Finite Group Databasebeta

← #28364995

Subgroups — #28364995

Order 13952.

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

normal subgroups only

This group has 210 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, complemented
2#20295462C211yesmaximal, characteristic, complemented
3#20295293C211yesmaximal, characteristic, complemented
4#20294842C211yesmaximal, characteristic, complemented
5#20294834C211yesmaximal, characteristic, complemented
6#20294809C211yesmaximal, characteristic, complemented
7C2×SD32×C109C211yesmaximal, characteristic, complemented
8#16812747—21no—
9#16812731—22no—
10#16812730—21no—
11#16812725—21no—
12#16812722—21no—
13#16812721C2211yescharacteristic
14Q16×D109—21no—
15#16812705C2211yescharacteristic
16#16812643—21no—
17#16812640—21no—
18#16812639C2211yescharacteristic
19#16812635C2211yescharacteristic
20#16812616—21no—
21C2×Q16×C109C2211yescharacteristic
22C2×D8×C109C2211yescharacteristic
23SD32×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#13182018—21no—
35#13182017—41no—
36#13182016—22no—
37D872D411yescharacteristic
38#13182014—41no—
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×C109D412yes—
48D8×C109—21no—
49D8×C109—21no—
50C2×C8×C109C2311yescharacteristic
51C16×C109—21no—
52C23×C109—41no—
53Q8×C109—22no—
54Q8×C109—41no—
55D4×C109—41no—
56D4×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×C109—81no—
76C22×C109—161no—
77C22×C109AGL(1,ℤ/8)11yescharacteristic
78C2×D109—21no—
79C2×D109—41no—
80C4×C109—42no—
81C4×C109#12011yescharacteristic
82C4×C109C2×D811yescharacteristic
83Dic109—21no—
84Dic109—41no—
85C2×C109—21no—
86C2×C109—161no—
87C2×C109#44711yescharacteristic
88D109—41no—
89D109—81no—
90#2193—1091nomaximal, Sylow
91C109#219311yescharacteristic, complemented, Sylow
92#578—1091no—
93#509—1091no—
94C2×SD32D10911yescharacteristic, complemented
95#472—1091no—
96#362—1091no—
97#359—1091no—
98#350—1091no—
992−1+4—2181no—
100#137—2181no—
101#137—2182no—
102AGL(1,ℤ/8)—2181no—
103#135—1091no—
104#135—2181no—
105C2×Q16—2181no—
106C2×Q16C2×D10911yescharacteristic
107C2×D8C2×D10911yescharacteristic
108#131—1091no—
109SD32—22no—
110SD32—2181no—
111D16—2181no—
112M32—1091no—
113C2×C16C2×D10911yescharacteristic
114#108—1091no—
115#100—2181no—
116#41—1091no—
117#41—4362no—
118#41—4361no—
119#41—2182no—
120#41—2181no—
121C2×Q8—21no—
122C2×Q8—4361no—
123C2×Q8—2182no—
124C2×D4—21no—
125Q16—21no—
126Q16—1091no—
127Q16—2182no—
128Q16C22⋊D10912yes—
129SD16—4361no—
130SD16—2182no—
131SD16—2181no—
132D8—21no—
133D8—21no—
134D8—1091no—
135D8—4361no—
136M16—1091no—
137M16—2181no—
138M16—2181no—
139C2×C8—2181no—
140C2×C8C22×D10911yescharacteristic
141C16—21no—
142C16—2181no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—1091no—
147Q8—4362no—
148Q8—2181no—
149D4—41no—
150D4—41no—
151D4—1091no—
152D4—4362no—
153D4—4361no—
154D4—2181no—
155D4—2181no—
156C2×C4—41no—
157C2×C4—4362no—
158C2×C4—4362no—
159C2×C4—4361no—
160C2×C4—2181no—
161C2×C4D4×D10911yescharacteristic
162C8—4361no—
163C8—2181no—
164C8D4×D10911yescharacteristic
165C8C2×C22⋊D10911yescharacteristic
166C22—81no—
167C22—161no—
168C22—4361no—
169C22—2181no—
170C22#1681272311yescharacteristic
171C4—42no—
172C4—4361no—
173C4—2181no—
174C4#1681266711yescharacteristic
175C4D8×D10911yescharacteristic
176C2—21no—
177C2—161no—
178C2—8721no—
179C2—4361no—
180C2#2029515811yescharacteristic
subgroupG/H
centerC2#20295158
commutator, cosocleC2×C8×C109C23
FrattiniC2×C8C22×D109
FittingC2×SD32×C109C2
socleC2×C109#447
hypercenterC2×SD32D109
hypocenterC109#2193
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
1. #20295839C2semidirect
2. #20295462C2semidirect
3. #20295293C2semidirect
4. #20294842C2semidirect
5. #20294834C2semidirect
6. #20294809C2semidirect
7. C2×SD32×C109C2semidirect
91. C109#2193semidirect
94. C2×SD32D109semidirect

Maximal subgroups

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

subgroupindex
#202958392
#202954622
#202952932
#202948422
#202948342
#202948092
C2×SD32×C1092
#2193109