Finite Group Databasebeta

← #29594448

Subgroups — #29594448

Order 15616.

224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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
1C16×D244C211yesmaximal, characteristic
2#21445205C211yesmaximal, characteristic
3#21445181C211yesmaximal, characteristic
4#21443893C211yesmaximal, characteristic, complemented
5#21443874C211yesmaximal, characteristic, complemented
6#21443868C211yesmaximal, characteristic, complemented
7C61×#2241C211yesmaximal, characteristic, complemented
8C2×C16×D61—21no—
9#16840039—21no—
10#16839964—21no—
11C8×D244C2211yescharacteristic
12C4⋊#11758185C2211yescharacteristic
13#16839541—21no—
14#16839515C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839508—21no—
17#16839508—21no—
18C61×#500C2211yescharacteristic
19C61×#494C2211yescharacteristic
20C61×#358—21no—
21C61×#358—21no—
22C4×C16×C61C2211yescharacteristic
23C2×#11758201—41no—
24C2×C8×D61—21no—
25C4×D244D411yescharacteristic
26C2×#11758185—21no—
27C16×D61—42no—
28#14519710—41no—
29C4⋊#92418—21no—
30C4⋊#92418—21no—
31C4⋊#92418D411yescharacteristic
32#14519701—41no—
33#14519697—41no—
34#14519689—21no—
35C2×Q16×C61—21no—
36C2×Q16×C61—21no—
37C4⋊Q8×C61—21no—
38C4⋊Q8×C61—21no—
39C2×C16×C61D411yescharacteristic
40C2×C16×C61D411yescharacteristic
41#107×C61—21no—
42#107×C61—21no—
43C4×C8×C61C2311yescharacteristic
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C2×D244D811yescharacteristic
47C2×C4×D61—21no—
48Q16×C61—41no—
49Q16×C61—41no—
50Q16×C61—81no—
51C2×C8×C61C2×D411yescharacteristic
52C2×C8×C61#4111yescharacteristic
53C4⋊C4×C61—41no—
54C4⋊C4×C61—41no—
55C4⋊C4×C61—41no—
56C4⋊C4×C61—41no—
57C42×C61C2×D411yescharacteristic
58#11758201—82no—
59#11758198—21no—
60C4⋊Dic61D811yescharacteristic
61C2×#92418—21no—
62C2×#92418—41no—
63C2×#92418—41no—
64C8×D61—41no—
65C8×D61—41no—
66C16×C61—21no—
67C16×C61—21no—
68#11758185—41no—
69C22×D61—21no—
70Q8×C61—81no—
71Q8×C61—81no—
72Q8×C61—81no—
73Q8×C61—81no—
74C2×C4×C61—81no—
75C2×C4×C61—81no—
76C2×C4×C61#12111yescharacteristic
77C2×C4×C61C2×D811yescharacteristic
78C2×C4×C61#13511yescharacteristic
79C2×Dic61—21no—
80D244—21no—
81D244SD3212yes—
82C4×D61—41no—
83C4×D61—41no—
84C8×C61—21no—
85C8×C61#13511yescharacteristic
86C8×C61AGL(1,ℤ/8)11yescharacteristic
87#92418—41no—
88#92418—81no—
89#92418—81no—
90#12470—611nomaximal, Sylow
91C22×C61#46611yescharacteristic
92C2×D61—22no—
93C2×D61—41no—
94C2×D61—41no—
95C4×C61—21no—
96C4×C61—161no—
97C4×C61—161no—
98C4×C61#46311yescharacteristic
99C4×C61#47111yescharacteristic
100C4×C61C2×SD3211yescharacteristic
101C4×C61#50811yescharacteristic
102Dic61—41no—
103#2241D6111yescharacteristic, complemented
104D4×C16—611no—
105#1673—611no—
106#1669—611no—
107#1372—611no—
108#1364—611no—
109#1362—611no—
110C2×C61#168111yescharacteristic
111C2×C61#221711yescharacteristic
112C2×C61#222211yescharacteristic
113D61—42no—
114C22×C16—1221no—
115#500C2×D6111yescharacteristic
116#494C2×D6111yescharacteristic
117#474—1221no—
118#461—1221no—
119C8×D4—611no—
120C4⋊C16—611no—
121#358—21no—
122#358—21no—
123C22⋊C16—1221no—
124C4×C16C2×D6111yescharacteristic
125#335—611no—
126#335—611no—
127#332—1221no—
128#332—1221no—
129C61#1247011yescharacteristic, complemented, Sylow
130C2×Q16—21no—
131C2×Q16—21no—
132C2×SD16—2441no—
133C22×C8—1221no—
134C4⋊Q8—21no—
135C4⋊Q8—21no—
136C4×D4—611no—
137C2×C16—1221no—
138C2×C16—2442no—
139C2×C16C22⋊D6111yescharacteristic
140C2×C16C22⋊D6111yescharacteristic
141#107—21no—
142#107—21no—
143#107—2441no—
144C4⋊C8—611no—
145C4⋊C8—1221no—
146C4⋊C8—1221no—
147#103—2441no—
148#102—2441no—
149C22⋊C8—1221no—
150C4×C8C22×D6111yescharacteristic
151C2×Q8—41no—
152C2×Q8—41no—
153C2×D4—611no—
154C22×C4—1221no—
155Q16—41no—
156Q16—41no—
157Q16—81no—
158SD16—4882no—
159C2×C8—1221no—
160C2×C8—2441no—
161C2×C8—2441no—
162C2×C8—2441no—
163C2×C8—2441no—
164C2×C8#1175822411yescharacteristic
165C2×C8C2×C22⋊D6111yescharacteristic
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—611no—
171C22⋊C4—1221no—
172C42D4×D6111yescharacteristic
173C16—21no—
174C16—21no—
175C16—2441no—
176C23—1221no—
177Q8—81no—
178Q8—81no—
179Q8—81no—
180Q8—81no—
181D4—612no—
182D4—1221no—
183C2×C4—81no—
184C2×C4—81no—
185C2×C4—1221no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4#1451974811yescharacteristic
189C2×C4D8×D6111yescharacteristic
190C2×C4#1451979611yescharacteristic
191C8—21no—
192C8—4881no—
193C8—4881no—
194C8—2441no—
195C8#1451979711yescharacteristic
196C8#1451980211yescharacteristic
197C22—1222no—
198C22—2441no—
199C22—2441no—
200C22#1683999511yescharacteristic
201C4—21no—
202C4—161no—
203C4—161no—
204C4—2441no—
205C4#1683997411yescharacteristic
206C4#1684002211yescharacteristic
207C4SD32×D6111yescharacteristic
208C4#1684019311yescharacteristic
209C2—2442no—
210C2#2144525311yescharacteristic
211C2#2144791211yescharacteristic
212C2#2144794111yescharacteristic
subgroupG/H
centerC22#16839995
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#2241C2
socleC22×C61#466
prime radicalC2×D244D8
hypercenter#2241D61
hypocenterC61#12470
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2241

Complements

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

NH ≅ G/Ntype
4. #21443893C2semidirect
5. #21443874C2semidirect
6. #21443868C2semidirect
7. C61×#2241C2semidirect
103. #2241D61semidirect
129. C61#12470semidirect

Maximal subgroups

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

subgroupindex
C16×D2442
#214452052
#214451812
#214438932
#214438742
#214438682
C61×#22412
#1247061