Finite Group Databasebeta

← #497×D283 #49131697

Subgroups — #497×D283 #49131697

Order 36224.

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

normal subgroups only

This group has 564 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×Q16×D283C212yesmaximal, complemented
2C2×SD16×D283C212yesmaximal
3C4⋊Q8×D283C211yesmaximal, characteristic, complemented
4#124×D283C211yesmaximal, characteristic
5#31826860C211yesmaximal, characteristic, complemented
6#31826859C211yesmaximal, characteristic, complemented
7#31826858C212yesmaximal, complemented
8#31826857C211yesmaximal, characteristic, complemented
9#31826856C212yesmaximal, complemented
10#97×D283C211yesmaximal, characteristic, complemented
11#497×C283C211yesmaximal, characteristic, complemented
12C2×Q8×D283C2211yescharacteristic
13C2×Q8×D283C2212yes—
14C2×D4×D283C2211yescharacteristic
15C2×Dic1132C2212yescomplemented
16C2×#17985382C2212yescomplemented
17C2×#17985382C2212yescomplemented
18Q16×D283—28no—
19C2×#17985381C2212yes—
20C2×#17985380C2212yes—
21C2×#17985379C2212yes—
22SD16×D283—28no—
23C2×C8×D283C2212yes—
24#22583610C2211yescharacteristic, complemented
25#22583609—22no—
26#22583608C2212yescomplemented
27#22583599C2211yescharacteristic
28#22583598C2211yescharacteristic
29#22583597C2211yescharacteristic
30#22583596—22no—
31C4⋊C4×D283—22no—
32C22⋊C4×D283—22no—
33C42×D283C2211yescharacteristic
34#22583521C2211yescharacteristic, complemented
35#22583520C2212yescomplemented
36C2×Q16×C283C2212yescomplemented
37C2×SD16×C283C2212yes—
38C4⋊Q8×C283C2211yescharacteristic, complemented
39#124×C283C2211yescharacteristic
40#97×C283C2211yescharacteristic, complemented
41C23×D283—21no—
42C2×Dic566—21no—
43C2×Dic566—22no—
44C2×Dic566C2311yescharacteristic
45C2×Dic566C2312yes—
46Q8×D283—24no—
47Q8×D283—24no—
48Q8×D283—24no—
49C2×D1132C2311yescharacteristic
50C2×C22⋊D283—21no—
51D4×D283—24no—
52C2×C4×D283—21no—
53C2×C4×D283—22no—
54C2×C4×D283D412yes—
55C2×C4×D283C2311yescharacteristic
56Dic1132—24no—
57#17985382—24no—
58#17985382—24no—
59#17985381—24no—
60#17985380—24no—
61#17985379—24no—
62C2×C283⋊C8C2312yes—
63C8×D283D418yes—
64C4⋊Dic283—22no—
65Dic283⋊C4—24no—
66C22⋊Dic283—22no—
67(C2×D283)⋊C4—22no—
68(C2×D283)⋊C4—22no—
69C4×Dic283D412yes—
70C4×Dic283C2311yescharacteristic
71C2×Q8×C283C2311yescharacteristic
72C2×Q8×C283C2312yes—
73C2×D4×C283C2311yescharacteristic
74Q16×C283—24no—
75SD16×C283—24no—
76C2×C8×C283C2312yes—
77C4⋊C4×C283—22no—
78C22⋊C4×C283—22no—
79C42×C283C2311yescharacteristic
80C22×D283—21no—
81C22×D283—42no—
82C22×D283—44no—
83C22×D283C2×D411yescharacteristic
84Dic566—22no—
85Dic566—22no—
86Dic566—22no—
87Dic566—44no—
88Dic566—42no—
89D1132—22no—
90C22⋊D283—42no—
91C2×Dic283—21no—
92C2×Dic283—22no—
93C2×Dic283C2×D412yes—
94C2×Dic283C2×D411yescharacteristic
95C4×D283—24no—
96C4×D283—42no—
97C4×D283—44no—
98C4×D283C2×D414yes—
99C283⋊C8C2×D414yes—
100C23×C283—21no—
101Q8×C283—22no—
102Q8×C283—22no—
103Q8×C283—22no—
104D4×C283—22no—
105C2×C4×C283—21no—
106C2×C4×C283—22no—
107C2×C4×C283C2×D412yes—
108C2×C4×C283C2411yescharacteristic
109C8×C283C2×D414yes—
110C22×C283—41no—
111C22×C283—42no—
112C22×C283C22×D411yescharacteristic
113C2×D283—41no—
114C2×D283—42no—
115C2×D283—84no—
116C2×D283#12712yes—
117C2×D283#13714yes—
118C4×C283—22no—
119C4×C283—41no—
120C4×C283—42no—
121C4×C283C22×D412yes—
122Dic283—22no—
123Dic283—41no—
124Dic283—42no—
125Dic283#12712yes—
126C2×C283—81no—
127C2×C283C2×#12711yescharacteristic
128C2×C283C2×#13712yes—
129D283—81no—
130D283#49714yesdirect product factor
131C283C2×#49711yescharacteristic, complemented, Sylow
132C2×#497—2831nomaximal, Sylow
133C22×Q16—2832no—
134C22×SD16—2832no—
135C2×C4⋊Q8—2831no—
136C2×#124—2831no—
137#497—2832no—
138#497—2832no—
139#497—2831no—
140#497—2831no—
141#497—2831no—
142#497D28311yescharacteristic, direct product factor
143C2×#97—2831no—
144C22×Q8—2831no—
145C22×Q8—2832no—
146C22×D4—2831no—
147C2×Q16—2832no—
148C2×Q16—2832no—
149C2×Q16—2832no—
150C2×Q16—5668no—
151C2×Q16C2×D28312yescomplemented
152C2×SD16—2832no—
153C2×SD16—2832no—
154C2×SD16—2832no—
155C2×SD16—5668no—
156C2×SD16C2×D28312yes—
157C22×C8—2832no—
158C4⋊Q8—2832no—
159C4⋊Q8—2831no—
160C4⋊Q8—5662no—
161C4⋊Q8C2×D28311yescharacteristic, complemented
162#124—2831no—
163#124—2831no—
164#124—2831no—
165#124—5662no—
166#124C2×D28311yescharacteristic
167C2×C4⋊C4—5662no—
168C2×C22⋊C4—5662no—
169C2×C42—2831no—
170#97—2832no—
171#97—2831no—
172#97C2×D28311yescharacteristic, complemented
173C24—5661no—
174C2×Q8—2831no—
175C2×Q8—2832no—
176C2×Q8—5661no—
177C2×Q8—5662no—
178C2×Q8—5664no—
179C2×Q8—5664no—
180C2×Q8—5664no—
181C2×Q8C22×D28311yescharacteristic
182C2×Q8C22×D28312yes—
183C2×D4—2831no—
184C2×D4—5664no—
185C2×D4—5661no—
186C2×D4C22×D28311yescharacteristic
187C22×C4—2831no—
188C22×C4—2832no—
189C22×C4—5661no—
190C22×C4—5662no—
191Q16—24no—
192Q16—5664no—
193Q16—5664no—
194Q16—5664no—
195SD16—24no—
196SD16—5664no—
197SD16—5664no—
198SD16—5664no—
199C2×C8—2832no—
200C2×C8—2838no—
201C2×C8C22×D28312yes—
202C4⋊C4—22no—
203C4⋊C4—5664no—
204C4⋊C4—5662no—
205C22⋊C4—22no—
206C22⋊C4—5662no—
207C22⋊C4—5662no—
208C22⋊C4—5662no—
209C42—2832no—
210C42—2831no—
211C42C22×D28311yescharacteristic
212C23—21no—
213C23—2831no—
214C23—5661no—
215C23—11322no—
216C23—11324no—
217Q8—22no—
218Q8—22no—
219Q8—22no—
220Q8—5662no—
221Q8—5662no—
222Q8—5662no—
223Q8—11322no—
224Q8—11324no—
225D4—22no—
226D4—5662no—
227D4—11322no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—2831no—
231C2×C4—2834no—
232C2×C4—2832no—
233C2×C4—5664no—
234C2×C4—5661no—
235C2×C4—5662no—
236C2×C4—11322no—
237C2×C4—11324no—
238C2×C4D4×D28312yes—
239C2×C4C23×D28311yescharacteristic
240C8—2834no—
241C8D4×D28314yes—
242C22—42no—
243C22—41no—
244C22—2834no—
245C22—2832no—
246C22—11322no—
247C22—11321no—
248C22—22644no—
249C22C2×D4×D28311yescharacteristic
250C4—22no—
251C4—41no—
252C4—42no—
253C4—2832no—
254C4—5662no—
255C4—11321no—
256C4—11322no—
257C4C2×D4×D28312yes—
258C2—81no—
259C2—2834no—
260C2—22641no—
261C2#127×D28311yescharacteristic
262C2#137×D28312yes—
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#497×C283C2
socleC22×C283C22×D4
prime radicalC2×D4×D283C22
hypercenter#497D283
hypocenterC283C2×#497
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D283C2semidirect
3. C4⋊Q8×D283C2semidirect
5. #31826860C2semidirect
6. #31826859C2semidirect
7. #31826858C2semidirect
8. #31826857C2semidirect
9. #31826856C2semidirect
10. #97×D283C2semidirect
11. #497×C283C2semidirect
15. C2×Dic1132C22semidirect
16. C2×#17985382C22semidirect
17. C2×#17985382C22semidirect
24. #22583610C22semidirect
26. #22583608C22semidirect
34. #22583521C22semidirect
35. #22583520C22semidirect
36. C2×Q16×C283C22semidirect
38. C4⋊Q8×C283C22semidirect
40. #97×C283C22semidirect
130. D283#497direct (N × H)
131. C283C2×#497semidirect
142. #497D283direct (N × H)
151. C2×Q16C2×D283semidirect
161. C4⋊Q8C2×D283semidirect
172. #97C2×D283semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×D2832
C2×SD16×D2832
C4⋊Q8×D2832
#124×D2832
#318268602
#318268592
#318268582
#318268572
#318268562
#97×D2832
#497×C2832
C2×#497283