Finite Group Databasebeta

← #49094332

Subgroups — #49094332

Order 35968.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#31824060C211yesmaximal, characteristic
2#31823798C211yesmaximal, characteristic, complemented
3#31823781C211yesmaximal, characteristic
4#31823199C211yesmaximal, characteristic, complemented
5#31823196C211yesmaximal, characteristic
6#31823189C211yesmaximal, characteristic, complemented
7#400×C281C211yesmaximal, characteristic, complemented
8#22582874—21no—
9#22582869—21no—
10#22582864—21no—
11#22582862—21no—
12#22582858C2211yescharacteristic
13#22582857—21no—
14#22582853C2211yescharacteristic
15C4×C22⋊D281—21no—
16#22582812—21no—
17#22582810—21no—
18#22582802—21no—
19#22582799—21no—
20C22⋊#14555886C2211yescharacteristic
21C22⋊#14555886C2211yescharacteristic
22C2×C4⋊C4×C281C2211yescharacteristic
23C2×C4⋊C4×C281C2211yescharacteristic
24#95×C281—21no—
25#95×C281—21no—
26#95×C281C2211yescharacteristic
27C2×Dic562D411yescharacteristic
28C2×D1124D411yescharacteristic
29C2×C22⋊D281—21no—
30C2×C4×D281—21no—
31C2×#14555886—21no—
32C2×#14555886—21no—
33C4⋊Dic281D411yescharacteristic
34C4⋊Dic281D411yescharacteristic
35#17985117—21no—
36#17985117—21no—
37#17985117—21no—
38#17985117—21no—
39C22⋊Dic281—21no—
40#17985115—21no—
41#17985115—21no—
42#17985115—21no—
43#17985115—21no—
44C4×Dic281—21no—
45C22×C4×C281—21no—
46C22×C4×C281—21no—
47C22×C4×C281D411yescharacteristic
48C22×C4×C281D411yescharacteristic
49C22×C4×C281C2311yescharacteristic
50C4⋊C4×C281—21no—
51C4⋊C4×C281—21no—
52C4⋊C4×C281—21no—
53C4⋊C4×C281—21no—
54C22×D281—21no—
55Dic562—41no—
56D1124—41no—
57C22⋊D281—41no—
58C22⋊D281—41no—
59C2×Dic281—21no—
60C2×Dic281—21no—
61C2×Dic281—21no—
62C4×D281—81no—
63#14555886—41no—
64#14555886—41no—
65C23×C281C2×D411yescharacteristic
66C2×C4×C281—21no—
67C2×C4×C281—21no—
68C2×C4×C281—21no—
69C2×C4×C281—21no—
70C2×C4×C281—41no—
71C2×C4×C281—41no—
72C2×C4×C281—41no—
73C2×C4×C281—41no—
74C2×C4×C281—42no—
75C2×C4×C281—41no—
76C2×C4×C281—41no—
77C2×C4×C281C2×D411yescharacteristic
78C2×C4×C281C2×D411yescharacteristic
79C22×C281—21no—
80C22×C281—21no—
81C22×C281#12011yescharacteristic
82C22×C281#13511yescharacteristic
83C22×C281#13711yescharacteristic
84C2×D281—41no—
85C2×D281—41no—
86C2×D281—41no—
87C4×C281—21no—
88C4×C281—21no—
89C4×C281—41no—
90C4×C281—41no—
91C4×C281—81no—
92C4×C281—81no—
93Dic281—41no—
94Dic281—41no—
95Dic281—41no—
96C2×C281—21no—
97C2×C281—21no—
98C2×C281#45211yescharacteristic
99C2×C281#45411yescharacteristic
100C2×C281#45811yescharacteristic
101D281—81no—
102C281#161511yescharacteristic, complemented, Sylow
103#1615—2811nomaximal, Sylow
104#539—2811no—
105#484—2811no—
106#481—2811no—
107#400D28111yescharacteristic, complemented
108#328—2811no—
109#327—2811no—
110#324—2811no—
111#126—5621no—
112#125—5621no—
113#123—5621no—
114#123—5621no—
115C22⋊Q8—2811no—
116C22⋊Q8—5621no—
117#121—2811no—
118C4×D4—5621no—
119C2×C4⋊C4C2×D28111yescharacteristic
120C2×C4⋊C4C2×D28111yescharacteristic
121#107—5621no—
122#106—5621no—
123#103—5621no—
124#102—5621no—
125C22⋊C8—2811no—
126C22⋊C8—2811no—
127#95—21no—
128#95—21no—
129#95C2×D28111yescharacteristic
130C2×Q8—2811no—
131C2×D4—2811no—
132C2×D4—5621no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—5621no—
136C22×C4C22⋊D28111yescharacteristic
137C22×C4C22⋊D28111yescharacteristic
138C22×C4C22×D28111yescharacteristic
139C2×C8—5621no—
140C2×C8—5621no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—2811no—
146C4⋊C4—2811no—
147C4⋊C4—5621no—
148C4⋊C4—5621no—
149C4⋊C4—5621no—
150C4⋊C4—5621no—
151C22⋊C4—5621no—
152C22⋊C4—5621no—
153C22⋊C4—5621no—
154C22⋊C4—5621no—
155C22⋊C4—5621no—
156C42—5621no—
157C23—5621no—
158C23C2×C22⋊D28111yescharacteristic
159Q8—11241no—
160D4—11241no—
161D4—11241no—
162D4—11241no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—5621no—
175C2×C4—5621no—
176C2×C4—5621no—
177C2×C4—22481no—
178C2×C4D4×D28111yescharacteristic
179C2×C4D4×D28111yescharacteristic
180C8—11241no—
181C8—11241no—
182C22—21no—
183C22—21no—
184C22—11241no—
185C22—11241no—
186C22—11241no—
187C22#2258284711yescharacteristic
188C22#2258289911yescharacteristic
189C22#2258291011yescharacteristic
190C4—21no—
191C4—21no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—81no—
196C4—11241no—
197C4—11241no—
198C4—11241no—
199C2—21no—
200C2—21no—
201C2—22481no—
202C2#3182362311yescharacteristic
203C2#3182363511yescharacteristic
204C2#3182365211yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#400×C281C2
socleC22×C281#120
prime radical#22582853C22
hypercenter#400D281
hypocenterC281#1615
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #31823798C2semidirect
4. #31823199C2semidirect
6. #31823189C2semidirect
7. #400×C281C2semidirect
102. C281#1615semidirect
107. #400D281semidirect

Maximal subgroups

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

subgroupindex
#318240602
#318237982
#318237812
#318231992
#318231962
#318231892
#400×C2812
#1615281