Finite Group Databasebeta

← #29600707

Subgroups — #29600707

Order 15616.

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

normal subgroups only

This group has 278 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#21458968C211yesmaximal, characteristic, complemented
2#21448134C211yesmaximal, characteristic, complemented
3C2×#16839599C211yesmaximal, characteristic, complemented
4#21447940C211yesmaximal, characteristic, complemented
5#21444002C211yesmaximal, characteristic, complemented
6#21443962C211yesmaximal, characteristic, complemented
7C61×#1420C211yesmaximal, characteristic, complemented
8#16840575—21no—
9#16840204—22no—
10#16840203—21no—
11#16840195—21no—
12#16840194C2211yescharacteristic
13Q32×D61—21no—
14C2×D976C2211yescharacteristic
15#16840178C2211yescharacteristic
16#16840033—21no—
17#16839601—21no—
18#16839599—22no—
19D1952—21no—
20C2×#14519683C2211yescharacteristic
21#16839574—21no—
22C2×Q32×C61C2211yescharacteristic
23C61×M64C2211yescharacteristic
24C61×#368C2211yescharacteristic
25#14519825—41no—
26#14519809—42no—
27#14519808—41no—
28#14519805—41no—
29#14519800—22no—
30#14519799—21no—
31Q16×D61—22no—
32C2×D488—21no—
33#14519783D411yescharacteristic
34Dic488D411yescharacteristic
35#14519723—22no—
36#14519722—21no—
37#14519720—22no—
38D976—21no—
39D976—21no—
40D976D411yescharacteristic
41#14519717D411yescharacteristic
42#14519716—21no—
43C16×D61—21no—
44#14519693—41no—
45#14519683—21no—
46C2×Q16×C61—21no—
47Q32×C61—21no—
48Q32×C61D412yes—
49C2×C16×C61C2311yescharacteristic
50#108×C61—21no—
51C32×C61—21no—
52C2×Q8×C61—41no—
53#11758226—42no—
54#11758226—81no—
55Q8×D61—42no—
56Q8×D61—81no—
57#11758222—41no—
58#11758222—82no—
59#11758222D811yescharacteristic
60C2×D244—41no—
61Q16×C61—22no—
62Q16×C61—41no—
63M16×C61—41no—
64C2×C8×C61C2×D411yescharacteristic
65#11758202—42no—
66#11758201—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—
80C22×D61—81no—
81Q8×C61—42no—
82Q8×C61—81no—
83C2×C4×C61—81no—
84C2×C4×C61C2×D811yescharacteristic
85C22⋊D61—21no—
86C22⋊D61—81no—
87D244—41no—
88D244—82no—
89D244—81no—
90D244—81no—
91D244D1611yescharacteristic
92C4×D61—21no—
93C4×D61—82no—
94C4×D61—82no—
95C4×D61—81no—
96Dic122—41no—
97Dic122—82no—
98Dic122D1611yescharacteristic
99C8×C61—81no—
100C8×C61#12011yescharacteristic
101C8×C61AGL(1,ℤ/8)11yescharacteristic
102#92418—21no—
103#13670—611nomaximal, Sylow
104C22×C61#50911yescharacteristic
105C2×D61—21no—
106C2×D61—81no—
107C2×D61—161no—
108C2×D61—321no—
109C4×C61—82no—
110C4×C61#44711yescharacteristic
111C4×C61C2×D1611yescharacteristic
112Dic61—21no—
113Dic61—81no—
114#3417—611no—
115#2263—611no—
116C2×SD64—611no—
117#2221—611no—
118#1420D6111yescharacteristic, complemented
119#1417—611no—
120#1401—611no—
121C2×C61—21no—
122C2×C61#218411yescharacteristic
123D61—41no—
124D61—161no—
125D61—321no—
126#578—1221no—
127#510—1221no—
128#510—1222no—
129#508—611no—
130#508—1221no—
131C2×Q32—1221no—
132C2×Q32C2×D6111yescharacteristic
133C2×D16—611no—
134#504—611no—
135#472—1221no—
136SD64—1221no—
137SD64—1222no—
138D32—1221no—
139M64C2×D6111yescharacteristic
140C2×C32—611no—
141#368C2×D6111yescharacteristic
142#361—1221no—
143C61#1367011yescharacteristic, complemented, Sylow
1442−1+4—2441no—
145#137—2441no—
146#137—2442no—
147AGL(1,ℤ/8)—2441no—
148#135—1222no—
149#135—1221no—
150C2×Q16—21no—
151C2×Q16—1222no—
152C2×D8—1221no—
153#131—611no—
154Q32—21no—
155Q32—611no—
156Q32—1222no—
157Q32D24412yes—
158SD32—1222no—
159SD32—1221no—
160D16—611no—
161D16—1221no—
162D16—1221no—
163M32—611no—
164M32—1221no—
165C2×C16—1221no—
166C2×C16C22×D6111yescharacteristic
167#108—21no—
168#100—2441no—
169C32—21no—
170C32—1221no—
171#41—611no—
172#41—4882no—
173#41—4881no—
174#41—2442no—
175#41—2441no—
176C2×Q8—41no—
177C2×Q8—4881no—
178C2×Q8—2442no—
179C2×D4—2441no—
180Q16—22no—
181Q16—41no—
182Q16—1221no—
183Q16—2442no—
184SD16—4881no—
185SD16—2442no—
186SD16—2441no—
187D8—1221no—
188D8—4881no—
189D8—2441no—
190D8—2441no—
191M16—41no—
192M16—611no—
193M16—1221no—
194C2×C8—1221no—
195C2×C8D4×D6111yescharacteristic
196C16—1221no—
197C16C2×D24411yescharacteristic
198C16D4×D6111yescharacteristic
199C23—4881no—
200Q8—42no—
201Q8—81no—
202Q8—611no—
203Q8—4882no—
204Q8—2441no—
205D4—611no—
206D4—1221no—
207D4—4882no—
208D4—4881no—
209D4—4881no—
210D4—4881no—
211D4—2441no—
212C2×C4—81no—
213C2×C4—1221no—
214C2×C4—4882no—
215C2×C4—4882no—
216C2×C4—4881no—
217C2×C4D8×D6111yescharacteristic
218C8—81no—
219C8—1221no—
220C8#1451974711yescharacteristic
221C8#1451980411yescharacteristic
222C22—1221no—
223C22—19521no—
224C22—9761no—
225C22—4881no—
226C22#1684019911yescharacteristic
227C4—82no—
228C4—1221no—
229C4—4881no—
230C4#1683989711yescharacteristic
231C4D16×D6111yescharacteristic
232C2—21no—
233C2—19521no—
234C2—9761no—
235C2—2441no—
236C2#2144773211yescharacteristic
subgroupG/H
centerC2#21447732
commutator, cosocleC2×C16×C61C23
FrattiniC2×C16C22×D61
FittingC61×#1420C2
socleC2×C61#2184
hypercenter#1420D61
hypocenterC61#13670
LCSG ▷ C2×C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1420

Complements

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

NH ≅ G/Ntype
1. #21458968C2semidirect
2. #21448134C2semidirect
3. C2×#16839599C2semidirect
4. #21447940C2semidirect
5. #21444002C2semidirect
6. #21443962C2semidirect
7. C61×#1420C2semidirect
118. #1420D61semidirect
143. C61#13670semidirect

Maximal subgroups

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

subgroupindex
#214589682
#214481342
C2×#168395992
#214479402
#214440022
#214439622
C61×#14202
#1367061