Finite Group Databasebeta

← #49094564

Subgroups — #49094564

Order 35968.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic562C211yesmaximal, characteristic
2#31823859C211yesmaximal, characteristic, complemented
3#31823745C211yesmaximal, characteristic, complemented
4#31823208C211yesmaximal, characteristic, complemented
5#31823193C211yesmaximal, characteristic, complemented
6D4⋊#14555886C211yesmaximal, characteristic
7#461×C281C211yesmaximal, characteristic
8C22×Dic562—21no—
9#22582879C2211yescharacteristic
10#22582878—21no—
11#22582858—21no—
12#22582856—22no—
13C4×Dic562C2211yescharacteristic
14D4×Dic281—21no—
15#22582810—21no—
16#22582810—22no—
17C4⋊#14555886C2211yescharacteristic
18#22582802—21no—
19C4×#14555886C2211yescharacteristic
20C2×SD16×C281—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4×D4×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24#103×C281—21no—
25C2×Dic562—22no—
26C2×Dic562—21no—
27C2×Dic562—42no—
28C2×Dic562—42no—
29C2×Dic562D411yescharacteristic
30C22×Dic281—22no—
31C2×#14555886—21no—
32C2×#14555886—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281D411yescharacteristic
35C4⋊Dic281D412yes—
36#17985117—22no—
37#17985117—21no—
38C22⋊Dic281—22no—
39C4×Dic281—21no—
40C2×Q8×C281—21no—
41C2×D4×C281D411yescharacteristic
42C22×C4×C281—21no—
43SD16×C281—42no—
44C2×C8×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281D411yescharacteristic
48C22⋊C4×C281—21no—
49C42×C281C2311yescharacteristic
50Dic562—21no—
51Dic562—44no—
52Dic562—41no—
53Dic562—41no—
54Dic562SD1612yescomplemented
55C2×Dic281—21no—
56C2×Dic281—21no—
57C2×Dic281—22no—
58C2×Dic281—44no—
59#14555886—22no—
60#14555886—41no—
61C23×C281—21no—
62Q8×C281—41no—
63Q8×C281—41no—
64D4×C281—21no—
65D4×C281SD1612yes—
66C2×C4×C281—21no—
67C2×C4×C281—41no—
68C2×C4×C281—41no—
69C2×C4×C281—41no—
70C2×C4×C281C2×D411yescharacteristic
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C8×C281—41no—
74C22×C281—22no—
75C22×C281—41no—
76C22×C281—41no—
77C22×C281#12011yescharacteristic
78C4×C281—21no—
79C4×C281—41no—
80C4×C281—81no—
81C4×C281C2×SD1611yescharacteristic
82C4×C281C2×SD1611yescharacteristic
83C4×C281AGL(1,ℤ/8)11yescharacteristic
84C4×C281#13711yescharacteristic
85Dic281—22no—
86Dic281—42no—
87Dic281—41no—
88C2×C281—42no—
89C2×C281#44811yescharacteristic
90C2×C281#45011yescharacteristic
91C2×C281#45611yescharacteristic
92C281#165111yescharacteristic, complemented, Sylow
93#1651—2811nomaximal, Sylow
94D4×Q8—2811no—
95#498—2811no—
96#475—2811no—
97#461D28111yescharacteristic
98#332—2811no—
99Q8⋊C8—2811no—
100D4⋊C8—2811no—
101C22×Q8—5621no—
102C2×SD16—21no—
103C4⋊Q8—2811no—
104C4⋊Q8—5621no—
105C4⋊Q8C2×D28111yescharacteristic
106C22⋊Q8—5622no—
107C22⋊Q8—5621no—
108C4×Q8—2811no—
109C4×D4—5621no—
110C4×D4C2×D28111yescharacteristic
111#106—5621no—
112#106—5622no—
113C4⋊C8—2811no—
114C4⋊C8C2×D28111yescharacteristic
115#103—21no—
116#103—5621no—
117C4×C8—2811no—
118C2×Q8—21no—
119C2×Q8—2811no—
120C2×Q8—5622no—
121C2×Q8—5621no—
122C2×Q8—11242no—
123C2×Q8—11242no—
124C2×D4C22⋊D28111yescharacteristic
125C22×C4—21no—
126C22×C4—5622no—
127SD16—42no—
128C2×C8—21no—
129C2×C8—5621no—
130C2×C8—5621no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—2811no—
134C4⋊C4—2812no—
135C4⋊C4—5622no—
136C4⋊C4—5621no—
137C4⋊C4—5621no—
138C4⋊C4C22⋊D28111yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5622no—
141C42—5621no—
142C42C22×D28111yescharacteristic
143C23—21no—
144Q8—41no—
145Q8—41no—
146Q8—2812no—
147Q8—5621no—
148Q8—11244no—
149Q8—11241no—
150Q8—11241no—
151D4—21no—
152D4#1798512612yes—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—5621no—
158C2×C4—5621no—
159C2×C4—5622no—
160C2×C4—11244no—
161C2×C4D4×D28111yescharacteristic
162C2×C4D4×D28111yescharacteristic
163C2×C4C2×C22⋊D28111yescharacteristic
164C8—41no—
165C8—5622no—
166C8—11241no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#2258284711yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—5622no—
175C4—11241no—
176C4—11242no—
177C4SD16×D28111yescharacteristic
178C4C2×#1798512611yescharacteristic
179C4#2258290611yescharacteristic
180C4#2258290911yescharacteristic
181C2—42no—
182C2#3182360111yescharacteristic
183C2#3182361211yescharacteristic
184C2#3182364411yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#461×C281C2
socleC22×C281#120
prime radicalC2×D4×C281D4
hypercenter#461D281
hypocenterC281#1651
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #31823859C2semidirect
3. #31823745C2semidirect
4. #31823208C2semidirect
5. #31823193C2semidirect
54. Dic562SD16semidirect
92. C281#1651semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5622
#318238592
#318237452
#318232082
#318231932
D4⋊#145558862
#461×C2812
#1651281