Finite Group Databasebeta

← #49096524

Subgroups — #49096524

Order 35968.

306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C2×#22582806C212yesmaximal, complemented
2#31823464C212yesmaximal, complemented
3#31823332C211yesmaximal, characteristic, complemented
4#31823232C211yesmaximal, characteristic, complemented
5#537×C281C211yesmaximal, characteristic
6C2×#17985122C2212yes—
7C2×C4⋊Dic281C2211yescharacteristic
8C2×#17985117—22no—
9C2×C4×Dic281C2211yescharacteristic
10#22582806—24no—
11#22582803—22no—
12#22582800—22no—
13C2×#41×C281C2212yes—
14C22⋊Q8×C281—22no—
15#121×C281—22no—
16#121×C281—22no—
17C2×C4⋊C4×C281C2211yescharacteristic
18C22×Dic281—21no—
19C22×Dic281—21no—
20#17985122—22no—
21#17985122—22no—
22C2×#14555886—22no—
23C4⋊Dic281—22no—
24#17985117—44no—
25C4×Dic281—21no—
26C4×Dic281D412yescomplemented
27#41×C281—22no—
28#41×C281—22no—
29#41×C281—22no—
30#41×C281—22no—
31C2×Q8×C281D412yes—
32C2×D4×C281—22no—
33C2×D4×C281—22no—
34C2×D4×C281D412yes—
35C22×C4×C281—22no—
36C22×C4×C281D412yes—
37C22×C4×C281C2311yescharacteristic
38C4⋊C4×C281—22no—
39C4⋊C4×C281—22no—
40C22⋊C4×C281—24no—
41C2×Dic281—22no—
42C2×Dic281—22no—
43C2×Dic281—22no—
44C2×Dic281—42no—
45C2×Dic281—41no—
46#14555886—42no—
47C23×C281—22no—
48C23×C281C2×D411yescharacteristic
49Q8×C281—22no—
50Q8×C281—22no—
51D4×C281—22no—
52D4×C281—22no—
53D4×C281—42no—
54D4×C281—42no—
55D4×C281—82no—
56C2×C4×C281—22no—
57C2×C4×C281—22no—
58C2×C4×C281—42no—
59C2×C4×C281—42no—
60C2×C4×C281—42no—
61C2×C4×C281C2×D411yescharacteristic
62C2×C4×C281C2×D412yes—
63C2×C4×C281#4112yes—
64C2×C4×C281#4111yescharacteristic
65C22×C281—21no—
66C22×C281—21no—
67C22×C281—42no—
68C22×C281—42no—
69C22×C281—42no—
70C22×C281#12011yescharacteristic
71C22×C281#12111yescharacteristic
72C22×C281#12411yescharacteristic
73C4×C281—42no—
74C4×C281—42no—
75C4×C281#12112yes—
76C4×C281#12312yes—
77Dic281—24no—
78Dic281—81no—
79C2×C281—21no—
80C2×C281—21no—
81C2×C281—82no—
82C2×C281#39411yescharacteristic
83C2×C281#45311yescharacteristic
84C2×C281#45611yescharacteristic
85C281#203911yescharacteristic, complemented, Sylow
86#2039—2811nomaximal, Sylow
87#537D28111yescharacteristic
88C2×#104—2812no—
89#417—2812no—
90#384—2811no—
91#343—2811no—
92C2×#41C2×D28112yes—
93C2×M16—2812no—
94C22⋊Q8—22no—
95#121—22no—
96#121—22no—
97C2×C4⋊C4—2811no—
98C2×C4⋊C4—5622no—
99C2×C4⋊C4C2×D28111yescharacteristic
100C2×C42—2811no—
101#104—5624no—
102#103—5622no—
103#102—5622no—
104#41—22no—
105#41—22no—
106#41—22no—
107#41—22no—
108C2×Q8C22⋊D28112yes—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4C22⋊D28112yes—
112C22×C4—22no—
113C22×C4—5621no—
114C22×C4—5621no—
115C22×C4C22⋊D28112yes—
116C22×C4C22×D28111yescharacteristic
117M16—5622no—
118M16—5622no—
119C2×C8—5622no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—5622no—
123C4⋊C4—11244no—
124C22⋊C4—24no—
125C42—2812no—
126C42—5621no—
127C23—22no—
128C23C2×C22⋊D28111yescharacteristic
129Q8—22no—
130Q8—22no—
131D4—22no—
132D4—22no—
133D4—42no—
134D4—42no—
135D4—82no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—5622no—
142C2×C4—5622no—
143C2×C4—5622no—
144C2×C4—11242no—
145C2×C4—11241no—
146C2×C4D4×D28111yescharacteristic
147C2×C4C2×C22⋊D28112yes—
148C2×C4#1798513712yes—
149C2×C4#1798513711yescharacteristic
150C8—11242no—
151C22—21no—
152C22—21no—
153C22—42no—
154C22—42no—
155C22—42no—
156C22#2258284811yescharacteristic
157C22#2258285011yescharacteristic
158C22#2258286611yescharacteristic
159C4—42no—
160C4—42no—
161C4—5624no—
162C4—22481no—
163C4#2258285112yes—
164C4#2258286012yes—
165C2—21no—
166C2—21no—
167C2—82no—
168C2#3182337711yescharacteristic
169C2#3182363111yescharacteristic
170C2#3182364611yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting, prime radical#537×C281C2
socleC22×C281#120
hypercenter#537D281
hypocenterC281#2039
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#22582806C2semidirect
2. #31823464C2semidirect
3. #31823332C2semidirect
4. #31823232C2semidirect
26. C4×Dic281D4semidirect
85. C281#2039semidirect

Maximal subgroups

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

subgroupindex
C2×#225828062
#318234642
#318233322
#318232322
#537×C2812
#2039281