Finite Group Databasebeta

← #49094226

Subgroups — #49094226

Order 35968.

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

normal subgroups only

This group has 316 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, complemented
2#31823372C211yesmaximal, characteristic
3#31823200C212yesmaximal, complemented
4#31823187C211yesmaximal, characteristic, complemented
5#543×C281C211yesmaximal, characteristic, complemented
6C22×D1124C2211yescharacteristic
7C22×C22⋊D281—21no—
8C2×#17985125—22no—
9C2×#17985115—21no—
10#22582799—22no—
11C22⋊#14555886C2212yes—
12#22582786C2211yescharacteristic
13C22⋊Q8×C281—22no—
14C22⋊Q8×C281—21no—
15C22⋊Q8×C281—22no—
16C22⋊Q8×C281C2212yes—
17C2×C22⋊C4×C281—21no—
18C2×C22⋊C4×C281C2211yescharacteristic
19C23×D281—21no—
20C2×D1124—22no—
21C2×D1124—42no—
22C2×C22⋊D281—42no—
23C2×C22⋊D281—42no—
24C2×C22⋊D281—42no—
25C22×Dic281—21no—
26#17985125—44no—
27C2×#14555886—22no—
28#17985115—42no—
29C24×C281D411yescharacteristic
30C2×Q8×C281—21no—
31C2×Q8×C281D412yescomplemented
32C22×C4×C281—21no—
33C22×C4×C281—21no—
34C22×C4×C281D411yescharacteristic
35C22×C4×C281C2311yescharacteristic
36C4⋊C4×C281—21no—
37C4⋊C4×C281—22no—
38C4⋊C4×C281—22no—
39C4⋊C4×C281D412yescomplemented
40C22⋊C4×C281—22no—
41C22⋊C4×C281—22no—
42C22⋊C4×C281—22no—
43C22×D281—22no—
44C22×D281—41no—
45C22×D281—41no—
46C22×D281—41no—
47C22×D281—41no—
48C22×D281—41no—
49C22×D281—41no—
50D1124—24no—
51D1124—42no—
52C22⋊D281—48no—
53C2×Dic281—22no—
54C2×Dic281—41no—
55C2×Dic281—41no—
56#14555886—42no—
57C23×C281—21no—
58C23×C281—21no—
59C23×C281—41no—
60C23×C281—41no—
61C23×C281SD1612yescomplemented
62C23×C281C2×D411yescharacteristic
63Q8×C281—42no—
64Q8×C281—81no—
65C2×C4×C281—22no—
66C2×C4×C281—21no—
67C2×C4×C281—22no—
68C2×C4×C281—41no—
69C2×C4×C281—41no—
70C2×C4×C281—81no—
71C2×C4×C281—81no—
72C2×C4×C281C2×D412yes—
73C22×C281—21no—
74C22×C281—21no—
75C22×C281—22no—
76C22×C281—42no—
77C22×C281—41no—
78C22×C281—41no—
79C22×C281—81no—
80C22×C281#12011yescharacteristic
81C22×C281C2×SD1611yescharacteristic
82C22×C281#13711yescharacteristic
83C2×D281—42no—
84C2×D281—42no—
85C2×D281—42no—
86C2×D281—81no—
87C2×D281—81no—
88C2×D281—81no—
89C2×D281—81no—
90C4×C281—22no—
91C4×C281—41no—
92C4×C281—42no—
93C4×C281—42no—
94Dic281—42no—
95C2×C281—21no—
96C2×C281—21no—
97C2×C281—42no—
98C2×C281#44811yescharacteristic
99C2×C281#45311yescharacteristic
100C2×C281B(4,𝔽2)11yescharacteristic
101D281—82no—
102C281#159611yescharacteristic, complemented, Sylow
103#1596—2811nomaximal, Sylow
104#543D28111yescharacteristic, complemented
105#450—2812no—
106#392—2811no—
107#328—2812no—
108#323—2811no—
109C22×D4—2811no—
110C22×D4—5621no—
111C2×SD16—5622no—
112C22⋊Q8—22no—
113C22⋊Q8—21no—
114C22⋊Q8—22no—
115C22⋊Q8C2×D28112yes—
116C2×C22⋊C4—21no—
117C2×C22⋊C4—5621no—
118C2×C22⋊C4C2×D28111yescharacteristic
119#102—5622no—
120C22⋊C8—2812no—
121#95—2811no—
122C24—5621no—
123C24C22⋊D28111yescharacteristic
124C2×Q8—21no—
125C2×Q8C22⋊D28112yescomplemented
126C2×D4—5622no—
127C2×D4—11242no—
128C2×D4—11242no—
129C2×D4—11242no—
130C2×D4—11242no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—5621no—
134C22×C4C22⋊D28111yescharacteristic
135C22×C4C22×D28111yescharacteristic
136SD16—11244no—
137C2×C8—5622no—
138C4⋊C4—21no—
139C4⋊C4—22no—
140C4⋊C4—22no—
141C4⋊C4C22⋊D28112yescomplemented
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—22no—
145C22⋊C4—11242no—
146C23—21no—
147C23—21no—
148C23—41no—
149C23—41no—
150C23—5622no—
151C23—11241no—
152C23—11241no—
153C23—11241no—
154C23—11241no—
155C23—11241no—
156C23—11241no—
157C23#1798512512yescomplemented
158C23C2×C22⋊D28111yescharacteristic
159Q8—42no—
160Q8—81no—
161D4—5624no—
162D4—11242no—
163D4—11248no—
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—81no—
170C2×C4—81no—
171C2×C4—5622no—
172C2×C4—11241no—
173C2×C4—11241no—
174C2×C4C2×C22⋊D28112yes—
175C8—11242no—
176C22—21no—
177C22—21no—
178C22—22no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—11242no—
184C22—11242no—
185C22—11242no—
186C22—22481no—
187C22—22481no—
188C22—22481no—
189C22—22481no—
190C22#2258284811yescharacteristic
191C22C2×#1798512511yescharacteristic
192C22#2258291011yescharacteristic
193C4—22no—
194C4—41no—
195C4—42no—
196C4—42no—
197C4—11242no—
198C2—21no—
199C2—21no—
200C2—42no—
201C2—22482no—
202C2#3182360211yescharacteristic
203C2#3182363111yescharacteristic
204C2#3182365011yescharacteristic
subgroupG/H
centerC22#22582848
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#543×C281C2
socleC22×C281#120
prime radical#31823372C2
hypercenter#543D281
hypocenterC281#1596
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #543

Complements

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

NH ≅ G/Ntype
1. #31823613C2semidirect
3. #31823200C2semidirect
4. #31823187C2semidirect
5. #543×C281C2semidirect
31. C2×Q8×C281D4semidirect
39. C4⋊C4×C281D4semidirect
61. C23×C281SD16semidirect
102. C281#1596semidirect
104. #543D281semidirect
125. C2×Q8C22⋊D281semidirect
141. C4⋊C4C22⋊D281semidirect
157. C23#17985125semidirect

Maximal subgroups

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

subgroupindex
#318236132
#318233722
#318232002
#318231872
#543×C2812
#1596281