Finite Group Databasebeta

← #30595658

Subgroups — #30595658

Order 15616.

456 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 122 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#21461736C212yesmaximal
2#21460640C212yesmaximal
3#21460639C212yesmaximal
4C4×#14519775C211yesmaximal, characteristic
5C2×C4⋊#92420—22no—
6#16840628—22no—
7#16840628C2214yes—
8C2×#14519775C411yescharacteristic
9C2×C4×Dic122C411yescharacteristic
10#16839669C2211yescharacteristic
11#16839667C2211yescharacteristic
12#16839657—22no—
13#16839631C411yescharacteristic
14C4×#11758196—22no—
15C42×Dic61C2211yescharacteristic
16C2×C4×Q8×C61C411yescharacteristic
17C22×#92420—24no—
18C4⋊#92420—44no—
19C22×Dic122C2×C411yescharacteristic
20#14519775—22no—
21#14519775—22no—
22C4×Dic122—42no—
23C2×C4⋊Dic61C2×C411yescharacteristic
24C2×#11758196—22no—
25C2×#11758196—21no—
26C2×#11758196—22no—
27C2×C4×Dic61—21no—
28C2×C4×Dic61C2×C411yescharacteristic
29C2×C4×Dic61D412yes—
30C2×C4×Dic61D412yes—
31C2×C4×Dic61C2311yescharacteristic
32#14519684—22no—
33#14519684—22no—
34C22×Q8×C61C2×C411yescharacteristic
35C4×Q8×C61—42no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C2×C42×C61—21no—
39C2×C42×C61C2×C411yescharacteristic
40C2×Q8×C61—21no—
41C2×Q8×C61—41no—
42C2×Q8×C61—41no—
43C2×Q8×C61M1612yes—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C22×C411yescharacteristic
49C22×Dic61—21no—
50C22×Dic61—21no—
51C22×Dic61C22⋊C412yes—
52C22×Dic61C2×D412yes—
53C2×Dic122—21no—
54C2×Dic122—41no—
55C2×Dic122—41no—
56C2×Dic122M1612yes—
57C2×#92420—44no—
58C2×#92420—44no—
59C2×#92420—44no—
60C4⋊C4×C61—42no—
61C4⋊C4×C61—41no—
62C42×C61—22no—
63C42×C61—42no—
64C4⋊Dic61—41no—
65#11758196—28no—
66#11758196—44no—
67#11758196—42no—
68C4×Dic61—21no—
69C4×Dic61—21no—
70C4×Dic61—42no—
71C4×Dic61—41no—
72C4×Dic61—42no—
73C4×Dic61SD1614yes—
74C4×Dic61Q1614yes—
75C23×C61C2×C22⋊C411yescharacteristic
76Q8×C61—42no—
77Q8×C61—42no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—41no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—42no—
87C2×C4×C61#10012yes—
88C2×C4×C61#10314yes—
89C2×C4×C61C2×M1611yescharacteristic
90C2×C4×C61C2×M1611yescharacteristic
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—41no—
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61—42no—
100C2×Dic61#10314yes—
101C2×Dic61C2×SD1612yes—
102C2×Dic61C2×Q1612yes—
103Dic122—42no—
104Dic122—42no—
105#92420—84no—
106#7653—611nomaximal, Sylow
107C22×C61#40711yescharacteristic
108C22×C61#41011yescharacteristic
109C22×C61C2×#10011yescharacteristic
110C22×C61C2×#10312yes—
111C22×C61#42112yes—
112C4×C61—21no—
113C4×C61—21no—
114C4×C61—41no—
115C4×C61—42no—
116C4×C61—81no—
117C4×C61#33314yes—
118Dic61—24no—
119Dic61—22no—
120Dic61—22no—
121Dic61—42no—
122Dic61—81no—
123C4×C4⋊Q8—611no—
124#1831—612no—
125#1272—612no—
126#1272—612no—
127C2×C61#146611yescharacteristic
128C2×C61#148712yes—
129C2×C61#151812yes—
130C2×C61#153611yescharacteristic
131C2×C61C2×#33311yescharacteristic
132C2×C4⋊Q8—611no—
133C2×C4×Q8—611no—
134C2×C4×Q8#692311yescharacteristic
135C2×C4⋊C8—1222no—
136#391—611no—
137#391—611no—
138#389—1222no—
139#384—611no—
140C4×C4⋊C4—1222no—
141C43—611no—
142#336—614no—
143#336—1222no—
144C61#765311yescharacteristic, complemented, Sylow
145C22×Q8—611no—
146C22×Q8C2×#692311yescharacteristic
147C22×C8—1224no—
148C4⋊Q8—1222no—
149C4⋊Q8—1222no—
150C4×Q8—42no—
151C4×Q8—2442no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—611no—
154C2×C4⋊C4—1222no—
155C2×C4⋊C4—1222no—
156C2×C4⋊C4—1221no—
157C2×C4⋊C4C2×#692311yescharacteristic
158C2×C42—21no—
159C2×C42—612no—
160C2×C42—611no—
161C2×C42—612no—
162C2×C42—611no—
163C2×C42—1221no—
164C2×C42C2×#692311yescharacteristic
165C4⋊C8—2444no—
166#95—1222no—
167#95—1222no—
168C2×Q8—21no—
169C2×Q8—41no—
170C2×Q8—41no—
171C2×Q8—612no—
172C2×Q8—1221no—
173C2×Q8—2441no—
174C2×Q8—2441no—
175C2×Q8#1175821312yes—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—612no—
179C22×C4—612no—
180C22×C4—1221no—
181C22×C4—1221no—
182C22×C4C22⋊#692311yescharacteristic
183C22×C4C22⋊#692311yescharacteristic
184C22×C4C22×#692311yescharacteristic
185C2×C8—2444no—
186C2×C8—2444no—
187C2×C8—2444no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—1228no—
191C4⋊C4—2441no—
192C4⋊C4—2442no—
193C4⋊C4—2444no—
194C42—22no—
195C42—42no—
196C42—614no—
197C42—614no—
198C42—1221no—
199C42—1221no—
200C42—2441no—
201C42—2442no—
202C42—2442no—
203C23C2×C22⋊#692311yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—2442no—
207Q8—2442no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—42no—
217C2×C4—614no—
218C2×C4—612no—
219C2×C4—612no—
220C2×C4—1222no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—2441no—
226C2×C4—2442no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4#1451983712yes—
230C2×C4#1451984014yes—
231C2×C4D61⋊M1611yescharacteristic
232C2×C4C2×#1175821311yescharacteristic
233C8—4884no—
234C22#1684073311yescharacteristic
235C22#1684074111yescharacteristic
236C22C2×#1451983711yescharacteristic
237C22C2×#1451984012yes—
238C22#1684075912yes—
239C4—21no—
240C4—21no—
241C4—41no—
242C4—42no—
243C4—81no—
244C4—1222no—
245C4—1222no—
246C4—1224no—
247C4—4881no—
248C4—2442no—
249C4#1684062214yes—
250C2#2146107811yescharacteristic
251C2#2146114812yes—
252C2#2146125212yes—
253C2#2146130711yescharacteristic
254C2C2×#1684062211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#7653
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
144. C61#7653semidirect

Maximal subgroups

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

subgroupindex
#214617362
#214606402
#214606392
C4×#145197752
#765361