Finite Group Databasebeta

← #49130628

Subgroups — #49130628

Order 36224.

698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C2×#22583658C211yesmaximal, characteristic, complemented
2#31827265C212yesmaximal, complemented
3#31827039C211yesmaximal, characteristic, complemented
4#31826650C214yesmaximal, complemented
5#31826640C214yesmaximal, complemented
6#31826481C212yesmaximal, complemented
7C2×#101×C283C211yesmaximal, characteristic, complemented
8#22583658—24no—
9#22583658—22no—
10#22583658C2214yes—
11C2×#17985393—22no—
12C2×#17985392—22no—
13C2×#17985392C2212yes—
14C2×#17985392C2211yescharacteristic
15C2×Q8×D283—22no—
16#22583643—22no—
17#22583643C2214yescomplemented
18#22583638—22no—
19#22583638C2214yescomplemented
20#22583632—24no—
21#22583608C2212yescomplemented
22#22583599C2212yescomplemented
23#22583593—22no—
24#22583586—22no—
25#22583569C2211yescharacteristic
26#22583536C2218yescomplemented
27C22×Q8×C283C2211yescharacteristic
28C2×M16×C283C2212yes—
29#101×C283C2214yescomplemented
30#17985393—28no—
31#17985393—28no—
32#17985392—28no—
33#17985392—28no—
34#17985392—22no—
35#17985392—22no—
36#17985392—22no—
37#17985392—22no—
38#17985392D414yes—
39#17985392C2314yes—
40C2×Dic566—22no—
41C2×Dic566D412yes—
42C2×Dic566C2311yescharacteristic
43Q8×D283—28no—
44Q8×D283—28no—
45C2×D1132—22no—
46C2×D1132D412yes—
47C2×D1132C2311yescharacteristic
48C2×C22⋊D283—22no—
49C2×C22⋊D283—21no—
50C2×C4×D283—24no—
51C2×C4×D283—22no—
52C2×C4×D283—21no—
53Dic1132—24no—
54#17985381—24no—
55#17985381—24no—
56D2264—24no—
57C4⋊Dic283—21no—
58Dic283⋊C4—24no—
59C22⋊Dic283—21no—
60(C2×D283)⋊C4—24no—
61C4×Dic283C2312yes—
62C2×Q8×C283—22no—
63C2×Q8×C283—22no—
64C2×Q8×C283D412yes—
65C2×Q8×C283C2312yes—
66C22×C4×C283D412yes—
67C22×C4×C283C2311yescharacteristic
68M16×C283—22no—
69M16×C283C2314yes—
70C2×C8×C283—22no—
71C22×D283—22no—
72C22×D283—21no—
73Dic566—28no—
74Dic566—22no—
75Dic566—22no—
76Dic566C2×D414yes—
77D1132—28no—
78D1132—22no—
79D1132—22no—
80D1132C2×D414yes—
81C22⋊D283—24no—
82C22⋊D283—24no—
83C22⋊D283—41no—
84C22⋊D283—41no—
85C2×Dic283—22no—
86C2×Dic283—22no—
87C2×Dic283—21no—
88C4×D283—216no—
89C4×D283—24no—
90C4×D283—24no—
91C4×D283—42no—
92C23×C283C2×D411yescharacteristic
93Q8×C283—24no—
94Q8×C283—24no—
95C2×C4×C283—22no—
96C2×C4×C283—22no—
97C2×C4×C283C2×D412yes—
98C2×C4×C283C2×D412yes—
99C2×C4×C283C2×D414yes—
100C2×C4×C283C2×D411yescharacteristic
101C2×C4×C283C2411yescharacteristic
102C8×C283—24no—
103C22×C283—41no—
104C22×C283#12011yescharacteristic
105C22×C283#12011yescharacteristic
106C22×C283C22×D411yescharacteristic
107C2×D283—24no—
108C2×D283—44no—
109C2×D283—42no—
110C2×D283—41no—
111C4×C283—24no—
112C4×C283#12012yes—
113C4×C283C22×D412yes—
114Dic283—24no—
115Dic283—42no—
116Dic283—41no—
117C2×C283—21no—
118C2×C283—21no—
119C2×C283—21no—
120C2×C283C2×#12011yescharacteristic
121D283—44no—
122D283—81no—
123C283#302011yescharacteristic, complemented, Sylow
124#3020—2831nomaximal, Sylow
125C2×2−1+4—2831no—
126#575—2832no—
127#536—2831no—
128#456—2834no—
129#454—2834no—
130#421—2832no—
131C2×#101D28311yescharacteristic, complemented
1322−1+4—2834no—
1332−1+4—5664no—
1342−1+4—5662no—
135C2×#41—2832no—
136C2×#41—2831no—
137C2×#41—5662no—
138C2×#41—5662no—
139C22×Q8—5662no—
140C22×Q8C2×D28311yescharacteristic
141#137—2834no—
142#137—5662no—
143AGL(1,ℤ/8)—2834no—
144AGL(1,ℤ/8)—5662no—
145#135—5664no—
146C2×M16C2×D28312yes—
147C4⋊Q8—2832no—
148#124—2832no—
149#123—5662no—
150C22⋊Q8—5662no—
151#117—2831no—
152#104—2838no—
153#101C2×D28314yescomplemented
154#41—2834no—
155#41—2834no—
156#41—5668no—
157#41—5668no—
158#41—5668no—
159#41—5662no—
160#41—5662no—
161#41—5668no—
162#41—5662no—
163#41—5662no—
164C2×Q8—22no—
165C2×Q8—22no—
166C2×Q8—2832no—
167C2×Q8—2831no—
168C2×Q8—5662no—
169C2×Q8—5668no—
170C2×Q8—5668no—
171C2×Q8D113212yes—
172C2×Q8C22×D28312yes—
173C2×D4—2832no—
174C2×D4—2831no—
175C2×D4—5662no—
176C2×D4—5662no—
177C2×D4—5661no—
178C22×C4—5664no—
179C22×C4—5662no—
180C22×C4—5661no—
181C22×C4D113212yes—
182C22×C4C22×D28311yescharacteristic
183Q16—5664no—
184SD16—5664no—
185SD16—5664no—
186D8—5664no—
187M16—22no—
188M16C22×D28314yes—
189C2×C8—22no—
190C4⋊C4—5664no—
191C4⋊C4—5661no—
192C22⋊C4—5661no—
193C22⋊C4—5664no—
194C42—2832no—
195C23—5662no—
196C23—5661no—
197C23C2×D113211yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—2834no—
201Q8—5668no—
202Q8—5662no—
203Q8—5662no—
204D4—2834no—
205D4—5668no—
206D4—5664no—
207D4—5664no—
208D4—5662no—
209D4—5662no—
210D4—11321no—
211D4—11321no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—56616no—
215C2×C4—5662no—
216C2×C4—5664no—
217C2×C4—5664no—
218C2×C4—5662no—
219C2×C4—5661no—
220C2×C4—11322no—
221C2×C4D4×D28312yes—
222C2×C4D4×D28312yes—
223C2×C4C2×D113214yes—
224C2×C4C2×D113211yescharacteristic
225C2×C4C23×D28311yescharacteristic
226C8—24no—
227C22—41no—
228C22—5664no—
229C22—11324no—
230C22—11322no—
231C22—11321no—
232C22#2258358011yescharacteristic
233C22#2258358011yescharacteristic
234C22C22×D113211yescharacteristic
235C4—24no—
236C4—5664no—
237C4—11322no—
238C4—11321no—
239C4#2258358012yes—
240C4C2×D4×D28312yes—
241C2—21no—
242C2—21no—
243C2—21no—
244C2—11324no—
245C2—22641no—
246C2C2×#2258358011yescharacteristic
subgroupG/H
centerC2C2×#22583580
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#101×C283C2
socleC2×C283C2×#120
hypercenterC2×#101D283
hypocenterC283#3020
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
1. C2×#22583658C2semidirect
2. #31827265C2semidirect
3. #31827039C2semidirect
4. #31826650C2semidirect
5. #31826640C2semidirect
6. #31826481C2semidirect
7. C2×#101×C283C2semidirect
17. #22583643C22semidirect
19. #22583638C22semidirect
21. #22583608C22semidirect
22. #22583599C22semidirect
26. #22583536C22semidirect
29. #101×C283C22semidirect
123. C283#3020semidirect
131. C2×#101D283semidirect
153. #101C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836582
#318272652
#318270392
#318266502
#318266402
#318264812
C2×#101×C2832
#3020283