Finite Group Databasebeta

← #29600688

Subgroups — #29600688

Order 15616.

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

normal subgroups only

This group has 294 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#21458955C211yesmaximal, characteristic, complemented
2#21448134C212yesmaximal, complemented
3#21447922C211yesmaximal, characteristic, complemented
4#21444007C212yesmaximal, complemented
5C61×#1400C211yesmaximal, characteristic, complemented
6C2×#14519799—21no—
7#16840205—22no—
8#16840200—22no—
9#16840194—21no—
10#16840194C2212yes—
11C2×D976C2211yescharacteristic, complemented
12#16839998—21no—
13#16839601—22no—
14D1952—22no—
15#16839590C2211yescharacteristic, complemented
16#16839564—21no—
17C2×M32×C61C2211yescharacteristic
18C61×M64C2212yescomplemented
19C2×#11758222—41no—
20#14519799—22no—
21#14519799—22no—
22#14519799—41no—
23#14519799—41no—
24C2×Dic244—21no—
25C2×#11758190—41no—
26C2×D488—21no—
27C2×D488—21no—
28#14519751—41no—
29Dic488—21no—
30Dic488D412yescomplemented
31#14519722—22no—
32#14519722—22no—
33D976—21no—
34D976—22no—
35D976D412yescomplemented
36#14519711—21no—
37#14519699—41no—
38C22×C8×C61D411yescharacteristic
39M32×C61—22no—
40C2×C16×C61D411yescharacteristic
41C2×C16×C61C2311yescharacteristic
42C32×C61—22no—
43C22×C4×C61D811yescharacteristic
44C2×C22⋊D61—81no—
45C2×C22⋊D61—81no—
46#11758222—42no—
47#11758222—42no—
48#11758222—81no—
49#11758222—81no—
50C2×D244—41no—
51C2×D244—41no—
52C2×C4×D61—81no—
53C2×Dic122—41no—
54C2×C8×C61—21no—
55C2×C8×C61—21no—
56C2×C8×C61D811yescharacteristic
57C2×C8×C61C2×D411yescharacteristic
58#11758198—81no—
59C4⋊Dic61—41no—
60Dic244—22no—
61Dic244—41no—
62D488—22no—
63D488—41no—
64D488—41no—
65D488—41no—
66#11758190—42no—
67#11758190—42no—
68C16×C61—21no—
69C16×C61C2×D412yes—
70C23×C61D1611yescharacteristic
71C22×D61—81no—
72C22×D61—81no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61D1611yescharacteristic
76C2×C4×C61C2×D811yescharacteristic
77C22⋊D61—82no—
78C22⋊D61—82no—
79C22⋊D61—162no—
80C2×Dic61—81no—
81C2×Dic61—81no—
82D244—42no—
83D244—81no—
84D244—81no—
85D244—81no—
86C4×D61—82no—
87C4×D61—82no—
88Dic122—42no—
89Dic122—81no—
90C8×C61—21no—
91C8×C61#12011yescharacteristic
92C8×C61AGL(1,ℤ/8)11yescharacteristic
93#13667—611nomaximal, Sylow
94C22×C61—21no—
95C22×C61—41no—
96C22×C61C2×D1611yescharacteristic
97C2×D61—82no—
98C2×D61—162no—
99C2×D61—161no—
100C2×D61—161no—
101C2×D61—161no—
102C4×C61—21no—
103C4×C61#44711yescharacteristic
104C4×C61#50911yescharacteristic
105Dic61—82no—
106Dic61—161no—
107#3414—611no—
108#2263—612no—
109#2218—611no—
110#1418—612no—
111#1400D6111yescharacteristic, complemented
112C2×C61—21no—
113C2×C61—41no—
114C2×C61#218411yescharacteristic
115D61—162no—
116D61—321no—
117C2×#135—1221no—
118#510—1222no—
119#509—1222no—
120#508—612no—
121#508—1221no—
122C2×D16—611no—
123C2×M32C2×D6111yescharacteristic
124#466—1221no—
125SD64—1222no—
126D32—1222no—
127M64C2×D6112yescomplemented
128#367—611no—
129#357—1221no—
130C61#1366711yescharacteristic, complemented, Sylow
131C2×#41—2441no—
132#135—1222no—
133#135—1222no—
134#135—2441no—
135#135—2441no—
136C2×Q16—1221no—
137C2×SD16—2441no—
138C2×D8—1221no—
139C2×D8—1221no—
140C22×C8D24411yescharacteristic
141#121—2441no—
142Q32—612no—
143Q32—1221no—
144SD32—1222no—
145SD32—1222no—
146D16—612no—
147D16—1221no—
148D16—1222no—
149M32—22no—
150C2×C16D24411yescharacteristic
151C2×C16C22×D6111yescharacteristic
152#107—1221no—
153#102—2441no—
154C32—22no—
155#41—4881no—
156#41—4881no—
157#41—2442no—
158#41—2442no—
159C2×Q8—2441no—
160C2×D4—4881no—
161C2×D4—4881no—
162C2×D4—2441no—
163C2×D4—2441no—
164C22×C4—4881no—
165C22×C4D48811yescharacteristic
166Q16—1222no—
167Q16—2441no—
168SD16—2442no—
169SD16—2442no—
170D8—1222no—
171D8—2441no—
172D8—2441no—
173D8—2441no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8D48811yescharacteristic
177C2×C8C2×D24411yescharacteristic
178C4⋊C4—2441no—
179C22⋊C4—4881no—
180C16—21no—
181C16D4×D6112yes—
182C23—4881no—
183C23—4881no—
184C23D97611yescharacteristic
185Q8—4881no—
186Q8—2442no—
187D4—9762no—
188D4—4881no—
189D4—4882no—
190D4—4882no—
191D4—4881no—
192D4—4881no—
193D4—2442no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—4882no—
197C2×C4—4881no—
198C2×C4—4881no—
199C2×C4—4882no—
200C2×C4D97611yescharacteristic
201C2×C4C2×D48811yescharacteristic
202C8—21no—
203C8#1451974711yescharacteristic
204C8#1451980511yescharacteristic
205C22—21no—
206C22—41no—
207C22—9761no—
208C22—9761no—
209C22—9762no—
210C22—9761no—
211C22—4882no—
212C22C2×D97611yescharacteristic
213C4—21no—
214C4—9761no—
215C4—4882no—
216C4#1683989811yescharacteristic
217C4#1684020011yescharacteristic
218C2—21no—
219C2—41no—
220C2—19521no—
221C2—9762no—
222C2#2144773311yescharacteristic
subgroupG/H
centerC2#21447733
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1400C2
socleC2×C61#2184
hypercenter#1400D61
hypocenterC61#13667
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32 ◁ #1400

Complements

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

NH ≅ G/Ntype
1. #21458955C2semidirect
2. #21448134C2semidirect
3. #21447922C2semidirect
4. #21444007C2semidirect
5. C61×#1400C2semidirect
11. C2×D976C22semidirect
15. #16839590C22semidirect
18. C61×M64C22semidirect
30. Dic488D4semidirect
35. D976D4semidirect
111. #1400D61semidirect
127. M64C2×D61semidirect
130. C61#13667semidirect

Maximal subgroups

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

subgroupindex
#214589552
#214481342
#214479222
#214440072
C61×#14002
#1366761