Finite Group Databasebeta

← #29594443

Subgroups — #29594443

Order 15616.

218 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 63 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#21448046C211yesmaximal, characteristic, complemented
2#21447638C211yesmaximal, characteristic
3#21445219C211yesmaximal, characteristic
4#21445181C211yesmaximal, characteristic
5#21443890C211yesmaximal, characteristic, complemented
6#21443876C211yesmaximal, characteristic, complemented
7C61×#1362C211yesmaximal, characteristic, complemented
8C2×C16×D61—21no—
9#16840167C2211yescharacteristic
10#16840053—21no—
11#16840039—21no—
12C8×D244C2211yescharacteristic
13#16839566—21no—
14#16839566—21no—
15#16839541—21no—
16C4×#11758185C2211yescharacteristic
17#16839515C2211yescharacteristic
18#16839510—21no—
19#16839508—21no—
20C61×#494C2211yescharacteristic
21C61×C4⋊C16C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×C8×D61—21no—
24#14519777—21no—
25C4×D244D411yescharacteristic
26C2×#11758185D411yescharacteristic
27C2×#11758185D411yescharacteristic
28C16×D61—42no—
29#14519711—21no—
30#14519711—21no—
31#14519710—41no—
32#14519709—41no—
33C4⋊#92418—21no—
34C4⋊#92418D411yescharacteristic
35#14519699—41no—
36#14519697—41no—
37#14519689—21no—
38C2×Q16×C61—21no—
39C2×Q16×C61—21no—
40C4⋊Q8×C61—21no—
41C2×C16×C61—21no—
42C4⋊C8×C61—21no—
43C4×C8×C61C2311yescharacteristic
44C2×Q8×C61—41no—
45C2×D244D811yescharacteristic
46C2×C4×D61—21no—
47C2×Dic122—41no—
48Q16×C61—41no—
49Q16×C61—41no—
50Q16×C61—81no—
51C2×C8×C61—41no—
52C2×C8×C61C2×D411yescharacteristic
53C2×C8×C61#4111yescharacteristic
54C4⋊C4×C61—41no—
55C4⋊C4×C61—41no—
56C42×C61C2×D411yescharacteristic
57#11758198—21no—
58C4⋊Dic61—41no—
59C4⋊Dic61—41no—
60C4⋊Dic61D811yescharacteristic
61C2×#92418—21no—
62C2×#92418—41no—
63C8×D61—41no—
64C8×D61—41no—
65C16×C61—41no—
66#11758185—21no—
67#11758185—21no—
68C22×D61—21no—
69Q8×C61—81no—
70Q8×C61—81no—
71C2×C4×C61—81no—
72C2×C4×C61#12111yescharacteristic
73C2×C4×C61C2×D811yescharacteristic
74C2×C4×C61#13511yescharacteristic
75C2×Dic61—21no—
76C2×Dic61—81no—
77D244—21no—
78D244Q3212yes—
79C4×D61—41no—
80C4×D61—41no—
81Dic122—161no—
82C8×C61—21no—
83C8×C61—81no—
84C8×C61#13511yescharacteristic
85C8×C61AGL(1,ℤ/8)11yescharacteristic
86#92418—41no—
87#92418—81no—
88#12469—611nomaximal, Sylow
89C22×C61#46611yescharacteristic
90C2×D61—22no—
91C2×D61—41no—
92C2×D61—41no—
93C4×C61—21no—
94C4×C61—161no—
95C4×C61#46311yescharacteristic
96C4×C61#47111yescharacteristic
97C4×C61C2×Q3211yescharacteristic
98C4×C61#50811yescharacteristic
99Dic61—41no—
100Dic61—161no—
101#2241—611no—
102D4×C16—611no—
103#1675—611no—
104#1669—611no—
105#1371—611no—
106#1365—611no—
107#1362D6111yescharacteristic, complemented
108C2×C61#168111yescharacteristic
109C2×C61#221611yescharacteristic
110C2×C61#222311yescharacteristic
111D61—42no—
112C22×C16—1221no—
113#500—611no—
114#494C2×D6111yescharacteristic
115#476—1221no—
116#474—1221no—
117C8×D4—611no—
118C4⋊C16C2×D6111yescharacteristic
119#358—1221no—
120#358—1221no—
121C22⋊C16—1221no—
122C4×C16—611no—
123#335—611no—
124#335C2×D6111yescharacteristic
125#333—1221no—
126#332—1221no—
127C61#1246911yescharacteristic, complemented, Sylow
128C2×Q16—21no—
129C2×Q16—21no—
130C22×C8—1221no—
131C4⋊Q8—21no—
132C4⋊Q8—1221no—
133C4×D4—611no—
134C2×C16—21no—
135C2×C16—611no—
136C2×C16—611no—
137C2×C16—2442no—
138#107—1221no—
139#107—1221no—
140#107—2441no—
141#106—2441no—
142C4⋊C8—21no—
143C4⋊C8—611no—
144C4⋊C8—1221no—
145#102—2441no—
146#102—2441no—
147C22⋊C8—1221no—
148C4×C8C22×D6111yescharacteristic
149C2×Q8—41no—
150C2×Q8—2441no—
151C2×D4—611no—
152C22×C4—1221no—
153Q16—41no—
154Q16—41no—
155Q16—81no—
156C2×C8—41no—
157C2×C8—1221no—
158C2×C8—2441no—
159C2×C8—2441no—
160C2×C8—2441no—
161C2×C8#1175822211yescharacteristic
162C2×C8D4×D6111yescharacteristic
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—611no—
166C4⋊C4—2441no—
167C4⋊C4—2441no—
168C22⋊C4—1221no—
169C42D4×D6111yescharacteristic
170C16—41no—
171C16—1221no—
172C16—1221no—
173C23—1221no—
174Q8—81no—
175Q8—81no—
176Q8—9761no—
177D4—612no—
178D4—1221no—
179C2×C4—81no—
180C2×C4—1221no—
181C2×C4—4881no—
182C2×C4—2441no—
183C2×C4—2441no—
184C2×C4#1451975011yescharacteristic
185C2×C4D8×D6111yescharacteristic
186C2×C4#1451979811yescharacteristic
187C8—21no—
188C8—81no—
189C8—4881no—
190C8—2441no—
191C8#1451979811yescharacteristic
192C8#1451980111yescharacteristic
193C22—1222no—
194C22—2441no—
195C22—2441no—
196C22#1683999711yescharacteristic
197C4—21no—
198C4—161no—
199C4—9761no—
200C4—2441no—
201C4#1683997611yescharacteristic
202C4#1684002411yescharacteristic
203C4Q32×D6111yescharacteristic
204C4#1684019311yescharacteristic
205C2—2442no—
206C2#2144525511yescharacteristic
207C2#2144790911yescharacteristic
208C2#2144795211yescharacteristic
subgroupG/H
centerC22#16839997
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1362C2
socleC22×C61#466
prime radicalC2×D244D8
hypercenter#1362D61
hypocenterC61#12469
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
1. #21448046C2semidirect
5. #21443890C2semidirect
6. #21443876C2semidirect
7. C61×#1362C2semidirect
107. #1362D61semidirect
127. C61#12469semidirect

Maximal subgroups

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

subgroupindex
#214480462
#214476382
#214452192
#214451812
#214438902
#214438762
C61×#13622
#1246961