Finite Group Databasebeta

← #49094394

Subgroups — #49094394

Order 35968.

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

normal subgroups only

This group has 256 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#31824117C211yesmaximal, characteristic, complemented
2#31823810C211yesmaximal, characteristic, complemented
3#31823659C211yesmaximal, characteristic, complemented
4#31823658C211yesmaximal, characteristic, complemented
5#31823208C211yesmaximal, characteristic, complemented
6#31823192C211yesmaximal, characteristic, complemented
7D4⋊C8×C281C211yesmaximal, characteristic, complemented
8C2×#17985137—21no—
9C2×D2248—21no—
10C2×#17985123—21no—
11#22582879C2211yescharacteristic
12#22582876C2211yescharacteristic
13#22582863—22no—
14#22582859—21no—
15#22582853—21no—
16C4×D1124C2211yescharacteristic
17C2×C4⋊Dic281—21no—
18C4⋊#14555886C2211yescharacteristic
19#22582801—21no—
20#22582801—22no—
21#22582799—21no—
22C4×D4×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24C4×C8×C281C2211yescharacteristic
25#17985137—42no—
26#17985137—42no—
27C2×Dic562—21no—
28C2×D1124—21no—
29C2×D1124—21no—
30C2×D1124—21no—
31C2×D1124D411yescharacteristic
32C2×C22⋊D281—22no—
33C22×Dic281—22no—
34C2×C4×D281—21no—
35D2248—42no—
36#17985123—42no—
37C2×#14555886—21no—
38C4⋊Dic281—22no—
39C4⋊Dic281—21no—
40C4⋊Dic281D411yescharacteristic
41C4⋊Dic281D412yes—
42#17985115—22no—
43#17985115—21no—
44C2×D4×C281D411yescharacteristic
45C22×C4×C281—21no—
46C2×C8×C281—21no—
47C2×C8×C281—21no—
48C4⋊C4×C281D411yescharacteristic
49C22⋊C4×C281—21no—
50C42×C281C2311yescharacteristic
51C22×D281—21no—
52C22×D281—41no—
53Dic562—41no—
54Dic562—41no—
55D1124—21no—
56D1124—21no—
57D1124—42no—
58D1124—41no—
59D1124—41no—
60D1124—41no—
61D1124—41no—
62C22⋊D281—44no—
63C2×Dic281—21no—
64C2×Dic281—22no—
65C2×Dic281—44no—
66C4×D281—41no—
67C4×D281—41no—
68#14555886—41no—
69C23×C281—21no—
70D4×C281—21no—
71D4×C281D812yescomplemented
72C2×C4×C281—21no—
73C2×C4×C281—41no—
74C2×C4×C281—41no—
75C2×C4×C281C2×D411yescharacteristic
76C2×C4×C281C2×D411yescharacteristic
77C2×C4×C281C2×D411yescharacteristic
78C8×C281—41no—
79C8×C281—41no—
80C22×C281—22no—
81C22×C281—41no—
82C22×C281—41no—
83C22×C281#12011yescharacteristic
84C2×D281—41no—
85C2×D281—41no—
86C2×D281—41no—
87C2×D281—81no—
88C2×D281—81no—
89C2×D281—81no—
90C4×C281—21no—
91C4×C281—41no—
92C4×C281C2×D811yescharacteristic
93C4×C281#13511yescharacteristic
94C4×C281AGL(1,ℤ/8)11yescharacteristic
95C4×C281AGL(1,ℤ/8)11yescharacteristic
96Dic281—41no—
97Dic281—42no—
98C2×C281—42no—
99C2×C281#44711yescharacteristic
100C2×C281#44911yescharacteristic
101C2×C281#45411yescharacteristic
102D281—81no—
103D281—161no—
104C281#162511yescharacteristic, complemented, Sylow
105#1625—2811nomaximal, Sylow
106#547—2811no—
107#486—2811no—
108#459—2811no—
109#459—2811no—
110#332—2811no—
111D4⋊C8—2811no—
112D4⋊C8D28111yescharacteristic, complemented
113C2×#41—5621no—
114C2×D8—5621no—
115C2×D8—5621no—
116C4⋊Q8—2811no—
117#127—2811no—
118#123—5622no—
119C22⋊Q8—5621no—
120#121—5621no—
121C4×D4—2811no—
122C4×D4C2×D28111yescharacteristic
123C2×C4⋊C4—5621no—
124C4⋊C8—2811no—
125C4⋊C8C2×D28111yescharacteristic
126#102—5621no—
127#102—5622no—
128#102—5621no—
129C4×C8C2×D28111yescharacteristic
130#41—11242no—
131#41—11242no—
132C2×Q8—5621no—
133C2×D4—2811no—
134C2×D4—5622no—
135C2×D4—5621no—
136C2×D4—5621no—
137C2×D4—5621no—
138C2×D4D112411yescharacteristic
139C22×C4—21no—
140C22×C4—5622no—
141C22×C4—5621no—
142D8—11242no—
143D8—11242no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—5621no—
147C4⋊C4—2811no—
148C4⋊C4—2812no—
149C4⋊C4—5622no—
150C4⋊C4—5621no—
151C4⋊C4D112411yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—5622no—
154C22⋊C4—5621no—
155C42C22×D28111yescharacteristic
156C23—21no—
157C23—5621no—
158C23—11241no—
159Q8—11241no—
160Q8—11241no—
161D4—21no—
162D4—5621no—
163D4—5621no—
164D4—11242no—
165D4—11244no—
166D4—11241no—
167D4—11241no—
168D4—11241no—
169D4—11241no—
170D4D224812yescomplemented
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—5621no—
175C2×C4—5622no—
176C2×C4—11244no—
177C2×C4—11241no—
178C2×C4—11241no—
179C2×C4D4×D28111yescharacteristic
180C2×C4D4×D28111yescharacteristic
181C2×C4C2×D112411yescharacteristic
182C8—41no—
183C8—41no—
184C8—11241no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—11241no—
189C22—11241no—
190C22—11241no—
191C22—22481no—
192C22—22481no—
193C22—22481no—
194C22#2258284911yescharacteristic
195C4—21no—
196C4—41no—
197C4—11241no—
198C4—11242no—
199C4C2×D224811yescharacteristic
200C4#2258290011yescharacteristic
201C4#2258290311yescharacteristic
202C4#2258290711yescharacteristic
203C2—42no—
204C2—44961no—
205C2—22481no—
206C2#3182359911yescharacteristic
207C2#3182360911yescharacteristic
208C2#3182363711yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
FittingD4⋊C8×C281C2
socleC22×C281#120
hypercenterD4⋊C8D281
hypocenterC281#1625
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #31824117C2semidirect
2. #31823810C2semidirect
3. #31823659C2semidirect
4. #31823658C2semidirect
5. #31823208C2semidirect
6. #31823192C2semidirect
7. D4⋊C8×C281C2semidirect
71. D4×C281D8semidirect
104. C281#1625semidirect
112. D4⋊C8D281semidirect
170. D4D2248semidirect

Maximal subgroups

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

subgroupindex
#318241172
#318238102
#318236592
#318236582
#318232082
#318231922
D4⋊C8×C2812
#1625281