Finite Group Databasebeta

← #49094471

Subgroups — #49094471

Order 35968.

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

normal subgroups only

This group has 228 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×Dic562C211yesmaximal, characteristic
2#31823814C211yesmaximal, characteristic, complemented
3#31823759C211yesmaximal, characteristic, complemented
4#31823753C211yesmaximal, characteristic
5#31823210C211yesmaximal, characteristic, complemented
6#31823195C211yesmaximal, characteristic, complemented
7D4⋊C8×C281C211yesmaximal, characteristic
8C22×Dic562—21no—
9#22582879C2211yescharacteristic
10#22582879C2211yescharacteristic
11#22582878—21no—
12#22582858—21no—
13#22582856—22no—
14C4×Dic562C2211yescharacteristic
15D4×Dic281—21no—
16#22582813—21no—
17#22582810—21no—
18C4⋊#14555886C2211yescharacteristic
19#22582804—21no—
20#22582804—22no—
21#22582800—21no—
22C4×D4×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24C4×C8×C281C2211yescharacteristic
25C2×Dic562—22no—
26C2×Dic562—21no—
27C2×Dic562—21no—
28C2×Dic562—42no—
29C2×Dic562—42no—
30C2×Dic562D411yescharacteristic
31C22×Dic281—22no—
32C2×#14555886—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281D412yes—
37C4⋊Dic281D411yescharacteristic
38#17985117—22no—
39#17985117—21no—
40C22⋊Dic281—22no—
41C4×Dic281—21no—
42C2×D4×C281D411yescharacteristic
43C22×C4×C281—21no—
44C2×C8×C281—21no—
45C2×C8×C281—21no—
46C4⋊C4×C281D411yescharacteristic
47C22⋊C4×C281—21no—
48C42×C281C2311yescharacteristic
49Dic562—21no—
50Dic562—44no—
51Dic562—41no—
52Dic562—41no—
53Dic562—42no—
54Dic562SD1612yes—
55C2×Dic281—21no—
56C2×Dic281—21no—
57C2×Dic281—22no—
58C2×Dic281—44no—
59C2×Dic281—41no—
60#14555886—41no—
61C23×C281—21no—
62D4×C281—21no—
63D4×C281Q1612yes—
64C2×C4×C281—21no—
65C2×C4×C281—41no—
66C2×C4×C281—41no—
67C2×C4×C281C2×D411yescharacteristic
68C2×C4×C281C2×D411yescharacteristic
69C2×C4×C281C2×D411yescharacteristic
70C8×C281—41no—
71C8×C281—41no—
72C22×C281—22no—
73C22×C281—41no—
74C22×C281—41no—
75C22×C281#12011yescharacteristic
76C4×C281—21no—
77C4×C281—41no—
78C4×C281C2×SD1611yescharacteristic
79C4×C281C2×Q1611yescharacteristic
80C4×C281AGL(1,ℤ/8)11yescharacteristic
81C4×C281#13711yescharacteristic
82Dic281—22no—
83Dic281—42no—
84Dic281—41no—
85Dic281—81no—
86C2×C281—42no—
87C2×C281#45011yescharacteristic
88C2×C281#45111yescharacteristic
89C2×C281#45411yescharacteristic
90C281#163711yescharacteristic, complemented, Sylow
91#1637—2811nomaximal, Sylow
92D4×Q8—2811no—
93#487—2811no—
94#477—2811no—
95#476—2811no—
96#332—2811no—
97Q8⋊C8—2811no—
98D4⋊C8D28111yescharacteristic
99C22×Q8—5621no—
100C4⋊Q8—2811no—
101C4⋊Q8—2811no—
102C4⋊Q8—5621no—
103C22⋊Q8—5622no—
104C22⋊Q8—5621no—
105C4×Q8—2811no—
106C4×D4—5621no—
107C4×D4C2×D28111yescharacteristic
108#107—5621no—
109#106—5621no—
110C4⋊C8—2811no—
111C4⋊C8C2×D28111yescharacteristic
112#103—5622no—
113#103—5621no—
114#102—5621no—
115C4×C8C2×D28111yescharacteristic
116C2×Q8—2811no—
117C2×Q8—5622no—
118C2×Q8—5621no—
119C2×Q8—5621no—
120C2×Q8—11242no—
121C2×Q8—11242no—
122C2×D4D112411yescharacteristic
123C22×C4—21no—
124C22×C4—5622no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—5621no—
128C4⋊C4—2812no—
129C4⋊C4—2811no—
130C4⋊C4—5622no—
131C4⋊C4—5621no—
132C4⋊C4—5621no—
133C4⋊C4—5621no—
134C4⋊C4—5621no—
135C4⋊C4D112411yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—5622no—
138C42—5621no—
139C42C22×D28111yescharacteristic
140C23—21no—
141Q8—2812no—
142Q8—5621no—
143Q8—11242no—
144Q8—11244no—
145Q8—11241no—
146Q8—11241no—
147D4—21no—
148D4Dic112412yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—5621no—
153C2×C4—5621no—
154C2×C4—5622no—
155C2×C4—11244no—
156C2×C4—11241no—
157C2×C4D4×D28111yescharacteristic
158C2×C4D4×D28111yescharacteristic
159C2×C4C2×D112411yescharacteristic
160C8—41no—
161C8—41no—
162C8—11241no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#2258284911yescharacteristic
167C4—21no—
168C4—41no—
169C4—5622no—
170C4—11241no—
171C4—11242no—
172C4—22481no—
173C4SD16×D28111yescharacteristic
174C4C2×Dic112411yescharacteristic
175C4#2258290311yescharacteristic
176C4#2258291211yescharacteristic
177C2—42no—
178C2#3182361511yescharacteristic
179C2#3182362111yescharacteristic
180C2#3182363711yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
FittingD4⋊C8×C281C2
socleC22×C281#120
prime radicalC2×D4×C281D4
hypercenterD4⋊C8D281
hypocenterC281#1637
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #31823814C2semidirect
3. #31823759C2semidirect
5. #31823210C2semidirect
6. #31823195C2semidirect
90. C281#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5622
#318238142
#318237592
#318237532
#318232102
#318231952
D4⋊C8×C2812
#1637281