Finite Group Databasebeta

← #27173088

Subgroups — #27173088

Order 12928.

220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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#20265978C211yesmaximal, characteristic, complemented
2#20265613C211yesmaximal, characteristic, complemented
3#20265444C211yesmaximal, characteristic, complemented
4#20264990C211yesmaximal, characteristic, complemented
5#20264985C211yesmaximal, characteristic, complemented
6#20264960C211yesmaximal, characteristic, complemented
7C2×D16×C101C211yesmaximal, characteristic, complemented
8#15692300—21no—
9#15692281—21no—
10#15692281—21no—
11#15692279—22no—
12#15692277C2211yescharacteristic
13#15692274—21no—
14D8×D101—21no—
15#15692261C2211yescharacteristic
16#15692199—21no—
17#15692196—21no—
18#15692195C2211yescharacteristic, complemented
19#15692191C2211yescharacteristic, complemented
20#15692172—21no—
21C2×D8×C101C2211yescharacteristic
22C2×D8×C101C2211yescharacteristic, complemented
23D16×C101—22no—
24C2×C16×C101C2211yescharacteristic, complemented
25#13108074—21no—
26#13108074D411yescharacteristic
27#13108073—22no—
28#13108073—41no—
29C2×C22⋊D101—42no—
30D4×D101—22no—
31D4×D101—41no—
32Dic404D411yescharacteristic
33#13108063—21no—
34#13108062—22no—
35#13108062—41no—
36D808D411yescharacteristic
37#13108059—22no—
38#13108059—41no—
39#13108058—21no—
40#13108058D411yescharacteristic
41#13108057—21no—
42C8×D101—21no—
43#13108049—21no—
44C2×D4×C101—21no—
45C2×D4×C101—21no—
46D8×C101—21no—
47D8×C101—21no—
48D8×C101—21no—
49D8×C101D412yes—
50C2×C8×C101C2311yescharacteristic
51C16×C101—21no—
52C23×C101—41no—
53C23×C101—41no—
54C22×D101—42no—
55D4×C101—22no—
56D4×C101—41no—
57D4×C101—41no—
58D4×C101—41no—
59C2×C4×C101C2×D411yescharacteristic
60C22⋊D101—21no—
61C22⋊D101—42no—
62C22⋊D101—42no—
63C22⋊D101—41no—
64C2×Dic101—42no—
65D404—21no—
66D404D811yescharacteristic
67C4×D101—21no—
68C4×D101—41no—
69Dic202—21no—
70Dic202D811yescharacteristic
71C8×C101C2×D411yescharacteristic
72C8×C101C2×D411yescharacteristic
73#11717579—21no—
74#11717579—41no—
75C22×C101—42no—
76C22×C101—81no—
77C22×C101—161no—
78C22×C101—161no—
79C22×C101AGL(1,ℤ/8)11yescharacteristic
80C2×D101—21no—
81C2×D101—41no—
82C2×D101—162no—
83C4×C101#12011yescharacteristic
84C4×C101C2×D811yescharacteristic
85Dic101—21no—
86Dic101—41no—
87C2×C101—21no—
88C2×C101—82no—
89C2×C101—161no—
90C2×C101#44711yescharacteristic
91D101—41no—
92D101—81no—
93#2192—1011nomaximal, Sylow
94C101#219211yescharacteristic, complemented, Sylow
95#576—1011no—
96#509—1011no—
97C2×D16D10111yescharacteristic, complemented
98#472—1011no—
99#361—1011no—
100#359—1011no—
101#350—1011no—
102H(5,𝔽2)—2021no—
103AGL(1,ℤ/8)—2021no—
104AGL(1,ℤ/8)—2021no—
105AGL(1,ℤ/8)—2022no—
106#135—1011no—
107#135—2021no—
108C2×D8—2021no—
109C2×D8C2×D10111yescharacteristic
110C2×D8C2×D10111yescharacteristic, complemented
111#131—1011no—
112SD32—2021no—
113D16—22no—
114D16—2021no—
115M32—1011no—
116C2×C16C2×D10111yescharacteristic, complemented
117#108—1011no—
118#100—2021no—
119#41—1011no—
120#41—4041no—
121#41—2022no—
122#41—2021no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—4041no—
126C2×D4—4042no—
127C2×D4—2022no—
128Q16—1011no—
129SD16—4041no—
130SD16—2022no—
131SD16—2021no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—1011no—
136D8—4041no—
137D8—2022no—
138D8C22⋊D10112yes—
139M16—1011no—
140M16—2021no—
141M16—2021no—
142C2×C8—2021no—
143C2×C8C22×D10111yescharacteristic
144C16—21no—
145C16—2021no—
146C23—41no—
147C23—41no—
148C23—4042no—
149Q8—1011no—
150Q8—2021no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—1011no—
156D4—4042no—
157D4—4041no—
158D4—4042no—
159D4—2021no—
160D4—2021no—
161C2×C4—4042no—
162C2×C4—4041no—
163C2×C4—2021no—
164C2×C4D4×D10111yescharacteristic
165C8—4041no—
166C8—2021no—
167C8D4×D10111yescharacteristic
168C8C2×C22⋊D10111yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—16162no—
174C22—4041no—
175C22—2021no—
176C22#1569227911yescharacteristic
177C4—4041no—
178C4—2021no—
179C4#1569222311yescharacteristic
180C4D8×D10111yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—8081no—
185C2—4041no—
186C2#2026530911yescharacteristic
subgroupG/H
centerC2#20265309
commutator, cosocleC2×C8×C101C23
FrattiniC2×C8C22×D101
FittingC2×D16×C101C2
socleC2×C101#447
hypercenterC2×D16D101
hypocenterC101#2192
LCSG ▷ C2×C8×C101 ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #20265978C2semidirect
2. #20265613C2semidirect
3. #20265444C2semidirect
4. #20264990C2semidirect
5. #20264985C2semidirect
6. #20264960C2semidirect
7. C2×D16×C101C2semidirect
18. #15692195C22semidirect
19. #15692191C22semidirect
22. C2×D8×C101C22semidirect
24. C2×C16×C101C22semidirect
94. C101#2192semidirect
97. C2×D16D101semidirect
110. C2×D8C2×D101semidirect
116. C2×C16C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202659782
#202656132
#202654442
#202649902
#202649852
#202649602
C2×D16×C1012
#2192101