Finite Group Databasebeta

← C2×#31826846 #49131679

Subgroups — C2×#31826846 #49131679

Order 36224.

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

normal subgroups only

This group has 592 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×#17985382C211yesmaximal, characteristic, complemented
2C22×#17985381C211yesmaximal, characteristic, complemented
3C22×#17985377C211yesmaximal, characteristic
4C2×#22583599C211yesmaximal, characteristic, complemented
5C2×#22583597C211yesmaximal, characteristic, complemented
6#31826846C218yesmaximal, direct product factor
7C2×C8×Dic283C211yesmaximal, characteristic, complemented
8C22×SD16×C283C211yesmaximal, characteristic, complemented
9C22×Dic566C2211yescharacteristic
10C22×D1132C2211yescharacteristic
11C2×#17985382—24no—
12C2×#17985382C2214yescomplemented
13C2×#17985381—24no—
14C2×#17985381C2214yescomplemented
15C2×#17985377—24no—
16C2×#17985377C2214yes—
17C22×C283⋊C8C2211yescharacteristic
18#22583599—22no—
19#22583599C2214yescomplemented
20#22583597—22no—
21#22583597C2214yescomplemented
22C2×C22⋊Dic283—22no—
23C2×(C2×D283)⋊C4—22no—
24C2×C4×Dic283C2211yescharacteristic
25C8×Dic283C2214yescomplemented
26C22×Q8×C283C2211yescharacteristic
27C22×D4×C283C2211yescharacteristic
28C2×SD16×C283—24no—
29C2×SD16×C283C2214yescomplemented
30C22×C8×C283C2211yescharacteristic
31C23×D283—21no—
32C2×Dic566—21no—
33C2×Dic566—22no—
34C2×Dic566—22no—
35C2×Dic566C2312yes—
36C2×D1132—22no—
37C2×D1132—22no—
38C2×D1132—21no—
39C2×D1132C2312yes—
40C22×Dic283—21no—
41C22×Dic283D412yes—
42#17985382—28no—
43#17985381—28no—
44#17985377—28no—
45C2×C283⋊C8D414yes—
46C2×C283⋊C8C2312yes—
47C22⋊Dic283—28no—
48(C2×D283)⋊C4—28no—
49C4×Dic283D412yes—
50C4×Dic283C2312yes—
51C24×C283—21no—
52C2×Q8×C283—21no—
53C2×Q8×C283—22no—
54C2×Q8×C283—22no—
55C2×Q8×C283C2312yes—
56C2×D4×C283—22no—
57C2×D4×C283—22no—
58C2×D4×C283—21no—
59C2×D4×C283C2312yes—
60C22×C4×C283—21no—
61C22×C4×C283C2311yescharacteristic
62SD16×C283—28no—
63C2×C8×C283D414yes—
64C2×C8×C283C2312yes—
65C22×D283—22no—
66C22×D283—42no—
67C22×D283—44no—
68Dic566—22no—
69Dic566—22no—
70Dic566—42no—
71D1132—22no—
72D1132—22no—
73D1132—42no—
74C2×Dic283—24no—
75C2×Dic283—22no—
76C2×Dic283—42no—
77C2×Dic283C2×D414yes—
78C283⋊C8C2×D414yes—
79C23×C283—22no—
80C23×C283—42no—
81C23×C283—44no—
82C23×C283C2×D411yescharacteristic
83Q8×C283—22no—
84Q8×C283—22no—
85Q8×C283—42no—
86D4×C283—22no—
87D4×C283—22no—
88D4×C283—42no—
89C2×C4×C283—22no—
90C2×C4×C283—42no—
91C2×C4×C283C2×D411yescharacteristic
92C2×C4×C283C2×D412yes—
93C2×C4×C283C2×D412yes—
94C2×C4×C283C2411yescharacteristic
95C8×C283C2×D414yes—
96C22×C283—42no—
97C22×C283—44no—
98C22×C283—84no—
99C22×C283#12712yes—
100C22×C283#13514yes—
101C22×C283C22×D411yescharacteristic
102C2×D283—42no—
103C2×D283—44no—
104C2×D283—84no—
105C4×C283—42no—
106C4×C283#12712yes—
107C4×C283C22×D411yescharacteristic
108C4×C283C22×D411yescharacteristic
109Dic283—24no—
110Dic283—42no—
111C2×C283—82no—
112C2×C283#49514yescomplemented
113C2×C283C2×#12711yescharacteristic
114C2×C283C2×#13512yes—
115D283—82no—
116C283C2×#49511yescharacteristic, complemented, Sylow
117C2×#495—2831nomaximal, Sylow
118C22×Q16—2831no—
119C22×SD16—2831no—
120C22×SD16D28311yescharacteristic, complemented
121C22×D8—2831no—
122C2×#124—2831no—
123C2×#124—2831no—
124#495—2838no—
125C2×C4×C8—2831no—
126C22×Q8—2831no—
127C22×Q8C2×D28311yescharacteristic
128C22×D4—2831no—
129C22×D4C2×D28311yescharacteristic
130C2×Q16—2834no—
131C2×Q16—5664no—
132C2×SD16—24no—
133C2×SD16—2834no—
134C2×SD16—5664no—
135C2×SD16C2×D28314yescomplemented
136C2×D8—2834no—
137C2×D8—5664no—
138C22×C8—2831no—
139C22×C8C2×D28311yescharacteristic
140#124—2834no—
141#124—2834no—
142#124—5662no—
143#124—5662no—
144C2×C22⋊C4—5662no—
145C2×C22⋊C4—5662no—
146C2×C42—2831no—
147C4×C8—2834no—
148C24—21no—
149C24—5661no—
150C2×Q8—21no—
151C2×Q8—22no—
152C2×Q8—22no—
153C2×Q8—2832no—
154C2×Q8—5661no—
155C2×Q8—5662no—
156C2×Q8—5662no—
157C2×Q8C22×D28312yes—
158C2×D4—22no—
159C2×D4—21no—
160C2×D4—22no—
161C2×D4—2832no—
162C2×D4—5662no—
163C2×D4—5661no—
164C2×D4—5662no—
165C2×D4C22×D28312yes—
166C22×C4—21no—
167C22×C4—2832no—
168C22×C4—5661no—
169C22×C4C22×D28311yescharacteristic
170Q16—5668no—
171SD16—28no—
172SD16—5668no—
173D8—5668no—
174C2×C8—2834no—
175C2×C8—2832no—
176C2×C8C22⋊D28314yes—
177C2×C8C22×D28312yes—
178C22⋊C4—5668no—
179C22⋊C4—5668no—
180C42—2832no—
181C42—2832no—
182C23—22no—
183C23—42no—
184C23—44no—
185C23—5662no—
186C23—11322no—
187C23—11324no—
188C23D4×D28311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—42no—
192Q8—5662no—
193Q8—5662no—
194Q8—11322no—
195D4—22no—
196D4—22no—
197D4—42no—
198D4—5662no—
199D4—5662no—
200D4—11322no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—2834no—
204C2×C4—5664no—
205C2×C4—5662no—
206C2×C4—11322no—
207C2×C4D4×D28311yescharacteristic
208C2×C4D4×D28312yes—
209C2×C4C2×C22⋊D28312yes—
210C2×C4C23×D28311yescharacteristic
211C8—2834no—
212C8C2×C22⋊D28314yes—
213C22—44no—
214C22—42no—
215C22—84no—
216C22—11324no—
217C22—11322no—
218C22—22644no—
219C22#2258360612yes—
220C22#2258363114yes—
221C22C2×D4×D28311yescharacteristic
222C4—42no—
223C4—5664no—
224C4—11322no—
225C4#2258360612yes—
226C4C2×D4×D28311yescharacteristic
227C4C22×C22⋊D28311yescharacteristic
228C2—82no—
229C2—22642no—
230C2#3182684614yesdirect product factor
231C2C2×#2258360611yescharacteristic
232C2C2×#2258363112yes—
subgroupG/H
centerC23D4×D283
commutator, cosocleC2×C4×C283C24
FrattiniC2×C4C23×D283
FittingC22×SD16×C283C2
socleC23×C283C2×D4
prime radicalC22×#17985377C2
hypercenterC22×SD16D283
hypocenterC283C2×#495
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×#17985382C2semidirect
2. C22×#17985381C2semidirect
4. C2×#22583599C2semidirect
5. C2×#22583597C2semidirect
6. #31826846C2direct (N × H)
7. C2×C8×Dic283C2semidirect
8. C22×SD16×C283C2semidirect
12. C2×#17985382C22semidirect
14. C2×#17985381C22semidirect
19. #22583599C22semidirect
21. #22583597C22semidirect
25. C8×Dic283C22semidirect
29. C2×SD16×C283C22semidirect
112. C2×C283#495semidirect
116. C283C2×#495semidirect
120. C22×SD16D283semidirect
135. C2×SD16C2×D283semidirect
230. C2#31826846direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#179853822
C22×#179853812
C22×#179853772
C2×#225835992
C2×#225835972
#318268462
C2×C8×Dic2832
C22×SD16×C2832
C2×#495283