Finite Group Databasebeta

← #49096549

Subgroups — #49096549

Order 35968.

298 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 93 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×#22582879C211yesmaximal, characteristic
2C2×#22582802C212yesmaximal
3C2×#22582802C212yesmaximal
4#31823218C211yesmaximal, characteristic
5#389×C281C211yesmaximal, characteristic
6C22×Dic562C2212yes—
7C22×#14555886C2212yes—
8#22582879—24no—
9C2×C4⋊Dic281—21no—
10C2×C4⋊Dic281—21no—
11#22582802—24no—
12#22582802—24no—
13C2×C4⋊C4×C281—21no—
14C2×C4⋊C4×C281C2211yescharacteristic
15C2×C4⋊C4×C281C2211yescharacteristic
16C2×C42×C281C2211yescharacteristic
17#95×C281—21no—
18C2×Dic562—22no—
19C2×Dic562—22no—
20C2×Dic562—22no—
21C2×Dic562—22no—
22C2×Dic562—22no—
23C2×Dic562D414yes—
24C22×Dic281—22no—
25C2×#14555886—22no—
26C2×#14555886—22no—
27C2×#14555886—22no—
28C4⋊Dic281—24no—
29C4⋊Dic281—24no—
30C22×C4×C281—21no—
31C22×C4×C281—21no—
32C22×C4×C281D411yescharacteristic
33C22×C4×C281D411yescharacteristic
34C22×C4×C281C2311yescharacteristic
35C4⋊C4×C281—21no—
36C4⋊C4×C281—22no—
37C4⋊C4×C281—42no—
38C4⋊C4×C281D412yes—
39C42×C281—22no—
40Dic562—24no—
41Dic562—24no—
42Dic562—42no—
43Dic562—42no—
44C2×Dic281—24no—
45C2×Dic281—42no—
46C2×Dic281—42no—
47#14555886—42no—
48C23×C281C2×D411yescharacteristic
49C2×C4×C281—21no—
50C2×C4×C281—21no—
51C2×C4×C281—21no—
52C2×C4×C281—21no—
53C2×C4×C281—22no—
54C2×C4×C281—41no—
55C2×C4×C281—41no—
56C2×C4×C281—41no—
57C2×C4×C281—41no—
58C2×C4×C281—41no—
59C2×C4×C281SD1612yes—
60C2×C4×C281Q1612yes—
61C2×C4×C281C2×D412yes—
62C2×C4×C281C2×D411yescharacteristic
63C2×C4×C281#4111yescharacteristic
64C2×C4×C281#4112yes—
65C22×C281#12011yescharacteristic
66C22×C281#12111yescharacteristic
67C22×C281#12411yescharacteristic
68C22×C281C2×SD1611yescharacteristic
69C22×C281C2×Q1611yescharacteristic
70C22×C281#13711yescharacteristic
71C22×C281#13711yescharacteristic
72C4×C281—22no—
73C4×C281—22no—
74C4×C281—42no—
75C4×C281—81no—
76C4×C281#12112yes—
77C4×C281#12312yes—
78Dic281—44no—
79C2×C281#39411yescharacteristic
80C2×C281#44811yescharacteristic
81C2×C281#45111yescharacteristic
82C2×C281#46111yescharacteristic
83C2×C281#46211yescharacteristic
84C2×C281#48711yescharacteristic
85C2×C281#49111yescharacteristic
86C281#204311yescharacteristic, complemented, Sylow
87#2043—2811nomaximal, Sylow
88C2×C4⋊Q8—2811no—
89C2×#103—2812no—
90C2×#103—2812no—
91#389D28111yescharacteristic
92#336—2811no—
93C22×Q8—2812no—
94C22×C8—2812no—
95C4⋊Q8—5624no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—5621no—
98C2×C4⋊C4—5621no—
99C2×C4⋊C4C2×D28111yescharacteristic
100C2×C4⋊C4C2×D28111yescharacteristic
101C2×C42C2×D28111yescharacteristic
102#103—5624no—
103#103—5624no—
104#95—21no—
105C2×Q8—2814no—
106C2×Q8—5622no—
107C2×Q8—5622no—
108C2×Q8—5622no—
109C2×Q8—5622no—
110C2×Q8—5622no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—5622no—
114C22×C4C22⋊D28111yescharacteristic
115C22×C4C22⋊D28111yescharacteristic
116C22×C4C22×D28111yescharacteristic
117C2×C8—5622no—
118C2×C8—5622no—
119C2×C8—5622no—
120C4⋊C4—21no—
121C4⋊C4—22no—
122C4⋊C4—42no—
123C4⋊C4—5624no—
124C4⋊C4—5624no—
125C4⋊C4D112412yes—
126C42—22no—
127C23C2×C22⋊D28111yescharacteristic
128Q8—5624no—
129Q8—5624no—
130Q8—11242no—
131Q8—11242no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—5624no—
143C2×C4—11242no—
144C2×C4—11242no—
145C2×C4#1798512612yes—
146C2×C4#1798512812yes—
147C2×C4D4×D28112yes—
148C2×C4C2×D112411yescharacteristic
149C2×C4#1798513811yescharacteristic
150C2×C4#1798513912yes—
151C8—11242no—
152C22#2258284711yescharacteristic
153C22#2258285311yescharacteristic
154C22#2258286811yescharacteristic
155C22C2×#1798512611yescharacteristic
156C22C2×#1798512811yescharacteristic
157C22#2258290911yescharacteristic
158C22#2258290911yescharacteristic
159C4—22no—
160C4—22no—
161C4—42no—
162C4—81no—
163C4—11244no—
164C4#2258285412yes—
165C4#2258286412yes—
166C2#3182338011yescharacteristic
167C2#3182360111yescharacteristic
168C2#3182361811yescharacteristic
169C2#3182366811yescharacteristic
170C2#3182367311yescharacteristic
171C2#3182381511yescharacteristic
172C2#3182383311yescharacteristic
subgroupG/H
centerC23C2×C22⋊D281
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#389×C281C2
socle, prime radicalC23×C281C2×D4
hypercenter#389D281
hypocenterC281#2043
LCSG ▷ C22×C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
86. C281#2043semidirect

Maximal subgroups

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

subgroupindex
C2×#225828792
C2×#225828022
#318232182
#389×C2812
#2043281