Finite Group Databasebeta

← #29584510

Subgroups — #29584510

Order 15616.

406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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#21445985C212yesmaximal
3#21443701C212yesmaximal
4#21443700C211yesmaximal, characteristic
5C61×#1847C211yesmaximal, characteristic
6C2×#14519710—22no—
7C2×#14519708—22no—
8C2×#14519688C2212yes—
9#16839704—22no—
10#16839701—21no—
11#16839683—22no—
12#16839682—21no—
13#16839628C2212yes—
14C2×#107×C61—21no—
15C2×#106×C61—21no—
16C2×#97×C61C2211yescharacteristic
17C61×#384C2211yescharacteristic
18C61×#382C2211yescharacteristic
19C22×Dic122—21no—
20C22×#92418—22no—
21C2×C4⋊Dic61—21no—
22C2×C4⋊Dic61D412yes—
23C2×C4⋊Dic61D412yes—
24C2×#11758196—22no—
25#14519710—44no—
26#14519708—44no—
27#14519688—22no—
28#14519688Q814yescomplemented
29#14519684—21no—
30#14519684—22no—
31#14519684—21no—
32#14519684—22no—
33#14519684—22no—
34C22×C8×C61—21no—
35C2×C4⋊C4×C61—22no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61D411yescharacteristic
38C2×C4⋊C4×C61D411yescharacteristic
39C2×C42×C61C2311yescharacteristic
40#107×C61—42no—
41#106×C61—42no—
42#97×C61—21no—
43#97×C61Q812yescomplemented
44#95×C61—22no—
45C22×C4×C61—21no—
46C22×C4×C61—21no—
47C22×C4×C61—41no—
48C22×C4×C61C2×D412yes—
49C22×C4×C61C2×D411yescharacteristic
50C22×Dic61—22no—
51C22×Dic61—22no—
52C2×Dic122—82no—
53C2×Dic122—81no—
54C2×C8×C61—22no—
55C2×C8×C61—22no—
56C2×C8×C61—22no—
57C4⋊C4×C61—41no—
58C4⋊C4×C61—41no—
59C4⋊C4×C61—41no—
60C4⋊C4×C61—41no—
61C4⋊C4×C61—42no—
62C4⋊C4×C61—42no—
63C42×C61C2×Q811yescharacteristic
64C42×C61C2×Q812yes—
65C42×C61#4111yescharacteristic
66C4⋊Dic61—42no—
67C4⋊Dic61—42no—
68C4⋊Dic61—81no—
69#11758196—82no—
70C2×#92418—24no—
71C2×#92418—24no—
72C2×#92418—24no—
73C23×C61#12011yescharacteristic
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—21no—
78C2×C4×C61—42no—
79C2×C4×C61—41no—
80C2×C4×C61—41no—
81C2×C4×C61—42no—
82C2×C4×C61—82no—
83C2×C4×C61—81no—
84C2×C4×C61C22⋊Q812yes—
85C2×C4×C61C22⋊Q811yescharacteristic
86C2×C4×C61C4⋊Q811yescharacteristic
87C2×C4×C61C4⋊Q812yes—
88C2×Dic61—42no—
89C2×Dic61—42no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94Dic122—84no—
95C8×C61—24no—
96#92418—28no—
97#10583—611nomaximal, Sylow
98C22×C61#39511yescharacteristic
99C22×C61#45312yes—
100C22×C61#45311yescharacteristic
101C22×C61#45612yes—
102C22×C61#45611yescharacteristic
103C4×C61—22no—
104C4×C61—21no—
105C4×C61—22no—
106C4×C61—21no—
107C4×C61—81no—
108C4×C61—81no—
109C4×C61—161no—
110Dic61—82no—
111Dic61—82no—
112#2844—611no—
113#1847—612no—
114#1847D6111yescharacteristic
115#1295—612no—
116#1295—611no—
117C2×C61#165511yescharacteristic
118C2×C61#166011yescharacteristic
119C2×C61#166012yes—
120C2×C61#206012yes—
121C2×C61#206011yescharacteristic
122C2×#107—21no—
123C2×#107—1222no—
124C2×#106—21no—
125C2×#106—1222no—
126C2×#97—612no—
127C2×#97C2×D6111yescharacteristic
128#400—1222no—
129#400—1221no—
130#395—1222no—
131#395—1221no—
132#384C2×D6111yescharacteristic
133#382—612no—
134#382C2×D6111yescharacteristic
135C61#1058311yescharacteristic, complemented, Sylow
136C22×Q8—1221no—
137C22×C8—21no—
138C22×C8—1222no—
139C2×C4⋊C4—22no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—612no—
143C2×C4⋊C4—1222no—
144C2×C4⋊C4—1221no—
145C2×C4⋊C4C22⋊D6111yescharacteristic
146C2×C4⋊C4C22⋊D6111yescharacteristic
147C2×C42C22×D6111yescharacteristic
148#107—42no—
149#107—2444no—
150#106—42no—
151#106—2444no—
152#97—21no—
153#97—614no—
154#97—1222no—
155#97Dic12212yescomplemented
156#95—22no—
157#95—1222no—
158#95—1221no—
159#95—1221no—
160#95—1222no—
161#95—1222no—
162C2×Q8—4882no—
163C2×Q8—4881no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—41no—
167C22×C4—1222no—
168C22×C4—1222no—
169C22×C4D4×D6112yes—
170C22×C4C2×C22⋊D6111yescharacteristic
171C2×C8—22no—
172C2×C8—22no—
173C2×C8—22no—
174C2×C8—1224no—
175C2×C8—1224no—
176C2×C8—1224no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C4⋊C4—41no—
182C4⋊C4—42no—
183C4⋊C4—4882no—
184C4⋊C4—4881no—
185C4⋊C4—2442no—
186C4⋊C4—2442no—
187C42C2×Dic12211yescharacteristic
188C42#1175822211yescharacteristic
189C42Q8×D6112yes—
190C23#1451974511yescharacteristic
191Q8—4884no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—82no—
201C2×C4—81no—
202C2×C4—2442no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4—2442no—
208C2×C4#1451975512yes—
209C2×C4#1451975611yescharacteristic
210C2×C4#1451977511yescharacteristic
211C2×C4#1451977612yes—
212C8—24no—
213C8—1228no—
214C22#1683968211yescharacteristic
215C22#1683992812yes—
216C22#1683992911yescharacteristic
217C22#1683994312yes—
218C22#1683994411yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—81no—
224C4—81no—
225C4—161no—
226C4—4882no—
227C4—4882no—
228C2#2144510711yescharacteristic
229C2#2144512811yescharacteristic
230C2#2144512912yes—
231C2#2144716212yes—
232C2#2144716411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1847C2
socle, prime radicalC23×C61#120
hypercenter#1847D61
hypocenterC61#10583
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
28. #14519688Q8semidirect
43. #97×C61Q8semidirect
135. C61#10583semidirect
155. #97Dic122semidirect

Maximal subgroups

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

subgroupindex
#214540912
#214459852
#214437012
#214437002
C61×#18472
#1058361