Finite Group Databasebeta

← #30605166

Subgroups — #30605166

Order 15616.

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

normal subgroups only

This group has 434 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#21461718C211yesmaximal, characteristic
2#21461069C211yesmaximal, characteristic
3#21460818C214yesmaximal, complemented
4C2×#16839700C211yesmaximal, characteristic
5#16840732—21no—
6#16840732—21no—
7#16840642—21no—
8#16840642C2212yes—
9#16840608—21no—
10#16840608C2212yes—
11C22×#11758196C2211yescharacteristic
12#16839700—21no—
13#16839700—21no—
14#16839700C412yes—
15#16839700C2212yes—
16C2×#14519684—21no—
17C2×#14519684—21no—
18C2×#14519684C411yescharacteristic
19C22×C4⋊C4×C61C411yescharacteristic
20C2×#11758217—22no—
21C2×#11758217—41no—
22C22⋊#92420—22no—
23C22⋊#92420—41no—
24C22⋊#92420—41no—
25C22⋊#92420—41no—
26C23×Dic61—21no—
27C23×Dic61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C2×#11758196—41no—
30C2×#11758196—41no—
31C2×#11758196C2×C411yescharacteristic
32C2×#11758196D411yescharacteristic
33C2×#11758196D411yescharacteristic
34C2×#11758196C2311yescharacteristic
35#14519684—21no—
36#14519684—22no—
37#14519684—22no—
38#14519684—22no—
39#14519684—22no—
40#14519684C2×C412yes—
41C23×C4×C61—21no—
42C23×C4×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—41no—
45C2×C4⋊C4×C61—41no—
46C2×C4⋊C4×C61C2×C412yes—
47C24×C61C22⋊C411yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—22no—
51C22×C4×C61—42no—
52C22×C4×C61—44no—
53C22×C4×C61—41no—
54C22×C4×C61—41no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22×C411yescharacteristic
57C22×Dic61—21no—
58C22×Dic61—21no—
59C22×Dic61—21no—
60C22×Dic61—21no—
61C22×Dic61—22no—
62C22×Dic61—22no—
63C22×Dic61—41no—
64C22×Dic61—42no—
65C22×Dic61—42no—
66C22×Dic61—42no—
67C22×Dic61—42no—
68C22×Dic61C22⋊C411yescharacteristic
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72#11758217—42no—
73#11758217—42no—
74#11758217—82no—
75C2×#92420—42no—
76C2×#92420—42no—
77C4⋊C4×C61—42no—
78C4⋊C4×C61—42no—
79#11758196—41no—
80#11758196—41no—
81#11758196—41no—
82#11758196—41no—
83C23×C61—22no—
84C23×C61—22no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61#9911yescharacteristic
88C23×C61#9911yescharacteristic
89C23×C61C2×C22⋊C411yescharacteristic
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61—41no—
95C2×C4×C61—41no—
96C2×C4×C61—44no—
97C2×C4×C61—42no—
98C2×C4×C61—82no—
99C2×C4×C61—82no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—42no—
113C2×Dic61—42no—
114C2×Dic61—42no—
115C2×Dic61—81no—
116C2×Dic61—84no—
117C2×Dic61#13712yes—
118#92420—82no—
119#92420—82no—
120#11814—611nomaximal, Sylow
121C22×C61—24no—
122C22×C61—24no—
123C22×C61—21no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—21no—
129C22×C61#35212yes—
130C22×C61#35512yes—
131C22×C61C2×#9911yescharacteristic
132C22×C61#41911yescharacteristic
133C22×C61#42111yescharacteristic
134C4×C61—41no—
135C4×C61—41no—
136C4×C61—82no—
137Dic61—22no—
138Dic61—41no—
139Dic61—41no—
140Dic61—41no—
141Dic61—82no—
142C2×#400—611no—
143#1821—611no—
144#1463—611no—
145#1353—614no—
146C2×C61—21no—
147C2×C61—22no—
148C2×C61—22no—
149C2×C61—21no—
150C2×C61#151111yescharacteristic
151C2×C61C2×#35211yescharacteristic
152C2×C61C2×#35511yescharacteristic
153C22×C4⋊C4—611no—
154C22×C4⋊C4#692311yescharacteristic
155#407—1221no—
156#407—1221no—
157#400—612no—
158#400—612no—
159#400—1221no—
160#400—1221no—
161C2×#95—611no—
162C2×#95—1221no—
163C2×#95—1221no—
164#343—612no—
165#343—1221no—
166#324—612no—
167#324—1221no—
168C61#1181411yescharacteristic, complemented, Sylow
169C23×C4—21no—
170C23×C4—611no—
171C23×C4—611no—
172C23×C4—1221no—
173C23×C4C2×#692311yescharacteristic
174C2×M16—1222no—
175C2×M16—2441no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—41no—
178C2×C4⋊C4—41no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—611no—
183C2×C4⋊C4—2441no—
184C2×C4⋊C4—2441no—
185C2×C4⋊C4C2×#692312yes—
186C22⋊C8—1222no—
187C22⋊C8—2441no—
188C22⋊C8—2441no—
189C22⋊C8—2441no—
190#95—612no—
191#95—1222no—
192#95—1222no—
193#95—1222no—
194#95—1222no—
195#95—1221no—
196C24C22⋊#692311yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—44no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—1222no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—1222no—
214C22×C4—2441no—
215C22×C4—2442no—
216C22×C4—2442no—
217C22×C4—2442no—
218C22×C4—2442no—
219C22×C4C22⋊#692311yescharacteristic
220C22×C4C22×#692311yescharacteristic
221M16—4882no—
222M16—2442no—
223M16—2442no—
224C2×C8—2442no—
225C2×C8—2442no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C4⋊C4—2441no—
231C4⋊C4—2441no—
232C23—21no—
233C23—21no—
234C23—22no—
235C23—22no—
236C23#1451983511yescharacteristic
237C23#1451983511yescharacteristic
238C23C2×C22⋊#692311yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4—612no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—4884no—
258C2×C4—4881no—
259C2×C4—2442no—
260C2×C4—2442no—
261C2×C4—2442no—
262C2×C4—2442no—
263C2×C4—2442no—
264C2×C4—2442no—
265C2×C4—2441no—
266C2×C4—2441no—
267C8—4882no—
268C8—4882no—
269C22—24no—
270C22—24no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22#1684066412yes—
278C22#1684067012yes—
279C22C2×#1451983511yescharacteristic
280C22#1684075511yescharacteristic
281C22#1684076111yescharacteristic
282C4—41no—
283C4—41no—
284C4—82no—
285C4—1222no—
286C4—4882no—
287C4—2441no—
288C4—2441no—
289C4—2441no—
290C2—21no—
291C2—21no—
292C2—22no—
293C2—22no—
294C2#2146122911yescharacteristic
295C2C2×#1684066411yescharacteristic
296C2C2×#1684067011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×#11758196C23
hypercenterC22×C4⋊C4#6923
hypocenterC61#11814
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460818C2semidirect
168. C61#11814semidirect

Maximal subgroups

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

subgroupindex
#214617182
#214610692
#214608182
C2×#168397002
#1181461