Finite Group Databasebeta

← #30604407

Subgroups — #30604407

Order 15616.

450 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 102 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#21462026C211yesmaximal, characteristic, complemented
2#21461369C211yesmaximal, characteristic, complemented
3#21460774C212yesmaximal, complemented
4#21460773C212yesmaximal, complemented
5C4×D8×D61C211yesmaximal, characteristic
6C2×#14519852—21no—
7#16840781—21no—
8#16840650—21no—
9#16840648C2212yescomplemented
10#16840625C2212yescomplemented
11#16840624—21no—
12C2×D8×D61C411yescharacteristic
13C4×D4×D61—21no—
14C4×D488C411yescharacteristic
15D8×Dic61C2211yescharacteristic
16#16839844C2211yescharacteristic
17C4×#11758199—21no—
18#16839842—21no—
19#107×D61C411yescharacteristic
20#102×D61—21no—
21C4×C8×D61C2211yescharacteristic
22C4×D8×C61C411yescharacteristic
23#14519852—24no—
24C2×#11758187—22no—
25C4⋊#92420—22no—
26#14519834—41no—
27C4×#92420—41no—
28C2×D4×D61—21no—
29C22×C4×D61—41no—
30C2×D488C2×C411yescharacteristic
31C2×#11758199—21no—
32D8×D61—22no—
33D8×D61C814yescomplemented
34C2×C8×D61C2×C411yescharacteristic
35C2×C8×D61D411yescharacteristic
36C4×D244—21no—
37D4×Dic61—21no—
38#14519739—21no—
39C4×C22⋊D61—41no—
40#14519737—41no—
41C4⋊C4×D61—21no—
42C22⋊C4×D61—41no—
43C42×D61D411yescharacteristic
44#14519711C2×C411yescharacteristic
45#14519710—21no—
46#14519699—21no—
47#14519698—21no—
48#14519697—21no—
49C4×#92418D411yescharacteristic
50C8×Dic61D411yescharacteristic
51C8×Dic61C2311yescharacteristic
52C2×D8×C61C2×C411yescharacteristic
53C4×D4×C61—21no—
54#107×C61C2×C411yescharacteristic
55#102×C61—21no—
56C4×C8×C61C2×C411yescharacteristic
57C23×D61—41no—
58C2×D4×C61—21no—
59C22×C4×C61—41no—
60C2×C22⋊D61—41no—
61C22×Dic61—41no—
62D4×D61—24no—
63D4×D61—42no—
64C2×D244—21no—
65C2×C4×D61—41no—
66C2×C4×D61—41no—
67C2×C4×D61—41no—
68C2×C4×D61—84no—
69C2×C4×D61C22⋊C411yescharacteristic
70C2×C4×D61D811yescharacteristic
71C2×C4×D61SD1611yescharacteristic
72C2×#92420—42no—
73D8×C61—21no—
74D8×C61C2×C812yes—
75C2×C8×C61C22⋊C411yescharacteristic
76C2×C8×C61C22×C411yescharacteristic
77C4⋊C4×C61—21no—
78C22⋊C4×C61—41no—
79C42×C61C22⋊C411yescharacteristic
80C22⋊Dic61—41no—
81#11758199—24no—
82#11758198—41no—
83#11758198—41no—
84C4⋊Dic61—21no—
85#11758196—41no—
86C4×Dic61D811yescharacteristic
87C4×Dic61SD1611yescharacteristic
88C4×Dic61C2×D411yescharacteristic
89C2×#92418C22⋊C411yescharacteristic
90C2×#92418C2×D411yescharacteristic
91D488—21no—
92D488C2×C812yes—
93C8×D61—22no—
94C8×D61C2×C812yes—
95C8×D61M1612yes—
96#11758187—24no—
97C23×C61—41no—
98C22×D61—41no—
99C22×D61—44no—
100C22×D61—82no—
101C22×D61—82no—
102C22×D61#10211yescharacteristic
103D4×C61—22no—
104D4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—82no—
107C2×C4×C61#10211yescharacteristic
108C2×C4×C61#10211yescharacteristic
109C2×C4×C61C2×C22⋊C411yescharacteristic
110C22⋊D61—44no—
111C2×Dic61—41no—
112C2×Dic61—82no—
113C2×Dic61#10211yescharacteristic
114C2×Dic61C2×D811yescharacteristic
115C2×Dic61C2×SD1611yescharacteristic
116D244—22no—
117D244—41no—
118C4×D61—22no—
119C4×D61—41no—
120C4×D61—82no—
121C4×D61—82no—
122C4×D61—82no—
123C4×D61C22⋊C812yes—
124C4×D61#10412yes—
125#92420—82no—
126C8×C61—21no—
127C8×C61C22×C811yescharacteristic
128C8×C61C2×M1611yescharacteristic
129#92418—21no—
130#92418C22⋊C812yes—
131#11593—611nomaximal, Sylow
132C22×C61—42no—
133C22×C61—81no—
134C22×C61—81no—
135C22×C61C2×#10211yescharacteristic
136C2×D61—21no—
137C2×D61—21no—
138C2×D61—42no—
139C2×D61—88no—
140C2×D61—81no—
141C2×D61—81no—
142C2×D61D4⋊C812yes—
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—81no—
146C4×C61C2×C22⋊C811yescharacteristic
147C4×C61C2×#10411yescharacteristic
148Dic61—21no—
149Dic61—81no—
150Dic61D4⋊C812yes—
151Dic61#50912yes—
152C2×C4×D8—611no—
153C4×M32—611no—
154#1564—611no—
155#1331—612no—
156#1331—612no—
157C2×C61—82no—
158C2×C61C2×D4⋊C811yescharacteristic
159C2×C61#214011yescharacteristic
160C2×C61#214311yescharacteristic
161D61—22no—
162D61—82no—
163C22×D8—611no—
164C2×C4×D4—1221no—
165C2×M32—1221no—
166C4×D8—611no—
167C4×D8—611no—
168C4×D8—611no—
169C4×D8—1221no—
170C4×D8—1221no—
171C4×D8#692311yescharacteristic
172#431—1221no—
173C2×#107—611no—
174C2×#102—1221no—
175C2×C4×C8—611no—
176#346—1221no—
177C4×C16—612no—
178#335—612no—
179#334—1221no—
180C61#1159311yescharacteristic, complemented, Sylow
181C22×D4—1221no—
182C23×C4—2441no—
183C2×D8—614no—
184C2×D8—611no—
185C2×D8—1222no—
186C2×D8—1221no—
187C2×D8C2×#692311yescharacteristic
188C22×C8—611no—
189C22×C8—611no—
190C4×D4—21no—
191C4×D4—1221no—
192C4×D4—1221no—
193C4×D4—1221no—
194C4×D4—2441no—
195C4×D4—2441no—
196C2×C4⋊C4—1221no—
197C2×C22⋊C4—2441no—
198C2×C42—611no—
199M32—1224no—
200C2×C16—1222no—
201#107—611no—
202#107—1221no—
203#107C2×#692311yescharacteristic
204C4⋊C8—1222no—
205#102—21no—
206#102—1221no—
207#102—1221no—
208#102—1221no—
209C22⋊C8—2441no—
210C4×C8—611no—
211C4×C8—611no—
212C4×C8—611no—
213C4×C8—2441no—
214C4×C8C2×#692311yescharacteristic
215C24—2441no—
216C2×D4—21no—
217C2×D4—1224no—
218C2×D4—1221no—
219C2×D4—2442no—
220C2×D4—2441no—
221C22×C4—41no—
222C22×C4—611no—
223C22×C4—611no—
224C22×C4—611no—
225C22×C4—4884no—
226C22×C4—2441no—
227C22×C4—2441no—
228C22×C4—2441no—
229C22×C4—2441no—
230D8—21no—
231D8—612no—
232D8—1224no—
233D8—1221no—
234D8D61⋊C812yes—
235C2×C8—611no—
236C2×C8—612no—
237C2×C8—612no—
238C2×C8—611no—
239C2×C8—1222no—
240C2×C8—2442no—
241C2×C8C22⋊#692311yescharacteristic
242C2×C8C22×#692311yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—1221no—
245C4⋊C4—2441no—
246C22⋊C4—41no—
247C22⋊C4—2441no—
248C22⋊C4—2441no—
249C22⋊C4—2441no—
250C42—611no—
251C42—611no—
252C42—611no—
253C42C22⋊#692311yescharacteristic
254C16—1224no—
255C23—41no—
256C23—611no—
257C23—4882no—
258C23—4882no—
259C23—2444no—
260C23—2441no—
261D4—22no—
262D4—41no—
263D4—1222no—
264D4—2444no—
265D4—2441no—
266C2×C4—41no—
267C2×C4—82no—
268C2×C4—611no—
269C2×C4—611no—
270C2×C4—612no—
271C2×C4—612no—
272C2×C4—611no—
273C2×C4—1222no—
274C2×C4—4882no—
275C2×C4—4882no—
276C2×C4—4882no—
277C2×C4—4882no—
278C2×C4—2441no—
279C2×C4—2441no—
280C2×C4#1451983911yescharacteristic
281C2×C4#1451983911yescharacteristic
282C2×C4C2×C22⋊#692311yescharacteristic
283C8—21no—
284C8—612no—
285C8—1221no—
286C8—4882no—
287C8C2×D61⋊C811yescharacteristic
288C8D61⋊M1611yescharacteristic
289C22—42no—
290C22—81no—
291C22—81no—
292C22—612no—
293C22—1221no—
294C22—1221no—
295C22—4888no—
296C22—4881no—
297C22—4881no—
298C22—2442no—
299C22C2×#1451983911yescharacteristic
300C4—21no—
301C4—21no—
302C4—81no—
303C4—612no—
304C4—612no—
305C4—1221no—
306C4—4881no—
307C4D61⋊(C22⋊C8)11yescharacteristic
308C4D61⋊#10411yescharacteristic
309C2—82no—
310C2—1222no—
311C2—4882no—
312C2D61⋊(D4⋊C8)11yescharacteristic
313C2#2146212811yescharacteristic
314C2#2146213311yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC8×C61C22×C8
FrattiniC2×C8C22×#6923
FittingC4×D8×C61C4
socleC22×C61C2×#102
prime radicalC2×D8×D61C4
cosocleC8×Dic61C23
hypercenterC4×D8#6923
hypocenterC61#11593
LCSG ▷ C8×C61 ▷ 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. #21462026C2semidirect
2. #21461369C2semidirect
3. #21460774C2semidirect
4. #21460773C2semidirect
9. #16840648C22semidirect
10. #16840625C22semidirect
33. D8×D61C8semidirect
180. C61#11593semidirect

Maximal subgroups

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

subgroupindex
#214620262
#214613692
#214607742
#214607732
C4×D8×D612
#1159361