Finite Group Databasebeta

← #29594444

Subgroups — #29594444

Order 15616.

218 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 71 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
2#21445218C211yesmaximal, characteristic
3#21445184C211yesmaximal, characteristic
4#21443891C211yesmaximal, characteristic, complemented
5#21443876C211yesmaximal, characteristic, complemented
6#21443869C211yesmaximal, characteristic, complemented
7D4×C16×C61C211yesmaximal, characteristic
8#16840167C2211yescharacteristic
9#16840142C2211yescharacteristic
10#16840052—21no—
11#16840042—21no—
12#16839567—21no—
13#16839567—21no—
14#16839515C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839510—21no—
17#16839509—21no—
18C22×C16×C61—21no—
19C8×D4×C61C2211yescharacteristic
20C61×C4⋊C16C2211yescharacteristic
21C61×C22⋊C16—21no—
22C4×C16×C61C2211yescharacteristic
23C2×Dic244—21no—
24C2×Dic244—21no—
25#14519777—21no—
26#14519777—21no—
27#14519711—21no—
28#14519711—21no—
29#14519710—41no—
30#14519708—41no—
31C4⋊#92418—21no—
32C4⋊#92418—21no—
33#14519698—41no—
34#14519698—41no—
35C22×C8×C61—21no—
36C4×D4×C61D411yescharacteristic
37C2×C16×C61—21no—
38C2×C16×C61—42no—
39C2×C16×C61D411yescharacteristic
40C2×C16×C61D411yescharacteristic
41C4⋊C8×C61D411yescharacteristic
42C22⋊C8×C61—21no—
43C4×C8×C61C2311yescharacteristic
44C2×D4×C61D811yescharacteristic
45C22×C4×C61—21no—
46C2×Dic122—41no—
47C2×Dic122—41no—
48C2×C8×C61—21no—
49C2×C8×C61—41no—
50C2×C8×C61—41no—
51C2×C8×C61C2×D411yescharacteristic
52C2×C8×C61#4111yescharacteristic
53C4⋊C4×C61D811yescharacteristic
54C22⋊C4×C61—21no—
55C42×C61C2×D411yescharacteristic
56C4⋊Dic61—41no—
57C4⋊Dic61—41no—
58C4⋊Dic61—41no—
59C4⋊Dic61—41no—
60C2×#92418—41no—
61C2×#92418—41no—
62Dic244—41no—
63Dic244—41no—
64Dic244—81no—
65C16×C61—21no—
66C16×C61—21no—
67C16×C61—41no—
68C23×C61—21no—
69D4×C61—21no—
70D4×C61Q3212yes—
71C2×C4×C61—21no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61#12111yescharacteristic
75C2×C4×C61C2×D811yescharacteristic
76C2×C4×C61#13511yescharacteristic
77C2×Dic61—81no—
78C2×Dic61—81no—
79Dic122—81no—
80Dic122—81no—
81Dic122—161no—
82C8×C61—21no—
83C8×C61—41no—
84C8×C61#13511yescharacteristic
85C8×C61AGL(1,ℤ/8)11yescharacteristic
86#92418—81no—
87#92418—81no—
88#12469—611nomaximal, Sylow
89C22×C61—22no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61#46611yescharacteristic
93C4×C61—21no—
94C4×C61—41no—
95C4×C61#46311yescharacteristic
96C4×C61#47111yescharacteristic
97C4×C61C2×Q3211yescharacteristic
98C4×C61#50811yescharacteristic
99Dic61—161no—
100Dic61—161no—
101#2241—611no—
102D4×C16D6111yescharacteristic
103#1675—611no—
104#1669—611no—
105#1371—611no—
106#1365—611no—
107#1362—611no—
108C2×C61—42no—
109C2×C61#168111yescharacteristic
110C2×C61#221611yescharacteristic
111C2×C61#222311yescharacteristic
112C22×C16—21no—
113#500—611no—
114#494—611no—
115#476—1221no—
116#474—1221no—
117C8×D4C2×D6111yescharacteristic
118C4⋊C16C2×D6111yescharacteristic
119#358—1221no—
120#358—1221no—
121C22⋊C16—21no—
122C4×C16C2×D6111yescharacteristic
123#335—611no—
124#335—611no—
125#333—1221no—
126#332—1221no—
127C61#1246911yescharacteristic, complemented, Sylow
128C2×Q16—1221no—
129C2×Q16—1221no—
130C22×C8—21no—
131C4⋊Q8—1221no—
132C4⋊Q8—1221no—
133C4×D4D24411yescharacteristic
134C2×C16—21no—
135C2×C16—42no—
136C2×C16C22⋊D6111yescharacteristic
137C2×C16C22⋊D6111yescharacteristic
138#107—1221no—
139#107—1221no—
140#107—2441no—
141#106—2441no—
142C4⋊C8—1221no—
143C4⋊C8—1221no—
144C4⋊C8D24411yescharacteristic
145#102—2441no—
146#102—2441no—
147C22⋊C8—21no—
148C4×C8C22×D6111yescharacteristic
149C2×Q8—2441no—
150C2×Q8—2441no—
151C2×D4D48811yescharacteristic
152C22×C4—21no—
153Q16—4881no—
154Q16—2441no—
155Q16—2441no—
156C2×C8—21no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—2441no—
160C2×C8—2441no—
161C2×C8#1175822211yescharacteristic
162C2×C8C2×C22⋊D6111yescharacteristic
163C4⋊C4—2441no—
164C4⋊C4—2441no—
165C4⋊C4—2441no—
166C4⋊C4—2441no—
167C4⋊C4D48811yescharacteristic
168C22⋊C4—21no—
169C42C2×D24411yescharacteristic
170C16—21no—
171C16—21no—
172C16—41no—
173C23—21no—
174Q8—9761no—
175Q8—4881no—
176Q8—4881no—
177D4—21no—
178D4Dic48812yes—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—4881no—
183C2×C4—4881no—
184C2×C4#1451975111yescharacteristic
185C2×C4C2×D48811yescharacteristic
186C2×C4#1451979911yescharacteristic
187C8—21no—
188C8—41no—
189C8—4881no—
190C8—4881no—
191C8#1451979711yescharacteristic
192C8#1451980311yescharacteristic
193C22—22no—
194C22—41no—
195C22—41no—
196C22#1683999811yescharacteristic
197C4—21no—
198C4—41no—
199C4—9761no—
200C4—9761no—
201C4#1683997711yescharacteristic
202C4#1684002511yescharacteristic
203C4C2×Dic48811yescharacteristic
204C4#1684019411yescharacteristic
205C2—42no—
206C2#2144525611yescharacteristic
207C2#2144791011yescharacteristic
208C2#2144794911yescharacteristic
subgroupG/H
centerC22#16839998
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingD4×C16×C61C2
socleC22×C61#466
prime radicalC2×D4×C61D8
hypercenterD4×C16D61
hypocenterC61#12469
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4×C16

Complements

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

NH ≅ G/Ntype
1. #21448047C2semidirect
4. #21443891C2semidirect
5. #21443876C2semidirect
6. #21443869C2semidirect
127. C61#12469semidirect

Maximal subgroups

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

subgroupindex
#214480472
#214452182
#214451842
#214438912
#214438762
#214438692
D4×C16×C612
#1246961