Finite Group Databasebeta

← #30605733

Subgroups — #30605733

Order 15616.

360 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 64 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#21462188C212yesmaximal, complemented
2#21460830C212yesmaximal, complemented
3#21460828C212yesmaximal, complemented
4#21456276C211yesmaximal, characteristic
5#16840685C2214yes—
6#16840658—22no—
7#16840654—22no—
8C2×#14519808—22no—
9#16840312C411yescharacteristic
10#16840154—22no—
11#16840141C411yescharacteristic
12#16840141C2211yescharacteristic
13#16840136C411yescharacteristic
14#16840136C2211yescharacteristic
15C4×#11758194C2211yescharacteristic
16C2×C4⋊Q8×C61C411yescharacteristic
17#14519851—24no—
18C2×#11758222—21no—
19#14519808—48no—
20C2×#11758202—22no—
21C2×#11758202—22no—
22C2×#11758201—22no—
23C2×#11758201—22no—
24C2×#11758194D412yes—
25#14519777C2×C411yescharacteristic
26#14519774C2×C411yescharacteristic
27#14519765—21no—
28#14519751—41no—
29C4×D244—41no—
30#14519688D412yes—
31C4×#92418C2×C411yescharacteristic
32C4×#92418C2311yescharacteristic
33C22×Q8×C61—21no—
34C4⋊Q8×C61—21no—
35C4⋊Q8×C61—41no—
36C4⋊Q8×C61C2×C411yescharacteristic
37C4⋊Q8×C61C2×C411yescharacteristic
38C2×C4⋊C4×C61—41no—
39C2×C42×C61C2×C411yescharacteristic
40C2×Q8×C61—21no—
41C2×Q8×C61—21no—
42C2×Q8×C61—44no—
43C2×Q8×C61—41no—
44C22×C4×C61—21no—
45C22×C4×C61—41no—
46C22×C4×C61C22⋊C411yescharacteristic
47C2×C22⋊D61—41no—
48#11758222—44no—
49C2×D244—21no—
50C2×D244—41no—
51C2×C4×D61—41no—
52C2×Dic122—21no—
53C4⋊C4×C61—42no—
54C4⋊C4×C61—41no—
55C4⋊C4×C61—41no—
56C42×C61—21no—
57C42×C61C22⋊C411yescharacteristic
58C42×C61C22×C411yescharacteristic
59#11758202—44no—
60#11758202—44no—
61#11758201—44no—
62#11758201—44no—
63#11758198—42no—
64C4⋊Dic61—41no—
65#11758194—24no—
66C2×#92418C22⋊C412yes—
67C2×#92418C2×D412yes—
68#11758187—44no—
69C23×C61#10011yescharacteristic
70C22×D61—41no—
71Q8×C61—42no—
72Q8×C61—42no—
73Q8×C61—82no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—21no—
77C2×C4×C61—42no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61—82no—
81C2×C4×C61#10011yescharacteristic
82C2×C4×C61C2×C22⋊C411yescharacteristic
83C22⋊D61—82no—
84C2×Dic61—41no—
85D244—42no—
86D244—82no—
87C4×D61—82no—
88Dic122—42no—
89#92418—22no—
90#92418AGL(1,ℤ/8)14yes—
91#11993—611nomaximal, Sylow
92C22×C61—21no—
93C22×C61—41no—
94C22×C61C2×#10011yescharacteristic
95C2×D61—82no—
96C2×D61—81no—
97C4×C61—22no—
98C4×C61—21no—
99C4×C61—41no—
100C4×C61—81no—
101C4×C61—81no—
102C4×C61#41812yes—
103Dic61—81no—
104#3152—611no—
105#2165—612no—
106#1359—612no—
107#1358—612no—
108C2×C61—21no—
109C2×C61—41no—
110C2×C61#155511yescharacteristic
111D61—161no—
112C2×#137—1222no—
113#532—611no—
114C2×C4⋊Q8#692311yescharacteristic
115#497—1222no—
116#494—611no—
117#494—611no—
118#492—611no—
119#492—611no—
120C4×M16—611no—
121#364—614no—
122#349—1222no—
123#347—1222no—
124C61#1199311yescharacteristic, complemented, Sylow
125C2×#41—1221no—
126C22×Q8—21no—
127#137—2448no—
128C2×Q16—1222no—
129C2×Q16—1222no—
130C2×SD16—1222no—
131C2×SD16—1222no—
132C2×M16—612no—
133C4⋊Q8—21no—
134C4⋊Q8—41no—
135C4⋊Q8—611no—
136C4⋊Q8C2×#692311yescharacteristic
137C4⋊Q8C2×#692311yescharacteristic
138#127—611no—
139#124—1221no—
140#121—2441no—
141C4×D4—2441no—
142C2×C4⋊C4—41no—
143C2×C42C2×#692311yescharacteristic
144M32—1224no—
145#97—612no—
146C4×C8—611no—
147C4×C8—611no—
148#41—2444no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—44no—
152C2×Q8—41no—
153C2×Q8—1221no—
154C2×D4—1221no—
155C2×D4—2441no—
156C2×D4—2441no—
157C22×C4—21no—
158C22×C4—41no—
159C22×C4—2441no—
160C22×C4C22⋊#692311yescharacteristic
161Q16—2444no—
162Q16—2444no—
163SD16—2444no—
164SD16—2444no—
165M16—1224no—
166C2×C8—612no—
167C2×C8—612no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C4⋊C4—2441no—
172C22⋊C4—2442no—
173C42—21no—
174C42C22⋊#692311yescharacteristic
175C42C22×#692311yescharacteristic
176C16—2444no—
177C23—2441no—
178C23#1451983711yescharacteristic
179Q8—42no—
180Q8—42no—
181Q8—82no—
182Q8—2442no—
183D4—4882no—
184D4—4882no—
185D4—2442no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—82no—
193C2×C4—4882no—
194C2×C4—2441no—
195C2×C4#1451983711yescharacteristic
196C2×C4C2×C22⋊#692311yescharacteristic
197C8—614no—
198C8—1222no—
199C22—21no—
200C22—41no—
201C22—4882no—
202C22—4881no—
203C22C2×#1451983711yescharacteristic
204C4—22no—
205C4—21no—
206C4—41no—
207C4—81no—
208C4—81no—
209C4—4881no—
210C4#1684075412yes—
211C2—21no—
212C2—41no—
213C2—9761no—
214C2#2146134611yescharacteristic
subgroupG/H
centerC2#21461346
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC2×C4⋊Q8×C61C4
socleC2×C61#1555
prime radical#16840312C4
cosocleC4×#92418C23
hypercenterC2×C4⋊Q8#6923
hypocenterC61#11993
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21462188C2semidirect
2. #21460830C2semidirect
3. #21460828C2semidirect
124. C61#11993semidirect

Maximal subgroups

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

subgroupindex
#214621882
#214608302
#214608282
#214562762
#1199361