Finite Group Databasebeta

← #30608396

Subgroups — #30608396

Order 15616.

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

normal subgroups only

This group has 326 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#21462093C212yesmaximal
2#21460960C212yesmaximal, complemented
3#21460959C211yesmaximal, characteristic, complemented
4#21460958C211yesmaximal, characteristic, complemented
5#21456221C211yesmaximal, characteristic
6#16840743—22no—
7#16840668—22no—
8#16840667C2212yes—
9#16840667C2212yes—
10#16840313C2211yescharacteristic
11#125×D61C411yescharacteristic, complemented
12#16840130C411yescharacteristic, complemented
13#16840128C2211yescharacteristic
14#16840127C2211yescharacteristic
15#16840118—22no—
16#16839762—22no—
17#16839714C411yescharacteristic, complemented
18C61×#491C411yescharacteristic, complemented
19#14519856—42no—
20#14519836—22no—
21#14519836—22no—
22#14519836—42no—
23C2×#11758226D412yes—
24C2×#11758189—21no—
25#14519774C2311yescharacteristic
26#14519769C2×C411yescharacteristic
27#14519768—21no—
28#14519767—41no—
29#14519766D412yes—
30#14519752—41no—
31#14519739—41no—
32C4⋊C4×D61—21no—
33C4⋊C4×D61—41no—
34C42×D61C2×C411yescharacteristic
35#14519701—22no—
36#14519699—22no—
37#14519697—22no—
38#14519688C2×C411yescharacteristic
39C8×Dic61—21no—
40C4⋊Q8×C61C2×C411yescharacteristic
41#125×C61C2×C411yescharacteristic
42#103×C61—22no—
43#97×C61C2×C411yescharacteristic
44C2×Q8×C61C22⋊C412yes—
45#11758226—42no—
46#11758226—42no—
47C2×D244—22no—
48C2×D244—41no—
49C2×D244C2×D412yes—
50C2×C4×D61—22no—
51C2×C4×D61—21no—
52C2×C4×D61—41no—
53C2×C4×D61C22⋊C411yescharacteristic
54C22⋊#6923—42no—
55C22⋊#6923—42no—
56C4⋊#6923—82no—
57C4×#6923—82no—
58C2×C8×C61—21no—
59C4⋊C4×C61—21no—
60C4⋊C4×C61—41no—
61C4⋊C4×C61—41no—
62C42×C61C22×C411yescharacteristic
63#11758198—42no—
64C4⋊Dic61—21no—
65C4⋊Dic61—41no—
66#11758196—41no—
67#11758196—41no—
68#11758196—41no—
69C4×Dic61—21no—
70C4×Dic61C22⋊C411yescharacteristic
71C2×#92418—21no—
72#11758189—42no—
73C22×D61—22no—
74C22×D61#9911yescharacteristic
75C2×#6923—82no—
76C2×#6923—82no—
77Q8×C61—42no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—41no—
81C2×C4×C61C2×C22⋊C411yescharacteristic
82C2×Dic61—21no—
83C2×Dic61—41no—
84C2×Dic61#9911yescharacteristic
85D244—42no—
86D244—82no—
87D244—82no—
88C4×D61—22no—
89C4×D61—42no—
90C4×D61—42no—
91C4×D61—81no—
92C4×D61—82no—
93C8×C61—41no—
94#92418—41no—
95#13596—611nomaximal, Sylow
96C22×C61C2×#9911yescharacteristic
97C2×D61—21no—
98C2×D61—41no—
99C2×D61—42no—
100C2×D61—82no—
101#6923—162no—
102#6923—162no—
103C4×C61—21no—
104C4×C61—41no—
105C4×C61—42no—
106C4×C61—81no—
107Dic61—41no—
108Dic61—81no—
109Dic61#35412yes—
110#3142—611no—
111#2126—612no—
112#1412—611no—
113#1412—611no—
114#1412—612no—
115C2×C61—21no—
116C2×C61C2×#35411yescharacteristic
117D61—41no—
118D61—82no—
119#532—611no—
120C2×#125—611no—
121#491—611no—
122#491#692311yescharacteristic, complemented
123#490—611no—
124#490—611no—
125#488—1222no—
126#417—1222no—
127#410—1222no—
128C4×M16—611no—
129#354—1222no—
130#353—612no—
131#353—612no—
132C61#1359611yescharacteristic, complemented, Sylow
133C2×#41—612no—
134C2×M16—1221no—
135C4⋊Q8C2×#692311yescharacteristic
136#127—611no—
137#125—611no—
138#125—1221no—
139#125—2441no—
140#125C2×#692311yescharacteristic
141#124—612no—
142#121—2441no—
143C4×D4—2441no—
144#117—2442no—
145C2×C4⋊C4—1221no—
146C2×C4⋊C4—2441no—
147C2×C42—611no—
148#103—22no—
149#103—1222no—
150#102—1222no—
151#102—1222no—
152#99—1222no—
153#99—1222no—
154#99—2442no—
155#97—611no—
156#97C2×#692311yescharacteristic
157C4×C8—1221no—
158#41—2442no—
159#41—2442no—
160C2×Q8C22⋊#692312yes—
161C2×D4—612no—
162C2×D4—1222no—
163C2×D4—2441no—
164C22×C4—611no—
165C22×C4—1222no—
166C22×C4—1221no—
167C22×C4—2441no—
168M16—2442no—
169C2×C8—21no—
170C2×C8—1221no—
171C4⋊C4—21no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—1221no—
175C4⋊C4—4882no—
176C4⋊C4—2441no—
177C4⋊C4—2441no—
178C4⋊C4—2441no—
179C4⋊C4—2441no—
180C22⋊C4—2442no—
181C22⋊C4—2442no—
182C22⋊C4—2442no—
183C42—611no—
184C42—1221no—
185C42—4882no—
186C42C22×#692311yescharacteristic
187C23—611no—
188C23—1222no—
189Q8—42no—
190D4—4882no—
191D4—4882no—
192D4—2442no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—41no—
196C2×C4—611no—
197C2×C4—1222no—
198C2×C4—1221no—
199C2×C4—4881no—
200C2×C4—4882no—
201C2×C4—4882no—
202C2×C4—4882no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4—2441no—
206C2×C4C2×C22⋊#692311yescharacteristic
207C8—41no—
208C8—2441no—
209C22—1221no—
210C22—4882no—
211C22—2441no—
212C22—2442no—
213C22D61⋊#9911yescharacteristic
214C4—21no—
215C4—41no—
216C4—42no—
217C4—81no—
218C4—612no—
219C4—9762no—
220C4—9762no—
221C4—4881no—
222C4—2441no—
223C2—21no—
224C2—4882no—
225C2—2441no—
226C2D61⋊#35411yescharacteristic
subgroupG/H
centerC2D61⋊#354
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#491C4
socleC2×C61C2×#354
prime radical#16840313C22
cosocle#14519774C23
hypercenter#491#6923
hypocenterC61#13596
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #21460960C2semidirect
3. #21460959C2semidirect
4. #21460958C2semidirect
11. #125×D61C4semidirect
12. #16840130C4semidirect
17. #16839714C4semidirect
18. C61×#491C4semidirect
122. #491#6923semidirect
132. C61#13596semidirect

Maximal subgroups

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

subgroupindex
#214620932
#214609602
#214609592
#214609582
#214562212
#1359661