Finite Group Databasebeta

← #49097328

Subgroups — #49097328

Order 35968.

236 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 41 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#31824179C211yesmaximal, characteristic, complemented
2#31823636C212yesmaximal, complemented
3#31823262C211yesmaximal, characteristic, complemented
4#31823259C212yesmaximal, complemented
5#456×C281C211yesmaximal, characteristic, complemented
6#22582904—22no—
7#22582868—21no—
8#22582868C2212yes—
9#22582854—22no—
10C4×D1124—21no—
11#22582837—22no—
12#22582806—22no—
13#22582798C2212yes—
142−1+4×C281C2211yescharacteristic
15#137×C281—21no—
16C4⋊Q8×C281C2211yescharacteristic
17#104×C281—21no—
18#101×C281C2211yescharacteristic
19C2×D1124—21no—
20C2×D1124—21no—
21C2×D1124D412yes—
22C2×C4×D281—22no—
23#17985125—42no—
24#17985123—42no—
25#17985122—22no—
26C4⋊Dic281—21no—
27#17985115—22no—
28#17985115—22no—
29#17985115—22no—
30C4×Dic281—21no—
31C4×Dic281D412yes—
32#41×C281—22no—
33#41×C281—21no—
34#41×C281—41no—
35C2×Q8×C281—41no—
36C2×Q8×C281D411yescharacteristic
37C2×Q8×C281C2311yescharacteristic
38Q16×C281—41no—
39SD16×C281—41no—
40M16×C281—21no—
41C4⋊C4×C281—22no—
42C42×C281D411yescharacteristic
43C22×D281—22no—
44D1124—42no—
45D1124—42no—
46D1124—81no—
47C2×Dic281—22no—
48C4×D281—44no—
49#14555886—42no—
50Q8×C281—21no—
51Q8×C281—22no—
52Q8×C281—41no—
53Q8×C281—41no—
54D4×C281—21no—
55D4×C281—22no—
56D4×C281—41no—
57C2×C4×C281—21no—
58C2×C4×C281—21no—
59C2×C4×C281—41no—
60C2×C4×C281—42no—
61C2×C4×C281C2×D412yes—
62C2×C4×C281C2×D411yescharacteristic
63C8×C281—41no—
64C22×C281—41no—
65C22×C281#12011yescharacteristic
66C2×D281—42no—
67C2×D281—42no—
68C2×D281—42no—
69C4×C281—22no—
70C4×C281—21no—
71C4×C281—22no—
72C4×C281—41no—
73C4×C281—41no—
74Dic281—42no—
75C2×C281—21no—
76C2×C281—81no—
77C2×C281B(4,𝔽2)11yescharacteristic
78D281—82no—
79C281#220411yescharacteristic, complemented, Sylow
80#2204—2811nomaximal, Sylow
81#555—2811no—
82#456D28111yescharacteristic, complemented
83#454—2812no—
84#356—2811no—
85#355—2812no—
862−1+4C2×D28111yescharacteristic
87#137—21no—
88AGL(1,ℤ/8)—5622no—
89C4⋊Q8C2×D28111yescharacteristic
90#124—2812no—
91#124—5621no—
92#121—5622no—
93C4×D4—5621no—
94#117—5622no—
95#104—21no—
96#104—5622no—
97#101—2812no—
98#101C2×D28111yescharacteristic
99#41—22no—
100#41—21no—
101#41—41no—
102C2×Q8—41no—
103C2×Q8C22⋊D28111yescharacteristic
104C2×Q8C22×D28111yescharacteristic
105C2×D4—2812no—
106C2×D4—5621no—
107C2×D4—5621no—
108C22×C4—5622no—
109Q16—41no—
110SD16—41no—
111SD16—11242no—
112D8—11242no—
113M16—21no—
114M16—5622no—
115C4⋊C4—22no—
116C4⋊C4—5621no—
117C22⋊C4—5622no—
118C22⋊C4—5622no—
119C22⋊C4—5622no—
120C42—2812no—
121C42—5621no—
122C42C22⋊D28111yescharacteristic
123C23—5622no—
124Q8—22no—
125Q8—21no—
126Q8—41no—
127Q8—41no—
128D4—22no—
129D4—21no—
130D4—41no—
131D4—11242no—
132D4—11242no—
133D4—22481no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—5622no—
139C2×C4—11244no—
140C2×C4D4×D28112yes—
141C2×C4C2×C22⋊D28111yescharacteristic
142C8—41no—
143C8—11242no—
144C22—41no—
145C22—11242no—
146C22—11242no—
147C22—11242no—
148C22#2258284711yescharacteristic
149C4—22no—
150C4—21no—
151C4—22no—
152C4—41no—
153C4—41no—
154C4—11242no—
155C2—21no—
156C2—81no—
157C2—22482no—
158C2#3182364911yescharacteristic
subgroupG/H
centerC2#31823649
commutator, cosocleC2×Q8×C281C23
FrattiniC2×Q8C22×D281
Fitting#456×C281C2
socleC2×C281B(4,𝔽2)
hypercenter#456D281
hypocenterC281#2204
LCSG ▷ C2×Q8×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #31824179C2semidirect
2. #31823636C2semidirect
3. #31823262C2semidirect
4. #31823259C2semidirect
5. #456×C281C2semidirect
79. C281#2204semidirect
82. #456D281semidirect

Maximal subgroups

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

subgroupindex
#318241792
#318236362
#318232622
#318232592
#456×C2812
#2204281