Finite Group Databasebeta

← #30595370

Subgroups — #30595370

Order 15616.

516 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C4×#14519844C212yesmaximal
2#21460640C212yesmaximal
3#21460639C212yesmaximal
4C4×#14519775C211yesmaximal, characteristic
5C2×#14519844—22no—
6C2×C4×#92420—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—
18#14519844—28no—
19C4×#92420—44no—
20C22×Dic122C2×C411yescharacteristic
21#14519775—22no—
22#14519775C814yescomplemented
23C4×Dic122—42no—
24C2×C4⋊Dic61C2×C411yescharacteristic
25C2×#11758196—22no—
26C2×#11758196—21no—
27C2×#11758196—22no—
28C2×C4×Dic61—21no—
29C2×C4×Dic61C2×C411yescharacteristic
30C2×C4×Dic61D412yes—
31C2×C4×Dic61D412yes—
32C2×C4×Dic61C2311yescharacteristic
33#14519684—22no—
34#14519684—22no—
35C22×Q8×C61C2×C411yescharacteristic
36C4×Q8×C61—42no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C2×C42×C61—21no—
40C2×C42×C61C2×C411yescharacteristic
41C2×Q8×C61—21no—
42C2×Q8×C61—41no—
43C2×Q8×C61—41no—
44C2×Q8×C61C2×C812yes—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61C22⋊C412yes—
53C22×Dic61C2×D412yes—
54C2×Dic122—21no—
55C2×Dic122—41no—
56C2×Dic122—41no—
57C2×Dic122C2×C812yes—
58C2×#92420—28no—
59C2×#92420—44no—
60C2×#92420—44no—
61C4⋊C4×C61—42no—
62C4⋊C4×C61—41no—
63C42×C61—22no—
64C42×C61—42no—
65C4⋊Dic61—41no—
66#11758196—28no—
67#11758196—42no—
68#11758196—44no—
69C4×Dic61—24no—
70C4×Dic61—41no—
71C4×Dic61—42no—
72C4×Dic61C2×C812yes—
73C4×Dic61M1612yes—
74C4×Dic61SD1614yes—
75C4×Dic61Q1614yes—
76C23×C61C2×C22⋊C411yescharacteristic
77Q8×C61—42no—
78Q8×C61—42no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—42no—
88C2×C4×C61#10012yes—
89C2×C4×C61#10314yes—
90C2×C4×C61C22×C811yescharacteristic
91C2×C4×C61C2×M1611yescharacteristic
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—41no—
96C2×Dic61—41no—
97C2×Dic61—41no—
98C2×Dic61—42no—
99C2×Dic61C22⋊C814yes—
100C2×Dic61#10314yes—
101C2×Dic61#10414yes—
102C2×Dic61C2×SD1612yes—
103C2×Dic61C2×Q1612yes—
104Dic122—42no—
105Dic122—42no—
106#92420—48no—
107#7571—611nomaximal, Sylow
108C22×C61C2×C22⋊C811yescharacteristic
109C22×C61#41011yescharacteristic
110C22×C61C2×#10011yescharacteristic
111C22×C61C2×#10312yes—
112C22×C61C2×#10412yes—
113C4×C61—21no—
114C4×C61—21no—
115C4×C61—42no—
116C4×C61—41no—
117C4×C61—81no—
118C4×C61#33314yes—
119Dic61—22no—
120Dic61—22no—
121Dic61—42no—
122Dic61—81no—
123Dic61Q8⋊C818yes—
124C4×C4⋊Q8—611no—
125C4×C4⋊C8—612no—
126#1272—612no—
127#1272—612no—
128C2×C61#146011yescharacteristic
129C2×C61C2×Q8⋊C812yes—
130C2×C61#150312yes—
131C2×C61#152511yescharacteristic
132C2×C61C2×#33311yescharacteristic
133C2×C4⋊Q8—611no—
134C2×C4×Q8—611no—
135C2×C4×Q8#692311yescharacteristic
136C2×C4⋊C8—1222no—
137C2×C4×C8—1222no—
138#391—611no—
139#391—611no—
140#389—1222no—
141#384—611no—
142C4×C4⋊C4—1222no—
143C43—611no—
144#336—614no—
145C61#757111yescharacteristic, complemented, Sylow
146C22×Q8—611no—
147C22×Q8C2×#692311yescharacteristic
148C22×C8—1224no—
149C4⋊Q8—614no—
150C4⋊Q8—1222no—
151C4×Q8—42no—
152C4×Q8—2442no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—611no—
155C2×C4⋊C4—1222no—
156C2×C4⋊C4—1222no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4C2×#692311yescharacteristic
159C2×C42—21no—
160C2×C42—612no—
161C2×C42—611no—
162C2×C42—612no—
163C2×C42—611no—
164C2×C42—1221no—
165C2×C42C2×#692311yescharacteristic
166C4⋊C8—1228no—
167C4×C8—2444no—
168#95—1222no—
169#95—1222no—
170C2×Q8—21no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—612no—
174C2×Q8—1221no—
175C2×Q8—2441no—
176C2×Q8—2441no—
177C2×Q8D61⋊C812yes—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—612no—
181C22×C4—612no—
182C22×C4—1221no—
183C22×C4—1221no—
184C22×C4C22⋊#692311yescharacteristic
185C22×C4C22⋊#692311yescharacteristic
186C22×C4C22×#692311yescharacteristic
187C2×C8—1228no—
188C2×C8—2444no—
189C2×C8—2444no—
190C4⋊C4—41no—
191C4⋊C4—42no—
192C4⋊C4—1228no—
193C4⋊C4—2441no—
194C4⋊C4—2442no—
195C4⋊C4—2444no—
196C42—22no—
197C42—42no—
198C42—614no—
199C42—614no—
200C42—612no—
201C42—612no—
202C42—1224no—
203C42—2441no—
204C42—2442no—
205C23C2×C22⋊#692311yescharacteristic
206Q8—42no—
207Q8—42no—
208Q8—2442no—
209Q8—2442no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—614no—
220C2×C4—614no—
221C2×C4—614no—
222C2×C4—612no—
223C2×C4—612no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—2441no—
228C2×C4—2442no—
229C2×C4—2441no—
230C2×C4—2441no—
231C2×C4#1451983712yes—
232C2×C4#1451984014yes—
233C2×C4C2×D61⋊C811yescharacteristic
234C2×C4D61⋊M1611yescharacteristic
235C8—2448no—
236C22D61⋊(C22⋊C8)11yescharacteristic
237C22#1684074111yescharacteristic
238C22C2×#1451983711yescharacteristic
239C22C2×#1451984012yes—
240C22D61⋊#10412yes—
241C4—21no—
242C4—21no—
243C4—41no—
244C4—42no—
245C4—81no—
246C4—618no—
247C4—1222no—
248C4—1222no—
249C4—4881no—
250C4—2442no—
251C4#1684062214yes—
252C2#2146105811yescharacteristic
253C2D61⋊(Q8⋊C8)12yes—
254C2#2146120112yes—
255C2#2146127311yescharacteristic
256C2C2×#1684062211yescharacteristic
subgroupG/H
centerC22×C4C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×C4×Q8×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×C4×Q8#6923
hypocenterC61#7571
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
22. #14519775C8semidirect
145. C61#7571semidirect

Maximal subgroups

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

subgroupindex
C4×#145198442
#214606402
#214606392
C4×#145197752
#757161