Finite Group Databasebeta

← #49094452

Subgroups — #49094452

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#31824117C211yesmaximal, characteristic
2#31823813C211yesmaximal, characteristic, complemented
3#31823750C211yesmaximal, characteristic, complemented
4#31823210C211yesmaximal, characteristic, complemented
5D4⋊#14555886C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic, complemented
7#476×C281C211yesmaximal, characteristic, complemented
8C2×#17985137—21no—
9#22582879C2211yescharacteristic
10#22582863—22no—
11#22582859—21no—
12#22582853—21no—
13C4×D1124C2211yescharacteristic
14C2×C4⋊Dic281—21no—
15#22582810—21no—
16C4⋊#14555886C2211yescharacteristic
17#22582803—22no—
18#22582799—21no—
19C4×#14555886C2211yescharacteristic
20C4⋊Q8×C281C2211yescharacteristic
21C4×D4×C281C2211yescharacteristic
22#106×C281—21no—
23C4⋊C8×C281C2211yescharacteristic
24#102×C281—21no—
25#17985137—42no—
26#17985137—42no—
27C2×Dic562—21no—
28C2×D1124D411yescharacteristic
29C2×C22⋊D281—22no—
30C22×Dic281—22no—
31C2×C4×D281—21no—
32C2×#14555886—21no—
33C2×#14555886—21no—
34C4⋊Dic281—22no—
35C4⋊Dic281—21no—
36C4⋊Dic281D412yes—
37C4⋊Dic281D411yescharacteristic
38#17985115—22no—
39#17985115—21no—
40C2×Q8×C281—21no—
41C2×D4×C281D411yescharacteristic
42C22×C4×C281—21no—
43C2×C8×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281D411yescharacteristic
47C22⋊C4×C281—21no—
48C42×C281C2311yescharacteristic
49C22×D281—21no—
50Dic562—41no—
51Dic562—41no—
52D1124—21no—
53D1124—21no—
54C22⋊D281—44no—
55C2×Dic281—21no—
56C2×Dic281—22no—
57C2×Dic281—44no—
58C4×D281—41no—
59C4×D281—41no—
60#14555886—41no—
61#14555886—41no—
62C23×C281—21no—
63Q8×C281—42no—
64D4×C281—21no—
65D4×C281SD1612yes—
66C2×C4×C281—21no—
67C2×C4×C281—41no—
68C2×C4×C281—41no—
69C2×C4×C281—41no—
70C2×C4×C281C2×D411yescharacteristic
71C2×C4×C281C2×D411yescharacteristic
72C2×C4×C281C2×D411yescharacteristic
73C8×C281—41no—
74C22×C281—22no—
75C22×C281—41no—
76C22×C281—41no—
77C22×C281#12011yescharacteristic
78C2×D281—41no—
79C2×D281—41no—
80C2×D281—41no—
81C4×C281—21no—
82C4×C281—41no—
83C4×C281—81no—
84C4×C281C2×SD1611yescharacteristic
85C4×C281#13511yescharacteristic
86C4×C281AGL(1,ℤ/8)11yescharacteristic
87C4×C281#13711yescharacteristic
88Dic281—41no—
89Dic281—42no—
90C2×C281—42no—
91C2×C281#45011yescharacteristic
92C2×C281#45211yescharacteristic
93C2×C281#45411yescharacteristic
94D281—81no—
95C281#163511yescharacteristic, complemented, Sylow
96#1635—2811nomaximal, Sylow
97#547—2811no—
98#487—2811no—
99#476—2811no—
100#476D28111yescharacteristic, complemented
101#332—2811no—
102D4⋊C8—2811no—
103D4⋊C8—2811no—
104C2×#41—5621no—
105C4⋊Q8—2811no—
106C4⋊Q8C2×D28111yescharacteristic
107#123—5622no—
108C22⋊Q8—5621no—
109#121—5621no—
110C4×D4—2811no—
111C4×D4C2×D28111yescharacteristic
112C2×C4⋊C4—5621no—
113#106—21no—
114#106—5621no—
115C4⋊C8—2811no—
116C4⋊C8C2×D28111yescharacteristic
117#103—5622no—
118#102—21no—
119#102—5621no—
120C4×C8—2811no—
121#41—11242no—
122#41—11242no—
123C2×Q8—21no—
124C2×Q8—5621no—
125C2×D4—2811no—
126C2×D4—5622no—
127C2×D4C22⋊D28111yescharacteristic
128C22×C4—21no—
129C22×C4—5622no—
130C22×C4—5621no—
131C2×C8—21no—
132C2×C8—5621no—
133C2×C8—5621no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—2812no—
137C4⋊C4—2811no—
138C4⋊C4—5622no—
139C4⋊C4—5621no—
140C4⋊C4C22⋊D28111yescharacteristic
141C22⋊C4—21no—
142C22⋊C4—5622no—
143C22⋊C4—5621no—
144C42C22×D28111yescharacteristic
145C23—21no—
146C23—5621no—
147Q8—42no—
148Q8—11241no—
149Q8—11241no—
150D4—21no—
151D4—5621no—
152D4—5621no—
153D4—11244no—
154D4#1798512512yes—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—5621no—
160C2×C4—5622no—
161C2×C4—11244no—
162C2×C4—11241no—
163C2×C4—11241no—
164C2×C4D4×D28111yescharacteristic
165C2×C4D4×D28111yescharacteristic
166C2×C4C2×C22⋊D28111yescharacteristic
167C8—41no—
168C8—11241no—
169C8—11241no—
170C22—22no—
171C22—41no—
172C22—41no—
173C22—11241no—
174C22—11241no—
175C22—11241no—
176C22#2258284711yescharacteristic
177C4—21no—
178C4—41no—
179C4—81no—
180C4—11241no—
181C4—11242no—
182C4C2×#1798512511yescharacteristic
183C4#2258290011yescharacteristic
184C4#2258290411yescharacteristic
185C4#2258290811yescharacteristic
186C2—42no—
187C2—22481no—
188C2#3182361311yescharacteristic
189C2#3182362211yescharacteristic
190C2#3182363411yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#476×C281C2
socleC22×C281#120
prime radical#31824117C2
hypercenter#476D281
hypocenterC281#1635
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #31823813C2semidirect
3. #31823750C2semidirect
4. #31823210C2semidirect
5. D4⋊#14555886C2semidirect
6. #31823190C2semidirect
7. #476×C281C2semidirect
95. C281#1635semidirect
100. #476D281semidirect

Maximal subgroups

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

subgroupindex
#318241172
#318238132
#318237502
#318232102
D4⋊#145558862
#318231902
#476×C2812
#1635281