Finite Group Databasebeta

← #49094243

Subgroups — #49094243

Order 35968.

266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 57 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#31823613C212yesmaximal
2#31823380C211yesmaximal, characteristic
3#31823200C212yesmaximal, complemented
4#31823189C211yesmaximal, characteristic, complemented
5#544×C281C211yesmaximal, characteristic, complemented
6C22×D1124C2211yescharacteristic
7C2×#17985125—22no—
8C2×#17985115—21no—
9C2×#17985115—21no—
10#22582799—22no—
11C22⋊#14555886C2212yes—
12#22582786C2211yescharacteristic
13C4⋊Q8×C281—22no—
14#125×C281—22no—
15C22⋊Q8×C281—21no—
16C22⋊Q8×C281C2212yes—
17#117×C281—21no—
18C2×C4⋊C4×C281C2211yescharacteristic
19C23×D281—21no—
20C2×D1124—22no—
21C2×D1124—42no—
22C22×Dic281—21no—
23#17985125—44no—
24C2×#14555886—22no—
25#17985115—42no—
26#17985115—42no—
27C2×Q8×C281—21no—
28C2×Q8×C281D412yes—
29C22×C4×C281D411yescharacteristic
30C22×C4×C281D411yescharacteristic
31C22×C4×C281C2311yescharacteristic
32C4⋊C4×C281—21no—
33C4⋊C4×C281—21no—
34C4⋊C4×C281—21no—
35C4⋊C4×C281—22no—
36C4⋊C4×C281—22no—
37C4⋊C4×C281—22no—
38C4⋊C4×C281D412yes—
39C22⋊C4×C281—22no—
40C42×C281—22no—
41C22×D281—22no—
42C22×D281—41no—
43C22×D281—41no—
44C22×D281—41no—
45C22×D281—41no—
46C22×D281—41no—
47C22×D281—41no—
48D1124—24no—
49D1124—42no—
50C2×Dic281—41no—
51C2×Dic281—41no—
52C2×Dic281—41no—
53#14555886—42no—
54C23×C281C2×D411yescharacteristic
55Q8×C281—42no—
56Q8×C281—81no—
57C2×C4×C281—21no—
58C2×C4×C281—21no—
59C2×C4×C281—22no—
60C2×C4×C281—22no—
61C2×C4×C281—21no—
62C2×C4×C281—41no—
63C2×C4×C281—41no—
64C2×C4×C281SD1612yescomplemented
65C2×C4×C281C2×D412yes—
66C22×C281—21no—
67C22×C281—21no—
68C22×C281#12011yescharacteristic
69C22×C281C2×SD1611yescharacteristic
70C22×C281#13711yescharacteristic
71C2×D281—42no—
72C2×D281—42no—
73C2×D281—42no—
74C2×D281—81no—
75C2×D281—81no—
76C2×D281—81no—
77C2×D281—81no—
78C4×C281—22no—
79C4×C281—22no—
80C4×C281—42no—
81C4×C281—41no—
82C4×C281—42no—
83Dic281—81no—
84C2×C281—21no—
85C2×C281—21no—
86C2×C281#44811yescharacteristic
87C2×C281#45411yescharacteristic
88C2×C281B(4,𝔽2)11yescharacteristic
89D281—82no—
90C281#159911yescharacteristic, complemented, Sylow
91#1599—2811nomaximal, Sylow
92#544D28111yescharacteristic, complemented
93#450—2812no—
94#394—2811no—
95#328—2812no—
96#324—2811no—
97C22×D4—2811no—
98C2×SD16—5622no—
99C4⋊Q8—22no—
100#125—22no—
101C22⋊Q8—21no—
102C22⋊Q8C2×D28112yes—
103#117—21no—
104C2×C4⋊C4C2×D28111yescharacteristic
105C2×C22⋊C4—5621no—
106C2×C22⋊C4—5621no—
107#102—5622no—
108C22⋊C8—2812no—
109#95—2811no—
110C24—5621no—
111C2×Q8—21no—
112C2×Q8C22⋊D28112yes—
113C2×D4—5622no—
114C2×D4—11242no—
115C22×C4—5621no—
116C22×C4C22⋊D28111yescharacteristic
117C22×C4C22⋊D28111yescharacteristic
118C22×C4C22×D28111yescharacteristic
119SD16—11244no—
120C2×C8—5622no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—22no—
125C4⋊C4—22no—
126C4⋊C4—22no—
127C4⋊C4C22⋊D28112yes—
128C22⋊C4—22no—
129C22⋊C4—11242no—
130C22⋊C4—11242no—
131C42—22no—
132C23—5622no—
133C23—11241no—
134C23—11241no—
135C23—11241no—
136C23—11241no—
137C23—11241no—
138C23—11241no—
139C23C2×C22⋊D28111yescharacteristic
140Q8—42no—
141Q8—81no—
142D4—5624no—
143D4—11242no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—11241no—
152C2×C4—11241no—
153C2×C4—11241no—
154C2×C4#1798512512yescomplemented
155C2×C4C2×C22⋊D28112yes—
156C8—11242no—
157C22—21no—
158C22—21no—
159C22—11242no—
160C22—11242no—
161C22—11242no—
162C22—22481no—
163C22—22481no—
164C22—22481no—
165C22—22481no—
166C22#2258284811yescharacteristic
167C22C2×#1798512511yescharacteristic
168C22#2258291011yescharacteristic
169C4—22no—
170C4—22no—
171C4—42no—
172C4—41no—
173C4—42no—
174C4—22481no—
175C2—21no—
176C2—21no—
177C2—22482no—
178C2#3182360211yescharacteristic
179C2#3182363611yescharacteristic
180C2#3182365011yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#544×C281C2
socleC22×C281#120
prime radicalC22×D1124C22
hypercenter#544D281
hypocenterC281#1599
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #31823200C2semidirect
4. #31823189C2semidirect
5. #544×C281C2semidirect
64. C2×C4×C281SD16semidirect
90. C281#1599semidirect
92. #544D281semidirect
154. C2×C4#17985125semidirect

Maximal subgroups

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

subgroupindex
#318236132
#318233802
#318232002
#318231892
#544×C2812
#1599281