Finite Group Databasebeta

← #49094257

Subgroups — #49094257

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#31823604C212yesmaximal, complemented
3#31823375C211yesmaximal, characteristic, complemented
4#31823198C212yesmaximal, complemented
5#323×C281C211yesmaximal, characteristic, complemented
6C22×Dic562C2211yescharacteristic, complemented
7C22×C22⋊D281—21no—
8C2×#17985127—22no—
9#22582863—22no—
10#22582853—21no—
11#22582853C2212yes—
12#22582849—22no—
13C2×C22⋊Dic281—21no—
14#22582804—22no—
15#22582786—21no—
16#22582786C2211yescharacteristic, complemented
17C2×C22⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yescomplemented
19C23×D281—21no—
20C2×Dic562—22no—
21C2×Dic562—42no—
22C2×D1124—21no—
23C2×D1124D412yes—
24C2×C22⋊D281—22no—
25C2×C22⋊D281—22no—
26C2×C22⋊D281—42no—
27C2×C22⋊D281—42no—
28C22×Dic281—21no—
29C22×Dic281—21no—
30C22×Dic281—21no—
31#17985127—44no—
32C4⋊Dic281—21no—
33C4⋊Dic281D412yes—
34C22⋊Dic281—42no—
35#17985115—22no—
36#17985115—22no—
37C24×C281D411yescharacteristic
38C22×C4×C281D411yescharacteristic
39C22×C4×C281C2311yescharacteristic
40C2×C8×C281—22no—
41C22⋊C4×C281—22no—
42C22×D281—22no—
43C22×D281—42no—
44C22×D281—81no—
45C22×D281—81no—
46Dic562—24no—
47Dic562—42no—
48D1124—42no—
49D1124—81no—
50C22⋊D281—44no—
51C22⋊D281—42no—
52C22⋊D281—42no—
53C2×Dic281—22no—
54C2×Dic281—22no—
55C2×Dic281—42no—
56C2×Dic281—41no—
57C2×Dic281—41no—
58C2×Dic281—41no—
59C2×Dic281—41no—
60C2×Dic281—41no—
61C23×C281—21no—
62C23×C281—21no—
63C23×C281—41no—
64C23×C281—41no—
65C23×C281SD1612yescomplemented
66C23×C281C2×D411yescharacteristic
67C2×C4×C281—21no—
68C2×C4×C281—41no—
69C2×C4×C281—41no—
70C2×C4×C281C2×D412yes—
71C8×C281—42no—
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—
88Dic281—42no—
89Dic281—42no—
90Dic281—81no—
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#393—2811no—
103#327—2812no—
104#323D28111yescharacteristic, complemented
105C22×Q8—2811no—
106C22×D4—5621no—
107C2×SD16—5622no—
108#123—5622no—
109#121—2812no—
110#121—5621no—
111#120—5622no—
112C2×C22⋊C4—5621no—
113C2×C22⋊C4C2×D28111yescharacteristic
114#103—5622no—
115C22⋊C8C2×D28112yescomplemented
116#95—2811no—
117#95—5621no—
118C24—5621no—
119C24D112411yescharacteristic
120C2×Q8—5622no—
121C2×Q8—11242no—
122C2×D4—2812no—
123C2×D4—5621no—
124C2×D4—5622no—
125C2×D4—5622no—
126C2×D4—11242no—
127C2×D4—11242no—
128C22×C4—5621no—
129C22×C4—5621no—
130C22×C4—5621no—
131C22×C4D112411yescharacteristic
132C22×C4C22×D28111yescharacteristic
133SD16—11244no—
134C2×C8—22no—
135C4⋊C4—2812no—
136C4⋊C4—5621no—
137C22⋊C4—22no—
138C22⋊C4—5622no—
139C22⋊C4—5622no—
140C22⋊C4—11242no—
141C23—21no—
142C23—21no—
143C23—41no—
144C23—41no—
145C23—5622no—
146C23—11242no—
147C23—22481no—
148C23—22481no—
149C23#1798512712yescomplemented
150C23C2×D112411yescharacteristic
151Q8—5624no—
152Q8—11242no—
153D4—11242no—
154D4—11244no—
155D4—11242no—
156D4—11242no—
157D4—22481no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—5622no—
162C2×C4—5622no—
163C2×C4—11242no—
164C2×C4—11241no—
165C2×C4—11241no—
166C2×C4—11241no—
167C2×C4—11241no—
168C2×C4—11241no—
169C2×C4D4×D28112yes—
170C8—42no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—81no—
178C22—11242no—
179C22—11242no—
180C22—11242no—
181C22—22484no—
182C22#2258284911yescharacteristic
183C22C2×#1798512711yescharacteristic
184C22#2258290711yescharacteristic
185C4—22no—
186C4—41no—
187C4—11242no—
188C4—11242no—
189C4—22481no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—22482no—
194C2#3182361611yescharacteristic
195C2#3182364311yescharacteristic
196C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#323×C281C2
socleC22×C281#120
prime radical#31824025C2
hypercenter#323D281
hypocenterC281#1601
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #31823604C2semidirect
3. #31823375C2semidirect
4. #31823198C2semidirect
5. #323×C281C2semidirect
6. C22×Dic562C22semidirect
16. #22582786C22semidirect
18. C22⋊C8×C281C22semidirect
65. C23×C281SD16semidirect
98. C281#1601semidirect
104. #323D281semidirect
115. C22⋊C8C2×D281semidirect
149. C23#17985127semidirect

Maximal subgroups

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

subgroupindex
#318240252
#318236042
#318233752
#318231982
#323×C2812
#1601281