Finite Group Databasebeta

← #49094516

Subgroups — #49094516

Order 35968.

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

normal subgroups only

This group has 208 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#31824170C211yesmaximal, characteristic
2#31823815C211yesmaximal, characteristic, complemented
3#31823670C211yesmaximal, characteristic, complemented
4#31823211C211yesmaximal, characteristic, complemented
5#31823193C211yesmaximal, characteristic, complemented
6D4⋊#14555886C211yesmaximal, characteristic
7#474×C281C211yesmaximal, characteristic
8C2×#17985128—21no—
9#22582879C2211yescharacteristic
10#22582870—21no—
11#22582858—21no—
12#22582856—22no—
13C4×Dic562C2211yescharacteristic
14D4×Dic281—21no—
15C2×C4⋊Dic281—21no—
16C4⋊#14555886C2211yescharacteristic
17#22582803—21no—
18#22582802—22no—
19C4×#14555886C2211yescharacteristic
20C4⋊Q8×C281C2211yescharacteristic
21C4×D4×C281C2211yescharacteristic
22#107×C281—21no—
23C4⋊C8×C281C2211yescharacteristic
24#102×C281—21no—
25C2×Dic562D411yescharacteristic
26C2×Dic562D412yes—
27C22×Dic281—22no—
28#17985128—42no—
29C2×#14555886—21no—
30C2×#14555886—21no—
31C4⋊Dic281—22no—
32C4⋊Dic281—21no—
33C4⋊Dic281—21no—
34C4⋊Dic281D411yescharacteristic
35#17985117—22no—
36#17985117—21no—
37C22⋊Dic281—22no—
38C4×Dic281—21no—
39C2×Q8×C281—21no—
40C2×D4×C281D411yescharacteristic
41C22×C4×C281—21no—
42C2×C8×C281—21no—
43C4⋊C4×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281D411yescharacteristic
46C22⋊C4×C281—21no—
47C42×C281C2311yescharacteristic
48Dic562—21no—
49Dic562—21no—
50Dic562—42no—
51C2×Dic281—21no—
52C2×Dic281—21no—
53C2×Dic281—22no—
54C2×Dic281—82no—
55#14555886—41no—
56#14555886—41no—
57C23×C281—21no—
58Q8×C281—41no—
59Q8×C281—41no—
60D4×C281—21no—
61D4×C281Q1612yescomplemented
62C2×C4×C281—21no—
63C2×C4×C281—41no—
64C2×C4×C281—41no—
65C2×C4×C281—41no—
66C2×C4×C281C2×D411yescharacteristic
67C2×C4×C281C2×D411yescharacteristic
68C2×C4×C281C2×D411yescharacteristic
69C8×C281—41no—
70C22×C281—22no—
71C22×C281—41no—
72C22×C281—41no—
73C22×C281#12011yescharacteristic
74C4×C281—21no—
75C4×C281—41no—
76C4×C281—81no—
77C4×C281C2×Q1611yescharacteristic
78C4×C281#13511yescharacteristic
79C4×C281AGL(1,ℤ/8)11yescharacteristic
80C4×C281#13711yescharacteristic
81Dic281—41no—
82Dic281—41no—
83Dic281—42no—
84C2×C281—42no—
85C2×C281#44911yescharacteristic
86C2×C281#45111yescharacteristic
87C2×C281#45511yescharacteristic
88C281#164411yescharacteristic, complemented, Sylow
89#1644—2811nomaximal, Sylow
90#554—2811no—
91#487—2811no—
92#474D28111yescharacteristic
93#462—2811no—
94#333—2811no—
95Q8⋊C8—2811no—
96D4⋊C8—2811no—
97C2×Q16—5621no—
98C4⋊Q8—2811no—
99C4⋊Q8C2×D28111yescharacteristic
100#125—5621no—
101C22⋊Q8—5622no—
102C22⋊Q8—5621no—
103C4×Q8—2811no—
104C4×D4—5621no—
105C4×D4C2×D28111yescharacteristic
106C2×C4⋊C4—5621no—
107#107—21no—
108C4⋊C8—2811no—
109C4⋊C8C2×D28111yescharacteristic
110#103—5622no—
111#103—5621no—
112#102—21no—
113C4×C8—2811no—
114C2×Q8—21no—
115C2×Q8—2811no—
116C2×Q8—2812no—
117C2×D4C22⋊D28111yescharacteristic
118C22×C4—21no—
119C22×C4—5622no—
120Q16—11242no—
121C2×C8—21no—
122C2×C8—5621no—
123C2×C8—5621no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—2811no—
127C4⋊C4—5622no—
128C4⋊C4—5622no—
129C4⋊C4—5621no—
130C4⋊C4—5621no—
131C4⋊C4—5621no—
132C4⋊C4C22⋊D28111yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—5622no—
135C42—5621no—
136C42C22×D28111yescharacteristic
137C23—21no—
138Q8—41no—
139Q8—41no—
140Q8—5621no—
141Q8—5621no—
142Q8—11242no—
143D4—21no—
144D4#1798512812yescomplemented
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—5621no—
150C2×C4—5621no—
151C2×C4—5622no—
152C2×C4—22482no—
153C2×C4D4×D28111yescharacteristic
154C2×C4D4×D28111yescharacteristic
155C2×C4C2×C22⋊D28111yescharacteristic
156C8—41no—
157C8—11241no—
158C8—11241no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#2258284711yescharacteristic
163C4—21no—
164C4—41no—
165C4—81no—
166C4—11241no—
167C4—11242no—
168C4—11241no—
169C4C2×#1798512811yescharacteristic
170C4#2258289811yescharacteristic
171C4#2258290311yescharacteristic
172C4#2258290911yescharacteristic
173C2—42no—
174C2#3182360511yescharacteristic
175C2#3182361811yescharacteristic
176C2#3182363911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#474×C281C2
socleC22×C281#120
prime radicalC2×D4×C281D4
hypercenter#474D281
hypocenterC281#1644
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #31823815C2semidirect
3. #31823670C2semidirect
4. #31823211C2semidirect
5. #31823193C2semidirect
61. D4×C281Q16semidirect
88. C281#1644semidirect
144. D4#17985128semidirect

Maximal subgroups

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

subgroupindex
#318241702
#318238152
#318236702
#318232112
#318231932
D4⋊#145558862
#474×C2812
#1644281