Finite Group Databasebeta

← #49094254

Subgroups — #49094254

Order 35968.

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

normal subgroups only

This group has 308 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#31824025C211yesmaximal, characteristic
2#31823602C212yesmaximal, complemented
3#31823196C212yesmaximal, complemented
4#31823187C211yesmaximal, characteristic, complemented
5#393×C281C211yesmaximal, characteristic, complemented
6C22×C22⋊D281—21no—
7C2×#17985125—22no—
8#22582863—22no—
9#22582853—21no—
10#22582853C2212yes—
11#22582849—22no—
12#22582803—22no—
13C22⋊#14555886C2212yescomplemented
14C22×Q8×C281C2211yescharacteristic, complemented
15C2×C22⋊C4×C281—21no—
16C2×C22⋊C4×C281C2211yescharacteristic
17#95×C281—21no—
18#95×C281C2211yescharacteristic, complemented
19C23×D281—21no—
20C2×D1124—21no—
21C2×D1124D412yes—
22C2×C22⋊D281—22no—
23C2×C22⋊D281—22no—
24C2×C22⋊D281—42no—
25C2×C22⋊D281—42no—
26C22×Dic281—21no—
27#17985125—44no—
28C2×#14555886—22no—
29C4⋊Dic281—21no—
30C4⋊Dic281D412yes—
31#17985115—22no—
32#17985115—22no—
33C24×C281D411yescharacteristic
34C2×Q8×C281—22no—
35C2×Q8×C281—42no—
36C22×C4×C281—21no—
37C22×C4×C281—21no—
38C22×C4×C281D411yescharacteristic
39C22×C4×C281C2311yescharacteristic
40C22⋊C4×C281—22no—
41C22⋊C4×C281—42no—
42C22×D281—22no—
43C22×D281—42no—
44C22×D281—81no—
45C22×D281—81no—
46D1124—42no—
47D1124—81no—
48C22⋊D281—44no—
49C22⋊D281—42no—
50C22⋊D281—42no—
51C2×Dic281—22no—
52C2×Dic281—42no—
53#14555886—42no—
54C23×C281—21no—
55C23×C281—21no—
56C23×C281—41no—
57C23×C281—41no—
58C23×C281SD1612yescomplemented
59C23×C281C2×D411yescharacteristic
60Q8×C281—24no—
61Q8×C281—42no—
62C2×C4×C281—22no—
63C2×C4×C281—21no—
64C2×C4×C281—41no—
65C2×C4×C281—41no—
66C2×C4×C281—41no—
67C2×C4×C281—41no—
68C2×C4×C281—41no—
69C2×C4×C281—41no—
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—81no—
79C22×C281#12011yescharacteristic
80C22×C281C2×SD1611yescharacteristic
81C22×C281AGL(1,ℤ/8)11yescharacteristic
82C2×D281—42no—
83C2×D281—42no—
84C2×D281—42no—
85C2×D281—84no—
86C4×C281—22no—
87C4×C281—41no—
88C4×C281—42no—
89C4×C281—81no—
90Dic281—42no—
91C2×C281—21no—
92C2×C281—21no—
93C2×C281—42no—
94C2×C281#45011yescharacteristic
95C2×C281#45511yescharacteristic
96C2×C281B(4,𝔽2)11yescharacteristic
97D281—82no—
98C281#160111yescharacteristic, complemented, Sylow
99#1601—2811nomaximal, Sylow
100#534—2811no—
101#448—2812no—
102#393D28111yescharacteristic, complemented
103#327—2812no—
104#323—2811no—
105C22×Q8C2×D28111yescharacteristic, complemented
106C22×D4—5621no—
107C2×SD16—5622no—
108#123—5622no—
109#121—2812no—
110#121—5621no—
111#120—5622no—
112C2×C22⋊C4—21no—
113C2×C22⋊C4C2×D28111yescharacteristic
114#103—5622no—
115C22⋊C8—2812no—
116#95—21no—
117#95C2×D28111yescharacteristic, complemented
118C24—5621no—
119C24C22⋊D28111yescharacteristic
120C2×Q8—22no—
121C2×Q8—42no—
122C2×D4—2812no—
123C2×D4—5621no—
124C2×D4—5622no—
125C2×D4—5622no—
126C2×D4—11242no—
127C2×D4—11242no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—5621no—
131C22×C4C22⋊D28111yescharacteristic
132C22×C4C22×D28111yescharacteristic
133SD16—11244no—
134C2×C8—5622no—
135C4⋊C4—2812no—
136C4⋊C4—5621no—
137C22⋊C4—22no—
138C22⋊C4—42no—
139C22⋊C4—5622no—
140C22⋊C4—5622no—
141C23—21no—
142C23—21no—
143C23—41no—
144C23—41no—
145C23—5622no—
146C23—11242no—
147C23—22481no—
148C23—22481no—
149C23#1798512512yescomplemented
150C23C2×C22⋊D28111yescharacteristic
151Q8—24no—
152Q8—42no—
153D4—11242no—
154D4—11244no—
155D4—11242no—
156D4—11242no—
157D4—22481no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—5622no—
168C2×C4—11242no—
169C2×C4D4×D28112yes—
170C8—11242no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—81no—
178C22—11242no—
179C22—11242no—
180C22—11242no—
181C22—22484no—
182C22#2258284711yescharacteristic
183C22C2×#1798512511yescharacteristic
184C22#2258290411yescharacteristic
185C4—22no—
186C4—41no—
187C4—42no—
188C4—81no—
189C4—11242no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—22482no—
194C2#3182361311yescharacteristic
195C2#3182364011yescharacteristic
196C2#3182364911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#393×C281C2
socleC22×C281#120
prime radical#31824025C2
hypercenter#393D281
hypocenterC281#1601
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #31823602C2semidirect
3. #31823196C2semidirect
4. #31823187C2semidirect
5. #393×C281C2semidirect
13. C22⋊#14555886C22semidirect
14. C22×Q8×C281C22semidirect
18. #95×C281C22semidirect
58. C23×C281SD16semidirect
98. C281#1601semidirect
102. #393D281semidirect
105. C22×Q8C2×D281semidirect
117. #95C2×D281semidirect
149. C23#17985125semidirect

Maximal subgroups

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

subgroupindex
#318240252
#318236022
#318231962
#318231872
#393×C2812
#1601281