Finite Group Databasebeta

← #30604408

Subgroups — #30604408

Order 15616.

450 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 114 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#21462025C211yesmaximal, characteristic, complemented
2#21461366C211yesmaximal, characteristic, complemented
3#21460774C214yesmaximal, complemented
4C2×#16839844C211yesmaximal, characteristic
5C2×#14519851—21no—
6#16840778—21no—
7#16840651—21no—
8#16840648C2212yescomplemented
9#16840625C2212yescomplemented
10#16840623—21no—
11C22×D488C411yescharacteristic
12C2×#14519739—21no—
13#16839844—21no—
14#16839844—21no—
15#16839844C412yes—
16#16839844C2212yes—
17C2×#14519697—21no—
18C2×C8×Dic61C2211yescharacteristic
19C2×#107×C61C411yescharacteristic
20#14519851—24no—
21C2×#11758187—22no—
22C4⋊#92420—22no—
23C22⋊#92420—41no—
24C4×#92420—41no—
25C22×D244—21no—
26C22×C4×D61—41no—
27C2×D488—21no—
28C2×D488—22no—
29C2×D488C814yescomplemented
30C2×D488C2×C412yes—
31C22×#92418D411yescharacteristic
32#14519739—22no—
33#14519739—22no—
34#14519739—41no—
35#14519739—41no—
36C2×#11758198—41no—
37C2×C4×Dic61D411yescharacteristic
38#14519697—22no—
39#14519697—22no—
40C8×Dic61C2×C411yescharacteristic
41C8×Dic61D411yescharacteristic
42C8×Dic61D411yescharacteristic
43C8×Dic61C2311yescharacteristic
44C22×C8×C61C2×C411yescharacteristic
45C2×C4⋊C4×C61—21no—
46#107×C61—21no—
47#107×C61C2×C412yes—
48C23×D61—41no—
49C22×C4×C61—41no—
50C22×C4×C61C22⋊C411yescharacteristic
51C22×Dic61D811yescharacteristic
52C22×Dic61SD1611yescharacteristic
53C2×D244—24no—
54C2×D244—22no—
55C2×D244—41no—
56C2×D244—42no—
57C2×C4×D61—42no—
58C2×C4×D61—42no—
59C2×C4×D61—84no—
60C2×#92420—42no—
61C2×C8×C61C22⋊C411yescharacteristic
62C2×C8×C61C2×C812yes—
63C2×C8×C61M1612yes—
64C2×C8×C61C22×C411yescharacteristic
65C4⋊C4×C61—22no—
66C4⋊C4×C61—41no—
67#11758198—42no—
68#11758198—42no—
69C4×Dic61C22⋊C411yescharacteristic
70C4×Dic61D811yescharacteristic
71C4×Dic61SD1611yescharacteristic
72C4×Dic61C2×D411yescharacteristic
73C2×#92418—22no—
74C2×#92418C22⋊C411yescharacteristic
75C2×#92418C2×D411yescharacteristic
76D488—24no—
77D488—22no—
78D488C2×C814yes—
79#11758187—24no—
80C23×C61#10211yescharacteristic
81C22×D61—44no—
82C22×D61—42no—
83C22×D61—82no—
84C22×D61—82no—
85C2×C4×C61—42no—
86C2×C4×C61—82no—
87C2×C4×C61C22⋊C812yes—
88C2×C4×C61#10211yescharacteristic
89C2×C4×C61#10412yes—
90C2×C4×C61C2×C22⋊C411yescharacteristic
91C2×Dic61—22no—
92C2×Dic61—41no—
93C2×Dic61#10211yescharacteristic
94C2×Dic61#10211yescharacteristic
95C2×Dic61C2×D811yescharacteristic
96C2×Dic61C2×SD1611yescharacteristic
97D244—24no—
98D244—44no—
99D244—42no—
100C4×D61—84no—
101C4×D61—84no—
102#92420—82no—
103C8×C61C22⋊C812yes—
104C8×C61C22×C811yescharacteristic
105C8×C61C2×M1611yescharacteristic
106#92418—21no—
107#92418—21no—
108#11593—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—21no—
111C22×C61D4⋊C812yes—
112C22×C61C2×#10211yescharacteristic
113C2×D61—44no—
114C2×D61—88no—
115C2×D61—82no—
116C2×D61—82no—
117C4×C61—82no—
118C4×C61D4⋊C812yes—
119C4×C61C2×C22⋊C811yescharacteristic
120C4×C61C2×#10411yescharacteristic
121Dic61—21no—
122Dic61—21no—
123Dic61—21no—
124Dic61#50912yes—
125C2×C4×D8—611no—
126C4×M32—611no—
127#1564—611no—
128#1331—614no—
129C2×C61—22no—
130C2×C61C2×D4⋊C811yescharacteristic
131C2×C61#214011yescharacteristic
132C2×C61#214311yescharacteristic
133D61—84no—
134C22×D8—611no—
135C2×C4×D4—1221no—
136C2×M32—1221no—
137C4×D8—612no—
138C4×D8—612no—
139C4×D8—1221no—
140C4×D8—1221no—
141#431—1221no—
142C2×#107#692311yescharacteristic
143C2×#102—1221no—
144C2×C4×C8—611no—
145#346—1221no—
146C4×C16—612no—
147#335—612no—
148#334—1221no—
149C61#1159311yescharacteristic, complemented, Sylow
150C22×D4—1221no—
151C23×C4—2441no—
152C2×D8—614no—
153C2×D8—612no—
154C2×D8—1222no—
155C2×D8—1221no—
156C22×C8—611no—
157C22×C8C2×#692311yescharacteristic
158C4×D4—1222no—
159C4×D4—1222no—
160C4×D4—2441no—
161C4×D4—2441no—
162C2×C4⋊C4—21no—
163C2×C22⋊C4—2441no—
164C2×C42—611no—
165M32—1224no—
166C2×C16—1222no—
167#107—21no—
168#107C2×#692312yes—
169C4⋊C8—1222no—
170#102—1222no—
171#102—1222no—
172C22⋊C8—2441no—
173C4×C8—611no—
174C4×C8—611no—
175C4×C8—611no—
176C4×C8—611no—
177C4×C8—2441no—
178C24—2441no—
179C2×D4—1224no—
180C2×D4—1222no—
181C2×D4—2441no—
182C2×D4—2442no—
183C22×C4—41no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—4884no—
187C22×C4—2442no—
188C22×C4—2442no—
189C22×C4C22⋊#692311yescharacteristic
190D8—614no—
191D8—1224no—
192D8—1222no—
193C2×C8—611no—
194C2×C8—611no—
195C2×C8—1222no—
196C2×C8—2442no—
197C2×C8D61⋊C812yes—
198C2×C8#1175821312yes—
199C2×C8C22⋊#692311yescharacteristic
200C2×C8C22×#692311yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—41no—
203C22⋊C4—2442no—
204C22⋊C4—2442no—
205C42—611no—
206C42—611no—
207C42—611no—
208C42—611no—
209C16—1224no—
210C23—4882no—
211C23—4882no—
212C23—2442no—
213C23—2444no—
214C23#1451983911yescharacteristic
215D4—1224no—
216D4—2442no—
217D4—2444no—
218C2×C4—42no—
219C2×C4—82no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—611no—
224C2×C4—1222no—
225C2×C4—4884no—
226C2×C4—4884no—
227C2×C4—2441no—
228C2×C4#1451983412yes—
229C2×C4#1451983911yescharacteristic
230C2×C4#1451984212yes—
231C2×C4C2×C22⋊#692311yescharacteristic
232C8—1221no—
233C8—1221no—
234C8—4882no—
235C8#1451983412yes—
236C8C2×D61⋊C811yescharacteristic
237C8C2×#1175821311yescharacteristic
238C22—21no—
239C22—21no—
240C22—4888no—
241C22—4882no—
242C22—4882no—
243C22—2444no—
244C22#1684061012yes—
245C22C2×#1451983911yescharacteristic
246C4—82no—
247C4—612no—
248C4—1221no—
249C4—1221no—
250C4—1221no—
251C4#1684061012yes—
252C4C2×#1451983411yescharacteristic
253C4C2×#1451984211yescharacteristic
254C2—22no—
255C2—4884no—
256C2C2×#1684061011yescharacteristic
257C2#2146212811yescharacteristic
258C2#2146213511yescharacteristic
subgroupG/H
centerC22C2×#14519839
commutatorC8×C61C22×C8
FrattiniC2×C8C22×#6923
FittingC2×#107×C61C4
socleC22×C61C2×#102
prime radicalC22×D488C4
cosocleC8×Dic61C23
hypercenterC2×#107#6923
hypocenterC61#11593
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. #21462025C2semidirect
2. #21461366C2semidirect
3. #21460774C2semidirect
8. #16840648C22semidirect
9. #16840625C22semidirect
29. C2×D488C8semidirect
149. C61#11593semidirect

Maximal subgroups

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

subgroupindex
#214620252
#214613662
#214607742
C2×#168398442
#1159361