152C4×C61—81no—
153Dic61—22no—
154Dic61—41no—
155Dic61—41no—
156Dic61—81no—
157Dic61—81no—
158#2484—611no—
159#1821—611no—
160C2×#324—611no—
161#1353—612no—
162#1346—612no—
163C2×C61—21no—
164C2×C61—21no—
165C2×C61#151611yescharacteristic
166C2×C61C2×#35211yescharacteristic
167C2×C61#213311yescharacteristic
168D61—22no—
169D61—41no—
170C2×#117—611no—
171C22×C4⋊C4—611no—
172#407—1221no—
173C2×C22⋊C8—1221no—
174#400—611no—
175#400—611no—
176#398—611no—
177#398#692311yescharacteristic
178#387—1221no—
179#387—1221no—
180#385—1221no—
181#381—611no—
182#381—1221no—
183#343—612no—
184#343—1221no—
185#324—612no—
186#324—1221no—
187C61#1185011yescharacteristic, complemented, Sylow
188C23×C4—611no—
189C23×C4—611no—
190C23×C4—611no—
191C2×M16—1222no—
192C22×C8—2441no—
193#117—2441no—
194#117—2441no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4—611no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—1221no—
201C2×C4⋊C4—2441no—
202C2×C4⋊C4—2441no—
203C2×C4⋊C4C2×#692311yescharacteristic
204C2×C4⋊C4C2×#692311yescharacteristic
205C2×C22⋊C4—1221no—
206C2×C22⋊C4—1221no—
207C2×C42—1221no—
208C22⋊C8—1222no—
209C22⋊C8—2441no—
210C22⋊C8—2441no—
211C22⋊C8—2441no—
212#95—21no—
213#95—611no—
214#95—1221no—
215#95—1221no—
216#95—1221no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95C2×#692311yescharacteristic
221C24—611no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—1222no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—1221no—
236C22×C4—2441no—
237C22×C4—2442no—
238C22×C4—2442no—
239C22×C4C22⋊#692311yescharacteristic
240C22×C4C22⋊#692311yescharacteristic
241C22×C4C22×#692311yescharacteristic
242M16—2442no—
243M16—2442no—
244C2×C8—4882no—
245C2×C8—2442no—
246C2×C8—2442no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—2441no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C4⋊C4—2441no—
254C4⋊C4—2442no—
255C22⋊C4—2441no—
256C22⋊C4—2441no—
257C22⋊C4—2442no—
258C42—2442no—
259C23—611no—
260C23—611no—
261C23—1222no—
262C23—1221no—
263C23—1221no—
264C23—2441no—
265C23C2×C22⋊#692311yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
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—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—612no—
280C2×C4—1221no—
281C2×C4—1221no—
282C2×C4—1221no—
283C2×C4—1221no—
284C2×C4—4881no—
285C2×C4—2442no—
286C2×C4—2442no—
287C2×C4—2442no—
288C2×C4—2442no—
289C2×C4—2442no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2442no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C8—4882no—
298C8—4882no—
299C22—21no—
300C22—21no—
301C22—612no—
302C22—1221no—
303C22—1221no—
304C22—1221no—
305C22—1221no—
306C22—1221no—
307C22—2442no—
308C22—2442no—
309C22D61⋊#9911yescharacteristic
310C22#1684075211yescharacteristic
311C22#1684076011yescharacteristic
312C4—41no—
313C4—41no—
314C4—41no—
315C4—81no—
316C4—81no—
317C4—1222no—
318C4—4881no—
319C4—4881no—
320C4—2441no—
321C4—2441no—
322C2—21no—
323C2—21no—
324C2—1222no—
325C2—2441no—
326C2#2146124411yescharacteristic
327C2D61⋊#35211yescharacteristic
328C2#2146211711yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#398C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×#11758196C23
hypercenter#398#6923
hypocenterC61#11850
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
3. #21460817C2semidirect
4. #21460803C2semidirect
187. C61#11850semidirect

Maximal subgroups

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

subgroupindex
#214617192
D61⋊#3242
#214608172
#214608032
#214501012
#1185061