Finite Group Databasebeta

← #49130632

Subgroups — #49130632

Order 36224.

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

normal subgroups only

This group has 736 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
1#31827301C211yesmaximal, characteristic, complemented
2C2×#22583636C212yesmaximal, complemented
3#31826637C214yesmaximal, complemented
4#31826632C214yesmaximal, complemented
5#31826483C212yesmaximal, complemented
6#31826449C211yesmaximal, characteristic, complemented
7#535×C283C211yesmaximal, characteristic, complemented
8#22583658C2212yescomplemented
9#22583657—22no—
10#22583656—22no—
11#22583655—22no—
12#22583655C2212yescomplemented
13C2×#17985392—22no—
14C2×#17985392C2212yes—
15#41×D283—24no—
16#22583636—24no—
17#22583636C2218yescomplemented
18C2×#17985380—22no—
19C2×#17985377—22no—
20C2×#17985376C2212yescomplemented
21#22583538C2218yescomplemented
22#22583529C2212yescomplemented
23#22583527C2212yescomplemented
24C2×#41×C283C2211yescharacteristic
25C22×D4×C283C2211yescharacteristic, complemented
26#127×C283C2212yescomplemented
27#124×C283C2212yescomplemented
28#121×C283—22no—
29#120×C283—22no—
30#117×C283C2211yescharacteristic, complemented
31#17985393—24no—
32#17985392—24no—
33#17985392—24no—
34#17985392—22no—
35#17985392—24no—
36#17985392—22no—
37#17985392D414yescomplemented
38#17985392C2314yes—
39#17985391—28no—
40#17985391—24no—
41C2×Dic566—22no—
42C2×Dic566D412yescomplemented
43Q8×D283—24no—
44C2×D1132—22no—
45C2×D1132D412yescomplemented
46C2×C22⋊D283—24no—
47C2×C22⋊D283—22no—
48D4×D283—28no—
49D4×D283—24no—
50C2×C4×D283—24no—
51C2×C4×D283—22no—
52#17985380—28no—
53#17985377—28no—
54#17985376—22no—
55#17985376C2314yes—
56C2×C283⋊C8—22no—
57C24×C283—21no—
58#41×C283—22no—
59#41×C283—22no—
60C2×Q8×C283C2311yescharacteristic
61C2×D4×C283—24no—
62C2×D4×C283—22no—
63C2×D4×C283—22no—
64C2×D4×C283—21no—
65C2×D4×C283D412yes—
66C2×D4×C283C2312yes—
67C2×D4×C283C2311yescharacteristic
68C22×C4×C283D412yes—
69C22×C4×C283C2311yescharacteristic
70C4⋊C4×C283—21no—
71C22⋊C4×C283—21no—
72C22⋊C4×C283—24no—
73C42×C283C2312yes—
74C22×D283—24no—
75C22×D283—22no—
76Dic566—24no—
77Dic566—22no—
78Dic566C2×D414yes—
79D1132—24no—
80D1132—22no—
81D1132C2×D414yes—
82C22⋊D283—28no—
83C22⋊D283—24no—
84C22⋊D283—24no—
85C2×Dic283—24no—
86C2×Dic283—22no—
87C4×D283—28no—
88C4×D283—24no—
89C4×D283—24no—
90C283⋊C8—24no—
91C23×C283—22no—
92C23×C283—42no—
93C23×C283—82no—
94C23×C283C2×D412yes—
95C23×C283C2×D411yescharacteristic
96Q8×C283—22no—
97D4×C283—24no—
98D4×C283—22no—
99D4×C283—24no—
100D4×C283—41no—
101D4×C283—41no—
102D4×C283—84no—
103C2×C4×C283—22no—
104C2×C4×C283—22no—
105C2×C4×C283—22no—
106C2×C4×C283C2×D412yes—
107C2×C4×C283C2×D412yes—
108C2×C4×C283C2×D412yes—
109C2×C4×C283C2×D411yescharacteristic
110C2×C4×C283C2411yescharacteristic
111C22×C283—22no—
112C22×C283—41no—
113C22×C283—42no—
114C22×C283—44no—
115C22×C283—42no—
116C22×C283—84no—
117C22×C283#12012yes—
118C22×C283C22×D411yescharacteristic
119C2×D283—24no—
120C2×D283—82no—
121C2×D283—84no—
122C4×C283—22no—
123C4×C283—42no—
124C4×C283#12011yescharacteristic
125C4×C283#12011yescharacteristic
126C4×C283C22×D412yes—
127Dic283—24no—
128C2×C283—21no—
129C2×C283—22no—
130C2×C283—42no—
131C2×C283—82no—
132C2×C283C2×#12011yescharacteristic
133D283—44no—
134C283#302111yescharacteristic, complemented, Sylow
135#3021—2831nomaximal, Sylow
136#585—2831no—
137C2×AGL(1,ℤ/8)—2832no—
138#535D28311yescharacteristic, complemented
139#454—2834no—
140#453—2834no—
141#421—2832no—
142#413—2831no—
1432−1+4—2832no—
1442−1+4—5662no—
145H(5,𝔽2)—2832no—
146H(5,𝔽2)—5662no—
147H(5,𝔽2)—5662no—
148C2×#41—2832no—
149C2×#41—5664no—
150C2×#41—5662no—
151C2×#41C2×D28311yescharacteristic
152C22×D4C2×D28311yescharacteristic, complemented
153AGL(1,ℤ/8)—2838no—
154AGL(1,ℤ/8)—5664no—
155C2×SD16—5662no—
156C2×D8—5662no—
157C2×M16—2832no—
158#127C2×D28312yescomplemented
159#124C2×D28312yescomplemented
160#121—22no—
161#120—22no—
162#117C2×D28311yescharacteristic, complemented
163#104—2838no—
164#101—2832no—
165#100—2832no—
166C24—21no—
167#41—22no—
168#41—22no—
169#41—2834no—
170#41—2834no—
171#41—5664no—
172#41—5664no—
173#41—5664no—
174#41—5668no—
175#41—5664no—
176#41—5662no—
177#41—5662no—
178#41—5664no—
179C2×Q8—2832no—
180C2×Q8—5662no—
181C2×Q8—5664no—
182C2×Q8C22×D28311yescharacteristic
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—21no—
187C2×D4—2832no—
188C2×D4—5662no—
189C2×D4—5664no—
190C2×D4—5668no—
191C2×D4—5662no—
192C2×D4—5664no—
193C2×D4C22⋊D28312yes—
194C2×D4C22×D28312yes—
195C2×D4C22×D28311yescharacteristic
196C22×C4—5664no—
197C22×C4—5662no—
198C22×C4C22⋊D28312yes—
199C22×C4C22×D28311yescharacteristic
200SD16—5668no—
201D8—5668no—
202M16—2834no—
203M16—5662no—
204C2×C8—5662no—
205C4⋊C4—21no—
206C22⋊C4—21no—
207C22⋊C4—24no—
208C42C22×D28312yes—
209C23—22no—
210C23—42no—
211C23—82no—
212C23—5664no—
213C23—5662no—
214C23C2×C22⋊D28312yes—
215C23C2×C22⋊D28311yescharacteristic
216Q8—22no—
217Q8—2834no—
218Q8—5664no—
219Q8—5662no—
220D4—24no—
221D4—22no—
222D4—24no—
223D4—41no—
224D4—41no—
225D4—84no—
226D4—2834no—
227D4—5664no—
228D4—5668no—
229D4—5664no—
230D4—5664no—
231D4—5662no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—5668no—
236C2×C4—5664no—
237C2×C4—5662no—
238C2×C4—5664no—
239C2×C4—5664no—
240C2×C4D4×D28312yes—
241C2×C4D4×D28312yes—
242C2×C4C2×C22⋊D28312yes—
243C2×C4C2×C22⋊D28311yescharacteristic
244C2×C4C23×D28311yescharacteristic
245C8—5664no—
246C22—22no—
247C22—41no—
248C22—42no—
249C22—44no—
250C22—42no—
251C22—84no—
252C22—5664no—
253C22—22642no—
254C22—22644no—
255C22#2258357812yes—
256C22C22×C22⋊D28311yescharacteristic
257C4—22no—
258C4—42no—
259C4—5664no—
260C4#2258357811yescharacteristic
261C4#2258357811yescharacteristic
262C4C2×D4×D28312yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—82no—
267C2—11324no—
268C2C2×#2258357811yescharacteristic
subgroupG/H
centerC2C2×#22583578
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#535×C283C2
socleC2×C283C2×#120
hypercenter#535D283
hypocenterC283#3021
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

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

NH ≅ G/Ntype
1. #31827301C2semidirect
2. C2×#22583636C2semidirect
3. #31826637C2semidirect
4. #31826632C2semidirect
5. #31826483C2semidirect
6. #31826449C2semidirect
7. #535×C283C2semidirect
8. #22583658C22semidirect
12. #22583655C22semidirect
17. #22583636C22semidirect
20. C2×#17985376C22semidirect
21. #22583538C22semidirect
22. #22583529C22semidirect
23. #22583527C22semidirect
25. C22×D4×C283C22semidirect
26. #127×C283C22semidirect
27. #124×C283C22semidirect
30. #117×C283C22semidirect
37. #17985392D4semidirect
42. C2×Dic566D4semidirect
45. C2×D1132D4semidirect
134. C283#3021semidirect
138. #535D283semidirect
152. C22×D4C2×D283semidirect
158. #127C2×D283semidirect
159. #124C2×D283semidirect
162. #117C2×D283semidirect

Maximal subgroups

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

subgroupindex
#318273012
C2×#225836362
#318266372
#318266322
#318264832
#318264492
#535×C2832
#3021283