Finite Group Databasebeta

← #49094255

Subgroups — #49094255

Order 35968.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#31823601C212yesmaximal, complemented
2#31823375C211yesmaximal, characteristic, complemented
3#31823197C212yesmaximal, complemented
4#31823187C211yesmaximal, characteristic, complemented
5#534×C281C211yesmaximal, characteristic
6C22×Dic562C2211yescharacteristic, complemented
7C2×#17985126—22no—
8C2×C22⋊Dic281—21no—
9#22582802—22no—
10C22⋊#14555886C2212yescomplemented
11#22582786—21no—
12#22582786C2211yescharacteristic, complemented
13C22×D4×C281—21no—
14#123×C281—22no—
15#121×C281—21no—
16#121×C281C2212yes—
17#120×C281—22no—
18C2×C22⋊C4×C281C2211yescharacteristic
19C2×Dic562—22no—
20C2×Dic562—42no—
21C22×Dic281—21no—
22C22×Dic281—21no—
23#17985126—44no—
24C2×#14555886—22no—
25C22⋊Dic281—42no—
26C24×C281—21no—
27C24×C281D411yescharacteristic
28C2×D4×C281—22no—
29C2×D4×C281—22no—
30C2×D4×C281—21no—
31C2×D4×C281—42no—
32C2×D4×C281—42no—
33C2×D4×C281D412yes—
34C22×C4×C281—21no—
35C22×C4×C281D411yescharacteristic
36C22×C4×C281C2311yescharacteristic
37C4⋊C4×C281—21no—
38C4⋊C4×C281D412yes—
39C22⋊C4×C281—22no—
40C22⋊C4×C281—22no—
41C22⋊C4×C281—22no—
42Dic562—24no—
43Dic562—42no—
44C2×Dic281—22no—
45C2×Dic281—41no—
46C2×Dic281—41no—
47C2×Dic281—41no—
48C2×Dic281—41no—
49C2×Dic281—41no—
50#14555886—42no—
51C23×C281—21no—
52C23×C281—21no—
53C23×C281—22no—
54C23×C281—41no—
55C23×C281—41no—
56C23×C281—42no—
57C23×C281—81no—
58C23×C281—81no—
59C23×C281SD1612yescomplemented
60C23×C281C2×D411yescharacteristic
61D4×C281—42no—
62D4×C281—44no—
63D4×C281—42no—
64D4×C281—42no—
65D4×C281—81no—
66C2×C4×C281—21no—
67C2×C4×C281—22no—
68C2×C4×C281—41no—
69C2×C4×C281—42no—
70C2×C4×C281—41no—
71C2×C4×C281C2×D412yes—
72C22×C281—21no—
73C22×C281—21no—
74C22×C281—22no—
75C22×C281—42no—
76C22×C281—41no—
77C22×C281—41no—
78C22×C281—42no—
79C22×C281—42no—
80C22×C281—42no—
81C22×C281—81no—
82C22×C281—84no—
83C22×C281#12011yescharacteristic
84C22×C281C2×SD1611yescharacteristic
85C22×C281AGL(1,ℤ/8)11yescharacteristic
86C4×C281—22no—
87C4×C281—42no—
88C4×C281—41no—
89Dic281—42no—
90Dic281—81no—
91C2×C281—21no—
92C2×C281—21no—
93C2×C281—42no—
94C2×C281—82no—
95C2×C281#45011yescharacteristic
96C2×C281#45511yescharacteristic
97C2×C281B(4,𝔽2)11yescharacteristic
98C281#160111yescharacteristic, complemented, Sylow
99#1601—2811nomaximal, Sylow
100#534D28111yescharacteristic
101#448—2812no—
102#393—2811no—
103#327—2812no—
104#323—2811no—
105C22×Q8—2811no—
106C22×D4—21no—
107C2×SD16—5622no—
108#123—22no—
109#121—21no—
110#121C2×D28112yes—
111#120—22no—
112C2×C22⋊C4—5621no—
113C2×C22⋊C4C2×D28111yescharacteristic
114#103—5622no—
115C22⋊C8—2812no—
116#95—2811no—
117#95—5621no—
118C24—21no—
119C24C22⋊D28111yescharacteristic
120C2×Q8—5622no—
121C2×Q8—11242no—
122C2×D4—22no—
123C2×D4—22no—
124C2×D4—21no—
125C2×D4—42no—
126C2×D4—42no—
127C2×D4C22⋊D28112yes—
128C22×C4—21no—
129C22×C4—5621no—
130C22×C4—5621no—
131C22×C4C22⋊D28111yescharacteristic
132C22×C4C22×D28111yescharacteristic
133SD16—11244no—
134C2×C8—5622no—
135C4⋊C4—21no—
136C4⋊C4C22⋊D28112yes—
137C22⋊C4—22no—
138C22⋊C4—22no—
139C22⋊C4—22no—
140C22⋊C4—11242no—
141C23—21no—
142C23—21no—
143C23—22no—
144C23—41no—
145C23—41no—
146C23—42no—
147C23—81no—
148C23—81no—
149C23#1798512612yescomplemented
150C23C2×C22⋊D28111yescharacteristic
151Q8—5624no—
152Q8—11242no—
153D4—42no—
154D4—44no—
155D4—42no—
156D4—42no—
157D4—81no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—5622no—
164C2×C4—11241no—
165C2×C4—11241no—
166C2×C4—11241no—
167C2×C4—11241no—
168C2×C4—11241no—
169C2×C4C2×C22⋊D28112yes—
170C8—11242no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—42no—
178C22—42no—
179C22—42no—
180C22—81no—
181C22—84no—
182C22#2258284811yescharacteristic
183C22C2×#1798512611yescharacteristic
184C22#2258290511yescharacteristic
185C4—22no—
186C4—41no—
187C4—42no—
188C4—11242no—
189C4—22481no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—82no—
194C2#3182361411yescharacteristic
195C2#3182364111yescharacteristic
196C2#3182365011yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting, prime radical#534×C281C2
socleC22×C281#120
hypercenter#534D281
hypocenterC281#1601
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #31823601C2semidirect
2. #31823375C2semidirect
3. #31823197C2semidirect
4. #31823187C2semidirect
6. C22×Dic562C22semidirect
10. C22⋊#14555886C22semidirect
12. #22582786C22semidirect
59. C23×C281SD16semidirect
98. C281#1601semidirect
149. C23#17985126semidirect

Maximal subgroups

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

subgroupindex
#318236012
#318233752
#318231972
#318231872
#534×C2812
#1601281