Finite Group Databasebeta

← #46820492

Subgroups — #46820492

Order 34432.

500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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×#22575472C211yesmaximal, characteristic, complemented
2C2×M16×D269C211yesmaximal, characteristic, complemented
3#31771115C212yesmaximal, complemented
4#31770864C211yesmaximal, characteristic, complemented
5#31770863C211yesmaximal, characteristic, complemented
6#31770855C211yesmaximal, characteristic, complemented
7#31770850C212yesmaximal, complemented
8#31770849C212yesmaximal, complemented
9#31770640C211yesmaximal, characteristic, complemented
10#31770598C212yesmaximal, complemented
11#469×C269C211yesmaximal, characteristic, complemented
12C2×#16864401C2212yes—
13C22×C4×D269C2211yescharacteristic
14#22575472—24no—
15C2×Dic1076C2211yescharacteristic, complemented
16C2×#16864390C2212yescomplemented
17C2×#16864386C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19C2×#16864385C2211yescharacteristic
20M16×D269—24no—
21C2×C8×D269C2211yescharacteristic
22C2×C8×D269C2211yescharacteristic
23#22575435—22no—
24#22575433C2212yes—
25#22575432C2212yes—
26#22575424C2212yes—
27#22575421—22no—
28D4×Dic269—22no—
29#22575413—22no—
30#22575411C2212yes—
31#22575386C2212yescomplemented
32#22575385C2211yescharacteristic, complemented
33#22575378C2212yescomplemented
34#22575376C2212yescomplemented
35#22575374C2212yescomplemented
36C2×D8×C269C2211yescharacteristic, complemented
37C2×M16×C269C2211yescharacteristic
38#121×C269C2212yes—
39#106×C269C2211yescharacteristic, complemented
40#102×C269C2212yescomplemented
41C23×D269D411yescharacteristic
42#16864401—24no—
43#16864401—24no—
44C2×Dic538C2312yes—
45C2×C22⋊D269—22no—
46C2×C22⋊D269—22no—
47C22×Dic269—22no—
48C22×Dic269D411yescharacteristic
49C2×C4×D269—22no—
50C2×C4×D269—22no—
51C2×C4×D269D411yescharacteristic
52C2×C4×D269D411yescharacteristic
53C2×C4×D269C2311yescharacteristic
54C2×C4×D269C2311yescharacteristic
55Dic1076—22no—
56#16864390—24no—
57#16864386—22no—
58#16864385—22no—
59#16864385—22no—
60C2×#14524130C2311yescharacteristic
61C2×#14524130C2311yescharacteristic
62C8×D269—22no—
63C8×D269D414yescomplemented
64C4⋊Dic269—22no—
65C4⋊Dic269C2312yes—
66#16864381—22no—
67C22⋊Dic269—22no—
68C22⋊Dic269—22no—
69#16864379—22no—
70#16864379—22no—
71C4×Dic269—22no—
72C2×D4×C269—22no—
73C2×D4×C269C2312yes—
74C22×C4×C269C2311yescharacteristic
75D8×C269—22no—
76M16×C269—22no—
77C2×C8×C269C2311yescharacteristic
78C2×C8×C269C2311yescharacteristic
79C4⋊C4×C269C2312yes—
80C22⋊C4×C269—22no—
81C22×D269—22no—
82C22×D269—42no—
83C22×D269C2×D411yescharacteristic
84C22×D269C2×D411yescharacteristic
85Dic538—22no—
86Dic538—22no—
87C22⋊D269—44no—
88C22⋊D269—44no—
89C2×Dic269—22no—
90C2×Dic269—22no—
91C2×Dic269—22no—
92C2×Dic269—44no—
93C2×Dic269C2×D411yescharacteristic
94C2×Dic269C2×D411yescharacteristic
95C4×D269—22no—
96C4×D269—21no—
97C4×D269—21no—
98C4×D269—22no—
99C4×D269C2×D412yes—
100C4×D269#4112yes—
101#14524130—21no—
102#14524130C2×D412yes—
103C23×C269—22no—
104C23×C269C2×D411yescharacteristic
105D4×C269—22no—
106D4×C269—22no—
107D4×C269—44no—
108C2×C4×C269—21no—
109C2×C4×C269—21no—
110C2×C4×C269—22no—
111C2×C4×C269C2×D411yescharacteristic
112C2×C4×C269C2411yescharacteristic
113C8×C269—21no—
114C8×C269C2×D412yes—
115C22×C269—21no—
116C22×C269—22no—
117C22×C269—42no—
118C22×C269—42no—
119C22×C269—42no—
120C22×C269C22×D411yescharacteristic
121C2×D269—22no—
122C2×D269—21no—
123C2×D269—22no—
124C2×D269—44no—
125C2×D269#12112yes—
126C4×C269—21no—
127C4×C269—42no—
128C4×C269C22×D411yescharacteristic
129C4×C269C2×#4111yescharacteristic
130Dic269—21no—
131Dic269—42no—
132Dic269—42no—
133Dic269#12112yes—
134C2×C269—41no—
135C2×C269—82no—
136C2×C269C2×#12111yescharacteristic
137C2×C269#57512yes—
138D269—22no—
139D269—41no—
140C269#305411yescharacteristic, complemented, Sylow
141#3054—2691nomaximal, Sylow
142C2×#135—2691no—
143C22×M16—2691no—
144#525—2692no—
145#470—2691no—
146#470—2691no—
147#469—2691no—
148#469D26911yescharacteristic, complemented
149#468—2692no—
150#468—2692no—
151#427—2691no—
152#416—2692no—
153C2×#41—2692no—
154C23×C4—2691no—
155#135—5384no—
156C2×Q16—2691no—
157C2×SD16—2692no—
158C2×D8C2×D26911yescharacteristic, complemented
159C2×M16—2691no—
160C2×M16—2691no—
161C2×M16—2691no—
162C2×M16—5384no—
163C2×M16C2×D26911yescharacteristic
164C22×C8—2691no—
165C22×C8—2691no—
166#123—5382no—
167C22⋊Q8—2692no—
168C22⋊Q8—2692no—
169#121—2692no—
170#121C2×D26912yes—
171#120—5382no—
172C4×D4—5382no—
173C4×D4—5382no—
174#117—2692no—
175#107—2692no—
176#106—2691no—
177#106C2×D26911yescharacteristic, complemented
178#103—2692no—
179#103—2692no—
180#102—2692no—
181#102C2×D26912yescomplemented
182C24—2691no—
183#41—5384no—
184#41—5384no—
185C2×Q8—2692no—
186C2×D4—22no—
187C2×D4—5382no—
188C2×D4—5382no—
189C2×D4C22×D26912yes—
190C22×C4—2691no—
191C22×C4—2691no—
192C22×C4—2691no—
193C22×C4—2691no—
194C22×C4—2691no—
195C22×C4—5382no—
196C22×C4—5382no—
197C22×C4—5382no—
198C22×C4C22×D26911yescharacteristic
199Q16—5382no—
200SD16—5384no—
201D8—22no—
202M16—22no—
203M16—5382no—
204M16—5382no—
205M16—5382no—
206C2×C8—2691no—
207C2×C8—2694no—
208C2×C8—2691no—
209C2×C8—5382no—
210C2×C8C22×D26911yescharacteristic
211C2×C8C22×D26911yescharacteristic
212C4⋊C4—2692no—
213C4⋊C4—5382no—
214C4⋊C4—5382no—
215C4⋊C4C22×D26912yes—
216C22⋊C4—22no—
217C22⋊C4—5382no—
218C22⋊C4—5382no—
219C22⋊C4—5382no—
220C22⋊C4—5382no—
221C42—5382no—
222C23—22no—
223C23—2691no—
224C23—2691no—
225C23—5382no—
226C23—10762no—
227C23D4×D26911yescharacteristic
228Q8—5382no—
229Q8—5382no—
230D4—22no—
231D4—22no—
232D4—44no—
233D4—10764no—
234D4—10764no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—2691no—
239C2×C4—2692no—
240C2×C4—2692no—
241C2×C4—2691no—
242C2×C4—5382no—
243C2×C4—5382no—
244C2×C4—5382no—
245C2×C4—5381no—
246C2×C4—5381no—
247C2×C4—5382no—
248C2×C4—5382no—
249C2×C4—10764no—
250C2×C4D4×D26911yescharacteristic
251C2×C4C23×D26911yescharacteristic
252C8—21no—
253C8—2692no—
254C8—5381no—
255C8D4×D26912yes—
256C22—22no—
257C22—21no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—2692no—
262C22—5382no—
263C22—5382no—
264C22—5381no—
265C22—10764no—
266C22C2×D4×D26911yescharacteristic
267C4—21no—
268C4—42no—
269C4—2692no—
270C4—5381no—
271C4—10762no—
272C4—10762no—
273C4C2×D4×D26911yescharacteristic
274C4#41×D26911yescharacteristic
275C2—41no—
276C2—82no—
277C2—5382no—
278C2—10761no—
279C2#121×D26911yescharacteristic
280C2#3177140112yes—
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#469×C269C2
socleC22×C269C22×D4
hypercenter#469D269
hypocenterC269#3054
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×#22575472C2semidirect
2. C2×M16×D269C2semidirect
3. #31771115C2semidirect
4. #31770864C2semidirect
5. #31770863C2semidirect
6. #31770855C2semidirect
7. #31770850C2semidirect
8. #31770849C2semidirect
9. #31770640C2semidirect
10. #31770598C2semidirect
11. #469×C269C2semidirect
15. C2×Dic1076C22semidirect
16. C2×#16864390C22semidirect
31. #22575386C22semidirect
32. #22575385C22semidirect
33. #22575378C22semidirect
34. #22575376C22semidirect
35. #22575374C22semidirect
36. C2×D8×C269C22semidirect
39. #106×C269C22semidirect
40. #102×C269C22semidirect
63. C8×D269D4semidirect
140. C269#3054semidirect
148. #469D269semidirect
158. C2×D8C2×D269semidirect
177. #106C2×D269semidirect
181. #102C2×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754722
C2×M16×D2692
#317711152
#317708642
#317708632
#317708552
#317708502
#317708492
#317706402
#317705982
#469×C2692
#3054269