Finite Group Databasebeta

← #46813449

Subgroups — #46813449

Order 34432.

924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.

normal subgroups only

This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 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
1C2×#22575449C211yesmaximal, characteristic
2C2×D4×Dic269C211yesmaximal, characteristic, complemented
3C2×#22575415C211yesmaximal, characteristic, complemented
4C2×#22575413C214yesmaximal, complemented
5#31770507C211yesmaximal, characteristic, complemented
6#31770505C214yesmaximal, complemented
7#31770474C211yesmaximal, characteristic, complemented
8C42×Dic269C211yesmaximal, characteristic, complemented
9#390×C269C211yesmaximal, characteristic, complemented
10C22×D1076C2211yescharacteristic
11C22×C22⋊D269C2214yes—
12C23×Dic269C2212yes—
13C22×C4×D269C2212yes—
14#22575449C418yescomplemented
15D4×Dic269—24no—
16#22575415—24no—
17#22575413—216no—
18C2×C4⋊Dic269C2211yescharacteristic
19C2×#16864381C2214yes—
20C2×C22⋊Dic269C2212yes—
21C2×#16864379C2212yes—
22C2×#16864379C2214yes—
23C2×C4×Dic269C2212yes—
24C2×C4×Dic269C2211yescharacteristic
25C2×C4×Dic269C2212yes—
26C2×C4×Dic269C2211yescharacteristic
27C22×D4×C269C2211yescharacteristic
28C2×C4⋊C4×C269C2211yescharacteristic
29C2×C22⋊C4×C269C2214yes—
30C2×C42×C269C2211yescharacteristic
31C23×D269C2312yes—
32C2×D1076—22no—
33C2×D1076—22no—
34C2×D1076C2×C414yescomplemented
35C2×C22⋊D269—28no—
36C2×C22⋊D269—28no—
37C2×C22⋊D269C2×C4116yescomplemented
38C22×Dic269—28no—
39C22×Dic269—24no—
40C22×Dic269C2312yes—
41C22×Dic269C2311yescharacteristic
42C22×Dic269C2312yes—
43C22×Dic269C2311yescharacteristic
44C2×C4×D269—28no—
45C2×C4×D269—24no—
46C4⋊Dic269—22no—
47#16864381—28no—
48C22⋊Dic269—24no—
49#16864379—24no—
50#16864379—28no—
51C4×Dic269—24no—
52C4×Dic269C2×C414yescomplemented
53C4×Dic269D418yescomplemented
54C4×Dic269D414yescomplemented
55C24×C269C2312yes—
56C2×D4×C269—22no—
57C2×D4×C269—22no—
58C2×D4×C269C2×C414yescomplemented
59C22×C4×C269C2312yes—
60C22×C4×C269C2312yes—
61C22×C4×C269C2311yescharacteristic
62C4⋊C4×C269—22no—
63C22⋊C4×C269—28no—
64C42×C269—22no—
65C22×D269—24no—
66C22×D269—22no—
67C22×D269—24no—
68C22×D269—22no—
69C22×D269C22×C414yes—
70D1076—28no—
71C22⋊D269—232no—
72C2×Dic269—22no—
73C2×Dic269—24no—
74C2×Dic269—22no—
75C2×Dic269—48no—
76C2×Dic269C22×C414yes—
77C2×Dic269C2×D412yes—
78C2×Dic269C2×D414yes—
79C2×Dic269C2×D414yes—
80C2×Dic269C2×D412yes—
81C2×Dic269#4114yes—
82C4×D269—48no—
83C23×C269—24no—
84C23×C269—22no—
85C23×C269—22no—
86C23×C269—24no—
87C23×C269C22×C414yes—
88C23×C269C2411yescharacteristic
89D4×C269—28no—
90C2×C4×C269—22no—
91C2×C4×C269—22no—
92C2×C4×C269—24no—
93C2×C4×C269—22no—
94C2×C4×C269C22×C412yes—
95C2×C4×C269C2×D414yes—
96C2×C4×C269C2×D412yes—
97C2×C4×C269#4112yes—
98C22×C269—24no—
99C22×C269—28no—
100C22×C269—42no—
101C22×C269—44no—
102C22×C269—42no—
103C22×C269C23×C411yescharacteristic
104C22×C269C22×D412yes—
105C22×C269C22×D411yescharacteristic
106C22×C269C2×#4112yes—
107C22×C269C2×#4111yescharacteristic
108C2×D269—28no—
109C2×D269—24no—
110C2×D269—42no—
111C2×D269—44no—
112C2×D269—42no—
113C4×C269—24no—
114C4×C269—42no—
115C4×C269C4×D414yescomplemented
116Dic269—22no—
117Dic269—42no—
118Dic269C4×D418yescomplemented
119Dic269#12714yescomplemented
120C2×C269—44no—
121C2×C269C2×C4×D412yes—
122C2×C269C2×C4×D411yescharacteristic
123C2×C269C2×#12711yescharacteristic
124C2×C269#53212yes—
125C2×C269#53211yescharacteristic
126D269—44no—
127C269C4×#12711yescharacteristic, complemented, Sylow
128C4×#127—2691nomaximal, Sylow
129C2×#127—2691no—
130C2×C4×D4—2691no—
131C2×C4×D4—2691no—
132C2×C4×D4—2694no—
133#390—2694no—
134#390—2691no—
135#390D26911yescharacteristic, complemented
136#384—2691no—
137C43—2691no—
138C22×D4—2694no—
139C22×D4—2691no—
140C22×D4C2×D26911yescharacteristic
141C23×C4—2692no—
142C23×C4—2692no—
143#127—2698no—
144C4×D4—53816no—
145C4×D4—5384no—
146C4×D4—5384no—
147C2×C4⋊C4—2694no—
148C2×C4⋊C4—2691no—
149C2×C4⋊C4C2×D26911yescharacteristic
150C2×C22⋊C4—2692no—
151C2×C22⋊C4—2692no—
152C2×C22⋊C4—2694no—
153C2×C22⋊C4C2×D26914yes—
154C2×C42—2692no—
155C2×C42—2691no—
156C2×C42—2691no—
157C2×C42—2692no—
158C2×C42C2×D26911yescharacteristic
159C24—2692no—
160C24C22×D26912yes—
161C2×D4—22no—
162C2×D4—22no—
163C2×D4—26916no—
164C2×D4—2694no—
165C2×D4—5388no—
166C2×D4—5388no—
167C2×D4—5382no—
168C2×D4—5382no—
169C2×D4C4×D26914yescomplemented
170C22×C4—2692no—
171C22×C4—2691no—
172C22×C4—2691no—
173C22×C4—2692no—
174C22×C4—5388no—
175C22×C4—5384no—
176C22×C4—5388no—
177C22×C4—5384no—
178C22×C4C22×D26912yes—
179C22×C4C22×D26912yes—
180C22×C4C22×D26911yescharacteristic
181C4⋊C4—22no—
182C4⋊C4—5388no—
183C4⋊C4—5382no—
184C22⋊C4—28no—
185C22⋊C4—5384no—
186C22⋊C4—5384no—
187C22⋊C4—5388no—
188C42—22no—
189C42—2694no—
190C42—2698no—
191C42—2694no—
192C42—5384no—
193C23—24no—
194C23—22no—
195C23—24no—
196C23—22no—
197C23—2694no—
198C23—5384no—
199C23—5382no—
200C23—5384no—
201C23—5382no—
202C23C2×C4×D26914yes—
203C23C23×D26911yescharacteristic
204D4—28no—
205D4—53832no—
206D4—5388no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—2694no—
212C2×C4—2694no—
213C2×C4—2694no—
214C2×C4—2692no—
215C2×C4—2694no—
216C2×C4—2692no—
217C2×C4—5382no—
218C2×C4—5384no—
219C2×C4—5382no—
220C2×C4—10768no—
221C2×C4—10768no—
222C2×C4C2×C4×D26912yes—
223C2×C4D4×D26914yes—
224C2×C4D4×D26912yes—
225C2×C4#1686440112yes—
226C22—28no—
227C22—24no—
228C22—42no—
229C22—44no—
230C22—42no—
231C22—5388no—
232C22—5384no—
233C22—10762no—
234C22—10764no—
235C22—10762no—
236C22C22×C4×D26911yescharacteristic
237C22C2×D4×D26912yes—
238C22C2×D4×D26911yescharacteristic
239C22#41×D26912yes—
240C22C2×#1686440111yescharacteristic
241C4—24no—
242C4—42no—
243C4—2694no—
244C4—2698no—
245C4—5382no—
246C4—10762no—
247C4#2257541314yescomplemented
248C2—44no—
249C2—10764no—
250C2C4×D4×D26912yes—
251C2C2×#2257541311yescharacteristic
252C2#127×D26911yescharacteristic
253C2#3177115012yes—
254C2#3177115411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#390×C269C2
socle, cosocleC23×C269C24
prime radicalC2×#22575449C2
hypercenter#390D269
hypocenterC269C4×#127
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic269C2semidirect
3. C2×#22575415C2semidirect
4. C2×#22575413C2semidirect
5. #31770507C2semidirect
6. #31770505C2semidirect
7. #31770474C2semidirect
8. C42×Dic269C2semidirect
9. #390×C269C2semidirect
14. #22575449C4semidirect
34. C2×D1076C2×C4semidirect
37. C2×C22⋊D269C2×C4semidirect
52. C4×Dic269C2×C4semidirect
53. C4×Dic269D4semidirect
54. C4×Dic269D4semidirect
58. C2×D4×C269C2×C4semidirect
115. C4×C269C4×D4semidirect
118. Dic269C4×D4semidirect
119. Dic269#127semidirect
127. C269C4×#127semidirect
135. #390D269semidirect
169. C2×D4C4×D269semidirect
247. C4#22575413semidirect

Maximal subgroups

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

subgroupindex
C2×#225754492
C2×D4×Dic2692
C2×#225754152
C2×#225754132
#317705072
#317705052
#317704742
C42×Dic2692
#390×C2692
C4×#127269