Finite Group Databasebeta

← #30595830

Subgroups — #30595830

Order 15616.

394 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461536C211yesmaximal, characteristic
3#21460638C214yesmaximal
4#21454180C211yesmaximal, characteristic
5C2×#14519832—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#14519832—24no—
23#14519768—44no—
24C2×C4⋊Dic61—21no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61—22no—
27C2×C4⋊Dic61C2×C412yes—
28C2×#11758196—22no—
29C2×C4×Dic61C2×C411yescharacteristic
30C2×C4×Dic61D411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C2×C4×Dic61C2311yescharacteristic
35#14519684—22no—
36#14519684—22no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61C2×C412yes—
40C2×C42×C61C2×C411yescharacteristic
41C22×C4×C61—22no—
42C22×C4×C61C22⋊C411yescharacteristic
43C22×C4×C61C22⋊C411yescharacteristic
44C22×C4×C61C22×C411yescharacteristic
45C22×Dic61—22no—
46C22×Dic61C22⋊C411yescharacteristic
47C22×Dic61C22⋊C411yescharacteristic
48C22×Dic61C2×D411yescharacteristic
49C22×Dic61C2×D411yescharacteristic
50C2×#92420—24no—
51C2×#92420—42no—
52C2×#92420—42no—
53C2×#92420—42no—
54C2×#92420—42no—
55C2×#92420—42no—
56C4⋊C4×C61—42no—
57C4⋊C4×C61—42no—
58C4⋊C4×C61—42no—
59C42×C61—22no—
60C4⋊Dic61—24no—
61C4⋊Dic61—44no—
62C4⋊Dic61—42no—
63C4⋊Dic61—42no—
64#11758196—44no—
65C4×Dic61—22no—
66C4×Dic61—22no—
67C4×Dic61—22no—
68C4×Dic61—22no—
69C4×Dic61—41no—
70C4×Dic61—41no—
71C23×C61C2×C22⋊C411yescharacteristic
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—42no—
79C2×C4×C61—42no—
80C2×C4×C61—42no—
81C2×C4×C61#10112yes—
82C2×C4×C61#10412yes—
83C2×C4×C61#13112yes—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61AGL(1,ℤ/8)12yes—
98C2×Dic61#13712yes—
99#92420—44no—
100#92420—82no—
101#7700—611nomaximal, Sylow
102C22×C61#40811yescharacteristic
103C22×C61#41011yescharacteristic
104C22×C61C2×#10111yescharacteristic
105C22×C61#41811yescharacteristic
106C22×C61#41911yescharacteristic
107C22×C61C2×#10411yescharacteristic
108C22×C61#42111yescharacteristic
109C4×C61—22no—
110C4×C61—22no—
111C4×C61—22no—
112C4×C61—82no—
113Dic61—22no—
114Dic61—22no—
115Dic61—41no—
116Dic61—41no—
117Dic61—82no—
118#2859—611no—
119#1839—611no—
120#1745—611no—
121#1271—614no—
122C2×C61#147011yescharacteristic
123C2×C61#148511yescharacteristic
124C2×C61#149611yescharacteristic
125C2×C61#150511yescharacteristic
126C2×C61#151511yescharacteristic
127C2×C61#152811yescharacteristic
128C2×C61#155611yescharacteristic
129C2×#125—1221no—
130C2×#97—1221no—
131#389—612no—
132#389—612no—
133#389—1221no—
134#389—1221no—
135#384—611no—
136#384#692311yescharacteristic
137#382—1221no—
138C43—611no—
139#336—612no—
140#336—612no—
141#336—1221no—
142#336—1221no—
143#336—1221no—
144C61#770011yescharacteristic, complemented, Sylow
145C22×C8—1222no—
146C22×C8—1222no—
147#125—2444no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—1222no—
152C2×C4⋊C4—1222no—
153C2×C4⋊C4—1221no—
154C2×C4⋊C4—1221no—
155C2×C4⋊C4C2×#692312yes—
156C2×C42—611no—
157C2×C42—611no—
158C2×C42—611no—
159C2×C42—611no—
160C2×C42—611no—
161C2×C42—611no—
162C2×C42C2×#692311yescharacteristic
163#97—1224no—
164#95—1222no—
165#95—1222no—
166C22×C4—22no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—611no—
171C22×C4—1222no—
172C22×C4C22⋊#692311yescharacteristic
173C22×C4C22⋊#692311yescharacteristic
174C22×C4C22×#692311yescharacteristic
175C2×C8—1224no—
176C2×C8—2442no—
177C2×C8—2442no—
178C2×C8—2442no—
179C2×C8—2442no—
180C2×C8—2442no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—1224no—
185C4⋊C4—2442no—
186C4⋊C4—2442no—
187C4⋊C4—2444no—
188C4⋊C4—2444no—
189C42—22no—
190C42—1222no—
191C42—1222no—
192C42—1222no—
193C42—1222no—
194C42—2441no—
195C42—2441no—
196C23C2×C22⋊#692311yescharacteristic
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—612no—
207C2×C4—612no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—2442no—
219C2×C4—2442no—
220C2×C4—2442no—
221C2×C4#1451983812yes—
222C2×C4#1451984112yes—
223C2×C4#1451986512yes—
224C8—4882no—
225C8—2444no—
226C22#1684073711yescharacteristic
227C22#1684074211yescharacteristic
228C22C2×#1451983811yescharacteristic
229C22#1684075411yescharacteristic
230C22#1684075511yescharacteristic
231C22C2×#1451984111yescharacteristic
232C22#1684076111yescharacteristic
233C4—22no—
234C4—22no—
235C4—22no—
236C4—82no—
237C4—1222no—
238C4—1222no—
239C4—4882no—
240C4—2441no—
241C4—2441no—
242C2#2146109311yescharacteristic
243C2#2146114311yescharacteristic
244C2#2146118011yescharacteristic
245C2#2146120811yescharacteristic
246C2#2146124311yescharacteristic
247C2#2146128111yescharacteristic
248C2#2146134811yescharacteristic
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#7700
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
144. C61#7700semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214615362
#214606382
#214541802
#770061