Finite Group Databasebeta

← #30605413

Subgroups — #30605413

Order 15616.

476 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461685C211yesmaximal, characteristic, complemented
2#21461061C211yesmaximal, characteristic, complemented
3#21460801C214yesmaximal, complemented
4#21450822C211yesmaximal, characteristic
5#16840779—21no—
6#16840765—21no—
7C2×#14519838—21no—
8#16840642C2212yes—
9#16840608C2212yes—
10#16840607—21no—
11C2×#14519764—21no—
12C2×C4×Dic122C2211yescharacteristic
13#16839676C412yes—
14#16839676C2212yes—
15#16839665—21no—
16#16839665—21no—
17#16839665—21no—
18C4×C4⋊Dic61C411yescharacteristic
19C2×#127×C61C411yescharacteristic
20C2×#11758217—22no—
21#14519844—41no—
22#14519844—41no—
23C4⋊#92420—41no—
24#14519838—42no—
25C22⋊#92420—22no—
26C4×#92420—41no—
27C22×Dic122D411yescharacteristic
28#14519764—42no—
29#14519764—42no—
30C4×Dic122—41no—
31C4×Dic122—41no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61D411yescharacteristic
34C2×#11758196C2×C411yescharacteristic
35C2×#11758196C2311yescharacteristic
36C2×C22⋊Dic61—22no—
37C2×C22⋊Dic61—22no—
38C2×C22⋊Dic61—22no—
39C2×C22⋊Dic61—22no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61D411yescharacteristic
42C2×C4×Dic61D411yescharacteristic
43#14519684C2×C412yes—
44C22×D4×C61—21no—
45C22×D4×C61—21no—
46C22×D4×C61C2×C412yes—
47#127×C61—41no—
48#127×C61—41no—
49C2×C42×C61C2×C411yescharacteristic
50C24×C61—22no—
51C2×D4×C61—42no—
52C2×D4×C61—42no—
53C2×D4×C61—42no—
54C2×D4×C61—42no—
55C2×D4×C61—42no—
56C2×D4×C61—41no—
57C2×D4×C61—41no—
58C2×D4×C61—42no—
59C2×D4×C61—82no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22×C411yescharacteristic
63C22×Dic61—22no—
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C2×D411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C2×Dic122—41no—
69C2×Dic122—41no—
70C2×Dic122D812yes—
71C2×Dic122SD1612yes—
72#11758217—42no—
73#11758217—42no—
74C2×#92420—42no—
75C2×#92420—42no—
76C42×C61—21no—
77C42×C61—21no—
78C22⋊Dic61—44no—
79C22⋊Dic61—42no—
80C22⋊Dic61—42no—
81C22⋊Dic61—82no—
82C22⋊Dic61—82no—
83C4⋊Dic61—41no—
84C4⋊Dic61—42no—
85#11758196—41no—
86#11758196—41no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—42no—
92C23×C61—42no—
93C23×C61—42no—
94C23×C61—42no—
95C23×C61—42no—
96C23×C61—42no—
97C23×C61—42no—
98C23×C61—42no—
99C23×C61C2×C22⋊C411yescharacteristic
100D4×C61—82no—
101D4×C61—84no—
102D4×C61—84no—
103D4×C61—82no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—22no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61#9911yescharacteristic
110C2×C4×C61#9911yescharacteristic
111C2×C4×C61#10212yes—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—42no—
121C2×Dic61—42no—
122C2×Dic61—42no—
123C2×Dic61#10212yes—
124C2×Dic61C2×D811yescharacteristic
125C2×Dic61C2×SD1611yescharacteristic
126Dic122—42no—
127Dic122—42no—
128#92420—82no—
129#92420—82no—
130#11882—611nomaximal, Sylow
131C22×C61—21no—
132C22×C61—21no—
133C22×C61—82no—
134C22×C61—82no—
135C22×C61—82no—
136C22×C61—82no—
137C22×C61—82no—
138C22×C61—82no—
139C22×C61—82no—
140C22×C61C2×#9911yescharacteristic
141C22×C61C2×#10211yescharacteristic
142C22×C61#42111yescharacteristic
143C4×C61—21no—
144C4×C61—22no—
145C4×C61—41no—
146C4×C61#35512yes—
147Dic61—21no—
148Dic61—22no—
149Dic61—21no—
150Dic61—41no—
151Dic61—41no—
152Dic61—82no—
153#2548—611no—
154#1801—611no—
155#1461—611no—
156#1345—614no—
157C2×C61—21no—
158C2×C61—21no—
159C2×C61—162no—
160C2×C61#151911yescharacteristic
161C2×C61#212211yescharacteristic
162C2×C61C2×#35511yescharacteristic
163C2×#127#692311yescharacteristic
164C2×#124—1221no—
165C2×C4×Q8—611no—
166#431—1221no—
167#423—1221no—
168C2×#101—1221no—
169#394—612no—
170#394—612no—
171#390—1221no—
172#390—1221no—
173#390—1221no—
174C4×C4⋊C4—611no—
175#343—612no—
176#324—612no—
177#324—1221no—
178C61#1188211yescharacteristic, complemented, Sylow
179C22×Q8—611no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4C2×#692312yes—
183C2×M16—1222no—
184#127—41no—
185#127—41no—
186#124—2442no—
187#124—2442no—
188C4×Q8—2441no—
189C4×Q8—2441no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—611no—
193C2×C4⋊C4—1221no—
194C2×C22⋊C4—1222no—
195C2×C22⋊C4—1222no—
196C2×C22⋊C4—1222no—
197C2×C22⋊C4—1222no—
198C2×C42—611no—
199C2×C42—611no—
200C2×C42—1221no—
201C2×C42C2×#692311yescharacteristic
202C4⋊C8—2441no—
203C4⋊C8—2441no—
204C4⋊C8—2441no—
205#101—2442no—
206C22⋊C8—1222no—
207C4×C8—2441no—
208#95—612no—
209C24—22no—
210C2×Q8—612no—
211C2×Q8—612no—
212C2×Q8—2441no—
213C2×Q8—2441no—
214C2×D4—42no—
215C2×D4—42no—
216C2×D4—42no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—42no—
222C2×D4—82no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—611no—
226C22×C4—611no—
227C22×C4—1222no—
228C22×C4C22⋊#692311yescharacteristic
229C22×C4C22⋊#692311yescharacteristic
230C22×C4C22×#692311yescharacteristic
231M16—2442no—
232M16—2442no—
233C2×C8—2442no—
234C2×C8—2442no—
235C4⋊C4—2441no—
236C4⋊C4—2441no—
237C4⋊C4—2441no—
238C4⋊C4—2442no—
239C22⋊C4—4882no—
240C22⋊C4—4882no—
241C22⋊C4—2444no—
242C22⋊C4—2442no—
243C22⋊C4—2442no—
244C42—21no—
245C42—21no—
246C42—1221no—
247C42—1221no—
248C42—1221no—
249C42—1221no—
250C42—2442no—
251C23—42no—
252C23—42no—
253C23—42no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23C2×C22⋊#692311yescharacteristic
259Q8—2442no—
260Q8—2442no—
261D4—84no—
262D4—82no—
263D4—84no—
264D4—82no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—612no—
271C2×C4—611no—
272C2×C4—611no—
273C2×C4—1221no—
274C2×C4—1221no—
275C2×C4—1221no—
276C2×C4—1221no—
277C2×C4—1221no—
278C2×C4—1221no—
279C2×C4—2442no—
280C2×C4—2442no—
281C2×C4—2442no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4#1451983511yescharacteristic
285C2×C4#1451983511yescharacteristic
286C2×C4#1451983912yes—
287C8—4882no—
288C8—4882no—
289C22—21no—
290C22—21no—
291C22—82no—
292C22—82no—
293C22—82no—
294C22—82no—
295C22—82no—
296C22—82no—
297C22—82no—
298C22C2×#1451983511yescharacteristic
299C22C2×#1451983911yescharacteristic
300C22#1684076011yescharacteristic
301C4—22no—
302C4—21no—
303C4—41no—
304C4—1221no—
305C4—1222no—
306C4—1221no—
307C4—4882no—
308C4—2441no—
309C4—2441no—
310C4#1684067012yes—
311C2—21no—
312C2—21no—
313C2—162no—
314C2#2146125511yescharacteristic
315C2#2146207811yescharacteristic
316C2C2×#1684067011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC2×#127×C61C4
socleC22×C61C2×#99
cosocleC2×#11758196C23
hypercenterC2×#127#6923
hypocenterC61#11882
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #21461685C2semidirect
2. #21461061C2semidirect
3. #21460801C2semidirect
178. C61#11882semidirect

Maximal subgroups

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

subgroupindex
#214616852
#214610612
#214608012
#214508222
#1188261