Finite Group Databasebeta

← #27197100

Subgroups — #27197100

Order 13184.

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#20268592C211yesmaximal, characteristic, complemented
2#20268227C211yesmaximal, characteristic, complemented
3#20268058C211yesmaximal, characteristic, complemented
4#20267604C211yesmaximal, characteristic, complemented
5#20267599C211yesmaximal, characteristic, complemented
6#20267574C211yesmaximal, characteristic, complemented
7C2×D16×C103C211yesmaximal, characteristic, complemented
8#15693066—21no—
9#15693047—21no—
10#15693047—21no—
11#15693045—22no—
12#15693043C2211yescharacteristic
13#15693040—21no—
14D8×D103—21no—
15#15693027C2211yescharacteristic
16#15692965—21no—
17#15692962—21no—
18#15692961C2211yescharacteristic, complemented
19#15692957C2211yescharacteristic, complemented
20#15692938—21no—
21C2×D8×C103C2211yescharacteristic
22C2×D8×C103C2211yescharacteristic, complemented
23D16×C103—22no—
24C2×C16×C103C2211yescharacteristic, complemented
25#13110105—21no—
26#13110105D411yescharacteristic
27#13110104—22no—
28#13110104—41no—
29C2×C22⋊D103—42no—
30D4×D103—22no—
31D4×D103—41no—
32Dic412D411yescharacteristic
33#13110094—21no—
34#13110093—22no—
35#13110093—41no—
36D824D411yescharacteristic
37#13110090—22no—
38#13110090—41no—
39#13110089—21no—
40#13110089D411yescharacteristic
41#13110088—21no—
42C8×D103—21no—
43C103⋊C16—21no—
44C2×D4×C103—21no—
45C2×D4×C103—21no—
46D8×C103—21no—
47D8×C103—21no—
48D8×C103—21no—
49D8×C103D412yes—
50C2×C8×C103C2311yescharacteristic
51C16×C103—21no—
52C23×C103—41no—
53C23×C103—41no—
54C22×D103—42no—
55D4×C103—22no—
56D4×C103—41no—
57D4×C103—41no—
58D4×C103—41no—
59C2×C4×C103C2×D411yescharacteristic
60C22⋊D103—21no—
61C22⋊D103—42no—
62C22⋊D103—42no—
63C22⋊D103—41no—
64C2×Dic103—42no—
65D412—21no—
66D412D811yescharacteristic
67C4×D103—21no—
68C4×D103—41no—
69Dic206—21no—
70Dic206D811yescharacteristic
71C8×C103C2×D411yescharacteristic
72C8×C103C2×D411yescharacteristic
73C103⋊C8—21no—
74C103⋊C8—41no—
75C22×C103—42no—
76C22×C103—81no—
77C22×C103—161no—
78C22×C103—161no—
79C22×C103AGL(1,ℤ/8)11yescharacteristic
80C2×D103—21no—
81C2×D103—41no—
82C2×D103—162no—
83C4×C103#12011yescharacteristic
84C4×C103C2×D811yescharacteristic
85Dic103—21no—
86Dic103—41no—
87C2×C103—21no—
88C2×C103—82no—
89C2×C103—161no—
90C2×C103#44711yescharacteristic
91D103—41no—
92D103—81no—
93#2192—1031nomaximal, Sylow
94C103#219211yescharacteristic, complemented, Sylow
95#576—1031no—
96#509—1031no—
97C2×D16D10311yescharacteristic, complemented
98#472—1031no—
99#361—1031no—
100#359—1031no—
101#350—1031no—
102H(5,𝔽2)—2061no—
103AGL(1,ℤ/8)—2061no—
104AGL(1,ℤ/8)—2061no—
105AGL(1,ℤ/8)—2062no—
106#135—1031no—
107#135—2061no—
108C2×D8—2061no—
109C2×D8C2×D10311yescharacteristic
110C2×D8C2×D10311yescharacteristic, complemented
111#131—1031no—
112SD32—2061no—
113D16—22no—
114D16—2061no—
115M32—1031no—
116C2×C16C2×D10311yescharacteristic, complemented
117#108—1031no—
118#100—2061no—
119#41—1031no—
120#41—4121no—
121#41—2062no—
122#41—2061no—
123C2×D4—21no—
124C2×D4—21no—
125C2×D4—4121no—
126C2×D4—4122no—
127C2×D4—2062no—
128Q16—1031no—
129SD16—4121no—
130SD16—2062no—
131SD16—2061no—
132D8—21no—
133D8—21no—
134D8—21no—
135D8—1031no—
136D8—4121no—
137D8—2062no—
138D8C22⋊D10312yes—
139M16—1031no—
140M16—2061no—
141M16—2061no—
142C2×C8—2061no—
143C2×C8C22×D10311yescharacteristic
144C16—21no—
145C16—2061no—
146C23—41no—
147C23—41no—
148C23—4122no—
149Q8—1031no—
150Q8—2061no—
151D4—22no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—1031no—
156D4—4122no—
157D4—4121no—
158D4—4122no—
159D4—2061no—
160D4—2061no—
161C2×C4—4122no—
162C2×C4—4121no—
163C2×C4—2061no—
164C2×C4D4×D10311yescharacteristic
165C8—4121no—
166C8—2061no—
167C8D4×D10311yescharacteristic
168C8C2×C22⋊D10311yescharacteristic
169C22—42no—
170C22—81no—
171C22—161no—
172C22—161no—
173C22—16482no—
174C22—4121no—
175C22—2061no—
176C22#1569304511yescharacteristic
177C4—4121no—
178C4—2061no—
179C4#1569298911yescharacteristic
180C4D8×D10311yescharacteristic
181C2—21no—
182C2—82no—
183C2—161no—
184C2—8241no—
185C2—4121no—
186C2#2026792311yescharacteristic
subgroupG/H
centerC2#20267923
commutator, cosocleC2×C8×C103C23
FrattiniC2×C8C22×D103
FittingC2×D16×C103C2
socleC2×C103#447
hypercenterC2×D16D103
hypocenterC103#2192
LCSG ▷ C2×C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. #20268592C2semidirect
2. #20268227C2semidirect
3. #20268058C2semidirect
4. #20267604C2semidirect
5. #20267599C2semidirect
6. #20267574C2semidirect
7. C2×D16×C103C2semidirect
18. #15692961C22semidirect
19. #15692957C22semidirect
22. C2×D8×C103C22semidirect
24. C2×C16×C103C22semidirect
94. C103#2192semidirect
97. C2×D16D103semidirect
110. C2×D8C2×D103semidirect
116. C2×C16C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202685922
#202682272
#202680582
#202676042
#202675992
#202675742
C2×D16×C1032
#2192103