Finite Group Databasebeta

← #29600700

Subgroups — #29600700

Order 15616.

288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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#21458956C211yesmaximal, characteristic, complemented
2#21448134C211yesmaximal, characteristic, complemented
3C2×#16839597C211yesmaximal, characteristic, complemented
4#21447940C211yesmaximal, characteristic, complemented
5#21444002C211yesmaximal, characteristic, complemented
6#21443962C211yesmaximal, characteristic, complemented
7C61×#1419C211yesmaximal, characteristic, complemented
8#16840563—21no—
9#16840198—21no—
10#16840196—22no—
11#16840194C2211yescharacteristic
12#16840191—21no—
13C2×D976C2211yescharacteristic, complemented
14D16×D61—21no—
15#16840178C2211yescharacteristic
16#16840033—21no—
17#16839601—21no—
18D1952—21no—
19#16839597—22no—
20C2×#14519683C2211yescharacteristic, complemented
21#16839574—21no—
22C2×D16×C61C2211yescharacteristic
23C61×M64C2211yescharacteristic, complemented
24C61×#368C2211yescharacteristic, complemented
25#14519822—41no—
26#14519805—41no—
27#14519803—41no—
28#14519801—42no—
29#14519799—21no—
30#14519796—22no—
31C2×D488—21no—
32D8×D61—22no—
33#14519783D411yescharacteristic
34Dic488D411yescharacteristic
35#14519722—21no—
36#14519721—22no—
37D976—21no—
38D976—21no—
39D976D411yescharacteristic
40#14519718—22no—
41#14519717D411yescharacteristic
42#14519716—21no—
43C16×D61—21no—
44#14519693—41no—
45#14519683—21no—
46C2×D8×C61—21no—
47D16×C61—21no—
48D16×C61D412yes—
49C2×C16×C61C2311yescharacteristic
50#108×C61—21no—
51C32×C61—21no—
52C2×D4×C61—41no—
53C2×C22⋊D61—82no—
54#11758224—42no—
55#11758224—81no—
56D4×D61—42no—
57D4×D61—81no—
58#11758222—41no—
59#11758222D811yescharacteristic
60C2×D244—41no—
61D8×C61—22no—
62D8×C61—41no—
63M16×C61—41no—
64C2×C8×C61C2×D411yescharacteristic
65#11758200—42no—
66#11758199—42no—
67#11758194D811yescharacteristic
68Dic244—21no—
69D488—21no—
70D488—41no—
71D488—41no—
72D488—81no—
73#11758190—41no—
74#11758190—81no—
75#11758189—21no—
76C8×D61—21no—
77C16×C61C2×D411yescharacteristic
78C16×C61C2×D411yescharacteristic
79#11758185—21no—
80C23×C61—81no—
81C22×D61—82no—
82C22×D61—81no—
83D4×C61—42no—
84D4×C61—81no—
85C2×C4×C61C2×D811yescharacteristic
86C22⋊D61—21no—
87C22⋊D61—82no—
88C22⋊D61—82no—
89C22⋊D61—81no—
90C2×Dic61—82no—
91D244—41no—
92D244—81no—
93D244—81no—
94D244D1611yescharacteristic
95C4×D61—21no—
96C4×D61—81no—
97Dic122—41no—
98Dic122D1611yescharacteristic
99C8×C61—81no—
100C8×C61#12011yescharacteristic
101C8×C61AGL(1,ℤ/8)11yescharacteristic
102#92418—21no—
103#13669—611nomaximal, Sylow
104C22×C61—82no—
105C22×C61—321no—
106C22×C61#50911yescharacteristic
107C2×D61—21no—
108C2×D61—81no—
109C2×D61—161no—
110C2×D61—322no—
111C2×D61—321no—
112C4×C61#44711yescharacteristic
113C4×C61C2×D1611yescharacteristic
114Dic61—21no—
115Dic61—81no—
116#3415—611no—
117#2263—611no—
118C2×D32—611no—
119#2221—611no—
120#1419D6111yescharacteristic, complemented
121#1417—611no—
122#1401—611no—
123C2×C61—21no—
124C2×C61—162no—
125C2×C61#218411yescharacteristic
126D61—41no—
127D61—161no—
128D61—321no—
129#576—1221no—
130#509—1221no—
131#509—1222no—
132#508—611no—
133#508—1221no—
134C2×D16—611no—
135C2×D16—1221no—
136C2×D16C2×D6111yescharacteristic
137#504—611no—
138#472—1221no—
139SD64—1221no—
140D32—1221no—
141D32—1222no—
142M64C2×D6111yescharacteristic, complemented
143C2×C32—611no—
144#368C2×D6111yescharacteristic, complemented
145#361—1221no—
146C61#1366911yescharacteristic, complemented, Sylow
147H(5,𝔽2)—2441no—
148AGL(1,ℤ/8)—2441no—
149AGL(1,ℤ/8)—2441no—
150AGL(1,ℤ/8)—2442no—
151#135—1222no—
152#135—1221no—
153C2×D8—21no—
154C2×D8—1222no—
155C2×D8—1221no—
156#131—611no—
157Q32—611no—
158SD32—1222no—
159SD32—1221no—
160D16—21no—
161D16—611no—
162D16—1222no—
163D16—1221no—
164D16—1221no—
165D16D24412yes—
166M32—611no—
167M32—1221no—
168C2×C16—1221no—
169C2×C16C22×D6111yescharacteristic
170#108—21no—
171#100—2441no—
172C32—21no—
173C32—1221no—
174#41—611no—
175#41—4881no—
176#41—2442no—
177#41—2441no—
178C2×D4—41no—
179C2×D4—4881no—
180C2×D4—4882no—
181C2×D4—2442no—
182C2×D4—2441no—
183Q16—1221no—
184SD16—4881no—
185SD16—2442no—
186SD16—2441no—
187D8—22no—
188D8—41no—
189D8—1221no—
190D8—4881no—
191D8—2442no—
192D8—2441no—
193D8—2441no—
194M16—41no—
195M16—611no—
196M16—1221no—
197C2×C8—1221no—
198C2×C8D4×D6111yescharacteristic
199C16—1221no—
200C16C2×D24411yescharacteristic
201C16D4×D6111yescharacteristic
202C23—81no—
203C23—4882no—
204C23—4881no—
205Q8—611no—
206Q8—2441no—
207D4—42no—
208D4—81no—
209D4—611no—
210D4—1221no—
211D4—4882no—
212D4—4882no—
213D4—4881no—
214D4—4881no—
215D4—4881no—
216D4—2441no—
217C2×C4—1221no—
218C2×C4—4882no—
219C2×C4—4881no—
220C2×C4D8×D6111yescharacteristic
221C8—81no—
222C8—1221no—
223C8#1451974711yescharacteristic
224C8#1451980411yescharacteristic
225C22—82no—
226C22—321no—
227C22—1221no—
228C22—19521no—
229C22—19522no—
230C22—9761no—
231C22—4881no—
232C22#1684019911yescharacteristic
233C4—1221no—
234C4—4881no—
235C4#1683989711yescharacteristic
236C4D16×D6111yescharacteristic
237C2—21no—
238C2—162no—
239C2—19521no—
240C2—9761no—
241C2—2441no—
242C2#2144773211yescharacteristic
subgroupG/H
centerC2#21447732
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1419C2
socleC2×C61#2184
hypercenter#1419D61
hypocenterC61#13669
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
1. #21458956C2semidirect
2. #21448134C2semidirect
3. C2×#16839597C2semidirect
4. #21447940C2semidirect
5. #21444002C2semidirect
6. #21443962C2semidirect
7. C61×#1419C2semidirect
13. C2×D976C22semidirect
20. C2×#14519683C22semidirect
23. C61×M64C22semidirect
24. C61×#368C22semidirect
120. #1419D61semidirect
142. M64C2×D61semidirect
144. #368C2×D61semidirect
146. C61#13669semidirect

Maximal subgroups

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

subgroupindex
#214589562
#214481342
C2×#168395972
#214479402
#214440022
#214439622
C61×#14192
#1366961