Finite Group Databasebeta

← #49094418

Subgroups — #49094418

Order 35968.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D1124C211yesmaximal, characteristic
2#31823837C211yesmaximal, characteristic, complemented
3#31823750C211yesmaximal, characteristic, complemented
4#31823206C211yesmaximal, characteristic, complemented
5D4⋊#14555886C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic, complemented
7#476×C281C211yesmaximal, characteristic, complemented
8C22×D1124—21no—
9C2×D4×D281—21no—
10C2×#17985125—22no—
11#22582876C2211yescharacteristic
12#22582854—21no—
13#22582853—21no—
14#22582849—22no—
15C4×D1124C2211yescharacteristic
16#22582810—21no—
17C4⋊#14555886C2211yescharacteristic, complemented
18#22582799—21no—
19C4×#14555886C2211yescharacteristic, complemented
20C4⋊Q8×C281C2211yescharacteristic, complemented
21C4×D4×C281C2211yescharacteristic
22#106×C281—21no—
23C4⋊C8×C281C2211yescharacteristic, complemented
24#102×C281—21no—
25C23×D281—22no—
26C2×D1124—22no—
27C2×D1124—21no—
28C2×D1124—21no—
29C2×D1124—42no—
30C2×D1124—42no—
31C2×D1124D411yescharacteristic
32C2×D1124D412yes—
33C2×C22⋊D281—22no—
34D4×D281—42no—
35D4×D281—42no—
36C2×C4×D281—21no—
37#17985125—44no—
38C2×#14555886—21no—
39C2×#14555886—21no—
40C4⋊Dic281D411yescharacteristic
41#17985115—22no—
42#17985115—21no—
43C2×Q8×C281—21no—
44C2×D4×C281D411yescharacteristic
45C22×C4×C281—21no—
46C2×C8×C281—21no—
47C4⋊C4×C281—21no—
48C4⋊C4×C281—21no—
49C4⋊C4×C281D411yescharacteristic
50C22⋊C4×C281—21no—
51C42×C281C2311yescharacteristic
52C22×D281—21no—
53C22×D281—22no—
54C22×D281—44no—
55C22×D281—44no—
56C22×D281—82no—
57D1124—21no—
58D1124—42no—
59D1124—44no—
60D1124—41no—
61D1124—41no—
62D1124—41no—
63D1124—41no—
64D1124SD1612yescomplemented
65C22⋊D281—44no—
66C2×Dic281—21no—
67C4×D281—41no—
68C4×D281—41no—
69#14555886—22no—
70#14555886—41no—
71C23×C281—21no—
72Q8×C281—42no—
73D4×C281—21no—
74D4×C281SD1612yescomplemented
75C2×C4×C281—21no—
76C2×C4×C281—41no—
77C2×C4×C281—41no—
78C2×C4×C281—41no—
79C2×C4×C281C2×D411yescharacteristic
80C2×C4×C281C2×D411yescharacteristic
81C2×C4×C281C2×D411yescharacteristic
82C8×C281—41no—
83C22×C281—22no—
84C22×C281—41no—
85C22×C281—41no—
86C22×C281#12011yescharacteristic
87C2×D281—22no—
88C2×D281—41no—
89C2×D281—41no—
90C2×D281—42no—
91C2×D281—42no—
92C2×D281—42no—
93C2×D281—88no—
94C4×C281—21no—
95C4×C281—41no—
96C4×C281—81no—
97C4×C281C2×SD1611yescharacteristic
98C4×C281C2×SD1611yescharacteristic
99C4×C281AGL(1,ℤ/8)11yescharacteristic
100C4×C281AGL(1,ℤ/8)11yescharacteristic
101Dic281—41no—
102C2×C281—42no—
103C2×C281#45011yescharacteristic
104C2×C281#45011yescharacteristic
105C2×C281#45311yescharacteristic
106D281—42no—
107D281—82no—
108C281#162911yescharacteristic, complemented, Sylow
109#1629—2811nomaximal, Sylow
110D42—2811no—
111#492—2811no—
112#476—2811no—
113#476D28111yescharacteristic, complemented
114#331—2811no—
115D4⋊C8—2811no—
116D4⋊C8—2811no—
117C22×D4—5621no—
118C22×D4—5621no—
119C2×SD16—5622no—
120C4⋊Q8C2×D28111yescharacteristic, complemented
121#127—2811no—
122#121—5621no—
123#121—5621no—
124#120—5622no—
125C4×D4—2811no—
126C4×D4C2×D28111yescharacteristic
127#106—21no—
128#106—5621no—
129C4⋊C8—2811no—
130C4⋊C8C2×D28111yescharacteristic, complemented
131#102—21no—
132#102—5621no—
133C4×C8—2811no—
134C24—5622no—
135C2×Q8—21no—
136C2×D4—2811no—
137C2×D4—2812no—
138C2×D4—5622no—
139C2×D4—5622no—
140C2×D4—5621no—
141C2×D4—5621no—
142C2×D4—11242no—
143C2×D4—11242no—
144C2×D4—11242no—
145C2×D4—11242no—
146C2×D4C22⋊D28111yescharacteristic
147C22×C4—21no—
148C22×C4—5621no—
149SD16—11244no—
150C2×C8—21no—
151C2×C8—5621no—
152C2×C8—5621no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—2811no—
156C4⋊C4C22⋊D28111yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—5622no—
159C22⋊C4—5621no—
160C42C22×D28111yescharacteristic
161C23—21no—
162C23—5621no—
163C23—5622no—
164C23—11244no—
165C23—11244no—
166C23—22482no—
167Q8—42no—
168D4—21no—
169D4—2812no—
170D4—5621no—
171D4—11242no—
172D4—11244no—
173D4—11244no—
174D4—11241no—
175D4—11241no—
176D4—11241no—
177D4—11241no—
178D4#1798512512yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—5621no—
184C2×C4—11241no—
185C2×C4—11241no—
186C2×C4D4×D28111yescharacteristic
187C2×C4D4×D28111yescharacteristic
188C2×C4C2×C22⋊D28111yescharacteristic
189C8—41no—
190C8—5622no—
191C8—11241no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—5622no—
196C22—11241no—
197C22—11241no—
198C22—11242no—
199C22—11242no—
200C22—11242no—
201C22—22488no—
202C22#2258284711yescharacteristic
203C4—21no—
204C4—41no—
205C4—81no—
206C4—11241no—
207C4SD16×D28111yescharacteristic
208C4C2×#1798512511yescharacteristic
209C4#2258290411yescharacteristic
210C4#2258290611yescharacteristic
211C2—42no—
212C2—11242no—
213C2—22482no—
214C2#3182361211yescharacteristic
215C2#3182361311yescharacteristic
216C2#3182362911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#476×C281C2
socleC22×C281#120
prime radicalD4×D1124C2
hypercenter#476D281
hypocenterC281#1629
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #31823837C2semidirect
3. #31823750C2semidirect
4. #31823206C2semidirect
5. D4⋊#14555886C2semidirect
6. #31823190C2semidirect
7. #476×C281C2semidirect
17. C4⋊#14555886C22semidirect
19. C4×#14555886C22semidirect
20. C4⋊Q8×C281C22semidirect
23. C4⋊C8×C281C22semidirect
64. D1124SD16semidirect
74. D4×C281SD16semidirect
108. C281#1629semidirect
113. #476D281semidirect
120. C4⋊Q8C2×D281semidirect
130. C4⋊C8C2×D281semidirect
178. D4#17985125semidirect

Maximal subgroups

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

subgroupindex
D4×D11242
#318238372
#318237502
#318232062
D4⋊#145558862
#318231902
#476×C2812
#1629281