Finite Group Databasebeta

← #28365009

Subgroups — #28365009

Order 13952.

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

normal subgroups only

This group has 206 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#20295839C211yesmaximal, characteristic
2#20295467C211yesmaximal, characteristic, complemented
3#20295298C211yesmaximal, characteristic, complemented
4#20294842C211yesmaximal, characteristic, complemented
5#20294834C211yesmaximal, characteristic, complemented
6#20294809C211yesmaximal, characteristic, complemented
7C2×Q32×C109C211yesmaximal, characteristic, complemented
8#16812747—21no—
9#16812731—22no—
10#16812730—21no—
11#16812730—21no—
12#16812722—21no—
13#16812721C2211yescharacteristic
14Q16×D109—21no—
15#16812705C2211yescharacteristic
16#16812645—21no—
17#16812642—21no—
18#16812639C2211yescharacteristic
19#16812635C2211yescharacteristic
20#16812618—21no—
21C2×Q16×C109C2211yescharacteristic
22C2×Q16×C109C2211yescharacteristic
23Q32×C109—22no—
24C2×C16×C109C2211yescharacteristic
25#13182030—22no—
26#13182030—41no—
27#13182029—21no—
28#13182029—42no—
29#13182029D411yescharacteristic
30Q8×D109—22no—
31Q8×D109—41no—
32Dic436D411yescharacteristic
33#13182019—22no—
34#13182019—41no—
35#13182018—21no—
36#13182016—22no—
37#13182016—41no—
38D872D411yescharacteristic
39#13182013—21no—
40#13182013D411yescharacteristic
41#13182012—21no—
42C8×D109—21no—
43#13182004—21no—
44C2×Q8×C109—21no—
45C2×Q8×C109—21no—
46Q16×C109—21no—
47Q16×C109—21no—
48Q16×C109—21no—
49Q16×C109D412yes—
50C2×C8×C109C2311yescharacteristic
51C16×C109—21no—
52Q8×C109—22no—
53Q8×C109—41no—
54Q8×C109—41no—
55Q8×C109—41no—
56C2×C4×C109—41no—
57C2×C4×C109—41no—
58C2×C4×C109C2×D411yescharacteristic
59C22⋊D109—21no—
60C22⋊D109—41no—
61D436—21no—
62D436—42no—
63D436D811yescharacteristic
64C4×D109—21no—
65C4×D109—42no—
66C4×D109—42no—
67C4×D109—41no—
68Dic218—21no—
69Dic218—42no—
70Dic218D811yescharacteristic
71C8×C109C2×D411yescharacteristic
72C8×C109C2×D411yescharacteristic
73#11724784—21no—
74#11724784—41no—
75C22×C109AGL(1,ℤ/8)11yescharacteristic
76C2×D109—21no—
77C2×D109—41no—
78C4×C109—42no—
79C4×C109—81no—
80C4×C109#12011yescharacteristic
81C4×C109C2×D811yescharacteristic
82Dic109—21no—
83Dic109—41no—
84C2×C109—21no—
85C2×C109#44711yescharacteristic
86D109—41no—
87D109—81no—
88#2195—1091nomaximal, Sylow
89C109#219511yescharacteristic, complemented, Sylow
90#578—1091no—
91#510—1091no—
92C2×Q32D10911yescharacteristic, complemented
93#473—1091no—
94#362—1091no—
95#359—1091no—
96#350—1091no—
972−1+4—2181no—
98#137—2181no—
99#137—2181no—
100#137—2182no—
101#135—1091no—
102#135—2181no—
103C2×Q16—2181no—
104C2×Q16C2×D10911yescharacteristic
105C2×Q16C2×D10911yescharacteristic
106#131—1091no—
107Q32—22no—
108Q32—2181no—
109SD32—2181no—
110M32—1091no—
111C2×C16C2×D10911yescharacteristic
112#108—1091no—
113#101—2181no—
114#41—1091no—
115#41—4362no—
116#41—4361no—
117#41—2182no—
118#41—2181no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—4361no—
122C2×Q8—2182no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—1091no—
127Q16—4361no—
128Q16—2182no—
129Q16C22⋊D10912yes—
130SD16—4361no—
131SD16—2182no—
132SD16—2181no—
133D8—1091no—
134M16—1091no—
135M16—2181no—
136M16—2181no—
137C2×C8—2181no—
138C2×C8C22×D10911yescharacteristic
139C16—21no—
140C16—2181no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—1091no—
146Q8—4362no—
147Q8—2181no—
148D4—1091no—
149D4—4362no—
150D4—4361no—
151D4—2181no—
152D4—2181no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—4362no—
156C2×C4—4362no—
157C2×C4—4361no—
158C2×C4—2181no—
159C2×C4D4×D10911yescharacteristic
160C8—4361no—
161C8—2181no—
162C8D4×D10911yescharacteristic
163C8C2×C22⋊D10911yescharacteristic
164C22—4361no—
165C22—2181no—
166C22#1681272311yescharacteristic
167C4—42no—
168C4—81no—
169C4—4361no—
170C4—2181no—
171C4#1681266711yescharacteristic
172C4D8×D10911yescharacteristic
173C2—21no—
174C2—8721no—
175C2—4361no—
176C2#2029515811yescharacteristic
subgroupG/H
centerC2#20295158
commutator, cosocleC2×C8×C109C23
FrattiniC2×C8C22×D109
FittingC2×Q32×C109C2
socleC2×C109#447
prime radical#20295839C2
hypercenterC2×Q32D109
hypocenterC109#2195
LCSG ▷ C2×C8×C109 ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #20295467C2semidirect
3. #20295298C2semidirect
4. #20294842C2semidirect
5. #20294834C2semidirect
6. #20294809C2semidirect
7. C2×Q32×C109C2semidirect
89. C109#2195semidirect
92. C2×Q32D109semidirect

Maximal subgroups

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

subgroupindex
#202958392
#202954672
#202952982
#202948422
#202948342
#202948092
C2×Q32×C1092
#2195109