Finite Group Databasebeta

← #49094431

Subgroups — #49094431

Order 35968.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 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#31824133C211yesmaximal, characteristic
2#31823835C211yesmaximal, characteristic, complemented
3#31823759C211yesmaximal, characteristic, complemented
4#31823754C211yesmaximal, characteristic, complemented
5#31823193C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic, complemented
7#331×C281C211yesmaximal, characteristic, complemented
8C2×#17985137—21no—
9C2×#17985126—22no—
10#22582879C2211yescharacteristic
11#22582875—21no—
12#22582851—22no—
13#22582850—21no—
14C4×Dic562C2211yescharacteristic
15C4×D1124C2211yescharacteristic
16D4×Dic281—21no—
17#22582813—21no—
18#22582811—21no—
19#22582804—21no—
20#22582801—21no—
21C4×#14555886C2211yescharacteristic
22#127×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24C4⋊C8×C281C2211yescharacteristic
25#17985137—42no—
26#17985137—42no—
27C2×Dic562—21no—
28C2×Dic562D411yescharacteristic
29C2×D1124D411yescharacteristic
30C2×C22⋊D281—22no—
31C2×C22⋊D281—22no—
32C22×Dic281—22no—
33C2×C4×D281—21no—
34#17985126—44no—
35C2×#14555886—21no—
36C4⋊Dic281—21no—
37C4⋊Dic281—21no—
38C4⋊Dic281D411yescharacteristic
39C4⋊Dic281D411yescharacteristic
40#17985117—21no—
41C22⋊Dic281—22no—
42#17985115—21no—
43C4×Dic281—21no—
44C2×D4×C281—21no—
45C2×D4×C281—21no—
46C2×D4×C281D412yes—
47C2×C8×C281—21no—
48C2×C8×C281—21no—
49C42×C281C2311yescharacteristic
50C22×D281—21no—
51Dic562—21no—
52Dic562—42no—
53Dic562SD1612yescomplemented
54D1124—21no—
55D1124—21no—
56C22⋊D281—44no—
57C22⋊D281—82no—
58C2×Dic281—21no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—44no—
62C2×Dic281—41no—
63C4×D281—41no—
64C4×D281—41no—
65#14555886—22no—
66C23×C281—22no—
67D4×C281—42no—
68D4×C281—41no—
69D4×C281—41no—
70D4×C281—41no—
71D4×C281—41no—
72C2×C4×C281C2×D411yescharacteristic
73C2×C4×C281C2×D411yescharacteristic
74C2×C4×C281C2×D411yescharacteristic
75C8×C281—41no—
76C8×C281—41no—
77C22×C281—42no—
78C22×C281—42no—
79C22×C281—42no—
80C22×C281#12011yescharacteristic
81C2×D281—41no—
82C2×D281—41no—
83C2×D281—41no—
84C4×C281—21no—
85C4×C281C2×SD1611yescharacteristic
86C4×C281#13511yescharacteristic
87C4×C281AGL(1,ℤ/8)11yescharacteristic
88C4×C281#13711yescharacteristic
89Dic281—22no—
90Dic281—41no—
91Dic281—41no—
92Dic281—81no—
93C2×C281—82no—
94C2×C281#45011yescharacteristic
95C2×C281#45211yescharacteristic
96C2×C281#45311yescharacteristic
97D281—81no—
98C281#163111yescharacteristic, complemented, Sylow
99#1631—2811nomaximal, Sylow
100#550—2811no—
101#492—2811no—
102#477—2811no—
103#476—2811no—
104#331D28111yescharacteristic, complemented
105Q8⋊C8—2811no—
106D4⋊C8—2811no—
107C2×#41—5621no—
108C2×SD16—5622no—
109C4⋊Q8—2811no—
110#127—5621no—
111#127C2×D28111yescharacteristic
112#121—5621no—
113#121—5622no—
114C4×Q8—2811no—
115C4×D4—2811no—
116C4×D4—5621no—
117#107—5621no—
118#106—5621no—
119C4⋊C8C2×D28111yescharacteristic
120C4⋊C8C2×D28111yescharacteristic
121#103—5621no—
122#102—5621no—
123C4×C8—2811no—
124#41—11242no—
125#41—11242no—
126C2×Q8—2811no—
127C2×Q8—5621no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—2811no—
131C2×D4—5622no—
132C2×D4—5622no—
133C2×D4D112412yes—
134C22×C4—5622no—
135C22×C4—5621no—
136SD16—11244no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—5621no—
140C4⋊C4—2811no—
141C4⋊C4—2811no—
142C4⋊C4—5621no—
143C4⋊C4—5621no—
144C4⋊C4—5621no—
145C22⋊C4—5622no—
146C22⋊C4—5621no—
147C42—5621no—
148C42C22×D28111yescharacteristic
149C23—22no—
150C23—5621no—
151Q8—2812no—
152Q8—5621no—
153Q8—11242no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—5621no—
160D4—5621no—
161D4—11244no—
162D4—22482no—
163C2×C4—5621no—
164C2×C4—5621no—
165C2×C4—5621no—
166C2×C4—11244no—
167C2×C4—11241no—
168C2×C4—11241no—
169C2×C4—11241no—
170C2×C4D4×D28111yescharacteristic
171C2×C4D4×D28111yescharacteristic
172C2×C4C2×D112411yescharacteristic
173C8—41no—
174C8—41no—
175C8—5622no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—11241no—
180C22—11241no—
181C22—11241no—
182C22#2258284911yescharacteristic
183C4—21no—
184C4—5622no—
185C4—11241no—
186C4—11241no—
187C4—22481no—
188C4SD16×D28111yescharacteristic
189C4#2258289811yescharacteristic
190C4#2258290311yescharacteristic
191C4#2258290811yescharacteristic
192C2—82no—
193C2—22481no—
194C2#3182361511yescharacteristic
195C2#3182362611yescharacteristic
196C2#3182363311yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#331×C281C2
socleC22×C281#120
prime radical#31824133C2
hypercenter#331D281
hypocenterC281#1631
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #31823835C2semidirect
3. #31823759C2semidirect
4. #31823754C2semidirect
5. #31823193C2semidirect
6. #31823190C2semidirect
7. #331×C281C2semidirect
53. Dic562SD16semidirect
98. C281#1631semidirect
104. #331D281semidirect

Maximal subgroups

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

subgroupindex
#318241332
#318238352
#318237592
#318237542
#318231932
#318231902
#331×C2812
#1631281