Finite Group Databasebeta

← #29574389

Subgroups — #29574389

Order 15616.

428 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 119 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#21449005C211yesmaximal, characteristic
2#21446789C211yesmaximal, characteristic
3#21445987C212yesmaximal
4#21443701C212yesmaximal
5C2×C61×#330C211yesmaximal, characteristic
6C2×#14519711—22no—
7C2×#14519709—22no—
8C2×#14519688C2211yescharacteristic
9#16839661—22no—
10#16839648—22no—
11#16839648—22no—
12#16839632C2211yescharacteristic
13#16839628C2212yes—
14#16839524—22no—
15C2×#125×C61C2211yescharacteristic
16C2×#97×C61C2212yes—
17C61×#330C414yescomplemented
18C22×#92418—21no—
19C2×C4⋊Dic61—21no—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61—22no—
22C2×C4⋊Dic61D412yes—
23C2×C4⋊Dic61D412yes—
24C2×C4×Dic61—22no—
25#14519711—44no—
26#14519709—44no—
27#14519688—22no—
28#14519684—22no—
29#14519684—22no—
30#14519684—22no—
31#14519684—22no—
32C22×C8×C61—22no—
33#125×C61—22no—
34#125×C61C2×C412yes—
35#125×C61Q812yes—
36C2×C4⋊C4×C61—22no—
37C2×C4⋊C4×C61D412yes—
38C2×C42×C61C2311yescharacteristic
39#97×C61—22no—
40#97×C61C2×C414yes—
41C22×C4×C61—22no—
42C22×C4×C61C2×D411yescharacteristic
43C22×C4×C61C2×D412yes—
44C22×Dic61—22no—
45C22×Dic61—22no—
46C22×Dic61—41no—
47C2×C8×C61—24no—
48C2×C8×C61—24no—
49C2×C8×C61—24no—
50C4⋊C4×C61—24no—
51C4⋊C4×C61—24no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61C4⋊C414yes—
54C42×C61C22×C411yescharacteristic
55C42×C61C2×Q811yescharacteristic
56C42×C61#4112yes—
57C4⋊Dic61—42no—
58C4⋊Dic61—42no—
59C4⋊Dic61—42no—
60C4⋊Dic61—42no—
61C4⋊Dic61—42no—
62C4⋊Dic61—82no—
63C4×Dic61—82no—
64C2×#92418—22no—
65C2×#92418—41no—
66C2×#92418—41no—
67C23×C61#12011yescharacteristic
68C2×C4×C61—22no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—24no—
73C2×C4×C61—42no—
74C2×C4×C61—42no—
75C2×C4×C61C2×C4⋊C411yescharacteristic
76C2×C4×C61C4×D412yes—
77C2×C4×C61C22⋊Q812yes—
78C2×C4×C61#12311yescharacteristic
79C2×Dic61—42no—
80C2×Dic61—42no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—82no—
86C2×Dic61—81no—
87C8×C61—28no—
88#92418—42no—
89#8913—611nomaximal, Sylow
90C22×C61#38511yescharacteristic
91C22×C61#45312yes—
92C22×C61#45411yescharacteristic
93C22×C61#45612yes—
94C22×C61#45611yescharacteristic
95C4×C61—21no—
96C4×C61—21no—
97C4×C61—22no—
98C4×C61—22no—
99C4×C61—44no—
100Dic61—82no—
101Dic61—82no—
102Dic61—161no—
103#2382—611no—
104#1992—611no—
105#1847—612no—
106C2×#330D6111yescharacteristic
107#1295—612no—
108C2×C61#165611yescharacteristic
109C2×C61#166012yes—
110C2×C61#166311yescharacteristic
111C2×C61#185711yescharacteristic
112C2×C61#185912yes—
113C2×#125C2×D6111yescharacteristic
114C2×#107—1222no—
115C2×#106—1222no—
116C2×#97—611no—
117C2×#97C2×D6112yes—
118#389—1222no—
119#387—1222no—
120#387—1222no—
121#384—611no—
122#382—612no—
123#340—1222no—
124#330Dic6114yescomplemented
125C61#891311yescharacteristic, complemented, Sylow
126C22×C8—22no—
127C22×C8—1221no—
128#125—22no—
129#125Dic12212yes—
130#125C2×Dic6112yes—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—612no—
133C2×C4⋊C4—612no—
134C2×C4⋊C4—1222no—
135C2×C4⋊C4—1221no—
136C2×C4⋊C4—1222no—
137C2×C4⋊C4D24412yes—
138C2×C42—1222no—
139C2×C42C22×D6111yescharacteristic
140#107—2444no—
141#106—2444no—
142#97—22no—
143#97—1222no—
144#97C2×Dic6114yes—
145#95—1222no—
146#95—1222no—
147#95—1222no—
148#95—1222no—
149C22×C4—22no—
150C22×C4—1222no—
151C22×C4—1222no—
152C22×C4—2441no—
153C22×C4C2×D24411yescharacteristic
154C22×C4D4×D6112yes—
155C2×C8—24no—
156C2×C8—24no—
157C2×C8—24no—
158C2×C8—1222no—
159C2×C8—2441no—
160C2×C8—2441no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—4882no—
165C4⋊C4—2442no—
166C4⋊C4—2442no—
167C4⋊C4—2442no—
168C4⋊C4—2442no—
169C4⋊C4—2442no—
170C4⋊C4C4⋊Dic6114yes—
171C42—4882no—
172C42C2×Dic12211yescharacteristic
173C42#1175822412yes—
174C42C22×Dic6111yescharacteristic
175C23#1451974711yescharacteristic
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—4881no—
184C2×C4—4882no—
185C2×C4—2442no—
186C2×C4—2442no—
187C2×C4—2442no—
188C2×C4—2442no—
189C2×C4—2442no—
190C2×C4—2442no—
191C2×C4C2×C4⋊Dic6111yescharacteristic
192C2×C4D4×Dic6112yes—
193C2×C4#1451975412yes—
194C2×C4#1451976111yescharacteristic
195C8—28no—
196C8—2442no—
197C22#1683963711yescharacteristic
198C22#1683993112yes—
199C22#1683993711yescharacteristic
200C22#1683994612yes—
201C22#1683994711yescharacteristic
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—9761no—
208C4—4882no—
209C4—4882no—
210C2#2144511411yescharacteristic
211C2#2144513212yes—
212C2#2144514811yescharacteristic
213C2#2144603611yescharacteristic
214C2#2144604712yes—
subgroupG/H
centerC23#14519747
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC2×C61×#330C2
socle, prime radicalC23×C61#120
cosocleC2×C42×C61C23
hypercenterC2×#330D61
hypocenterC61#8913
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
17. C61×#330C4semidirect
124. #330Dic61semidirect
125. C61#8913semidirect

Maximal subgroups

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

subgroupindex
#214490052
#214467892
#214459872
#214437012
C2×C61×#3302
#891361