Finite Group Databasebeta

← #49094274

Subgroups — #49094274

Order 35968.

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

normal subgroups only

This group has 282 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#31824044C211yesmaximal, characteristic
2#31823604C212yesmaximal, complemented
3#31823383C211yesmaximal, characteristic, complemented
4#31823198C212yesmaximal, complemented
5#324×C281C211yesmaximal, characteristic, complemented
6C2×#17985138—21no—
7C22×Dic562C2211yescharacteristic
8C2×#17985127—22no—
9#22582859—22no—
10#22582854—22no—
11#22582853—21no—
12#22582853C2212yes—
13C2×#17985117—21no—
14#22582804—22no—
15#22582786—21no—
16#22582786C2211yescharacteristic
17C2×C4⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yes—
19#17985138—42no—
20#17985138—42no—
21C2×Dic562—21no—
22C2×Dic562—22no—
23C2×Dic562—42no—
24C2×D1124—21no—
25C2×D1124—21no—
26C2×D1124D412yes—
27C2×C22⋊D281—22no—
28C22×Dic281—21no—
29C22×Dic281—21no—
30C2×C4×D281—22no—
31#17985127—44no—
32C4⋊Dic281—21no—
33C4⋊Dic281D412yes—
34#17985117—42no—
35#17985115—22no—
36#17985115—22no—
37C22×C4×C281D411yescharacteristic
38C22×C4×C281D411yescharacteristic
39C22×C4×C281C2311yescharacteristic
40C2×C8×C281—22no—
41C4⋊C4×C281—22no—
42C22×D281—22no—
43Dic562—24no—
44Dic562—42no—
45Dic562—42no—
46D1124—42no—
47D1124—42no—
48D1124—81no—
49C22⋊D281—42no—
50C22⋊D281—42no—
51C2×Dic281—22no—
52C2×Dic281—22no—
53C2×Dic281—22no—
54C2×Dic281—41no—
55C2×Dic281—41no—
56C2×Dic281—41no—
57C2×Dic281—41no—
58C4×D281—44no—
59C23×C281C2×D411yescharacteristic
60C2×C4×C281—21no—
61C2×C4×C281—21no—
62C2×C4×C281—21no—
63C2×C4×C281—41no—
64C2×C4×C281—41no—
65C2×C4×C281SD1612yescomplemented
66C2×C4×C281C2×D412yes—
67C8×C281—42no—
68C22×C281—21no—
69C22×C281—21no—
70C22×C281#12011yescharacteristic
71C22×C281C2×SD1611yescharacteristic
72C22×C281AGL(1,ℤ/8)11yescharacteristic
73C2×D281—42no—
74C2×D281—42no—
75C2×D281—42no—
76C4×C281—22no—
77C4×C281—22no—
78C4×C281—41no—
79Dic281—42no—
80Dic281—42no—
81Dic281—42no—
82C2×C281—21no—
83C2×C281—21no—
84C2×C281#45011yescharacteristic
85C2×C281#45611yescharacteristic
86C2×C281B(4,𝔽2)11yescharacteristic
87D281—82no—
88C281#160411yescharacteristic, complemented, Sylow
89#1604—2811nomaximal, Sylow
90#537—2811no—
91#448—2812no—
92#395—2811no—
93#327—2812no—
94#324D28111yescharacteristic, complemented
95C2×#41—5621no—
96C22×Q8—2811no—
97C2×SD16—5622no—
98C22⋊Q8—5622no—
99#121—2812no—
100#121—5622no—
101#121—5621no—
102C2×C4⋊C4—5621no—
103C2×C4⋊C4C2×D28111yescharacteristic
104#103—5622no—
105C22⋊C8C2×D28112yes—
106#95—2811no—
107#95—5621no—
108#41—11242no—
109#41—11242no—
110C2×Q8—5621no—
111C2×Q8—5622no—
112C2×Q8—11242no—
113C2×D4—2812no—
114C2×D4—5621no—
115C2×D4—5621no—
116C2×D4—5622no—
117C22×C4—5622no—
118C22×C4—5621no—
119C22×C4—5621no—
120C22×C4D112411yescharacteristic
121C22×C4D112411yescharacteristic
122C22×C4C22×D28111yescharacteristic
123SD16—11244no—
124C2×C8—22no—
125C4⋊C4—22no—
126C4⋊C4—2812no—
127C4⋊C4—5621no—
128C4⋊C4—11242no—
129C22⋊C4—5622no—
130C22⋊C4—5622no—
131C23—5622no—
132C23C2×D112411yescharacteristic
133Q8—5624no—
134Q8—11242no—
135Q8—11242no—
136D4—11242no—
137D4—11242no—
138D4—11242no—
139D4—11242no—
140D4—22481no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—5622no—
147C2×C4—5622no—
148C2×C4—5622no—
149C2×C4—11244no—
150C2×C4—11241no—
151C2×C4—11241no—
152C2×C4—11241no—
153C2×C4—11241no—
154C2×C4#1798512712yescomplemented
155C2×C4D4×D28112yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—11242no—
160C22—11242no—
161C22—11242no—
162C22#2258284911yescharacteristic
163C22C2×#1798512711yescharacteristic
164C22#2258290711yescharacteristic
165C4—22no—
166C4—22no—
167C4—41no—
168C4—11242no—
169C4—11242no—
170C4—11242no—
171C2—21no—
172C2—21no—
173C2—22482no—
174C2#3182361611yescharacteristic
175C2#3182364811yescharacteristic
176C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#324×C281C2
socleC22×C281#120
prime radical#31824044C2
hypercenter#324D281
hypocenterC281#1604
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #31823604C2semidirect
3. #31823383C2semidirect
4. #31823198C2semidirect
5. #324×C281C2semidirect
65. C2×C4×C281SD16semidirect
88. C281#1604semidirect
94. #324D281semidirect
154. C2×C4#17985127semidirect

Maximal subgroups

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

subgroupindex
#318240442
#318236042
#318233832
#318231982
#324×C2812
#1604281