Finite Group Databasebeta

← #49095835

Subgroups — #49095835

Order 35968.

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

normal subgroups only

This group has 362 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#31824030C211yesmaximal, characteristic
2#31823481C212yesmaximal, complemented
3C2×#22582796C211yesmaximal, characteristic, complemented
4#31823219C212yesmaximal, complemented
5#518×C281C211yesmaximal, characteristic, complemented
6C2×#17985138C2211yescharacteristic
7C2×#17985122C2212yes—
8#22582875C412yescomplemented
9#22582866C412yescomplemented
10#22582850—22no—
11#22582848—22no—
12#22582838C2211yescharacteristic
13#22582807—24no—
14#22582796—22no—
15C22×D4×C281C2211yescharacteristic
16C4×D4×C281—24no—
17#117×C281C2212yes—
18C2×C22⋊C4×C281—22no—
19#17985138—22no—
20#17985138—22no—
21C2×Dic562C2×C411yescharacteristic, complemented
22C2×D1124C2×C411yescharacteristic, complemented
23C2×C22⋊D281—24no—
24C2×C22⋊D281—21no—
25C2×C4×D281—21no—
26#17985122—22no—
27#17985122—22no—
28C2×#14555886—22no—
29C4⋊Dic281—21no—
30C22⋊Dic281—24no—
31C22⋊Dic281—21no—
32C4×Dic281C2×C412yescomplemented
33C24×C281D412yes—
34C2×D4×C281—22no—
35C2×D4×C281—22no—
36C2×D4×C281C2×C412yes—
37C2×D4×C281D412yes—
38C22×C4×C281—24no—
39C22×C4×C281C2311yescharacteristic
40C4⋊C4×C281—22no—
41C22⋊C4×C281—24no—
42C22⋊C4×C281—22no—
43C42×C281D414yescomplemented
44C22×D281—21no—
45Dic562—22no—
46D1124—22no—
47C22⋊D281—41no—
48C22⋊D281—41no—
49C22⋊D281—84no—
50C2×Dic281—22no—
51C2×Dic281—21no—
52C4×D281—42no—
53#14555886—42no—
54C23×C281—22no—
55C23×C281—22no—
56C23×C281—82no—
57C23×C281C22⋊C414yes—
58C23×C281C2×D411yescharacteristic
59D4×C281—24no—
60D4×C281—24no—
61C2×C4×C281—24no—
62C2×C4×C281—84no—
63C2×C4×C281C22×C411yescharacteristic
64C2×C4×C281C2×D412yes—
65C2×C4×C281C2×D411yescharacteristic
66C2×C4×C281#4112yes—
67C22×C281—24no—
68C22×C281—41no—
69C22×C281—44no—
70C22×C281—44no—
71C22×C281—82no—
72C22×C281C2×C22⋊C411yescharacteristic
73C22×C281#12011yescharacteristic
74C22×C281#12311yescharacteristic
75C2×D281—42no—
76C2×D281—41no—
77C4×C281—44no—
78C4×C281C4×D412yes—
79C4×C281#12112yes—
80Dic281—42no—
81Dic281—41no—
82C2×C281—21no—
83C2×C281—21no—
84C2×C281—21no—
85C2×C281—44no—
86C2×C281#38611yescharacteristic
87D281—81no—
88C281#191111yescharacteristic, complemented, Sylow
89#1911—2811nomaximal, Sylow
90#535—2811no—
91#518D28111yescharacteristic, complemented
92#421—2812no—
93C2×#100—2811no—
94H(3,ℤ/4)—2812no—
95C2×#41—2811no—
96C22×D4C2×D28111yescharacteristic
97C2×M16—2812no—
98#127—2812no—
99#124—2812no—
100#121—5622no—
101#120—5622no—
102C4×D4—24no—
103#117—2811no—
104#117C2×D28112yes—
105C2×C22⋊C4—22no—
106#104—5624no—
107#100—5622no—
108C24C22⋊D28112yes—
109#41—5622no—
110#41—5622no—
111C2×Q8—2811no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—2811no—
115C2×D4—5621no—
116C2×D4—5624no—
117C2×D4C4×D28112yes—
118C2×D4D112412yes—
119C22×C4—24no—
120C22×C4—5621no—
121C22×C4C22×D28111yescharacteristic
122M16—5622no—
123M16—5622no—
124C2×C8—5622no—
125C4⋊C4—22no—
126C4⋊C4—5621no—
127C22⋊C4—24no—
128C22⋊C4—22no—
129C22⋊C4—5624no—
130C22⋊C4—5621no—
131C42—2812no—
132C42C22⋊D28114yescomplemented
133C23—22no—
134C23—22no—
135C23—82no—
136C23—5621no—
137C23#1798511514yes—
138C23C2×C22⋊D28111yescharacteristic
139Q8—5622no—
140D4—24no—
141D4—24no—
142D4—5622no—
143D4—11241no—
144D4—11241no—
145D4—22484no—
146C2×C4—24no—
147C2×C4—84no—
148C2×C4—5622no—
149C2×C4—5621no—
150C2×C4—11242no—
151C2×C4C2×C4×D28111yescharacteristic
152C2×C4C2×C22⋊D28112yes—
153C2×C4C2×D112411yescharacteristic
154C2×C4#1798513812yes—
155C8—11242no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—11242no—
162C22—11241no—
163C22C2×#1798511511yescharacteristic
164C22#2258284811yescharacteristic
165C22#2258286211yescharacteristic
166C4—44no—
167C4—11242no—
168C4—11241no—
169C4C4×C22⋊D28112yes—
170C4#2258285312yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—22481no—
176C2#3182334211yescharacteristic
subgroupG/H
centerC2#31823342
commutatorC2×C4×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#518×C281C2
socleC2×C281#386
prime radical#31824030C2
cosocleC22×C4×C281C23
hypercenter#518D281
hypocenterC281#1911
LCSG ▷ C2×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #31823481C2semidirect
3. C2×#22582796C2semidirect
4. #31823219C2semidirect
5. #518×C281C2semidirect
8. #22582875C4semidirect
9. #22582866C4semidirect
21. C2×Dic562C2×C4semidirect
22. C2×D1124C2×C4semidirect
32. C4×Dic281C2×C4semidirect
43. C42×C281D4semidirect
88. C281#1911semidirect
91. #518D281semidirect
132. C42C22⋊D281semidirect

Maximal subgroups

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

subgroupindex
#318240302
#318234812
C2×#225827962
#318232192
#518×C2812
#1911281