Finite Group Databasebeta

← C2×#31826851 #49131692

Subgroups — C2×#31826851 #49131692

Order 36224.

668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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×D2264C211yesmaximal, characteristic, complemented
3C22×#17985377C211yesmaximal, characteristic, complemented
4C2×#22583606C211yesmaximal, characteristic, complemented
5C2×#22583599C211yesmaximal, characteristic, complemented
6#31826851C218yesmaximal, direct product factor
7C2×#22583520C211yesmaximal, characteristic, complemented
8C22×SD16×C283C211yesmaximal, characteristic, complemented
9C22×D1132C2211yescharacteristic
10C22×D1132C2211yescharacteristic
11C22×C22⋊D283—22no—
12C2×#17985379—24no—
13C2×#17985379C2214yescomplemented
14C2×D2264—24no—
15C2×D2264C2214yescomplemented
16C2×#17985377—24no—
17C2×#17985377C2214yescomplemented
18C22×C283⋊C8C2211yescharacteristic
19#22583606—22no—
20#22583606C2214yescomplemented
21#22583599—22no—
22#22583599C2214yescomplemented
23C2×(C2×D283)⋊C4—22no—
24C2×C4×Dic283C2211yescharacteristic
25#22583520C2214yescomplemented
26C22×Q8×C283C2211yescharacteristic
27C22×D4×C283C2211yescharacteristic
28C2×SD16×C283—24no—
29C2×SD16×C283C2214yescomplemented
30C22×C8×C283C2211yescharacteristic
31C23×D283—21no—
32C23×D283—21no—
33C2×D1132—22no—
34C2×D1132—22no—
35C2×D1132—22no—
36C2×D1132—22no—
37C2×D1132—21no—
38C2×D1132—21no—
39C2×D1132C2312yes—
40C2×D1132C2312yes—
41C2×C22⋊D283—28no—
42C2×C22⋊D283—48no—
43C22×Dic283D412yes—
44#17985379—28no—
45D2264—28no—
46#17985377—28no—
47C2×C283⋊C8D414yescomplemented
48C2×C283⋊C8C2312yes—
49(C2×D283)⋊C4—28no—
50C4×Dic283D412yes—
51C4×Dic283C2312yes—
52C24×C283—21no—
53C2×Q8×C283—21no—
54C2×Q8×C283—22no—
55C2×Q8×C283—22no—
56C2×Q8×C283C2312yes—
57C2×D4×C283—22no—
58C2×D4×C283—22no—
59C2×D4×C283—21no—
60C2×D4×C283C2312yes—
61C22×C4×C283—21no—
62C22×C4×C283C2311yescharacteristic
63SD16×C283—28no—
64C2×C8×C283D414yescomplemented
65C2×C8×C283C2312yes—
66C22×D283—22no—
67C22×D283—22no—
68C22×D283—42no—
69C22×D283—42no—
70C22×D283—44no—
71C22×D283—44no—
72D1132—22no—
73D1132—22no—
74D1132—22no—
75D1132—22no—
76D1132—42no—
77D1132—42no—
78C22⋊D283—416no—
79C2×Dic283—24no—
80C2×Dic283C2×D414yes—
81C283⋊C8C2×D414yescomplemented
82C23×C283—22no—
83C23×C283—42no—
84C23×C283—44no—
85C23×C283C2×D411yescharacteristic
86Q8×C283—22no—
87Q8×C283—22no—
88Q8×C283—42no—
89D4×C283—22no—
90D4×C283—22no—
91D4×C283—42no—
92C2×C4×C283—22no—
93C2×C4×C283—42no—
94C2×C4×C283C2×D411yescharacteristic
95C2×C4×C283C2×D412yes—
96C2×C4×C283C2×D412yes—
97C2×C4×C283C2411yescharacteristic
98C8×C283C2×D414yescomplemented
99C22×C283—42no—
100C22×C283—44no—
101C22×C283—84no—
102C22×C283#12712yes—
103C22×C283AGL(1,ℤ/8)14yes—
104C22×C283C22×D411yescharacteristic
105C2×D283—42no—
106C2×D283—42no—
107C2×D283—44no—
108C2×D283—44no—
109C2×D283—84no—
110C2×D283—84no—
111C4×C283—42no—
112C4×C283#12712yes—
113C4×C283C22×D411yescharacteristic
114C4×C283C22×D411yescharacteristic
115Dic283—24no—
116C2×C283—82no—
117C2×C283#49614yescomplemented
118C2×C283C2×#12711yescharacteristic
119C2×C283C2×AGL(1,ℤ/8)12yes—
120D283—82no—
121D283—82no—
122C283C2×#49611yescharacteristic, complemented, Sylow
123C2×#496—2831nomaximal, Sylow
124C22×SD16—2831no—
125C22×SD16D28311yescharacteristic, complemented
126C22×D8—2831no—
127C22×D8—2831no—
128C2×#127—2831no—
129C2×#124—2831no—
130#496—2838no—
131C2×#97—2831no—
132C22×Q8C2×D28311yescharacteristic
133C22×D4—2831no—
134C22×D4—2831no—
135C22×D4—5662no—
136C22×D4C2×D28311yescharacteristic
137C2×SD16—24no—
138C2×SD16—2834no—
139C2×SD16—5664no—
140C2×SD16C2×D28314yescomplemented
141C2×D8—2834no—
142C2×D8—2834no—
143C2×D8—5664no—
144C2×D8—5664no—
145C22×C8—2831no—
146C22×C8C2×D28311yescharacteristic
147#127—2834no—
148#127—5662no—
149#124—2834no—
150#124—5662no—
151C2×C22⋊C4—5662no—
152C2×C42—2831no—
153#97—2834no—
154C24—21no—
155C24—5661no—
156C24—5661no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D28312yes—
161C2×D4—22no—
162C2×D4—21no—
163C2×D4—22no—
164C2×D4—2832no—
165C2×D4—2832no—
166C2×D4—5668no—
167C2×D4—5662no—
168C2×D4—5662no—
169C2×D4—5661no—
170C2×D4—5661no—
171C2×D4—5662no—
172C2×D4—5662no—
173C2×D4—11328no—
174C2×D4C22×D28312yes—
175C22×C4—21no—
176C22×C4—2832no—
177C22×C4C22×D28311yescharacteristic
178SD16—28no—
179SD16—5668no—
180D8—5668no—
181D8—5668no—
182C2×C8—2834no—
183C2×C8—2832no—
184C2×C8C22⋊D28314yescomplemented
185C2×C8C22×D28312yes—
186C22⋊C4—5668no—
187C42—2832no—
188C42—2832no—
189C23—22no—
190C23—42no—
191C23—44no—
192C23—5662no—
193C23—5662no—
194C23—11322no—
195C23—11322no—
196C23—11324no—
197C23—11324no—
198C23D4×D28311yescharacteristic
199Q8—22no—
200Q8—22no—
201Q8—42no—
202D4—22no—
203D4—22no—
204D4—42no—
205D4—5662no—
206D4—5662no—
207D4—5662no—
208D4—5662no—
209D4—113216no—
210D4—11322no—
211D4—11322no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—2834no—
215C2×C4—5664no—
216C2×C4D4×D28311yescharacteristic
217C2×C4D4×D28312yes—
218C2×C4C2×C22⋊D28312yes—
219C2×C4C23×D28311yescharacteristic
220C8—2834no—
221C8C2×C22⋊D28314yescomplemented
222C22—44no—
223C22—42no—
224C22—84no—
225C22—11324no—
226C22—11324no—
227C22—11322no—
228C22—11322no—
229C22—22644no—
230C22—22644no—
231C22#2258360612yes—
232C22#2258363714yes—
233C22C2×D4×D28311yescharacteristic
234C4—42no—
235C4—5664no—
236C4#2258360612yes—
237C4C2×D4×D28311yescharacteristic
238C4C22×C22⋊D28311yescharacteristic
239C2—82no—
240C2—22642no—
241C2—22642no—
242C2#3182685114yesdirect product factor
243C2C2×#2258360611yescharacteristic
244C2C2×#2258363712yes—
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×SD16×C283C2
socleC23×C283C2×D4
hypercenterC22×SD16D283
hypocenterC283C2×#496
LCSG ▷ C2×C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#17985379C2semidirect
2. C22×D2264C2semidirect
3. C22×#17985377C2semidirect
4. C2×#22583606C2semidirect
5. C2×#22583599C2semidirect
6. #31826851C2direct (N × H)
7. C2×#22583520C2semidirect
8. C22×SD16×C283C2semidirect
13. C2×#17985379C22semidirect
15. C2×D2264C22semidirect
17. C2×#17985377C22semidirect
20. #22583606C22semidirect
22. #22583599C22semidirect
25. #22583520C22semidirect
29. C2×SD16×C283C22semidirect
47. C2×C283⋊C8D4semidirect
64. C2×C8×C283D4semidirect
81. C283⋊C8C2×D4semidirect
98. C8×C283C2×D4semidirect
117. C2×C283#496semidirect
122. C283C2×#496semidirect
125. C22×SD16D283semidirect
140. C2×SD16C2×D283semidirect
184. C2×C8C22⋊D283semidirect
221. C8C2×C22⋊D283semidirect
242. C2#31826851direct (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×D22642
C22×#179853772
C2×#225836062
C2×#225835992
#318268512
C2×#225835202
C22×SD16×C2832
C2×#496283