Finite Group Databasebeta

← C2×#31770748 #46820084

Subgroups — C2×#31770748 #46820084

Order 34432.

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

normal subgroups only

This group has 812 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×#16864402C211yesmaximal, characteristic, complemented
2C22×#16864390C211yesmaximal, characteristic, complemented
3C22×#16864387C211yesmaximal, characteristic, complemented
4#31770748C218yesmaximal, direct product factor
5C2×#22575376C211yesmaximal, characteristic, complemented
6C2×#22575373C211yesmaximal, characteristic, complemented
7C2×C22⋊#14524130C211yesmaximal, characteristic, complemented
8C2×#121×C269C211yesmaximal, characteristic, complemented
9C2×#16864402—24no—
10C2×#16864402—24no—
11C2×#16864402—22no—
12C2×#16864402C2214yescomplemented
13C22×Dic538C2211yescharacteristic
14C22×D1076C2211yescharacteristic
15C22×C22⋊D269—21no—
16C22×C4×D269—21no—
17C2×#16864390—24no—
18C2×#16864390C2214yescomplemented
19C2×#16864387—24no—
20C2×#16864387C2214yescomplemented
21C22×#14524130C2211yescharacteristic
22C22×#14524130C2211yescharacteristic
23#22575376C2214yescomplemented
24#22575373C2214yescomplemented
25C22⋊#14524130C2214yescomplemented
26C22×D4×C269—21no—
27C22×D4×C269C2211yescharacteristic
28C23×C4×C269C2211yescharacteristic
29#121×C269—22no—
30#121×C269C2214yescomplemented
31C2×C4⋊C4×C269C2211yescharacteristic
32C2×C22⋊C4×C269—21no—
33C23×D269—21no—
34#16864402—216no—
35#16864402—28no—
36#16864402—28no—
37C2×Dic538—22no—
38C2×Dic538—21no—
39C2×Dic538D414yescomplemented
40C2×Dic538C2312yes—
41C2×D1076—22no—
42C2×D1076—21no—
43C2×D1076D414yescomplemented
44C2×D1076C2312yes—
45C2×C22⋊D269—28no—
46C2×C22⋊D269—24no—
47C22×Dic269—21no—
48C2×C4×D269—28no—
49C2×C4×D269—24no—
50#16864390—28no—
51#16864387—28no—
52C2×#14524130—22no—
53C2×#14524130—22no—
54C2×#14524130C2312yes—
55C2×#14524130C2312yes—
56C24×C269—21no—
57C24×C269D411yescharacteristic
58C2×D4×C269—24no—
59C2×D4×C269—22no—
60C2×D4×C269—22no—
61C2×D4×C269—21no—
62C2×D4×C269—44no—
63C2×D4×C269C2312yes—
64C22×C4×C269—22no—
65C22×C4×C269—22no—
66C22×C4×C269—21no—
67C22×C4×C269D411yescharacteristic
68C22×C4×C269D412yes—
69C22×C4×C269C2312yes—
70C22×C4×C269C2311yescharacteristic
71C4⋊C4×C269—21no—
72C4⋊C4×C269C2312yes—
73C22⋊C4×C269—24no—
74C22×D269—24no—
75C22×D269—22no—
76C22×D269—42no—
77C22×D269—42no—
78Dic538—24no—
79Dic538—22no—
80Dic538C2×D414yescomplemented
81D1076—24no—
82D1076—22no—
83D1076C2×D414yescomplemented
84C22⋊D269—216no—
85C2×Dic269—24no—
86C2×Dic269—22no—
87C4×D269—216no—
88#14524130—22no—
89#14524130—22no—
90C23×C269—22no—
91C23×C269—22no—
92C23×C269—22no—
93C23×C269—22no—
94C23×C269—42no—
95C23×C269—42no—
96C23×C269—42no—
97C23×C269C2×D412yes—
98C23×C269C2×D411yescharacteristic
99D4×C269—22no—
100D4×C269—22no—
101D4×C269—48no—
102D4×C269—42no—
103C2×C4×C269—22no—
104C2×C4×C269—24no—
105C2×C4×C269—22no—
106C2×C4×C269—22no—
107C2×C4×C269—22no—
108C2×C4×C269—42no—
109C2×C4×C269C2×D412yes—
110C2×C4×C269C2×D412yes—
111C2×C4×C269C2×D412yes—
112C2×C4×C269C2×D411yescharacteristic
113C2×C4×C269C2411yescharacteristic
114C22×C269—22no—
115C22×C269—22no—
116C22×C269—22no—
117C22×C269—44no—
118C22×C269—42no—
119C22×C269—42no—
120C22×C269—42no—
121C22×C269—84no—
122C22×C269#12012yes—
123C22×C269#13512yes—
124C22×C269AGL(1,ℤ/8)12yes—
125C22×C269C22×D411yescharacteristic
126C2×D269—24no—
127C2×D269—42no—
128C2×D269—42no—
129C2×D269—48no—
130C4×C269—22no—
131C4×C269—42no—
132C4×C269#12012yes—
133C4×C269C22×D411yescharacteristic
134C4×C269C22×D411yescharacteristic
135Dic269—24no—
136C2×C269—42no—
137C2×C269—82no—
138C2×C269#44914yescomplemented
139C2×C269C2×#12011yescharacteristic
140C2×C269C2×#13511yescharacteristic
141C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
142D269—44no—
143C269C2×#44911yescharacteristic, complemented, Sylow
144C2×#449—2691nomaximal, Sylow
145C22×#41—2691no—
146C22×SD16—2691no—
147C22×D8—2691no—
148C2×#121D26911yescharacteristic, complemented
149#449—2698no—
150C2×#103—2691no—
151C2×#102—2691no—
152C2×C22⋊C8—2691no—
153C2×#41—2694no—
154C2×#41—5384no—
155C2×#41—5384no—
156C2×#41—5382no—
157C22×Q8—2691no—
158C22×D4—21no—
159C22×D4—2691no—
160C22×D4—5381no—
161C22×D4C2×D26911yescharacteristic
162C23×C4—5381no—
163C23×C4C2×D26911yescharacteristic
164C2×SD16—2694no—
165C2×SD16—5384no—
166C2×D8—2694no—
167C2×D8—5384no—
168C22×C8—2691no—
169C22×C8—2691no—
170#121—22no—
171#121C2×D26914yescomplemented
172C2×C4⋊C4C2×D26911yescharacteristic
173C2×C22⋊C4—21no—
174#103—2694no—
175#102—2694no—
176C22⋊C8—2694no—
177C24—21no—
178C24—5381no—
179C24C22⋊D26911yescharacteristic
180#41—5388no—
181#41—5388no—
182#41—53816no—
183C2×Q8—2694no—
184C2×Q8—2692no—
185C2×Q8—5382no—
186C2×Q8—5381no—
187C2×D4—24no—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—44no—
192C2×D4—2694no—
193C2×D4—2692no—
194C2×D4—5388no—
195C2×D4—5384no—
196C2×D4—5382no—
197C2×D4—5381no—
198C2×D4C22×D26912yes—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—5388no—
203C22×C4—5381no—
204C22×C4—5384no—
205C22×C4C22⋊D26912yes—
206C22×C4C22⋊D26911yescharacteristic
207C22×C4C22×D26912yes—
208C22×C4C22×D26911yescharacteristic
209SD16—5388no—
210D8—5388no—
211C2×C8—2692no—
212C2×C8—2692no—
213C2×C8—5382no—
214C2×C8—5382no—
215C4⋊C4—21no—
216C4⋊C4C22×D26912yes—
217C22⋊C4—24no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—42no—
223C23—42no—
224C23—42no—
225C23—5384no—
226C23—5382no—
227C23—10762no—
228C23—10762no—
229C23C2×C22⋊D26912yes—
230C23C2×C22⋊D26911yescharacteristic
231Q8—2694no—
232Q8—5384no—
233Q8—5382no—
234D4—22no—
235D4—22no—
236D4—48no—
237D4—42no—
238D4—2694no—
239D4—53816no—
240D4—5384no—
241D4—5382no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—53816no—
249C2×C4—5384no—
250C2×C4—5382no—
251C2×C4D4×D26912yes—
252C2×C4D4×D26912yes—
253C2×C4C2×C22⋊D26912yes—
254C2×C4C2×C22⋊D26911yescharacteristic
255C2×C4C23×D26911yescharacteristic
256C8—5382no—
257C8—5382no—
258C22—22no—
259C22—22no—
260C22—22no—
261C22—44no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—5384no—
267C22—10762no—
268C22—10768no—
269C22—10762no—
270C22#2257542112yes—
271C22#2257547312yes—
272C22#2257547912yes—
273C22C22×C22⋊D26911yescharacteristic
274C4—22no—
275C4—42no—
276C4—5384no—
277C4#2257542112yes—
278C4C2×D4×D26911yescharacteristic
279C4C2×D4×D26911yescharacteristic
280C2—42no—
281C2—82no—
282C2—10764no—
283C2#3177074814yesdirect product factor
284C2C2×#2257542111yescharacteristic
285C2C2×#2257547311yescharacteristic
286C2C2×#2257547911yescharacteristic
subgroupG/H
centerC23C2×C22⋊D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
FittingC2×#121×C269C2
socleC23×C269C2×D4
hypercenterC2×#121D269
hypocenterC269C2×#449
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#16864402C2semidirect
2. C22×#16864390C2semidirect
3. C22×#16864387C2semidirect
4. #31770748C2direct (N × H)
5. C2×#22575376C2semidirect
6. C2×#22575373C2semidirect
7. C2×C22⋊#14524130C2semidirect
8. C2×#121×C269C2semidirect
12. C2×#16864402C22semidirect
18. C2×#16864390C22semidirect
20. C2×#16864387C22semidirect
23. #22575376C22semidirect
24. #22575373C22semidirect
25. C22⋊#14524130C22semidirect
30. #121×C269C22semidirect
39. C2×Dic538D4semidirect
43. C2×D1076D4semidirect
80. Dic538C2×D4semidirect
83. D1076C2×D4semidirect
138. C2×C269#449semidirect
143. C269C2×#449semidirect
148. C2×#121D269semidirect
171. #121C2×D269semidirect
283. C2#31770748direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#168644022
C22×#168643902
C22×#168643872
#317707482
C2×#225753762
C2×#225753732
C2×C22⋊#145241302
C2×#121×C2692
C2×#449269