Finite Group Databasebeta

← #49129741

Subgroups — #49129741

Order 36224.

704 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 209 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
2#31827231C212yesmaximal, complemented
3#31826448C214yesmaximal, complemented
4#31826447C212yesmaximal, complemented
5C2×#22583529C211yesmaximal, characteristic, complemented
6#101×D283C214yesmaximal, complemented
7C2×#101×C283C211yesmaximal, characteristic, complemented
8#22583658—24no—
9#22583658—24no—
10C2×#17985393C412yes—
11C2×#17985393C2212yes—
12C2×#17985392C414yes—
13C2×#17985392C2211yescharacteristic
14C2×#17985392C2211yescharacteristic
15C2×Q8×D283C412yes—
16C2×Q8×D283C2212yes—
17#22583618—24no—
18#22583616—24no—
19C2×#17985376C2212yes—
20M16×D283C2218yes—
21#22583529C2214yes—
22#22583528C2214yes—
23#22583526C2214yes—
24C22×Q8×C283C2211yescharacteristic
25C2×M16×C283C2212yes—
26#101×C283C2214yes—
27#17985393—28no—
28#17985393—28no—
29#17985392—28no—
30#17985392—28no—
31#17985392—22no—
32#17985392—22no—
33#17985392D414yes—
34#17985392D414yes—
35C2×Dic566C2×C414yes—
36C2×Dic566C2×C411yescharacteristic
37C2×Dic566C2311yescharacteristic
38Q8×D283—28no—
39Q8×D283—28no—
40C2×D1132C2×C414yes—
41C2×D1132C2×C411yescharacteristic
42C2×D1132C2311yescharacteristic
43C2×C22⋊D283C2×C412yes—
44C2×C22⋊D283C2×C412yes—
45C2×C4×D283C2×C414yes—
46C2×C4×D283C2×C412yes—
47C2×C4×D283C2×C414yes—
48C2×C4×D283C2312yes—
49#17985376—22no—
50#17985376C2314yes—
51#17985375—28no—
52C2×C283⋊C8—22no—
53C8×D283—28no—
54C2×Q8×C283—22no—
55C2×Q8×C283—22no—
56C2×Q8×C283C2×C412yes—
57C2×Q8×C283C2312yes—
58C22×C4×C283C2×C412yes—
59C22×C4×C283C2311yescharacteristic
60M16×C283—22no—
61M16×C283C2314yes—
62C2×C8×C283—22no—
63C22×D283C22×C412yes—
64C22×D283C22×C412yes—
65Dic566—22no—
66Dic566—28no—
67Dic566C22⋊C414yes—
68D1132—28no—
69D1132—22no—
70D1132C22⋊C414yes—
71C22⋊D283—22no—
72C22⋊D283—22no—
73C22⋊D283C22⋊C414yes—
74C22⋊D283C22⋊C414yes—
75C2×Dic283C22×C412yes—
76C2×Dic283C22×C412yes—
77C4×D283—28no—
78C4×D283—24no—
79C4×D283—28no—
80C4×D283C2×D418yes—
81C283⋊C8—24no—
82C23×C283C22×C411yescharacteristic
83Q8×C283—24no—
84Q8×C283—24no—
85C2×C4×C283—22no—
86C2×C4×C283—22no—
87C2×C4×C283C22×C414yes—
88C2×C4×C283C22×C411yescharacteristic
89C2×C4×C283C2×D412yes—
90C2×C4×C283C2×D412yes—
91C2×C4×C283C2411yescharacteristic
92C8×C283—24no—
93C22×C283—41no—
94C22×C283C2×C22⋊C411yescharacteristic
95C22×C283C2×C22⋊C411yescharacteristic
96C22×C283C23×C411yescharacteristic
97C2×D283—22no—
98C2×D283—42no—
99C2×D283—42no—
100C2×D283C2×C22⋊C414yes—
101C4×C283—24no—
102C4×C283C2×C22⋊C412yes—
103C4×C283C22×D412yes—
104Dic283—22no—
105Dic283C2×C22⋊C414yes—
106C2×C283—21no—
107C2×C283—21no—
108C2×C283—21no—
109C2×C283C22×C22⋊C411yescharacteristic
110D283—24no—
111D283—42no—
112C283#288911yescharacteristic, complemented, Sylow
113#2889—2831nomaximal, Sylow
114C2×2−1+4—2831no—
115#568—2832no—
116#413—2832no—
117#413—2834no—
118C2×#101—2831no—
119C2×#101—2834no—
120C2×#101D28311yescharacteristic, complemented
1212−1+4—5664no—
1222−1+4—5664no—
123C2×#41—2832no—
124C2×#41—2832no—
125C2×#41—2834no—
126C2×#41—2831no—
127C2×#41—2831no—
128C22×Q8—2832no—
129C22×Q8—2832no—
130C22×Q8C2×D28311yescharacteristic
131#131—5664no—
132#131—5664no—
133C2×M16—2832no—
134C2×M16—2838no—
135C2×M16C2×D28312yes—
136#101—2834no—
137#101—2834no—
138#101C2×D28314yes—
139#100—2834no—
140#41—2834no—
141#41—2834no—
142#41—5668no—
143#41—5668no—
144#41—5668no—
145#41—5668no—
146#41—5662no—
147#41—5662no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—2831no—
151C2×Q8—2834no—
152C2×Q8—2831no—
153C2×Q8—5668no—
154C2×Q8—5668no—
155C2×Q8C4×D28312yes—
156C2×Q8C22×D28312yes—
157C2×D4—2832no—
158C2×D4—2832no—
159C2×D4—2831no—
160C2×D4—2834no—
161C2×D4—2831no—
162C22×C4—2832no—
163C22×C4—2834no—
164C22×C4—2834no—
165C22×C4—2832no—
166C22×C4C4×D28312yes—
167C22×C4C22×D28311yescharacteristic
168M16—22no—
169M16—2834no—
170M16—5668no—
171M16—5662no—
172M16C22×D28314yes—
173C2×C8—22no—
174C2×C8—5668no—
175C2×C8—5662no—
176C23—2832no—
177C23—2832no—
178C23C2×C4×D28311yescharacteristic
179Q8—24no—
180Q8—24no—
181Q8—2834no—
182Q8—5668no—
183Q8—5662no—
184D4—2834no—
185D4—2834no—
186D4—2834no—
187D4—5668no—
188D4—5662no—
189D4—5662no—
190D4—5662no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—2832no—
194C2×C4—2838no—
195C2×C4—2832no—
196C2×C4—5668no—
197C2×C4—5668no—
198C2×C4—5664no—
199C2×C4C2×C4×D28314yes—
200C2×C4C2×C4×D28311yescharacteristic
201C2×C4D4×D28312yes—
202C2×C4D4×D28312yes—
203C2×C4C23×D28311yescharacteristic
204C8—24no—
205C8—5664no—
206C22—41no—
207C22—2834no—
208C22—5662no—
209C22—11322no—
210C22—11322no—
211C22C22⋊C4×D28311yescharacteristic
212C22C22⋊C4×D28311yescharacteristic
213C22C22×C4×D28311yescharacteristic
214C4—24no—
215C4—2834no—
216C4—5662no—
217C4C22⋊C4×D28312yes—
218C4C2×D4×D28312yes—
219C2—21no—
220C2—21no—
221C2—21no—
222C2—5664no—
223C2—11322no—
224C2C2×C22⋊C4×D28311yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D283
commutatorC22×C283C23×C4
FrattiniC2×C4C23×D283
FittingC2×#101×C283C2
socleC2×C283C22×C22⋊C4
prime radicalC2×#22583658C2
cosocleC2×C4×C283C24
hypercenterC2×#101D283
hypocenterC283#2889
LCSG ▷ C22×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #31827231C2semidirect
3. #31826448C2semidirect
4. #31826447C2semidirect
5. C2×#22583529C2semidirect
6. #101×D283C2semidirect
7. C2×#101×C283C2semidirect
112. C283#2889semidirect
120. C2×#101D283semidirect

Maximal subgroups

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

subgroupindex
C2×#225836582
#318272312
#318264482
#318264472
C2×#225835292
#101×D2832
C2×#101×C2832
#2889283