Finite Group Databasebeta

← C22×#22575474 #46825612

Subgroups — C22×#22575474 #46825612

Order 34432.

1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.

normal subgroups only

This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 525 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×#16864403C211yesmaximal, characteristic, complemented
2C22×#16864401C211yesmaximal, characteristic, complemented
3C2×#22575474C2124yesmaximal, direct product factor
4C22×#16864392C211yesmaximal, characteristic, complemented
5C22×#16864391C211yesmaximal, characteristic, complemented
6C22×#16864387C211yesmaximal, characteristic, complemented
7C22×C8×D269C211yesmaximal, characteristic, complemented
8C22×SD16×C269C211yesmaximal, characteristic, complemented
9C2×#16864403—26no—
10C2×#16864403C22112yescomplemented
11C2×#16864401—26no—
12C2×#16864401C22112yescomplemented
13C22×Dic538C2211yescharacteristic
14C22×D1076—21no—
15C22×D1076C2211yescharacteristic
16C22×C22⋊D269—21no—
17C23×Dic269—21no—
18C22×C4×D269—21no—
19C22×C4×D269C2211yescharacteristic
20#22575474C22164yesdirect product factor
21C2×#16864392C22112yescomplemented
22C2×#16864391C22112yescomplemented
23C2×#16864387C22112yescomplemented
24C22×#14524130C2211yescharacteristic
25C2×C8×D269C22112yescomplemented
26C22×Q8×C269C2211yescharacteristic
27C22×D4×C269C2211yescharacteristic
28C2×SD16×C269C22112yescomplemented
29C22×C8×C269C2211yescharacteristic
30C23×D269—21no—
31C23×D269D411yescharacteristic
32#16864403—224no—
33#16864403C23116yescomplemented
34#16864401—224no—
35#16864401C23116yescomplemented
36C2×Dic538—23no—
37C2×Dic538C2316yes—
38C2×D1076—212no—
39C2×D1076—23no—
40C2×D1076C2316yes—
41C2×C22⋊D269—212no—
42C22×Dic269—212no—
43C22×Dic269—21no—
44C22×Dic269D411yescharacteristic
45C2×C4×D269—212no—
46C2×C4×D269D416yes—
47C2×C4×D269C2316yes—
48#16864392C23116yescomplemented
49#16864391C23116yescomplemented
50#16864387C23116yescomplemented
51C2×#14524130C2316yes—
52C8×D269C23116yescomplemented
53C24×C269—21no—
54C2×Q8×C269—23no—
55C2×Q8×C269C2316yes—
56C2×D4×C269—23no—
57C2×D4×C269C2316yes—
58C22×C4×C269—21no—
59C22×C4×C269C2311yescharacteristic
60SD16×C269C23116yescomplemented
61C2×C8×C269C2316yes—
62C22×D269—24no—
63C22×D269—26no—
64C22×D269—44no—
65C22×D269C2×D416yes—
66Dic538—26no—
67Dic538C2414yes—
68D1076—216no—
69D1076—26no—
70D1076C2414yes—
71C22⋊D269—216no—
72C2×Dic269—26no—
73C2×Dic269—216no—
74C2×Dic269C2×D416yes—
75C4×D269—216no—
76C4×D269C2×D4112yes—
77C4×D269C2414yes—
78#14524130C2414yes—
79C23×C269—26no—
80C23×C269—44no—
81C23×C269C2×D411yescharacteristic
82Q8×C269—26no—
83Q8×C269C2414yes—
84D4×C269—26no—
85D4×C269C2414yes—
86C2×C4×C269—26no—
87C2×C4×C269C2×D413yes—
88C2×C4×C269C2413yes—
89C8×C269C2414yes—
90C22×C269—24no—
91C22×C269—412no—
92C22×C269#13514yescomplemented
93C22×C269C22×D413yes—
94C2×D269—212no—
95C2×D269—24no—
96C2×D269—412no—
97C2×D269C22×D414yes—
98C4×C269—24no—
99C4×C269C22×D413yes—
100C4×C269C2511yescharacteristic
101Dic269—24no—
102Dic269C22×D414yes—
103C2×C269—44no—
104C2×C269C2×#13516yescomplemented
105C2×C269C23×D411yescharacteristic
106D269—24no—
107D269—44no—
108C269C22×#13511yescharacteristic, complemented, Sylow
109C22×#135—2691nomaximal, Sylow
110C22×#41—2691no—
111C22×#41—2691no—
112C2×#135—26924no—
113C22×Q16—2691no—
114C22×SD16—2691no—
115C22×SD16D26911yescharacteristic, complemented
116C22×D8—2691no—
117C23×C8—2691no—
118C2×#41—26912no—
119C2×#41—26912no—
120C2×#41—5386no—
121C2×#41—5386no—
122C22×Q8—2691no—
123C22×Q8C2×D26911yescharacteristic
124C22×D4—2691no—
125C22×D4—5381no—
126C22×D4—5381no—
127C22×D4C2×D26911yescharacteristic
128C23×C4—2691no—
129C23×C4—5381no—
130C23×C4—5381no—
131#135—26964no—
132C2×Q16—26912no—
133C2×SD16—26912no—
134C2×SD16C2×D269112yescomplemented
135C2×D8—26912no—
136C22×C8—2691no—
137C22×C8—26912no—
138C22×C8C2×D26911yescharacteristic
139C24—21no—
140C24—2691no—
141C24—5381no—
142#41—26916no—
143#41—26916no—
144#41—53824no—
145#41—53824no—
146C2×Q8—23no—
147C2×Q8—2696no—
148C2×Q8—5383no—
149C2×Q8C22×D26916yes—
150C2×D4—23no—
151C2×D4—2696no—
152C2×D4—53812no—
153C2×D4—53812no—
154C2×D4—5383no—
155C2×D4C22×D26916yes—
156C22×C4—21no—
157C22×C4—2691no—
158C22×C4—2696no—
159C22×C4—2696no—
160C22×C4—53812no—
161C22×C4—53812no—
162C22×C4—5381no—
163C22×C4C22×D26911yescharacteristic
164Q16—26916no—
165SD16—26916no—
166SD16C22×D269116yescomplemented
167D8—26916no—
168C2×C8—2696no—
169C2×C8—26916no—
170C2×C8C22×D26916yes—
171C23—26no—
172C23—44no—
173C23—2696no—
174C23—5384no—
175C23—5386no—
176C23—10764no—
177C23D4×D26911yescharacteristic
178Q8—26no—
179Q8—2694no—
180Q8—5386no—
181Q8C23×D26914yes—
182D4—26no—
183D4—2694no—
184D4—53816no—
185D4—53816no—
186D4—5386no—
187D4C23×D26914yes—
188C2×C4—26no—
189C2×C4—2696no—
190C2×C4—26912no—
191C2×C4—2694no—
192C2×C4—53816no—
193C2×C4—53816no—
194C2×C4—5386no—
195C2×C4D4×D26913yes—
196C2×C4C23×D26913yes—
197C8—2694no—
198C8C23×D26914yes—
199C22—24no—
200C22—412no—
201C22—2694no—
202C22—53812no—
203C22—5384no—
204C22—107612no—
205C22#2257547414yesdirect product factor
206C22C2×D4×D26913yes—
207C4—24no—
208C4—2694no—
209C4—5384no—
210C4C2×D4×D26913yes—
211C4C24×D26911yescharacteristic
212C2—44no—
213C2—5384no—
214C2—10764no—
215C2C2×#2257547416yesdirect product factor
216C2C22×D4×D26911yescharacteristic
subgroupG/H
centerC23D4×D269
commutator, cosocleC4×C269C25
FrattiniC4C24×D269
FittingC22×SD16×C269C2
socleC23×C269C2×D4
hypercenterC22×SD16D269
hypocenterC269C22×#135
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#16864403C2semidirect
2. C22×#16864401C2semidirect
3. C2×#22575474C2direct (N × H)
4. C22×#16864392C2semidirect
5. C22×#16864391C2semidirect
6. C22×#16864387C2semidirect
7. C22×C8×D269C2semidirect
8. C22×SD16×C269C2semidirect
10. C2×#16864403C22semidirect
12. C2×#16864401C22semidirect
20. #22575474C22direct (N × H)
21. C2×#16864392C22semidirect
22. C2×#16864391C22semidirect
23. C2×#16864387C22semidirect
25. C2×C8×D269C22semidirect
28. C2×SD16×C269C22semidirect
33. #16864403C23semidirect
35. #16864401C23semidirect
48. #16864392C23semidirect
49. #16864391C23semidirect
50. #16864387C23semidirect
52. C8×D269C23semidirect
60. SD16×C269C23semidirect
92. C22×C269#135semidirect
104. C2×C269C2×#135semidirect
108. C269C22×#135semidirect
115. C22×SD16D269semidirect
134. C2×SD16C2×D269semidirect
166. SD16C22×D269semidirect
205. C22#22575474direct (N × H)
215. C2C2×#22575474direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#168644032
C22×#168644012
C2×#225754742
C22×#168643922
C22×#168643912
C22×#168643872
C22×C8×D2692
C22×SD16×C2692
C22×#135269