Finite Group Databasebeta

← #49097273

Subgroups — #49097273

Order 35968.

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

normal subgroups only

This group has 216 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#31824264C211yesmaximal, characteristic
2#31823904C211yesmaximal, characteristic, complemented
3#31823735C211yesmaximal, characteristic, complemented
4#31823276C211yesmaximal, characteristic, complemented
5#31823271C211yesmaximal, characteristic, complemented
6#31823246C211yesmaximal, characteristic, complemented
7C2×SD32×C281C211yesmaximal, characteristic, complemented
8#22582924—21no—
9#22582910—21no—
10#22582905—21no—
11#22582903—22no—
12#22582901C2211yescharacteristic
13#22582898—21no—
14D8×D281—21no—
15#22582885C2211yescharacteristic
16#22582825—21no—
17#22582822—21no—
18#22582819C2211yescharacteristic, complemented
19#22582815C2211yescharacteristic, complemented
20#22582798—21no—
21C2×Q16×C281C2211yescharacteristic, complemented
22C2×D8×C281C2211yescharacteristic
23SD32×C281—22no—
24C2×C16×C281C2211yescharacteristic, complemented
25#17985138—21no—
26#17985138D411yescharacteristic
27#17985137—22no—
28#17985137—41no—
29C2×C22⋊D281—42no—
30D4×D281—22no—
31D4×D281—41no—
32Dic1124D411yescharacteristic
33#17985128—41no—
34#17985127—21no—
35#17985126—22no—
36#17985125—41no—
37D2248D411yescharacteristic
38#17985123—22no—
39#17985122—21no—
40#17985122D411yescharacteristic
41#17985121—21no—
42C8×D281—21no—
43#17985113—21no—
44C2×Q8×C281—21no—
45C2×D4×C281—21no—
46Q16×C281—21no—
47Q16×C281—21no—
48D8×C281—21no—
49D8×C281D412yes—
50C2×C8×C281C2311yescharacteristic
51C16×C281—21no—
52C22×D281—42no—
53Dic562—21no—
54Dic562D811yescharacteristic
55D1124—21no—
56D1124D811yescharacteristic
57C22⋊D281—21no—
58C22⋊D281—42no—
59C22⋊D281—42no—
60C22⋊D281—41no—
61C2×Dic281—42no—
62C4×D281—21no—
63C4×D281—41no—
64#14555886—21no—
65#14555886—41no—
66C23×C281—41no—
67Q8×C281—41no—
68Q8×C281—41no—
69D4×C281—22no—
70D4×C281—41no—
71C2×C4×C281—41no—
72C2×C4×C281C2×D411yescharacteristic
73C8×C281C2×D411yescharacteristic
74C8×C281C2×D411yescharacteristic
75C22×C281—42no—
76C22×C281—161no—
77C22×C281AGL(1,ℤ/8)11yescharacteristic
78C2×D281—21no—
79C2×D281—41no—
80C2×D281—162no—
81C4×C281—81no—
82C4×C281#12011yescharacteristic
83C4×C281C2×D811yescharacteristic
84Dic281—21no—
85Dic281—41no—
86C2×C281—21no—
87C2×C281—82no—
88C2×C281#44711yescharacteristic
89D281—41no—
90D281—81no—
91C281#219411yescharacteristic, complemented, Sylow
92#2194—2811nomaximal, Sylow
93#576—2811no—
94#510—2811no—
95C2×SD32D28111yescharacteristic, complemented
96#473—2811no—
97#361—2811no—
98#359—2811no—
99#350—2811no—
100H(5,𝔽2)—5621no—
101#137—5621no—
102AGL(1,ℤ/8)—5621no—
103AGL(1,ℤ/8)—5622no—
104#135—2811no—
105#135—5621no—
106C2×Q16C2×D28111yescharacteristic, complemented
107C2×D8—5621no—
108C2×D8C2×D28111yescharacteristic
109#131—2811no—
110Q32—5621no—
111SD32—22no—
112SD32—5621no—
113M32—2811no—
114C2×C16C2×D28111yescharacteristic, complemented
115#108—2811no—
116#101—5621no—
117#41—2811no—
118#41—5622no—
119#41—5621no—
120#41—11241no—
121C2×Q8—21no—
122C2×D4—21no—
123C2×D4—5622no—
124C2×D4—11241no—
125C2×D4—11242no—
126Q16—21no—
127Q16—21no—
128Q16—2811no—
129Q16—11241no—
130SD16—5622no—
131SD16—5621no—
132SD16—11241no—
133D8—21no—
134D8—2811no—
135D8—5622no—
136D8C22⋊D28112yes—
137M16—2811no—
138M16—5621no—
139M16—5621no—
140C2×C8—5621no—
141C2×C8C22×D28111yescharacteristic
142C16—21no—
143C16—5621no—
144C23—41no—
145C23—11242no—
146Q8—41no—
147Q8—41no—
148Q8—2811no—
149Q8—5621no—
150D4—22no—
151D4—41no—
152D4—2811no—
153D4—5621no—
154D4—5621no—
155D4—11242no—
156D4—11242no—
157D4—11241no—
158C2×C4—41no—
159C2×C4—5621no—
160C2×C4—11242no—
161C2×C4—11241no—
162C2×C4D4×D28111yescharacteristic
163C8—5621no—
164C8—11241no—
165C8D4×D28111yescharacteristic
166C8C2×C22⋊D28111yescharacteristic
167C22—42no—
168C22—161no—
169C22—5621no—
170C22—11241no—
171C22—44962no—
172C22#2258290311yescharacteristic
173C4—81no—
174C4—5621no—
175C4—11241no—
176C4#2258284711yescharacteristic
177C4D8×D28111yescharacteristic
178C2—21no—
179C2—82no—
180C2—11241no—
181C2—22481no—
182C2#3182359511yescharacteristic
subgroupG/H
centerC2#31823595
commutator, cosocleC2×C8×C281C23
FrattiniC2×C8C22×D281
FittingC2×SD32×C281C2
socleC2×C281#447
prime radical#31824264C2
hypercenterC2×SD32D281
hypocenterC281#2194
LCSG ▷ C2×C8×C281 ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
2. #31823904C2semidirect
3. #31823735C2semidirect
4. #31823276C2semidirect
5. #31823271C2semidirect
6. #31823246C2semidirect
7. C2×SD32×C281C2semidirect
18. #22582819C22semidirect
19. #22582815C22semidirect
21. C2×Q16×C281C22semidirect
24. C2×C16×C281C22semidirect
91. C281#2194semidirect
95. C2×SD32D281semidirect
106. C2×Q16C2×D281semidirect
114. C2×C16C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318242642
#318239042
#318237352
#318232762
#318232712
#318232462
C2×SD32×C2812
#2194281