Finite Group Databasebeta

← #29594445

Subgroups — #29594445

Order 15616.

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

normal subgroups only

This group has 218 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
1#21448047C211yesmaximal, characteristic, complemented
2C16×D244C211yesmaximal, characteristic
3#21445219C211yesmaximal, characteristic
4#21445185C211yesmaximal, characteristic
5#21443878C211yesmaximal, characteristic, complemented
6#21443867C211yesmaximal, characteristic, complemented
7C61×#1371C211yesmaximal, characteristic, complemented
8C2×C16×D61—21no—
9#16840167C2211yescharacteristic
10#16840142C2211yescharacteristic
11#16840053—21no—
12#16840043—21no—
13C8×D244C2211yescharacteristic
14C4⋊#11758185C2211yescharacteristic
15#16839567—21no—
16#16839567—21no—
17#16839541—21no—
18#16839510—21no—
19#16839507—21no—
20C4×C16×C61C2211yescharacteristic
21C61×#335C2211yescharacteristic
22C61×#335C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25C2×C8×D61—21no—
26#14519777—21no—
27#14519777—21no—
28C4×D244D411yescharacteristic
29C2×#11758185—21no—
30C16×D61—42no—
31#14519711—21no—
32#14519711—21no—
33#14519711—41no—
34#14519709—41no—
35C4⋊#92418D411yescharacteristic
36#14519699—41no—
37#14519699—41no—
38#14519689—21no—
39C2×C16×C61D411yescharacteristic
40C2×C16×C61D411yescharacteristic
41C4⋊C8×C61—21no—
42C4⋊C8×C61—21no—
43C4×C8×C61C2311yescharacteristic
44C2×D244D811yescharacteristic
45C2×C4×D61—21no—
46C2×Dic122—41no—
47C2×Dic122—41no—
48C2×C8×C61—41no—
49C2×C8×C61—41no—
50C2×C8×C61C2×D411yescharacteristic
51C2×C8×C61#4111yescharacteristic
52C42×C61C2×D411yescharacteristic
53#11758198—21no—
54C4⋊Dic61—41no—
55C4⋊Dic61—41no—
56C4⋊Dic61—41no—
57C4⋊Dic61—41no—
58C4⋊Dic61D811yescharacteristic
59C2×#92418—21no—
60Dic244—41no—
61Dic244—41no—
62Dic244—81no—
63C8×D61—41no—
64C8×D61—41no—
65C16×C61—21no—
66C16×C61—21no—
67#11758185—41no—
68C22×D61—21no—
69C2×C4×C61#12111yescharacteristic
70C2×C4×C61C2×D811yescharacteristic
71C2×C4×C61#13511yescharacteristic
72C2×Dic61—21no—
73C2×Dic61—81no—
74C2×Dic61—81no—
75D244—21no—
76D244Q3212yes—
77C4×D61—41no—
78C4×D61—41no—
79Dic122—81no—
80Dic122—81no—
81Dic122—161no—
82C8×C61—21no—
83C8×C61—81no—
84C8×C61—81no—
85C8×C61#13511yescharacteristic
86C8×C61AGL(1,ℤ/8)11yescharacteristic
87#92418—41no—
88#12469—611nomaximal, Sylow
89C22×C61#46611yescharacteristic
90C2×D61—22no—
91C2×D61—41no—
92C2×D61—41no—
93C4×C61—21no—
94C4×C61#46311yescharacteristic
95C4×C61#47111yescharacteristic
96C4×C61C2×Q3211yescharacteristic
97C4×C61#50811yescharacteristic
98Dic61—41no—
99Dic61—161no—
100Dic61—161no—
101#2241—611no—
102D4×C16—611no—
103#1675—611no—
104#1669—611no—
105#1371D6111yescharacteristic, complemented
106#1365—611no—
107#1362—611no—
108C2×C61#168111yescharacteristic
109C2×C61#221611yescharacteristic
110C2×C61#222311yescharacteristic
111D61—42no—
112C22×C16—1221no—
113#500—611no—
114#494—611no—
115#476—1221no—
116#474—1221no—
117C8×D4—611no—
118C4⋊C16—611no—
119#358—1221no—
120#358—1221no—
121C22⋊C16—1221no—
122C4×C16C2×D6111yescharacteristic
123#335C2×D6111yescharacteristic
124#335C2×D6111yescharacteristic
125#333—1221no—
126#332—1221no—
127C61#1246911yescharacteristic, complemented, Sylow
128C2×Q16—1221no—
129C2×Q16—1221no—
130C22×C8—1221no—
131C4⋊Q8—1221no—
132C4⋊Q8—1221no—
133C4×D4—611no—
134C2×C16—1221no—
135C2×C16—2442no—
136C2×C16D24411yescharacteristic
137C2×C16D24411yescharacteristic
138#107—1221no—
139#107—1221no—
140#107—2441no—
141#106—2441no—
142C4⋊C8—21no—
143C4⋊C8—21no—
144C4⋊C8—611no—
145#102—2441no—
146#102—2441no—
147C22⋊C8—1221no—
148C4×C8C22×D6111yescharacteristic
149C2×Q8—2441no—
150C2×Q8—2441no—
151C2×D4—611no—
152C22×C4—1221no—
153Q16—4881no—
154Q16—2441no—
155Q16—2441no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8—1221no—
159C2×C8—2441no—
160C2×C8—2441no—
161C2×C8C2×D24411yescharacteristic
162C2×C8#1175822611yescharacteristic
163C4⋊C4—611no—
164C4⋊C4—2441no—
165C4⋊C4—2441no—
166C4⋊C4—2441no—
167C4⋊C4—2441no—
168C22⋊C4—1221no—
169C42D4×D6111yescharacteristic
170C16—21no—
171C16—21no—
172C16—2441no—
173C23—1221no—
174Q8—9761no—
175Q8—4881no—
176Q8—4881no—
177D4—612no—
178D4—1221no—
179C2×C4—1221no—
180C2×C4—4881no—
181C2×C4—4881no—
182C2×C4—2441no—
183C2×C4—2441no—
184C2×C4#1451975211yescharacteristic
185C2×C4D8×D6111yescharacteristic
186C2×C4#1451980011yescharacteristic
187C8—21no—
188C8—81no—
189C8—81no—
190C8—2441no—
191C8#1451979911yescharacteristic
192C8#1451980511yescharacteristic
193C22—1222no—
194C22—2441no—
195C22—2441no—
196C22#1683999911yescharacteristic
197C4—21no—
198C4—9761no—
199C4—9761no—
200C4—2441no—
201C4#1683997811yescharacteristic
202C4#1684002611yescharacteristic
203C4Q32×D6111yescharacteristic
204C4#1684019111yescharacteristic
205C2—2442no—
206C2#2144525711yescharacteristic
207C2#2144791111yescharacteristic
208C2#2144795011yescharacteristic
subgroupG/H
centerC22#16839999
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#1371C2
socleC22×C61#466
prime radicalC2×D244D8
hypercenter#1371D61
hypocenterC61#12469
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1371

Complements

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

NH ≅ G/Ntype
1. #21448047C2semidirect
5. #21443878C2semidirect
6. #21443867C2semidirect
7. C61×#1371C2semidirect
105. #1371D61semidirect
127. C61#12469semidirect

Maximal subgroups

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

subgroupindex
#214480472
C16×D2442
#214452192
#214451852
#214438782
#214438672
C61×#13712
#1246961