Finite Group Databasebeta

← #29579502

Subgroups — #29579502

Order 15616.

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

normal subgroups only

This group has 506 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
1C2×#16840135C211yesmaximal, characteristic
2#21444492C212yesmaximal, complemented
3#21444488C212yesmaximal
4#21444111C211yesmaximal, characteristic, complemented
5C61×#1837C211yesmaximal, characteristic, complemented
6C22×#11758190—22no—
7C2×#14519777C2211yescharacteristic
8C2×#14519774C2211yescharacteristic
9#16840135—22no—
10#16840135C414yes—
11#16839815C2212yes—
12#16839509—24no—
13#16839505—24no—
14#16839484—22no—
15C61×#423C2212yes—
16C2×C4×C8×C61C2211yescharacteristic
17C61×#341—22no—
18C22×Dic122—21no—
19C22×D244—21no—
20C22×D244—22no—
21C2×#11758190—28no—
22C2×#11758190—48no—
23#14519777—22no—
24#14519777—21no—
25#14519777C2×C412yes—
26#14519774—22no—
27#14519774—21no—
28#14519774C2×C412yes—
29C2×C4⋊Dic61—22no—
30C4⋊#92418D414yes—
31C22⋊#92418—22no—
32C4×#92418—22no—
33C2×M16×C61—22no—
34C22×C8×C61D412yes—
35C2×C42×C61C2311yescharacteristic
36C4⋊C8×C61—22no—
37C4⋊C8×C61—22no—
38C4×C8×C61C2×C412yes—
39C4×C8×C61D412yes—
40C23×D61—41no—
41C22×C4×C61C2×D411yescharacteristic
42C22×C4×C61#4112yes—
43C22×Dic61—41no—
44C2×D244—22no—
45C2×D244—24no—
46C2×D244—44no—
47C2×D244—42no—
48C2×D244—41no—
49C2×D244—84no—
50C2×Dic122—22no—
51C2×Dic122—44no—
52C2×Dic122—41no—
53M16×C61—44no—
54C2×C8×C61—24no—
55C2×C8×C61—42no—
56C2×C8×C61C22⋊C414yes—
57C42×C61C22×C411yescharacteristic
58C42×C61C2×D411yescharacteristic
59C42×C61C2×D412yes—
60C4⋊Dic61—24no—
61C4⋊Dic61—42no—
62C2×#92418—24no—
63#11758190—416no—
64C23×C61#12411yescharacteristic
65C22×D61—42no—
66C22×D61—84no—
67C22×D61—82no—
68C2×C4×C61—24no—
69C2×C4×C61C2×C22⋊C411yescharacteristic
70C2×C4×C61C4×D412yes—
71C2×C4×C61#12112yes—
72C2×C4×C61#12711yescharacteristic
73C2×C4×C61AGL(1,ℤ/8)14yes—
74C2×Dic61—42no—
75C2×Dic61—82no—
76D244—44no—
77D244—84no—
78D244—84no—
79D244—82no—
80Dic122—44no—
81Dic122—82no—
82C8×C61—24no—
83C8×C61—82no—
84#92418—44no—
85#9777—611nomaximal, Sylow
86C22×C61—22no—
87C22×C61#39011yescharacteristic
88C22×C61#49012yes—
89C2×D61—82no—
90C2×D61—84no—
91C2×D61—164no—
92C4×C61—22no—
93C4×C61#41812yes—
94C4×C61#47114yes—
95C4×C61#49612yes—
96Dic61—82no—
97C2×#492—611no—
98#1837D6111yescharacteristic, complemented
99#1546—612no—
100#1545—612no—
101#1452—611no—
102C2×C61—22no—
103C2×C61#196111yescharacteristic
104C2×C61#197712yes—
105D61—162no—
106C22×SD16—1222no—
107C2×C4⋊Q8—611no—
108C2×#127—611no—
109#492—614no—
110#492—1222no—
111#431—612no—
112#423C2×D6112yes—
113C2×C4×C8C2×D6111yescharacteristic
114#341—22no—
115#332—1224no—
116#331—1224no—
117#322—1222no—
118C61#977711yescharacteristic, complemented, Sylow
119C22×Q8—1221no—
120C22×D4—1222no—
121C22×D4—1221no—
122C2×SD16—1228no—
123C2×SD16—2448no—
124C2×M16—22no—
125C22×C8C22⋊D6112yes—
126C4⋊Q8—612no—
127C4⋊Q8—1221no—
128C4⋊Q8—1222no—
129#127—612no—
130#127—1221no—
131#127—1222no—
132C2×C4⋊C4—1222no—
133C2×C42C22×D6111yescharacteristic
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—614no—
137C22⋊C8—1222no—
138C4×C8—1222no—
139C4×C8C4×D6112yes—
140C4×C8D24412yes—
141C24—2441no—
142C2×Q8—1222no—
143C2×Q8—2444no—
144C2×Q8—2441no—
145C2×D4—1222no—
146C2×D4—1224no—
147C2×D4—4884no—
148C2×D4—2442no—
149C2×D4—2441no—
150C2×D4—2444no—
151C22×C4—2441no—
152C22×C4#1175822612yes—
153C22×C4C2×C22⋊D6111yescharacteristic
154SD16—24416no—
155M16—44no—
156C2×C8—24no—
157C2×C8—42no—
158C2×C8—1224no—
159C2×C8#1175819814yes—
160C4⋊C4—1224no—
161C4⋊C4—2442no—
162C42C2×C4×D6111yescharacteristic
163C42C2×D24411yescharacteristic
164C42D4×D6112yes—
165C23—4884no—
166C23—4882no—
167C23—2442no—
168C23#1451976611yescharacteristic
169Q8—4882no—
170Q8—2444no—
171D4—4884no—
172D4—4884no—
173D4—4882no—
174D4—2444no—
175C2×C4—24no—
176C2×C4—4882no—
177C2×C4—2442no—
178C2×C4C2×#1175819811yescharacteristic
179C2×C4#1451973912yes—
180C2×C4#1451975212yes—
181C2×C4#1451977311yescharacteristic
182C2×C4#1451980214yes—
183C8—24no—
184C8—82no—
185C8—2444no—
186C22—22no—
187C22—9764no—
188C22—4884no—
189C22—4882no—
190C22#1683966311yescharacteristic
191C22#1684012812yes—
192C4—22no—
193C4—4882no—
194C4#1683976612yes—
195C4#1684002614yes—
196C4#1684015212yes—
197C2—22no—
198C2—9762no—
199C2#2144664211yescharacteristic
200C2#2144672012yes—
subgroupG/H
centerC22#16839663
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1837C2
socleC22×C61#390
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1837D61
hypocenterC61#9777
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1837

Complements

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

NH ≅ G/Ntype
2. #21444492C2semidirect
4. #21444111C2semidirect
5. C61×#1837C2semidirect
98. #1837D61semidirect
118. C61#9777semidirect

Maximal subgroups

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

subgroupindex
C2×#168401352
#214444922
#214444882
#214441112
C61×#18372
#977761