Finite Group Databasebeta

← C2×#31826713 #49130851

Subgroups — C2×#31826713 #49130851

Order 36224.

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

normal subgroups only

This group has 544 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×#17985379C211yesmaximal, characteristic, complemented
2C22×#17985376C211yesmaximal, characteristic, complemented
3C2×#22583584C211yesmaximal, characteristic
4#31826713C218yesmaximal, direct product factor
5C2×#22583543C211yesmaximal, characteristic, complemented
6C2×#22583534C211yesmaximal, characteristic, complemented
7C2×#22583530C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C283C211yesmaximal, characteristic, complemented
9C22×D1132C2211yescharacteristic
10C22×C22⋊D283—21no—
11C2×#17985379—24no—
12C2×#17985379C2214yescomplemented
13C2×#17985376—24no—
14C2×#17985376C2214yescomplemented
15C22×C283⋊C8C2211yescharacteristic
16C22×C283⋊C8C2211yescharacteristic
17#22583584—22no—
18#22583584C2214yes—
19C2×C4⋊Dic283C2211yescharacteristic
20C2×(C2×D283)⋊C4—21no—
21#22583543C2214yescomplemented
22#22583534C2214yescomplemented
23#22583530C2214yescomplemented
24C22×Q8×C283C2211yescharacteristic
25C23×C4×C283C2211yescharacteristic
26C22⋊Q8×C283—22no—
27C22⋊Q8×C283C2214yescomplemented
28C2×C4⋊C4×C283—21no—
29C2×C4⋊C4×C283C2211yescharacteristic
30C2×C22⋊C4×C283—21no—
31C23×D283—21no—
32C2×D1132—22no—
33C2×D1132—21no—
34C2×D1132—22no—
35C2×D1132C2312yes—
36C2×C22⋊D283—24no—
37C2×C22⋊D283—44no—
38C22×Dic283—21no—
39#17985379—28no—
40#17985376—28no—
41C2×C283⋊C8—22no—
42C2×C283⋊C8D414yescomplemented
43C2×C283⋊C8C2312yes—
44C2×C283⋊C8C2312yes—
45C4⋊Dic283—21no—
46C4⋊Dic283C2312yes—
47(C2×D283)⋊C4—24no—
48C24×C283D411yescharacteristic
49C2×Q8×C283—21no—
50C2×Q8×C283—22no—
51C2×Q8×C283—22no—
52C2×Q8×C283C2312yes—
53C22×C4×C283—22no—
54C22×C4×C283—22no—
55C22×C4×C283—21no—
56C22×C4×C283—21no—
57C22×C4×C283D411yescharacteristic
58C22×C4×C283D412yes—
59C22×C4×C283C2312yes—
60C22×C4×C283C2311yescharacteristic
61C4⋊C4×C283—24no—
62C4⋊C4×C283—21no—
63C4⋊C4×C283C2312yes—
64C22⋊C4×C283—24no—
65C22×D283—22no—
66C22×D283—42no—
67C22×D283—42no—
68C22×D283—42no—
69D1132—22no—
70D1132—22no—
71D1132—42no—
72C22⋊D283—48no—
73C2×Dic283—22no—
74C2×Dic283—42no—
75C283⋊C8—22no—
76C283⋊C8C2×D414yescomplemented
77C23×C283—22no—
78C23×C283—22no—
79C23×C283—22no—
80C23×C283C2×D412yes—
81C23×C283C2×D411yescharacteristic
82Q8×C283—22no—
83Q8×C283—22no—
84Q8×C283—42no—
85C2×C4×C283—22no—
86C2×C4×C283—24no—
87C2×C4×C283—22no—
88C2×C4×C283—22no—
89C2×C4×C283—22no—
90C2×C4×C283—22no—
91C2×C4×C283—42no—
92C2×C4×C283—42no—
93C2×C4×C283C2×D412yes—
94C2×C4×C283C2×D412yes—
95C2×C4×C283C2×D411yescharacteristic
96C2×C4×C283#4112yes—
97C2×C4×C283C2411yescharacteristic
98C22×C283—22no—
99C22×C283—22no—
100C22×C283—22no—
101C22×C283—44no—
102C22×C283#12112yes—
103C22×C283AGL(1,ℤ/8)12yes—
104C22×C283#13712yes—
105C22×C283C22×D411yescharacteristic
106C2×D283—42no—
107C2×D283—42no—
108C2×D283—42no—
109C2×D283—84no—
110C4×C283—22no—
111C4×C283—42no—
112C4×C283—42no—
113C4×C283#12112yes—
114C4×C283C22×D411yescharacteristic
115C4×C283C2×#4111yescharacteristic
116Dic283—42no—
117C2×C283—42no—
118C2×C283#46814yescomplemented
119C2×C283C2×#12111yescharacteristic
120C2×C283C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C283C2×#13711yescharacteristic
122D283—82no—
123C283C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—2831nomaximal, Sylow
125C22×SD16—2831no—
126C22×M16—2831no—
127C2×C22⋊Q8D28311yescharacteristic, complemented
128C2×#121—2831no—
129#468—2838no—
130C2×#107—2831no—
131C2×#103—2831no—
132C2×#102—2831no—
133C22×Q8C2×D28311yescharacteristic
134C22×D4—2831no—
135C22×D4—5661no—
136C23×C4C2×D28311yescharacteristic
137C2×SD16—2834no—
138C2×SD16—5664no—
139C2×M16—2834no—
140C2×M16—5664no—
141C22×C8—2831no—
142C22×C8—2831no—
143C22⋊Q8—22no—
144C22⋊Q8C2×D28314yescomplemented
145#121—2834no—
146#121—5662no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—2831no—
149C2×C4⋊C4C2×D28311yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—5661no—
152#107—2834no—
153#103—2834no—
154#102—2834no—
155C24—5661no—
156C24C22⋊D28311yescharacteristic
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D28312yes—
161C2×D4—2832no—
162C2×D4—5664no—
163C2×D4—5662no—
164C2×D4—5661no—
165C2×D4—5662no—
166C2×D4—11324no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—5661no—
172C22×C4C22⋊D28312yes—
173C22×C4C22⋊D28311yescharacteristic
174C22×C4C22×D28312yes—
175C22×C4C22×D28311yescharacteristic
176SD16—5668no—
177M16—5668no—
178C2×C8—2834no—
179C2×C8—2832no—
180C2×C8—2832no—
181C2×C8—5662no—
182C4⋊C4—24no—
183C4⋊C4—21no—
184C4⋊C4—2832no—
185C4⋊C4—5661no—
186C4⋊C4C22×D28312yes—
187C22⋊C4—24no—
188C22⋊C4—5664no—
189C23—22no—
190C23—22no—
191C23—22no—
192C23—5662no—
193C23—11322no—
194C23—11322no—
195C23—11322no—
196C23C2×C22⋊D28312yes—
197C23C2×C22⋊D28311yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—5662no—
202D4—5662no—
203D4—11328no—
204D4—11322no—
205C2×C4—22no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—5662no—
214C2×C4—11322no—
215C2×C4D4×D28312yes—
216C2×C4C2×C22⋊D28312yes—
217C2×C4C2×C22⋊D28311yescharacteristic
218C2×C4#1798539112yes—
219C2×C4C23×D28311yescharacteristic
220C8—2834no—
221C8—5662no—
222C22—22no—
223C22—22no—
224C22—22no—
225C22—44no—
226C22—11322no—
227C22—11322no—
228C22—11322no—
229C22—22644no—
230C22#2258358212yes—
231C22#2258363512yes—
232C22#2258364112yes—
233C22C22×C22⋊D28311yescharacteristic
234C4—22no—
235C4—42no—
236C4—42no—
237C4—11322no—
238C4#2258358212yes—
239C4C2×D4×D28311yescharacteristic
240C4C2×#1798539111yescharacteristic
241C2—42no—
242C2—22642no—
243C2#3182671314yesdirect product factor
244C2C2×#2258358211yescharacteristic
245C2C2×#2258363511yescharacteristic
246C2C2×#2258364111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC2×C22⋊Q8×C283C2
socleC23×C283C2×D4
prime radicalC2×#22583584C2
hypercenterC2×C22⋊Q8D283
hypocenterC283C2×#468
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#17985379C2semidirect
2. C22×#17985376C2semidirect
4. #31826713C2direct (N × H)
5. C2×#22583543C2semidirect
6. C2×#22583534C2semidirect
7. C2×#22583530C2semidirect
8. C2×C22⋊Q8×C283C2semidirect
12. C2×#17985379C22semidirect
14. C2×#17985376C22semidirect
21. #22583543C22semidirect
22. #22583534C22semidirect
23. #22583530C22semidirect
27. C22⋊Q8×C283C22semidirect
42. C2×C283⋊C8D4semidirect
76. C283⋊C8C2×D4semidirect
118. C2×C283#468semidirect
123. C283C2×#468semidirect
127. C2×C22⋊Q8D283semidirect
144. C22⋊Q8C2×D283semidirect
243. C2#31826713direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179853792
C22×#179853762
C2×#225835842
#318267132
C2×#225835432
C2×#225835342
C2×#225835302
C2×C22⋊Q8×C2832
C2×#468283