Finite Group Databasebeta

← #49094563

Subgroups — #49094563

Order 35968.

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

normal subgroups only

This group has 234 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
2#31823745C211yesmaximal, characteristic, complemented
3#31823665C211yesmaximal, characteristic
4#31823209C211yesmaximal, characteristic, complemented
5#31823195C211yesmaximal, characteristic, complemented
6#31823192C211yesmaximal, characteristic
7#498×C281C211yesmaximal, characteristic, complemented
8C2×Q8×D281—21no—
9C2×#17985125—21no—
10#22582878—21no—
11#22582857—22no—
12#22582855—21no—
13C4×Dic562C2211yescharacteristic
14C4×D1124C2211yescharacteristic
15#22582841—21no—
16#22582810—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582803—21no—
20#22582802—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23#106×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#17985125—42no—
33C2×#14555886—21no—
34C2×#14555886—21no—
35C4⋊Dic281D411yescharacteristic
36C4⋊Dic281D411yescharacteristic
37#17985117—22no—
38#17985117—21no—
39#17985115—22no—
40#17985115—21no—
41C4×Dic281—21no—
42C2×Q8×C281—21no—
43C2×Q8×C281—21no—
44C2×C8×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281—21no—
48C4⋊C4×C281D412yes—
49C42×C281C2311yescharacteristic
50C22×D281—21no—
51Dic562—21no—
52Dic562—44no—
53Dic562SD1612yescomplemented
54D1124—21no—
55D1124SD1612yes—
56C2×Dic281—21no—
57C2×Dic281—21no—
58C2×Dic281—21no—
59C4×D281—44no—
60C4×D281—41no—
61C4×D281—41no—
62#14555886—41no—
63#14555886—41no—
64Q8×C281—41no—
65Q8×C281—41no—
66Q8×C281—41no—
67Q8×C281—41no—
68C2×C4×C281—22no—
69C2×C4×C281—41no—
70C2×C4×C281C2×D411yescharacteristic
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C8×C281—22no—
74C22×C281#12011yescharacteristic
75C2×D281—22no—
76C2×D281—41no—
77C2×D281—41no—
78C4×C281—21no—
79C4×C281—42no—
80C4×C281—81no—
81C4×C281C2×SD1611yescharacteristic
82C4×C281C2×SD1611yescharacteristic
83C4×C281AGL(1,ℤ/8)11yescharacteristic
84C4×C281#13711yescharacteristic
85Dic281—22no—
86Dic281—41no—
87Dic281—41no—
88C2×C281#44811yescharacteristic
89C2×C281#45011yescharacteristic
90C2×C281#45611yescharacteristic
91D281—42no—
92C281#165111yescharacteristic, complemented, Sylow
93#1651—2811nomaximal, Sylow
94D4×Q8—2811no—
95#498D28111yescharacteristic, complemented
96#475—2811no—
97#461—2811no—
98#332—2811no—
99Q8⋊C8—2811no—
100D4⋊C8—2811no—
101C22×Q8—5621no—
102C2×SD16—5621no—
103C4⋊Q8—5621no—
104C4⋊Q8C2×D28111yescharacteristic
105C4⋊Q8C2×D28111yescharacteristic
106C22⋊Q8—5621no—
107C22⋊Q8—5622no—
108C4×Q8—2811no—
109C4×D4—2811no—
110C4×D4—5621no—
111#106—22no—
112#106—5621no—
113C4⋊C8—2811no—
114C4⋊C8—2811no—
115#103—5621no—
116#103—5621no—
117C4×C8C2×D28111yescharacteristic
118C2×Q8—21no—
119C2×Q8—21no—
120C2×Q8—2811no—
121C2×Q8—5622no—
122C2×Q8—11242no—
123C2×Q8—11242no—
124C2×D4—2811no—
125C22×C4—5622no—
126C22×C4—5621no—
127SD16—11242no—
128C2×C8—21no—
129C2×C8—5621no—
130C2×C8—5621no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—2811no—
135C4⋊C4—2811no—
136C4⋊C4—5622no—
137C4⋊C4—5621no—
138C4⋊C4C22⋊D28112yes—
139C22⋊C4—5622no—
140C22⋊C4—5621no—
141C42—5621no—
142C42C22×D28111yescharacteristic
143C23—5621no—
144Q8—41no—
145Q8—41no—
146Q8—41no—
147Q8—41no—
148Q8—2812no—
149Q8—5621no—
150Q8—11244no—
151D4—2812no—
152D4—5621no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—5621no—
156C2×C4—5621no—
157C2×C4—5621no—
158C2×C4—11244no—
159C2×C4—11241no—
160C2×C4—11241no—
161C2×C4D4×D28111yescharacteristic
162C2×C4D4×D28111yescharacteristic
163C2×C4C2×C22⋊D28111yescharacteristic
164C8—22no—
165C8—11241no—
166C8—11241no—
167C22—5622no—
168C22—11241no—
169C22—11241no—
170C22#2258284711yescharacteristic
171C4—21no—
172C4—42no—
173C4—81no—
174C4—5622no—
175C4—11241no—
176C4—11241no—
177C4SD16×D28111yescharacteristic
178C4SD16×D28111yescharacteristic
179C4#2258290611yescharacteristic
180C4#2258290811yescharacteristic
181C2—11242no—
182C2#3182360011yescharacteristic
183C2#3182361211yescharacteristic
184C2#3182364511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#498×C281C2
socleC22×C281#120
prime radicalC2×D1124D4
hypercenter#498D281
hypocenterC281#1651
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
2. #31823745C2semidirect
4. #31823209C2semidirect
5. #31823195C2semidirect
7. #498×C281C2semidirect
53. Dic562SD16semidirect
92. C281#1651semidirect
95. #498D281semidirect

Maximal subgroups

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

subgroupindex
#318241282
#318237452
#318236652
#318232092
#318231952
#318231922
#498×C2812
#1651281