Finite Group Databasebeta

← #49120207

Subgroups — #49120207

Order 36224.

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

normal subgroups only

This group has 320 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#31826615C211yesmaximal, characteristic, complemented
2#31826598C211yesmaximal, characteristic, complemented
3#31826374C211yesmaximal, characteristic, complemented
4#31826202C211yesmaximal, characteristic, complemented
5#31826199C211yesmaximal, characteristic, complemented
6#31826189C211yesmaximal, characteristic, complemented
7#538×C283C211yesmaximal, characteristic, complemented
8C22×D1132C2211yescharacteristic
9C22×C22⋊D283—21no—
10C2×#17985379—21no—
11C2×#17985377—21no—
12C2×(C2×D283)⋊C4—21no—
13#22583530—21no—
14#22583530—21no—
15C22⋊(C283⋊C8)C2211yescharacteristic
16C22⋊(C283⋊C8)C2211yescharacteristic
17C283⋊#95C2211yescharacteristic
18#126×C283—21no—
19#124×C283—21no—
20#123×C283—21no—
21C22⋊Q8×C283C2211yescharacteristic
22#121×C283—21no—
23#121×C283C2211yescharacteristic
24#120×C283—21no—
25C4×D4×C283—21no—
26C2×C22⋊C4×C283C2211yescharacteristic
27C23×D283—21no—
28C2×D1132—21no—
29C2×D1132—21no—
30C2×D1132—42no—
31C2×C22⋊D283—42no—
32C2×C22⋊D283—42no—
33C2×C22⋊D283—42no—
34C22×Dic283—21no—
35#17985379—42no—
36#17985377—42no—
37C2×C283⋊C8—21no—
38C2×C283⋊C8—21no—
39(C2×D283)⋊C4—42no—
40C24×C283D411yescharacteristic
41C2×Q8×C283D411yescharacteristic, complemented
42C2×D4×C283—21no—
43C2×D4×C283—21no—
44C2×D4×C283—21no—
45C2×D4×C283D411yescharacteristic, complemented
46C22×C4×C283—21no—
47C22×C4×C283D411yescharacteristic
48C22×C4×C283C2311yescharacteristic
49C4⋊C4×C283—21no—
50C4⋊C4×C283—21no—
51C4⋊C4×C283D411yescharacteristic, complemented
52C4⋊C4×C283D411yescharacteristic, complemented
53C22⋊C4×C283—21no—
54C22⋊C4×C283—21no—
55C22⋊C4×C283—21no—
56C22⋊C4×C283—21no—
57C22⋊C4×C283—21no—
58C22⋊C4×C283—21no—
59C22⋊C4×C283—21no—
60C42×C283—21no—
61C22×D283—22no—
62C22×D283—41no—
63C22×D283—41no—
64C22×D283—41no—
65C22×D283—41no—
66C22×D283—41no—
67C22×D283—41no—
68D1132—22no—
69D1132—22no—
70D1132—41no—
71D1132—41no—
72C22⋊D283—48no—
73C2×Dic283—22no—
74C2×Dic283—41no—
75C2×Dic283—41no—
76C283⋊C8—41no—
77C283⋊C8—41no—
78C23×C283—21no—
79C23×C283—21no—
80C23×C283—21no—
81C23×C283—21no—
82C23×C283—41no—
83C23×C283—41no—
84C23×C283C2×D411yescharacteristic
85Q8×C283—41no—
86D4×C283—41no—
87D4×C283—41no—
88D4×C283—41no—
89D4×C283—81no—
90D4×C283—81no—
91C2×C4×C283—21no—
92C2×C4×C283—21no—
93C2×C4×C283—21no—
94C2×C4×C283—21no—
95C2×C4×C283—41no—
96C2×C4×C283—41no—
97C2×C4×C283—81no—
98C2×C4×C283C2×D411yescharacteristic
99C2×C4×C283C2×D411yescharacteristic
100C22×C283—21no—
101C22×C283—21no—
102C22×C283—42no—
103C22×C283—41no—
104C22×C283—41no—
105C22×C283—41no—
106C22×C283—41no—
107C22×C283—41no—
108C22×C283—41no—
109C22×C283—81no—
110C22×C283#12011yescharacteristic
111C22×C283#13511yescharacteristic
112C22×C283AGL(1,ℤ/8)11yescharacteristic
113C2×D283—42no—
114C2×D283—42no—
115C2×D283—42no—
116C2×D283—81no—
117C2×D283—81no—
118C2×D283—81no—
119C2×D283—81no—
120C4×C283—21no—
121C4×C283—21no—
122C4×C283—41no—
123C4×C283—41no—
124C4×C283—41no—
125C4×C283—41no—
126Dic283—42no—
127C2×C283—21no—
128C2×C283—21no—
129C2×C283—81no—
130C2×C283—81no—
131C2×C283#44911yescharacteristic
132C2×C283#45311yescharacteristic
133C2×C283B(4,𝔽2)11yescharacteristic
134D283—82no—
135C283#160011yescharacteristic, complemented, Sylow
136#1600—2831nomaximal, Sylow
137#538D28311yescharacteristic, complemented
138#450—2831no—
139#447—2831no—
140#392—2831no—
141#328—2831no—
142#327—2831no—
143#323—2831no—
144C22×D4—2831no—
145C22×D4—5661no—
146C2×SD16—5661no—
147C2×D8—5661no—
148#126—21no—
149#124—21no—
150#123—21no—
151C22⋊Q8C2×D28311yescharacteristic
152#121—21no—
153#121C2×D28311yescharacteristic
154#120—21no—
155C4×D4—21no—
156C2×C22⋊C4—5661no—
157C2×C22⋊C4C2×D28311yescharacteristic
158#102—5661no—
159#102—5661no—
160C22⋊C8—2831no—
161C22⋊C8—2831no—
162#95—2831no—
163C24—5661no—
164C24C22⋊D28311yescharacteristic
165C2×Q8C22⋊D28311yescharacteristic, complemented
166C2×D4—21no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—5661no—
170C2×D4—5661no—
171C2×D4—11322no—
172C2×D4—11322no—
173C2×D4—11322no—
174C2×D4—11322no—
175C2×D4C22⋊D28311yescharacteristic, complemented
176C22×C4—21no—
177C22×C4—5661no—
178C22×C4C22⋊D28311yescharacteristic
179C22×C4C22×D28311yescharacteristic
180SD16—11322no—
181D8—11322no—
182C2×C8—5661no—
183C2×C8—5661no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4C22⋊D28311yescharacteristic, complemented
187C4⋊C4C22⋊D28311yescharacteristic, complemented
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—21no—
191C22⋊C4—21no—
192C22⋊C4—21no—
193C22⋊C4—21no—
194C22⋊C4—21no—
195C22⋊C4—11322no—
196C42—21no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23—21no—
201C23—41no—
202C23—41no—
203C23—5662no—
204C23—11321no—
205C23—11321no—
206C23—11321no—
207C23—11321no—
208C23—11321no—
209C23—11321no—
210C23C2×C22⋊D28311yescharacteristic
211Q8—41no—
212D4—41no—
213D4—41no—
214D4—41no—
215D4—81no—
216D4—81no—
217D4—5662no—
218D4—5662no—
219D4—11321no—
220D4—11321no—
221D4—11328no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—81no—
229C2×C4—5662no—
230C2×C4—11321no—
231C2×C4—11321no—
232C2×C4C2×C22⋊D28311yescharacteristic
233C2×C4C2×C22⋊D28311yescharacteristic
234C8—11321no—
235C8—11321no—
236C22—21no—
237C22—21no—
238C22—42no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—81no—
246C22—11322no—
247C22—11322no—
248C22—11322no—
249C22—22641no—
250C22—22641no—
251C22—22641no—
252C22—22641no—
253C22#2258357911yescharacteristic
254C22#2258363011yescharacteristic
255C22#2258363511yescharacteristic
256C4—21no—
257C4—21no—
258C4—41no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4—11322no—
263C2—21no—
264C2—21no—
265C2—81no—
266C2—81no—
267C2—22642no—
268C2#3182661011yescharacteristic
269C2#3182663311yescharacteristic
270C2#3182665211yescharacteristic
subgroupG/H
centerC22#22583579
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#538×C283C2
socleC22×C283#120
hypercenter#538D283
hypocenterC283#1600
LCSG ▷ C22×C4×C283 ▷ C22×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #31826615C2semidirect
2. #31826598C2semidirect
3. #31826374C2semidirect
4. #31826202C2semidirect
5. #31826199C2semidirect
6. #31826189C2semidirect
7. #538×C283C2semidirect
41. C2×Q8×C283D4semidirect
45. C2×D4×C283D4semidirect
51. C4⋊C4×C283D4semidirect
52. C4⋊C4×C283D4semidirect
135. C283#1600semidirect
137. #538D283semidirect
165. C2×Q8C22⋊D283semidirect
175. C2×D4C22⋊D283semidirect
186. C4⋊C4C22⋊D283semidirect
187. C4⋊C4C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
#318266152
#318265982
#318263742
#318262022
#318261992
#318261892
#538×C2832
#1600283