Finite Group Databasebeta

← #29583122

Subgroups — #29583122

Order 15616.

402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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#21454206C211yesmaximal, characteristic, complemented
2#21446647C211yesmaximal, characteristic
3#21444380C212yesmaximal
4#21443678C212yesmaximal, complemented
5C61×#1276C211yesmaximal, characteristic, complemented
6#16840312C2211yescharacteristic
7#16839786C2211yescharacteristic
8C2×#14519705—22no—
9#16839660—22no—
10#16839646—24no—
11#16839628C2212yes—
12#16839497—24no—
13C61×#431C2212yes—
14C43×C61C2211yescharacteristic
15C2×#11758222—21no—
16C2×#11758194—21no—
17#14519777Q811yescharacteristic
18#14519774Q811yescharacteristic
19#14519765—21no—
20#14519751—22no—
21C4×D244—22no—
22C2×C4⋊Dic61—22no—
23C2×#11758196—24no—
24C4⋊#92418—22no—
25#14519705—44no—
26#14519684—24no—
27#14519684—22no—
28#14519684D414yes—
29C2×C42×C61—22no—
30C2×C42×C61D412yes—
31C2×C42×C61C2311yescharacteristic
32C4⋊C8×C61—22no—
33C22⋊C8×C61—22no—
34C4×C8×C61—22no—
35C22×C4×C61—22no—
36C22×C4×C61C2×D412yes—
37C22×C4×C61C2×D411yescharacteristic
38C2×C22⋊D61—41no—
39C22×Dic61—24no—
40#11758222—42no—
41#11758222—42no—
42C2×D244—21no—
43C2×D244—22no—
44C2×C4×D61—41no—
45C2×Dic122—21no—
46C2×C8×C61—42no—
47C42×C61—22no—
48C42×C61—22no—
49C42×C61—44no—
50C42×C61C2×Q811yescharacteristic
51C42×C61#4112yes—
52C42×C61#4111yescharacteristic
53#11758198—42no—
54C4⋊Dic61—22no—
55C4⋊Dic61—42no—
56C4⋊Dic61—42no—
57#11758196—48no—
58#11758194—42no—
59C2×#92418—41no—
60C23×C61#12011yescharacteristic
61C22×D61—41no—
62C2×C4×C61—24no—
63C2×C4×C61—42no—
64C2×C4×C61—42no—
65C2×C4×C61—42no—
66C2×C4×C61C22⋊Q812yes—
67C2×C4×C61C22⋊Q811yescharacteristic
68C2×C4×C61#12412yes—
69C2×C4×C61#12411yescharacteristic
70C2×C4×C61#13512yes—
71C2×C4×C61AGL(1,ℤ/8)12yes—
72C22⋊D61—82no—
73C2×Dic61—48no—
74C2×Dic61—41no—
75C2×Dic61—44no—
76D244—42no—
77D244—82no—
78C4×D61—81no—
79C4×D61—81no—
80Dic122—42no—
81C8×C61—82no—
82#92418—81no—
83#10366—611nomaximal, Sylow
84C22×C61—22no—
85C22×C61#39311yescharacteristic
86C22×C61#44912yes—
87C2×D61—81no—
88C2×D61—82no—
89C4×C61—22no—
90C4×C61—22no—
91C4×C61—44no—
92C4×C61#47812yes—
93C4×C61#48811yescharacteristic
94C4×C61#49011yescharacteristic
95Dic61—84no—
96Dic61—81no—
97#2864—611no—
98#1962—611no—
99#1517—612no—
100#1286—612no—
101#1276D6111yescharacteristic, complemented
102C2×C61—22no—
103C2×C61#202511yescharacteristic
104C2×C61#203112yes—
105D61—161no—
106#532—611no—
107#431C2×D6112yes—
108#423—611no—
109C2×#104—1222no—
110#389—1222no—
111#387—1224no—
112#382—612no—
113C43C2×D6111yescharacteristic
114#327—1224no—
115C61#1036611yescharacteristic, complemented, Sylow
116C2×#41—1221no—
117C2×M16—1221no—
118C4⋊Q8—611no—
119#127—611no—
120#124—1221no—
121#121—1222no—
122C4×D4—1222no—
123C2×C4⋊C4—1224no—
124C2×C4⋊C4—1222no—
125C2×C42—22no—
126C2×C42D24412yes—
127C2×C42C22×D6111yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—1222no—
130#104—2444no—
131C22⋊C8—22no—
132C4×C8—22no—
133#95—614no—
134#95—1224no—
135#95—1222no—
136#41—2442no—
137#41—2442no—
138C2×Q8—1221no—
139C2×D4—1222no—
140C2×D4—1221no—
141C2×D4—2441no—
142C22×C4—22no—
143C22×C4—1224no—
144C22×C4—2441no—
145C22×C4C2×D24411yescharacteristic
146C22×C4D4×D6112yes—
147M16—2442no—
148C2×C8—42no—
149C2×C8—2441no—
150C4⋊C4—1222no—
151C4⋊C4—2448no—
152C4⋊C4—2442no—
153C4⋊C4—2442no—
154C22⋊C4—2442no—
155C42—22no—
156C42—22no—
157C42—44no—
158C42#1175822212yes—
159C42#1175822411yescharacteristic
160C42Q8×D6111yescharacteristic
161C23—2441no—
162C23#1451974711yescharacteristic
163Q8—2442no—
164D4—4882no—
165D4—4882no—
166D4—2442no—
167C2×C4—24no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—4881no—
172C2×C4—4881no—
173C2×C4—2448no—
174C2×C4—2444no—
175C2×C4—2441no—
176C2×C4#1451975512yes—
177C2×C4#1451975711yescharacteristic
178C2×C4#1451976312yes—
179C2×C4#1451976511yescharacteristic
180C2×C4#1451979912yes—
181C2×C4#1451980512yes—
182C8—82no—
183C8—4881no—
184C22—22no—
185C22—4881no—
186C22—4882no—
187C22#1683967511yescharacteristic
188C22#1683990912yes—
189C4—22no—
190C4—22no—
191C4—44no—
192C4—4884no—
193C4—4881no—
194C4#1684006312yes—
195C4#1684011711yescharacteristic
196C4#1684012711yescharacteristic
197C2—22no—
198C2—9761no—
199C2#2144696611yescharacteristic
200C2#2144699212yes—
subgroupG/H
centerC22#16839675
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1276C2
socleC22×C61#393
prime radical#16840312C22
hypercenter#1276D61
hypocenterC61#10366
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
1. #21454206C2semidirect
4. #21443678C2semidirect
5. C61×#1276C2semidirect
101. #1276D61semidirect
115. C61#10366semidirect

Maximal subgroups

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

subgroupindex
#214542062
#214466472
#214443802
#214436782
C61×#12762
#1036661