Finite Group Databasebeta

← C2×#31826693 #49130820

Subgroups — C2×#31826693 #49130820

Order 36224.

564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×#17985380C211yesmaximal, characteristic, complemented
2C22×C8×D283C211yesmaximal, characteristic, complemented
3C2×#22583590C211yesmaximal, characteristic, complemented
4C2×#22583581C211yesmaximal, characteristic
5#31826693C218yesmaximal, direct product factor
6C2×#22583541C211yesmaximal, characteristic, complemented
7C2×#22583535C211yesmaximal, characteristic, complemented
8C2×#102×C283C211yesmaximal, characteristic, complemented
9C22×Dic566C2211yescharacteristic
10C22×C22⋊D283—21no—
11C22×C4×D283C2211yescharacteristic
12C2×#17985380—24no—
13C2×#17985380C2214yescomplemented
14C22×C283⋊C8C2211yescharacteristic
15C2×C8×D283—24no—
16C2×C8×D283C2214yescomplemented
17#22583590—22no—
18#22583590C2214yescomplemented
19#22583581—22no—
20#22583581C2214yes—
21C2×C4⋊Dic283—21no—
22C2×C4⋊Dic283C2211yescharacteristic
23C2×C22⋊Dic283—21no—
24C2×(C2×D283)⋊C4—21no—
25#22583541C2214yescomplemented
26#22583535C2214yescomplemented
27C22×D4×C283C2211yescharacteristic
28C22×C8×C283C2211yescharacteristic
29C2×C4⋊C4×C283C2211yescharacteristic
30#102×C283C2214yescomplemented
31C23×D283D411yescharacteristic
32C2×Dic566—21no—
33C2×Dic566—22no—
34C2×Dic566—22no—
35C2×Dic566C2312yes—
36C2×C22⋊D283—24no—
37C2×C22⋊D283—44no—
38C22×Dic283—21no—
39C22×Dic283—21no—
40C22×Dic283D411yescharacteristic
41C2×C4×D283—22no—
42C2×C4×D283—22no—
43C2×C4×D283D412yes—
44C2×C4×D283C2312yes—
45#17985380—28no—
46C2×C283⋊C8D414yescomplemented
47C2×C283⋊C8C2312yes—
48C8×D283—28no—
49C4⋊Dic283—24no—
50C4⋊Dic283—21no—
51C4⋊Dic283C2312yes—
52C22⋊Dic283—24no—
53(C2×D283)⋊C4—24no—
54C24×C283—21no—
55C2×D4×C283—22no—
56C2×D4×C283—21no—
57C2×D4×C283—22no—
58C2×D4×C283C2312yes—
59C22×C4×C283—21no—
60C22×C4×C283C2311yescharacteristic
61C2×C8×C283—22no—
62C2×C8×C283C2312yes—
63C4⋊C4×C283—21no—
64C4⋊C4×C283C2312yes—
65C22×D283—22no—
66C22×D283—22no—
67C22×D283SD1614yescomplemented
68C22×D283C2×D412yes—
69Dic566—22no—
70Dic566—22no—
71Dic566—42no—
72C22⋊D283—48no—
73C2×Dic283—22no—
74C2×Dic283—22no—
75C2×Dic283—22no—
76C2×Dic283—42no—
77C2×Dic283—42no—
78C2×Dic283C2×D412yes—
79C4×D283—24no—
80C4×D283—22no—
81C4×D283—22no—
82C283⋊C8C2×D414yescomplemented
83C23×C283—22no—
84C23×C283—42no—
85C23×C283—42no—
86C23×C283—42no—
87C23×C283C2×D411yescharacteristic
88D4×C283—22no—
89D4×C283—22no—
90D4×C283—42no—
91C2×C4×C283—22no—
92C2×C4×C283—42no—
93C2×C4×C283C2×D411yescharacteristic
94C2×C4×C283C2×D412yes—
95C2×C4×C283#4112yes—
96C2×C4×C283C2411yescharacteristic
97C8×C283—22no—
98C22×C283—42no—
99C22×C283—42no—
100C22×C283—42no—
101C22×C283—84no—
102C22×C283#12112yes—
103C22×C283C2×SD1612yes—
104C22×C283#13512yes—
105C22×C283C22×D411yescharacteristic
106C2×D283—22no—
107C2×D283—22no—
108C2×D283—28no—
109C2×D283C2×SD1614yescomplemented
110C4×C283—42no—
111C4×C283#12112yes—
112C4×C283C22×D411yescharacteristic
113C4×C283C2×#4111yescharacteristic
114Dic283—22no—
115Dic283—42no—
116Dic283—42no—
117C2×C283—82no—
118C2×C283#46514yescomplemented
119C2×C283C2×#12111yescharacteristic
120C2×C283C22×SD1611yescharacteristic
121C2×C283C2×#13511yescharacteristic
122D283—24no—
123C283C2×#46511yescharacteristic, complemented, Sylow
124C2×#465—2831nomaximal, Sylow
125C22×SD16—2831no—
126C23×C8—2831no—
127C2×C22⋊Q8—2831no—
128C2×#121—2831no—
129#465—2838no—
130C2×#106—2831no—
131C2×#103—2831no—
132C2×#102D28311yescharacteristic, complemented
133C22×Q8—2831no—
134C22×D4—5661no—
135C22×D4C2×D28311yescharacteristic
136C23×C4—2831no—
137C2×SD16—2834no—
138C2×SD16—5664no—
139C22×C8—2831no—
140C22×C8—2834no—
141C22×C8—5664no—
142C22×C8C2×D28311yescharacteristic
143C22⋊Q8—2834no—
144C22⋊Q8—5662no—
145#121—2834no—
146#121—5662no—
147C2×C4⋊C4—2831no—
148C2×C4⋊C4—5661no—
149C2×C4⋊C4C2×D28311yescharacteristic
150C2×C22⋊C4—5661no—
151C2×C22⋊C4—5661no—
152#106—2834no—
153#103—2834no—
154#102C2×D28314yescomplemented
155C24—21no—
156C24—2831no—
157C2×Q8—2832no—
158C2×Q8—5661no—
159C2×Q8—5662no—
160C2×Q8—5662no—
161C2×D4—22no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—5664no—
165C2×D4—11324no—
166C2×D4C22×D28312yes—
167C22×C4—21no—
168C22×C4—2831no—
169C22×C4—2832no—
170C22×C4—2832no—
171C22×C4—5662no—
172C22×C4—5662no—
173C22×C4—5661no—
174C22×C4—5661no—
175C22×C4C22×D28311yescharacteristic
176SD16—5668no—
177C2×C8—22no—
178C2×C8—2834no—
179C2×C8—2832no—
180C2×C8—5668no—
181C2×C8C22×D28312yes—
182C4⋊C4—21no—
183C4⋊C4—2832no—
184C4⋊C4—5664no—
185C4⋊C4—5661no—
186C4⋊C4C22×D28312yes—
187C22⋊C4—5664no—
188C22⋊C4—5664no—
189C23—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—2834no—
194C23—2832no—
195C23—5662no—
196C23—5662no—
197C23D4×D28311yescharacteristic
198Q8—5662no—
199Q8—5662no—
200Q8—11322no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—11328no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—2832no—
208C2×C4—5662no—
209C2×C4—5664no—
210C2×C4—5662no—
211C2×C4—5662no—
212C2×C4—5662no—
213C2×C4—5662no—
214C2×C4—11322no—
215C2×C4—11322no—
216C2×C4D4×D28311yescharacteristic
217C2×C4D4×D28312yes—
218C2×C4#1798539212yes—
219C2×C4C23×D28311yescharacteristic
220C8—22no—
221C8—2834no—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—2834no—
227C22—5668no—
228C22—5662no—
229C22—5662no—
230C22#2258358312yes—
231C22SD16×D28312yes—
232C22#2258362912yes—
233C22C2×D4×D28311yescharacteristic
234C4—42no—
235C4—5662no—
236C4—11322no—
237C4—11322no—
238C4#2258358312yes—
239C4C2×D4×D28311yescharacteristic
240C4C2×#1798539211yescharacteristic
241C2—82no—
242C2—5664no—
243C2#3182669314yesdirect product factor
244C2C2×#2258358311yescharacteristic
245C2C2×SD16×D28311yescharacteristic
246C2C2×#2258362911yescharacteristic
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×#102×C283C2
socleC23×C283C2×D4
prime radicalC2×#22583581C2
hypercenterC2×#102D283
hypocenterC283C2×#465
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#17985380C2semidirect
2. C22×C8×D283C2semidirect
3. C2×#22583590C2semidirect
5. #31826693C2direct (N × H)
6. C2×#22583541C2semidirect
7. C2×#22583535C2semidirect
8. C2×#102×C283C2semidirect
13. C2×#17985380C22semidirect
16. C2×C8×D283C22semidirect
18. #22583590C22semidirect
25. #22583541C22semidirect
26. #22583535C22semidirect
30. #102×C283C22semidirect
46. C2×C283⋊C8D4semidirect
67. C22×D283SD16semidirect
82. C283⋊C8C2×D4semidirect
109. C2×D283C2×SD16semidirect
118. C2×C283#465semidirect
123. C283C2×#465semidirect
132. C2×#102D283semidirect
154. #102C2×D283semidirect
243. C2#31826693direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179853802
C22×C8×D2832
C2×#225835902
C2×#225835812
#318266932
C2×#225835412
C2×#225835352
C2×#102×C2832
C2×#465283