Finite Group Databasebeta

← #30608410

Subgroups — #30608410

Order 15616.

318 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 56 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#21462111C212yesmaximal
2#21460963C212yesmaximal, complemented
3#21460962C211yesmaximal, characteristic, complemented
4#21460961C211yesmaximal, characteristic, complemented
5#21456218C211yesmaximal, characteristic
6#16840749—22no—
7#16840673C2212yes—
8#16840673C2212yes—
9#16840670—22no—
10#16840310C2211yescharacteristic
11#125×D61C411yescharacteristic
12#16840132C2211yescharacteristic
13#16840131C2211yescharacteristic
14#16840126C411yescharacteristic
15#16840115—22no—
16#16839760—22no—
17#16839714C411yescharacteristic
18C61×#490C411yescharacteristic
19C2×#11758217—42no—
20#14519838—22no—
21#14519838—22no—
22#14519837—42no—
23C2×#11758224D412yes—
24C2×#11758189—21no—
25#14519777C2311yescharacteristic
26#14519769C2×C411yescharacteristic
27#14519768—21no—
28#14519767—41no—
29#14519764D412yes—
30#14519748—41no—
31D4×Dic61—41no—
32C4⋊C4×D61—21no—
33C4⋊C4×D61—41no—
34C42×D61C2×C411yescharacteristic
35#14519702—22no—
36#14519700—22no—
37#14519698—22no—
38#14519688C2×C411yescharacteristic
39C8×Dic61—21no—
40#127×C61C2×C411yescharacteristic
41#125×C61C2×C411yescharacteristic
42#102×C61—22no—
43#97×C61C2×C411yescharacteristic
44C2×D4×C61—41no—
45C2×D4×C61C22⋊C412yes—
46C2×C22⋊D61—22no—
47C22×Dic61—22no—
48#11758224—42no—
49#11758224—42no—
50C2×C4×D61—21no—
51C2×C4×D61—41no—
52C2×C4×D61C22⋊C411yescharacteristic
53C2×Dic122C2×D412yes—
54#11758217—42no—
55#11758217—42no—
56#11758217—82no—
57C2×#92420—82no—
58C2×C8×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61—41no—
61C42×C61C22×C411yescharacteristic
62C22⋊Dic61—42no—
63C4⋊Dic61—21no—
64C4⋊Dic61—41no—
65C4⋊Dic61—41no—
66#11758196—41no—
67#11758196—41no—
68#11758196—41no—
69C4×Dic61—21no—
70C4×Dic61C22⋊C411yescharacteristic
71C2×#92418—21no—
72#11758189—42no—
73C23×C61—22no—
74C22×D61#9911yescharacteristic
75D4×C61—42no—
76D4×C61—82no—
77C2×C4×C61—21no—
78C2×C4×C61—41no—
79C2×C4×C61C2×C22⋊C411yescharacteristic
80C22⋊D61—82no—
81C2×Dic61—21no—
82C2×Dic61—22no—
83C2×Dic61—42no—
84C2×Dic61—42no—
85C2×Dic61—41no—
86C2×Dic61#9911yescharacteristic
87C4×D61—22no—
88C4×D61—81no—
89C4×D61—82no—
90Dic122—42no—
91#92420—82no—
92#92420—82no—
93C8×C61—41no—
94#92418—41no—
95#13600—611nomaximal, Sylow
96C22×C61—42no—
97C22×C61—82no—
98C22×C61C2×#9911yescharacteristic
99C2×D61—21no—
100C2×D61—41no—
101C4×C61—21no—
102C4×C61—41no—
103C4×C61—81no—
104Dic61—41no—
105Dic61—42no—
106Dic61—81no—
107Dic61#35412yes—
108#3142—611no—
109#2132—612no—
110#1413—611no—
111#1413—611no—
112#1413—612no—
113C2×C61—21no—
114C2×C61—82no—
115C2×C61C2×#35411yescharacteristic
116D61—41no—
117#532—611no—
118C2×#125—611no—
119#491—611no—
120#491—611no—
121#490—611no—
122#490#692311yescharacteristic
123#488—1222no—
124#417—1222no—
125#413—1222no—
126C4×M16—611no—
127#356—612no—
128#356—612no—
129#355—1222no—
130C61#1360011yescharacteristic, complemented, Sylow
131C2×#41—612no—
132C2×M16—1221no—
133C2×M16—2442no—
134C4⋊Q8—611no—
135#127C2×#692311yescharacteristic
136#125—611no—
137#125—1221no—
138#125—2441no—
139#125C2×#692311yescharacteristic
140#124—612no—
141#121—2441no—
142C4×D4—2441no—
143C2×C4⋊C4—1221no—
144C2×C4⋊C4—2441no—
145C2×C42—611no—
146#103—1222no—
147#103—1222no—
148#102—22no—
149#102—1222no—
150#101—1222no—
151#101—1222no—
152#100—2442no—
153#97—611no—
154#97C2×#692311yescharacteristic
155C4×C8—1221no—
156#41—2442no—
157#41—2442no—
158C2×Q8—612no—
159C2×D4—41no—
160C2×D4—1222no—
161C2×D4C22⋊#692312yes—
162C22×C4—611no—
163C22×C4—1221no—
164C22×C4—1222no—
165C22×C4—2441no—
166M16—4882no—
167M16—2442no—
168M16—2442no—
169M16—2442no—
170C2×C8—21no—
171C2×C8—1221no—
172C2×C8—4882no—
173C4⋊C4—21no—
174C4⋊C4—41no—
175C4⋊C4—1221no—
176C4⋊C4—2441no—
177C4⋊C4—2441no—
178C4⋊C4—2441no—
179C4⋊C4—2441no—
180C4⋊C4—2441no—
181C22⋊C4—2442no—
182C42—611no—
183C42—1221no—
184C42C22×#692311yescharacteristic
185C23—22no—
186C23—611no—
187Q8—2442no—
188D4—42no—
189D4—82no—
190D4—4882no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—611no—
194C2×C4—1222no—
195C2×C4—1221no—
196C2×C4—1222no—
197C2×C4—4881no—
198C2×C4—4882no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4—2441no—
202C2×C4C2×C22⋊#692311yescharacteristic
203C8—41no—
204C8—4882no—
205C8—4882no—
206C8—2441no—
207C22—42no—
208C22—82no—
209C22—1221no—
210C22—2441no—
211C22D61⋊#9911yescharacteristic
212C4—21no—
213C4—41no—
214C4—81no—
215C4—612no—
216C4—4881no—
217C4—2441no—
218C4—2442no—
219C2—21no—
220C2—82no—
221C2—2441no—
222C2D61⋊#35411yescharacteristic
subgroupG/H
centerC2D61⋊#354
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#490C4
socleC2×C61C2×#354
prime radical#16840310C22
cosocle#14519777C23
hypercenter#490#6923
hypocenterC61#13600
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #21460963C2semidirect
3. #21460962C2semidirect
4. #21460961C2semidirect
130. C61#13600semidirect

Maximal subgroups

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

subgroupindex
#214621112
#214609632
#214609622
#214609612
#214562182
#1360061