Finite Group Databasebeta

← #30594758

Subgroups — #30594758

Order 15616.

338 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 56 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#21461680C211yesmaximal, characteristic
2#21461076C211yesmaximal, characteristic
3#21446616C211yesmaximal, characteristic
4C2×#14519836C412yes—
5#16840733—21no—
6#16840704—21no—
7#16840640—21no—
8#16840607C412yescomplemented
9#16840606—21no—
10C2×C4×D244C2211yescharacteristic
11C2×#14519689—21no—
12C2×#14519689—21no—
13C2×#14519688C411yescharacteristic, complemented
14C2×C4⋊C8×C61C411yescharacteristic, complemented
15C2×#11758213—41no—
16C2×C4⋊#6923—41no—
17C2×C22⋊#6923—22no—
18#14519836—42no—
19#14519834—41no—
20C22⋊#92420—22no—
21(C2×#6923)⋊C4—41no—
22C22×D244C2×C411yescharacteristic
23C22×C4×D61D411yescharacteristic
24C22×C4×D61D411yescharacteristic
25C22×#92418—21no—
26C4×D244—41no—
27C4×D244—41no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×#11758198D411yescharacteristic
30C2×#11758198Q811yescharacteristic
31#14519689—42no—
32#14519689—42no—
33#14519688—41no—
34C22×C8×C61—21no—
35C2×C42×C61C2×C411yescharacteristic
36C4⋊C8×C61—41no—
37C23×D61C22⋊C411yescharacteristic
38C23×D61C4⋊C411yescharacteristic
39C22×#6923—42no—
40C22×C4×C61C4211yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C22×C4×C61C4⋊C411yescharacteristic
43C22×Dic61C22⋊C411yescharacteristic
44C22×Dic61C4⋊C411yescharacteristic
45C2×D244—21no—
46C2×D244—21no—
47C2×D244—41no—
48C2×D244—41no—
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—41no—
54C2×C4×D61—41no—
55C2×C4×D61—41no—
56C2×C4×D61—41no—
57C22⋊#6923—42no—
58C22⋊#6923—42no—
59C2×#92420—42no—
60C4⋊#6923—81no—
61C4⋊#6923—81no—
62#11758213—81no—
63#11758213—81no—
64C2×C8×C61—41no—
65C2×C8×C61—41no—
66C2×C8×C61—41no—
67C42×C61—21no—
68C42×C61—21no—
69#11758198—41no—
70#11758198—41no—
71C4⋊Dic61—41no—
72C2×#92418—22no—
73C2×#92418—41no—
74C2×#92418—41no—
75C23×C61#9511yescharacteristic
76C22×D61—21no—
77C22×D61—21no—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—41no—
82C22×D61—41no—
83C22×D61—41no—
84C22×D61—41no—
85C22×D61#10011yescharacteristic
86C22×D61#10111yescharacteristic
87C2×#6923—82no—
88C2×#6923—82no—
89C2×#6923—82no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61#9911yescharacteristic
98C2×C4×C61#9911yescharacteristic
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103D244—42no—
104D244—42no—
105C4×D61—41no—
106C4×D61—41no—
107C4×D61—41no—
108C4×D61—41no—
109C4×D61—81no—
110C4×D61—81no—
111#92420—82no—
112C8×C61—81no—
113#92418—42no—
114#7322—611nomaximal, Sylow
115C22×C61—21no—
116C22×C61—21no—
117C22×C61#34211yescharacteristic
118C22×C61#34311yescharacteristic
119C22×C61#34411yescharacteristic
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—41no—
126C2×D61—42no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—81no—
131C2×D61—81no—
132#6923—162no—
133C4×C61—21no—
134C4×C61—41no—
135C4×C61—41no—
136C4×C61#35311yescharacteristic
137C4×C61#35411yescharacteristic
138Dic61—41no—
139Dic61—41no—
140#1955—611no—
141#1799—611no—
142#1465—611no—
143C2×C61—21no—
144C2×C61—21no—
145C2×C61#130511yescharacteristic
146C2×C61#139311yescharacteristic
147C2×C61#139511yescharacteristic
148D61—41no—
149D61—41no—
150D61—81no—
151C2×C4×D4—611no—
152C2×C4⋊C8#692311yescharacteristic, complemented
153C2×#99—612no—
154#407—1221no—
155C2×C22⋊C8—1221no—
156C2×C22⋊C8—1221no—
157C2×#97—611no—
158#380—1221no—
159#342—1221no—
160#324—612no—
161#323—1221no—
162C61#732211yescharacteristic, complemented, Sylow
163C22×D4—611no—
164C23×C4—611no—
165C23×C4—611no—
166C2×M16—2441no—
167C22×C8—21no—
168C22×C8—1221no—
169C4×D4—2441no—
170C4×D4—2441no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—2441no—
173C2×C22⋊C4—611no—
174C2×C22⋊C4—611no—
175C2×C22⋊C4—1222no—
176C2×C42C2×#692311yescharacteristic
177C4⋊C8—41no—
178#99—2442no—
179C22⋊C8—1222no—
180C22⋊C8—2442no—
181C22⋊C8—2442no—
182C22⋊C8—2441no—
183#97—2441no—
184#95—2441no—
185C24—611no—
186C24—611no—
187C2×D4—1221no—
188C2×D4—1221no—
189C2×D4—2441no—
190C2×D4—2441no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—1221no—
194C22×C4—1221no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4—2441no—
198C22×C4—2441no—
199C22×C4—2441no—
200C22×C4—2441no—
201C22×C4—2442no—
202C22×C4C4×#692311yescharacteristic
203C22×C4C4⋊#692311yescharacteristic
204C22×C4C22⋊#692311yescharacteristic
205M16—4881no—
206M16—4881no—
207C2×C8—41no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—1222no—
211C2×C8—2442no—
212C2×C8—2441no—
213C2×C8—2441no—
214C4⋊C4—4881no—
215C4⋊C4—4881no—
216C4⋊C4—2441no—
217C22⋊C4—2441no—
218C22⋊C4—2441no—
219C22⋊C4—2442no—
220C22⋊C4—2442no—
221C42—21no—
222C42—21no—
223C23—611no—
224C23—611no—
225C23—1221no—
226C23—1221no—
227C23—1221no—
228C23—1221no—
229C23—1221no—
230C23—2441no—
231C23—2441no—
232C23—2441no—
233C23—2441no—
234C23(C2×#6923)⋊C411yescharacteristic
235D4—2442no—
236D4—2442no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—4881no—
247C2×C4—4881no—
248C2×C4—4882no—
249C2×C4—4882no—
250C2×C4—4882no—
251C2×C4—2441no—
252C2×C4—2441no—
253C2×C4—2441no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4—2441no—
257C2×C4#1451983511yescharacteristic
258C2×C4#1451983611yescharacteristic
259C8—81no—
260C8—4882no—
261C8—2442no—
262C22—21no—
263C22—21no—
264C22—1221no—
265C22—1221no—
266C22—4881no—
267C22—4881no—
268C22—2442no—
269C22—2441no—
270C22—2441no—
271C22—2441no—
272C22—2441no—
273C22—2441no—
274C22—2441no—
275C22—2441no—
276C22#1684064011yescharacteristic
277C22#1684064111yescharacteristic
278C22#1684064511yescharacteristic
279C4—21no—
280C4—41no—
281C4—41no—
282C4—9762no—
283C4—2441no—
284C4—2441no—
285C4#1684066611yescharacteristic
286C4#1684066811yescharacteristic
287C2—21no—
288C2—21no—
289C2—4881no—
290C2—2441no—
291C2—2441no—
292C2#2146071911yescharacteristic
293C2#2146091411yescharacteristic
294C2#2146091911yescharacteristic
subgroupG/H
centerC22#16840640
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61#342
prime radicalC22×D244C2×C4
cosocleC2×C4×D244C22
hypercenterC2×C4⋊C8#6923
hypocenterC61#7322
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
8. #16840607C4semidirect
13. C2×#14519688C4semidirect
14. C2×C4⋊C8×C61C4semidirect
152. C2×C4⋊C8#6923semidirect
162. C61#7322semidirect

Maximal subgroups

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

subgroupindex
#214616802
#214610762
#214466162
#732261