Finite Group Databasebeta

← #27197054

Subgroups — #27197054

Order 13184.

266 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 53 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
1C2×D8×D103C211yesmaximal, characteristic, complemented
2C2×#15692962C211yesmaximal, characteristic, complemented
3#20268024C211yesmaximal, characteristic, complemented
4#20267593C211yesmaximal, characteristic, complemented
5#20267592C211yesmaximal, characteristic, complemented
6(C2×D103)⋊C16C211yesmaximal, characteristic, complemented
7C2×D16×C103C211yesmaximal, characteristic, complemented
8C2×D4×D103—21no—
9C2×D824C2211yescharacteristic
10C2×#13110090—21no—
11D8×D103—22no—
12D8×D103—22no—
13C2×C8×D103C2211yescharacteristic
14#15692992—21no—
15#15692962—22no—
16C2×C103⋊C16C2211yescharacteristic, complemented
17#15692955C2211yescharacteristic, complemented
18#15692942—21no—
19C2×D8×C103C2211yescharacteristic
20C2×D8×C103C2211yescharacteristic, complemented
21D16×C103—22no—
22C2×C16×C103C2211yescharacteristic, complemented
23C23×D103—41no—
24C2×D412—21no—
25C2×C22⋊D103—41no—
26C2×C22⋊D103—41no—
27D4×D103—24no—
28D4×D103—42no—
29C2×C4×D103D411yescharacteristic
30D824—21no—
31D824D412yescomplemented
32#13110090—24no—
33C2×C103⋊C8D411yescharacteristic
34C8×D103—21no—
35C8×D103—21no—
36C4⋊Dic103—21no—
37C22⋊Dic103—41no—
38C103⋊C16—21no—
39C2×D4×C103—21no—
40C2×D4×C103—21no—
41D8×C103—21no—
42D8×C103—21no—
43D8×C103—21no—
44D8×C103D412yescomplemented
45C2×C8×C103C2311yescharacteristic
46C16×C103—21no—
47C23×C103—41no—
48C23×C103—41no—
49C22×D103—44no—
50C22×D103—41no—
51C22×D103—82no—
52C22×D103—82no—
53C22×D103D811yescharacteristic
54D4×C103—22no—
55D4×C103—41no—
56D4×C103—41no—
57D4×C103—41no—
58C2×C4×C103C2×D411yescharacteristic
59C22⋊D103—44no—
60C22⋊D103—82no—
61C2×Dic103—41no—
62C2×Dic103D811yescharacteristic
63D412—22no—
64D412—41no—
65C4×D103—21no—
66C4×D103—21no—
67C8×C103C2×D411yescharacteristic
68C8×C103C2×D411yescharacteristic
69C103⋊C8—21no—
70C22×C103—42no—
71C22×C103—81no—
72C22×C103—81no—
73C22×C103—81no—
74C22×C103—81no—
75C22×C103—81no—
76C22×C103C2×D811yescharacteristic
77C2×D103—21no—
78C2×D103—21no—
79C2×D103—42no—
80C2×D103—88no—
81C2×D103—81no—
82C2×D103—81no—
83C2×D103D1612yescomplemented
84C4×C103#12011yescharacteristic
85C4×C103AGL(1,ℤ/8)11yescharacteristic
86Dic103—21no—
87Dic103—81no—
88C2×C103—82no—
89C2×C103—161no—
90C2×C103#44711yescharacteristic
91C2×C103C2×D1611yescharacteristic
92C2×C103#50911yescharacteristic
93D103—22no—
94D103—82no—
95#2184—1031nomaximal, Sylow
96C103#218411yescharacteristic, complemented, Sylow
97C22×D8—1031no—
98C2×D16—1031no—
99C2×D16D10311yescharacteristic, complemented
100#466—1031no—
101#357—1031no—
102#357—1031no—
103C22⋊C16—1031no—
104C22×D4—2061no—
105C2×D8—1031no—
106C2×D8—2061no—
107C2×D8—2062no—
108C2×D8—2062no—
109C2×D8C2×D10311yescharacteristic
110C2×D8C2×D10311yescharacteristic, complemented
111C22×C8—1031no—
112#121—2061no—
113D16—22no—
114D16—2062no—
115C2×C16—1031no—
116C2×C16C2×D10311yescharacteristic, complemented
117#107—1031no—
118#102—2061no—
119C24—4121no—
120C2×D4—21no—
121C2×D4—21no—
122C2×D4—4121no—
123C2×D4—4121no—
124C2×D4—4122no—
125C2×D4—2064no—
126C2×D4—2061no—
127C22×C4—1031no—
128D8—21no—
129D8—21no—
130D8—21no—
131D8—1032no—
132D8—2064no—
133D8—2061no—
134D8C22⋊D10312yescomplemented
135C2×C8—1031no—
136C2×C8—2061no—
137C2×C8—2061no—
138C2×C8C22×D10311yescharacteristic
139C4⋊C4—2061no—
140C22⋊C4—4121no—
141C16—21no—
142C16—2061no—
143C23—41no—
144C23—41no—
145C23—8242no—
146C23—8242no—
147C23—1031no—
148C23—4124no—
149C23—4121no—
150D4—22no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—8242no—
155D4—4124no—
156D4—4121no—
157D4—2062no—
158C2×C4—1031no—
159C2×C4—4121no—
160C2×C4—2061no—
161C2×C4—2061no—
162C2×C4D4×D10311yescharacteristic
163C8—2061no—
164C8D4×D10311yescharacteristic
165C8C2×C22⋊D10311yescharacteristic
166C22—42no—
167C22—81no—
168C22—81no—
169C22—81no—
170C22—81no—
171C22—81no—
172C22—8248no—
173C22—8241no—
174C22—8241no—
175C22—1032no—
176C22—4122no—
177C22—2061no—
178C22—2061no—
179C22D8×D10311yescharacteristic
180C4—8241no—
181C4—2061no—
182C4#1569298911yescharacteristic
183C4#1569304511yescharacteristic
184C2—82no—
185C2—161no—
186C2—8242no—
187C2—2062no—
188C2#2026792311yescharacteristic
189C2D16×D10311yescharacteristic
190C2#2026822511yescharacteristic
subgroupG/H
centerC22D8×D103
commutator, cosocleC2×C8×C103C23
FrattiniC2×C8C22×D103
FittingC2×D16×C103C2
socleC22×C103C2×D8
hypercenterC2×D16D103
hypocenterC103#2184
LCSG ▷ C2×C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×D8×D103C2semidirect
2. C2×#15692962C2semidirect
3. #20268024C2semidirect
4. #20267593C2semidirect
5. #20267592C2semidirect
6. (C2×D103)⋊C16C2semidirect
7. C2×D16×C103C2semidirect
16. C2×C103⋊C16C22semidirect
17. #15692955C22semidirect
20. C2×D8×C103C22semidirect
22. C2×C16×C103C22semidirect
31. D824D4semidirect
44. D8×C103D4semidirect
83. C2×D103D16semidirect
96. C103#2184semidirect
99. C2×D16D103semidirect
110. C2×D8C2×D103semidirect
116. C2×C16C2×D103semidirect
134. D8C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1032
C2×#156929622
#202680242
#202675932
#202675922
(C2×D103)⋊C162
C2×D16×C1032
#2184103