Finite Group Databasebeta

← #30599276

Subgroups — #30599276

Order 15616.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461545C212yesmaximal
2#21460695C212yesmaximal, complemented
3#21460695C212yesmaximal, complemented
4#21448222C211yesmaximal, characteristic
5C2×C22⋊#92420—22no—
6C2×#14519832C2214yes—
7#16840628—22no—
8C2×#14519736C411yescharacteristic
9C22×C4×Dic61C2211yescharacteristic
10#16839631C411yescharacteristic
11#16839631C411yescharacteristic
12#16839627C2211yescharacteristic
13#16839627C2211yescharacteristic
14#16839620—22no—
15C4×#11758196—22no—
16C2×#117×C61C411yescharacteristic
17C22×#92420—24no—
18C22⋊#92420—28no—
19#14519832—28no—
20C23×Dic61D412yes—
21#14519736—42no—
22C2×C4⋊Dic61C2×C411yescharacteristic
23C2×C4⋊Dic61C2×C411yescharacteristic
24C2×#11758196—22no—
25C2×#11758196—22no—
26C2×C22⋊Dic61—21no—
27C2×C4×Dic61—24no—
28C2×C4×Dic61—21no—
29C2×C4×Dic61C2×C411yescharacteristic
30C2×C4×Dic61D412yes—
31C2×C4×Dic61C2311yescharacteristic
32#14519684—22no—
33#14519684—22no—
34C23×C4×C61C2×C411yescharacteristic
35#117×C61—42no—
36C2×C4⋊C4×C61C2×C411yescharacteristic
37C2×C4⋊C4×C61C2×C411yescharacteristic
38C2×C22⋊C4×C61—21no—
39C2×C42×C61—21no—
40C24×C61C22⋊C411yescharacteristic
41C22×C4×C61—22no—
42C22×C4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61—24no—
49C22×Dic61—24no—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61—42no—
53C22×Dic61C22⋊C412yes—
54C22×Dic61C2×D412yes—
55C2×#92420—28no—
56C2×#92420—44no—
57C2×#92420—44no—
58C4⋊C4×C61—41no—
59C4⋊C4×C61—41no—
60C22⋊C4×C61—42no—
61C42×C61—42no—
62C22⋊Dic61—42no—
63C4⋊Dic61—41no—
64C4⋊Dic61—41no—
65#11758196—44no—
66#11758196—44no—
67C4×Dic61—22no—
68C4×Dic61—24no—
69C4×Dic61—42no—
70C4×Dic61#4114yes—
71C23×C61—21no—
72C23×C61—21no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61#10112yes—
76C23×C61C2×C22⋊C411yescharacteristic
77C2×C4×C61—28no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61#10012yes—
87C2×C4×C61#11712yes—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—48no—
93C2×Dic61—41no—
94C2×Dic61—41no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61#10414yes—
98C2×Dic61#12314yes—
99#92420—48no—
100#8721—611nomaximal, Sylow
101C22×C61—22no—
102C22×C61—24no—
103C22×C61—41no—
104C22×C61—42no—
105C22×C61—41no—
106C22×C61#38111yescharacteristic
107C22×C61C2×#10011yescharacteristic
108C22×C61C2×#10111yescharacteristic
109C22×C61C2×#10412yes—
110C22×C61#42112yes—
111C4×C61—22no—
112C4×C61—22no—
113C4×C61—81no—
114C4×C61—81no—
115Dic61—24no—
116Dic61—24no—
117Dic61—81no—
118Dic61—81no—
119#2285—611no—
120#1749—612no—
121#1295—612no—
122#1295—612no—
123C2×C61—42no—
124C2×C61#152511yescharacteristic
125C2×C61#153112yes—
126C2×C61#153611yescharacteristic
127C2×C61#182111yescharacteristic
128C2×C61#182612yes—
129C2×#117—611no—
130C2×#117#692311yescharacteristic
131C22×C42—611no—
132C2×C22⋊C8—1222no—
133C2×#97—614no—
134#384—611no—
135#384—611no—
136#382—611no—
137#382—611no—
138#380—1222no—
139C4×C4⋊C4—1222no—
140#336—1222no—
141C61#872111yescharacteristic, complemented, Sylow
142C23×C4—612no—
143C23×C4C2×#692311yescharacteristic
144C22×C8—1224no—
145#117—42no—
146#117—2442no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—1222no—
150C2×C4⋊C4—1222no—
151C2×C4⋊C4C2×#692311yescharacteristic
152C2×C4⋊C4C2×#692311yescharacteristic
153C2×C22⋊C4—21no—
154C2×C22⋊C4—1221no—
155C2×C42—21no—
156C2×C42—611no—
157C2×C42—612no—
158C2×C42—611no—
159C2×C42—1224no—
160C2×C42—1221no—
161C22⋊C8—1228no—
162#97—1228no—
163#95—1222no—
164#95—1222no—
165C24C22⋊#692311yescharacteristic
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—612no—
172C22×C4—612no—
173C22×C4—1224no—
174C22×C4—1224no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4—2442no—
178C22×C4C22⋊#692311yescharacteristic
179C22×C4C22×#692311yescharacteristic
180C2×C8—1228no—
181C2×C8—2444no—
182C2×C8—2444no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—2441no—
186C4⋊C4—2441no—
187C4⋊C4—2444no—
188C4⋊C4—2444no—
189C22⋊C4—42no—
190C22⋊C4—2442no—
191C42—42no—
192C42—614no—
193C42—1224no—
194C42—1222no—
195C42—2442no—
196C23—21no—
197C23—21no—
198C23—22no—
199C23—22no—
200C23#1451983812yes—
201C23C2×C22⋊#692311yescharacteristic
202C2×C4—28no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—614no—
212C2×C4—614no—
213C2×C4—1222no—
214C2×C4—1222no—
215C2×C4—1222no—
216C2×C4—1222no—
217C2×C4—2448no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4—2442no—
221C2×C4—2442no—
222C2×C4#1451983712yes—
223C2×C4#1451985612yes—
224C8—2448no—
225C22—24no—
226C22—22no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22#1684070511yescharacteristic
231C22C2×#1451983711yescharacteristic
232C22C2×#1451983811yescharacteristic
233C22D61⋊#10412yes—
234C22#1684075912yes—
235C4—22no—
236C4—22no—
237C4—81no—
238C4—81no—
239C4—1224no—
240C4—1224no—
241C4—4881no—
242C4—4881no—
243C2—42no—
244C2#2146127311yescharacteristic
245C2#2146129112yes—
246C2#2146130711yescharacteristic
247C2#2146171811yescharacteristic
248C2#2146172712yes—
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8721
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460695C2semidirect
3. #21460695C2semidirect
141. C61#8721semidirect

Maximal subgroups

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

subgroupindex
#214615452
#214606952
#214482222
#872161