Finite Group Databasebeta

← #30601783

Subgroups — #30601783

Order 15616.

456 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 102 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#21461604C211yesmaximal, characteristic
2#21461536C211yesmaximal, characteristic
3C2×#16840619C214yesmaximal
4#21454180C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×#14519832C2212yes—
7C2×#14519832C2212yes—
8#16840628—21no—
9#16840628—21no—
10#16840628—21no—
11#16840619—28no—
12C2×#14519768C2212yes—
13#16839661—21no—
14#16839661—21no—
15#16839658—21no—
16#16839658—21no—
17#16839632C411yescharacteristic
18#16839627C412yes—
19C42×Dic61C2211yescharacteristic
20C61×#384C411yescharacteristic
21C22×#92420—22no—
22C22×#92420—22no—
23#14519844—24no—
24#14519832—24no—
25#14519832—22no—
26#14519832D414yes—
27#14519768—24no—
28#14519768—24no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—22no—
32C2×C4⋊Dic61C2×C412yes—
33C2×#11758196—22no—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61C2311yescharacteristic
40#14519684—22no—
41#14519684—22no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61C2×C412yes—
45C2×C42×C61C2×C411yescharacteristic
46C22×C4×C61—22no—
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—22no—
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C22⋊C411yescharacteristic
53C22×Dic61C2×D411yescharacteristic
54C22×Dic61C2×D411yescharacteristic
55C2×#92420—24no—
56C2×#92420—24no—
57C2×#92420—42no—
58C2×#92420—42no—
59C2×#92420—42no—
60C2×#92420—42no—
61C4⋊C4×C61—24no—
62C4⋊C4×C61—42no—
63C4⋊C4×C61—42no—
64C42×C61—22no—
65C4⋊Dic61—24no—
66C4⋊Dic61—42no—
67C4⋊Dic61—42no—
68C4⋊Dic61—44no—
69#11758196—42no—
70#11758196—42no—
71C4×Dic61—22no—
72C4×Dic61—22no—
73C4×Dic61—41no—
74C4×Dic61—41no—
75C4×Dic61—41no—
76C4×Dic61C2×D412yes—
77C4×Dic61#4112yes—
78C23×C61C2×C22⋊C411yescharacteristic
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—42no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61#10112yes—
89C2×C4×C61#10412yes—
90C2×C4×C61C4×D412yes—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61#10112yes—
104C2×Dic61#12112yes—
105C2×Dic61#12411yescharacteristic
106C2×Dic61#12711yescharacteristic
107#92420—44no—
108#92420—44no—
109#9690—611nomaximal, Sylow
110C22×C61#39011yescharacteristic
111C22×C61C2×#10111yescharacteristic
112C22×C61C2×#10111yescharacteristic
113C22×C61C2×#10411yescharacteristic
114C22×C61#42111yescharacteristic
115C22×C61#42111yescharacteristic
116C22×C61#42111yescharacteristic
117C4×C61—22no—
118C4×C61—22no—
119C4×C61—22no—
120C4×C61—82no—
121Dic61—22no—
122Dic61—21no—
123Dic61—21no—
124Dic61—22no—
125Dic61—41no—
126Dic61—82no—
127#2859—611no—
128#1767—611no—
129#1745—611no—
130C2×#330—614no—
131C2×C61#152811yescharacteristic
132C2×C61#153111yescharacteristic
133C2×C61#153411yescharacteristic
134C2×C61#153711yescharacteristic
135C2×C61#196311yescharacteristic
136C2×C61#196611yescharacteristic
137C2×C61#198011yescharacteristic
138C2×#125—612no—
139C2×C4⋊C8—1221no—
140C2×#97—612no—
141C2×#97—612no—
142#389—1221no—
143#389—1221no—
144#389—1221no—
145#389—1221no—
146#384—611no—
147#384#692311yescharacteristic
148#382—612no—
149C43—611no—
150#336—1221no—
151#336—1221no—
152#336—1221no—
153#330—1228no—
154C61#969011yescharacteristic, complemented, Sylow
155C22×C8—1222no—
156C22×C8—1222no—
157#125—1224no—
158#125—1224no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—612no—
162C2×C4⋊C4—1222no—
163C2×C4⋊C4—1222no—
164C2×C4⋊C4—1221no—
165C2×C4⋊C4—1221no—
166C2×C4⋊C4C2×#692312yes—
167C2×C42—611no—
168C2×C42—611no—
169C2×C42—611no—
170C2×C42—611no—
171C2×C42—611no—
172C2×C42—611no—
173C2×C42C2×#692311yescharacteristic
174C4⋊C8—1224no—
175#97—614no—
176#97—1222no—
177#97—1224no—
178#95—1222no—
179#95—1222no—
180C22×C4—22no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—1222no—
186C22×C4C22⋊#692311yescharacteristic
187C22×C4C22⋊#692311yescharacteristic
188C22×C4C22×#692311yescharacteristic
189C2×C8—1224no—
190C2×C8—1224no—
191C2×C8—2442no—
192C2×C8—2442no—
193C2×C8—2442no—
194C2×C8—2442no—
195C4⋊C4—24no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—1224no—
199C4⋊C4—2442no—
200C4⋊C4—2442no—
201C4⋊C4—2442no—
202C4⋊C4—2442no—
203C4⋊C4—2444no—
204C42—22no—
205C42—612no—
206C42—612no—
207C42—1222no—
208C42—1222no—
209C42—2441no—
210C42—2441no—
211C42—2441no—
212C23C2×C22⋊#692311yescharacteristic
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—612no—
223C2×C4—611no—
224C2×C4—611no—
225C2×C4—612no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4—2442no—
238C2×C4#1451983812yes—
239C2×C4#1451984112yes—
240C2×C4D4×#692312yes—
241C8—2444no—
242C8—2444no—
243C22#1684071411yescharacteristic
244C22C2×#1451983811yescharacteristic
245C22D61⋊#10111yescharacteristic
246C22C2×#1451984111yescharacteristic
247C22#1684076011yescharacteristic
248C22#1684076111yescharacteristic
249C22#1684076111yescharacteristic
250C4—22no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—1222no—
255C4—1222no—
256C4—1221no—
257C4—1221no—
258C4—4882no—
259C4—2441no—
260C2#2146128111yescharacteristic
261C2#2146129211yescharacteristic
262C2#2146130111yescharacteristic
263C2#2146131111yescharacteristic
264C2#2146195511yescharacteristic
265C2#2146196211yescharacteristic
266C2#2146198311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#9690
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
154. C61#9690semidirect

Maximal subgroups

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

subgroupindex
#214616042
#214615362
C2×#168406192
#214541802
#969061