Finite Group Databasebeta

← #30604119

Subgroups — #30604119

Order 15616.

446 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461073C212yesmaximal
2#21460762C212yesmaximal, complemented
3#21460759C212yesmaximal, complemented
4#21448225C211yesmaximal, characteristic
5#16840783—22no—
6#16840607C2214yes—
7#16840606—22no—
8C2×#14519735C411yescharacteristic
9C2×#14519735C2211yescharacteristic
10C2×C42×D61C411yescharacteristic
11#16839631C411yescharacteristic
12#16839631C2211yescharacteristic
13#16839628C2211yescharacteristic
14#16839621—22no—
15#16839613—22no—
16C61×#382C411yescharacteristic
17C4⋊#92420—42no—
18C22⋊#92420—24no—
19#14519832—42no—
20C22×C4×D61—21no—
21C22×C4×D61C2×C411yescharacteristic
22#14519735—41no—
23#14519735—41no—
24#14519735—41no—
25#14519735—41no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2311yescharacteristic
28C2×#11758196—22no—
29C2×#11758196—22no—
30C2×#11758198—21no—
31C2×#11758198D412yes—
32C2×C4×Dic61—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61D412yes—
36C42×D61—22no—
37C42×D61—22no—
38#14519684—22no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42#95×C61—22no—
43C23×D61C22⋊C411yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61—21no—
46C22×C4×C61C22⋊C412yes—
47C22×C4×C61C22×C411yescharacteristic
48C22×Dic61—21no—
49C22×Dic61—21no—
50C22×Dic61C22⋊C411yescharacteristic
51C22×Dic61C2×D412yes—
52C2×C4×D61—22no—
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—21no—
56C2×C4×D61—21no—
57C2×C4×D61—24no—
58C2×C4×D61—42no—
59C2×C4×D61—42no—
60C2×#92420—44no—
61C4⋊C4×C61—41no—
62C4⋊C4×C61—41no—
63C42×C61—21no—
64C42×C61M1612yes—
65#11758198—42no—
66#11758198—42no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69#11758196—44no—
70#11758196—44no—
71C4×Dic61—24no—
72C4×Dic61—21no—
73C4×Dic61—22no—
74C4×Dic61—22no—
75C4×Dic61—41no—
76C4×Dic61—41no—
77C4×Dic61M1612yes—
78C23×C61C2×C22⋊C411yescharacteristic
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—41no—
82C22×D61—41no—
83C22×D61#10112yes—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—41no—
89C2×C4×C61—41no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—41no—
93C2×C4×C61C2×M1611yescharacteristic
94C2×C4×C61C2×M1611yescharacteristic
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—22no—
99C2×Dic61—21no—
100C2×Dic61—22no—
101C2×Dic61—42no—
102C2×Dic61—42no—
103C2×Dic61—41no—
104C2×Dic61#9911yescharacteristic
105C2×Dic61#9911yescharacteristic
106C4×D61—22no—
107C4×D61—22no—
108C4×D61—22no—
109C4×D61—22no—
110C4×D61—48no—
111#92420—84no—
112#11513—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—21no—
115C22×C61#40711yescharacteristic
116C22×C61C2×#9911yescharacteristic
117C22×C61C2×#10111yescharacteristic
118C2×D61—22no—
119C2×D61—42no—
120C2×D61—41no—
121C2×D61—41no—
122C2×D61—42no—
123C4×C61—21no—
124C4×C61—21no—
125C4×C61—42no—
126C4×C61—42no—
127C4×C61—81no—
128Dic61—24no—
129Dic61—21no—
130Dic61—21no—
131Dic61—42no—
132Dic61—81no—
133#2285—611no—
134#1464—612no—
135#1325—612no—
136#1324—612no—
137C2×C61—21no—
138C2×C61—21no—
139C2×C61#146311yescharacteristic
140C2×C61#212611yescharacteristic
141C2×C61#213211yescharacteristic
142D61—42no—
143C2×#117—611no—
144C2×#117—611no—
145C22×C42—611no—
146#432—1222no—
147#384—611no—
148#384—611no—
149#382—611no—
150#382#692311yescharacteristic
151#380—1222no—
152C4×C4⋊C4—1222no—
153#324—614no—
154#323—1222no—
155C61#1151311yescharacteristic, complemented, Sylow
156C23×C4—611no—
157C23×C4—1221no—
158#117—2441no—
159#117—2441no—
160#117—2441no—
161#117—2441no—
162C2×C4⋊C4—611no—
163C2×C4⋊C4—611no—
164C2×C4⋊C4—1222no—
165C2×C4⋊C4—1222no—
166C2×C4⋊C4C2×#692311yescharacteristic
167C2×C4⋊C4C2×#692311yescharacteristic
168C2×C22⋊C4—612no—
169C2×C22⋊C4—1221no—
170C2×C42—611no—
171C2×C42—612no—
172C2×C42—1222no—
173C2×C42—1221no—
174C2×C42—1222no—
175C2×C42—1221no—
176C2×C42C2×#692311yescharacteristic
177C4⋊C8—2442no—
178C22⋊C8—1224no—
179#97—2442no—
180#95—22no—
181#95—1222no—
182C24—611no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—611no—
186C22×C4—612no—
187C22×C4—1221no—
188C22×C4—1221no—
189C22×C4—1222no—
190C22×C4—1224no—
191C22×C4—1221no—
192C22×C4—1221no—
193C22×C4—1221no—
194C22×C4—1221no—
195C22×C4—2442no—
196C22×C4—2442no—
197C22×C4C22⋊#692312yes—
198C22×C4C22×#692311yescharacteristic
199C2×C8—2444no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—2441no—
203C4⋊C4—2441no—
204C4⋊C4—2444no—
205C4⋊C4—2444no—
206C22⋊C4—2442no—
207C22⋊C4—2442no—
208C42—21no—
209C42—612no—
210C42—1222no—
211C42—1222no—
212C42—1224no—
213C42—1221no—
214C42—2441no—
215C42—2441no—
216C42#1175821312yes—
217C23—612no—
218C23—1221no—
219C23—1221no—
220C23—2441no—
221C23—2441no—
222C23C2×C22⋊#692311yescharacteristic
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—611no—
233C2×C4—611no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—1222no—
244C2×C4—2448no—
245C2×C4—2442no—
246C2×C4—2441no—
247C2×C4—2442no—
248C2×C4D61⋊M1611yescharacteristic
249C2×C4C2×#1175821311yescharacteristic
250C8—4884no—
251C22—21no—
252C22—21no—
253C22—1222no—
254C22—2442no—
255C22—2442no—
256C22—2441no—
257C22—2441no—
258C22#1684073311yescharacteristic
259C22D61⋊#9911yescharacteristic
260C22D61⋊#10111yescharacteristic
261C4—21no—
262C4—21no—
263C4—42no—
264C4—42no—
265C4—81no—
266C4—1224no—
267C4—1221no—
268C4—1221no—
269C4—4881no—
270C4—2442no—
271C2—21no—
272C2—21no—
273C2—2442no—
274C2#2146106811yescharacteristic
275C2#2146209111yescharacteristic
276C2#2146211311yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenter#382#6923
hypocenterC61#11513
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #21460762C2semidirect
3. #21460759C2semidirect
155. C61#11513semidirect

Maximal subgroups

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

subgroupindex
#214610732
#214607622
#214607592
#214482252
#1151361