Finite Group Databasebeta

← #45664422

Subgroups — #45664422

Order 32896.

262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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#30657205C211yesmaximal, characteristic
2#30656719C211yesmaximal, characteristic
3#30656710C211yesmaximal, characteristic
4#30656498C211yesmaximal, characteristic, complemented
5#30656496C211yesmaximal, characteristic, complemented
6#30656493C211yesmaximal, characteristic, complemented
7H(3,ℤ/4)×C257C211yesmaximal, characteristic, complemented
8C2×#16861618C2211yescharacteristic
9C2×#16861602C2211yescharacteristic
10#22551557—21no—
11#22551554—21no—
12#22551552—22no—
13#22551551C2211yescharacteristic
14#22551549C412yescomplemented
15C2×C4×Dic257C2211yescharacteristic
16C42×D257C412yescomplemented
17#22551510—21no—
18#22551508—21no—
19#22551506—22no—
20C2×M16×C257C2211yescharacteristic
21#117×C257C2211yescharacteristic
22#117×C257C2211yescharacteristic
23#16861618—21no—
24#16861618—21no—
25#16861618—21no—
26#16861618—21no—
27C2×Dic514D411yescharacteristic
28C2×D1028D411yescharacteristic
29C2×C22⋊D257D412yes—
30C22×Dic257—21no—
31C2×C4×D257—22no—
32C2×C4×D257C2×C412yes—
33#16861602—21no—
34#16861602—21no—
35C2×#14523339—21no—
36C4⋊Dic257—21no—
37#16861597—22no—
38C22⋊Dic257—21no—
39#16861595—22no—
40C4×Dic257—22no—
41C4×Dic257—21no—
42C4×Dic257—21no—
43C4×Dic257C2×C411yescharacteristic
44C4×Dic257C2×C411yescharacteristic
45C22×C4×C257C2311yescharacteristic
46M16×C257—21no—
47M16×C257—21no—
48C2×C8×C257—21no—
49C4⋊C4×C257—21no—
50C4⋊C4×C257—21no—
51C22⋊C4×C257—21no—
52C22⋊C4×C257—21no—
53C42×C257—21no—
54C42×C257C2×C412yes—
55C22×D257C22⋊C412yes—
56Dic514—21no—
57Dic514—21no—
58D1028—21no—
59D1028—21no—
60C22⋊D257—22no—
61C22⋊D257—22no—
62C2×Dic257—21no—
63C2×Dic257—21no—
64C2×Dic257—42no—
65C2×Dic257—41no—
66C2×Dic257C22⋊C412yes—
67C4×D257—22no—
68C4×D257—22no—
69C4×D257—44no—
70#14523339—41no—
71C23×C257C2×D411yescharacteristic
72C2×C4×C257—22no—
73C2×C4×C257—41no—
74C2×C4×C257C22×C411yescharacteristic
75C2×C4×C257C2×D411yescharacteristic
76C2×C4×C257#4111yescharacteristic
77C2×C4×C257#4111yescharacteristic
78C2×C4×C257#4111yescharacteristic
79C2×C4×C257#4111yescharacteristic
80C8×C257—41no—
81C22×C257—41no—
82C22×C257C2×C22⋊C411yescharacteristic
83C22×C257#12311yescharacteristic
84C22×C257#12311yescharacteristic
85C2×D257—22no—
86C2×D257—42no—
87C4×C257—42no—
88C4×C257—81no—
89C4×C257#11711yescharacteristic
90C4×C257#11711yescharacteristic
91C4×C257#12311yescharacteristic
92C4×C257#12311yescharacteristic
93Dic257—22no—
94Dic257—22no—
95Dic257—41no—
96Dic257—81no—
97C2×C257—21no—
98C2×C257—21no—
99C2×C257—21no—
100C2×C257#38111yescharacteristic
101D257—42no—
102C257#182711yescharacteristic, complemented, Sylow
103#1827—2571nomaximal, Sylow
104C4×#41—2571no—
105#413—2571no—
106#410—2571no—
107#339—2571no—
108#339—2571no—
109H(3,ℤ/4)—2571no—
110H(3,ℤ/4)D25711yescharacteristic, complemented
111C2×#41—2571no—
112C2×M16—2571no—
113C2×M16C2×D25711yescharacteristic
114C4×Q8—5141no—
115C4×D4—5142no—
116C4×D4—5141no—
117#117—2572no—
118#117—2571no—
119#117C2×D25711yescharacteristic
120#117C2×D25711yescharacteristic
121C2×C42—2571no—
122C2×C42—2572no—
123#101—5141no—
124#100—5141no—
125#99—5142no—
126#41—5141no—
127#41—5141no—
128#41—5141no—
129#41—5141no—
130C2×Q8—2571no—
131C2×D4—2572no—
132C2×D4—2571no—
133C22×C4—2572no—
134C22×C4—5142no—
135C22×C4—5141no—
136C22×C4C22×D25711yescharacteristic
137M16—21no—
138M16—21no—
139M16—5141no—
140M16—5141no—
141C2×C8—21no—
142C2×C8—5141no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—5142no—
146C4⋊C4—5141no—
147C22⋊C4—21no—
148C22⋊C4—21no—
149C22⋊C4—5142no—
150C22⋊C4—5141no—
151C42—2571no—
152C42—2571no—
153C42—21no—
154C42—5142no—
155C42—5141no—
156C42—5141no—
157C42C4×D25712yes—
158C23—2572no—
159C23D4×D25711yescharacteristic
160Q8—5141no—
161Q8—5141no—
162D4—5142no—
163D4—5142no—
164D4—5141no—
165D4—5141no—
166C2×C4—2572no—
167C2×C4—22no—
168C2×C4—5141no—
169C2×C4—5142no—
170C2×C4—5142no—
171C2×C4—5141no—
172C2×C4—41no—
173C2×C4—10284no—
174C2×C4—10282no—
175C2×C4—10281no—
176C2×C4C2×C4×D25711yescharacteristic
177C2×C4D4×D25711yescharacteristic
178C2×C4#1686161711yescharacteristic
179C2×C4#1686161811yescharacteristic
180C2×C4#1686161811yescharacteristic
181C2×C4#1686161911yescharacteristic
182C8—41no—
183C8—10281no—
184C22—5142no—
185C22—41no—
186C22—10282no—
187C22C22⋊C4×D25711yescharacteristic
188C22#2255157411yescharacteristic
189C22#2255157711yescharacteristic
190C4—5142no—
191C4—5142no—
192C4—42no—
193C4—10281no—
194C4—81no—
195C4—20561no—
196C4#2255154911yescharacteristic
197C4#2255155011yescharacteristic
198C4#2255157411yescharacteristic
199C4#2255157711yescharacteristic
200C2—21no—
201C2—21no—
202C2—21no—
203C2—10282no—
204C2#3065659911yescharacteristic
subgroupG/H
centerC4#22551549
commutatorC2×C4×C257C22×C4
FrattiniC22×C4C22×D257
FittingH(3,ℤ/4)×C257C2
socleC2×C257#381
prime radicalC2×#16861618C22
cosocleC22×C4×C257C23
hypercenterH(3,ℤ/4)D257
hypocenterC257#1827
LCSG ▷ C2×C4×C257 ▷ C2×C257 ▷ C257
UCSC1 ◁ C4 ◁ #117 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. #30656498C2semidirect
5. #30656496C2semidirect
6. #30656493C2semidirect
7. H(3,ℤ/4)×C257C2semidirect
14. #22551549C4semidirect
16. C42×D257C4semidirect
102. C257#1827semidirect
110. H(3,ℤ/4)D257semidirect

Maximal subgroups

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

subgroupindex
#306572052
#306567192
#306567102
#306564982
#306564962
#306564932
H(3,ℤ/4)×C2572
#1827257