Finite Group Databasebeta

← #30594757

Subgroups — #30594757

Order 15616.

338 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 54 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#21461943C211yesmaximal, characteristic
2#21461075C211yesmaximal, characteristic
3#21445805C211yesmaximal, characteristic
4C2×#14519844C411yescharacteristic, complemented
5#16840732—21no—
6C2×C22⋊#92420—21no—
7C2×C22⋊#92420—21no—
8C2×#14519832C411yescharacteristic, complemented
9#16840607C412yescomplemented
10#16840605—21no—
11C2×D4×Dic61C2211yescharacteristic
12C2×#14519692C411yescharacteristic
13#16839620—21no—
14#16839528—21no—
15C2×#99×C61C411yescharacteristic
16C2×#11758217—41no—
17C22×#92420—21no—
18C22×#92420—21no—
19#14519844—41no—
20C22⋊#92420—22no—
21C22⋊#92420—42no—
22C22⋊#92420—42no—
23C22⋊#92420—41no—
24#14519832—41no—
25C23×Dic61D411yescharacteristic
26C23×Dic61D411yescharacteristic
27D4×Dic61—41no—
28D4×Dic61—41no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×#11758196—41no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61D411yescharacteristic
33C2×C22⋊Dic61Q811yescharacteristic
34C2×C4×Dic61C2×C411yescharacteristic
35#14519692—41no—
36#14519684—41no—
37C22×D4×C61C2×C411yescharacteristic
38C2×C22⋊C4×C61—21no—
39#99×C61—41no—
40C24×C61C22⋊C411yescharacteristic
41C24×C61C4⋊C411yescharacteristic
42C2×D4×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61—41no—
45C2×D4×C61—41no—
46C22×C4×C61—41no—
47C22×C4×C61C4211yescharacteristic
48C22×Dic61—21no—
49C22×Dic61—21no—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61—41no—
53C22×Dic61—41no—
54C22×Dic61—41no—
55C22×Dic61—41no—
56C22×Dic61—41no—
57C22×Dic61C22⋊C411yescharacteristic
58C22×Dic61C22⋊C411yescharacteristic
59C22×Dic61C4⋊C411yescharacteristic
60C22×Dic61C4⋊C411yescharacteristic
61#11758217—81no—
62#11758217—81no—
63C2×#92420—22no—
64C2×#92420—41no—
65C2×#92420—41no—
66C2×#92420—42no—
67C2×#92420—41no—
68C2×#92420—41no—
69C2×#92420—41no—
70C22⋊C4×C61—41no—
71C22⋊C4×C61—41no—
72C22⋊Dic61—41no—
73C22⋊Dic61—41no—
74C22⋊Dic61—41no—
75C22⋊Dic61—41no—
76C4⋊Dic61—41no—
77#11758196—81no—
78#11758196—81no—
79C4×Dic61—21no—
80C4×Dic61—21no—
81C23×C61—21no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61—21no—
85C23×C61—21no—
86C23×C61—41no—
87C23×C61—41no—
88C23×C61—41no—
89C23×C61—41no—
90C23×C61#9511yescharacteristic
91C23×C61#10011yescharacteristic
92C23×C61#10111yescharacteristic
93D4×C61—42no—
94D4×C61—42no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—81no—
99C2×C4×C61—81no—
100C2×C4×C61—81no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—81no—
114C2×Dic61—81no—
115C2×Dic61—81no—
116C2×Dic61—81no—
117C2×Dic61—81no—
118C2×Dic61#9911yescharacteristic
119C2×Dic61#9911yescharacteristic
120#92420—42no—
121#92420—82no—
122#92420—81no—
123#7322—611nomaximal, Sylow
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—41no—
129C22×C61—41no—
130C22×C61—42no—
131C22×C61—41no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—41no—
135C22×C61—41no—
136C22×C61—81no—
137C22×C61—81no—
138C22×C61#34211yescharacteristic
139C22×C61#34311yescharacteristic
140C22×C61#34411yescharacteristic
141C4×C61—41no—
142C4×C61—161no—
143Dic61—21no—
144Dic61—41no—
145Dic61—41no—
146Dic61—41no—
147Dic61—161no—
148Dic61#35311yescharacteristic
149Dic61#35411yescharacteristic
150#1955—611no—
151#1799—611no—
152#1465—611no—
153C2×C61—21no—
154C2×C61—21no—
155C2×C61—41no—
156C2×C61—41no—
157C2×C61—81no—
158C2×C61#130511yescharacteristic
159C2×C61#139311yescharacteristic
160C2×C61#139511yescharacteristic
161C2×C4×D4—611no—
162C2×C4⋊C8—611no—
163C2×#99—611no—
164C2×#99#692311yescharacteristic
165#407—1221no—
166C2×C22⋊C8—1221no—
167C2×C22⋊C8—1221no—
168C2×#97—611no—
169#380—1221no—
170#342—1221no—
171#324—612no—
172#323—1221no—
173C61#732211yescharacteristic, complemented, Sylow
174C22×D4C2×#692311yescharacteristic
175C23×C4—611no—
176C23×C4—611no—
177C2×M16—2441no—
178C22×C8—1221no—
179C22×C8—1221no—
180C4×D4—2441no—
181C4×D4—2441no—
182C2×C4⋊C4—611no—
183C2×C4⋊C4—2441no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—611no—
186C2×C22⋊C4—611no—
187C2×C22⋊C4—1221no—
188C2×C42—611no—
189C4⋊C8—2441no—
190#99—41no—
191#99—2441no—
192C22⋊C8—1222no—
193C22⋊C8—2442no—
194C22⋊C8—2442no—
195C22⋊C8—2441no—
196#97—2441no—
197#95—2441no—
198C24C4⋊#692311yescharacteristic
199C24C22⋊#692311yescharacteristic
200C2×D4—21no—
201C2×D4—21no—
202C2×D4—41no—
203C2×D4—41no—
204C22×C4—41no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1221no—
213C22×C4—2441no—
214C22×C4—2441no—
215C22×C4—2441no—
216C22×C4—2441no—
217C22×C4—2441no—
218C22×C4C4×#692311yescharacteristic
219M16—4881no—
220M16—4881no—
221C2×C8—1222no—
222C2×C8—2441no—
223C2×C8—2442no—
224C2×C8—2441no—
225C2×C8—2441no—
226C2×C8—2441no—
227C2×C8—2441no—
228C4⋊C4—4881no—
229C4⋊C4—4881no—
230C4⋊C4—2441no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—2441no—
234C22⋊C4—2441no—
235C22⋊C4—2441no—
236C22⋊C4—2441no—
237C42—1221no—
238C42—1221no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23—41no—
248C23(C2×#6923)⋊C411yescharacteristic
249C23#1451983711yescharacteristic
250C23#1451983811yescharacteristic
251D4—42no—
252D4—42no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—4881no—
267C2×C4—4881no—
268C2×C4—4881no—
269C2×C4—4881no—
270C2×C4—4881no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C8—4881no—
279C8—4882no—
280C8—2442no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—41no—
286C22—41no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22—81no—
295C22#1684063911yescharacteristic
296C22#1684064211yescharacteristic
297C22#1684064311yescharacteristic
298C4—41no—
299C4—161no—
300C4—611no—
301C4—611no—
302C4—1221no—
303C4—9761no—
304C4—2441no—
305C4—2441no—
306C4—2441no—
307C2—21no—
308C2—21no—
309C2—41no—
310C2—41no—
311C2—81no—
312C2#2146072011yescharacteristic
313C2#2146091211yescharacteristic
314C2#2146091811yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC22×D4C2×#6923
FittingC2×#99×C61C4
socleC22×C61#342
prime radicalC22×D4×C61C2×C4
cosocleC2×D4×Dic61C22
hypercenterC2×#99#6923
hypocenterC61#7322
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
4. C2×#14519844C4semidirect
8. C2×#14519832C4semidirect
9. #16840607C4semidirect
173. C61#7322semidirect

Maximal subgroups

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

subgroupindex
#214619432
#214610752
#214458052
#732261