Finite Group Databasebeta

← #29600696

Subgroups — #29600696

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#21448132C211yesmaximal, characteristic, complemented
3#21447936C211yesmaximal, characteristic, complemented
4#21444009C211yesmaximal, characteristic, complemented
5#21444004C211yesmaximal, characteristic, complemented
6#21443960C211yesmaximal, characteristic, complemented
7C2×C61×D32C211yesmaximal, characteristic, complemented
8#16840563—21no—
9#16840198—21no—
10#16840196—22no—
11#16840194C2211yescharacteristic
12#16840191—21no—
13D16×D61—21no—
14#16840178C2211yescharacteristic
15#16840029—21no—
16#16839600—21no—
17#16839597—21no—
18#16839596C2211yescharacteristic, complemented
19#16839592C2211yescharacteristic, complemented
20#16839575—21no—
21C2×D16×C61C2211yescharacteristic
22C2×D16×C61C2211yescharacteristic, complemented
23C61×D32—22no—
24C2×C32×C61C2211yescharacteristic, complemented
25#14519822—41no—
26#14519803—41no—
27#14519803—41no—
28#14519801—42no—
29#14519799—21no—
30#14519796—22no—
31D8×D61—22no—
32#14519783D411yescharacteristic
33Dic488D411yescharacteristic
34#14519722—21no—
35#14519721—22no—
36D976D411yescharacteristic
37#14519718—22no—
38#14519717D411yescharacteristic
39#14519716—21no—
40C16×D61—21no—
41#14519713—21no—
42#14519694—41no—
43#14519683—21no—
44C2×D8×C61—21no—
45C2×D8×C61—21no—
46D16×C61—21no—
47D16×C61—21no—
48D16×C61—21no—
49D16×C61D412yes—
50C2×C16×C61C2311yescharacteristic
51C32×C61—21no—
52C2×D4×C61—41no—
53C2×D4×C61—41no—
54C2×C22⋊D61—82no—
55#11758224—42no—
56#11758224—81no—
57D4×D61—42no—
58D4×D61—81no—
59#11758222—41no—
60#11758222D811yescharacteristic
61D8×C61—22no—
62D8×C61—41no—
63D8×C61—41no—
64D8×C61—41no—
65C2×C8×C61C2×D411yescharacteristic
66#11758200—42no—
67#11758200—81no—
68#11758199—42no—
69#11758199—81no—
70#11758194—41no—
71#11758194D811yescharacteristic
72Dic244—21no—
73D488—21no—
74#11758190—41no—
75#11758189—21no—
76C8×D61—21no—
77C16×C61C2×D411yescharacteristic
78C16×C61C2×D411yescharacteristic
79#11758185—21no—
80C23×C61—81no—
81C23×C61—81no—
82C22×D61—82no—
83D4×C61—42no—
84D4×C61—81no—
85D4×C61—81no—
86D4×C61—81no—
87C2×C4×C61C2×D811yescharacteristic
88C22⋊D61—21no—
89C22⋊D61—82no—
90C22⋊D61—82no—
91C22⋊D61—81no—
92C2×Dic61—82no—
93D244—41no—
94D244D1611yescharacteristic
95C4×D61—21no—
96C4×D61—81no—
97Dic122—41no—
98Dic122D1611yescharacteristic
99C8×C61#12011yescharacteristic
100C8×C61AGL(1,ℤ/8)11yescharacteristic
101#92418—21no—
102#92418—81no—
103#13669—611nomaximal, Sylow
104C22×C61—82no—
105C22×C61—161no—
106C22×C61—321no—
107C22×C61—321no—
108C22×C61#50911yescharacteristic
109C2×D61—21no—
110C2×D61—81no—
111C2×D61—322no—
112C4×C61#44711yescharacteristic
113C4×C61C2×D1611yescharacteristic
114Dic61—21no—
115Dic61—81no—
116#3415—611no—
117#2263—611no—
118C2×D32D6111yescharacteristic, complemented
119#2221—611no—
120#1419—611no—
121#1417—611no—
122#1401—611no—
123C2×C61—21no—
124C2×C61—162no—
125C2×C61—321no—
126C2×C61#218411yescharacteristic
127D61—41no—
128D61—161no—
129#576—1221no—
130#509—1221no—
131#509—1222no—
132#508—611no—
133#508—1221no—
134C2×D16—1221no—
135C2×D16C2×D6111yescharacteristic
136C2×D16C2×D6111yescharacteristic, complemented
137#504—611no—
138#472—1221no—
139SD64—1221no—
140D32—22no—
141D32—1221no—
142M64—611no—
143C2×C32C2×D6111yescharacteristic, complemented
144#368—611no—
145#361—1221no—
146C61#1366911yescharacteristic, complemented, Sylow
147H(5,𝔽2)—2441no—
148AGL(1,ℤ/8)—2441no—
149AGL(1,ℤ/8)—2442no—
150AGL(1,ℤ/8)—2441no—
151#135—1222no—
152#135—1221no—
153C2×D8—21no—
154C2×D8—21no—
155C2×D8—1222no—
156#131—611no—
157Q32—611no—
158SD32—1222no—
159SD32—1221no—
160D16—21no—
161D16—21no—
162D16—21no—
163D16—611no—
164D16—1222no—
165D16C22⋊D6112yes—
166M32—611no—
167M32—1221no—
168C2×C16—1221no—
169C2×C16C22×D6111yescharacteristic
170#108—1221no—
171#100—2441no—
172C32—21no—
173C32—1221no—
174#41—611no—
175#41—4881no—
176#41—2442no—
177#41—2441no—
178C2×D4—41no—
179C2×D4—41no—
180C2×D4—4881no—
181C2×D4—4882no—
182C2×D4—2442no—
183Q16—1221no—
184SD16—4881no—
185SD16—2442no—
186SD16—2441no—
187D8—22no—
188D8—41no—
189D8—41no—
190D8—41no—
191D8—1221no—
192D8—4881no—
193D8—2442no—
194M16—611no—
195M16—1221no—
196M16—2441no—
197C2×C8—1221no—
198C2×C8D4×D6111yescharacteristic
199C16—1221no—
200C16D4×D6111yescharacteristic
201C16C2×C22⋊D6111yescharacteristic
202C23—81no—
203C23—81no—
204C23—4882no—
205Q8—611no—
206Q8—2441no—
207D4—42no—
208D4—81no—
209D4—81no—
210D4—81no—
211D4—611no—
212D4—1221no—
213D4—4882no—
214D4—4882no—
215D4—4881no—
216D4—2441no—
217C2×C4—1221no—
218C2×C4—4882no—
219C2×C4—4881no—
220C2×C4D8×D6111yescharacteristic
221C8—1221no—
222C8—4881no—
223C8#1451974511yescharacteristic
224C8#1451980111yescharacteristic
225C22—82no—
226C22—161no—
227C22—321no—
228C22—321no—
229C22—1221no—
230C22—19522no—
231C22—4881no—
232C22#1684019611yescharacteristic
233C4—1221no—
234C4—4881no—
235C4#1683989411yescharacteristic
236C4D16×D6111yescharacteristic
237C2—21no—
238C2—162no—
239C2—321no—
240C2—9761no—
241C2—2441no—
242C2#2144772911yescharacteristic
subgroupG/H
centerC2#21447729
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC2×C61×D32C2
socleC2×C61#2184
hypercenterC2×D32D61
hypocenterC61#13669
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D32

Complements

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

NH ≅ G/Ntype
1. #21458956C2semidirect
2. #21448132C2semidirect
3. #21447936C2semidirect
4. #21444009C2semidirect
5. #21444004C2semidirect
6. #21443960C2semidirect
7. C2×C61×D32C2semidirect
18. #16839596C22semidirect
19. #16839592C22semidirect
22. C2×D16×C61C22semidirect
24. C2×C32×C61C22semidirect
118. C2×D32D61semidirect
136. C2×D16C2×D61semidirect
143. C2×C32C2×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
#214481322
#214479362
#214440092
#214440042
#214439602
C2×C61×D322
#1366961