Finite Group Databasebeta

← #29584514

Subgroups — #29584514

Order 15616.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#21454091C211yesmaximal, characteristic
2#21445988C211yesmaximal, characteristic
3#21445953C212yesmaximal
4#21443701C212yesmaximal
5C61×#1295C211yesmaximal, characteristic
6C2×#14519710—21no—
7C2×#14519708—21no—
8C2×#14519688C2211yescharacteristic
9#16839704—22no—
10#16839701—21no—
11#16839683—22no—
12#16839682—21no—
13#16839632C2211yescharacteristic
14#16839628C2212yes—
15#16839525—22no—
16#16839525—22no—
17C2×#97×C61C2212yes—
18C61×#382C2211yescharacteristic
19C22×Dic122—21no—
20C22×#92418—21no—
21C2×C4⋊Dic61—22no—
22C2×C4⋊Dic61—21no—
23C2×C4⋊Dic61—21no—
24C2×C4⋊Dic61D412yes—
25C2×C4⋊Dic61D412yes—
26C2×#11758196—22no—
27#14519710—42no—
28#14519708—42no—
29#14519688—21no—
30#14519688Q812yescomplemented
31#14519684—21no—
32#14519684—22no—
33#14519684—21no—
34#14519684—22no—
35#14519684—22no—
36C22×C8×C61—22no—
37C2×C4⋊C4×C61D411yescharacteristic
38C2×C4⋊C4×C61D411yescharacteristic
39C2×C42×C61C2311yescharacteristic
40#97×C61—22no—
41#97×C61Q814yescomplemented
42#95×C61—22no—
43C22×C4×C61—21no—
44C22×C4×C61—21no—
45C22×C4×C61C2×D411yescharacteristic
46C22×C4×C61C2×D412yes—
47C22×Dic61—22no—
48C22×Dic61—22no—
49C22×Dic61—41no—
50C2×Dic122—81no—
51C2×Dic122—82no—
52C2×C8×C61—24no—
53C2×C8×C61—42no—
54C2×C8×C61—42no—
55C4⋊C4×C61—41no—
56C4⋊C4×C61—41no—
57C42×C61C2×Q812yes—
58C42×C61C2×Q811yescharacteristic
59C42×C61#4111yescharacteristic
60C4⋊Dic61—42no—
61C4⋊Dic61—42no—
62C4⋊Dic61—41no—
63C4⋊Dic61—41no—
64C4⋊Dic61—44no—
65C4⋊Dic61—81no—
66#11758196—82no—
67C2×#92418—22no—
68C2×#92418—22no—
69C2×#92418—22no—
70C23×C61#12011yescharacteristic
71C2×C4×C61—21no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—21no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61C22⋊Q812yes—
80C2×C4×C61C22⋊Q811yescharacteristic
81C2×C4×C61C4⋊Q812yes—
82C2×C4×C61C4⋊Q811yescharacteristic
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—42no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89C2×Dic61—81no—
90C2×Dic61—82no—
91Dic122—84no—
92C8×C61—44no—
93#92418—24no—
94#10584—611nomaximal, Sylow
95C22×C61#39511yescharacteristic
96C22×C61#45311yescharacteristic
97C22×C61#45412yes—
98C22×C61#45512yes—
99C22×C61#45611yescharacteristic
100C4×C61—21no—
101C4×C61—21no—
102C4×C61—22no—
103C4×C61—22no—
104C4×C61—81no—
105C4×C61—81no—
106Dic61—82no—
107Dic61—82no—
108Dic61—161no—
109#2844—611no—
110#1847—611no—
111#1836—612no—
112#1295—612no—
113#1295D6111yescharacteristic
114C2×C61#165711yescharacteristic
115C2×C61#165911yescharacteristic
116C2×C61#166412yes—
117C2×C61#206011yescharacteristic
118C2×C61#206112yes—
119C2×#107—1221no—
120C2×#106—1221no—
121C2×#97—611no—
122C2×#97C2×D6112yes—
123#400—1222no—
124#400—1221no—
125#395—1222no—
126#395—1221no—
127#384—611no—
128#382—612no—
129#382C2×D6111yescharacteristic
130#340—1222no—
131#340—1222no—
132C61#1058411yescharacteristic, complemented, Sylow
133C22×Q8—1221no—
134C22×C8—22no—
135C22×C8—1221no—
136C2×C4⋊C4—612no—
137C2×C4⋊C4—612no—
138C2×C4⋊C4—1222no—
139C2×C4⋊C4—1221no—
140C2×C4⋊C4—1221no—
141C2×C4⋊C4—1222no—
142C2×C4⋊C4D24411yescharacteristic
143C2×C4⋊C4D24411yescharacteristic
144C2×C42C22×D6111yescharacteristic
145#107—2442no—
146#106—2442no—
147#97—22no—
148#97—612no—
149#97—1221no—
150#97Dic12214yescomplemented
151#95—22no—
152#95—1222no—
153#95—1221no—
154#95—1221no—
155#95—1222no—
156#95—1222no—
157C2×Q8—4882no—
158C2×Q8—4881no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—1222no—
162C22×C4—1222no—
163C22×C4—2441no—
164C22×C4C2×D24411yescharacteristic
165C22×C4D4×D6112yes—
166C2×C8—24no—
167C2×C8—42no—
168C2×C8—42no—
169C2×C8—1222no—
170C2×C8—1222no—
171C2×C8—1222no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—4882no—
175C4⋊C4—4881no—
176C4⋊C4—2441no—
177C4⋊C4—2441no—
178C4⋊C4—2444no—
179C4⋊C4—2442no—
180C4⋊C4—2442no—
181C42C2×Dic12212yes—
182C42#1175822411yescharacteristic
183C42Q8×D6111yescharacteristic
184C23#1451974711yescharacteristic
185Q8—4884no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—4882no—
195C2×C4—4881no—
196C2×C4—2442no—
197C2×C4—2442no—
198C2×C4—2442no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4—2442no—
202C2×C4#1451975412yes—
203C2×C4#1451975711yescharacteristic
204C2×C4#1451977612yes—
205C2×C4#1451977711yescharacteristic
206C8—44no—
207C8—1224no—
208C22#1683968311yescharacteristic
209C22#1683993211yescharacteristic
210C22#1683993612yes—
211C22#1683994112yes—
212C22#1683994711yescharacteristic
213C4—22no—
214C4—22no—
215C4—21no—
216C4—21no—
217C4—81no—
218C4—81no—
219C4—9761no—
220C4—4882no—
221C4—4882no—
222C2#2144511811yescharacteristic
223C2#2144512611yescharacteristic
224C2#2144515512yes—
225C2#2144716511yescharacteristic
226C2#2144716812yes—
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1295C2
socle, prime radicalC23×C61#120
hypercenter#1295D61
hypocenterC61#10584
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
30. #14519688Q8semidirect
41. #97×C61Q8semidirect
132. C61#10584semidirect
150. #97Dic122semidirect

Maximal subgroups

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

subgroupindex
#214540912
#214459882
#214459532
#214437012
C61×#12952
#1058461