Finite Group Databasebeta

← #30604907

Subgroups — #30604907

Order 15616.

358 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 68 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#21461572C211yesmaximal, characteristic
2#21461063C211yesmaximal, characteristic
3#21460817C212yesmaximal
4#21460803C212yesmaximal
5#21451700C211yesmaximal, characteristic
6#16840778—21no—
7C2×#14519838—21no—
8C4×#11758217—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519768C411yescharacteristic
13C2×#14519742C2211yescharacteristic
14#16839703—21no—
15#16839702C2211yescharacteristic
16#16839701C411yescharacteristic
17#16839693C2211yescharacteristic
18#16839682—21no—
19#16839649—21no—
20#16839648—21no—
21#16839629C411yescharacteristic
22C61×#398C411yescharacteristic
23C2×#11758217—22no—
24C4⋊#92420—41no—
25#14519838—24no—
26C22⋊#92420—22no—
27#14519832—41no—
28C4×#92420—41no—
29C4×#92420—41no—
30C22×Dic122D411yescharacteristic
31#14519768—41no—
32#14519768—41no—
33#14519742—41no—
34#14519742—41no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196D411yescharacteristic
40C2×#11758196C2311yescharacteristic
41C2×C4×Dic61C2×C411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43C2×C4×Dic61D411yescharacteristic
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
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—22no—
69C2×Dic122—22no—
70C2×Dic122—41no—
71#11758217—24no—
72#11758217—42no—
73C2×#92420—42no—
74C2×#92420—42no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—42no—
78C4⋊Dic61—41no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81#11758196—41no—
82#11758196—41no—
83#11758196—42no—
84#11758196—42no—
85C4×Dic61—21no—
86C4×Dic61—21no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C23×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61#10412yes—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—42no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61#9911yescharacteristic
119C2×Dic61#9911yescharacteristic
120C2×Dic61#13512yes—
121Dic122—44no—
122#92420—44no—
123#92420—82no—
124#11740—611nomaximal, Sylow
125C22×C61—21no—
126C22×C61—21no—
127C22×C61C2×#9911yescharacteristic
128C22×C61#41611yescharacteristic
129C22×C61C2×#10411yescharacteristic
130C4×C61—22no—
131C4×C61—41no—
132C4×C61—41no—
133C4×C61—81no—
134C4×C61—81no—
135Dic61—21no—
136Dic61—21no—
137Dic61—22no—
138Dic61—41no—
139Dic61—41no—
140Dic61—81no—
141Dic61—81no—
142#2634—611no—
143C4×#101—611no—
144#1461—611no—
145#1353—612no—
146#1346—612no—
147C2×C61—21no—
148C2×C61—21no—
149C2×C61#150111yescharacteristic
150C2×C61#212311yescharacteristic
151C2×C61#213311yescharacteristic
152C2×#125—611no—
153C2×C4×Q8—611no—
154#431—1221no—
155C2×#101—1221no—
156C4×M16—1221no—
157#400—611no—
158#400—611no—
159#400—1221no—
160#398—611no—
161#398#692311yescharacteristic
162#395—1221no—
163#387—1221no—
164#387—1221no—
165#383—611no—
166#343—612no—
167#324—612no—
168#324—1221no—
169C61#1174011yescharacteristic, complemented, Sylow
170C22×Q8—611no—
171C2×M16—1222no—
172#125—2441no—
173#125—2441no—
174C4×Q8—2441no—
175C4×Q8—2441no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—1221no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4C2×#692311yescharacteristic
184C2×C4⋊C4C2×#692311yescharacteristic
185C2×C42—611no—
186C2×C42—611no—
187C2×C42—611no—
188C4⋊C8—2441no—
189#101—1224no—
190C22⋊C8—1222no—
191#97—2441no—
192C4×C8—2441no—
193C4×C8—2441no—
194#95—21no—
195#95—611no—
196#95—1221no—
197#95—1221no—
198#95—1221no—
199#95—1221no—
200#95—1221no—
201#95—1221no—
202#95—1221no—
203#95C2×#692311yescharacteristic
204C2×Q8—1222no—
205C2×Q8—1222no—
206C2×Q8—2441no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—611no—
213C22×C4—1221no—
214C22×C4—1221no—
215C22×C4C22⋊#692311yescharacteristic
216C22×C4C22⋊#692311yescharacteristic
217C22×C4C22×#692311yescharacteristic
218M16—1224no—
219M16—2442no—
220C2×C8—2442no—
221C2×C8—2442no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4—2442no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C4⋊C4—2442no—
232C42—1221no—
233C42—1221no—
234C42—1221no—
235C42—1221no—
236C42—1221no—
237C42—1221no—
238C23C2×C22⋊#692311yescharacteristic
239Q8—2444no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—611no—
253C2×C4—611no—
254C2×C4—612no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4—2442no—
265C2×C4—2441no—
266C2×C4—2441no—
267C2×C4—2441no—
268C2×C4#1451984112yes—
269C8—4882no—
270C8—2444no—
271C22—21no—
272C22—21no—
273C22D61⋊#9911yescharacteristic
274C22#1684075211yescharacteristic
275C22C2×#1451984111yescharacteristic
276C4—22no—
277C4—41no—
278C4—41no—
279C4—81no—
280C4—81no—
281C4—1221no—
282C4—1221no—
283C4—1222no—
284C4—4881no—
285C4—4881no—
286C4—2441no—
287C4—2441no—
288C2—21no—
289C2—21no—
290C2#2146119511yescharacteristic
291C2#2146208211yescharacteristic
292C2#2146211711yescharacteristic
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#11740
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
169. C61#11740semidirect

Maximal subgroups

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

subgroupindex
#214615722
#214610632
#214608172
#214608032
#214517002
#1174061