Finite Group Databasebeta

← #30605483

Subgroups — #30605483

Order 15616.

440 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461683C211yesmaximal, characteristic
2#21461054C211yesmaximal, characteristic
3#21460817C214yesmaximal, complemented
4#21450137C211yesmaximal, characteristic
5#16840765—21no—
6C2×#14519837—21no—
7D61⋊(C22⋊C8)—21no—
8#16840642C2212yes—
9#16840608C2212yes—
10#16840605—21no—
11C2×C4×C22⋊D61C2211yescharacteristic
12C22×C4⋊Dic61C411yescharacteristic
13#16839702C2212yes—
14#16839699C412yes—
15#16839661—21no—
16#16839639—21no—
17#16839637—21no—
18#16839619—21no—
19C61×#380C411yescharacteristic
20C2×#11758217—22no—
21C2×D61⋊C8—41no—
22#14519844—41no—
23C4⋊#92420—41no—
24#14519837—42no—
25#14519834—41no—
26C22⋊#92420—22no—
27C22×C22⋊D61D411yescharacteristic
28C23×Dic61—21no—
29C22×C4×D61D411yescharacteristic
30C4×C22⋊D61—41no—
31C4×C22⋊D61—41no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—22no—
34C2×C4⋊Dic61—41no—
35C2×C4⋊Dic61—41no—
36C2×C4⋊Dic61C2×C412yes—
37C2×#11758196C2311yescharacteristic
38C2×C22⋊Dic61D411yescharacteristic
39C2×#11758198—22no—
40C2×#11758198C2×C411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42#14519684—22no—
43#14519684—22no—
44C23×C4×C61C2×C411yescharacteristic
45C2×C4⋊C4×C61—21no—
46C2×C22⋊C4×C61—21no—
47#95×C61C2×C412yes—
48C24×C61C22⋊C411yescharacteristic
49C23×D61C22⋊C411yescharacteristic
50C22×C4×C61—21no—
51C22×C4×C61—21no—
52C22×C4×C61—22no—
53C22×C4×C61—42no—
54C22×C4×C61C22⋊C411yescharacteristic
55C22×C4×C61C22×C411yescharacteristic
56C2×C22⋊D61—41no—
57C2×C22⋊D61—41no—
58C2×C22⋊D61SD1612yes—
59C2×C22⋊D61Q1612yes—
60C22×Dic61—22no—
61C22×Dic61—42no—
62C22×Dic61—82no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—42no—
69#11758217—42no—
70#11758217—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73D61⋊C8—82no—
74C4⋊C4×C61—42no—
75C22⋊C4×C61—42no—
76C22⋊Dic61—41no—
77#11758198—41no—
78#11758198—82no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C4⋊Dic61—42no—
82C4⋊Dic61—82no—
83#11758196—41no—
84C4×Dic61—21no—
85C4×Dic61—21no—
86C23×C61—21no—
87C23×C61—21no—
88C23×C61—41no—
89C23×C61—41no—
90C23×C61#10312yes—
91C23×C61C2×C22⋊C411yescharacteristic
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—41no—
95C22×D61—41no—
96C22×D61#10312yes—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61—41no—
102C2×C4×C61—42no—
103C2×C4×C61—42no—
104C2×C4×C61—42no—
105C2×C4×C61#9911yescharacteristic
106C2×C4×C61#9911yescharacteristic
107C22⋊D61—42no—
108C22⋊D61—42no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—42no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—84no—
119C2×Dic61C2×SD1611yescharacteristic
120C2×Dic61C2×Q1611yescharacteristic
121C4×D61—42no—
122C4×D61—81no—
123#92420—82no—
124#92420—82no—
125#11903—611nomaximal, Sylow
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—22no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61—41no—
132C22×C61—41no—
133C22×C61C2×#9911yescharacteristic
134C22×C61C2×#10311yescharacteristic
135C22×C61#42111yescharacteristic
136C2×D61—22no—
137C2×D61—41no—
138C2×D61—41no—
139C2×D61—42no—
140C2×D61—81no—
141C4×C61—21no—
142C4×C61—41no—
143C4×C61—82no—
144C4×C61#35212yes—
145Dic61—21no—
146Dic61—21no—
147Dic61—41no—
148Dic61—41no—
149Dic61—82no—
150#2487—611no—
151#1800—611no—
152#1459—611no—
153#1353—614no—
154C2×C61—21no—
155C2×C61—21no—
156C2×C61—42no—
157C2×C61#152011yescharacteristic
158C2×C61C2×#35211yescharacteristic
159C2×C61#213411yescharacteristic
160D61—42no—
161C2×C4×D4—611no—
162C22×C4⋊C4—611no—
163#423—1221no—
164C2×#100—1221no—
165C2×C22⋊C8—1221no—
166#400—612no—
167#399—612no—
168#389—1221no—
169#386—1221no—
170#385—1221no—
171#380—1221no—
172#380#692311yescharacteristic
173#343—612no—
174#324—612no—
175#323—1221no—
176C61#1190311yescharacteristic, complemented, Sylow
177C22×D4—611no—
178C23×C4—611no—
179C23×C4—1221no—
180C23×C4C2×#692311yescharacteristic
181C2×M16—1222no—
182C22×C8—2441no—
183C4×D4—2441no—
184C4×D4—2441no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—611no—
187C2×C4⋊C4—612no—
188C2×C4⋊C4—1222no—
189C2×C4⋊C4—1221no—
190C2×C4⋊C4—2441no—
191C2×C4⋊C4—2441no—
192C2×C22⋊C4—21no—
193C2×C22⋊C4—611no—
194C2×C22⋊C4—611no—
195C2×C22⋊C4—1222no—
196C2×C42—611no—
197C4⋊C8—2441no—
198C4⋊C8—2441no—
199#100—2442no—
200C22⋊C8—1222no—
201C22⋊C8—2441no—
202#95—1222no—
203#95—1222no—
204#95C2×#692312yes—
205C24—611no—
206C24C22⋊#692311yescharacteristic
207C2×D4—612no—
208C2×D4—612no—
209C2×D4—2441no—
210C2×D4—2441no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—42no—
215C22×C4—611no—
216C22×C4—611no—
217C22×C4—611no—
218C22×C4—1221no—
219C22×C4—1221no—
220C22×C4—1222no—
221C22×C4—4882no—
222C22×C4—2442no—
223C22×C4—2442no—
224C22×C4C22⋊#692311yescharacteristic
225C22×C4C22×#692311yescharacteristic
226M16—2442no—
227M16—2442no—
228C2×C8—4882no—
229C2×C8—2442no—
230C2×C8—2442no—
231C4⋊C4—42no—
232C4⋊C4—4882no—
233C4⋊C4—2441no—
234C4⋊C4—2442no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C22⋊C4—42no—
238C22⋊C4—4882no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C42—1221no—
242C42—1221no—
243C23—21no—
244C23—21no—
245C23—41no—
246C23—41no—
247C23—612no—
248C23—1221no—
249C23—1221no—
250C23—2441no—
251C23—2441no—
252C23#1451984012yes—
253C23C2×C22⋊#692311yescharacteristic
254D4—2442no—
255D4—2442no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—4881no—
271C2×C4—4884no—
272C2×C4—2442no—
273C2×C4—2442no—
274C2×C4—2442no—
275C2×C4—2442no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4#1451983611yescharacteristic
279C2×C4#1451983611yescharacteristic
280C8—4882no—
281C8—4882no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—1222no—
290C22—4881no—
291C22—2442no—
292C22—2441no—
293C22—2441no—
294C22C2×#1451983611yescharacteristic
295C22C2×#1451984011yescharacteristic
296C22#1684076011yescharacteristic
297C4—21no—
298C4—41no—
299C4—82no—
300C4—1221no—
301C4—1221no—
302C4—4882no—
303C4—2441no—
304C4—2441no—
305C4#1684066512yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—2442no—
310C2#2146125811yescharacteristic
311C2C2×#1684066511yescharacteristic
312C2#2146212011yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC22×C61C2×#99
prime radicalC22×C22⋊D61D4
cosocleC2×#11758196C23
hypercenter#380#6923
hypocenterC61#11903
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460817C2semidirect
176. C61#11903semidirect

Maximal subgroups

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

subgroupindex
#214616832
#214610542
#214608172
#214501372
#1190361