Finite Group Databasebeta

← C22×#22575473 #46825611

Subgroups — C22×#22575473 #46825611

Order 34432.

1504 conjugacy classes of subgroups; only the 565 normal subgroups are shown.

normal subgroups only

This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 565 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×#16864402C211yesmaximal, characteristic, complemented
2C2×#22575473C2124yesmaximal, direct product factor
3C22×#16864392C211yesmaximal, characteristic, complemented
4C22×#16864390C211yesmaximal, characteristic, complemented
5C22×#16864389C211yesmaximal, characteristic, complemented
6C22×#16864387C211yesmaximal, characteristic, complemented
7C23×#14524130C211yesmaximal, characteristic, complemented
8C22×#41×C269C211yesmaximal, characteristic, complemented
9C2×#16864402—26no—
10C2×#16864402C22112yescomplemented
11C22×Dic538C2211yescharacteristic
12C22×D1076C2211yescharacteristic
13C22×C22⋊D269—21no—
14C22×C4×D269—21no—
15#22575473C22164yesdirect product factor
16C2×#16864392C22112yescomplemented
17C2×#16864390C22112yescomplemented
18C2×#16864389C22112yescomplemented
19C2×#16864387C22112yescomplemented
20C22×#14524130C2211yescharacteristic
21C22×#14524130C2211yescharacteristic
22C22×#14524130C22112yescomplemented
23C2×#41×C269—26no—
24C2×#41×C269C22112yescomplemented
25C22×Q8×C269C2211yescharacteristic
26C22×D4×C269—21no—
27C22×D4×C269C2211yescharacteristic
28C23×C4×C269—21no—
29C23×C4×C269C2211yescharacteristic
30C23×D269—21no—
31#16864402—224no—
32#16864402C23116yescomplemented
33C2×Dic538—23no—
34C2×Dic538C2316yes—
35C2×D1076—23no—
36C2×D1076C2316yes—
37C2×C22⋊D269—212no—
38C22×Dic269—21no—
39C2×C4×D269—212no—
40#16864392C23116yescomplemented
41#16864390C23116yescomplemented
42#16864389C23116yescomplemented
43#16864387C23116yescomplemented
44C2×#14524130C2316yes—
45C2×#14524130C2316yes—
46C2×#14524130C23116yescomplemented
47C24×C269—21no—
48C24×C269D411yescharacteristic
49#41×C269—224no—
50#41×C269C23116yescomplemented
51C2×Q8×C269—23no—
52C2×Q8×C269C2316yes—
53C2×D4×C269—212no—
54C2×D4×C269—23no—
55C2×D4×C269C2316yes—
56C22×C4×C269—21no—
57C22×C4×C269—212no—
58C22×C4×C269D416yes—
59C22×C4×C269D411yescharacteristic
60C22×C4×C269C2311yescharacteristic
61C22×C4×C269C2316yes—
62C22×D269—26no—
63C22×D269—44no—
64Dic538—26no—
65Dic538C2414yes—
66D1076—26no—
67D1076C2414yes—
68C22⋊D269—216no—
69C2×Dic269—26no—
70C4×D269—216no—
71#14524130C2414yes—
72#14524130C2414yes—
73C23×C269—24no—
74C23×C269—26no—
75C23×C269—44no—
76C23×C269C2×D416yes—
77C23×C269C2×D411yescharacteristic
78Q8×C269—26no—
79Q8×C269C2414yes—
80D4×C269—216no—
81D4×C269—26no—
82D4×C269C2414yes—
83C2×C4×C269—26no—
84C2×C4×C269—216no—
85C2×C4×C269C2×D416yes—
86C2×C4×C269C2×D413yes—
87C2×C4×C269C2×D4112yes—
88C2×C4×C269C2413yes—
89C2×C4×C269C2414yes—
90C22×C269—212no—
91C22×C269—24no—
92C22×C269—412no—
93C22×C269#13514yescomplemented
94C22×C269C22×D414yes—
95C22×C269C22×D413yes—
96C2×D269—24no—
97C2×D269—412no—
98C4×C269—24no—
99C4×C269C22×D414yes—
100C4×C269C22×D413yes—
101C4×C269C2511yescharacteristic
102Dic269—24no—
103C2×C269—24no—
104C2×C269—44no—
105C2×C269C2×#13516yescomplemented
106C2×C269C23×D411yescharacteristic
107D269—44no—
108C269C22×#13511yescharacteristic, complemented, Sylow
109C22×#135—2691nomaximal, Sylow
110C22×#41—2691no—
111C22×#41D26911yescharacteristic, complemented
112C2×#135—26924no—
113C22×Q16—2691no—
114C22×SD16—2691no—
115C22×SD16—2691no—
116C22×D8—2691no—
117C23×C8—2691no—
118C2×#41—26no—
119C2×#41—26912no—
120C2×#41—5386no—
121C2×#41C2×D269112yescomplemented
122C22×Q8—2691no—
123C22×Q8C2×D26911yescharacteristic
124C22×D4—21no—
125C22×D4—2691no—
126C22×D4—5381no—
127C22×D4C2×D26911yescharacteristic
128C23×C4—21no—
129C23×C4—5381no—
130C23×C4C2×D26911yescharacteristic
131#135—26964no—
132C2×Q16—26912no—
133C2×SD16—26912no—
134C2×SD16—26912no—
135C2×D8—26912no—
136C22×C8—2691no—
137C22×C8—2691no—
138C22×C8—26912no—
139C24—21no—
140C24—5381no—
141C24C22⋊D26911yescharacteristic
142#41—224no—
143#41—26916no—
144#41—53824no—
145#41C22×D269116yescomplemented
146C2×Q8—23no—
147C2×Q8—2696no—
148C2×Q8—5383no—
149C2×Q8C22×D26916yes—
150C2×D4—212no—
151C2×D4—23no—
152C2×D4—2696no—
153C2×D4—53812no—
154C2×D4—5383no—
155C2×D4C22×D26916yes—
156C22×C4—21no—
157C22×C4—212no—
158C22×C4—5381no—
159C22×C4—53812no—
160C22×C4C22⋊D26916yes—
161C22×C4C22⋊D26911yescharacteristic
162C22×C4C22×D26911yescharacteristic
163C22×C4C22×D26916yes—
164Q16—26916no—
165SD16—26916no—
166SD16—26916no—
167D8—26916no—
168C2×C8—2696no—
169C2×C8—2696no—
170C2×C8—26916no—
171C23—24no—
172C23—26no—
173C23—44no—
174C23—5386no—
175C23—10764no—
176C23C2×C22⋊D26916yes—
177C23C2×C22⋊D26911yescharacteristic
178Q8—26no—
179Q8—2694no—
180Q8—5386no—
181Q8C23×D26914yes—
182D4—216no—
183D4—26no—
184D4—2694no—
185D4—53816no—
186D4—5386no—
187D4C23×D26914yes—
188C2×C4—26no—
189C2×C4—216no—
190C2×C4—5386no—
191C2×C4—53816no—
192C2×C4C2×C22⋊D26916yes—
193C2×C4C2×C22⋊D26913yes—
194C2×C4C2×C22⋊D269112yes—
195C2×C4C23×D26913yes—
196C2×C4C23×D26914yes—
197C8—2694no—
198C8—2694no—
199C22—212no—
200C22—24no—
201C22—412no—
202C22—5384no—
203C22—107612no—
204C22#2257547314yesdirect product factor
205C22C22×C22⋊D26914yes—
206C22C22×C22⋊D26913yes—
207C4—24no—
208C4—5384no—
209C4C22×C22⋊D26914yes—
210C4C22×C22⋊D26913yes—
211C4C24×D26911yescharacteristic
212C2—24no—
213C2—44no—
214C2—10764no—
215C2C2×#2257547316yesdirect product factor
216C2C23×C22⋊D26911yescharacteristic
subgroupG/H
centerC22×C4C22⋊D269
commutator, cosocleC4×C269C25
FrattiniC4C24×D269
FittingC22×#41×C269C2
socleC23×C269C2×D4
hypercenterC22×#41D269
hypocenterC269C22×#135
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#16864402C2semidirect
2. C2×#22575473C2direct (N × H)
3. C22×#16864392C2semidirect
4. C22×#16864390C2semidirect
5. C22×#16864389C2semidirect
6. C22×#16864387C2semidirect
7. C23×#14524130C2semidirect
8. C22×#41×C269C2semidirect
10. C2×#16864402C22semidirect
15. #22575473C22direct (N × H)
16. C2×#16864392C22semidirect
17. C2×#16864390C22semidirect
18. C2×#16864389C22semidirect
19. C2×#16864387C22semidirect
22. C22×#14524130C22semidirect
24. C2×#41×C269C22semidirect
32. #16864402C23semidirect
40. #16864392C23semidirect
41. #16864390C23semidirect
42. #16864389C23semidirect
43. #16864387C23semidirect
46. C2×#14524130C23semidirect
50. #41×C269C23semidirect
93. C22×C269#135semidirect
105. C2×C269C2×#135semidirect
108. C269C22×#135semidirect
111. C22×#41D269semidirect
121. C2×#41C2×D269semidirect
145. #41C22×D269semidirect
204. C22#22575473direct (N × H)
215. C2C2×#22575473direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#168644022
C2×#225754732
C22×#168643922
C22×#168643902
C22×#168643892
C22×#168643872
C23×#145241302
C22×#41×C2692
C22×#135269