Finite Group Databasebeta

← #30605624

Subgroups — #30605624

Order 15616.

340 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 76 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#21462182C211yesmaximal, characteristic, complemented
2#21461367C211yesmaximal, characteristic, complemented
3#21460837C212yesmaximal, complemented
4#21460833C212yesmaximal, complemented
5#21456395C211yesmaximal, characteristic
6#16840781—21no—
7#16840683C2212yes—
8#16840657—21no—
9#16840650—21no—
10#16840626C2212yes—
11#16840623—21no—
12#16840309—21no—
13#16840166C2211yescharacteristic
14#16840137C2211yescharacteristic
15#16840107—21no—
16#16839999C411yescharacteristic
17#16839997—21no—
18#16839995C411yescharacteristic
19C4×D488C411yescharacteristic
20C4×#11758199—21no—
21C4×C8×D61C2211yescharacteristic
22C4×D8×C61C411yescharacteristic
23C2×#11758187—22no—
24C4⋊#92420—22no—
25#14519834—41no—
26C4×#92420—41no—
27C2×#11758222—41no—
28C2×D488C2×C411yescharacteristic
29C2×#11758199—21no—
30C2×C8×D61C2×C411yescharacteristic
31C2×C8×D61D411yescharacteristic
32#14519776—21no—
33#14519773—21no—
34#14519763—41no—
35#14519752—21no—
36#14519750—41no—
37#14519748—21no—
38C4×D244—21no—
39C4×C22⋊D61—41no—
40C42×D61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519710—21no—
43#14519699—21no—
44#14519698—21no—
45#14519697—21no—
46C4×#92418D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61C2311yescharacteristic
49C2×D8×C61C2×C411yescharacteristic
50C4×D4×C61—21no—
51#107×C61C2×C411yescharacteristic
52#102×C61—21no—
53C4×C8×C61C2×C411yescharacteristic
54C2×D4×C61—21no—
55C22×C4×C61—41no—
56C2×C22⋊D61—41no—
57C2×C22⋊D61—41no—
58C2×C22⋊D61—41no—
59#11758222—84no—
60C2×D244—21no—
61C2×D244—41no—
62C2×C4×D61—41no—
63C2×C4×D61C22⋊C411yescharacteristic
64C2×C4×D61D811yescharacteristic
65C2×C4×D61SD1611yescharacteristic
66C2×Dic122—41no—
67C2×#92420—42no—
68D8×C61—41no—
69C2×C8×C61C22⋊C411yescharacteristic
70C2×C8×C61C22×C411yescharacteristic
71C4⋊C4×C61—21no—
72C22⋊C4×C61—41no—
73C42×C61C22⋊C411yescharacteristic
74C22⋊Dic61—41no—
75#11758199—42no—
76#11758198—41no—
77#11758198—41no—
78C4⋊Dic61—21no—
79#11758196—41no—
80C4×Dic61D811yescharacteristic
81C4×Dic61SD1611yescharacteristic
82C4×Dic61C2×D411yescharacteristic
83C2×#92418C22⋊C411yescharacteristic
84C2×#92418C2×D411yescharacteristic
85D488—41no—
86C8×D61—22no—
87C8×D61—41no—
88#11758187—42no—
89C23×C61—41no—
90C22×D61—41no—
91C22×D61#10211yescharacteristic
92D4×C61—41no—
93D4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61—82no—
96C2×C4×C61#10211yescharacteristic
97C2×C4×C61#10211yescharacteristic
98C2×C4×C61C2×C22⋊C411yescharacteristic
99C22⋊D61—82no—
100C22⋊D61—82no—
101C22⋊D61—82no—
102C2×Dic61—41no—
103C2×Dic61#10211yescharacteristic
104C2×Dic61C2×D811yescharacteristic
105C2×Dic61C2×SD1611yescharacteristic
106D244—41no—
107D244—41no—
108D244—82no—
109C4×D61—21no—
110C4×D61—21no—
111C4×D61—22no—
112C4×D61—41no—
113C4×D61—82no—
114Dic122—82no—
115#92420—82no—
116C8×C61—21no—
117C8×C61—21no—
118#92418—21no—
119#92418#13512yes—
120#11951—611nomaximal, Sylow
121C22×C61—81no—
122C22×C61—81no—
123C22×C61—81no—
124C22×C61C2×#10211yescharacteristic
125C2×D61—21no—
126C2×D61—21no—
127C2×D61—21no—
128C2×D61—81no—
129C2×D61—81no—
130C2×D61—81no—
131C4×C61—21no—
132C4×C61—21no—
133C4×C61—81no—
134C4×C61#41311yescharacteristic
135C4×C61#41611yescharacteristic
136Dic61—21no—
137Dic61—21no—
138Dic61—81no—
139Dic61#50912yes—
140#3169—611no—
141#2163—611no—
142#1564—611no—
143#1364—612no—
144#1361—612no—
145C2×C61—161no—
146C2×C61#154011yescharacteristic
147C2×C61#214011yescharacteristic
148C2×C61#214811yescharacteristic
149D61—41no—
150D61—161no—
151#532—1221no—
152#500—611no—
153#493—611no—
154#486—1221no—
155#466—611no—
156#466—611no—
157#466—1221no—
158C4×D8—611no—
159C4×D8—1221no—
160C4×D8#692311yescharacteristic
161#431—1221no—
162C2×C4×C8—611no—
163C4⋊C16—612no—
164C22⋊C16—1221no—
165#346—1221no—
166#335—612no—
167#334—1221no—
168C61#1195111yescharacteristic, complemented, Sylow
169C2×#41—2441no—
170C2×D8—611no—
171C2×D8—1221no—
172C2×D8C2×#692311yescharacteristic
173C22×C8—611no—
174C22×C8—611no—
175C4⋊Q8—1221no—
176#127—1221no—
177#124—2441no—
178#121—1221no—
179#121—1221no—
180#121—2441no—
181C4×D4—21no—
182C4×D4—1221no—
183C4×D4—2441no—
184C2×C42—611no—
185C2×C16—1222no—
186#107—611no—
187#107—1221no—
188#107C2×#692311yescharacteristic
189C4⋊C8—1222no—
190#102—21no—
191#102—1221no—
192#102—1221no—
193#102—1221no—
194C22⋊C8—2441no—
195C4×C8—611no—
196C4×C8—611no—
197C4×C8—611no—
198C4×C8—2441no—
199C4×C8C2×#692311yescharacteristic
200#41—4884no—
201C2×Q8—2441no—
202C2×D4—21no—
203C2×D4—1221no—
204C2×D4—2441no—
205C2×D4—2441no—
206C2×D4—2441no—
207C2×D4—2441no—
208C22×C4—41no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—2441no—
213D8—41no—
214D8—2441no—
215D8—2442no—
216C2×C8—611no—
217C2×C8—611no—
218C2×C8—1222no—
219C2×C8—2441no—
220C2×C8—2442no—
221C2×C8C22⋊#692311yescharacteristic
222C2×C8C22×#692311yescharacteristic
223C4⋊C4—21no—
224C4⋊C4—1221no—
225C4⋊C4—2441no—
226C22⋊C4—41no—
227C22⋊C4—2441no—
228C22⋊C4—2441no—
229C22⋊C4—2441no—
230C42—611no—
231C42—611no—
232C42—611no—
233C42C22⋊#692311yescharacteristic
234C16—2442no—
235C23—41no—
236C23—611no—
237C23—2441no—
238Q8—4882no—
239D4—41no—
240D4—41no—
241D4—4882no—
242D4—4882no—
243D4—4882no—
244D4—4882no—
245D4—2441no—
246D4—2441no—
247C2×C4—41no—
248C2×C4—82no—
249C2×C4—611no—
250C2×C4—611no—
251C2×C4—611no—
252C2×C4—1222no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—4882no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4#1451983911yescharacteristic
259C2×C4#1451983911yescharacteristic
260C2×C4C2×C22⋊#692311yescharacteristic
261C8—21no—
262C8—21no—
263C8—612no—
264C8—1221no—
265C8—4882no—
266C22—81no—
267C22—81no—
268C22—81no—
269C22—1221no—
270C22—1221no—
271C22—1221no—
272C22—4881no—
273C22—4881no—
274C22—4881no—
275C22C2×#1451983911yescharacteristic
276C4—21no—
277C4—21no—
278C4—81no—
279C4—612no—
280C4—1221no—
281C4—1221no—
282C4—4881no—
283C4#1684074811yescharacteristic
284C4#1684075211yescharacteristic
285C2—161no—
286C2—9761no—
287C2—2441no—
288C2#2146131611yescharacteristic
289C2#2146212811yescharacteristic
290C2#2146214711yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC4×D8×C61C4
socleC22×C61C2×#102
prime radical#21456395C2
cosocleC8×Dic61C23
hypercenterC4×D8#6923
hypocenterC61#11951
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #21462182C2semidirect
2. #21461367C2semidirect
3. #21460837C2semidirect
4. #21460833C2semidirect
168. C61#11951semidirect

Maximal subgroups

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

subgroupindex
#214621822
#214613672
#214608372
#214608332
#214563952
#1195161