Finite Group Databasebeta

← #30595912

Subgroups — #30595912

Order 15616.

388 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 98 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#21461747C211yesmaximal, characteristic
2#21461735C211yesmaximal, characteristic
3#21460638C214yesmaximal
4#21454180C211yesmaximal, characteristic
5C2×#14519844—21no—
6#16840628—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519768—21no—
12#16839661—21no—
13#16839661C412yes—
14#16839658—21no—
15#16839658C2212yes—
16#16839632C411yescharacteristic
17#16839627—21no—
18C42×Dic61C2211yescharacteristic
19C61×#384C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519844—42no—
23#14519768—42no—
24#14519768—42no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61C2×C412yes—
29C2×#11758196—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×#92420—42no—
52C2×#92420—42no—
53C2×#92420—42no—
54C2×#92420—42no—
55C2×#92420—42no—
56C2×#92420—42no—
57C4⋊C4×C61—42no—
58C4⋊C4×C61—42no—
59C4⋊C4×C61—42no—
60C42×C61—22no—
61C4⋊Dic61—24no—
62C4⋊Dic61—42no—
63C4⋊Dic61—42no—
64C4⋊Dic61—44no—
65#11758196—42no—
66#11758196—42no—
67C4×Dic61—22no—
68C4×Dic61—22no—
69C4×Dic61—41no—
70C4×Dic61—41no—
71C4×Dic61—41no—
72C4×Dic61D812yes—
73C4×Dic61SD1612yes—
74C23×C61C2×C22⋊C411yescharacteristic
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—42no—
82C2×C4×C61—42no—
83C2×C4×C61—42no—
84C2×C4×C61#10112yes—
85C2×C4×C61#10212yes—
86C2×C4×C61#13112yes—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61#10212yes—
100C2×Dic61C2×D811yescharacteristic
101C2×Dic61C2×SD1611yescharacteristic
102C2×Dic61#13712yes—
103#92420—82no—
104#92420—82no—
105#7723—611nomaximal, Sylow
106C22×C61#40811yescharacteristic
107C22×C61#41011yescharacteristic
108C22×C61C2×#10111yescharacteristic
109C22×C61C2×#10211yescharacteristic
110C22×C61#41911yescharacteristic
111C22×C61#42111yescharacteristic
112C22×C61#42111yescharacteristic
113C4×C61—22no—
114C4×C61—22no—
115C4×C61—22no—
116C4×C61—82no—
117Dic61—22no—
118Dic61—22no—
119Dic61—21no—
120Dic61—21no—
121Dic61—41no—
122Dic61—82no—
123#2859—611no—
124#1839—611no—
125#1831—611no—
126#1271—614no—
127C2×C61#147011yescharacteristic
128C2×C61#148011yescharacteristic
129C2×C61#149711yescharacteristic
130C2×C61#151511yescharacteristic
131C2×C61#151711yescharacteristic
132C2×C61#153411yescharacteristic
133C2×C61#154611yescharacteristic
134C2×#125—1221no—
135C2×C4⋊C8—1221no—
136#389—612no—
137#389—612no—
138#389—1221no—
139#389—1221no—
140#384—611no—
141#384#692311yescharacteristic
142#382—1221no—
143C43—611no—
144#336—612no—
145#336—612no—
146#336—1221no—
147#336—1221no—
148#336—1221no—
149C61#772311yescharacteristic, complemented, Sylow
150C22×C8—1222no—
151C22×C8—1222no—
152#125—2442no—
153#125—2442no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—1222no—
158C2×C4⋊C4—1222no—
159C2×C4⋊C4—1221no—
160C2×C4⋊C4—1221no—
161C2×C4⋊C4C2×#692312yes—
162C2×C42—611no—
163C2×C42—611no—
164C2×C42—611no—
165C2×C42—611no—
166C2×C42—611no—
167C2×C42—611no—
168C2×C42C2×#692311yescharacteristic
169C4⋊C8—2442no—
170#95—1222no—
171#95—1222no—
172C22×C4—22no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—1222no—
178C22×C4C22⋊#692311yescharacteristic
179C22×C4C22⋊#692311yescharacteristic
180C22×C4C22×#692311yescharacteristic
181C2×C8—2442no—
182C2×C8—2442no—
183C2×C8—2442no—
184C2×C8—2442no—
185C2×C8—2442no—
186C2×C8—2442no—
187C4⋊C4—42no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—1224no—
191C4⋊C4—2442no—
192C4⋊C4—2442no—
193C4⋊C4—2442no—
194C4⋊C4—2444no—
195C4⋊C4—2442no—
196C42—22no—
197C42—612no—
198C42—612no—
199C42—1222no—
200C42—1222no—
201C42—2441no—
202C42—2441no—
203C42—2441no—
204C23C2×C22⋊#692311yescharacteristic
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—612no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—612no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—2442no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4#1451983812yes—
231C2×C4#1451983912yes—
232C2×C4#1451986512yes—
233C8—4882no—
234C8—4882no—
235C22#1684073711yescharacteristic
236C22#1684074211yescharacteristic
237C22C2×#1451983811yescharacteristic
238C22C2×#1451983911yescharacteristic
239C22#1684075511yescharacteristic
240C22#1684076011yescharacteristic
241C22#1684076111yescharacteristic
242C4—22no—
243C4—22no—
244C4—22no—
245C4—82no—
246C4—1221no—
247C4—1221no—
248C4—1222no—
249C4—1222no—
250C4—4882no—
251C4—2441no—
252C2#2146109311yescharacteristic
253C2#2146112611yescharacteristic
254C2#2146118311yescharacteristic
255C2#2146124311yescharacteristic
256C2#2146124811yescharacteristic
257C2#2146130111yescharacteristic
258C2#2146132811yescharacteristic
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#7723
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
149. C61#7723semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214617352
#214606382
#214541802
#772361