Finite Group Databasebeta

← #30605723

Subgroups — #30605723

Order 15616.

280 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 64 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#21462192C211yesmaximal, characteristic, complemented
2#21462162C211yesmaximal, characteristic, complemented
3#21460839C212yesmaximal, complemented
4#21460829C212yesmaximal, complemented
5#21456441C211yesmaximal, characteristic
6C2×#14519851—21no—
7#16840685—21no—
8#16840685C2212yes—
9#16840685C2212yes—
10#16840658—21no—
11#16840654—21no—
12#16840374C411yescharacteristic
13#16840161C2211yescharacteristic
14#16840134C2211yescharacteristic
15#16840132C411yescharacteristic
16#16840126C411yescharacteristic
17#16840006—21no—
18#16839989—21no—
19#16839862—21no—
20C4×#11758200—21no—
21#16839718C2211yescharacteristic
22C61×#540C411yescharacteristic
23#14519851—22no—
24#14519851—22no—
25#14519851—41no—
26C2×#11758187—41no—
27C2×#11758200—21no—
28C2×#11758200—21no—
29C2×#11758194D411yescharacteristic
30C22×#92418D411yescharacteristic
31#14519777C2×C411yescharacteristic
32#14519770—41no—
33#14519769C2×C411yescharacteristic
34#14519767—41no—
35#14519756—21no—
36C4×Dic122—21no—
37#14519710—21no—
38#14519708—21no—
39#14519700—21no—
40#14519700—21no—
41#14519698—21no—
42#14519698—21no—
43#14519688C2×C411yescharacteristic
44#14519688D411yescharacteristic
45C4×#92418D411yescharacteristic
46C4×#92418C2311yescharacteristic
47#127×C61C2×C411yescharacteristic
48#125×C61C2×C411yescharacteristic
49#123×C61—41no—
50#121×C61—21no—
51#121×C61—41no—
52C4×D4×C61—21no—
53#117×C61C2×C411yescharacteristic
54C2×D4×C61—21no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61C22⋊C411yescharacteristic
59C2×Dic122—21no—
60C4⋊C4×C61—21no—
61C4⋊C4×C61—21no—
62C4⋊C4×C61—41no—
63C22⋊C4×C61—21no—
64C22⋊C4×C61—41no—
65C22⋊C4×C61—41no—
66C42×C61C22⋊C411yescharacteristic
67C42×C61C22×C411yescharacteristic
68C22⋊Dic61—41no—
69#11758200—42no—
70#11758200—41no—
71#11758200—41no—
72C4⋊Dic61—21no—
73C4⋊Dic61—41no—
74#11758196—41no—
75#11758196—41no—
76#11758196—41no—
77C4×Dic61—41no—
78#11758194—22no—
79C2×#92418—21no—
80C2×#92418—21no—
81C2×#92418C22⋊C411yescharacteristic
82C2×#92418C22⋊C411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84C2×#92418C2×D411yescharacteristic
85#11758187—42no—
86#11758187—42no—
87C23×C61—41no—
88C23×C61#10011yescharacteristic
89D4×C61—41no—
90D4×C61—41no—
91D4×C61—161no—
92D4×C61—161no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—41no—
98C2×C4×C61—161no—
99C2×C4×C61#10011yescharacteristic
100C2×C4×C61C2×C22⋊C411yescharacteristic
101C2×Dic61—41no—
102C2×Dic61—41no—
103Dic122—41no—
104Dic122—41no—
105#92418—21no—
106#92418—21no—
107#92418#13512yes—
108#92418AGL(1,ℤ/8)11yescharacteristic
109#92418#13711yescharacteristic
110#11991—611nomaximal, Sylow
111C22×C61—21no—
112C22×C61—41no—
113C22×C61—81no—
114C22×C61—81no—
115C22×C61—81no—
116C22×C61C2×#10011yescharacteristic
117C4×C61—21no—
118C4×C61—41no—
119C4×C61—41no—
120C4×C61—81no—
121C4×C61#41611yescharacteristic
122C4×C61#41711yescharacteristic
123Dic61—81no—
124Dic61—81no—
125#3174—611no—
126#2166—611no—
127#2153—611no—
128#1366—612no—
129#1359—612no—
130C2×C61—21no—
131C2×C61—41no—
132C2×C61—161no—
133C2×C61#155111yescharacteristic
134#541—611no—
135#540#692311yescharacteristic
136C2×M32—1221no—
137#499—611no—
138#492—611no—
139#491—611no—
140#490—611no—
141#468—1221no—
142#465—1221no—
143#440—1221no—
144C4×SD16—1221no—
145#405—611no—
146#364—612no—
147#364—612no—
148#364—1221no—
149#349—1221no—
150#347—1221no—
151C61#1199111yescharacteristic, complemented, Sylow
152C2×SD16—1221no—
153C2×SD16—1221no—
154C2×M16—611no—
155C22×C8—611no—
156C4⋊Q8—611no—
157#127C2×#692311yescharacteristic
158#126—2441no—
159#125—611no—
160#125—2441no—
161#125C2×#692311yescharacteristic
162#123—41no—
163C22⋊Q8—1221no—
164#121—21no—
165#121—41no—
166C4×Q8—1221no—
167C4×D4—21no—
168#117C2×#692311yescharacteristic
169M32—1222no—
170M32—1222no—
171M32—2441no—
172C2×C16—2441no—
173#107—1221no—
174#106—1221no—
175#103—1221no—
176#103—1221no—
177#102—1221no—
178#102—1221no—
179#97—611no—
180#97—611no—
181C4×C8—611no—
182C4×C8—611no—
183C2×Q8—1221no—
184C2×D4—21no—
185C2×D4—41no—
186C2×D4—41no—
187C22×C4—41no—
188C22×C4C22⋊#692311yescharacteristic
189SD16—2442no—
190SD16—2441no—
191SD16—2441no—
192M16—1222no—
193C2×C8—611no—
194C2×C8—611no—
195C2×C8—611no—
196C2×C8—611no—
197C2×C8—1221no—
198C2×C8—1221no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—41no—
202C4⋊C4—1221no—
203C4⋊C4—2441no—
204C4⋊C4—2441no—
205C4⋊C4—2441no—
206C4⋊C4—2441no—
207C22⋊C4—21no—
208C22⋊C4—41no—
209C22⋊C4—41no—
210C22⋊C4—2441no—
211C42—2441no—
212C42C22⋊#692311yescharacteristic
213C42C22×#692311yescharacteristic
214C16—2442no—
215C16—2442no—
216C23—41no—
217C23#1451983711yescharacteristic
218Q8—2441no—
219Q8—2441no—
220D4—41no—
221D4—41no—
222D4—161no—
223D4—161no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—161no—
230C2×C4—2441no—
231C2×C4—2441no—
232C2×C4#1451983711yescharacteristic
233C2×C4C2×C22⋊#692311yescharacteristic
234C8—612no—
235C8—611no—
236C8—611no—
237C8—1221no—
238C8—1221no—
239C22—21no—
240C22—41no—
241C22—81no—
242C22—81no—
243C22—81no—
244C22C2×#1451983711yescharacteristic
245C4—21no—
246C4—41no—
247C4—41no—
248C4—81no—
249C4—4881no—
250C4—4881no—
251C4#1684075211yescharacteristic
252C4#1684075311yescharacteristic
253C2—21no—
254C2—41no—
255C2—161no—
256C2#2146133811yescharacteristic
subgroupG/H
centerC2#21461338
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
Fitting, prime radicalC61×#540C4
socleC2×C61#1551
cosocleC4×#92418C23
hypercenter#540#6923
hypocenterC61#11991
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #21462192C2semidirect
2. #21462162C2semidirect
3. #21460839C2semidirect
4. #21460829C2semidirect
151. C61#11991semidirect

Maximal subgroups

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

subgroupindex
#214621922
#214621622
#214608392
#214608292
#214564412
#1199161