Finite Group Databasebeta

← #29569283

Subgroups — #29569283

Order 15616.

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

normal subgroups only

This group has 418 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#21447383C212yesmaximal, complemented
3#21447352C211yesmaximal, characteristic
4#21443641C212yesmaximal, complemented
5C61×#1270C211yesmaximal, characteristic
6C2×#14519758—21no—
7C2×#14519708—21no—
8C2×#14519698—21no—
9#16839692—21no—
10#16839687—22no—
11#16839660C2212yes—
12#16839637—22no—
13#16839632C2211yescharacteristic
14#16839525—22no—
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#14519708—42no—
32#14519698—42no—
33#14519684—21no—
34#14519684—22no—
35#14519684—22no—
36C22×D4×C61D411yescharacteristic
37C22×C8×C61—22no—
38C2×C4⋊C4×C61D411yescharacteristic
39C2×C22⋊C4×C61—22no—
40C2×C42×C61C2311yescharacteristic
41C24×C61—21no—
42C2×D4×C61—21no—
43C2×D4×C61—41no—
44C2×D4×C61—41no—
45C2×D4×C61SD1612yes—
46C22×C4×C61—21no—
47C22×C4×C61C2×D411yescharacteristic
48C22×C4×C61C2×D412yes—
49C22×Dic61—22no—
50C22×Dic61—22no—
51C22×Dic61—42no—
52C22×Dic61—41no—
53C22×Dic61—81no—
54C22×Dic61—81no—
55C2×C8×C61—42no—
56C2×C8×C61—42no—
57C2×C8×C61—42no—
58C4⋊C4×C61—41no—
59C22⋊C4×C61—42no—
60C22⋊C4×C61—42no—
61C42×C61—41no—
62C22⋊Dic61—42no—
63C22⋊Dic61—44no—
64C4⋊Dic61—22no—
65C4⋊Dic61—22no—
66C4⋊Dic61—42no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69C4⋊Dic61—44no—
70C4⋊Dic61—81no—
71#11758196—42no—
72#11758196—42no—
73C2×#92418—22no—
74C2×#92418—41no—
75C2×#92418—41no—
76C23×C61—22no—
77C23×C61—42no—
78C23×C61—41no—
79C23×C61—42no—
80C23×C61—41no—
81C23×C61#12011yescharacteristic
82D4×C61—42no—
83D4×C61—81no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—42no—
89C2×C4×C61—41no—
90C2×C4×C61C2×SD1611yescharacteristic
91C2×C4×C61#13512yes—
92C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
93C2×C4×C61#13712yes—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—42no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—84no—
101C2×Dic61—81no—
102C2×Dic61—82no—
103C8×C61—82no—
104#92418—42no—
105#7824—611nomaximal, Sylow
106C22×C61—42no—
107C22×C61—44no—
108C22×C61—82no—
109C22×C61—81no—
110C22×C61—81no—
111C22×C61#45011yescharacteristic
112C22×C61#45212yes—
113C22×C61#45311yescharacteristic
114C22×C61#45412yes—
115C22×C61#45811yescharacteristic
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—22no—
119C4×C61—22no—
120C4×C61—81no—
121Dic61—82no—
122Dic61—82no—
123Dic61—161no—
124#2724—611no—
125#2100—612no—
126#2094—611no—
127#1271—612no—
128#1270D6111yescharacteristic
129C2×C61—82no—
130C2×C61#161311yescharacteristic
131C2×C61#161512yes—
132C2×C61#163011yescharacteristic
133C2×C61#163512yes—
134C2×C61#165711yescharacteristic
135C2×#123—1221no—
136C2×#106—1221no—
137C2×#102—1221no—
138#398—1221no—
139#397—1222no—
140#390C2×D6111yescharacteristic
141#389—612no—
142#385—1222no—
143#384—611no—
144#340—1222no—
145#340—1222no—
146#336—611no—
147#336C2×D6112yes—
148C61#782411yescharacteristic, complemented, Sylow
149C22×D4D24411yescharacteristic
150C23×C4—1221no—
151C22×C8—22no—
152C22×C8—1221no—
153#123—2442no—
154#123—2442no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—1221no—
158C2×C4⋊C4—1222no—
159C2×C4⋊C4—1221no—
160C2×C4⋊C4—1222no—
161C2×C4⋊C4D24411yescharacteristic
162C2×C22⋊C4—22no—
163C2×C22⋊C4—1222no—
164C2×C22⋊C4—1221no—
165C2×C42C22×D6111yescharacteristic
166#106—2442no—
167#102—2442no—
168#95—1222no—
169#95—1221no—
170#95—1222no—
171C24—21no—
172C2×D4—21no—
173C2×D4—41no—
174C2×D4—41no—
175C2×D4#1175819012yes—
176C22×C4—21no—
177C22×C4—1222no—
178C22×C4—1222no—
179C22×C4—4881no—
180C22×C4—4881no—
181C22×C4—2441no—
182C22×C4—2442no—
183C22×C4C2×D24411yescharacteristic
184C22×C4D4×D6112yes—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—42no—
188C2×C8—1222no—
189C2×C8—2441no—
190C2×C8—2441no—
191C4⋊C4—41no—
192C4⋊C4—1222no—
193C4⋊C4—1222no—
194C4⋊C4—4881no—
195C4⋊C4—2441no—
196C4⋊C4—2441no—
197C4⋊C4—2444no—
198C4⋊C4—2442no—
199C4⋊C4—2442no—
200C4⋊C4—2442no—
201C22⋊C4—42no—
202C22⋊C4—42no—
203C22⋊C4—2442no—
204C22⋊C4—2444no—
205C42—41no—
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23#1451974711yescharacteristic
212D4—42no—
213D4—81no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—4882no—
221C2×C4—4881no—
222C2×C4—4884no—
223C2×C4—2442no—
224C2×C4—2442no—
225C2×C4—2442no—
226C2×C4—2442no—
227C2×C4—2442no—
228C2×C4—2442no—
229C2×C4C2×#1175819011yescharacteristic
230C2×C4#1451979612yes—
231C2×C4#1451980511yescharacteristic
232C2×C4#1451980612yes—
233C8—82no—
234C8—2442no—
235C22—44no—
236C22—42no—
237C22—81no—
238C22—82no—
239C22—81no—
240C22#1683991511yescharacteristic
241C22#1683992512yes—
242C22#1683993211yescharacteristic
243C22#1683993612yes—
244C22#1683995311yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—81no—
250C4—9761no—
251C4—4882no—
252C4—4882no—
253C2—82no—
254C2#2144484111yescharacteristic
255C2#2144485112yes—
256C2#2144494111yescharacteristic
257C2#2144497212yes—
258C2#2144511811yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#1270D61
hypocenterC61#7824
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
2. #21447383C2semidirect
4. #21443641C2semidirect
148. C61#7824semidirect

Maximal subgroups

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

subgroupindex
#214527492
#214473832
#214473522
#214436412
C61×#12702
#782461