Finite Group Databasebeta

← #30604034

Subgroups — #30604034

Order 15616.

364 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462056C212yesmaximal, complemented
2#21460765C212yesmaximal, complemented
3#21460754C212yesmaximal, complemented
4#21454538C211yesmaximal, characteristic
5D61⋊M32—22no—
6#16840659—22no—
7#16840658C2214yes—
8C2×#14519783C411yescharacteristic
9C2×#14519783C2211yescharacteristic
10#16840312C411yescharacteristic
11#16839835—22no—
12#16839835—22no—
13#16839786C2211yescharacteristic
14#16839728C411yescharacteristic
15#16839728C2211yescharacteristic
16C2×#97×C61C411yescharacteristic
17#14519852—42no—
18#14519851—24no—
19D61⋊C16—42no—
20C2×#11758222C2×C411yescharacteristic
21C2×#11758222C2×C411yescharacteristic
22#14519783—42no—
23#14519783—42no—
24C2×#11758194C2×C411yescharacteristic
25C2×#11758194C2311yescharacteristic
26C2×#11758189—21no—
27C2×#11758189D412yes—
28C2×C8×D61—21no—
29C2×C8×D61D412yes—
30#14519777C811yescharacteristic
31#14519774C811yescharacteristic
32#14519765C811yescharacteristic
33#14519765C811yescharacteristic
34#14519751—22no—
35C4×D244—22no—
36C4⋊#92418—22no—
37#14519689—22no—
38#14519689—22no—
39C22×C8×C61C2×C411yescharacteristic
40C22×C8×C61C2×C411yescharacteristic
41C2×C42×C61C2×C411yescharacteristic
42#97×C61—21no—
43#97×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61C22×C411yescharacteristic
46C2×C22⋊D61—21no—
47C2×C22⋊D61M1612yes—
48#11758222—41no—
49#11758222—41no—
50#11758222—41no—
51#11758222—41no—
52C2×D244—22no—
53C2×D244C2×C811yescharacteristic
54C2×D244C2×C811yescharacteristic
55C2×C4×D61—21no—
56C2×C4×D61C22⋊C412yes—
57C2×Dic122C2×C811yescharacteristic
58C2×Dic122C2×C811yescharacteristic
59C2×C8×C61—22no—
60C2×C8×C61—21no—
61C2×C8×C61—41no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22⋊C411yescharacteristic
64C42×C61—21no—
65C42×C61C2×C811yescharacteristic
66C42×C61C2×C811yescharacteristic
67#11758198—22no—
68#11758198—22no—
69C4⋊Dic61—22no—
70#11758194—41no—
71#11758194—41no—
72C2×#92418—21no—
73C2×#92418C2×D412yes—
74#11758189—42no—
75#11758189—42no—
76C8×D61—22no—
77C8×D61—22no—
78C8×D61—42no—
79#11758187—44no—
80C23×C61C2×M1611yescharacteristic
81C22×D61—21no—
82C22×D61C22⋊C812yes—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—81no—
88C2×C4×C61C2×C22⋊C411yescharacteristic
89C2×C4×C61C22×C811yescharacteristic
90C22⋊D61—42no—
91C22⋊D61—42no—
92C2×Dic61—21no—
93C2×Dic61C22⋊C812yes—
94D244—41no—
95D244—41no—
96D244—82no—
97C4×D61—22no—
98C4×D61—22no—
99C4×D61—41no—
100C4×D61—41no—
101Dic122—41no—
102Dic122—41no—
103C8×C61—21no—
104C8×C61—41no—
105C8×C61#9912yes—
106#92418—22no—
107#92418—41no—
108#11486—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—41no—
111C22×C61C2×C22⋊C811yescharacteristic
112C2×D61—22no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61—41no—
116C4×C61—21no—
117C4×C61—41no—
118C4×C61—41no—
119C4×C61C2×#9911yescharacteristic
120C4×C61#41311yescharacteristic
121Dic61—22no—
122Dic61—41no—
123#2932—611no—
124#2115—612no—
125#1327—612no—
126#1321—612no—
127C2×C61—21no—
128C2×C61—41no—
129C2×C61#145911yescharacteristic
130D61—42no—
131D61—81no—
132C2×#131—611no—
133C2×#131—611no—
134#532—611no—
135C2×M32—1222no—
136#435—1222no—
137#435—1222no—
138#423—611no—
139#408—611no—
140#408—611no—
141C2×#97#692311yescharacteristic
142#349—614no—
143#349—1222no—
144C61#1148611yescharacteristic, complemented, Sylow
145C2×#41—611no—
146C2×#41—611no—
147#131—2442no—
148#131—2442no—
149C2×M16—611no—
150C2×M16—612no—
151C2×M16—611no—
152C2×M16—1221no—
153C22×C8—612no—
154C22×C8—1221no—
155C22×C8C2×#692311yescharacteristic
156C22×C8C2×#692311yescharacteristic
157C4⋊Q8—611no—
158#127—611no—
159#124—611no—
160#124—611no—
161#121—1222no—
162C4×D4—1222no—
163C2×C42C2×#692311yescharacteristic
164M32—1224no—
165M32—2442no—
166C2×C16—2442no—
167C4⋊C8—1222no—
168C22⋊C8—1222no—
169C22⋊C8—1222no—
170#97—21no—
171#97—21no—
172#41—2441no—
173#41—2441no—
174#41—2441no—
175#41—2441no—
176C2×Q8—611no—
177C2×Q8—611no—
178C2×D4—612no—
179C2×D4—611no—
180C2×D4—611no—
181C2×D4—1222no—
182C2×D4—1221no—
183C22×C4—21no—
184C22×C4—612no—
185C22×C4—1221no—
186C22×C4C22×#692311yescharacteristic
187M16—2442no—
188M16—2441no—
189M16—2442no—
190M16—2441no—
191C2×C8—22no—
192C2×C8—21no—
193C2×C8—41no—
194C2×C8—612no—
195C2×C8—1222no—
196C2×C8—1222no—
197C2×C8—1221no—
198C2×C8—2442no—
199C2×C8C22⋊#692311yescharacteristic
200C2×C8C22⋊#692311yescharacteristic
201C4⋊C4—1222no—
202C22⋊C4—1222no—
203C22⋊C4—1222no—
204C42—21no—
205C42D61⋊C811yescharacteristic
206C42D61⋊C811yescharacteristic
207C16—2444no—
208C23—612no—
209C23—1221no—
210C23D61⋊M1611yescharacteristic
211Q8—2441no—
212Q8—2441no—
213D4—4882no—
214D4—2441no—
215D4—2441no—
216D4—2442no—
217D4—2442no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—81no—
223C2×C4—612no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1221no—
227C2×C4—2441no—
228C2×C4—2441no—
229C2×C4C2×C22⋊#692311yescharacteristic
230C2×C4C2×D61⋊C811yescharacteristic
231C8—21no—
232C8—41no—
233C8—1222no—
234C8—2441no—
235C8#1451983612yes—
236C22—21no—
237C22—41no—
238C22—1222no—
239C22—2442no—
240C22—2442no—
241C22—2441no—
242C22D61⋊(C22⋊C8)11yescharacteristic
243C4—21no—
244C4—41no—
245C4—41no—
246C4—1222no—
247C4—2441no—
248C4C2×#1451983611yescharacteristic
249C4#1684074811yescharacteristic
250C2—21no—
251C2—41no—
252C2—4881no—
253C2—2442no—
254C2#2146105611yescharacteristic
subgroupG/H
centerC4C2×#14519836
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#97×C61C4
socleC2×C61#1459
prime radical#16840312C4
cosocleC2×#11758194C23
hypercenterC2×#97#6923
hypocenterC61#11486
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C22×C8 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
1. #21462056C2semidirect
2. #21460765C2semidirect
3. #21460754C2semidirect
144. C61#11486semidirect

Maximal subgroups

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

subgroupindex
#214620562
#214607652
#214607542
#214545382
#1148661