Finite Group Databasebeta

← #49094231

Subgroups — #49094231

Order 35968.

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

normal subgroups only

This group has 272 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#31824062C211yesmaximal, characteristic, complemented
2#31823597C211yesmaximal, characteristic
3#31823377C211yesmaximal, characteristic, complemented
4#31823200C211yesmaximal, characteristic, complemented
5#31823198C211yesmaximal, characteristic, complemented
6#31823188C211yesmaximal, characteristic, complemented
7#450×C281C211yesmaximal, characteristic, complemented
8C2×#17985123—21no—
9#22582874—21no—
10#22582870—21no—
11#22582864—21no—
12#22582863—21no—
13#22582855—21no—
14#22582853C2211yescharacteristic
15#22582839—21no—
16C2×#17985117C2211yescharacteristic
17C2×C22⋊Dic281—21no—
18C2×C22⋊Dic281—21no—
19#22582800—21no—
20C22⋊#14555886C2211yescharacteristic
21#22582786C2211yescharacteristic
22C22×D4×C281C2211yescharacteristic
23C2×SD16×C281—21no—
24C22⋊Q8×C281C2211yescharacteristic
25#102×C281—21no—
26C22⋊C8×C281C2211yescharacteristic
27C2×D1124D411yescharacteristic
28C2×C22⋊D281—21no—
29C22×Dic281—21no—
30C22×Dic281D411yescharacteristic
31C22×Dic281D411yescharacteristic
32C2×C4×D281—21no—
33#17985123—42no—
34C2×#14555886—21no—
35C4⋊Dic281—21no—
36C4⋊Dic281—21no—
37C4⋊Dic281D411yescharacteristic
38#17985117—21no—
39#17985117—21no—
40#17985117—21no—
41C22⋊Dic281—42no—
42C22⋊Dic281—42no—
43#17985115—21no—
44#17985115—21no—
45#17985115—21no—
46#17985115—21no—
47C4×Dic281—21no—
48C24×C281—21no—
49C2×Q8×C281D411yescharacteristic
50C2×D4×C281—21no—
51C2×D4×C281—21no—
52C2×D4×C281—42no—
53C22×C4×C281C2311yescharacteristic
54SD16×C281—42no—
55C2×C8×C281—21no—
56C4⋊C4×C281—21no—
57C4⋊C4×C281D411yescharacteristic
58C22⋊C4×C281—21no—
59C22×D281—21no—
60D1124—41no—
61C22⋊D281—41no—
62C22⋊D281—41no—
63C2×Dic281—21no—
64C2×Dic281—21no—
65C2×Dic281—21no—
66C2×Dic281—21no—
67C2×Dic281—21no—
68C2×Dic281—41no—
69C2×Dic281—41no—
70C2×Dic281—41no—
71C2×Dic281—41no—
72C4×D281—81no—
73#14555886—41no—
74C23×C281—22no—
75C23×C281—41no—
76C23×C281—41no—
77C23×C281—41no—
78C23×C281—41no—
79C23×C281—41no—
80C23×C281—41no—
81C23×C281C2×D411yescharacteristic
82Q8×C281—41no—
83D4×C281—22no—
84D4×C281—22no—
85D4×C281—41no—
86D4×C281—41no—
87C2×C4×C281—21no—
88C2×C4×C281—21no—
89C2×C4×C281—41no—
90C2×C4×C281C2×D411yescharacteristic
91C2×C4×C281C2×D411yescharacteristic
92C8×C281—41no—
93C22×C281—21no—
94C22×C281—21no—
95C22×C281—42no—
96C22×C281—42no—
97C22×C281—42no—
98C22×C281—81no—
99C22×C281—81no—
100C22×C281—81no—
101C22×C281—81no—
102C22×C281#12011yescharacteristic
103C22×C281#13511yescharacteristic
104C22×C281AGL(1,ℤ/8)11yescharacteristic
105C2×D281—41no—
106C2×D281—41no—
107C2×D281—41no—
108C4×C281—21no—
109C4×C281—21no—
110C4×C281—41no—
111C4×C281—41no—
112Dic281—41no—
113Dic281—41no—
114Dic281—41no—
115Dic281—81no—
116C2×C281—21no—
117C2×C281—21no—
118C2×C281—82no—
119C2×C281#44911yescharacteristic
120C2×C281#45411yescharacteristic
121C2×C281B(4,𝔽2)11yescharacteristic
122D281—81no—
123C281#159711yescharacteristic, complemented, Sylow
124#1597—2811nomaximal, Sylow
125#539—2811no—
126#450D28111yescharacteristic, complemented
127#447—2811no—
128#394—2811no—
129#328—2811no—
130#327—2811no—
131#324—2811no—
132C22×D4C2×D28111yescharacteristic
133C2×SD16—21no—
134C2×D8—5621no—
135#126—5621no—
136#125—5621no—
137#123—5621no—
138#123—5621no—
139C22⋊Q8—5621no—
140C22⋊Q8C2×D28111yescharacteristic
141#121—2811no—
142C4×D4—5621no—
143C2×C4⋊C4—2811no—
144C2×C22⋊C4—5621no—
145C2×C22⋊C4—5621no—
146#102—21no—
147#102—5621no—
148C22⋊C8—2811no—
149C22⋊C8C2×D28111yescharacteristic
150#95—2811no—
151C24—21no—
152C2×Q8C22⋊D28111yescharacteristic
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—42no—
156C2×D4—2811no—
157C2×D4—5621no—
158C22×C4—2811no—
159C22×C4—2811no—
160C22×C4—5621no—
161C22×C4—5621no—
162C22×C4C22×D28111yescharacteristic
163SD16—42no—
164D8—11242no—
165C2×C8—21no—
166C2×C8—5621no—
167C4⋊C4—21no—
168C4⋊C4—2811no—
169C4⋊C4—5621no—
170C4⋊C4—5621no—
171C4⋊C4—5621no—
172C4⋊C4—5621no—
173C4⋊C4—5621no—
174C4⋊C4C22⋊D28111yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—5621no—
177C22⋊C4—5621no—
178C22⋊C4—5621no—
179C22⋊C4—5621no—
180C22⋊C4—11242no—
181C22⋊C4—11242no—
182C42—5621no—
183C23—22no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23—41no—
188C23—41no—
189C23—41no—
190C23—5621no—
191C23D4×D28111yescharacteristic
192Q8—41no—
193D4—22no—
194D4—22no—
195D4—41no—
196D4—41no—
197D4—11241no—
198D4—11241no—
199D4—11241no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—5621no—
204C2×C4—5621no—
205C2×C4—5621no—
206C2×C4—5621no—
207C2×C4—5621no—
208C2×C4—11241no—
209C2×C4—11241no—
210C2×C4—11241no—
211C2×C4—11241no—
212C2×C4—22481no—
213C2×C4D4×D28111yescharacteristic
214C2×C4C2×C22⋊D28111yescharacteristic
215C8—41no—
216C8—11241no—
217C22—21no—
218C22—21no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—81no—
223C22—81no—
224C22—81no—
225C22—81no—
226C22—11241no—
227C22—11241no—
228C22—11241no—
229C22#2258284711yescharacteristic
230C22#2258290011yescharacteristic
231C22#2258290611yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—41no—
236C4—11241no—
237C4—11241no—
238C4—11241no—
239C4—22481no—
240C2—21no—
241C2—21no—
242C2—82no—
243C2—22481no—
244C2#3182360711yescharacteristic
245C2#3182363411yescharacteristic
246C2#3182364911yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#450×C281C2
socleC22×C281#120
prime radical#31823597C2
hypercenter#450D281
hypocenterC281#1597
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #31824062C2semidirect
3. #31823377C2semidirect
4. #31823200C2semidirect
5. #31823198C2semidirect
6. #31823188C2semidirect
7. #450×C281C2semidirect
123. C281#1597semidirect
126. #450D281semidirect

Maximal subgroups

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

subgroupindex
#318240622
#318235972
#318233772
#318232002
#318231982
#318231882
#450×C2812
#1597281