Finite Group Databasebeta

← #29600365

Subgroups — #29600365

Order 15616.

326 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 59 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#21456218C211yesmaximal, characteristic
2#21447481C212yesmaximal
3#21443990C211yesmaximal, characteristic, complemented
4#21443989C212yesmaximal, complemented
5C61×#1412C211yesmaximal, characteristic, complemented
6#16840310C2211yescharacteristic
7#125×D61C411yescharacteristic, complemented
8#16840132C411yescharacteristic, complemented
9#16840131C411yescharacteristic, complemented
10#16840126C2211yescharacteristic
11#16840115—22no—
12#16839760—22no—
13#16839734—22no—
14#16839714C411yescharacteristic, complemented
15#16839556—22no—
16#16839555C2212yes—
17C61×#490C2211yescharacteristic
18C61×#353C2212yes—
19C2×#11758224D412yes—
20C2×#11758189—21no—
21#14519777C2×C411yescharacteristic
22#14519769C2×C411yescharacteristic
23#14519768—21no—
24#14519767—41no—
25#14519764D412yes—
26#14519748—41no—
27D4×Dic61—41no—
28#14519733—42no—
29C4⋊C4×D61—21no—
30C4⋊C4×D61—41no—
31C42×D61C2×C411yescharacteristic
32#14519702—22no—
33#14519700—22no—
34#14519698—22no—
35#14519692—22no—
36#14519691—42no—
37#14519688C2×C411yescharacteristic
38C8×Dic61—21no—
39#127×C61C2311yescharacteristic
40#125×C61C2×C411yescharacteristic
41#102×C61—22no—
42#99×C61—22no—
43#97×C61C2×C411yescharacteristic
44C2×D4×C61—41no—
45C2×D4×C61C2×D412yes—
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×Dic122C22⋊C412yes—
54C2×C8×C61—21no—
55C4⋊C4×C61—21no—
56C4⋊C4×C61—41no—
57C22⋊C4×C61—42no—
58C42×C61C22×C411yescharacteristic
59C22⋊Dic61—42no—
60C22⋊Dic61—42no—
61C4⋊Dic61—21no—
62C4⋊Dic61—41no—
63C4⋊Dic61—41no—
64#11758196—41no—
65#11758196—41no—
66#11758196—41no—
67#11758196—82no—
68C4×Dic61—21no—
69C4×Dic61—82no—
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×C61—82no—
80C2×C4×C61C2×C22⋊C411yescharacteristic
81C22⋊D61—82no—
82C2×Dic61—21no—
83C2×Dic61—22no—
84C2×Dic61—42no—
85C2×Dic61—42no—
86C2×Dic61—41no—
87C2×Dic61—82no—
88C2×Dic61#9911yescharacteristic
89C4×D61—22no—
90C4×D61—81no—
91C4×D61—82no—
92Dic122—42no—
93C8×C61—41no—
94#92418—41no—
95#13596—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—
104C4×C61—162no—
105Dic61—41no—
106Dic61—42no—
107Dic61—81no—
108Dic61—162no—
109Dic61#35412yes—
110#3142—611no—
111#2126—612no—
112#1412—611no—
113#1412—612no—
114#1412D6111yescharacteristic, complemented
115C2×C61—21no—
116C2×C61—82no—
117C2×C61C2×#35411yescharacteristic
118D61—41no—
119#532—611no—
120C2×#125—611no—
121#491—611no—
122#491—611no—
123#490—611no—
124#490C2×D6111yescharacteristic
125#488—1222no—
126#417—1222no—
127#410—1222no—
128C4×M16—611no—
129#354—1222no—
130#353—612no—
131#353C2×D6112yes—
132C61#1359611yescharacteristic, complemented, Sylow
133C2×#41—612no—
134C2×M16—1221no—
135C4⋊Q8—611no—
136#127C22×D6111yescharacteristic
137#125—611no—
138#125—1221no—
139#125—2441no—
140#125C4×D6111yescharacteristic
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—1222no—
149#103—1222no—
150#102—22no—
151#102—1222no—
152#99—22no—
153#99—1222no—
154#99—2442no—
155#97—611no—
156#97C4×D6111yescharacteristic
157C4×C8—1221no—
158#41—2442no—
159#41—2442no—
160C2×Q8—612no—
161C2×D4—41no—
162C2×D4—1222no—
163C2×D4D4×D6112yes—
164C22×C4—611no—
165C22×C4—1221no—
166C22×C4—1222no—
167C22×C4—2441no—
168M16—2442no—
169C2×C8—21no—
170C2×C8—1221no—
171C4⋊C4—21no—
172C4⋊C4—41no—
173C4⋊C4—1221no—
174C4⋊C4—4882no—
175C4⋊C4—2441no—
176C4⋊C4—2441no—
177C4⋊C4—2441no—
178C4⋊C4—2441no—
179C4⋊C4—2441no—
180C22⋊C4—42no—
181C22⋊C4—2442no—
182C22⋊C4—2442no—
183C42—611no—
184C42—1221no—
185C42—4882no—
186C42C2×C4×D6111yescharacteristic
187C23—22no—
188C23—611no—
189Q8—2442no—
190D4—42no—
191D4—82no—
192D4—4882no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—82no—
196C2×C4—611no—
197C2×C4—1222no—
198C2×C4—1221no—
199C2×C4—1222no—
200C2×C4—4881no—
201C2×C4—4882no—
202C2×C4—4882no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4—2441no—
206C2×C4C22⋊C4×D6111yescharacteristic
207C8—41no—
208C8—2441no—
209C22—42no—
210C22—82no—
211C22—1221no—
212C22—2441no—
213C22#99×D6111yescharacteristic
214C4—21no—
215C4—41no—
216C4—81no—
217C4—162no—
218C4—612no—
219C4—9762no—
220C4—4881no—
221C4—2441no—
222C4—2442no—
223C2—21no—
224C2—82no—
225C2—2441no—
226C2#354×D6111yescharacteristic
subgroupG/H
centerC2#354×D61
commutatorC42×C61C22×C4
Frattini#127C22×D61
FittingC61×#1412C2
socleC2×C61C2×#354
prime radical#16840310C22
cosocle#127×C61C23
hypercenter#1412D61
hypocenterC61#13596
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #1412

Complements

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

NH ≅ G/Ntype
3. #21443990C2semidirect
4. #21443989C2semidirect
5. C61×#1412C2semidirect
7. #125×D61C4semidirect
8. #16840132C4semidirect
9. #16840131C4semidirect
14. #16839714C4semidirect
114. #1412D61semidirect
132. C61#13596semidirect

Maximal subgroups

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

subgroupindex
#214562182
#214474812
#214439902
#214439892
C61×#14122
#1359661