Finite Group Databasebeta

← #46813464

Subgroups — #46813464

Order 34432.

1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 229 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×D4×D269C211yesmaximal, characteristic
2C2×#22575411C211yesmaximal, characteristic, complemented
3C2×#22575410C211yesmaximal, characteristic, complemented
4#31770508C211yesmaximal, characteristic, complemented
5#31770507C211yesmaximal, characteristic, complemented
6#31770506C211yesmaximal, characteristic, complemented
7#31770505C214yesmaximal, complemented
8#31770460C214yesmaximal, complemented
9#390×C269C211yesmaximal, characteristic, complemented
10C24×D269C2212yes—
11C22×D1076C2211yescharacteristic
12C22×C22⋊D269C2212yes—
13C2×D4×D269—24no—
14C2×D4×D269—24no—
15C2×D4×D269C418yescomplemented
16C22×C4×D269C2211yescharacteristic
17#22575411—24no—
18#22575410—24no—
19C2×C4⋊Dic269C2211yescharacteristic, complemented
20C2×#16864381C2212yescomplemented
21C2×C22⋊Dic269C2214yescomplemented
22C2×#16864379C2212yes—
23C2×#16864379C2212yes—
24C2×#16864379C2214yescomplemented
25C2×#16864379C2214yescomplemented
26C2×C4×Dic269C2212yescomplemented
27C2×C4×Dic269C2211yescharacteristic, complemented
28C22×D4×C269C2211yescharacteristic
29C2×C4⋊C4×C269C2211yescharacteristic, complemented
30C2×C22⋊C4×C269C2214yescomplemented
31C2×C42×C269C2211yescharacteristic, complemented
32C23×D269—24no—
33C23×D269—24no—
34C23×D269—44no—
35C23×D269—44no—
36C23×D269C2×C418yes—
37C23×D269C2312yes—
38C23×D269C2311yescharacteristic
39C2×D1076—22no—
40C2×D1076—22no—
41C2×D1076C2×C414yes—
42C2×C22⋊D269—24no—
43C2×C22⋊D269—24no—
44C2×C22⋊D269C2×C418yes—
45D4×D269—232no—
46C22×Dic269C2312yes—
47C22×Dic269C2312yes—
48C22×Dic269C2311yescharacteristic
49C2×C4×D269C2×C414yes—
50C2×C4×D269D414yes—
51C2×C4×D269D414yes—
52C4⋊Dic269—22no—
53#16864381—24no—
54C22⋊Dic269—44no—
55#16864379—24no—
56#16864379—24no—
57#16864379—44no—
58#16864379—44no—
59C4×Dic269—24no—
60C4×Dic269—22no—
61C24×C269C2312yes—
62C2×D4×C269—22no—
63C2×D4×C269—22no—
64C2×D4×C269C2×C414yes—
65C22×C4×C269C2312yes—
66C22×C4×C269C2312yes—
67C22×C4×C269C2311yescharacteristic
68C4⋊C4×C269—22no—
69C22⋊C4×C269—44no—
70C42×C269—22no—
71C22×D269—22no—
72C22×D269—22no—
73C22×D269—22no—
74C22×D269—22no—
75C22×D269—24no—
76C22×D269—24no—
77C22×D269—216no—
78C22×D269—416no—
79C22×D269—48no—
80C22×D269—416no—
81C22×D269—48no—
82C22×D269C22×C414yes—
83C22×D269C22×C412yes—
84C22×D269C2×D412yes—
85C22×D269C2×D412yes—
86D1076—28no—
87C22⋊D269—216no—
88C2×Dic269—22no—
89C2×Dic269—22no—
90C2×Dic269—22no—
91C2×Dic269—24no—
92C2×Dic269—22no—
93C2×Dic269C22×C412yes—
94C2×Dic269C2×D412yes—
95C2×Dic269C2×D412yes—
96C4×D269C22⋊C4116yescomplemented
97C23×C269—22no—
98C23×C269—22no—
99C23×C269—24no—
100C23×C269—24no—
101C23×C269C22×C414yes—
102C23×C269C2411yescharacteristic
103D4×C269—28no—
104C2×C4×C269—22no—
105C2×C4×C269—22no—
106C2×C4×C269—22no—
107C2×C4×C269—24no—
108C2×C4×C269—22no—
109C2×C4×C269C22×C412yes—
110C2×C4×C269C2×D412yes—
111C2×C4×C269C2×D412yes—
112C22×C269—24no—
113C22×C269—28no—
114C22×C269—42no—
115C22×C269—44no—
116C22×C269—42no—
117C22×C269C23×C411yescharacteristic
118C22×C269C22×D411yescharacteristic
119C22×C269C22×D411yescharacteristic
120C22×C269H(5,𝔽2)12yes—
121C22×C269H(5,𝔽2)12yes—
122C2×D269—24no—
123C2×D269—22no—
124C2×D269—24no—
125C2×D269—22no—
126C2×D269—24no—
127C2×D269—28no—
128C2×D269—432no—
129C2×D269—42no—
130C2×D269—44no—
131C2×D269—42no—
132C2×D269C2×C22⋊C414yes—
133C4×C269—42no—
134C4×C269—42no—
135C4×C269C2×C22⋊C414yes—
136Dic269—42no—
137Dic269—42no—
138Dic269C2×C22⋊C414yes—
139C2×C269—44no—
140C2×C269C22×C22⋊C411yescharacteristic
141C2×C269#51812yes—
142C2×C269#53511yescharacteristic
143C2×C269#53512yes—
144C2×C269#53511yescharacteristic
145D269—24no—
146D269—44no—
147C269#230911yescharacteristic, complemented, Sylow
148#2309—2691nomaximal, Sylow
149C23×D4—2691no—
150C2×#117—2691no—
151C2×#117—2691no—
152#390—2691no—
153#390—2691no—
154#390—2694no—
155#390—2691no—
156#390D26911yescharacteristic, complemented
157#379—2694no—
158C25—2692no—
159C22×D4—2692no—
160C22×D4—2698no—
161C22×D4—2691no—
162C22×D4—5384no—
163C22×D4—5384no—
164C22×D4C2×D26911yescharacteristic
165C23×C4—2691no—
166#117—5384no—
167#117—5384no—
168C2×C4⋊C4—2692no—
169C2×C4⋊C4—2691no—
170C2×C4⋊C4C2×D26911yescharacteristic, complemented
171C2×C22⋊C4—2692no—
172C2×C22⋊C4—2692no—
173C2×C22⋊C4—2694no—
174C2×C22⋊C4—2694no—
175C2×C22⋊C4—2694no—
176C2×C22⋊C4C2×D26914yescomplemented
177C2×C42—2692no—
178C2×C42—2691no—
179C2×C42C2×D26911yescharacteristic, complemented
180C24—2691no—
181C24—2692no—
182C24—2698no—
183C24—5384no—
184C24—5384no—
185C24—10764no—
186C24—10764no—
187C24C22×D26912yes—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—2698no—
191C2×D4—2694no—
192C2×D4—53832no—
193C2×D4—5384no—
194C2×D4—5384no—
195C2×D4—5382no—
196C2×D4—5382no—
197C2×D4C4×D26914yes—
198C22×C4—2691no—
199C22×C4—2694no—
200C22×C4—2694no—
201C22×C4—2694no—
202C22×C4—2692no—
203C22×C4—2692no—
204C22×C4C22×D26912yes—
205C22×C4C22×D26912yes—
206C22×C4C22×D26911yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—5384no—
209C4⋊C4—5382no—
210C22⋊C4—44no—
211C22⋊C4—5384no—
212C22⋊C4—5384no—
213C22⋊C4—10764no—
214C22⋊C4—10764no—
215C22⋊C4—10764no—
216C42—22no—
217C42—5384no—
218C42—5382no—
219C23—22no—
220C23—22no—
221C23—24no—
222C23—24no—
223C23—2692no—
224C23—2692no—
225C23—2692no—
226C23—2694no—
227C23—53816no—
228C23—5382no—
229C23—5382no—
230C23—5382no—
231C23—5382no—
232C23—5384no—
233C23—5384no—
234C23—107616no—
235C23—10768no—
236C23—107616no—
237C23—10768no—
238C23C2×C4×D26914yes—
239C23C23×D26911yescharacteristic
240D4—28no—
241D4—53816no—
242D4—5388no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—24no—
247C2×C4—22no—
248C2×C4—2692no—
249C2×C4—2692no—
250C2×C4—2692no—
251C2×C4—26916no—
252C2×C4—5382no—
253C2×C4—5382no—
254C2×C4—5382no—
255C2×C4—5382no—
256C2×C4—5384no—
257C2×C4C2×C4×D26912yes—
258C2×C4D4×D26912yes—
259C2×C4D4×D26912yes—
260C22—24no—
261C22—28no—
262C22—42no—
263C22—44no—
264C22—42no—
265C22—2694no—
266C22—5382no—
267C22—5384no—
268C22—5382no—
269C22—5384no—
270C22—5384no—
271C22—5388no—
272C22—107632no—
273C22—10762no—
274C22—10764no—
275C22—10762no—
276C22C22×C4×D26911yescharacteristic
277C22C2×D4×D26911yescharacteristic
278C22C2×D4×D26911yescharacteristic
279C22#2257549812yes—
280C22#2257549912yes—
281C4—42no—
282C4—42no—
283C4—2694no—
284C4—10762no—
285C4—10762no—
286C4C22⋊C4×D26914yes—
287C2—44no—
288C2—5384no—
289C2—10764no—
290C2C2×C22⋊C4×D26911yescharacteristic
291C2#3177107712yes—
292C2#3177116811yescharacteristic
293C2#3177117112yes—
294C2#3177117311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D269
commutatorC22×C269C23×C4
Fitting#390×C269C2
socle, cosocleC23×C269C24
prime radicalC22×D4×D269C2
hypercenter#390D269
hypocenterC269#2309
LCSG ▷ C22×C269 ▷ C269
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#22575411C2semidirect
3. C2×#22575410C2semidirect
4. #31770508C2semidirect
5. #31770507C2semidirect
6. #31770506C2semidirect
7. #31770505C2semidirect
8. #31770460C2semidirect
9. #390×C269C2semidirect
15. C2×D4×D269C4semidirect
19. C2×C4⋊Dic269C22semidirect
20. C2×#16864381C22semidirect
21. C2×C22⋊Dic269C22semidirect
24. C2×#16864379C22semidirect
25. C2×#16864379C22semidirect
26. C2×C4×Dic269C22semidirect
27. C2×C4×Dic269C22semidirect
29. C2×C4⋊C4×C269C22semidirect
30. C2×C22⋊C4×C269C22semidirect
31. C2×C42×C269C22semidirect
96. C4×D269C22⋊C4semidirect
147. C269#2309semidirect
156. #390D269semidirect
170. C2×C4⋊C4C2×D269semidirect
176. C2×C22⋊C4C2×D269semidirect
179. C2×C42C2×D269semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D2692
C2×#225754112
C2×#225754102
#317705082
#317705072
#317705062
#317705052
#317704602
#390×C2692
#2309269