Finite Group Databasebeta

← #30599419

Subgroups — #30599419

Order 15616.

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

normal subgroups only

This group has 384 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
1C4×#14519838C211yesmaximal, characteristic
2#21461081C211yesmaximal, characteristic
3#21460707C212yesmaximal
4#21460678C212yesmaximal
5#21448782C211yesmaximal, characteristic
6#16840783C2212yes—
7C2×#14519838—21no—
8C4×#11758217C2212yes—
9#16840642—21no—
10#16840608—21no—
11#16840607—21no—
12C2×C4×Dic122C2211yescharacteristic
13#16839668—21no—
14#16839643—21no—
15#16839643—21no—
16#16839629C411yescharacteristic
17#16839629C2211yescharacteristic
18#16839628C411yescharacteristic
19C4×C4⋊Dic61—21no—
20#16839607C411yescharacteristic
21#16839607C2211yescharacteristic
22C4×C4⋊C4×C61C411yescharacteristic
23C2×#11758217—22no—
24C4⋊#92420—22no—
25#14519838—24no—
26C22⋊#92420—22no—
27#14519832—22no—
28#14519832—22no—
29C4×#92420—22no—
30C22×Dic122D411yescharacteristic
31C4×Dic122—22no—
32C4×Dic122—22no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61D411yescharacteristic
35C2×#11758196D411yescharacteristic
36C2×#11758196D411yescharacteristic
37C2×C4×Dic61—21no—
38C2×C4×Dic61—21no—
39C2×C4×Dic61C2×C411yescharacteristic
40C2×C4×Dic61C2311yescharacteristic
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C2×C4⋊C4×C61—21no—
51C2×C42×C61—21no—
52C2×C42×C61C2×C411yescharacteristic
53#95×C61C2×C411yescharacteristic
54#95×C61C2×C411yescharacteristic
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×Dic122—22no—
67C2×Dic122—22no—
68C2×Dic122—41no—
69#11758217—24no—
70#11758217—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C4⋊C4×C61—42no—
74C42×C61—21no—
75C42×C61—21no—
76C42×C61—42no—
77C4⋊Dic61—22no—
78C4⋊Dic61—42no—
79#11758196—22no—
80#11758196—22no—
81C4×Dic61—21no—
82C4×Dic61—21no—
83C4×Dic61—42no—
84C4×Dic61—42no—
85C4×Dic61#4112yes—
86C4×Dic61#4112yes—
87C23×C61C2×C22⋊C411yescharacteristic
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61—41no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61#10412yes—
100C2×C4×C61#11711yescharacteristic
101C2×C4×C61#11711yescharacteristic
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61#12312yes—
117C2×Dic61#12312yes—
118Dic122—44no—
119#92420—44no—
120#92420—82no—
121#8775—611nomaximal, Sylow
122C22×C61—21no—
123C22×C61—21no—
124C22×C61#38111yescharacteristic
125C22×C61C2×#10411yescharacteristic
126C22×C61#42111yescharacteristic
127C4×C61—22no—
128C4×C61—21no—
129C4×C61—21no—
130C4×C61—42no—
131C4×C61—41no—
132C4×C61—81no—
133Dic61—22no—
134Dic61—22no—
135Dic61—41no—
136Dic61—41no—
137Dic61—81no—
138Dic61—81no—
139#2356—611no—
140C4×#101—611no—
141#1467—611no—
142#1300—612no—
143#1288—612no—
144C2×C61—21no—
145C2×C61—21no—
146C2×C61#182611yescharacteristic
147C2×C61#182711yescharacteristic
148C2×C61#183011yescharacteristic
149C2×C4×Q8—611no—
150#432—612no—
151C2×#101—1221no—
152C4×M16—612no—
153#391—1221no—
154#387—1221no—
155#387—1221no—
156#383—611no—
157#383—611no—
158#382—611no—
159C4×C4⋊C4—1221no—
160C4×C4⋊C4#692311yescharacteristic
161#376—611no—
162#376—611no—
163#343—1221no—
164#324—1221no—
165#324—1221no—
166C61#877511yescharacteristic, complemented, Sylow
167C22×Q8—611no—
168C2×M16—1222no—
169C4×Q8—1222no—
170C4×Q8—1222no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—611no—
173C2×C4⋊C4—611no—
174C2×C4⋊C4—611no—
175C2×C4⋊C4—1221no—
176C2×C42—21no—
177C2×C42—611no—
178C2×C42—611no—
179C2×C42—1221no—
180C2×C42—1221no—
181C2×C42C2×#692311yescharacteristic
182C4⋊C8—1222no—
183#101—1224no—
184C22⋊C8—1222no—
185#97—1222no—
186#97—1222no—
187C4×C8—1222no—
188#95—611no—
189#95—611no—
190#95—1221no—
191#95—1221no—
192#95—1221no—
193#95—1221no—
194#95—1221no—
195#95—1221no—
196#95—1221no—
197#95C2×#692311yescharacteristic
198#95C2×#692311yescharacteristic
199C2×Q8—1222no—
200C2×Q8—1222no—
201C2×Q8—2441no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4C22⋊#692311yescharacteristic
211C22×C4C22⋊#692311yescharacteristic
212C22×C4C22×#692311yescharacteristic
213M16—1224no—
214M16—2442no—
215C2×C8—2442no—
216C2×C8—2442no—
217C4⋊C4—42no—
218C4⋊C4—1222no—
219C4⋊C4—1222no—
220C4⋊C4—1222no—
221C4⋊C4—2442no—
222C42—21no—
223C42—21no—
224C42—42no—
225C42—612no—
226C42—612no—
227C42—1221no—
228C42—1221no—
229C42—2442no—
230C42—2442no—
231C23C2×C22⋊#692311yescharacteristic
232Q8—2444no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—612no—
245C2×C4—612no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4#1451984212yes—
261C2×C4#1451985611yescharacteristic
262C2×C4#1451985611yescharacteristic
263C8—4882no—
264C8—2444no—
265C22—21no—
266C22—21no—
267C22#1684070511yescharacteristic
268C22C2×#1451984211yescharacteristic
269C22#1684076011yescharacteristic
270C4—22no—
271C4—21no—
272C4—21no—
273C4—42no—
274C4—41no—
275C4—81no—
276C4—1222no—
277C4—1222no—
278C4—4881no—
279C4—4881no—
280C4—2441no—
281C4—2441no—
282C2—21no—
283C2—21no—
284C2#2146172611yescharacteristic
285C2#2146172811yescharacteristic
286C2#2146173311yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC22×C61#381
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8775
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
166. C61#8775semidirect

Maximal subgroups

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

subgroupindex
C4×#145198382
#214610812
#214607072
#214606782
#214487822
#877561