Finite Group Databasebeta

← #49094403

Subgroups — #49094403

Order 35968.

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

normal subgroups only

This group has 250 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#31824128C211yesmaximal, characteristic, complemented
2#31823660C211yesmaximal, characteristic, complemented
3#31823655C211yesmaximal, characteristic
4#31823209C211yesmaximal, characteristic, complemented
5#31823195C211yesmaximal, characteristic, complemented
6#31823192C211yesmaximal, characteristic, complemented
7#486×C281C211yesmaximal, characteristic, complemented
8C2×Q8×D281—21no—
9C2×#17985126—21no—
10C2×#17985123—21no—
11#22582878—21no—
12#22582857—22no—
13#22582855—21no—
14C4×Dic562C2211yescharacteristic
15C4×D1124C2211yescharacteristic
16#22582841—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582800—21no—
20#22582800—21no—
21C4⋊Q8×C281C2211yescharacteristic
22#127×C281C2211yescharacteristic
23#102×C281—22no—
24C4×C8×C281C2211yescharacteristic
25C2×Dic562—22no—
26C2×Dic562D411yescharacteristic
27Q8×D281—42no—
28Q8×D281—42no—
29C2×D1124D411yescharacteristic
30C2×C4×D281—22no—
31C2×C4×D281—21no—
32#17985126—42no—
33#17985123—42no—
34C2×#14555886—21no—
35C2×#14555886—21no—
36C4⋊Dic281D411yescharacteristic
37C4⋊Dic281D411yescharacteristic
38#17985117—22no—
39#17985117—21no—
40#17985115—22no—
41#17985115—21no—
42C4×Dic281—21no—
43C2×Q8×C281—21no—
44C2×D4×C281—21no—
45C2×D4×C281—21no—
46C2×D4×C281—21no—
47C2×C8×C281—21no—
48C4⋊C4×C281—21no—
49C4⋊C4×C281D412yes—
50C42×C281C2311yescharacteristic
51C22×D281—21no—
52Dic562—21no—
53Dic562—44no—
54Dic562D812yescomplemented
55D1124—21no—
56D1124SD1612yescomplemented
57C2×Dic281—21no—
58C2×Dic281—21no—
59C2×Dic281—21no—
60C4×D281—44no—
61C4×D281—41no—
62C4×D281—41no—
63#14555886—41no—
64#14555886—41no—
65C23×C281—41no—
66Q8×C281—41no—
67Q8×C281—41no—
68D4×C281—42no—
69D4×C281—41no—
70D4×C281—41no—
71D4×C281—41no—
72D4×C281—41no—
73C2×C4×C281—22no—
74C2×C4×C281C2×D411yescharacteristic
75C2×C4×C281C2×D411yescharacteristic
76C2×C4×C281C2×D411yescharacteristic
77C8×C281—41no—
78C22×C281—81no—
79C22×C281—81no—
80C22×C281—81no—
81C22×C281#12011yescharacteristic
82C2×D281—22no—
83C2×D281—41no—
84C2×D281—41no—
85C4×C281—21no—
86C4×C281—42no—
87C4×C281C2×D811yescharacteristic
88C4×C281C2×SD1611yescharacteristic
89C4×C281AGL(1,ℤ/8)11yescharacteristic
90C4×C281#13711yescharacteristic
91Dic281—22no—
92Dic281—41no—
93Dic281—41no—
94C2×C281—161no—
95C2×C281#44711yescharacteristic
96C2×C281#44811yescharacteristic
97C2×C281#45411yescharacteristic
98D281—42no—
99C281#162711yescharacteristic, complemented, Sylow
100#1627—2811nomaximal, Sylow
101D4×Q8—2811no—
102#486D28111yescharacteristic, complemented
103#460—2811no—
104#459—2811no—
105#332—2811no—
106Q8⋊C8—2811no—
107D4⋊C8—2811no—
108C22×Q8—5621no—
109C2×SD16—5621no—
110C2×D8—5621no—
111C4⋊Q8—5621no—
112C4⋊Q8C2×D28111yescharacteristic
113#127C2×D28111yescharacteristic
114C22⋊Q8—5621no—
115C22⋊Q8—5622no—
116C4×Q8—2811no—
117C4×D4—2811no—
118C4×D4—5621no—
119C4⋊C8—2811no—
120C4⋊C8—2811no—
121#102—22no—
122#102—5621no—
123#102—5621no—
124C4×C8C2×D28111yescharacteristic
125C2×Q8—21no—
126C2×Q8—2811no—
127C2×Q8—5622no—
128C2×Q8—11242no—
129C2×Q8—11242no—
130C2×D4—21no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—2811no—
134C22×C4—5622no—
135C22×C4—5621no—
136SD16—11242no—
137D8—11242no—
138C2×C8—21no—
139C2×C8—5621no—
140C2×C8—5621no—
141C4⋊C4—21no—
142C4⋊C4—2811no—
143C4⋊C4—2811no—
144C4⋊C4—5622no—
145C4⋊C4—5621no—
146C4⋊C4C22⋊D28112yes—
147C22⋊C4—5622no—
148C22⋊C4—5621no—
149C42—5621no—
150C42C22×D28111yescharacteristic
151C23—41no—
152C23—5621no—
153Q8—41no—
154Q8—41no—
155Q8—2812no—
156Q8—5621no—
157Q8—11244no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—2812no—
164D4—5621no—
165C2×C4—22no—
166C2×C4—5621no—
167C2×C4—5621no—
168C2×C4—5621no—
169C2×C4—11244no—
170C2×C4—11241no—
171C2×C4—11241no—
172C2×C4D4×D28111yescharacteristic
173C2×C4D4×D28111yescharacteristic
174C2×C4C2×C22⋊D28111yescharacteristic
175C8—41no—
176C8—11241no—
177C8—11241no—
178C22—81no—
179C22—81no—
180C22—81no—
181C22—5622no—
182C22—11241no—
183C22—11241no—
184C22#2258284711yescharacteristic
185C4—21no—
186C4—42no—
187C4—5622no—
188C4—11241no—
189C4—11241no—
190C4D8×D28111yescharacteristic
191C4SD16×D28111yescharacteristic
192C4#2258290311yescharacteristic
193C4#2258290811yescharacteristic
194C2—161no—
195C2—11242no—
196C2#3182359511yescharacteristic
197C2#3182360011yescharacteristic
198C2#3182363511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#486×C281C2
socleC22×C281#120
prime radical#31823655C2
hypercenter#486D281
hypocenterC281#1627
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #31824128C2semidirect
2. #31823660C2semidirect
4. #31823209C2semidirect
5. #31823195C2semidirect
6. #31823192C2semidirect
7. #486×C281C2semidirect
54. Dic562D8semidirect
56. D1124SD16semidirect
99. C281#1627semidirect
102. #486D281semidirect

Maximal subgroups

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

subgroupindex
#318241282
#318236602
#318236552
#318232092
#318231952
#318231922
#486×C2812
#1627281