Finite Group Databasebeta

← #49132916

Subgroups — #49132916

Order 36224.

476 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 121 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×#22583639C212yesmaximal, complemented
2#31827123C212yesmaximal, complemented
3#31826708C212yesmaximal, complemented
4#31826684C212yesmaximal, complemented
5#31826619C212yesmaximal, complemented
6#31826607C212yesmaximal, complemented
7C4×Dic1132C211yesmaximal, characteristic, complemented
8#31826544C211yesmaximal, characteristic, complemented
9#495×C283C211yesmaximal, characteristic, complemented
10C2×#17985391C2212yes—
11C2×Q8×D283C2212yes—
12#22583639—28no—
13C2×Dic1132C2211yescharacteristic
14C2×#17985382C2212yes—
15C2×#17985380C2212yes—
16C2×#17985375C2212yes—
17#22583596—22no—
18#22583587—22no—
19#22583586C2212yes—
20#22583583—22no—
21#22583581C2212yes—
22C4×Dic566C2212yes—
23C4×D1132C2211yescharacteristic
24(C22⋊D283)⋊C4—22no—
25#22583544C2211yescharacteristic
26C4⋊(C283⋊C8)C2211yescharacteristic
27#22583535C2212yes—
28#22583534C2212yes—
29#22583531C2212yes—
30(C2×D283)⋊C8C2212yes—
31C2×Q16×C283C2211yescharacteristic
32C2×SD16×C283C2212yes—
33C2×D8×C283C2211yescharacteristic
34#124×C283C2212yes—
35C4×C8×C283C2211yescharacteristic
36#17985391—24no—
37#17985391—42no—
38C2×Dic566—22no—
39C2×Dic566C2312yes—
40Q8×D283—24no—
41Q8×D283—42no—
42C2×D1132D411yescharacteristic
43C2×C22⋊D283—22no—
44C2×C22⋊D283—22no—
45C22×Dic283—22no—
46C2×C4×D283—22no—
47C2×C4×D283C2312yes—
48Dic1132D414yescomplemented
49#17985382—24no—
50#17985380—24no—
51#17985375—24no—
52C2×C283⋊C8C2312yes—
53C4⋊Dic283D411yescharacteristic
54C4⋊Dic283C2312yes—
55Dic283⋊C4—22no—
56Dic283⋊C4—22no—
57C22⋊Dic283—22no—
58(C2×D283)⋊C4—22no—
59(C2×D283)⋊C4D412yes—
60C4×Dic283—22no—
61C2×Q8×C283C2312yes—
62C2×D4×C283C2312yes—
63Q16×C283—41no—
64SD16×C283—24no—
65D8×C283—41no—
66C2×C8×C283C2311yescharacteristic
67C2×C8×C283C2311yescharacteristic
68C22⋊C4×C283—22no—
69C22⋊C4×C283—22no—
70C42×C283C2311yescharacteristic
71C22×D283C2×D412yes—
72Dic566—22no—
73Dic566—44no—
74Dic566C2×D414yes—
75D1132—41no—
76C22⋊D283—44no—
77C22⋊D283—44no—
78C2×Dic283—22no—
79C2×Dic283—22no—
80C2×Dic283—44no—
81C2×Dic283C2×D412yes—
82C4×D283—22no—
83C4×D283—22no—
84C4×D283—44no—
85C283⋊C8—22no—
86C23×C283—22no—
87Q8×C283—22no—
88Q8×C283—22no—
89D4×C283—22no—
90D4×C283—22no—
91C2×C4×C283—22no—
92C2×C4×C283C2×D411yescharacteristic
93C2×C4×C283C2×D411yescharacteristic
94C2×C4×C283C2411yescharacteristic
95C8×C283—21no—
96C8×C283C2×D412yes—
97C22×C283—42no—
98C22×C283—42no—
99C22×C283—42no—
100C22×C283C22×D411yescharacteristic
101C2×D283—22no—
102C2×D283—22no—
103C2×D283—22no—
104C4×C283—21no—
105C4×C283—21no—
106C4×C283—42no—
107C4×C283C22×D411yescharacteristic
108C4×C283H(5,𝔽2)11yescharacteristic
109Dic283—22no—
110Dic283—24no—
111Dic283—42no—
112C2×C283—82no—
113C2×C283D4211yescharacteristic
114C2×C283#57511yescharacteristic
115C2×C283#57811yescharacteristic
116D283—42no—
117C283#327711yescharacteristic, complemented, Sylow
118#3277—2831nomaximal, Sylow
119C2×#137—2832no—
120#548—2832no—
121#495D28311yescharacteristic, complemented
122#468—2832no—
123#464—2832no—
124#451—2832no—
125#449—2832no—
126C4×Q16—2831no—
127#436—2831no—
128C2×#41—2832no—
129C22×Q8—2832no—
130#137—5668no—
131C2×Q16—2832no—
132C2×Q16—2831no—
133C2×Q16C2×D28311yescharacteristic
134C2×SD16—2832no—
135C2×SD16C2×D28312yes—
136C2×D8C2×D28311yescharacteristic
137C2×M16—2832no—
138#124—5662no—
139#124C2×D28312yes—
140C22⋊Q8—2832no—
141C22⋊Q8—5662no—
142#121—2832no—
143#121—5662no—
144C4×Q8—2832no—
145C4×D4—2831no—
146C4×D4—5662no—
147#107—2831no—
148C4⋊C8—2831no—
149#103—2832no—
150#103—2832no—
151#102—2832no—
152C22⋊C8—2832no—
153C4×C8C2×D28311yescharacteristic
154#41—5664no—
155#41—11322no—
156C2×Q8—2832no—
157C2×Q8—5662no—
158C2×Q8—5664no—
159C2×Q8—11322no—
160C2×Q8C22×D28312yes—
161C2×D4—2831no—
162C2×D4—5662no—
163C2×D4—5662no—
164C2×D4C22×D28312yes—
165C22×C4—2832no—
166C22×C4—5662no—
167C22×C4—5662no—
168Q16—41no—
169Q16—2834no—
170Q16—5664no—
171SD16—24no—
172SD16—5664no—
173D8—41no—
174M16—5664no—
175C2×C8—2832no—
176C2×C8C22×D28311yescharacteristic
177C2×C8C22×D28311yescharacteristic
178C4⋊C4—2831no—
179C4⋊C4—2832no—
180C4⋊C4—5662no—
181C4⋊C4—5662no—
182C22⋊C4—22no—
183C22⋊C4—22no—
184C22⋊C4—2832no—
185C22⋊C4—5662no—
186C22⋊C4—5662no—
187C42—5662no—
188C42C22×D28311yescharacteristic
189C23—22no—
190C23—2832no—
191Q8—22no—
192Q8—22no—
193Q8—2834no—
194Q8—5662no—
195Q8—11324no—
196D4—22no—
197D4—22no—
198D4—11321no—
199D4—11324no—
200D4—11324no—
201C2×C4—22no—
202C2×C4—2832no—
203C2×C4—5662no—
204C2×C4—5662no—
205C2×C4—5662no—
206C2×C4—5662no—
207C2×C4—11324no—
208C2×C4—11324no—
209C2×C4D4×D28311yescharacteristic
210C2×C4D4×D28311yescharacteristic
211C2×C4C23×D28311yescharacteristic
212C8—21no—
213C8—5662no—
214C8D4×D28312yes—
215C22—42no—
216C22—42no—
217C22—42no—
218C22—5662no—
219C22—5662no—
220C22—5662no—
221C22C2×D4×D28311yescharacteristic
222C4—21no—
223C4—21no—
224C4—42no—
225C4—5662no—
226C4—5664no—
227C4—11322no—
228C4C2×D4×D28311yescharacteristic
229C4#2258365511yescharacteristic
230C2—82no—
231C2—11322no—
232C2#3182710011yescharacteristic
233C2#3182726211yescharacteristic
234C2#3182727911yescharacteristic
subgroupG/H
centerC22C2×D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
Fitting#495×C283C2
socleC22×C283C22×D4
hypercenter#495D283
hypocenterC283#3277
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. C2×#22583639C2semidirect
2. #31827123C2semidirect
3. #31826708C2semidirect
4. #31826684C2semidirect
5. #31826619C2semidirect
6. #31826607C2semidirect
7. C4×Dic1132C2semidirect
8. #31826544C2semidirect
9. #495×C283C2semidirect
48. Dic1132D4semidirect
117. C283#3277semidirect
121. #495D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836392
#318271232
#318267082
#318266842
#318266192
#318266072
C4×Dic11322
#318265442
#495×C2832
#3277283