Finite Group Databasebeta

← #49094465

Subgroups — #49094465

Order 35968.

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

normal subgroups only

This group has 228 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#31824128C211yesmaximal, characteristic
2#31823755C211yesmaximal, characteristic, complemented
3#31823750C211yesmaximal, characteristic
4#31823209C211yesmaximal, characteristic, complemented
5#31823195C211yesmaximal, characteristic, complemented
6#31823192C211yesmaximal, characteristic
7#487×C281C211yesmaximal, characteristic, complemented
8C2×Q8×D281—21no—
9#22582878—21no—
10#22582857—22no—
11#22582855—21no—
12C4×Dic562C2211yescharacteristic
13C4×D1124C2211yescharacteristic
14#22582841—21no—
15#22582812—21no—
16#22582810—21no—
17C4⋊#14555886C2211yescharacteristic
18C4⋊#14555886C2211yescharacteristic
19#22582802—21no—
20#22582799—21no—
21C4⋊Q8×C281C2211yescharacteristic
22C4⋊Q8×C281C2211yescharacteristic
23#103×C281—22no—
24C4×C8×C281C2211yescharacteristic
25C2×Dic562—22no—
26C2×Dic562D411yescharacteristic
27Q8×D281—42no—
28Q8×D281—42no—
29C2×D1124D411yescharacteristic
30C2×C4×D281—22no—
31C2×C4×D281—21no—
32C2×#14555886—21no—
33C2×#14555886—21no—
34C4⋊Dic281D411yescharacteristic
35C4⋊Dic281D411yescharacteristic
36#17985117—22no—
37#17985117—21no—
38#17985115—22no—
39#17985115—21no—
40C4×Dic281—21no—
41C2×Q8×C281—21no—
42C2×Q8×C281—21no—
43C2×C8×C281—21no—
44C4⋊C4×C281—21no—
45C4⋊C4×C281—21no—
46C4⋊C4×C281—21no—
47C4⋊C4×C281D412yes—
48C42×C281C2311yescharacteristic
49C22×D281—21no—
50Dic562—21no—
51Dic562—44no—
52Dic562SD1612yes—
53D1124—21no—
54D1124Q1612yes—
55C2×Dic281—21no—
56C2×Dic281—21no—
57C2×Dic281—21no—
58C4×D281—44no—
59C4×D281—41no—
60C4×D281—41no—
61#14555886—41no—
62#14555886—41no—
63Q8×C281—42no—
64Q8×C281—41no—
65Q8×C281—41no—
66C2×C4×C281—22no—
67C2×C4×C281—41no—
68C2×C4×C281C2×D411yescharacteristic
69C2×C4×C281C2×D411yescharacteristic
70C2×C4×C281C2×D411yescharacteristic
71C8×C281—41no—
72C22×C281#12011yescharacteristic
73C2×D281—22no—
74C2×D281—41no—
75C2×D281—41no—
76C4×C281—21no—
77C4×C281—42no—
78C4×C281—81no—
79C4×C281C2×SD1611yescharacteristic
80C4×C281C2×Q1611yescharacteristic
81C4×C281AGL(1,ℤ/8)11yescharacteristic
82C4×C281#13711yescharacteristic
83Dic281—22no—
84Dic281—41no—
85Dic281—41no—
86C2×C281#45011yescharacteristic
87C2×C281#45111yescharacteristic
88C2×C281#45411yescharacteristic
89D281—42no—
90C281#163711yescharacteristic, complemented, Sylow
91#1637—2811nomaximal, Sylow
92D4×Q8—2811no—
93#487D28111yescharacteristic, complemented
94#477—2811no—
95#476—2811no—
96#332—2811no—
97Q8⋊C8—2811no—
98D4⋊C8—2811no—
99C22×Q8—5621no—
100C4⋊Q8—5621no—
101C4⋊Q8C2×D28111yescharacteristic
102C4⋊Q8C2×D28111yescharacteristic
103C22⋊Q8—5621no—
104C22⋊Q8—5622no—
105C4×Q8—2811no—
106C4×D4—2811no—
107C4×D4—5621no—
108#107—5621no—
109#106—5621no—
110C4⋊C8—2811no—
111C4⋊C8—2811no—
112#103—22no—
113#103—5621no—
114#102—5621no—
115C4×C8C2×D28111yescharacteristic
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—2811no—
119C2×Q8—5622no—
120C2×Q8—11242no—
121C2×Q8—11242no—
122C2×D4—2811no—
123C22×C4—5622no—
124C22×C4—5621no—
125C2×C8—21no—
126C2×C8—5621no—
127C2×C8—5621no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—2811no—
132C4⋊C4—2811no—
133C4⋊C4—5622no—
134C4⋊C4—5621no—
135C4⋊C4C22⋊D28112yes—
136C22⋊C4—5622no—
137C22⋊C4—5621no—
138C42—5621no—
139C42C22×D28111yescharacteristic
140C23—5621no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—2812no—
145Q8—5621no—
146Q8—11244no—
147D4—2812no—
148D4—5621no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—5621no—
152C2×C4—5621no—
153C2×C4—5621no—
154C2×C4—11244no—
155C2×C4—11241no—
156C2×C4—11241no—
157C2×C4D4×D28111yescharacteristic
158C2×C4D4×D28111yescharacteristic
159C2×C4C2×C22⋊D28111yescharacteristic
160C8—41no—
161C8—11241no—
162C8—11241no—
163C22—5622no—
164C22—11241no—
165C22—11241no—
166C22#2258284711yescharacteristic
167C4—21no—
168C4—42no—
169C4—81no—
170C4—5622no—
171C4—11241no—
172C4—11241no—
173C4SD16×D28111yescharacteristic
174C4Q16×D28111yescharacteristic
175C4#2258290611yescharacteristic
176C4#2258291111yescharacteristic
177C2—11242no—
178C2#3182361211yescharacteristic
179C2#3182361711yescharacteristic
180C2#3182363511yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC42×C281C23
FrattiniC42C22×D281
Fitting#487×C281C2
socleC22×C281#120
prime radicalC2×D1124D4
hypercenter#487D281
hypocenterC281#1637
LCSG ▷ C42×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #31823755C2semidirect
4. #31823209C2semidirect
5. #31823195C2semidirect
7. #487×C281C2semidirect
90. C281#1637semidirect
93. #487D281semidirect

Maximal subgroups

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

subgroupindex
#318241282
#318237552
#318237502
#318232092
#318231952
#318231922
#487×C2812
#1637281