Finite Group Databasebeta

← #49094515

Subgroups — #49094515

Order 35968.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#31824173C211yesmaximal, characteristic
2#31823815C211yesmaximal, characteristic, complemented
3#31823740C211yesmaximal, characteristic
4#31823211C211yesmaximal, characteristic, complemented
5Q8⋊#14555886C211yesmaximal, characteristic, complemented
6#31823190C211yesmaximal, characteristic
7#462×C281C211yesmaximal, characteristic, complemented
8#22582879C2211yescharacteristic
9#22582871—21no—
10#22582857—22no—
11#22582855—21no—
12C4×D1124—21no—
13C4×D1124C2211yescharacteristic
14C4⋊C4×D281—21no—
15#22582812—21no—
16C4⋊#14555886C2211yescharacteristic
17#22582802—22no—
18#22582799—21no—
19C4×#14555886C2211yescharacteristic
20C2×Q16×C281—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4×Q8×C281C2211yescharacteristic
23C4⋊C8×C281C2211yescharacteristic
24#103×C281—21no—
25C2×Dic562D412yes—
26C2×D1124D411yescharacteristic
27C2×C4×D281—22no—
28C2×C4×D281—21no—
29C2×#14555886—21no—
30C2×#14555886—21no—
31C4⋊Dic281—21no—
32C4⋊Dic281—21no—
33C4⋊Dic281D411yescharacteristic
34#17985117—22no—
35#17985117—22no—
36#17985115—22no—
37#17985115—21no—
38C2×Q8×C281—21no—
39C2×Q8×C281D411yescharacteristic
40Q16×C281—42no—
41C2×C8×C281—21no—
42C4⋊C4×C281—21no—
43C4⋊C4×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281D411yescharacteristic
46C42×C281—21no—
47C42×C281C2311yescharacteristic
48C22×D281—21no—
49Dic562—42no—
50D1124—21no—
51D1124Q1612yescomplemented
52C2×Dic281—21no—
53C2×Dic281—22no—
54C4×D281—41no—
55C4×D281—41no—
56C4×D281—82no—
57#14555886—41no—
58#14555886—41no—
59Q8×C281—21no—
60Q8×C281—21no—
61Q8×C281—41no—
62Q8×C281—41no—
63C2×C4×C281—21no—
64C2×C4×C281—21no—
65C2×C4×C281—41no—
66C2×C4×C281C2×D411yescharacteristic
67C2×C4×C281C2×D411yescharacteristic
68C2×C4×C281C2×D411yescharacteristic
69C8×C281—41no—
70C22×C281#12011yescharacteristic
71C2×D281—22no—
72C2×D281—41no—
73C2×D281—41no—
74C4×C281—21no—
75C4×C281—41no—
76C4×C281—41no—
77C4×C281—81no—
78C4×C281C2×Q1611yescharacteristic
79C4×C281#13511yescharacteristic
80C4×C281AGL(1,ℤ/8)11yescharacteristic
81C4×C281#13711yescharacteristic
82Dic281—41no—
83Dic281—42no—
84C2×C281#44911yescharacteristic
85C2×C281#45111yescharacteristic
86C2×C281#45511yescharacteristic
87D281—42no—
88C281#164411yescharacteristic, complemented, Sylow
89#1644—2811nomaximal, Sylow
90#554—2811no—
91#487—2811no—
92#474—2811no—
93#462D28111yescharacteristic, complemented
94#333—2811no—
95Q8⋊C8—2811no—
96D4⋊C8—2811no—
97C2×Q16—21no—
98C4⋊Q8—2811no—
99C4⋊Q8C2×D28111yescharacteristic
100#125—5621no—
101C22⋊Q8—5622no—
102C22⋊Q8—5621no—
103C4×Q8C2×D28111yescharacteristic
104C4×D4—2811no—
105C4×D4—5621no—
106C2×C4⋊C4—5621no—
107#107—5621no—
108C4⋊C8—2811no—
109C4⋊C8C2×D28111yescharacteristic
110#103—21no—
111#103—5622no—
112#102—5621no—
113C4×C8—2811no—
114C2×Q8—21no—
115C2×Q8—2812no—
116C2×Q8C22⋊D28111yescharacteristic
117C2×D4—2811no—
118C22×C4—5622no—
119C22×C4—5621no—
120Q16—42no—
121C2×C8—21no—
122C2×C8—5621no—
123C2×C8—5621no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—2811no—
128C4⋊C4—5622no—
129C4⋊C4—5622no—
130C4⋊C4—5621no—
131C4⋊C4—5621no—
132C4⋊C4C22⋊D28111yescharacteristic
133C22⋊C4—5622no—
134C22⋊C4—5621no—
135C42—21no—
136C42C22×D28111yescharacteristic
137C23—5621no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—11242no—
143D4—2812no—
144D4—5621no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—5621no—
149C2×C4—5622no—
150C2×C4—11241no—
151C2×C4—11241no—
152C2×C4—22482no—
153C2×C4D4×D28111yescharacteristic
154C2×C4D4×D28111yescharacteristic
155C2×C4C2×C22⋊D28111yescharacteristic
156C8—41no—
157C8—11241no—
158C8—11241no—
159C22—5622no—
160C22—11241no—
161C22—11241no—
162C22#2258284711yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—11242no—
168C4—11241no—
169C4Q16×D28111yescharacteristic
170C4#2258289911yescharacteristic
171C4#2258290511yescharacteristic
172C4#2258291111yescharacteristic
173C2—11242no—
174C2#3182360611yescharacteristic
175C2#3182361711yescharacteristic
176C2#3182363911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#462×C281C2
socleC22×C281#120
prime radicalC2×D1124D4
hypercenter#462D281
hypocenterC281#1644
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #31823815C2semidirect
4. #31823211C2semidirect
5. Q8⋊#14555886C2semidirect
7. #462×C281C2semidirect
51. D1124Q16semidirect
88. C281#1644semidirect
93. #462D281semidirect

Maximal subgroups

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

subgroupindex
#318241732
#318238152
#318237402
#318232112
Q8⋊#145558862
#318231902
#462×C2812
#1644281