Finite Group Databasebeta

← #28364942

Subgroups — #28364942

Order 13952.

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×D109C211yesmaximal, characteristic, complemented
2C2×#16812640C211yesmaximal, characteristic, complemented
3#20295259C211yesmaximal, characteristic, complemented
4#20294828C211yesmaximal, characteristic, complemented
5#20294827C211yesmaximal, characteristic, complemented
6#20294805C211yesmaximal, characteristic, complemented
7C2×D16×C109C211yesmaximal, characteristic, complemented
8C2×D4×D109—21no—
9C2×D872C2211yescharacteristic
10C2×#13182014—21no—
11D8×D109—22no—
12D8×D109—22no—
13C2×C8×D109C2211yescharacteristic
14#16812670—21no—
15#16812640—22no—
16C2×#13182004C2211yescharacteristic, complemented
17#16812633C2211yescharacteristic, complemented
18#16812620—21no—
19C2×D8×C109C2211yescharacteristic
20C2×D8×C109C2211yescharacteristic, complemented
21D16×C109—22no—
22C2×C16×C109C2211yescharacteristic, complemented
23C23×D109—41no—
24C2×D436—21no—
25C2×C22⋊D109—41no—
26C2×C22⋊D109—41no—
27D4×D109—24no—
28D4×D109—42no—
29C2×C4×D109D411yescharacteristic
30D872—21no—
31D872D412yescomplemented
32#13182014—24no—
33C2×#11724784D411yescharacteristic
34C8×D109—21no—
35C8×D109—21no—
36C4⋊Dic109—21no—
37C22⋊Dic109—41no—
38#13182004—21no—
39C2×D4×C109—21no—
40C2×D4×C109—21no—
41D8×C109—21no—
42D8×C109—21no—
43D8×C109—21no—
44D8×C109D412yescomplemented
45C2×C8×C109C2311yescharacteristic
46C16×C109—21no—
47C23×C109—41no—
48C23×C109—41no—
49C22×D109—44no—
50C22×D109—41no—
51C22×D109—82no—
52C22×D109—82no—
53C22×D109D811yescharacteristic
54D4×C109—22no—
55D4×C109—41no—
56D4×C109—41no—
57D4×C109—41no—
58C2×C4×C109C2×D411yescharacteristic
59C22⋊D109—44no—
60C22⋊D109—82no—
61C2×Dic109—41no—
62C2×Dic109D811yescharacteristic
63D436—22no—
64D436—41no—
65C4×D109—21no—
66C4×D109—21no—
67C8×C109C2×D411yescharacteristic
68C8×C109C2×D411yescharacteristic
69#11724784—21no—
70C22×C109—42no—
71C22×C109—81no—
72C22×C109—81no—
73C22×C109—81no—
74C22×C109—81no—
75C22×C109—81no—
76C22×C109C2×D811yescharacteristic
77C2×D109—21no—
78C2×D109—21no—
79C2×D109—42no—
80C2×D109—88no—
81C2×D109—81no—
82C2×D109—81no—
83C2×D109D1612yescomplemented
84C4×C109#12011yescharacteristic
85C4×C109AGL(1,ℤ/8)11yescharacteristic
86Dic109—21no—
87Dic109—81no—
88C2×C109—82no—
89C2×C109—161no—
90C2×C109#44711yescharacteristic
91C2×C109C2×D1611yescharacteristic
92C2×C109#50911yescharacteristic
93D109—22no—
94D109—82no—
95#2184—1091nomaximal, Sylow
96C109#218411yescharacteristic, complemented, Sylow
97C22×D8—1091no—
98C2×D16—1091no—
99C2×D16D10911yescharacteristic, complemented
100#466—1091no—
101#357—1091no—
102#357—1091no—
103C22⋊C16—1091no—
104C22×D4—2181no—
105C2×D8—1091no—
106C2×D8—2181no—
107C2×D8—2182no—
108C2×D8—2182no—
109C2×D8C2×D10911yescharacteristic
110C2×D8C2×D10911yescharacteristic, complemented
111C22×C8—1091no—
112#121—2181no—
113D16—22no—
114D16—2182no—
115C2×C16—1091no—
116C2×C16C2×D10911yescharacteristic, complemented
117#107—1091no—
118#102—2181no—
119C24—4361no—
120C2×D4—21no—
121C2×D4—21no—
122C2×D4—4361no—
123C2×D4—4361no—
124C2×D4—4362no—
125C2×D4—2184no—
126C2×D4—2181no—
127C22×C4—1091no—
128D8—21no—
129D8—21no—
130D8—21no—
131D8—1092no—
132D8—2184no—
133D8—2181no—
134D8C22⋊D10912yescomplemented
135C2×C8—1091no—
136C2×C8—2181no—
137C2×C8—2181no—
138C2×C8C22×D10911yescharacteristic
139C4⋊C4—2181no—
140C22⋊C4—4361no—
141C16—21no—
142C16—2181no—
143C23—41no—
144C23—41no—
145C23—8722no—
146C23—8722no—
147C23—1091no—
148C23—4364no—
149C23—4361no—
150D4—22no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—8722no—
155D4—4364no—
156D4—4361no—
157D4—2182no—
158C2×C4—1091no—
159C2×C4—4361no—
160C2×C4—2181no—
161C2×C4—2181no—
162C2×C4D4×D10911yescharacteristic
163C8—2181no—
164C8D4×D10911yescharacteristic
165C8C2×C22⋊D10911yescharacteristic
166C22—42no—
167C22—81no—
168C22—81no—
169C22—81no—
170C22—81no—
171C22—81no—
172C22—8728no—
173C22—8721no—
174C22—8721no—
175C22—1092no—
176C22—4362no—
177C22—2181no—
178C22—2181no—
179C22D8×D10911yescharacteristic
180C4—8721no—
181C4—2181no—
182C4#1681266711yescharacteristic
183C4#1681272311yescharacteristic
184C2—82no—
185C2—161no—
186C2—8722no—
187C2—2182no—
188C2#2029515811yescharacteristic
189C2D16×D10911yescharacteristic
190C2#2029546011yescharacteristic
subgroupG/H
centerC22D8×D109
commutator, cosocleC2×C8×C109C23
FrattiniC2×C8C22×D109
FittingC2×D16×C109C2
socleC22×C109C2×D8
hypercenterC2×D16D109
hypocenterC109#2184
LCSG ▷ C2×C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
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×D109C2semidirect
2. C2×#16812640C2semidirect
3. #20295259C2semidirect
4. #20294828C2semidirect
5. #20294827C2semidirect
6. #20294805C2semidirect
7. C2×D16×C109C2semidirect
16. C2×#13182004C22semidirect
17. #16812633C22semidirect
20. C2×D8×C109C22semidirect
22. C2×C16×C109C22semidirect
31. D872D4semidirect
44. D8×C109D4semidirect
83. C2×D109D16semidirect
96. C109#2184semidirect
99. C2×D16D109semidirect
110. C2×D8C2×D109semidirect
116. C2×C16C2×D109semidirect
134. D8C22⋊D109semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D1092
C2×#168126402
#202952592
#202948282
#202948272
#202948052
C2×D16×C1092
#2184109