Finite Group Databasebeta

← #49094223

Subgroups — #49094223

Order 35968.

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

normal subgroups only

This group has 368 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#31824025C211yesmaximal, characteristic, complemented
2#31823599C212yesmaximal, complemented
3#31823372C211yesmaximal, characteristic, complemented
4#31823198C212yesmaximal, complemented
5#323×C281C211yesmaximal, characteristic, complemented
6C22×D1124C2211yescharacteristic, complemented
7C22×C22⋊D281—21no—
8C22×C22⋊D281—21no—
9C2×D2248—22no—
10#22582863—22no—
11#22582853—21no—
12#22582853C2212yes—
13#22582849—22no—
14C2×#17985115—21no—
15#22582801—22no—
16#22582786C2211yescharacteristic, complemented
17C2×C22⋊C4×C281C2211yescharacteristic
18C22⋊C8×C281C2212yescomplemented
19C23×D281—21no—
20C23×D281—21no—
21C2×D1124—21no—
22C2×D1124—22no—
23C2×D1124—42no—
24C2×D1124D412yescomplemented
25C2×C22⋊D281—22no—
26C2×C22⋊D281—22no—
27C2×C22⋊D281—42no—
28C2×C22⋊D281—42no—
29C2×C22⋊D281—42no—
30C2×C22⋊D281—42no—
31C2×C22⋊D281—42no—
32C22×Dic281—21no—
33C22×Dic281—21no—
34D2248—44no—
35C4⋊Dic281—21no—
36C4⋊Dic281D412yescomplemented
37#17985115—22no—
38#17985115—22no—
39#17985115—42no—
40C24×C281D411yescharacteristic
41C22×C4×C281D411yescharacteristic
42C22×C4×C281C2311yescharacteristic
43C2×C8×C281—22no—
44C22⋊C4×C281—22no—
45C22×D281—22no—
46C22×D281—22no—
47C22×D281—41no—
48C22×D281—41no—
49C22×D281—42no—
50C22×D281—41no—
51C22×D281—41no—
52C22×D281—41no—
53C22×D281—41no—
54C22×D281—81no—
55C22×D281—81no—
56D1124—24no—
57D1124—42no—
58D1124—42no—
59D1124—81no—
60C22⋊D281—44no—
61C22⋊D281—48no—
62C22⋊D281—42no—
63C22⋊D281—42no—
64C2×Dic281—22no—
65C2×Dic281—22no—
66C2×Dic281—41no—
67C2×Dic281—42no—
68C2×Dic281—41no—
69C23×C281—21no—
70C23×C281—21no—
71C23×C281—41no—
72C23×C281—41no—
73C23×C281D812yescomplemented
74C23×C281C2×D411yescharacteristic
75C2×C4×C281—21no—
76C2×C4×C281—41no—
77C2×C4×C281—41no—
78C2×C4×C281C2×D412yes—
79C8×C281—42no—
80C22×C281—21no—
81C22×C281—21no—
82C22×C281—22no—
83C22×C281—42no—
84C22×C281—41no—
85C22×C281—41no—
86C22×C281—81no—
87C22×C281#12011yescharacteristic
88C22×C281C2×D811yescharacteristic
89C22×C281AGL(1,ℤ/8)11yescharacteristic
90C2×D281—42no—
91C2×D281—42no—
92C2×D281—42no—
93C2×D281—42no—
94C2×D281—42no—
95C2×D281—42no—
96C2×D281—81no—
97C2×D281—81no—
98C2×D281—84no—
99C2×D281—81no—
100C2×D281—81no—
101C4×C281—22no—
102C4×C281—41no—
103Dic281—42no—
104Dic281—42no—
105C2×C281—21no—
106C2×C281—21no—
107C2×C281—42no—
108C2×C281#44711yescharacteristic
109C2×C281#45311yescharacteristic
110C2×C281B(4,𝔽2)11yescharacteristic
111D281—82no—
112D281—82no—
113C281#159511yescharacteristic, complemented, Sylow
114#1595—2811nomaximal, Sylow
115#534—2811no—
116#447—2812no—
117#392—2811no—
118#327—2812no—
119#323D28111yescharacteristic, complemented
120C22×D4—2811no—
121C22×D4—5621no—
122C22×D4—5621no—
123C2×D8—5622no—
124#123—5622no—
125#121—2812no—
126#121—5621no—
127#120—5622no—
128C2×C22⋊C4—5621no—
129C2×C22⋊C4C2×D28111yescharacteristic
130#102—5622no—
131C22⋊C8C2×D28112yescomplemented
132#95—2811no—
133C24—5621no—
134C24—5621no—
135C24D112411yescharacteristic
136C2×D4—2812no—
137C2×D4—5621no—
138C2×D4—5622no—
139C2×D4—5622no—
140C2×D4—5622no—
141C2×D4—11242no—
142C2×D4—11242no—
143C2×D4—11242no—
144C2×D4—11242no—
145C2×D4—11242no—
146C2×D4—11242no—
147C22×C4—5621no—
148C22×C4—5621no—
149C22×C4D112411yescharacteristic
150C22×C4C22×D28111yescharacteristic
151D8—11244no—
152C2×C8—22no—
153C4⋊C4—2812no—
154C4⋊C4—5621no—
155C22⋊C4—22no—
156C22⋊C4—5622no—
157C22⋊C4—5622no—
158C22⋊C4—11242no—
159C23—21no—
160C23—21no—
161C23—41no—
162C23—41no—
163C23—5622no—
164C23—5622no—
165C23—11241no—
166C23—11241no—
167C23—11241no—
168C23—11242no—
169C23—11241no—
170C23—11241no—
171C23—11241no—
172C23—22481no—
173C23—22481no—
174C23D224812yescomplemented
175C23C2×D112411yescharacteristic
176D4—5624no—
177D4—11242no—
178D4—11242no—
179D4—11244no—
180D4—11248no—
181D4—11242no—
182D4—11242no—
183D4—22481no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—5622no—
188C2×C4—5622no—
189C2×C4—11241no—
190C2×C4—11242no—
191C2×C4—11241no—
192C2×C4D4×D28112yes—
193C8—42no—
194C22—21no—
195C22—21no—
196C22—22no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22—81no—
201C22—11242no—
202C22—11242no—
203C22—11242no—
204C22—11242no—
205C22—11242no—
206C22—11242no—
207C22—22481no—
208C22—22481no—
209C22—22484no—
210C22—22481no—
211C22—22481no—
212C22#2258284911yescharacteristic
213C22C2×D224811yescharacteristic
214C22#2258290711yescharacteristic
215C4—22no—
216C4—41no—
217C4—11242no—
218C4—11242no—
219C2—21no—
220C2—21no—
221C2—42no—
222C2—22482no—
223C2—22482no—
224C2#3182359911yescharacteristic
225C2#3182363311yescharacteristic
226C2#3182365111yescharacteristic
subgroupG/H
centerC22#22582849
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#323×C281C2
socleC22×C281#120
hypercenter#323D281
hypocenterC281#1595
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. #31824025C2semidirect
2. #31823599C2semidirect
3. #31823372C2semidirect
4. #31823198C2semidirect
5. #323×C281C2semidirect
6. C22×D1124C22semidirect
16. #22582786C22semidirect
18. C22⋊C8×C281C22semidirect
24. C2×D1124D4semidirect
36. C4⋊Dic281D4semidirect
73. C23×C281D8semidirect
113. C281#1595semidirect
119. #323D281semidirect
131. C22⋊C8C2×D281semidirect
174. C23D2248semidirect

Maximal subgroups

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

subgroupindex
#318240252
#318235992
#318233722
#318231982
#323×C2812
#1595281