Finite Group Databasebeta

← #49097280

Subgroups — #49097280

Order 35968.

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#31824276C211yesmaximal, characteristic
2#31823904C211yesmaximal, characteristic, complemented
3#31823735C211yesmaximal, characteristic, complemented
4#31823279C211yesmaximal, characteristic, complemented
5#31823271C211yesmaximal, characteristic, complemented
6#31823246C211yesmaximal, characteristic, complemented
7C2×Q32×C281C211yesmaximal, characteristic, complemented
8#22582927—21no—
9#22582911—22no—
10#22582910—21no—
11#22582910—21no—
12#22582902—21no—
13#22582901C2211yescharacteristic
14Q16×D281—21no—
15#22582885C2211yescharacteristic
16#22582825—21no—
17#22582822—21no—
18#22582819C2211yescharacteristic
19#22582815C2211yescharacteristic
20#22582798—21no—
21C2×Q16×C281C2211yescharacteristic
22C2×Q16×C281C2211yescharacteristic
23Q32×C281—22no—
24C2×C16×C281C2211yescharacteristic
25#17985139—22no—
26#17985139—41no—
27#17985138—21no—
28#17985138—42no—
29#17985138D411yescharacteristic
30Q8×D281—22no—
31Q8×D281—41no—
32Dic1124D411yescharacteristic
33#17985128—22no—
34#17985128—41no—
35#17985127—21no—
36#17985125—22no—
37#17985125—41no—
38D2248D411yescharacteristic
39#17985122—21no—
40#17985122D411yescharacteristic
41#17985121—21no—
42C8×D281—21no—
43#17985113—21no—
44C2×Q8×C281—21no—
45C2×Q8×C281—21no—
46Q16×C281—21no—
47Q16×C281—21no—
48Q16×C281—21no—
49Q16×C281D412yes—
50C2×C8×C281C2311yescharacteristic
51C16×C281—21no—
52Dic562—21no—
53Dic562—42no—
54Dic562D811yescharacteristic
55D1124—21no—
56D1124—42no—
57D1124D811yescharacteristic
58C22⋊D281—21no—
59C22⋊D281—41no—
60C4×D281—21no—
61C4×D281—42no—
62C4×D281—42no—
63C4×D281—41no—
64#14555886—21no—
65#14555886—41no—
66Q8×C281—22no—
67Q8×C281—41no—
68Q8×C281—41no—
69Q8×C281—41no—
70C2×C4×C281—41no—
71C2×C4×C281—41no—
72C2×C4×C281C2×D411yescharacteristic
73C8×C281C2×D411yescharacteristic
74C8×C281C2×D411yescharacteristic
75C22×C281AGL(1,ℤ/8)11yescharacteristic
76C2×D281—21no—
77C2×D281—41no—
78C4×C281—42no—
79C4×C281—81no—
80C4×C281#12011yescharacteristic
81C4×C281C2×D811yescharacteristic
82Dic281—21no—
83Dic281—41no—
84C2×C281—21no—
85C2×C281#44711yescharacteristic
86D281—41no—
87D281—81no—
88C281#219511yescharacteristic, complemented, Sylow
89#2195—2811nomaximal, Sylow
90#578—2811no—
91#510—2811no—
92C2×Q32D28111yescharacteristic, complemented
93#473—2811no—
94#362—2811no—
95#359—2811no—
96#350—2811no—
972−1+4—5621no—
98#137—5621no—
99#137—5622no—
100#137—5621no—
101#135—2811no—
102#135—5621no—
103C2×Q16—5621no—
104C2×Q16C2×D28111yescharacteristic
105C2×Q16C2×D28111yescharacteristic
106#131—2811no—
107Q32—22no—
108Q32—5621no—
109SD32—5621no—
110M32—2811no—
111C2×C16C2×D28111yescharacteristic
112#108—2811no—
113#101—5621no—
114#41—2811no—
115#41—5622no—
116#41—5621no—
117#41—11242no—
118#41—11241no—
119C2×Q8—21no—
120C2×Q8—21no—
121C2×Q8—5622no—
122C2×Q8—11241no—
123Q16—21no—
124Q16—21no—
125Q16—21no—
126Q16—2811no—
127Q16—5622no—
128Q16—11241no—
129Q16C22⋊D28112yes—
130SD16—5622no—
131SD16—5621no—
132SD16—11241no—
133D8—2811no—
134M16—2811no—
135M16—5621no—
136M16—5621no—
137C2×C8—5621no—
138C2×C8C22×D28111yescharacteristic
139C16—21no—
140C16—5621no—
141Q8—22no—
142Q8—41no—
143Q8—41no—
144Q8—41no—
145Q8—2811no—
146Q8—5621no—
147Q8—11242no—
148D4—2811no—
149D4—5621no—
150D4—5621no—
151D4—11242no—
152D4—11241no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—5621no—
156C2×C4—11242no—
157C2×C4—11242no—
158C2×C4—11241no—
159C2×C4D4×D28111yescharacteristic
160C8—5621no—
161C8—11241no—
162C8D4×D28111yescharacteristic
163C8C2×C22⋊D28111yescharacteristic
164C22—5621no—
165C22—11241no—
166C22#2258290311yescharacteristic
167C4—42no—
168C4—81no—
169C4—5621no—
170C4—11241no—
171C4#2258284711yescharacteristic
172C4D8×D28111yescharacteristic
173C2—21no—
174C2—11241no—
175C2—22481no—
176C2#3182359511yescharacteristic
subgroupG/H
centerC2#31823595
commutator, cosocleC2×C8×C281C23
FrattiniC2×C8C22×D281
FittingC2×Q32×C281C2
socleC2×C281#447
prime radical#31824276C2
hypercenterC2×Q32D281
hypocenterC281#2195
LCSG ▷ C2×C8×C281 ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q32

Complements

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

NH ≅ G/Ntype
2. #31823904C2semidirect
3. #31823735C2semidirect
4. #31823279C2semidirect
5. #31823271C2semidirect
6. #31823246C2semidirect
7. C2×Q32×C281C2semidirect
88. C281#2195semidirect
92. C2×Q32D281semidirect

Maximal subgroups

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

subgroupindex
#318242762
#318239042
#318237352
#318232792
#318232712
#318232462
C2×Q32×C2812
#2195281