Finite Group Databasebeta

← #49123238

Subgroups — #49123238

Order 36224.

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#31827278C211yesmaximal, characteristic
2#31826906C211yesmaximal, characteristic, complemented
3#31826737C211yesmaximal, characteristic, complemented
4#31826281C211yesmaximal, characteristic, complemented
5#31826273C211yesmaximal, characteristic, complemented
6#31826248C211yesmaximal, characteristic, complemented
7C2×Q32×C283C211yesmaximal, characteristic, complemented
8#22583658—21no—
9#22583642—22no—
10#22583641—21no—
11#22583641—21no—
12#22583633—21no—
13#22583632C2211yescharacteristic
14Q16×D283—21no—
15#22583616C2211yescharacteristic
16#22583556—21no—
17#22583553—21no—
18#22583550C2211yescharacteristic
19#22583546C2211yescharacteristic
20#22583529—21no—
21C2×Q16×C283C2211yescharacteristic
22C2×Q16×C283C2211yescharacteristic
23Q32×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#17985382—41no—
35#17985381—21no—
36#17985379—22no—
37#17985379—41no—
38D2264D411yescharacteristic
39#17985376—21no—
40#17985376D411yescharacteristic
41#17985375—21no—
42C8×D283—21no—
43C283⋊C16—21no—
44C2×Q8×C283—21no—
45C2×Q8×C283—21no—
46Q16×C283—21no—
47Q16×C283—21no—
48Q16×C283—21no—
49Q16×C283D412yes—
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—
66Q8×C283—22no—
67Q8×C283—41no—
68Q8×C283—41no—
69Q8×C283—41no—
70C2×C4×C283—41no—
71C2×C4×C283—41no—
72C2×C4×C283C2×D411yescharacteristic
73C8×C283C2×D411yescharacteristic
74C8×C283C2×D411yescharacteristic
75C22×C283AGL(1,ℤ/8)11yescharacteristic
76C2×D283—21no—
77C2×D283—41no—
78C4×C283—42no—
79C4×C283—81no—
80C4×C283#12011yescharacteristic
81C4×C283C2×D811yescharacteristic
82Dic283—21no—
83Dic283—41no—
84C2×C283—21no—
85C2×C283#44711yescharacteristic
86D283—41no—
87D283—81no—
88C283#219511yescharacteristic, complemented, Sylow
89#2195—2831nomaximal, Sylow
90#578—2831no—
91#510—2831no—
92C2×Q32D28311yescharacteristic, complemented
93#473—2831no—
94#362—2831no—
95#359—2831no—
96#350—2831no—
972−1+4—5661no—
98#137—5661no—
99#137—5662no—
100#137—5661no—
101#135—2831no—
102#135—5661no—
103C2×Q16—5661no—
104C2×Q16C2×D28311yescharacteristic
105C2×Q16C2×D28311yescharacteristic
106#131—2831no—
107Q32—22no—
108Q32—5661no—
109SD32—5661no—
110M32—2831no—
111C2×C16C2×D28311yescharacteristic
112#108—2831no—
113#101—5661no—
114#41—2831no—
115#41—5662no—
116#41—5661no—
117#41—11322no—
118#41—11321no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—5662no—
122C2×Q8—11321no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—2831no—
127Q16—5662no—
128Q16—11321no—
129Q16C22⋊D28312yes—
130SD16—5662no—
131SD16—5661no—
132SD16—11321no—
133D8—2831no—
134M16—2831no—
135M16—5661no—
136M16—5661no—
137C2×C8—5661no—
138C2×C8C22×D28311yescharacteristic
139C16—21no—
140C16—5661no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—2831no—
146Q8—5661no—
147Q8—11322no—
148D4—2831no—
149D4—5661no—
150D4—5661no—
151D4—11322no—
152D4—11321no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—5661no—
156C2×C4—11322no—
157C2×C4—11322no—
158C2×C4—11321no—
159C2×C4D4×D28311yescharacteristic
160C8—5661no—
161C8—11321no—
162C8D4×D28311yescharacteristic
163C8C2×C22⋊D28311yescharacteristic
164C22—5661no—
165C22—11321no—
166C22#2258363411yescharacteristic
167C4—42no—
168C4—81no—
169C4—5661no—
170C4—11321no—
171C4#2258357811yescharacteristic
172C4D8×D28311yescharacteristic
173C2—21no—
174C2—11321no—
175C2—22641no—
176C2#3182659711yescharacteristic
subgroupG/H
centerC2#31826597
commutator, cosocleC2×C8×C283C23
FrattiniC2×C8C22×D283
FittingC2×Q32×C283C2
socleC2×C283#447
prime radical#31827278C2
hypercenterC2×Q32D283
hypocenterC283#2195
LCSG ▷ C2×C8×C283 ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #31826906C2semidirect
3. #31826737C2semidirect
4. #31826281C2semidirect
5. #31826273C2semidirect
6. #31826248C2semidirect
7. C2×Q32×C283C2semidirect
88. C283#2195semidirect
92. C2×Q32D283semidirect

Maximal subgroups

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

subgroupindex
#318272782
#318269062
#318267372
#318262812
#318262732
#318262482
C2×Q32×C2832
#2195283