Finite Group Databasebeta

← #49094560

Subgroups — #49094560

Order 35968.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#31824187C211yesmaximal, characteristic
2#31823866C211yesmaximal, characteristic, complemented
3#31823749C211yesmaximal, characteristic, complemented
4#31823669C211yesmaximal, characteristic
5#31823193C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic
7#332×C281C211yesmaximal, characteristic, complemented
8C2×#17985127—21no—
9#22582879C2211yescharacteristic
10#22582874—22no—
11#22582868—21no—
12#22582859—21no—
13Q8×Dic281—21no—
14C4×Dic562C2211yescharacteristic
15C4×D1124C2211yescharacteristic
16#22582837—21no—
17#22582812—22no—
18#22582811—21no—
19#22582804—21no—
20#22582804—21no—
21C4×#14555886C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24C4⋊C8×C281C2211yescharacteristic
25C2×Dic562—21no—
26C2×Dic562D411yescharacteristic
27C2×D1124D411yescharacteristic
28C2×C4×D281—21no—
29#17985127—42no—
30C2×#14555886—21no—
31C4⋊Dic281—22no—
32C4⋊Dic281—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281D411yescharacteristic
35C4⋊Dic281D411yescharacteristic
36#17985117—21no—
37#17985115—22no—
38#17985115—22no—
39#17985115—21no—
40C4×Dic281—22no—
41C4×Dic281—21no—
42C2×Q8×C281—21no—
43C2×C8×C281—21no—
44C2×C8×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281D412yes—
47C42×C281C2311yescharacteristic
48C22×D281—21no—
49Dic562—21no—
50Dic562—21no—
51Dic562—41no—
52Dic562—41no—
53D1124—21no—
54D1124—21no—
55C2×Dic281—21no—
56C2×Dic281—21no—
57C2×Dic281—21no—
58C2×Dic281—41no—
59C4×D281—41no—
60C4×D281—41no—
61#14555886—22no—
62Q8×C281—41no—
63Q8×C281—41no—
64C2×C4×C281—22no—
65C2×C4×C281C2×D411yescharacteristic
66C2×C4×C281C2×D411yescharacteristic
67C2×C4×C281C2×D411yescharacteristic
68C8×C281—41no—
69C8×C281—41no—
70C22×C281#12011yescharacteristic
71C2×D281—41no—
72C2×D281—41no—
73C2×D281—41no—
74C4×C281—21no—
75C4×C281—42no—
76C4×C281#13511yescharacteristic
77C4×C281#13511yescharacteristic
78C4×C281AGL(1,ℤ/8)11yescharacteristic
79C4×C281#13711yescharacteristic
80Dic281—41no—
81Dic281—41no—
82Dic281—41no—
83Dic281—81no—
84C2×C281#44911yescharacteristic
85C2×C281#45211yescharacteristic
86C2×C281#45611yescharacteristic
87D281—81no—
88C281#165011yescharacteristic, complemented, Sylow
89#1650—2811nomaximal, Sylow
90#556—2811no—
91#500—2811no—
92#475—2811no—
93#461—2811no—
94#332D28111yescharacteristic, complemented
95Q8⋊C8—2811no—
96D4⋊C8—2811no—
97C2×SD16—5621no—
98C4⋊Q8—2811no—
99C4⋊Q8C2×D28111yescharacteristic
100#126—5622no—
101#124—5621no—
102C22⋊Q8—5621no—
103C4×Q8—2811no—
104C4×Q8—5621no—
105C4×D4—2811no—
106#117—5621no—
107#107—5622no—
108#106—5621no—
109C4⋊C8C2×D28111yescharacteristic
110C4⋊C8C2×D28111yescharacteristic
111#103—5621no—
112#103—5621no—
113C4×C8—2811no—
114C2×Q8—21no—
115C2×Q8—2811no—
116C2×Q8—5621no—
117C2×D4—2811no—
118C22×C4—5621no—
119SD16—11242no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—5621no—
123C4⋊C4—21no—
124C4⋊C4—2811no—
125C4⋊C4—2811no—
126C4⋊C4—5622no—
127C4⋊C4—5621no—
128C4⋊C4—5621no—
129C4⋊C4—5621no—
130C4⋊C4D112412yes—
131C22⋊C4—5622no—
132C22⋊C4—5622no—
133C22⋊C4—5621no—
134C42—5622no—
135C42—5621no—
136C42C22×D28111yescharacteristic
137C23—5621no—
138Q8—41no—
139Q8—41no—
140Q8—5621no—
141Q8—5621no—
142Q8—11241no—
143Q8—11241no—
144D4—5621no—
145D4—5621no—
146C2×C4—22no—
147C2×C4—5621no—
148C2×C4—5621no—
149C2×C4—5621no—
150C2×C4—11241no—
151C2×C4—11241no—
152C2×C4—11241no—
153C2×C4D4×D28111yescharacteristic
154C2×C4D4×D28111yescharacteristic
155C2×C4C2×D112411yescharacteristic
156C8—41no—
157C8—41no—
158C8—5622no—
159C22—11241no—
160C22—11241no—
161C22—11241no—
162C22#2258284911yescharacteristic
163C4—21no—
164C4—42no—
165C4—11241no—
166C4—11241no—
167C4—11241no—
168C4—22481no—
169C4#2258290011yescharacteristic
170C4#2258290011yescharacteristic
171C4#2258290311yescharacteristic
172C4#2258291111yescharacteristic
173C2—22481no—
174C2#3182360911yescharacteristic
175C2#3182362811yescharacteristic
176C2#3182364811yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#332×C281C2
socleC22×C281#120
prime radicalC2×D1124D4
hypercenter#332D281
hypocenterC281#1650
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #31823866C2semidirect
3. #31823749C2semidirect
5. #31823193C2semidirect
7. #332×C281C2semidirect
88. C281#1650semidirect
94. #332D281semidirect

Maximal subgroups

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

subgroupindex
#318241872
#318238662
#318237492
#318236692
#318231932
#318231902
#332×C2812
#1650281