Finite Group Databasebeta

← #28365002

Subgroups — #28365002

Order 13952.

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

normal subgroups only

This group has 216 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#20295827C211yesmaximal, characteristic
2#20295467C211yesmaximal, characteristic, complemented
3#20295298C211yesmaximal, characteristic, complemented
4#20294839C211yesmaximal, characteristic, complemented
5#20294834C211yesmaximal, characteristic, complemented
6#20294809C211yesmaximal, characteristic, complemented
7C2×SD32×C109C211yesmaximal, characteristic, complemented
8#16812744—21no—
9#16812730—21no—
10#16812725—21no—
11#16812723—22no—
12#16812721C2211yescharacteristic
13#16812718—21no—
14D8×D109—21no—
15#16812705C2211yescharacteristic
16#16812645—21no—
17#16812642—21no—
18#16812639C2211yescharacteristic, complemented
19#16812635C2211yescharacteristic, complemented
20#16812618—21no—
21C2×Q16×C109C2211yescharacteristic, complemented
22C2×D8×C109C2211yescharacteristic
23SD32×C109—22no—
24C2×C16×C109C2211yescharacteristic, complemented
25#13182029—21no—
26#13182029D411yescharacteristic
27#13182028—22no—
28#13182028—41no—
29C2×C22⋊D109—42no—
30D4×D109—22no—
31D4×D109—41no—
32Dic436D411yescharacteristic
33#13182019—41no—
34#13182018—21no—
35#13182017—22no—
36#13182016—41no—
37D872D411yescharacteristic
38#13182014—22no—
39#13182013—21no—
40#13182013D411yescharacteristic
41#13182012—21no—
42C8×D109—21no—
43#13182004—21no—
44C2×Q8×C109—21no—
45C2×D4×C109—21no—
46Q16×C109—21no—
47Q16×C109—21no—
48D8×C109—21no—
49D8×C109D412yes—
50C2×C8×C109C2311yescharacteristic
51C16×C109—21no—
52C23×C109—41no—
53C22×D109—42no—
54Q8×C109—41no—
55Q8×C109—41no—
56D4×C109—22no—
57D4×C109—41no—
58C2×C4×C109—41no—
59C2×C4×C109C2×D411yescharacteristic
60C22⋊D109—21no—
61C22⋊D109—42no—
62C22⋊D109—42no—
63C22⋊D109—41no—
64C2×Dic109—42no—
65D436—21no—
66D436D811yescharacteristic
67C4×D109—21no—
68C4×D109—41no—
69Dic218—21no—
70Dic218D811yescharacteristic
71C8×C109C2×D411yescharacteristic
72C8×C109C2×D411yescharacteristic
73#11724784—21no—
74#11724784—41no—
75C22×C109—42no—
76C22×C109—161no—
77C22×C109AGL(1,ℤ/8)11yescharacteristic
78C2×D109—21no—
79C2×D109—41no—
80C2×D109—162no—
81C4×C109—81no—
82C4×C109#12011yescharacteristic
83C4×C109C2×D811yescharacteristic
84Dic109—21no—
85Dic109—41no—
86C2×C109—21no—
87C2×C109—82no—
88C2×C109#44711yescharacteristic
89D109—41no—
90D109—81no—
91#2194—1091nomaximal, Sylow
92C109#219411yescharacteristic, complemented, Sylow
93#576—1091no—
94#510—1091no—
95C2×SD32D10911yescharacteristic, complemented
96#473—1091no—
97#361—1091no—
98#359—1091no—
99#350—1091no—
100H(5,𝔽2)—2181no—
101#137—2181no—
102AGL(1,ℤ/8)—2181no—
103AGL(1,ℤ/8)—2182no—
104#135—1091no—
105#135—2181no—
106C2×Q16C2×D10911yescharacteristic, complemented
107C2×D8—2181no—
108C2×D8C2×D10911yescharacteristic
109#131—1091no—
110Q32—2181no—
111SD32—22no—
112SD32—2181no—
113M32—1091no—
114C2×C16C2×D10911yescharacteristic, complemented
115#108—1091no—
116#101—2181no—
117#41—1091no—
118#41—4361no—
119#41—2182no—
120#41—2181no—
121C2×Q8—21no—
122C2×D4—21no—
123C2×D4—4361no—
124C2×D4—4362no—
125C2×D4—2182no—
126Q16—21no—
127Q16—21no—
128Q16—1091no—
129Q16—4361no—
130SD16—4361no—
131SD16—2182no—
132SD16—2181no—
133D8—21no—
134D8—1091no—
135D8—2182no—
136D8C22⋊D10912yes—
137M16—1091no—
138M16—2181no—
139M16—2181no—
140C2×C8—2181no—
141C2×C8C22×D10911yescharacteristic
142C16—21no—
143C16—2181no—
144C23—41no—
145C23—4362no—
146Q8—41no—
147Q8—41no—
148Q8—1091no—
149Q8—2181no—
150D4—22no—
151D4—41no—
152D4—1091no—
153D4—4362no—
154D4—4361no—
155D4—4362no—
156D4—2181no—
157D4—2181no—
158C2×C4—41no—
159C2×C4—4362no—
160C2×C4—4361no—
161C2×C4—2181no—
162C2×C4D4×D10911yescharacteristic
163C8—4361no—
164C8—2181no—
165C8D4×D10911yescharacteristic
166C8C2×C22⋊D10911yescharacteristic
167C22—42no—
168C22—161no—
169C22—4361no—
170C22—17442no—
171C22—2181no—
172C22#1681272311yescharacteristic
173C4—81no—
174C4—4361no—
175C4—2181no—
176C4#1681266711yescharacteristic
177C4D8×D10911yescharacteristic
178C2—21no—
179C2—82no—
180C2—8721no—
181C2—4361no—
182C2#2029515811yescharacteristic
subgroupG/H
centerC2#20295158
commutator, cosocleC2×C8×C109C23
FrattiniC2×C8C22×D109
FittingC2×SD32×C109C2
socleC2×C109#447
prime radical#20295827C2
hypercenterC2×SD32D109
hypocenterC109#2194
LCSG ▷ C2×C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. #20295467C2semidirect
3. #20295298C2semidirect
4. #20294839C2semidirect
5. #20294834C2semidirect
6. #20294809C2semidirect
7. C2×SD32×C109C2semidirect
18. #16812639C22semidirect
19. #16812635C22semidirect
21. C2×Q16×C109C22semidirect
24. C2×C16×C109C22semidirect
92. C109#2194semidirect
95. C2×SD32D109semidirect
106. C2×Q16C2×D109semidirect
114. C2×C16C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202958272
#202954672
#202952982
#202948392
#202948342
#202948092
C2×SD32×C1092
#2194109