Finite Group Databasebeta

← #30605496

Subgroups — #30605496

Order 15616.

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

normal subgroups only

This group has 372 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#21460818C212yesmaximal
4#21460817C212yesmaximal
5#21451030C211yesmaximal, characteristic
6#16840778—21no—
7#16840765—21no—
8C2×#14519838—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519776C411yescharacteristic
13C2×#14519742C2211yescharacteristic
14#16839702C2211yescharacteristic
15#16839701C411yescharacteristic
16#16839700C2211yescharacteristic
17#16839666—21no—
18#16839666—21no—
19#16839666—21no—
20#16839626—21no—
21#16839613C411yescharacteristic
22C61×#400C411yescharacteristic
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#14519742—41no—
35#14519742—41no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196D411yescharacteristic
40C2×#11758196C2311yescharacteristic
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44C2×C4×Dic61D411yescharacteristic
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54#95×C61—21no—
55#95×C61—21no—
56#95×C61C2×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×Dic61C22⋊C411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×Dic122—41no—
69C2×Dic122—41no—
70C2×Dic122—44no—
71C2×Dic122—41no—
72C2×Dic122—41no—
73C2×Dic122SD1612yes—
74C2×Dic122Q1612yes—
75#11758217—42no—
76#11758217—42no—
77C2×#92420—42no—
78C2×#92420—42no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊Dic61—41no—
82#11758196—41no—
83#11758196—41no—
84#11758196—42no—
85#11758196—42no—
86C4×Dic61—21no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—42no—
93C23×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—42no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61#10312yes—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—22no—
111C2×Dic61—21no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—42no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61#9911yescharacteristic
119C2×Dic61#9911yescharacteristic
120C2×Dic61#10312yes—
121C2×Dic61C2×SD1611yescharacteristic
122C2×Dic61C2×Q1611yescharacteristic
123Dic122—42no—
124Dic122—42no—
125Dic122—82no—
126Dic122—82no—
127#92420—82no—
128#92420—82no—
129#11907—611nomaximal, Sylow
130C22×C61—21no—
131C22×C61—21no—
132C22×C61C2×#9911yescharacteristic
133C22×C61C2×#10311yescharacteristic
134C22×C61#42111yescharacteristic
135C4×C61—22no—
136C4×C61—41no—
137C4×C61—41no—
138C4×C61—81no—
139C4×C61—81no—
140Dic61—21no—
141Dic61—21no—
142Dic61—22no—
143Dic61—21no—
144Dic61—41no—
145Dic61—81no—
146Dic61—81no—
147Dic61#35512yes—
148#2568—611no—
149#1801—611no—
150#1461—611no—
151#1353—612no—
152#1353—612no—
153C2×C61—21no—
154C2×C61—21no—
155C2×C61#152011yescharacteristic
156C2×C61#212311yescharacteristic
157C2×C61C2×#35511yescharacteristic
158C2×C4⋊Q8—611no—
159C2×C4×Q8—611no—
160#431—1221no—
161#423—1221no—
162C2×#101—1221no—
163#400—611no—
164#400—611no—
165#400—611no—
166#400#692311yescharacteristic
167#391—1221no—
168#391—1221no—
169#391—1221no—
170#382—1221no—
171C4×C4⋊C4—611no—
172#343—612no—
173#324—612no—
174#324—1221no—
175C61#1190711yescharacteristic, complemented, Sylow
176C22×Q8—611no—
177C22×Q8—1221no—
178C2×M16—1222no—
179C4⋊Q8—2441no—
180C4⋊Q8—2441no—
181C4×Q8—2441no—
182C4×Q8—2441no—
183C2×C4⋊C4—611no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—611no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4C2×#692311yescharacteristic
189C2×C4⋊C4C2×#692311yescharacteristic
190C2×C42—611no—
191C2×C42—611no—
192C2×C42—611no—
193C2×C42—1221no—
194C4⋊C8—2441no—
195C4⋊C8—2441no—
196C4⋊C8—2441no—
197#101—2442no—
198C22⋊C8—1222no—
199C4×C8—2441no—
200#95—21no—
201#95—21no—
202#95—611no—
203#95—1221no—
204#95—1221no—
205#95—1221no—
206#95—1221no—
207#95—1221no—
208#95—1221no—
209#95C2×#692311yescharacteristic
210C2×Q8—612no—
211C2×Q8—612no—
212C2×Q8—2441no—
213C2×Q8—2441no—
214C2×Q8—2441no—
215C2×Q8—2441no—
216C2×Q8—2444no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—611no—
223C22×C4—1221no—
224C22×C4—1221no—
225C22×C4C22⋊#692311yescharacteristic
226C22×C4C22⋊#692311yescharacteristic
227C22×C4C22×#692311yescharacteristic
228M16—2442no—
229M16—2442no—
230C2×C8—2442no—
231C2×C8—2442no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—2441no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C4⋊C4—2442no—
238C4⋊C4—2442no—
239C42—1221no—
240C42—1221no—
241C42—1221no—
242C42—1221no—
243C42—1221no—
244C42—1221no—
245C42—2442no—
246C23C2×C22⋊#692311yescharacteristic
247Q8—4882no—
248Q8—4882no—
249Q8—2442no—
250Q8—2442no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—612no—
265C2×C4—611no—
266C2×C4—611no—
267C2×C4—1222no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1221no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2442no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C2×C4#1451984012yes—
280C8—4882no—
281C8—4882no—
282C22—21no—
283C22—21no—
284C22D61⋊#9911yescharacteristic
285C22C2×#1451984011yescharacteristic
286C22#1684075911yescharacteristic
287C4—22no—
288C4—41no—
289C4—41no—
290C4—81no—
291C4—81no—
292C4—612no—
293C4—1221no—
294C4—1222no—
295C4—1221no—
296C4—1221no—
297C4—4881no—
298C4—4881no—
299C4—2441no—
300C2—21no—
301C2—21no—
302C2#2146125711yescharacteristic
303C2#2146208211yescharacteristic
304C2D61⋊#35511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#400C4
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×#11758196C23
hypercenter#400#6923
hypocenterC61#11907
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #400

Complements

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

NH ≅ G/Ntype
175. C61#11907semidirect

Maximal subgroups

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

subgroupindex
#214616862
#214610632
#214608182
#214608172
#214510302
#1190761