Finite Group Databasebeta

← #49094501

Subgroups — #49094501

Order 35968.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#31824134C211yesmaximal, characteristic
2#31823811C211yesmaximal, characteristic, complemented
3#31823745C211yesmaximal, characteristic, complemented
4#31823206C211yesmaximal, characteristic, complemented
5#31823193C211yesmaximal, characteristic, complemented
6D4⋊#14555886C211yesmaximal, characteristic, complemented
7#461×C281C211yesmaximal, characteristic, complemented
8C2×#17985138—21no—
9#22582876C2211yescharacteristic
10#22582875—21no—
11#22582853—21no—
12#22582852—22no—
13C4×Dic562C2211yescharacteristic
14#22582841—21no—
15#22582810—21no—
16C4⋊#14555886C2211yescharacteristic
17#22582802—21no—
18#22582799—22no—
19C4×#14555886C2211yescharacteristic
20C2×SD16×C281—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4×D4×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24#103×C281—21no—
25#17985138—42no—
26#17985138—42no—
27C2×Dic562D411yescharacteristic
28C2×D1124—21no—
29C2×D1124—21no—
30C2×D1124D412yes—
31C2×C22⋊D281—22no—
32C2×C22⋊D281—22no—
33C2×C4×D281—22no—
34C2×#14555886—21no—
35C2×#14555886—21no—
36C4⋊Dic281D411yescharacteristic
37#17985117—21no—
38#17985115—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
50C22×D281—22no—
51Dic562—21no—
52Dic562SD1612yescomplemented
53D1124—42no—
54D1124—41no—
55D1124—41no—
56D1124—41no—
57D1124—41no—
58C22⋊D281—44no—
59C22⋊D281—82no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C4×D281—44no—
63#14555886—41no—
64#14555886—41no—
65C23×C281—21no—
66Q8×C281—41no—
67Q8×C281—41no—
68D4×C281—21no—
69D4×C281—21no—
70C2×C4×C281—21no—
71C2×C4×C281—41no—
72C2×C4×C281—41no—
73C2×C4×C281—41no—
74C2×C4×C281C2×D411yescharacteristic
75C2×C4×C281C2×D411yescharacteristic
76C2×C4×C281C2×D411yescharacteristic
77C8×C281—41no—
78C22×C281—41no—
79C22×C281—41no—
80C22×C281—41no—
81C22×C281#12011yescharacteristic
82C2×D281—42no—
83C2×D281—42no—
84C2×D281—42no—
85C4×C281—21no—
86C4×C281—41no—
87C4×C281—81no—
88C4×C281C2×SD1611yescharacteristic
89C4×C281#13511yescharacteristic
90C4×C281AGL(1,ℤ/8)11yescharacteristic
91C4×C281AGL(1,ℤ/8)11yescharacteristic
92Dic281—22no—
93Dic281—41no—
94C2×C281—81no—
95C2×C281#44911yescharacteristic
96C2×C281#45011yescharacteristic
97C2×C281#45511yescharacteristic
98D281—82no—
99C281#164211yescharacteristic, complemented, Sylow
100#1642—2811nomaximal, Sylow
101#550—2811no—
102#486—2811no—
103#475—2811no—
104#461D28111yescharacteristic, complemented
105#331—2811no—
106Q8⋊C8—2811no—
107D4⋊C8—2811no—
108C2×#41—5621no—
109C2×SD16—21no—
110C4⋊Q8C2×D28111yescharacteristic
111#127—2811no—
112#127—5621no—
113#121—5622no—
114#121—5621no—
115C4×Q8—2811no—
116C4×D4—5621no—
117C4×D4C2×D28111yescharacteristic
118#106—5621no—
119C4⋊C8—2811no—
120C4⋊C8C2×D28111yescharacteristic
121#103—21no—
122#103—5621no—
123#102—5622no—
124C4×C8—2811no—
125#41—11242no—
126#41—11242no—
127C2×Q8—21no—
128C2×Q8—2811no—
129C2×D4—2812no—
130C2×D4—5622no—
131C2×D4—5622no—
132C2×D4—5621no—
133C2×D4—5621no—
134C2×D4C22⋊D28111yescharacteristic
135C22×C4—21no—
136C22×C4—5622no—
137SD16—42no—
138C2×C8—21no—
139C2×C8—5621no—
140C2×C8—5621no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2811no—
144C4⋊C4—5621no—
145C4⋊C4C22⋊D28111yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—5622no—
148C42—5621no—
149C42C22×D28111yescharacteristic
150C23—21no—
151C23—5622no—
152Q8—41no—
153Q8—41no—
154Q8—2812no—
155Q8—5621no—
156D4—21no—
157D4—21no—
158D4—11242no—
159D4—11244no—
160D4—11241no—
161D4—11241no—
162D4—11241no—
163D4—11241no—
164D4—22482no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—5621no—
170C2×C4—5621no—
171C2×C4—11244no—
172C2×C4D4×D28111yescharacteristic
173C2×C4D4×D28111yescharacteristic
174C2×C4C2×C22⋊D28111yescharacteristic
175C8—41no—
176C8—11241no—
177C8—11241no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—11242no—
182C22—11242no—
183C22—11242no—
184C22#2258284711yescharacteristic
185C4—21no—
186C4—41no—
187C4—81no—
188C4—5622no—
189C4—11241no—
190C4SD16×D28111yescharacteristic
191C4#2258289911yescharacteristic
192C4#2258290511yescharacteristic
193C4#2258290611yescharacteristic
194C2—81no—
195C2—22482no—
196C2#3182360611yescharacteristic
197C2#3182361211yescharacteristic
198C2#3182363911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#461×C281C2
socleC22×C281#120
prime radical#31824134C2
hypercenter#461D281
hypocenterC281#1642
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. #31823811C2semidirect
3. #31823745C2semidirect
4. #31823206C2semidirect
5. #31823193C2semidirect
6. D4⋊#14555886C2semidirect
7. #461×C281C2semidirect
52. Dic562SD16semidirect
99. C281#1642semidirect
104. #461D281semidirect

Maximal subgroups

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

subgroupindex
#318241342
#318238112
#318237452
#318232062
#318231932
D4⋊#145558862
#461×C2812
#1642281