Finite Group Databasebeta

← #49094555

Subgroups — #49094555

Order 35968.

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

normal subgroups only

This group has 234 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#31823868C211yesmaximal, characteristic, complemented
3#31823743C211yesmaximal, characteristic
4#31823674C211yesmaximal, characteristic, complemented
5#31823210C211yesmaximal, characteristic, complemented
6#31823195C211yesmaximal, characteristic, complemented
7D4⋊C8×C281C211yesmaximal, characteristic
8C22×Dic562—21no—
9C2×Dic1124—21no—
10#22582879C2211yescharacteristic
11#22582879C2211yescharacteristic
12#22582878—21no—
13#22582858—21no—
14#22582856—22no—
15C4×Dic562C2211yescharacteristic
16D4×Dic281—21no—
17#22582813—22no—
18#22582812—21no—
19C4⋊#14555886C2211yescharacteristic
20#22582804—21no—
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—
32Dic1124—42no—
33C2×#14555886—21no—
34C4⋊Dic281—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281—21no—
37C4⋊Dic281D411yescharacteristic
38C4⋊Dic281D412yes—
39#17985117—22no—
40#17985117—21no—
41C22⋊Dic281—22no—
42C4×Dic281—21no—
43C2×D4×C281D411yescharacteristic
44C22×C4×C281—21no—
45C2×C8×C281—21no—
46C2×C8×C281—21no—
47C4⋊C4×C281D411yescharacteristic
48C22⋊C4×C281—21no—
49C42×C281C2311yescharacteristic
50Dic562—21no—
51Dic562—44no—
52Dic562—41no—
53Dic562—41no—
54Dic562—41no—
55Dic562—41no—
56Dic562D812yes—
57C2×Dic281—21no—
58C2×Dic281—21no—
59C2×Dic281—22no—
60C2×Dic281—44no—
61C2×Dic281—41no—
62#14555886—41no—
63C23×C281—21no—
64D4×C281—21no—
65D4×C281Q1612yescomplemented
66C2×C4×C281—21no—
67C2×C4×C281—41no—
68C2×C4×C281—41no—
69C2×C4×C281C2×D411yescharacteristic
70C2×C4×C281C2×D411yescharacteristic
71C2×C4×C281C2×D411yescharacteristic
72C8×C281—22no—
73C8×C281—41no—
74C22×C281—22no—
75C22×C281—41no—
76C22×C281—41no—
77C22×C281#12011yescharacteristic
78C4×C281—21no—
79C4×C281—41no—
80C4×C281C2×D811yescharacteristic
81C4×C281C2×Q1611yescharacteristic
82C4×C281AGL(1,ℤ/8)11yescharacteristic
83C4×C281#13711yescharacteristic
84Dic281—22no—
85Dic281—42no—
86Dic281—41no—
87Dic281—81no—
88C2×C281—42no—
89C2×C281#44711yescharacteristic
90C2×C281#45111yescharacteristic
91C2×C281#45611yescharacteristic
92C281#164911yescharacteristic, complemented, Sylow
93#1649—2811nomaximal, Sylow
94D4×Q8—2811no—
95#500—2811no—
96#474—2811no—
97#462—2811no—
98#332—2811no—
99Q8⋊C8—2811no—
100D4⋊C8D28111yescharacteristic
101C22×Q8—5621no—
102C2×Q16—5621no—
103C4⋊Q8—2811no—
104C4⋊Q8—2811no—
105C4⋊Q8—5621no—
106C22⋊Q8—5622no—
107C22⋊Q8—5621no—
108C4×Q8—2811no—
109C4×D4—5621no—
110C4×D4C2×D28111yescharacteristic
111#107—5622no—
112#107—5621no—
113C4⋊C8—2811no—
114C4⋊C8C2×D28111yescharacteristic
115#103—5621no—
116#102—5621no—
117C4×C8C2×D28111yescharacteristic
118C2×Q8—2811no—
119C2×Q8—5622no—
120C2×Q8—5621no—
121C2×Q8—5621no—
122C2×Q8—11242no—
123C2×Q8—11242no—
124C2×D4D112411yescharacteristic
125C22×C4—21no—
126C22×C4—5622no—
127Q16—11242no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—5621no—
131C4⋊C4—2811no—
132C4⋊C4—2812no—
133C4⋊C4—5622no—
134C4⋊C4—5621no—
135C4⋊C4—5621no—
136C4⋊C4—5621no—
137C4⋊C4—5621no—
138C4⋊C4D112411yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—5622no—
141C42—5621no—
142C42C22×D28111yescharacteristic
143C23—21no—
144Q8—2812no—
145Q8—5621no—
146Q8—11244no—
147Q8—11241no—
148Q8—11241no—
149Q8—11241no—
150Q8—11241no—
151D4—21no—
152D4Dic112412yescomplemented
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—5621no—
157C2×C4—5621no—
158C2×C4—5622no—
159C2×C4—11244no—
160C2×C4—11241no—
161C2×C4D4×D28111yescharacteristic
162C2×C4D4×D28111yescharacteristic
163C2×C4C2×D112411yescharacteristic
164C8—22no—
165C8—41no—
166C8—11241no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#2258284911yescharacteristic
171C4—21no—
172C4—41no—
173C4—5622no—
174C4—11241no—
175C4—11242no—
176C4—22481no—
177C4D8×D28111yescharacteristic
178C4C2×Dic112411yescharacteristic
179C4#2258290611yescharacteristic
180C4#2258291211yescharacteristic
181C2—42no—
182C2#3182359811yescharacteristic
183C2#3182362111yescharacteristic
184C2#3182364711yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
FittingD4⋊C8×C281C2
socleC22×C281#120
prime radicalC2×D4×C281D4
hypercenterD4⋊C8D281
hypocenterC281#1649
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. #31823868C2semidirect
4. #31823674C2semidirect
5. #31823210C2semidirect
6. #31823195C2semidirect
65. D4×C281Q16semidirect
92. C281#1649semidirect
152. D4Dic1124semidirect

Maximal subgroups

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

subgroupindex
D4×Dic5622
#318238682
#318237432
#318236742
#318232102
#318231952
D4⋊C8×C2812
#1649281