Finite Group Databasebeta

← #29569257

Subgroups — #29569257

Order 15616.

434 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 83 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#21452749C211yesmaximal, characteristic
2#21447347C211yesmaximal, characteristic
3#21447297C212yesmaximal, complemented
4#21443641C212yesmaximal, complemented
5C61×#1270C211yesmaximal, characteristic
6C2×#14519758—21no—
7C2×#14519710—21no—
8C2×#14519709—22no—
9C2×#14519698—21no—
10#16839692—21no—
11#16839687—22no—
12#16839660C2212yes—
13#16839637—22no—
14#16839632C2211yescharacteristic
15#16839525—22no—
16#16839517C2211yescharacteristic
17C61×#390C2211yescharacteristic
18C61×#336C2212yes—
19C23×Dic61—21no—
20C22×#92418—21no—
21#14519758—42no—
22#14519758—42no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61—22no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61D412yes—
27C2×C4⋊Dic61D412yes—
28C2×#11758196—22no—
29C2×C22⋊Dic61—21no—
30C2×C22⋊Dic61—22no—
31#14519710—42no—
32#14519709—44no—
33#14519698—42no—
34#14519684—21no—
35#14519684—22no—
36#14519684—22no—
37C22×D4×C61D411yescharacteristic
38C22×C8×C61—22no—
39C2×C4⋊C4×C61D411yescharacteristic
40C2×C22⋊C4×C61—22no—
41C2×C42×C61C2311yescharacteristic
42C24×C61—21no—
43C2×D4×C61—21no—
44C2×D4×C61—41no—
45C2×D4×C61—41no—
46C2×D4×C61SD1612yes—
47C22×C4×C61—21no—
48C22×C4×C61C2×D411yescharacteristic
49C22×C4×C61C2×D412yes—
50C22×Dic61—22no—
51C22×Dic61—22no—
52C22×Dic61—42no—
53C22×Dic61—41no—
54C22×Dic61—81no—
55C22×Dic61—81no—
56C2×C8×C61—24no—
57C2×C8×C61—42no—
58C2×C8×C61—42no—
59C4⋊C4×C61—41no—
60C22⋊C4×C61—42no—
61C22⋊C4×C61—42no—
62C42×C61—41no—
63C22⋊Dic61—42no—
64C22⋊Dic61—44no—
65C4⋊Dic61—22no—
66C4⋊Dic61—22no—
67C4⋊Dic61—42no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70C4⋊Dic61—42no—
71C4⋊Dic61—42no—
72C4⋊Dic61—81no—
73#11758196—42no—
74#11758196—42no—
75C2×#92418—22no—
76C2×#92418—41no—
77C2×#92418—41no—
78C23×C61—22no—
79C23×C61—42no—
80C23×C61—41no—
81C23×C61—42no—
82C23×C61—41no—
83C23×C61#12011yescharacteristic
84D4×C61—42no—
85D4×C61—81no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—42no—
91C2×C4×C61—41no—
92C2×C4×C61C2×SD1611yescharacteristic
93C2×C4×C61#13512yes—
94C2×C4×C61AGL(1,ℤ/8)12yes—
95C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102C2×Dic61—84no—
103C2×Dic61—82no—
104C2×Dic61—81no—
105C8×C61—44no—
106#92418—42no—
107#7819—611nomaximal, Sylow
108C22×C61—42no—
109C22×C61—44no—
110C22×C61—82no—
111C22×C61—81no—
112C22×C61—81no—
113C22×C61#44912yes—
114C22×C61#45011yescharacteristic
115C22×C61#45311yescharacteristic
116C22×C61#45612yes—
117C22×C61#45811yescharacteristic
118C4×C61—22no—
119C4×C61—22no—
120C4×C61—21no—
121C4×C61—21no—
122C4×C61—81no—
123Dic61—82no—
124Dic61—82no—
125Dic61—161no—
126#2724—611no—
127#2093—611no—
128#2084—612no—
129#1271—612no—
130#1270D6111yescharacteristic
131C2×C61—82no—
132C2×C61#160912yes—
133C2×C61#161311yescharacteristic
134C2×C61#162011yescharacteristic
135C2×C61#165412yes—
136C2×C61#166011yescharacteristic
137C2×#123—1221no—
138C2×#107—1221no—
139C2×#106—1222no—
140C2×#102—1221no—
141#398—1221no—
142#397—1222no—
143#390C2×D6111yescharacteristic
144#389—612no—
145#385—1222no—
146#384—611no—
147#340—1222no—
148#336—611no—
149#336C2×D6112yes—
150C61#781911yescharacteristic, complemented, Sylow
151C22×D4D24411yescharacteristic
152C23×C4—1221no—
153C22×C8—22no—
154C22×C8—1221no—
155#123—2442no—
156#123—2442no—
157C2×C4⋊C4—612no—
158C2×C4⋊C4—612no—
159C2×C4⋊C4—1221no—
160C2×C4⋊C4—1222no—
161C2×C4⋊C4—1221no—
162C2×C4⋊C4—1222no—
163C2×C4⋊C4D24411yescharacteristic
164C2×C22⋊C4—22no—
165C2×C22⋊C4—1222no—
166C2×C22⋊C4—1221no—
167C2×C42C22×D6111yescharacteristic
168#107—2442no—
169#106—2444no—
170#102—2442no—
171#95—1222no—
172#95—1221no—
173#95—1222no—
174C24—21no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4#1175819012yes—
179C22×C4—21no—
180C22×C4—1222no—
181C22×C4—1222no—
182C22×C4—4881no—
183C22×C4—4881no—
184C22×C4—2441no—
185C22×C4—2442no—
186C22×C4C2×D24411yescharacteristic
187C22×C4D4×D6112yes—
188C2×C8—24no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—1222no—
192C2×C8—2441no—
193C2×C8—2441no—
194C4⋊C4—41no—
195C4⋊C4—1222no—
196C4⋊C4—1222no—
197C4⋊C4—4881no—
198C4⋊C4—2441no—
199C4⋊C4—2441no—
200C4⋊C4—2442no—
201C4⋊C4—2442no—
202C4⋊C4—2442no—
203C4⋊C4—2442no—
204C4⋊C4—2442no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C22⋊C4—2442no—
208C22⋊C4—2444no—
209C42—41no—
210C23—22no—
211C23—42no—
212C23—41no—
213C23—42no—
214C23—41no—
215C23#1451974711yescharacteristic
216D4—42no—
217D4—81no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—4882no—
225C2×C4—4881no—
226C2×C4—4884no—
227C2×C4—2442no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4—2442no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4C2×#1175819011yescharacteristic
234C2×C4#1451979812yes—
235C2×C4#1451980112yes—
236C2×C4#1451980511yescharacteristic
237C8—44no—
238C8—2442no—
239C22—42no—
240C22—44no—
241C22—81no—
242C22—81no—
243C22—82no—
244C22#1683990812yes—
245C22#1683991511yescharacteristic
246C22#1683993211yescharacteristic
247C22#1683994612yes—
248C22#1683995311yescharacteristic
249C4—22no—
250C4—22no—
251C4—21no—
252C4—21no—
253C4—81no—
254C4—9761no—
255C4—4882no—
256C4—4882no—
257C2—82no—
258C2#2144481712yes—
259C2#2144484111yescharacteristic
260C2#2144487911yescharacteristic
261C2#2144510612yes—
262C2#2144513111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#1270D61
hypocenterC61#7819
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
3. #21447297C2semidirect
4. #21443641C2semidirect
150. C61#7819semidirect

Maximal subgroups

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

subgroupindex
#214527492
#214473472
#214472972
#214436412
C61×#12702
#781961