Finite Group Databasebeta

← #49094321

Subgroups — #49094321

Order 35968.

288 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 51 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#31824021C211yesmaximal, characteristic
2#31823781C211yesmaximal, characteristic, complemented
3#31823398C211yesmaximal, characteristic, complemented
4#31823198C211yesmaximal, characteristic, complemented
5#31823197C211yesmaximal, characteristic, complemented
6#31823186C211yesmaximal, characteristic, complemented
7#481×C281C211yesmaximal, characteristic, complemented
8C2×D4×D281—21no—
9#22582864—21no—
10#22582861—21no—
11#22582853C2211yescharacteristic
12#22582851—21no—
13#22582849—21no—
14#22582847—21no—
15C2×#17985117—21no—
16C2×#17985115—21no—
17C2×#17985115C2211yescharacteristic
18#22582810—21no—
19#22582799—21no—
20C22⋊#14555886C2211yescharacteristic, complemented
21#22582786C2211yescharacteristic, complemented
22#121×C281C2211yescharacteristic
23C2×C4⋊C4×C281C2211yescharacteristic, complemented
24#106×C281—21no—
25#102×C281—21no—
26C22⋊C8×C281C2211yescharacteristic, complemented
27C23×D281—21no—
28C23×D281D411yescharacteristic
29C2×D1124—21no—
30C2×D1124D411yescharacteristic
31C2×C22⋊D281—21no—
32C2×C22⋊D281—21no—
33C2×C22⋊D281—21no—
34D4×D281—42no—
35D4×D281—42no—
36C22×Dic281—21no—
37C22×Dic281D411yescharacteristic
38C2×C4×D281—21no—
39C2×#14555886—21no—
40C4⋊Dic281D411yescharacteristic
41#17985117—21no—
42#17985117—42no—
43C22⋊Dic281—21no—
44#17985115—21no—
45#17985115—21no—
46#17985115—21no—
47#17985115—21no—
48#17985115—42no—
49C2×D4×C281—21no—
50C2×D4×C281D411yescharacteristic
51C22×C4×C281—21no—
52C22×C4×C281C2311yescharacteristic
53C2×C8×C281—21no—
54C4⋊C4×C281—21no—
55C4⋊C4×C281—21no—
56C4⋊C4×C281D411yescharacteristic
57C22⋊C4×C281—21no—
58C22×D281—21no—
59C22×D281—21no—
60C22×D281—21no—
61C22×D281—42no—
62C22×D281—41no—
63C22×D281—41no—
64C22×D281—81no—
65C22×D281—81no—
66C22×D281SD1612yes—
67D1124—41no—
68D1124—42no—
69C22⋊D281—42no—
70C22⋊D281—41no—
71C22⋊D281—41no—
72C22⋊D281—81no—
73C2×Dic281—22no—
74C2×Dic281—21no—
75C2×Dic281—21no—
76C2×Dic281—41no—
77C2×Dic281—41no—
78C2×Dic281—41no—
79C4×D281—42no—
80#14555886—41no—
81C23×C281—21no—
82C23×C281C2×D411yescharacteristic
83D4×C281—41no—
84D4×C281—41no—
85D4×C281—41no—
86C2×C4×C281—21no—
87C2×C4×C281—41no—
88C2×C4×C281—41no—
89C2×C4×C281—41no—
90C2×C4×C281—41no—
91C2×C4×C281C2×D411yescharacteristic
92C2×C4×C281C2×D411yescharacteristic
93C8×C281—41no—
94C22×C281—21no—
95C22×C281—21no—
96C22×C281—41no—
97C22×C281—41no—
98C22×C281—41no—
99C22×C281#12011yescharacteristic
100C22×C281C2×SD1611yescharacteristic
101C22×C281AGL(1,ℤ/8)11yescharacteristic
102C2×D281—22no—
103C2×D281—41no—
104C2×D281—41no—
105C2×D281—42no—
106C2×D281—41no—
107C2×D281—41no—
108C2×D281—41no—
109C2×D281—81no—
110C2×D281—84no—
111C4×C281—21no—
112C4×C281—21no—
113C4×C281—41no—
114C4×C281—81no—
115Dic281—42no—
116Dic281—41no—
117Dic281—41no—
118C2×C281—21no—
119C2×C281—21no—
120C2×C281—81no—
121C2×C281#45011yescharacteristic
122C2×C281#45311yescharacteristic
123C2×C281#45811yescharacteristic
124D281—42no—
125D281—81no—
126C281#161311yescharacteristic, complemented, Sylow
127#1613—2811nomaximal, Sylow
128#534—2811no—
129#481—2811no—
130#481D28111yescharacteristic, complemented
131#399—2811no—
132#327—2811no—
133#327—2811no—
134#323—2811no—
135C22×D4—5621no—
136#123—5621no—
137#123—5621no—
138#121—2811no—
139#121—5621no—
140#121C2×D28111yescharacteristic
141#120—5621no—
142#120—5621no—
143C2×C4⋊C4—5621no—
144C2×C4⋊C4C2×D28111yescharacteristic, complemented
145C2×C22⋊C4—2811no—
146C2×C22⋊C4—5621no—
147#106—21no—
148#106—5621no—
149#102—21no—
150#102—5621no—
151C22⋊C8—2811no—
152C22⋊C8C2×D28111yescharacteristic, complemented
153#95—2811no—
154C24—2811no—
155C24—5621no—
156C2×D4—21no—
157C2×D4—2811no—
158C2×D4—5621no—
159C2×D4—5621no—
160C2×D4—5621no—
161C2×D4—5621no—
162C2×D4—11242no—
163C2×D4—11242no—
164C2×D4C22⋊D28111yescharacteristic
165C22×C4—21no—
166C22×C4—2811no—
167C22×C4—5621no—
168C22×C4—5621no—
169C22×C4C22×D28111yescharacteristic
170C2×C8—21no—
171C2×C8—5621no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—2811no—
175C4⋊C4—5621no—
176C4⋊C4—11242no—
177C4⋊C4C22⋊D28111yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—5621no—
180C22⋊C4—5621no—
181C22⋊C4—5621no—
182C22⋊C4—5621no—
183C22⋊C4—5621no—
184C22⋊C4—11242no—
185C23—21no—
186C23—2812no—
187C23—5621no—
188C23—5621no—
189C23—5621no—
190C23—11241no—
191C23—11241no—
192C23—11242no—
193C23—22481no—
194C23—22481no—
195C23D4×D28111yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—11241no—
200D4—11242no—
201D4—11242no—
202D4—11241no—
203D4—11241no—
204D4—22481no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—5622no—
211C2×C4—5621no—
212C2×C4—5621no—
213C2×C4—11242no—
214C2×C4—11241no—
215C2×C4—11241no—
216C2×C4—11241no—
217C2×C4D4×D28111yescharacteristic
218C2×C4C2×C22⋊D28111yescharacteristic
219C8—41no—
220C8—11241no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—5622no—
227C22—11242no—
228C22—11241no—
229C22—11241no—
230C22—11241no—
231C22—11241no—
232C22—11241no—
233C22—22481no—
234C22—22484no—
235C22#2258284711yescharacteristic
236C22SD16×D28111yescharacteristic
237C22#2258290611yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—11242no—
243C4—11241no—
244C4—11241no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—11242no—
249C2—22481no—
250C2#3182361211yescharacteristic
251C2#3182362911yescharacteristic
252C2#3182365211yescharacteristic
subgroupG/H
centerC22#22582847
commutator, cosocleC22×C4×C281C23
FrattiniC22×C4C22×D281
Fitting#481×C281C2
socleC22×C281#120
prime radical#31824021C2
hypercenter#481D281
hypocenterC281#1613
LCSG ▷ C22×C4×C281 ▷ C22×C281 ▷ C281
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #31823781C2semidirect
3. #31823398C2semidirect
4. #31823198C2semidirect
5. #31823197C2semidirect
6. #31823186C2semidirect
7. #481×C281C2semidirect
20. C22⋊#14555886C22semidirect
21. #22582786C22semidirect
23. C2×C4⋊C4×C281C22semidirect
26. C22⋊C8×C281C22semidirect
126. C281#1613semidirect
130. #481D281semidirect
144. C2×C4⋊C4C2×D281semidirect
152. C22⋊C8C2×D281semidirect

Maximal subgroups

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

subgroupindex
#318240212
#318237812
#318233982
#318231982
#318231972
#318231862
#481×C2812
#1613281