Finite Group Databasebeta

← #30605712

Subgroups — #30605712

Order 15616.

352 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 78 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#21462153C211yesmaximal, characteristic, complemented
2#21461376C211yesmaximal, characteristic, complemented
3#21460838C212yesmaximal, complemented
4#21460833C212yesmaximal, complemented
5#21456393C211yesmaximal, characteristic
6C2×#14519851—21no—
7#16840765—21no—
8#16840683—21no—
9#16840683C2212yes—
10#16840626C2212yes—
11#16840625—21no—
12#16840307—21no—
13#16840166C2211yescharacteristic
14#16840137C2211yescharacteristic
15#16840107—21no—
16#16839998C411yescharacteristic
17#16839996—21no—
18D8×Dic61C411yescharacteristic
19#16839844C411yescharacteristic
20#16839842—21no—
21C2×C8×Dic61C2211yescharacteristic
22C61×#466C411yescharacteristic
23C2×#11758217—41no—
24#14519851—42no—
25C2×#11758187—22no—
26#14519844—41no—
27C4⋊#92420—22no—
28C2×#11758224—41no—
29C2×D488C2×C411yescharacteristic
30C2×#11758199—21no—
31C22×#92418D411yescharacteristic
32#14519776—21no—
33#14519773—21no—
34#14519763—41no—
35#14519751—21no—
36#14519749—41no—
37D4×Dic61—21no—
38#14519739—21no—
39#14519737—41no—
40C2×C4×Dic61D411yescharacteristic
41#14519711C2×C411yescharacteristic
42#14519710—21no—
43#14519699—21no—
44#14519698—21no—
45#14519697—21no—
46C8×Dic61C2×C411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61C2311yescharacteristic
50C2×D8×C61C2×C411yescharacteristic
51C22×C8×C61C2×C411yescharacteristic
52#121×C61—21no—
53#107×C61C2×C411yescharacteristic
54#102×C61—21no—
55C2×D4×C61—21no—
56C2×D4×C61—41no—
57C22×C4×C61C22⋊C411yescharacteristic
58C2×C22⋊D61—41no—
59C2×C22⋊D61—41no—
60C2×C22⋊D61—41no—
61C22×Dic61—41no—
62C22×Dic61D811yescharacteristic
63C22×Dic61SD1611yescharacteristic
64#11758224—84no—
65C2×D244—21no—
66C2×C4×D61—41no—
67C2×Dic122—41no—
68#11758217—82no—
69C2×#92420—42no—
70D8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61C22⋊C411yescharacteristic
73C2×C8×C61C22×C411yescharacteristic
74C4⋊C4×C61—21no—
75C22⋊C4×C61—41no—
76C22⋊Dic61—41no—
77#11758199—41no—
78#11758199—41no—
79#11758198—41no—
80#11758198—41no—
81C4⋊Dic61—21no—
82#11758196—41no—
83C4×Dic61C22⋊C411yescharacteristic
84C4×Dic61D811yescharacteristic
85C4×Dic61SD1611yescharacteristic
86C4×Dic61C2×D411yescharacteristic
87C2×#92418—21no—
88C2×#92418—21no—
89C2×#92418C22⋊C411yescharacteristic
90C2×#92418C2×D411yescharacteristic
91D488—41no—
92#11758187—42no—
93C23×C61—41no—
94C23×C61#10211yescharacteristic
95C22×D61—41no—
96D4×C61—41no—
97D4×C61—41no—
98D4×C61—82no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—41no—
102C2×C4×C61#10211yescharacteristic
103C2×C4×C61C2×C22⋊C411yescharacteristic
104C22⋊D61—82no—
105C22⋊D61—82no—
106C22⋊D61—81no—
107C22⋊D61—81no—
108C2×Dic61—22no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—41no—
112C2×Dic61—82no—
113C2×Dic61#10211yescharacteristic
114C2×Dic61#10211yescharacteristic
115C2×Dic61C2×D811yescharacteristic
116C2×Dic61C2×SD1611yescharacteristic
117D244—41no—
118D244—41no—
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—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—81no—
132C22×C61—81no—
133C22×C61—81no—
134C22×C61C2×#10211yescharacteristic
135C2×D61—81no—
136C2×D61—81no—
137C2×D61—81no—
138C4×C61—21no—
139C4×C61—81no—
140C4×C61#41311yescharacteristic
141C4×C61#41711yescharacteristic
142Dic61—21no—
143Dic61—21no—
144Dic61—81no—
145Dic61#36112yes—
146Dic61#50911yescharacteristic
147Dic61#51011yescharacteristic
148#3169—611no—
149#2150—611no—
150#1567—611no—
151#1365—612no—
152#1361—612no—
153C2×C61—41no—
154C2×C61—161no—
155C2×C61#154711yescharacteristic
156C2×C61#213911yescharacteristic
157C2×C61C2×#36111yescharacteristic
158D61—161no—
159#532—1221no—
160C2×M32—1221no—
161#500—611no—
162#493—611no—
163#486—1221no—
164#466—611no—
165#466—1221no—
166#466#692311yescharacteristic
167C4×D8—611no—
168C4×D8—611no—
169C4×D8—1221no—
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×C8C2×#692311yescharacteristic
184C4⋊Q8—1221no—
185#127—1221no—
186#124—2441no—
187#121—21no—
188#121—1221no—
189#121—2441no—
190C4×D4—1221no—
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×C8—611no—
209#41—4884no—
210C2×Q8—2441no—
211C2×D4—21no—
212C2×D4—41no—
213C2×D4—1221no—
214C2×D4—2441no—
215C2×D4—2441no—
216C2×D4—2441no—
217C22×C4—611no—
218C22×C4—611no—
219C22×C4—2441no—
220C22×C4—2441no—
221C22×C4C22⋊#692311yescharacteristic
222D8—41no—
223D8—2441no—
224D8—2441no—
225D8—2441no—
226M16—4882no—
227C2×C8—41no—
228C2×C8—611no—
229C2×C8—611no—
230C2×C8—1221no—
231C2×C8—1221no—
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—
245C42—611no—
246C16—2442no—
247C23—41no—
248C23—2441no—
249C23#1451983911yescharacteristic
250Q8—4882no—
251D4—41no—
252D4—41no—
253D4—82no—
254D4—4881no—
255D4—4881no—
256D4—4882no—
257D4—4882no—
258D4—2441no—
259D4—2441no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—611no—
266C2×C4—611no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1222no—
270C2×C4—4882no—
271C2×C4—4882no—
272C2×C4—2441no—
273C2×C4#1451983911yescharacteristic
274C2×C4C2×C22⋊#692311yescharacteristic
275C8—21no—
276C8—21no—
277C8—611no—
278C8—611no—
279C8—1221no—
280C8—4882no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—81no—
285C22—81no—
286C22—81no—
287C22—4881no—
288C22—4881no—
289C22—4881no—
290C22C2×#1451983911yescharacteristic
291C4—21no—
292C4—81no—
293C4—611no—
294C4—611no—
295C4—612no—
296C4—1221no—
297C4—1221no—
298C4—4881no—
299C4#1684074911yescharacteristic
300C4#1684075311yescharacteristic
301C2—41no—
302C2—161no—
303C2—9761no—
304C2#2146133111yescharacteristic
305C2#2146212711yescharacteristic
306C2D61⋊#36111yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#466C4
socleC22×C61C2×#102
prime radical#21456393C2
cosocleC8×Dic61C23
hypercenter#466#6923
hypocenterC61#11986
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #21462153C2semidirect
2. #21461376C2semidirect
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
#214621532
#214613762
#214608382
#214608332
#214563932
#1198661