Finite Group Databasebeta

← #49130908

Subgroups — #49130908

Order 36224.

524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 133 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
1C22×#17985377C211yesmaximal, characteristic, complemented
2C2×#22583618C211yesmaximal, characteristic, complemented
3#31827034C211yesmaximal, characteristic, complemented
4#31827032C211yesmaximal, characteristic, complemented
5#31826717C214yesmaximal, complemented
6#31826700C214yesmaximal, complemented
7#31826501C211yesmaximal, characteristic, complemented
8#31826471C211yesmaximal, characteristic, complemented
9#418×C283C211yesmaximal, characteristic, complemented
10C2×#17985392C2211yescharacteristic
11C22×D1132C2211yescharacteristic
12C2×#17985377—24no—
13C2×#17985377C2212yes—
14C2×#17985377C2212yes—
15#22583618—24no—
16C2×#17985375C2212yescomplemented
17C22×C283⋊C8C2211yescharacteristic
18C2×C8×D283C2212yescomplemented
19#22583607—21no—
20#22583606—21no—
21#22583598—21no—
22#22583597—21no—
23#22583585C2214yescomplemented
24#22583581C2214yescomplemented
25#22583580—22no—
26#22583579—22no—
27#22583569C2211yescharacteristic
28#22583543C2212yescomplemented
29#22583541C2212yescomplemented
30#22583532C2214yescomplemented
31C22×D4×C283C2211yescharacteristic
32C2×M16×C283C2211yescharacteristic
33#117×C283C2211yescharacteristic
34#102×C283C2214yescomplemented
35C23×D283—21no—
36#17985392—22no—
37#17985392—22no—
38C2×Dic566D411yescharacteristic
39C2×D1132—24no—
40C2×D1132—22no—
41C2×D1132—21no—
42C2×D1132—22no—
43C2×D1132D411yescharacteristic
44C2×D1132C2312yes—
45C2×C22⋊D283—24no—
46C2×C22⋊D283D412yes—
47C2×C4×D283C2312yes—
48#17985377—24no—
49#17985377—24no—
50#17985375—24no—
51C2×C283⋊C8D414yescomplemented
52C2×C283⋊C8C2311yescharacteristic
53C2×C283⋊C8C2311yescharacteristic
54C8×D283—24no—
55C4⋊Dic283C2312yes—
56C22⋊Dic283—24no—
57C22⋊Dic283—21no—
58(C2×D283)⋊C4—24no—
59C4×Dic283—21no—
60C24×C283—21no—
61C2×D4×C283—22no—
62C2×D4×C283—21no—
63C2×D4×C283—22no—
64C2×D4×C283C2312yes—
65C22×C4×C283C2311yescharacteristic
66M16×C283—22no—
67C2×C8×C283C2312yes—
68C4⋊C4×C283C2312yes—
69C22⋊C4×C283—21no—
70C42×C283—21no—
71C22×D283—22no—
72C22×D283—42no—
73C22×D283—82no—
74C22×D283C2×D412yes—
75Dic566—22no—
76D1132—22no—
77D1132—22no—
78D1132—22no—
79D1132—42no—
80D1132—84no—
81C22⋊D283—24no—
82C22⋊D283—84no—
83C2×Dic283—22no—
84C2×Dic283C2×D412yes—
85C4×D283—22no—
86C4×D283—22no—
87C283⋊C8C2×D412yes—
88C283⋊C8C2×D412yes—
89C23×C283—22no—
90C23×C283—42no—
91C23×C283—82no—
92C23×C283C2×D411yescharacteristic
93D4×C283—22no—
94D4×C283—22no—
95D4×C283—42no—
96C2×C4×C283—22no—
97C2×C4×C283C2×D411yescharacteristic
98C2×C4×C283C2×D412yes—
99C2×C4×C283#4112yes—
100C2×C4×C283C2411yescharacteristic
101C8×C283—22no—
102C22×C283—22no—
103C22×C283—42no—
104C22×C283—44no—
105C22×C283—84no—
106C22×C283#12112yes—
107C22×C283C22×D411yescharacteristic
108C2×D283—22no—
109C2×D283—24no—
110C2×D283—42no—
111C2×D283—44no—
112C2×D283—84no—
113C4×C283—42no—
114C4×C283#12112yes—
115C4×C283C22×D411yescharacteristic
116C4×C283C2×#4111yescharacteristic
117Dic283—22no—
118Dic283—42no—
119C2×C283—22no—
120C2×C283—82no—
121C2×C283C2×#12111yescharacteristic
122C2×C283#57612yes—
123D283—42no—
124D283—82no—
125C283#305811yescharacteristic, complemented, Sylow
126#3058—2831nomaximal, Sylow
127C22×D8—2831no—
128C2×#131—2831no—
129#535—2831no—
130#535—2831no—
131#469—2834no—
132#466—2834no—
133#427—2831no—
134#418—2831no—
135#418D28311yescharacteristic, complemented
136C2×#41—2831no—
137C22×D4—2831no—
138C22×D4C2×D28311yescharacteristic
139C2×D8—2832no—
140C2×D8—2832no—
141C2×D8—5664no—
142#131—5664no—
143C2×M16—2832no—
144C2×M16C2×D28311yescharacteristic
145C22×C8—2831no—
146C22×C8—2832no—
147#127—5661no—
148#127—5661no—
149#124—5661no—
150#124—5661no—
151#121—2834no—
152#121—2834no—
153#120—5662no—
154#120—5662no—
155#117—2831no—
156#117C2×D28311yescharacteristic
157#107—2832no—
158#106—2832no—
159#102—2834no—
160#102C2×D28314yescomplemented
161C24—21no—
162C24—5661no—
163#41—5662no—
164#41—5662no—
165C2×Q8—2831no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—22no—
169C2×D4—2832no—
170C2×D4—2831no—
171C2×D4—2832no—
172C2×D4—5664no—
173C2×D4—5664no—
174C2×D4—5662no—
175C2×D4—5661no—
176C2×D4—5662no—
177C2×D4C22×D28312yes—
178C22×C4—2832no—
179C22×C4C22×D28311yescharacteristic
180D8—5664no—
181D8—5664no—
182M16—22no—
183M16—5664no—
184C2×C8—2834no—
185C2×C8—2831no—
186C2×C8—2831no—
187C2×C8—5664no—
188C2×C8C22×D28312yes—
189C4⋊C4—2832no—
190C4⋊C4C22×D28312yes—
191C22⋊C4—21no—
192C22⋊C4—5664no—
193C22⋊C4—5664no—
194C22⋊C4—5661no—
195C42—21no—
196C42—5661no—
197C23—22no—
198C23—42no—
199C23—82no—
200C23—2832no—
201C23—5662no—
202C23—11322no—
203C23—22642no—
204C23D4×D28311yescharacteristic
205Q8—5662no—
206D4—22no—
207D4—22no—
208D4—42no—
209D4—5664no—
210D4—5662no—
211D4—5662no—
212D4—5662no—
213D4—11322no—
214D4—22644no—
215D4—22644no—
216C2×C4—22no—
217C2×C4—2832no—
218C2×C4—5662no—
219C2×C4—5662no—
220C2×C4—5662no—
221C2×C4D4×D28311yescharacteristic
222C2×C4D4×D28312yes—
223C2×C4#1798539212yes—
224C2×C4C23×D28311yescharacteristic
225C8—22no—
226C8—2832no—
227C8—2832no—
228C22—22no—
229C22—42no—
230C22—44no—
231C22—84no—
232C22—5662no—
233C22—5664no—
234C22—11322no—
235C22—11324no—
236C22—22644no—
237C22#2258358312yes—
238C22C2×D4×D28311yescharacteristic
239C4—42no—
240C4—5662no—
241C4—11322no—
242C4#2258358312yes—
243C4C2×D4×D28311yescharacteristic
244C4C2×#1798539211yescharacteristic
245C2—22no—
246C2—82no—
247C2—11322no—
248C2—22642no—
249C2C2×#2258358311yescharacteristic
250C2#3182726912yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#418×C283C2
socleC22×C283C22×D4
hypercenter#418D283
hypocenterC283#3058
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C22×#17985377C2semidirect
2. C2×#22583618C2semidirect
3. #31827034C2semidirect
4. #31827032C2semidirect
5. #31826717C2semidirect
6. #31826700C2semidirect
7. #31826501C2semidirect
8. #31826471C2semidirect
9. #418×C283C2semidirect
16. C2×#17985375C22semidirect
18. C2×C8×D283C22semidirect
23. #22583585C22semidirect
24. #22583581C22semidirect
28. #22583543C22semidirect
29. #22583541C22semidirect
30. #22583532C22semidirect
34. #102×C283C22semidirect
51. C2×C283⋊C8D4semidirect
125. C283#3058semidirect
135. #418D283semidirect
160. #102C2×D283semidirect

Maximal subgroups

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

subgroupindex
C22×#179853772
C2×#225836182
#318270342
#318270322
#318267172
#318267002
#318265012
#318264712
#418×C2832
#3058283