Finite Group Databasebeta

← #49093636

Subgroups — #49093636

Order 35968.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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×#22582837C211yesmaximal, characteristic
2#31823517C212yesmaximal, complemented
3#31823189C211yesmaximal, characteristic, complemented
4#31823186C212yesmaximal
5#324×C281C211yesmaximal, characteristic, complemented
6C22×C4×D281C411yescharacteristic
7#22582837—22no—
8#22582837—22no—
9C2×C4⋊Dic281C411yescharacteristic
10C2×#17985115C411yescharacteristic
11C2×#17985115C2211yescharacteristic
12C2×C4×Dic281C411yescharacteristic
13C2×C4×Dic281C2211yescharacteristic
14#22582808—22no—
15C22⋊#14555886C2212yes—
16#22582789—22no—
17C2×C4⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yes—
19C23×D281C2×C411yescharacteristic
20C22×Dic281C2×C411yescharacteristic
21C22×Dic281C2×C411yescharacteristic
22C22×Dic281C2×C411yescharacteristic
23C2×C4×D281—22no—
24C2×C4×D281—21no—
25C2×C4×D281—21no—
26C2×C4×D281—22no—
27C2×#14555886—22no—
28C4⋊Dic281—22no—
29#17985115—22no—
30#17985115—22no—
31C4×Dic281—21no—
32C4×Dic281—21no—
33C4×Dic281D412yes—
34C4×Dic281D412yes—
35C22×C4×C281C2×C411yescharacteristic
36C22×C4×C281C2×C411yescharacteristic
37C22×C4×C281C2311yescharacteristic
38C2×C8×C281—22no—
39C4⋊C4×C281—22no—
40C22×D281—21no—
41C22×D281—21no—
42C22×D281—41no—
43C22×D281—41no—
44C22×D281M1612yes—
45C2×Dic281—21no—
46C2×Dic281—21no—
47C2×Dic281—21no—
48C2×Dic281—41no—
49C2×Dic281—41no—
50C2×Dic281C22⋊C411yescharacteristic
51C2×Dic281C22⋊C411yescharacteristic
52C2×Dic281C22⋊C412yes—
53C4×D281—24no—
54C4×D281—24no—
55#14555886—42no—
56C23×C281C22×C411yescharacteristic
57C2×C4×C281—21no—
58C2×C4×C281—21no—
59C2×C4×C281—21no—
60C2×C4×C281—41no—
61C2×C4×C281—41no—
62C2×C4×C281M1612yes—
63C2×C4×C281C2×D412yes—
64C8×C281—42no—
65C22×C281—21no—
66C22×C281—21no—
67C22×C281C2×C22⋊C411yescharacteristic
68C22×C281C2×M1611yescharacteristic
69C22×C281C2×M1611yescharacteristic
70C2×D281—22no—
71C2×D281—42no—
72C2×D281—41no—
73C2×D281—41no—
74C2×D281—42no—
75C4×C281—22no—
76C4×C281—22no—
77C4×C281—41no—
78Dic281—21no—
79Dic281—21no—
80Dic281—22no—
81Dic281—41no—
82C2×C281—21no—
83C2×C281—21no—
84C2×C281#40711yescharacteristic
85C2×C281#41011yescharacteristic
86C2×C281#41311yescharacteristic
87D281—42no—
88C281#146411yescharacteristic, complemented, Sylow
89#1464—2811nomaximal, Sylow
90C2×#117—2811no—
91#432—2812no—
92#324—2811no—
93#324D28111yescharacteristic, complemented
94#323—2812no—
95C23×C4—2811no—
96#117—5622no—
97#117—5622no—
98C2×C4⋊C4—2811no—
99C2×C4⋊C4C2×D28111yescharacteristic
100C2×C22⋊C4—2811no—
101C2×C22⋊C4—2811no—
102C2×C42—2811no—
103C2×C42—2811no—
104C4⋊C8—5622no—
105C22⋊C8—2812no—
106C22⋊C8C2×D28112yes—
107#97—5622no—
108C24—2811no—
109C22×C4—2811no—
110C22×C4—2811no—
111C22×C4—2811no—
112C22×C4—5621no—
113C22×C4—5621no—
114C22×C4—5622no—
115C22×C4—5622no—
116C22×C4C4×D28111yescharacteristic
117C22×C4C4×D28111yescharacteristic
118C22×C4C22×D28111yescharacteristic
119C2×C8—22no—
120C2×C8—5622no—
121C4⋊C4—22no—
122C4⋊C4—5622no—
123C22⋊C4—5622no—
124C22⋊C4—5622no—
125C42—2812no—
126C42—2812no—
127C42—5621no—
128C42—5621no—
129C23—2812no—
130C23—5621no—
131C23—5621no—
132C23—11241no—
133C23—11241no—
134C23C2×C4×D28111yescharacteristic
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—2811no—
141C2×C4—2811no—
142C2×C4—2812no—
143C2×C4—5624no—
144C2×C4—5624no—
145C2×C4—5621no—
146C2×C4—5621no—
147C2×C4—5621no—
148C2×C4—11241no—
149C2×C4—11241no—
150C2×C4#1798512112yes—
151C2×C4D4×D28112yes—
152C8—42no—
153C8—11242no—
154C22—21no—
155C22—21no—
156C22—5622no—
157C22—11242no—
158C22—11242no—
159C22—11241no—
160C22—11241no—
161C22C22⋊C4×D28111yescharacteristic
162C22M16×D28111yescharacteristic
163C22C2×#1798512111yescharacteristic
164C4—22no—
165C4—22no—
166C4—41no—
167C4—5621no—
168C4—5621no—
169C4—5622no—
170C4—11241no—
171C2—21no—
172C2—21no—
173C2—11242no—
174C2#3182342511yescharacteristic
175C2#3182343511yescharacteristic
176C2#3182344611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D281
commutatorC23×C281C22×C4
FrattiniC22×C4C22×D281
Fitting#324×C281C2
socleC22×C281C2×C22⋊C4
prime radicalC23×D281C2×C4
cosocleC22×C4×C281C23
hypercenter#324D281
hypocenterC281#1464
LCSG ▷ C23×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #31823517C2semidirect
3. #31823189C2semidirect
5. #324×C281C2semidirect
88. C281#1464semidirect
93. #324D281semidirect

Maximal subgroups

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

subgroupindex
C2×#225828372
#318235172
#318231892
#318231862
#324×C2812
#1464281