Finite Group Databasebeta

← #49095828

Subgroups — #49095828

Order 35968.

344 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 85 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#31824230C211yesmaximal, characteristic, complemented
2#31824027C211yesmaximal, characteristic
3#31823467C212yesmaximal, complemented
4#31823219C212yesmaximal, complemented
5#410×C281C211yesmaximal, characteristic, complemented
6C22×D1124C2211yescharacteristic
7#22582886—24no—
8C2×#17985122—22no—
9C2×#17985122C2212yes—
10#22582875C412yescomplemented
11#22582868C412yescomplemented
12#22582853—22no—
13#22582847—22no—
14#22582838C2211yescharacteristic
15#22582799—24no—
16C2×#41×C281C2211yescharacteristic
17#117×C281C2212yes—
18#99×C281—22no—
19C23×D281—21no—
20C2×D1124—22no—
21C2×D1124—21no—
22C2×D1124—22no—
23C2×D1124C2×C412yes—
24C2×C22⋊D281—24no—
25#17985122—24no—
26#17985122—22no—
27#17985122—22no—
28C2×#14555886—24no—
29C2×#14555886D414yescomplemented
30C4⋊Dic281—21no—
31C22⋊Dic281—21no—
32#17985115—24no—
33C4×Dic281C2×C412yes—
34#41×C281—22no—
35#41×C281—22no—
36C2×Q8×C281C2×C411yescharacteristic
37C2×D4×C281C2×C411yescharacteristic
38C2×D4×C281D412yes—
39C22×C4×C281D412yes—
40C22×C4×C281C2311yescharacteristic
41C4⋊C4×C281—22no—
42C22⋊C4×C281—22no—
43C42×C281—22no—
44C22×D281—22no—
45C22×D281—42no—
46C22×D281—82no—
47D1124—24no—
48D1124—41no—
49D1124—41no—
50C22⋊D281—84no—
51C2×Dic281—22no—
52#14555886—24no—
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×C281—42no—
61C2×C4×C281C22⋊C412yes—
62C2×C4×C281C22×C411yescharacteristic
63C2×C4×C281C2×D412yes—
64C2×C4×C281C2×D411yescharacteristic
65C2×C4×C281#4112yes—
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×C281—82no—
76C4×C281C4×D412yes—
77C4×C281#12011yescharacteristic
78C4×C281#12311yescharacteristic
79Dic281—42no—
80C2×C281—21no—
81C2×C281—22no—
82C2×C281—42no—
83C2×C281#38611yescharacteristic
84D281—82no—
85C281#191011yescharacteristic, complemented, Sylow
86#1910—2811nomaximal, Sylow
87#568—2811no—
88#535—2811no—
89#418—2812no—
90#410D28111yescharacteristic, complemented
91H(3,ℤ/4)—2812no—
92C2×#41C2×D28111yescharacteristic
93C22×D4—2811no—
94#131—5624no—
95C2×M16—2812no—
96C2×M16—5622no—
97#127—2812no—
98#124—2812no—
99#121—5622no—
100#120—5622no—
101#117—2811no—
102#117C2×D28112yes—
103#102—5624no—
104#99—22no—
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×D4C22⋊D28112yes—
116C22×C4D112412yes—
117C22×C4C22×D28111yescharacteristic
118M16—5624no—
119M16—5622no—
120M16—5622no—
121C2×C8—2814no—
122C2×C8—5624no—
123C4⋊C4—22no—
124C4⋊C4—5621no—
125C22⋊C4—22no—
126C22⋊C4—5621no—
127C22⋊C4—5624no—
128C42—22no—
129C42—2812no—
130C23—5622no—
131C23—11242no—
132C23—22482no—
133C23#1798511512yes—
134C23C2×C22⋊D28111yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—5624no—
139D4—11241no—
140D4—11241no—
141D4—22484no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—5622no—
146C2×C4#1798511512yes—
147C2×C4C2×C4×D28111yescharacteristic
148C2×C4D4×D28112yes—
149C2×C4C2×D112411yescharacteristic
150C2×C4#1798513712yes—
151C8—5624no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—11244no—
156C22—11242no—
157C22—22484no—
158C22C2×#1798511511yescharacteristic
159C22#2258285112yes—
160C4—22no—
161C4—82no—
162C4—11242no—
163C4#2258283912yes—
164C4#2258284911yescharacteristic
165C4#2258286311yescharacteristic
166C2—22no—
167C2—21no—
168C2—42no—
169C2—22482no—
170C2#3182334011yescharacteristic
subgroupG/H
centerC2#31823340
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#410×C281C2
socleC2×C281#386
prime radical#31824027C2
cosocleC22×C4×C281C23
hypercenter#410D281
hypocenterC281#1910
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #31824230C2semidirect
3. #31823467C2semidirect
4. #31823219C2semidirect
5. #410×C281C2semidirect
10. #22582875C4semidirect
11. #22582868C4semidirect
29. C2×#14555886D4semidirect
85. C281#1910semidirect
90. #410D281semidirect

Maximal subgroups

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

subgroupindex
#318242302
#318240272
#318234672
#318232192
#410×C2812
#1910281