Finite Group Databasebeta

← #30595489

Subgroups — #30595489

Order 15616.

440 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 110 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#21461746C211yesmaximal, characteristic
2#21461746C211yesmaximal, characteristic
3#21460638C214yesmaximal
4#21448386C211yesmaximal, characteristic
5#16840628—21no—
6#16840628—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519777C411yescharacteristic
12C2×#14519742—21no—
13#16839667—21no—
14#16839658—21no—
15#16839658C2212yes—
16C4⋊C4×Dic61—21no—
17C4⋊C4×Dic61C412yes—
18C42×Dic61C2211yescharacteristic
19C61×#384C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22C22×Dic122—21no—
23#14519777—22no—
24#14519777C814yescomplemented
25#14519742—44no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61C2×C412yes—
28C2×#11758196—22no—
29C2×C4×Dic61—22no—
30C2×C4×Dic61C2×C411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C2×C4×Dic61D411yescharacteristic
35C2×C4×Dic61C2311yescharacteristic
36#14519684—22no—
37#14519684—22no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61C2×C412yes—
41C2×C42×C61C2×C411yescharacteristic
42C22×C4×C61—22no—
43C22×C4×C61C22⋊C411yescharacteristic
44C22×C4×C61C22⋊C411yescharacteristic
45C22×C4×C61C22×C411yescharacteristic
46C22×Dic61—22no—
47C22×Dic61C22⋊C411yescharacteristic
48C22×Dic61C22⋊C411yescharacteristic
49C22×Dic61C2×D411yescharacteristic
50C22×Dic61C2×D411yescharacteristic
51C2×Dic122—24no—
52C2×Dic122—42no—
53C2×Dic122—42no—
54C2×#92420—42no—
55C2×#92420—42no—
56C2×#92420—42no—
57C2×#92420—42no—
58C2×#92420—42no—
59C2×#92420—42no—
60C4⋊C4×C61—42no—
61C4⋊C4×C61—42no—
62C4⋊C4×C61—42no—
63C42×C61C2×C812yes—
64C42×C61M1612yes—
65C4⋊Dic61—24no—
66C4⋊Dic61—22no—
67C4⋊Dic61C2×C814yes—
68#11758196—44no—
69C4×Dic61—22no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C4×Dic61—41no—
73C4×Dic61—41no—
74C4×Dic61—41no—
75C4×Dic61—44no—
76C23×C61C2×C22⋊C411yescharacteristic
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—42no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61C22⋊C812yes—
87C2×C4×C61C22⋊C812yes—
88C2×C4×C61C22×C811yescharacteristic
89C2×C4×C61C2×M1611yescharacteristic
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—24no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61#10112yes—
103C2×Dic61AGL(1,ℤ/8)12yes—
104C2×Dic61#13712yes—
105Dic122—48no—
106#92420—82no—
107#92420—82no—
108#7604—611nomaximal, Sylow
109C22×C61C2×C22⋊C811yescharacteristic
110C22×C61#41011yescharacteristic
111C22×C61C2×#10111yescharacteristic
112C22×C61#41811yescharacteristic
113C22×C61#41911yescharacteristic
114C22×C61#42111yescharacteristic
115C22×C61#42111yescharacteristic
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—22no—
119C4×C61—22no—
120C4×C61—82no—
121Dic61—22no—
122Dic61—22no—
123Dic61—22no—
124Dic61—41no—
125Dic61—44no—
126C4×C4⋊Q8—611no—
127#1839—611no—
128#1839—611no—
129#1271—614no—
130C2×C61#146111yescharacteristic
131C2×C61#147811yescharacteristic
132C2×C61#147911yescharacteristic
133C2×C61#151411yescharacteristic
134C2×C61#151511yescharacteristic
135C2×C61#153711yescharacteristic
136C2×C61#155611yescharacteristic
137C2×C4⋊Q8—611no—
138C2×C4×Q8—1221no—
139#391—1221no—
140#389—612no—
141#389—1221no—
142#384#692311yescharacteristic
143C4×C4⋊C4—612no—
144C4×C4⋊C4—1221no—
145C43—611no—
146#336—612no—
147#336—612no—
148#336—1221no—
149#336—1221no—
150#336—1221no—
151#336—1221no—
152C61#760411yescharacteristic, complemented, Sylow
153C22×Q8—1221no—
154C22×C8—1222no—
155C22×C8—1222no—
156C4⋊Q8—614no—
157C4⋊Q8—1222no—
158C4×Q8—2444no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—612no—
162C2×C4⋊C4—1221no—
163C2×C4⋊C4—1222no—
164C2×C4⋊C4C2×#692312yes—
165C2×C42—611no—
166C2×C42—611no—
167C2×C42—611no—
168C2×C42—611no—
169C2×C42—611no—
170C2×C42—611no—
171C2×C42—1222no—
172C2×C42C2×#692311yescharacteristic
173#95—1222no—
174#95—1222no—
175C2×Q8—1224no—
176C2×Q8—2442no—
177C2×Q8—2442no—
178C22×C4—22no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—1222no—
184C22×C4C22⋊#692311yescharacteristic
185C22×C4C22⋊#692311yescharacteristic
186C22×C4C22×#692311yescharacteristic
187C2×C8—2442no—
188C2×C8—2442no—
189C2×C8—2442no—
190C2×C8—2442no—
191C2×C8—2442no—
192C2×C8—2442no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—614no—
197C4⋊C4—1224no—
198C4⋊C4—1222no—
199C4⋊C4—2444no—
200C42—1222no—
201C42—1222no—
202C42—1222no—
203C42—2441no—
204C42—2441no—
205C42—2441no—
206C42—2444no—
207C42D61⋊C812yes—
208C42#1175821312yes—
209C23C2×C22⋊#692311yescharacteristic
210Q8—2448no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—612no—
221C2×C4—612no—
222C2×C4—612no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1224no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—2442no—
234C2×C4—2442no—
235C2×C4#1451983412yes—
236C2×C4#1451983412yes—
237C2×C4C2×D61⋊C811yescharacteristic
238C2×C4C2×#1175821311yescharacteristic
239C8—4882no—
240C8—4882no—
241C22C2×#1451983411yescharacteristic
242C22#1684074211yescharacteristic
243C22D61⋊#10111yescharacteristic
244C22#1684075411yescharacteristic
245C22#1684075511yescharacteristic
246C22#1684076011yescharacteristic
247C22#1684076111yescharacteristic
248C4—21no—
249C4—21no—
250C4—22no—
251C4—22no—
252C4—82no—
253C4—1222no—
254C4—1222no—
255C4—1222no—
256C4—2441no—
257C4—2444no—
258C2#2146106311yescharacteristic
259C2#2146112011yescharacteristic
260C2#2146112311yescharacteristic
261C2#2146123911yescharacteristic
262C2#2146124311yescharacteristic
263C2#2146131111yescharacteristic
264C2#2146134911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#7604
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
24. #14519777C8semidirect
152. C61#7604semidirect

Maximal subgroups

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

subgroupindex
#214617462
#214606382
#214483862
#760461