Finite Group Databasebeta

← #49123224

Subgroups — #49123224

Order 36224.

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#31827278C211yesmaximal, characteristic, complemented
2#31826901C211yesmaximal, characteristic, complemented
3#31826732C211yesmaximal, characteristic, complemented
4#31826281C211yesmaximal, characteristic, complemented
5#31826273C211yesmaximal, characteristic, complemented
6#31826248C211yesmaximal, characteristic, complemented
7C2×SD32×C283C211yesmaximal, characteristic, complemented
8#22583658—21no—
9#22583642—22no—
10#22583641—21no—
11#22583636—21no—
12#22583633—21no—
13#22583632C2211yescharacteristic
14Q16×D283—21no—
15#22583616C2211yescharacteristic
16#22583554—21no—
17#22583551—21no—
18#22583550C2211yescharacteristic
19#22583546C2211yescharacteristic
20#22583527—21no—
21C2×Q16×C283C2211yescharacteristic
22C2×D8×C283C2211yescharacteristic
23SD32×C283—22no—
24C2×C16×C283C2211yescharacteristic
25#17985393—22no—
26#17985393—41no—
27#17985392—21no—
28#17985392—42no—
29#17985392D411yescharacteristic
30Q8×D283—22no—
31Q8×D283—41no—
32Dic1132D411yescharacteristic
33#17985382—22no—
34#17985381—21no—
35#17985380—41no—
36#17985379—22no—
37D2264D411yescharacteristic
38#17985377—41no—
39#17985376—21no—
40#17985376D411yescharacteristic
41#17985375—21no—
42C8×D283—21no—
43C283⋊C16—21no—
44C2×Q8×C283—21no—
45C2×D4×C283—21no—
46Q16×C283—21no—
47Q16×C283D412yes—
48D8×C283—21no—
49D8×C283—21no—
50C2×C8×C283C2311yescharacteristic
51C16×C283—21no—
52Dic566—21no—
53Dic566—42no—
54Dic566D811yescharacteristic
55D1132—21no—
56D1132—42no—
57D1132D811yescharacteristic
58C22⋊D283—21no—
59C22⋊D283—41no—
60C4×D283—21no—
61C4×D283—42no—
62C4×D283—42no—
63C4×D283—41no—
64C283⋊C8—21no—
65C283⋊C8—41no—
66C23×C283—41no—
67Q8×C283—22no—
68Q8×C283—41no—
69D4×C283—41no—
70D4×C283—41no—
71C2×C4×C283—41no—
72C2×C4×C283C2×D411yescharacteristic
73C8×C283C2×D411yescharacteristic
74C8×C283C2×D411yescharacteristic
75C22×C283—81no—
76C22×C283—161no—
77C22×C283AGL(1,ℤ/8)11yescharacteristic
78C2×D283—21no—
79C2×D283—41no—
80C4×C283—42no—
81C4×C283#12011yescharacteristic
82C4×C283C2×D811yescharacteristic
83Dic283—21no—
84Dic283—41no—
85C2×C283—21no—
86C2×C283—161no—
87C2×C283#44711yescharacteristic
88D283—41no—
89D283—81no—
90C283#219311yescharacteristic, complemented, Sylow
91#2193—2831nomaximal, Sylow
92#578—2831no—
93#509—2831no—
94C2×SD32D28311yescharacteristic, complemented
95#472—2831no—
96#362—2831no—
97#359—2831no—
98#350—2831no—
992−1+4—5661no—
100#137—5661no—
101#137—5662no—
102AGL(1,ℤ/8)—5661no—
103#135—2831no—
104#135—5661no—
105C2×Q16—5661no—
106C2×Q16C2×D28311yescharacteristic
107C2×D8C2×D28311yescharacteristic
108#131—2831no—
109SD32—22no—
110SD32—5661no—
111D16—5661no—
112M32—2831no—
113C2×C16C2×D28311yescharacteristic
114#108—2831no—
115#100—5661no—
116#41—2831no—
117#41—5662no—
118#41—5661no—
119#41—11322no—
120#41—11321no—
121C2×Q8—21no—
122C2×Q8—5662no—
123C2×Q8—11321no—
124C2×D4—21no—
125Q16—21no—
126Q16—2831no—
127Q16—5662no—
128Q16C22⋊D28312yes—
129SD16—5662no—
130SD16—5661no—
131SD16—11321no—
132D8—21no—
133D8—21no—
134D8—2831no—
135D8—11321no—
136M16—2831no—
137M16—5661no—
138M16—5661no—
139C2×C8—5661no—
140C2×C8C22×D28311yescharacteristic
141C16—21no—
142C16—5661no—
143C23—41no—
144Q8—22no—
145Q8—41no—
146Q8—2831no—
147Q8—5661no—
148Q8—11322no—
149D4—41no—
150D4—41no—
151D4—2831no—
152D4—5661no—
153D4—5661no—
154D4—11322no—
155D4—11321no—
156C2×C4—41no—
157C2×C4—5661no—
158C2×C4—11322no—
159C2×C4—11322no—
160C2×C4—11321no—
161C2×C4D4×D28311yescharacteristic
162C8—5661no—
163C8—11321no—
164C8D4×D28311yescharacteristic
165C8C2×C22⋊D28311yescharacteristic
166C22—81no—
167C22—161no—
168C22—5661no—
169C22—11321no—
170C22#2258363411yescharacteristic
171C4—42no—
172C4—5661no—
173C4—11321no—
174C4#2258357811yescharacteristic
175C4D8×D28311yescharacteristic
176C2—21no—
177C2—161no—
178C2—11321no—
179C2—22641no—
180C2#3182659711yescharacteristic
subgroupG/H
centerC2#31826597
commutator, cosocleC2×C8×C283C23
FrattiniC2×C8C22×D283
FittingC2×SD32×C283C2
socleC2×C283#447
hypercenterC2×SD32D283
hypocenterC283#2193
LCSG ▷ C2×C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #31827278C2semidirect
2. #31826901C2semidirect
3. #31826732C2semidirect
4. #31826281C2semidirect
5. #31826273C2semidirect
6. #31826248C2semidirect
7. C2×SD32×C283C2semidirect
90. C283#2193semidirect
94. C2×SD32D283semidirect

Maximal subgroups

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

subgroupindex
#318272782
#318269012
#318267322
#318262812
#318262732
#318262482
C2×SD32×C2832
#2193283