Finite Group Databasebeta

← #49095830

Subgroups — #49095830

Order 35968.

344 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 89 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#31824027C211yesmaximal, characteristic
2#31823469C212yesmaximal, complemented
3#31823437C211yesmaximal, characteristic, complemented
4#31823220C212yesmaximal, complemented
5#568×C281C211yesmaximal, characteristic, complemented
6C22×D1124C2211yescharacteristic
7#22582875C412yescomplemented
8#22582868C412yescomplemented
9#22582853—22no—
10#22582847—22no—
11#22582838C2212yes—
12#22582838C2211yescharacteristic
13#22582801—24no—
14#22582794—22no—
15C2×#41×C281C2211yescharacteristic
16#131×C281—24no—
17C2×M16×C281—22no—
18C2×M16×C281C2212yes—
19C23×D281—21no—
20C2×D1124—22no—
21C2×D1124—21no—
22C2×D1124—22no—
23C2×D1124C2×C412yes—
24C2×C22⋊D281—24no—
25C4⋊Dic281—21no—
26C4⋊Dic281—22no—
27C22⋊Dic281—21no—
28C22⋊Dic281—22no—
29#17985115—24no—
30C4×Dic281—22no—
31C4×Dic281C2×C412yes—
32#41×C281—22no—
33#41×C281—22no—
34C2×Q8×C281C2×C411yescharacteristic
35C2×D4×C281C2×C411yescharacteristic
36C2×D4×C281D412yes—
37C22×C4×C281D412yes—
38C22×C4×C281C2311yescharacteristic
39M16×C281—24no—
40M16×C281—22no—
41M16×C281—22no—
42C2×C8×C281—24no—
43C2×C8×C281D414yescomplemented
44C22×D281—22no—
45C22×D281—42no—
46C22×D281—82no—
47D1124—24no—
48D1124—41no—
49D1124—41no—
50C22⋊D281—84no—
51C2×Dic281—22no—
52C2×Dic281—42no—
53C23×C281C22⋊C412yes—
54C23×C281C2×D411yescharacteristic
55Q8×C281—22no—
56D4×C281—24no—
57D4×C281—22no—
58C2×C4×C281—22no—
59C2×C4×C281—22no—
60C2×C4×C281C22⋊C412yes—
61C2×C4×C281C22×C411yescharacteristic
62C2×C4×C281C2×D412yes—
63C2×C4×C281C2×D411yescharacteristic
64C2×C4×C281#4112yes—
65C8×C281—24no—
66C22×C281—22no—
67C22×C281—41no—
68C22×C281—42no—
69C22×C281C2×C22⋊C411yescharacteristic
70C22×C281#12112yes—
71C2×D281—44no—
72C2×D281—42no—
73C2×D281—84no—
74C4×C281—22no—
75C4×C281C4×D412yes—
76C4×C281#12011yescharacteristic
77C4×C281#12311yescharacteristic
78Dic281—42no—
79Dic281—82no—
80C2×C281—21no—
81C2×C281—22no—
82C2×C281—42no—
83C2×C281#38611yescharacteristic
84D281—82no—
85C281#191011yescharacteristic, complemented, Sylow
86#1910—2811nomaximal, Sylow
87#568D28111yescharacteristic, complemented
88#535—2811no—
89#418—2812no—
90#410—2811no—
91H(3,ℤ/4)—2812no—
92C2×#41C2×D28111yescharacteristic
93C22×D4—2811no—
94#131—24no—
95C2×M16—22no—
96C2×M16C2×D28112yes—
97#127—2812no—
98#124—2812no—
99#121—5622no—
100#120—5622no—
101#117—2811no—
102#117—2812no—
103#102—5624no—
104#99—5622no—
105C24—5621no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D28111yescharacteristic
109C2×D4—2812no—
110C2×D4—5624no—
111C2×D4—5622no—
112C2×D4—5621no—
113C2×D4—5622no—
114C2×D4C4×D28111yescharacteristic
115C2×D4D112412yes—
116C22×C4C22⋊D28112yes—
117C22×C4C22×D28111yescharacteristic
118M16—24no—
119M16—22no—
120M16—22no—
121C2×C8—24no—
122C2×C8C22⋊D28114yescomplemented
123C4⋊C4—5621no—
124C4⋊C4—5622no—
125C22⋊C4—5621no—
126C22⋊C4—5624no—
127C22⋊C4—5622no—
128C42—2812no—
129C42—5622no—
130C23—5622no—
131C23—11242no—
132C23—22482no—
133C23#1798511512yes—
134C23C2×D112411yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—5624no—
139D4—11241no—
140D4—11241no—
141D4—22484no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—5622no—
145C2×C4—11242no—
146C2×C4#1798511512yes—
147C2×C4C2×C4×D28111yescharacteristic
148C2×C4C2×C22⋊D28112yes—
149C2×C4C2×C22⋊D28111yescharacteristic
150C2×C4#1798513812yes—
151C8—24no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—11244no—
156C22—11242no—
157C22—22484no—
158C22C2×#1798511511yescharacteristic
159C22#2258285312yes—
160C4—22no—
161C4—11242no—
162C4—22482no—
163C4C4×C22⋊D28112yes—
164C4#2258284811yescharacteristic
165C4#2258286211yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—22482no—
170C2#3182334211yescharacteristic
subgroupG/H
centerC2#31823342
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#568×C281C2
socleC2×C281#386
prime radical#31824027C2
cosocleC22×C4×C281C23
hypercenter#568D281
hypocenterC281#1910
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #31823469C2semidirect
3. #31823437C2semidirect
4. #31823220C2semidirect
5. #568×C281C2semidirect
7. #22582875C4semidirect
8. #22582868C4semidirect
43. C2×C8×C281D4semidirect
85. C281#1910semidirect
87. #568D281semidirect
122. C2×C8C22⋊D281semidirect

Maximal subgroups

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

subgroupindex
#318240272
#318234692
#318234372
#318232202
#568×C2812
#1910281