Finite Group Databasebeta

← #49094271

Subgroups — #49094271

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#31823602C212yesmaximal, complemented
3#31823196C212yesmaximal, complemented
4#31823189C211yesmaximal, characteristic, complemented
5#395×C281C211yesmaximal, characteristic, complemented
6C2×#17985138—21no—
7C2×#17985125—22no—
8#22582859—22no—
9#22582854—22no—
10#22582853—21no—
11#22582853C2212yes—
12#22582803—22no—
13C22⋊#14555886C2212yes—
14C22×Q8×C281C2211yescharacteristic
15C2×C4⋊C4×C281—21no—
16C2×C4⋊C4×C281C2211yescharacteristic
17#95×C281—21no—
18#95×C281C2211yescharacteristic
19#17985138—42no—
20#17985138—42no—
21C2×Dic562—21no—
22C2×D1124—21no—
23C2×D1124—21no—
24C2×D1124D412yes—
25C2×C22⋊D281—22no—
26C2×C4×D281—22no—
27#17985125—44no—
28C2×#14555886—22no—
29C4⋊Dic281—21no—
30C4⋊Dic281D412yes—
31#17985115—22no—
32#17985115—22no—
33C2×Q8×C281—22no—
34C2×Q8×C281—42no—
35C22×C4×C281—21no—
36C22×C4×C281—21no—
37C22×C4×C281D411yescharacteristic
38C22×C4×C281D411yescharacteristic
39C22×C4×C281C2311yescharacteristic
40C4⋊C4×C281—22no—
41C4⋊C4×C281—42no—
42C22×D281—22no—
43Dic562—42no—
44D1124—42no—
45D1124—42no—
46D1124—81no—
47C22⋊D281—42no—
48C22⋊D281—42no—
49C2×Dic281—22no—
50C4×D281—44no—
51#14555886—42no—
52C23×C281C2×D411yescharacteristic
53Q8×C281—24no—
54Q8×C281—42no—
55C2×C4×C281—21no—
56C2×C4×C281—21no—
57C2×C4×C281—22no—
58C2×C4×C281—22no—
59C2×C4×C281—21no—
60C2×C4×C281—41no—
61C2×C4×C281—41no—
62C2×C4×C281—41no—
63C2×C4×C281—41no—
64C2×C4×C281—41no—
65C2×C4×C281—41no—
66C2×C4×C281SD1612yescomplemented
67C2×C4×C281C2×D412yes—
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—42no—
79C4×C281—42no—
80C4×C281—41no—
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#395D28111yescharacteristic, complemented
93#327—2812no—
94#324—2811no—
95C2×#41—5621no—
96C22×Q8C2×D28111yescharacteristic
97C2×SD16—5622no—
98C22⋊Q8—5622no—
99#121—2812no—
100#121—5622no—
101#121—5621no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4C2×D28111yescharacteristic
104#103—5622no—
105C22⋊C8—2812no—
106#95—21no—
107#95C2×D28111yescharacteristic
108#41—11242no—
109#41—11242no—
110C2×Q8—22no—
111C2×Q8—42no—
112C2×Q8—5621no—
113C2×D4—2812no—
114C2×D4—5621no—
115C2×D4—5621no—
116C2×D4—5622no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—5622no—
120C22×C4C22⋊D28111yescharacteristic
121C22×C4C22⋊D28111yescharacteristic
122C22×C4C22×D28111yescharacteristic
123SD16—11244no—
124C2×C8—5622no—
125C4⋊C4—22no—
126C4⋊C4—42no—
127C4⋊C4—2812no—
128C4⋊C4—5621no—
129C22⋊C4—5622no—
130C22⋊C4—5622no—
131C23—5622no—
132C23C2×C22⋊D28111yescharacteristic
133Q8—24no—
134Q8—42no—
135Q8—11242no—
136D4—11242no—
137D4—11242no—
138D4—11242no—
139D4—11242no—
140D4—22481no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—5622no—
153C2×C4—11244no—
154C2×C4#1798512512yescomplemented
155C2×C4D4×D28112yes—
156C8—11242no—
157C22—21no—
158C22—21no—
159C22—11242no—
160C22—11242no—
161C22—11242no—
162C22#2258284711yescharacteristic
163C22C2×#1798512511yescharacteristic
164C22#2258290411yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—42no—
169C4—41no—
170C4—11242no—
171C2—21no—
172C2—21no—
173C2—22482no—
174C2#3182361311yescharacteristic
175C2#3182364511yescharacteristic
176C2#3182364911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#395×C281C2
socleC22×C281#120
prime radical#31824044C2
hypercenter#395D281
hypocenterC281#1604
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #31823602C2semidirect
3. #31823196C2semidirect
4. #31823189C2semidirect
5. #395×C281C2semidirect
66. C2×C4×C281SD16semidirect
88. C281#1604semidirect
92. #395D281semidirect
154. C2×C4#17985125semidirect

Maximal subgroups

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

subgroupindex
#318240442
#318236022
#318231962
#318231892
#395×C2812
#1604281