Finite Group Databasebeta

← #49097329

Subgroups — #49097329

Order 35968.

236 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 45 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#31823645C211yesmaximal, characteristic, complemented
2#31823635C212yesmaximal, complemented
3#31823262C211yesmaximal, characteristic, complemented
4#31823260C212yesmaximal, complemented
5#555×C281C211yesmaximal, characteristic, complemented
6#22582927C2211yescharacteristic
7#22582910—21no—
8#22582905—22no—
9#22582807—22no—
10#22582807—21no—
11#22582798C2212yes—
12#22582798C2211yescharacteristic
13C4⋊Q8×C281C2211yescharacteristic
14#124×C281—21no—
15#124×C281C2212yes—
16#121×C281—22no—
17C4×D4×C281—21no—
18#117×C281—22no—
19#17985139—41no—
20#17985138—22no—
21#17985138—21no—
22Q8×D281—41no—
23#17985128—41no—
24#17985126—42no—
25#17985125—41no—
26#17985123—42no—
27#17985122—22no—
28#17985122—21no—
29C2×Q8×C281D411yescharacteristic
30C2×Q8×C281C2311yescharacteristic
31C2×D4×C281—21no—
32C2×D4×C281—21no—
33C2×D4×C281D412yes—
34C22×C4×C281—22no—
35C4⋊C4×C281—21no—
36C4⋊C4×C281—22no—
37C22⋊C4×C281—22no—
38C22⋊C4×C281—22no—
39C22⋊C4×C281—22no—
40C42×C281—21no—
41C42×C281D412yes—
42C42×C281D411yescharacteristic
43Dic562—22no—
44Dic562—21no—
45D1124—22no—
46D1124—21no—
47C22⋊D281—41no—
48C4×D281—42no—
49C4×D281—41no—
50#14555886—42no—
51#14555886—41no—
52C23×C281—22no—
53Q8×C281—41no—
54Q8×C281—41no—
55D4×C281—42no—
56D4×C281—42no—
57D4×C281—81no—
58C2×C4×C281—21no—
59C2×C4×C281—22no—
60C2×C4×C281—21no—
61C2×C4×C281—44no—
62C2×C4×C281C2×D411yescharacteristic
63C2×C4×C281C2×D412yes—
64C22×C281—42no—
65C22×C281—42no—
66C22×C281—42no—
67C22×C281#12011yescharacteristic
68C2×D281—41no—
69C4×C281—22no—
70C4×C281—22no—
71C4×C281—21no—
72C4×C281—42no—
73C4×C281—41no—
74Dic281—41no—
75C2×C281—21no—
76C2×C281—82no—
77C2×C281B(4,𝔽2)11yescharacteristic
78D281—81no—
79C281#220411yescharacteristic, complemented, Sylow
80#2204—2811nomaximal, Sylow
81#555D28111yescharacteristic, complemented
82#456—2811no—
83#454—2812no—
84#356—2811no—
85#355—2812no—
862−1+4—2811no—
87#137—5621no—
88AGL(1,ℤ/8)—5622no—
89C4⋊Q8C2×D28111yescharacteristic
90#124—21no—
91#124C2×D28112yes—
92#121—22no—
93C4×D4—21no—
94#117—22no—
95#104—5622no—
96#104—5621no—
97#101—2811no—
98#101—2812no—
99#41—5622no—
100#41—5621no—
101#41—11241no—
102C2×Q8—11241no—
103C2×Q8C22⋊D28111yescharacteristic
104C2×Q8C22×D28111yescharacteristic
105C2×D4—21no—
106C2×D4—21no—
107C2×D4C22⋊D28112yes—
108C22×C4—22no—
109Q16—11241no—
110SD16—11242no—
111SD16—11241no—
112D8—11242no—
113M16—5622no—
114M16—5621no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—22no—
119C22⋊C4—22no—
120C42—21no—
121C42C22⋊D28112yes—
122C42C22⋊D28111yescharacteristic
123C23—22no—
124Q8—41no—
125Q8—41no—
126Q8—5622no—
127Q8—5621no—
128D4—42no—
129D4—42no—
130D4—81no—
131D4—5622no—
132D4—5621no—
133D4—11241no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—44no—
138C2×C4—11242no—
139C2×C4—11241no—
140C2×C4C2×C22⋊D28111yescharacteristic
141C2×C4C2×C22⋊D28112yes—
142C8—11242no—
143C8—11241no—
144C22—42no—
145C22—42no—
146C22—42no—
147C22—11241no—
148C22#2258284811yescharacteristic
149C4—22no—
150C4—22no—
151C4—21no—
152C4—42no—
153C4—41no—
154C4—11241no—
155C2—21no—
156C2—82no—
157C2—22481no—
158C2#3182365011yescharacteristic
subgroupG/H
centerC2#31823650
commutator, cosocleC2×Q8×C281C23
FrattiniC2×Q8C22×D281
Fitting#555×C281C2
socleC2×C281B(4,𝔽2)
hypercenter#555D281
hypocenterC281#2204
LCSG ▷ C2×Q8×C281 ▷ C22×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #31823645C2semidirect
2. #31823635C2semidirect
3. #31823262C2semidirect
4. #31823260C2semidirect
5. #555×C281C2semidirect
79. C281#2204semidirect
81. #555D281semidirect

Maximal subgroups

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

subgroupindex
#318236452
#318236352
#318232622
#318232602
#555×C2812
#2204281