Finite Group Databasebeta

← #30605702

Subgroups — #30605702

Order 15616.

358 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 86 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
1C2×#16840683C211yesmaximal, characteristic, complemented
2#21461376C211yesmaximal, characteristic, complemented
3#21460837C212yesmaximal, complemented
4#21460833C212yesmaximal, complemented
5#21456393C211yesmaximal, characteristic
6C22×#11758187—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—
24C2×#11758187—22no—
25C2×#11758187—42no—
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—82no—
65#11758224—82no—
66C2×D244—21no—
67C2×C4×D61—41no—
68C2×Dic122—41no—
69#11758217—82no—
70C2×#92420—42no—
71D8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61C22⋊C411yescharacteristic
74C2×C8×C61C22×C411yescharacteristic
75C4⋊C4×C61—21no—
76C22⋊C4×C61—41no—
77C22⋊Dic61—41no—
78#11758199—41no—
79#11758199—41no—
80#11758198—41no—
81#11758198—41no—
82C4⋊Dic61—21no—
83#11758196—41no—
84C4×Dic61C22⋊C411yescharacteristic
85C4×Dic61D811yescharacteristic
86C4×Dic61SD1611yescharacteristic
87C4×Dic61C2×D411yescharacteristic
88C2×#92418—21no—
89C2×#92418—21no—
90C2×#92418C22⋊C411yescharacteristic
91C2×#92418C2×D411yescharacteristic
92D488—41no—
93#11758187—42no—
94C23×C61—41no—
95C23×C61#10211yescharacteristic
96C22×D61—41no—
97D4×C61—41no—
98D4×C61—41no—
99D4×C61—82no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—41no—
103C2×C4×C61#10211yescharacteristic
104C2×C4×C61C2×C22⋊C411yescharacteristic
105C22⋊D61—82no—
106C22⋊D61—82no—
107C22⋊D61—81no—
108C22⋊D61—81no—
109C2×Dic61—41no—
110C2×Dic61—41no—
111C2×Dic61—82no—
112C2×Dic61#10211yescharacteristic
113C2×Dic61#10211yescharacteristic
114C2×Dic61D1612yes—
115C2×Dic61SD3212yes—
116C2×Dic61C2×D811yescharacteristic
117C2×Dic61C2×SD1611yescharacteristic
118D244—41no—
119D244—41no—
120C4×D61—82no—
121Dic122—81no—
122Dic122—81no—
123#92420—82no—
124C8×C61—21no—
125C8×C61—21no—
126#92418—21no—
127#92418AGL(1,ℤ/8)11yescharacteristic
128#92418#13711yescharacteristic
129#11981—611nomaximal, Sylow
130C22×C61—21no—
131C22×C61—21no—
132C22×C61—81no—
133C22×C61—81no—
134C22×C61—81no—
135C22×C61#35712yes—
136C22×C61C2×#10211yescharacteristic
137C2×D61—81no—
138C2×D61—81no—
139C2×D61—81no—
140C4×C61—21no—
141C4×C61—81no—
142C4×C61#41311yescharacteristic
143C4×C61#41711yescharacteristic
144Dic61—21no—
145Dic61—21no—
146Dic61—81no—
147Dic61#35712yes—
148Dic61C2×D1611yescharacteristic
149Dic61C2×SD3211yescharacteristic
150#3169—611no—
151C2×C4⋊C16—611no—
152#1567—611no—
153#1364—612no—
154#1361—612no—
155C2×C61—22no—
156C2×C61—161no—
157C2×C61#154711yescharacteristic
158C2×C61C2×#35711yescharacteristic
159C2×C61#214811yescharacteristic
160D61—161no—
161#532—1221no—
162C22×C16—1221no—
163#500—611no—
164#493—611no—
165#486—1221no—
166#466—611no—
167#466—1221no—
168#466#692311yescharacteristic
169C4×D8—611no—
170C4×D8—611no—
171C4×D8—1221no—
172#423—1221no—
173C2×C4×C8—611no—
174C4⋊C16—612no—
175C4⋊C16—1221no—
176#335—612no—
177#335—1221no—
178C61#1198111yescharacteristic, complemented, Sylow
179C2×#41—2441no—
180C2×D8—611no—
181C2×D8—1221no—
182C2×D8C2×#692311yescharacteristic
183C2×M16—2441no—
184C22×C8—611no—
185C22×C8C2×#692311yescharacteristic
186C4⋊Q8—1221no—
187#127—1221no—
188#124—2441no—
189#121—21no—
190#121—1221no—
191#121—2441no—
192C4×D4—1221no—
193C4×D4—1221no—
194C4×D4—2441no—
195C2×C42—611no—
196C2×C16—1222no—
197C2×C16—2442no—
198#107—611no—
199#107—1221no—
200#107C2×#692311yescharacteristic
201C4⋊C8—1222no—
202C4⋊C8—2441no—
203#102—21no—
204#102—1221no—
205#102—1221no—
206#102—1221no—
207C4×C8—611no—
208C4×C8—611no—
209C4×C8—611no—
210C4×C8—611no—
211#41—4882no—
212#41—4882no—
213C2×Q8—2441no—
214C2×D4—21no—
215C2×D4—41no—
216C2×D4—1221no—
217C2×D4—2441no—
218C2×D4—2441no—
219C2×D4—2441no—
220C22×C4—611no—
221C22×C4—611no—
222C22×C4—2441no—
223C22×C4—2441no—
224C22×C4C22⋊#692311yescharacteristic
225D8—41no—
226D8—2441no—
227D8—2441no—
228D8—2441no—
229M16—4882no—
230C2×C8—41no—
231C2×C8—611no—
232C2×C8—611no—
233C2×C8—1221no—
234C2×C8—1221no—
235C2×C8—2442no—
236C2×C8C22⋊#692311yescharacteristic
237C2×C8C22×#692311yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—1221no—
240C4⋊C4—2441no—
241C22⋊C4—41no—
242C22⋊C4—2441no—
243C22⋊C4—2441no—
244C22⋊C4—2441no—
245C42—611no—
246C42—611no—
247C42—611no—
248C42—611no—
249C16—2442no—
250C23—41no—
251C23—2441no—
252C23#1451983911yescharacteristic
253Q8—4881no—
254Q8—4881no—
255D4—41no—
256D4—41no—
257D4—82no—
258D4—4881no—
259D4—4881no—
260D4—4882no—
261D4—4882no—
262D4—2441no—
263D4—2441no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—611no—
268C2×C4—611no—
269C2×C4—612no—
270C2×C4—612no—
271C2×C4—611no—
272C2×C4—611no—
273C2×C4—4882no—
274C2×C4—4882no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4#1451983911yescharacteristic
278C2×C4C2×C22⋊#692311yescharacteristic
279C8—21no—
280C8—21no—
281C8—611no—
282C8—611no—
283C8—1221no—
284C8—4882no—
285C22—21no—
286C22—21no—
287C22—81no—
288C22—81no—
289C22—81no—
290C22—4881no—
291C22—4881no—
292C22—4881no—
293C22#1684067412yes—
294C22C2×#1451983911yescharacteristic
295C4—21no—
296C4—81no—
297C4—612no—
298C4—611no—
299C4—611no—
300C4—1221no—
301C4—1221no—
302C4—4881no—
303C4#1684074911yescharacteristic
304C4#1684075311yescharacteristic
305C2—22no—
306C2—161no—
307C2—9761no—
308C2#2146133111yescharacteristic
309C2C2×#1684067411yescharacteristic
310C2#2146214611yescharacteristic
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#11981
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. C2×#16840683C2semidirect
2. #21461376C2semidirect
3. #21460837C2semidirect
4. #21460833C2semidirect
178. C61#11981semidirect

Maximal subgroups

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

subgroupindex
C2×#168406832
#214613762
#214608372
#214608332
#214563932
#1198161