Finite Group Databasebeta

← #30605711

Subgroups — #30605711

Order 15616.

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

normal subgroups only

This group has 352 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#21462152C211yesmaximal, characteristic, complemented
2#21461378C211yesmaximal, characteristic, complemented
3#21460838C212yesmaximal, complemented
4#21460833C212yesmaximal, complemented
5#21456395C211yesmaximal, characteristic
6C2×#14519852—21no—
7#16840766—21no—
8#16840683C2212yes—
9C4⋊#11758187—21no—
10#16840626—21no—
11#16840626C2212yes—
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×#11758213—41no—
24#14519852—42no—
25C2×#11758187—22no—
26C4⋊#92420—22no—
27C4⋊#92420—41no—
28C2×#11758222—41no—
29C2×D488C2×C411yescharacteristic
30C2×#11758199—21no—
31C2×C8×D61C2×C411yescharacteristic
32C2×C8×D61D411yescharacteristic
33#14519776—21no—
34#14519773—21no—
35#14519763—41no—
36#14519752—21no—
37#14519750—41no—
38#14519748—21no—
39C4×D244—21no—
40C4×C22⋊D61—41no—
41C42×D61D411yescharacteristic
42#14519711C2×C411yescharacteristic
43#14519710—21no—
44#14519699—21no—
45#14519698—21no—
46#14519697—21no—
47C4×#92418D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×D8×C61C2×C411yescharacteristic
51C4×D4×C61—21no—
52#107×C61C2×C411yescharacteristic
53#102×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×D4×C61—21no—
56C22×C4×C61—41no—
57C2×C22⋊D61—41no—
58C2×C22⋊D61—41no—
59C2×C22⋊D61—41no—
60#11758222—84no—
61C2×D244—21no—
62C2×D244—41no—
63C2×C4×D61—41no—
64C2×C4×D61C22⋊C411yescharacteristic
65C2×C4×D61D811yescharacteristic
66C2×C4×D61SD1611yescharacteristic
67C2×Dic122—41no—
68C2×#92420—42no—
69#11758213—82no—
70D8×C61—41no—
71C2×C8×C61C22⋊C411yescharacteristic
72C2×C8×C61C22×C411yescharacteristic
73C4⋊C4×C61—21no—
74C22⋊C4×C61—41no—
75C42×C61C22⋊C411yescharacteristic
76C22⋊Dic61—41no—
77#11758199—41no—
78#11758199—41no—
79#11758198—41no—
80#11758198—41no—
81C4⋊Dic61—21no—
82#11758196—41no—
83C4×Dic61D811yescharacteristic
84C4×Dic61SD1611yescharacteristic
85C4×Dic61C2×D411yescharacteristic
86C2×#92418C22⋊C411yescharacteristic
87C2×#92418C2×D411yescharacteristic
88D488—41no—
89C8×D61—21no—
90C8×D61—21no—
91C8×D61—41no—
92#11758187—42no—
93C23×C61—41no—
94C22×D61—41no—
95C22×D61#10211yescharacteristic
96D4×C61—41no—
97D4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—82no—
100C2×C4×C61#10211yescharacteristic
101C2×C4×C61#10211yescharacteristic
102C2×C4×C61C2×C22⋊C411yescharacteristic
103C22⋊D61—82no—
104C22⋊D61—82no—
105C22⋊D61—81no—
106C22⋊D61—81no—
107C2×Dic61—41no—
108C2×Dic61#10211yescharacteristic
109C2×Dic61C2×D811yescharacteristic
110C2×Dic61C2×SD1611yescharacteristic
111D244—41no—
112D244—41no—
113D244—82no—
114C4×D61—22no—
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—21no—
118C4×D61—21no—
119C4×D61—82no—
120Dic122—82no—
121#92420—82no—
122C8×C61—21no—
123C8×C61—21no—
124#92418—21no—
125#92418AGL(1,ℤ/8)11yescharacteristic
126#92418#13711yescharacteristic
127#11986—611nomaximal, Sylow
128C22×C61—81no—
129C22×C61—81no—
130C22×C61—81no—
131C22×C61C2×#10211yescharacteristic
132C2×D61—21no—
133C2×D61—21no—
134C2×D61—21no—
135C2×D61—81no—
136C2×D61—81no—
137C2×D61—81no—
138C4×C61—21no—
139C4×C61—81no—
140C4×C61#36112yes—
141C4×C61#41311yescharacteristic
142C4×C61#41711yescharacteristic
143Dic61—21no—
144Dic61—21no—
145Dic61—81no—
146Dic61#50911yescharacteristic
147Dic61#51011yescharacteristic
148#3169—611no—
149#2150—611no—
150#1567—611no—
151#1365—612no—
152#1361—612no—
153C2×C61—161no—
154C2×C61#154711yescharacteristic
155C2×C61#213911yescharacteristic
156C2×C61C2×#36111yescharacteristic
157D61—41no—
158D61—161no—
159#532—1221no—
160C2×M32—1221no—
161#500—611no—
162#493—611no—
163#486—1221no—
164#466—611no—
165#466—611no—
166#466—1221no—
167C4×D8—611no—
168C4×D8—1221no—
169C4×D8#692311yescharacteristic
170#423—1221no—
171C2×C4×C8—611no—
172C4⋊C16—612no—
173C4⋊C16—1221no—
174#335—612no—
175#335—1221no—
176C61#1198611yescharacteristic, complemented, Sylow
177C2×#41—2441no—
178C2×D8—611no—
179C2×D8—1221no—
180C2×D8C2×#692311yescharacteristic
181C2×M16—2441no—
182C22×C8—611no—
183C22×C8—611no—
184C4⋊Q8—1221no—
185#127—1221no—
186#124—2441no—
187#121—1221no—
188#121—1221no—
189#121—2441no—
190C4×D4—21no—
191C4×D4—1221no—
192C4×D4—2441no—
193C2×C42—611no—
194M32—2442no—
195C2×C16—1222no—
196#107—611no—
197#107—1221no—
198#107C2×#692311yescharacteristic
199C4⋊C8—1222no—
200C4⋊C8—2441no—
201#102—21no—
202#102—1221no—
203#102—1221no—
204#102—1221no—
205C4×C8—611no—
206C4×C8—611no—
207C4×C8—611no—
208C4×C8C2×#692311yescharacteristic
209#41—4884no—
210C2×Q8—2441no—
211C2×D4—21no—
212C2×D4—1221no—
213C2×D4—2441no—
214C2×D4—2441no—
215C2×D4—2441no—
216C2×D4—2441no—
217C22×C4—41no—
218C22×C4—611no—
219C22×C4—611no—
220C22×C4—611no—
221C22×C4—2441no—
222D8—41no—
223D8—2441no—
224D8—2441no—
225D8—2441no—
226M16—4882no—
227C2×C8—611no—
228C2×C8—611no—
229C2×C8—1221no—
230C2×C8—1221no—
231C2×C8—2441no—
232C2×C8—2442no—
233C2×C8C22⋊#692311yescharacteristic
234C2×C8C22×#692311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—1221no—
237C4⋊C4—2441no—
238C22⋊C4—41no—
239C22⋊C4—2441no—
240C22⋊C4—2441no—
241C22⋊C4—2441no—
242C42—611no—
243C42—611no—
244C42—611no—
245C42C22⋊#692311yescharacteristic
246C16—2442no—
247C23—41no—
248C23—611no—
249C23—2441no—
250Q8—4882no—
251D4—41no—
252D4—41no—
253D4—4882no—
254D4—4881no—
255D4—4881no—
256D4—4882no—
257D4—4882no—
258D4—2441no—
259D4—2441no—
260C2×C4—41no—
261C2×C4—82no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1222no—
270C2×C4—4882no—
271C2×C4—2441no—
272C2×C4#1451983911yescharacteristic
273C2×C4#1451983911yescharacteristic
274C2×C4C2×C22⋊#692311yescharacteristic
275C8—21no—
276C8—21no—
277C8—611no—
278C8—611no—
279C8—1221no—
280C8—4882no—
281C22—81no—
282C22—81no—
283C22—81no—
284C22—1221no—
285C22—1221no—
286C22—1221no—
287C22—4881no—
288C22—4881no—
289C22—4881no—
290C22C2×#1451983911yescharacteristic
291C4—21no—
292C4—81no—
293C4—611no—
294C4—611no—
295C4—1221no—
296C4—1221no—
297C4—4881no—
298C4#1684068012yes—
299C4#1684074811yescharacteristic
300C4#1684075311yescharacteristic
301C2—161no—
302C2—9761no—
303C2—2441no—
304C2#2146133011yescharacteristic
305C2#2146212711yescharacteristic
306C2C2×#1684068011yescharacteristic
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#11986
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. #21462152C2semidirect
2. #21461378C2semidirect
3. #21460838C2semidirect
4. #21460833C2semidirect
176. C61#11986semidirect

Maximal subgroups

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

subgroupindex
#214621522
#214613782
#214608382
#214608332
#214563952
#1198661