Finite Group Databasebeta

← #30601065

Subgroups — #30601065

Order 15616.

488 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 74 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#21462704C211yesmaximal, characteristic
2#21461349C212yesmaximal, complemented
3#21461308C211yesmaximal, characteristic
4#21460686C212yesmaximal, complemented
5#21456273C211yesmaximal, characteristic
6#16840793—24no—
7#16840785C2212yes—
8#16840785C2212yes—
9#16840735—22no—
10#16840621—24no—
11#16840617—22no—
12C2×#14519806—22no—
13#16840310C2211yescharacteristic
14C4⋊Q8×D61C2211yescharacteristic
15#16840153—22no—
16#16840142C411yescharacteristic
17#16840141C411yescharacteristic
18#16840134C411yescharacteristic
19C4×#11758189C2211yescharacteristic
20C61×#492C411yescharacteristic
21C2×#11758217—22no—
22C22×#92420—22no—
23#14519844—22no—
24#14519844D414yes—
25#14519834—22no—
26#14519834—22no—
27C22⋊#92420—24no—
28#14519832—22no—
29#14519832—22no—
30C2×#11758224D412yes—
31C2×Q8×D61—21no—
32#14519806—44no—
33#14519806—44no—
34C2×Dic244—22no—
35C2×#11758202—22no—
36C2×#11758200—22no—
37C2×#11758189—21no—
38#14519777C2×C411yescharacteristic
39#14519777C2×C411yescharacteristic
40#14519776—22no—
41#14519775—21no—
42#14519764D412yes—
43#14519748—22no—
44D4×Dic61—22no—
45C4⋊C4×D61—22no—
46C42×D61C2311yescharacteristic
47#14519687—21no—
48C4×#92418C2×C411yescharacteristic
49C2×SD16×C61—22no—
50C4⋊Q8×C61C2×C411yescharacteristic
51#127×C61C2×C411yescharacteristic
52C4×C8×C61C2×C411yescharacteristic
53C2×Q8×C61—21no—
54C2×D4×C61—22no—
55C2×D4×C61C22⋊C412yes—
56C2×C22⋊D61—22no—
57C22×Dic61—22no—
58Q8×D61—42no—
59Q8×D61—42no—
60#11758224—42no—
61#11758224—42no—
62C2×C4×D61—41no—
63C2×C4×D61C2×D411yescharacteristic
64C2×C4×D61#4112yes—
65C2×Dic122—21no—
66C2×Dic122—41no—
67C2×Dic122C22⋊C412yes—
68#11758217—82no—
69C2×#92420—24no—
70C2×#92420—42no—
71C2×#92420—82no—
72SD16×C61—44no—
73C2×C8×C61—21no—
74C4⋊C4×C61—22no—
75C42×C61C22×C411yescharacteristic
76C22⋊Dic61—24no—
77#11758202—44no—
78#11758200—44no—
79C4⋊Dic61—22no—
80C4⋊Dic61—22no—
81#11758196—42no—
82C4×Dic61C2×D412yes—
83C4×Dic61C2×D411yescharacteristic
84C2×#92418—21no—
85Dic244—44no—
86#11758189—24no—
87C23×C61—22no—
88C22×D61#12311yescharacteristic
89Q8×C61—42no—
90D4×C61—42no—
91D4×C61—82no—
92C2×C4×C61—41no—
93C2×C4×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61C4×D412yes—
95C22⋊D61—82no—
96C2×Dic61—22no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—41no—
100C2×Dic61#12011yescharacteristic
101C2×Dic61#12112yes—
102C4×D61—22no—
103C4×D61—42no—
104C4×D61—81no—
105C4×D61—81no—
106Dic122—42no—
107Dic122—42no—
108Dic122—82no—
109#92420—44no—
110#92420—82no—
111C8×C61—22no—
112#92418—22no—
113#9421—611nomaximal, Sylow
114C22×C61—42no—
115C22×C61—44no—
116C22×C61#38611yescharacteristic
117C2×D61—21no—
118C2×D61—22no—
119C4×C61—21no—
120C4×C61—22no—
121C4×C61—81no—
122Dic61—22no—
123Dic61—42no—
124Dic61—81no—
125Dic61#45312yes—
126#3152—611no—
127#2980—611no—
128#1556—612no—
129#1536—611no—
130#1291—612no—
131C2×C61—82no—
132C2×C61#188711yescharacteristic
133C2×C61#190212yes—
134D61—41no—
135C2×#137—1222no—
136#532—611no—
137C2×C4⋊Q8—611no—
138#497—1222no—
139#494—611no—
140#494—611no—
141#492—611no—
142#492#692311yescharacteristic
143#435—1224no—
144#432—612no—
145#432—612no—
146#408—1222no—
147C4×M16—611no—
148#332—1224no—
149#329—1222no—
150C61#942111yescharacteristic, complemented, Sylow
151C2×#41—612no—
152C22×Q8—1221no—
153#137—2444no—
154#137—2444no—
155C2×Q16—1222no—
156C2×Q16—1222no—
157C2×SD16—22no—
158C2×SD16—1222no—
159C2×M16—1221no—
160C2×M16—1222no—
161C22×C8—1222no—
162C4⋊Q8—611no—
163C4⋊Q8—611no—
164C4⋊Q8—1222no—
165C4⋊Q8—1221no—
166C4⋊Q8C2×#692311yescharacteristic
167#127C2×#692311yescharacteristic
168#124—612no—
169#121—1222no—
170C4×D4—1222no—
171C2×C4⋊C4—1222no—
172C2×C42—611no—
173C4⋊C8—614no—
174C4⋊C8—1222no—
175C22⋊C8—1222no—
176C22⋊C8—1224no—
177C22⋊C8—1222no—
178#97—1221no—
179#97—1222no—
180#97—1222no—
181C4×C8—611no—
182C4×C8C2×#692311yescharacteristic
183#41—2442no—
184#41—2442no—
185C2×Q8—21no—
186C2×Q8—612no—
187C2×Q8—1221no—
188C2×Q8—2441no—
189C2×Q8—2442no—
190C2×Q8—2442no—
191C2×D4—22no—
192C2×D4—1222no—
193C2×D4C22⋊#692312yes—
194C22×C4—611no—
195C22×C4—612no—
196C22×C4—1222no—
197C22×C4—2441no—
198Q16—2444no—
199Q16—2444no—
200SD16—44no—
201SD16—2444no—
202M16—1224no—
203M16—4882no—
204C2×C8—21no—
205C2×C8—1221no—
206C2×C8—1224no—
207C2×C8—4882no—
208C2×C8—2442no—
209C4⋊C4—22no—
210C4⋊C4—1222no—
211C4⋊C4—1222no—
212C4⋊C4—2442no—
213C22⋊C4—1224no—
214C42—611no—
215C42—612no—
216C42C22×#692311yescharacteristic
217C23—22no—
218C23—611no—
219Q8—42no—
220Q8—4882no—
221Q8—2442no—
222Q8—2442no—
223D4—42no—
224D4—82no—
225D4—4882no—
226C2×C4—41no—
227C2×C4—611no—
228C2×C4—612no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—4881no—
232C2×C4—4881no—
233C2×C4—2442no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2441no—
237C2×C4C2×C22⋊#692311yescharacteristic
238C2×C4D4×#692312yes—
239C8—22no—
240C8—1222no—
241C8—4882no—
242C8—2444no—
243C22—42no—
244C22—44no—
245C22—1221no—
246C22—1222no—
247C22#1684071011yescharacteristic
248C4—21no—
249C4—22no—
250C4—81no—
251C4—612no—
252C4—1222no—
253C4—4881no—
254C4—2442no—
255C2—82no—
256C2—2441no—
257C2#2146182611yescharacteristic
258C2#2146184812yes—
subgroupG/H
centerC22#16840710
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC22×C61#386
prime radical#16840310C22
cosocleC42×D61C23
hypercenter#492#6923
hypocenterC61#9421
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #21461349C2semidirect
4. #21460686C2semidirect
150. C61#9421semidirect

Maximal subgroups

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

subgroupindex
#214627042
#214613492
#214613082
#214606862
#214562732
#942161