Finite Group Databasebeta

← #49094228

Subgroups — #49094228

Order 35968.

316 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 53 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#31824089C211yesmaximal, characteristic, complemented
2#31823616C212yesmaximal, complemented
3#31823372C211yesmaximal, characteristic
4#31823201C212yesmaximal, complemented
5#323×C281C211yesmaximal, characteristic, complemented
6C22×D1124C2211yescharacteristic
7C22×C22⋊D281—21no—
8C2×#17985127—22no—
9#22582858—21no—
10#22582858C2212yes—
11#22582856—22no—
12#22582856—22no—
13C2×C22⋊Dic281—21no—
14C2×#17985115—21no—
15#22582801—22no—
16#22582786C2211yescharacteristic
17C2×C22⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yes—
19C23×D281—21no—
20C2×Dic562—21no—
21C2×Dic562D412yescomplemented
22C2×D1124—22no—
23C2×D1124—42no—
24C2×C22⋊D281—42no—
25C2×C22⋊D281—42no—
26C2×C22⋊D281—42no—
27C22×Dic281—21no—
28C22×Dic281—21no—
29C22×Dic281—21no—
30#17985127—44no—
31C4⋊Dic281—21no—
32C4⋊Dic281D412yescomplemented
33#17985117—22no—
34#17985117—22no—
35C22⋊Dic281—22no—
36C22⋊Dic281—22no—
37#17985115—42no—
38C24×C281D411yescharacteristic
39C22×C4×C281D411yescharacteristic
40C22×C4×C281C2311yescharacteristic
41C2×C8×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—
50Dic562—42no—
51Dic562—81no—
52D1124—24no—
53D1124—42no—
54C22⋊D281—48no—
55C2×Dic281—22no—
56C2×Dic281—22no—
57C2×Dic281—22no—
58C2×Dic281—41no—
59C2×Dic281—41no—
60C2×Dic281—81no—
61C2×Dic281—81no—
62C23×C281—21no—
63C23×C281—21no—
64C23×C281—41no—
65C23×C281—41no—
66C23×C281SD1612yescomplemented
67C23×C281C2×D411yescharacteristic
68C2×C4×C281—21no—
69C2×C4×C281—41no—
70C2×C4×C281—41no—
71C2×C4×C281C2×D412yes—
72C8×C281—42no—
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—
92Dic281—42no—
93Dic281—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#543—2811no—
105#450—2812no—
106#392—2811no—
107#328—2812no—
108#323D28111yescharacteristic, complemented
109C22×D4—2811no—
110C22×D4—5621no—
111C2×SD16—5622no—
112C22⋊Q8—2812no—
113C22⋊Q8—5622no—
114C22⋊Q8—5622no—
115C22⋊Q8—5621no—
116C2×C22⋊C4—5621no—
117C2×C22⋊C4—5621no—
118C2×C22⋊C4C2×D28111yescharacteristic
119#102—5622no—
120C22⋊C8C2×D28112yes—
121#95—2811no—
122C24—5621no—
123C24D112411yescharacteristic
124C2×Q8—2812no—
125C2×Q8—5621no—
126C2×D4—5622no—
127C2×D4—11242no—
128C2×D4—11242no—
129C2×D4—11242no—
130C2×D4—11242no—
131C22×C4—5621no—
132C22×C4—5621no—
133C22×C4—5621no—
134C22×C4D112411yescharacteristic
135C22×C4C22×D28111yescharacteristic
136SD16—11244no—
137C2×C8—22no—
138C4⋊C4—2812no—
139C4⋊C4—5622no—
140C4⋊C4—5621no—
141C4⋊C4—5622no—
142C22⋊C4—22no—
143C22⋊C4—5622no—
144C22⋊C4—5622no—
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#1798512712yescomplemented
158C23C2×D112411yescharacteristic
159Q8—11242no—
160Q8—22481no—
161D4—5624no—
162D4—11242no—
163D4—11248no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—5622no—
168C2×C4—5622no—
169C2×C4—5622no—
170C2×C4—11241no—
171C2×C4—11241no—
172C2×C4—22481no—
173C2×C4—22481no—
174C2×C4D4×D28112yes—
175C8—42no—
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#2258284911yescharacteristic
191C22C2×#1798512711yescharacteristic
192C22#2258291211yescharacteristic
193C4—22no—
194C4—41no—
195C4—11242no—
196C4—11242no—
197C4—11242no—
198C2—21no—
199C2—21no—
200C2—42no—
201C2—22482no—
202C2#3182360411yescharacteristic
203C2#3182363311yescharacteristic
204C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#323×C281C2
socleC22×C281#120
prime radical#31823372C2
hypercenter#323D281
hypocenterC281#1596
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
1. #31824089C2semidirect
2. #31823616C2semidirect
4. #31823201C2semidirect
5. #323×C281C2semidirect
21. C2×Dic562D4semidirect
32. C4⋊Dic281D4semidirect
66. C23×C281SD16semidirect
102. C281#1596semidirect
108. #323D281semidirect
157. C23#17985127semidirect

Maximal subgroups

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

subgroupindex
#318240892
#318236162
#318233722
#318232012
#323×C2812
#1596281