Finite Group Databasebeta

← #49122274

Subgroups — #49122274

Order 36224.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22583635C211yesmaximal, characteristic, complemented
2C2×#22583606C211yesmaximal, characteristic, complemented
3C2×#22583537C211yesmaximal, characteristic, complemented
4#31826469C211yesmaximal, characteristic, complemented
5C2×#22583527C211yesmaximal, characteristic, complemented
6#31826224C211yesmaximal, characteristic, complemented
7#535×C283C211yesmaximal, characteristic, complemented
8C22×D1132C2211yescharacteristic
9C22×C22⋊D283—22no—
10#22583635—22no—
11#22583635—22no—
12C2×#17985379—21no—
13C2×#17985377—21no—
14C2×#17985376C2211yescharacteristic
15C2×#17985376C2211yescharacteristic
16#22583606—22no—
17#22583606—22no—
18C2×C4×Dic283C2211yescharacteristic
19#22583537—22no—
20#22583530—22no—
21#22583527—22no—
22C2×#41×C283C2211yescharacteristic
23C22×D4×C283C2211yescharacteristic
24#127×C283—21no—
25#124×C283—21no—
26#121×C283—22no—
27#120×C283—22no—
28#117×C283C2211yescharacteristic
29C23×D283—21no—
30C2×D1132—21no—
31C2×D1132—21no—
32C2×D1132—21no—
33C2×D1132—21no—
34C2×D1132—21no—
35C2×D1132D412yescomplemented
36C2×C22⋊D283—28no—
37C2×C22⋊D283—48no—
38C22×Dic283—21no—
39#17985379—24no—
40#17985377—24no—
41#17985376—21no—
42#17985376—21no—
43#17985376—21no—
44#17985376D412yescomplemented
45C2×C283⋊C8—21no—
46C2×C283⋊C8—21no—
47C4×Dic283—21no—
48C4×Dic283D412yescomplemented
49C24×C283D412yes—
50#41×C283—21no—
51#41×C283—21no—
52#41×C283—21no—
53#41×C283—21no—
54C2×Q8×C283D411yescharacteristic, complemented
55C2×D4×C283—21no—
56C2×D4×C283—24no—
57C2×D4×C283—21no—
58C2×D4×C283—21no—
59C2×D4×C283—21no—
60C2×D4×C283—21no—
61C2×D4×C283—21no—
62C2×D4×C283—21no—
63C2×D4×C283D411yescharacteristic, complemented
64C22×C4×C283—21no—
65C22×C4×C283C2311yescharacteristic
66C4⋊C4×C283D412yescomplemented
67C22⋊C4×C283—24no—
68C22⋊C4×C283—21no—
69C42×C283—21no—
70C22×D283—22no—
71C22×D283—44no—
72C22×D283—41no—
73C22×D283—41no—
74D1132—22no—
75D1132—22no—
76D1132—41no—
77D1132—41no—
78C22⋊D283—416no—
79C2×Dic283—24no—
80C2×Dic283—22no—
81C283⋊C8—22no—
82C283⋊C8—41no—
83C23×C283—22no—
84C23×C283—21no—
85C23×C283—22no—
86C23×C283—22no—
87C23×C283—44no—
88C23×C283C2×D411yescharacteristic
89Q8×C283—21no—
90Q8×C283—21no—
91D4×C283—21no—
92D4×C283—21no—
93D4×C283—41no—
94D4×C283—41no—
95D4×C283—41no—
96D4×C283—41no—
97D4×C283—41no—
98D4×C283—41no—
99D4×C283—84no—
100C2×C4×C283—22no—
101C2×C4×C283—21no—
102C2×C4×C283—41no—
103C2×C4×C283—41no—
104C2×C4×C283C2×D411yescharacteristic
105C2×C4×C283C2×D411yescharacteristic
106C2×C4×C283C2×D411yescharacteristic
107C2×C4×C283C2×D411yescharacteristic
108C2×C4×C283C2×D411yescharacteristic
109C2×C4×C283#4111yescharacteristic
110C22×C283—22no—
111C22×C283—44no—
112C22×C283—41no—
113C22×C283—42no—
114C22×C283—42no—
115C22×C283—44no—
116C22×C283—82no—
117C22×C283#12011yescharacteristic
118C22×C283#12011yescharacteristic
119C22×C283#12111yescharacteristic
120C2×D283—44no—
121C2×D283—42no—
122C2×D283—82no—
123C2×D283—82no—
124C4×C283—41no—
125C4×C283—42no—
126C4×C283#12011yescharacteristic
127C4×C283#12111yescharacteristic
128C4×C283#12111yescharacteristic
129C4×C283#12711yescharacteristic
130Dic283—24no—
131C2×C283—21no—
132C2×C283—21no—
133C2×C283—81no—
134C2×C283—82no—
135C2×C283#39211yescharacteristic
136C2×C283#45312yes—
137D283—82no—
138C283#200211yescharacteristic, complemented, Sylow
139#2002—2831nomaximal, Sylow
140C2×AGL(1,ℤ/8)—2831no—
141#535D28311yescharacteristic, complemented
142C2×#127—2831no—
143C2×#104—2831no—
144#418—2831no—
145C2×#100—2831no—
146#339—2831no—
147C2×#41C2×D28311yescharacteristic
148C22×D4—2831no—
149C22×D4—5662no—
150C22×D4C2×D28311yescharacteristic
151AGL(1,ℤ/8)—5662no—
152AGL(1,ℤ/8)—5662no—
153C2×SD16—5661no—
154C2×D8—5661no—
155C2×M16—2831no—
156C2×M16—2831no—
157#127—21no—
158#127—5662no—
159#127—5662no—
160#124—21no—
161#121—22no—
162#120—22no—
163#117C2×D28311yescharacteristic
164C2×C42—2831no—
165#104—5662no—
166#102—5662no—
167#100—5662no—
168C24—5661no—
169C24C22⋊D28312yes—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8C22⋊D28311yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—24no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—2832no—
184C2×D4—5668no—
185C2×D4—5661no—
186C2×D4—5661no—
187C2×D4—5661no—
188C2×D4—5661no—
189C2×D4—5661no—
190C2×D4—11328no—
191C2×D4C22⋊D28311yescharacteristic, complemented
192C22×C4—21no—
193C22×C4—5661no—
194C22×C4C22×D28311yescharacteristic
195SD16—5664no—
196D8—5664no—
197M16—2832no—
198M16—5661no—
199M16—5661no—
200M16—5661no—
201C2×C8—5661no—
202C2×C8—5661no—
203C4⋊C4C22⋊D28312yescomplemented
204C22⋊C4—24no—
205C22⋊C4—21no—
206C42—21no—
207C42—2832no—
208C42—5661no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23—22no—
213C23—44no—
214C23—5662no—
215C23—11324no—
216C23—11321no—
217C23—11321no—
218C23C2×C22⋊D28311yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—21no—
223D4—41no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—84no—
230D4—5662no—
231D4—5662no—
232D4—113216no—
233D4—11321no—
234D4—11321no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—5664no—
240C2×C4—5662no—
241C2×C4D4×D28311yescharacteristic
242C2×C4D4×D28311yescharacteristic
243C2×C4D4×D28311yescharacteristic
244C2×C4C2×C22⋊D28311yescharacteristic
245C2×C4C2×C22⋊D28311yescharacteristic
246C2×C4#1798539111yescharacteristic
247C8—5662no—
248C8—11321no—
249C22—22no—
250C22—44no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—11324no—
257C22—11322no—
258C22—22642no—
259C22—22642no—
260C22#2258357811yescharacteristic
261C22#2258357911yescharacteristic
262C22#2258358211yescharacteristic
263C4—41no—
264C4—42no—
265C4—5664no—
266C4#2258357811yescharacteristic
267C4#2258358111yescharacteristic
268C4#2258358211yescharacteristic
269C4#2258360611yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—81no—
274C2—22642no—
275C2#3182637311yescharacteristic
276C2#3182663312yes—
subgroupG/H
centerC22#22583579
commutator, cosocleC22×C4×C283C23
FrattiniC22×C4C22×D283
Fitting#535×C283C2
socleC22×C283#120
hypercenter#535D283
hypocenterC283#2002
LCSG ▷ C22×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#22583635C2semidirect
2. C2×#22583606C2semidirect
3. C2×#22583537C2semidirect
4. #31826469C2semidirect
5. C2×#22583527C2semidirect
6. #31826224C2semidirect
7. #535×C283C2semidirect
35. C2×D1132D4semidirect
44. #17985376D4semidirect
48. C4×Dic283D4semidirect
54. C2×Q8×C283D4semidirect
63. C2×D4×C283D4semidirect
66. C4⋊C4×C283D4semidirect
138. C283#2002semidirect
141. #535D283semidirect
174. C2×Q8C22⋊D283semidirect
191. C2×D4C22⋊D283semidirect
203. C4⋊C4C22⋊D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836352
C2×#225836062
C2×#225835372
#318264692
C2×#225835272
#318262242
#535×C2832
#2002283