Finite Group Databasebeta

← #49094430

Subgroups — #49094430

Order 35968.

256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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#31823835C211yesmaximal, characteristic, complemented
2#31823758C211yesmaximal, characteristic, complemented
3#31823753C211yesmaximal, characteristic, complemented
4#31823207C211yesmaximal, characteristic, complemented
5Q8⋊#14555886C211yesmaximal, characteristic, complemented
6D4⋊#14555886C211yesmaximal, characteristic, complemented
7#550×C281C211yesmaximal, characteristic
8C2×#17985126—22no—
9#22582879C2211yescharacteristic
10#22582812—21no—
11#22582810—21no—
12C4⋊#14555886C2211yescharacteristic
13C4⋊#14555886C2211yescharacteristic
14#22582803—21no—
15#22582800—21no—
16C4×#14555886C2211yescharacteristic
17C2×#41×C281—21no—
18#127×C281—21no—
19#127×C281C2211yescharacteristic
20#121×C281—22no—
21#121×C281—21no—
22C4×Q8×C281C2211yescharacteristic
23C4×D4×C281—21no—
24C4×D4×C281C2211yescharacteristic
25C2×Dic562—21no—
26#17985126—44no—
27C2×#14555886—21no—
28C2×#14555886—21no—
29C2×#14555886—21no—
30C4⋊Dic281—21no—
31C4⋊Dic281—21no—
32#41×C281—42no—
33#41×C281—42no—
34C2×Q8×C281D411yescharacteristic
35C2×D4×C281—22no—
36C2×D4×C281—22no—
37C2×D4×C281—21no—
38C2×D4×C281—21no—
39C2×D4×C281D411yescharacteristic
40C2×D4×C281D412yes—
41C22×C4×C281—22no—
42C22×C4×C281—21no—
43C4⋊C4×C281—21no—
44C4⋊C4×C281D411yescharacteristic
45C4⋊C4×C281D411yescharacteristic
46C22⋊C4×C281—22no—
47C22⋊C4×C281—21no—
48C42×C281—21no—
49C42×C281C2311yescharacteristic
50Dic562—42no—
51C2×Dic281—41no—
52#14555886—22no—
53#14555886—41no—
54#14555886—41no—
55C23×C281—21no—
56C23×C281—22no—
57Q8×C281—21no—
58Q8×C281SD1612yescomplemented
59D4×C281—21no—
60D4×C281—21no—
61D4×C281—42no—
62D4×C281—44no—
63D4×C281—41no—
64D4×C281—41no—
65D4×C281—41no—
66D4×C281—41no—
67D4×C281—82no—
68C2×C4×C281—21no—
69C2×C4×C281—21no—
70C2×C4×C281—21no—
71C2×C4×C281—44no—
72C2×C4×C281—41no—
73C2×C4×C281—41no—
74C2×C4×C281C2×D411yescharacteristic
75C2×C4×C281C2×D411yescharacteristic
76C2×C4×C281C2×D411yescharacteristic
77C22×C281—42no—
78C22×C281—41no—
79C22×C281—41no—
80C22×C281—42no—
81C22×C281—42no—
82C22×C281—41no—
83C22×C281#12011yescharacteristic
84C4×C281—22no—
85C4×C281—21no—
86C4×C281—41no—
87C4×C281—41no—
88C4×C281C2×SD1611yescharacteristic
89C4×C281#13511yescharacteristic
90C4×C281AGL(1,ℤ/8)11yescharacteristic
91C4×C281#13711yescharacteristic
92Dic281—81no—
93C2×C281—81no—
94C2×C281—82no—
95C2×C281#45011yescharacteristic
96C2×C281#45211yescharacteristic
97C2×C281#45311yescharacteristic
98C281#163111yescharacteristic, complemented, Sylow
99#1631—2811nomaximal, Sylow
100#550D28111yescharacteristic
101#492—2811no—
102#477—2811no—
103#476—2811no—
104#331—2811no—
105Q8⋊C8—2811no—
106D4⋊C8—2811no—
107C2×#41—21no—
108C2×SD16—5622no—
109C4⋊Q8—2811no—
110#127—21no—
111#127C2×D28111yescharacteristic
112#121—22no—
113#121—21no—
114C4×Q8C2×D28111yescharacteristic
115C4×D4—21no—
116C4×D4C2×D28111yescharacteristic
117#107—5621no—
118#106—5621no—
119C4⋊C8—2811no—
120C4⋊C8—2811no—
121#103—5621no—
122#102—5621no—
123C4×C8—2811no—
124#41—42no—
125#41—42no—
126C2×Q8—5621no—
127C2×Q8C22⋊D28111yescharacteristic
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4C22⋊D28111yescharacteristic
133C2×D4C22⋊D28112yes—
134C22×C4—22no—
135C22×C4—21no—
136SD16—11244no—
137C2×C8—5621no—
138C2×C8—5621no—
139C2×C8—5621no—
140C4⋊C4—21no—
141C4⋊C4—5621no—
142C4⋊C4—5621no—
143C4⋊C4C22⋊D28111yescharacteristic
144C4⋊C4C22⋊D28111yescharacteristic
145C22⋊C4—22no—
146C22⋊C4—21no—
147C42—21no—
148C42C22×D28111yescharacteristic
149C23—21no—
150C23—22no—
151Q8—21no—
152Q8—11242no—
153Q8#1798512612yescomplemented
154D4—21no—
155D4—21no—
156D4—42no—
157D4—44no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—82no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—44no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—11241no—
170C2×C4C2×C22⋊D28111yescharacteristic
171C2×C4C2×C22⋊D28111yescharacteristic
172C2×C4C2×C22⋊D28111yescharacteristic
173C8—5622no—
174C8—11241no—
175C8—11241no—
176C22—41no—
177C22—42no—
178C22—42no—
179C22—41no—
180C22—42no—
181C22—41no—
182C22#2258284811yescharacteristic
183C4—21no—
184C4—22no—
185C4—41no—
186C4—41no—
187C4—22481no—
188C4C2×#1798512611yescharacteristic
189C4#2258289911yescharacteristic
190C4#2258290511yescharacteristic
191C4#2258290911yescharacteristic
192C2—81no—
193C2—82no—
194C2#3182361411yescharacteristic
195C2#3182362511yescharacteristic
196C2#3182363111yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting, prime radical#550×C281C2
socleC22×C281#120
hypercenter#550D281
hypocenterC281#1631
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #31823835C2semidirect
2. #31823758C2semidirect
3. #31823753C2semidirect
4. #31823207C2semidirect
5. Q8⋊#14555886C2semidirect
6. D4⋊#14555886C2semidirect
58. Q8×C281SD16semidirect
98. C281#1631semidirect
153. Q8#17985126semidirect

Maximal subgroups

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

subgroupindex
#318238352
#318237582
#318237532
#318232072
Q8⋊#145558862
D4⋊#145558862
#550×C2812
#1631281