Finite Group Databasebeta

← #46822925

Subgroups — #46822925

Order 34432.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771326C211yesmaximal, characteristic, complemented
2#31771243C211yesmaximal, characteristic
3#31770966C211yesmaximal, characteristic, complemented
4#31770945C211yesmaximal, characteristic, complemented
5#31770930C211yesmaximal, characteristic, complemented
6#31770893C211yesmaximal, characteristic, complemented
7#31770860C211yesmaximal, characteristic, complemented
8#31770836C211yesmaximal, characteristic, complemented
9#31770829C211yesmaximal, characteristic, complemented
10#31770754C211yesmaximal, characteristic, complemented
11#31770706C211yesmaximal, characteristic, complemented
12#31770673C211yesmaximal, characteristic, complemented
13#31770608C211yesmaximal, characteristic, complemented
14#31770601C211yesmaximal, characteristic, complemented
15#452×C269C211yesmaximal, characteristic, complemented
16C2×D4×D269C2211yescharacteristic
17C2×#16864389C2211yescharacteristic
18C2×#16864385C2211yescharacteristic
19C22×#14524130C2211yescharacteristic, complemented
20#22575452C2211yescharacteristic, complemented
21#22575448—21no—
22#22575446—21no—
23#22575442C2211yescharacteristic
24#22575439—21no—
25#22575436—21no—
26#22575429C2211yescharacteristic
27#22575429C2211yescharacteristic
28#22575427C2211yescharacteristic
29#22575425—21no—
30#22575421—21no—
31Q8×Dic269C2211yescharacteristic, complemented
32#22575418—21no—
33D4×Dic269C2211yescharacteristic
34C4×C22⋊D269C2211yescharacteristic
35#22575412C2211yescharacteristic, complemented
36#22575411C2211yescharacteristic
37C2×#16864379—21no—
38#22575387C2211yescharacteristic, complemented
39#22575385C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41#22575382C2211yescharacteristic, complemented
42#22575377C2211yescharacteristic, complemented
43#22575377C2211yescharacteristic, complemented
44#22575377C2211yescharacteristic, complemented
45#22575375C2211yescharacteristic
46#22575375C2211yescharacteristic
47#22575374C2211yescharacteristic
48#22575374C2211yescharacteristic
49#22575373C2211yescharacteristic
50#22575365C2211yescharacteristic
51#22575363C2211yescharacteristic, complemented
52C2×#41×C269C2211yescharacteristic
53C2×Q16×C269C2211yescharacteristic, complemented
54C2×SD16×C269C2211yescharacteristic
55C22⋊Q8×C269C2211yescharacteristic, complemented
56#103×C269C2211yescharacteristic, complemented
57#102×C269C2211yescharacteristic
58C22⋊C8×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60C2×Dic538—21no—
61C2×D1076C2311yescharacteristic
62C2×C22⋊D269—21no—
63C2×C22⋊D269—21no—
64C2×C22⋊D269D411yescharacteristic
65D4×D269—22no—
66D4×D269—41no—
67C22×Dic269—21no—
68C2×C4×D269C2311yescharacteristic
69#16864389—41no—
70#16864385—41no—
71C2×#14524130—41no—
72C2×#14524130C2311yescharacteristic
73C2×#14524130C2311yescharacteristic
74C4⋊Dic269—21no—
75C4⋊Dic269C2311yescharacteristic
76C4⋊Dic269C2311yescharacteristic
77C4⋊Dic269C2311yescharacteristic
78#16864381—21no—
79#16864381—21no—
80#16864381—21no—
81#16864381D411yescharacteristic
82C22⋊Dic269—21no—
83C22⋊Dic269—21no—
84C22⋊Dic269D411yescharacteristic
85#16864379—21no—
86#16864379—21no—
87#16864379—21no—
88#16864379—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379D411yescharacteristic
92C4×Dic269—21no—
93C4×Dic269—21no—
94C4×Dic269—21no—
95C4×Dic269C2311yescharacteristic
96#41×C269—22no—
97#41×C269—41no—
98C2×Q8×C269C2311yescharacteristic
99C2×Q8×C269C2311yescharacteristic
100C2×D4×C269—21no—
101C2×D4×C269C2311yescharacteristic
102C22×C4×C269—21no—
103C22×C4×C269C2311yescharacteristic
104Q16×C269—41no—
105SD16×C269—22no—
106C2×C8×C269C2311yescharacteristic
107C2×C8×C269C2311yescharacteristic
108C4⋊C4×C269—21no—
109C4⋊C4×C269C2311yescharacteristic
110C22⋊C4×C269—21no—
111C22×D269—21no—
112C22×D269—42no—
113C22×D269—42no—
114C22×D269—81no—
115C22×D269C2×D411yescharacteristic
116Dic538—42no—
117D1076—21no—
118D1076—21no—
119C22⋊D269—41no—
120C22⋊D269—42no—
121C22⋊D269—81no—
122C2×Dic269—21no—
123C2×Dic269—21no—
124C2×Dic269—21no—
125C2×Dic269—81no—
126C2×Dic269C2×D411yescharacteristic
127C2×Dic269C2×D411yescharacteristic
128C2×Dic269C2×D411yescharacteristic
129C4×D269—21no—
130C4×D269—21no—
131#14524130—21no—
132#14524130—21no—
133C23×C269—21no—
134C23×C269C2×D411yescharacteristic
135Q8×C269—21no—
136Q8×C269—21no—
137Q8×C269—21no—
138Q8×C269—21no—
139D4×C269—21no—
140D4×C269—42no—
141D4×C269#4112yes—
142C2×C4×C269—21no—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—21no—
146C2×C4×C269—21no—
147C2×C4×C269—42no—
148C2×C4×C269C2×D411yescharacteristic
149C2×C4×C269C2411yescharacteristic
150C8×C269—21no—
151C8×C269—21no—
152C22×C269—21no—
153C22×C269—22no—
154C22×C269—21no—
155C22×C269—21no—
156C22×C269—41no—
157C22×C269—41no—
158C22×C269C22×D411yescharacteristic
159C2×D269—21no—
160C2×D269—21no—
161C2×D269—21no—
162C2×D269—41no—
163C2×D269—41no—
164C2×D269—41no—
165C2×D269—84no—
166C4×C269—21no—
167C4×C269—41no—
168C4×C269—41no—
169C4×C269—41no—
170C4×C269C2×#4111yescharacteristic
171C4×C269H(5,𝔽2)11yescharacteristic
172Dic269—21no—
173Dic269—21no—
174Dic269—21no—
175Dic269—41no—
176Dic269—41no—
177Dic269—41no—
178C2×C269—42no—
179C2×C269—41no—
180C2×C269#54611yescharacteristic
181C2×C269#57511yescharacteristic
182C2×C269#57711yescharacteristic
183D269—41no—
184D269—81no—
185C269#331111yescharacteristic, complemented, Sylow
186#3311—2691nomaximal, Sylow
187#556—2691no—
188#546—2691no—
189#489—2691no—
190#485—2691no—
191#482—2691no—
192#476—2691no—
193#470—2691no—
194#465—2691no—
195#464—2691no—
196#452D26911yescharacteristic, complemented
197#450—2691no—
198#440—2691no—
199#435—2691no—
200#418—2691no—
201#416—2691no—
202C2×#41C2×D26911yescharacteristic
203C22×D4—2691no—
204C2×Q16C2×D26911yescharacteristic, complemented
205C2×SD16—2691no—
206C2×SD16C2×D26911yescharacteristic
207C2×M16—2691no—
208C22×C8—2691no—
209C4⋊Q8—2691no—
210#126—5381no—
211#126—5381no—
212#124—2691no—
213#124—5381no—
214#123—5381no—
215C22⋊Q8—2691no—
216C22⋊Q8—2691no—
217C22⋊Q8C2×D26911yescharacteristic, complemented
218#121—2691no—
219#121—5381no—
220#120—5381no—
221C4×Q8—2691no—
222C4×Q8—5381no—
223C4×D4—2691no—
224C4×D4—2691no—
225#117—2691no—
226#117—2691no—
227C2×C22⋊C4—5381no—
228#107—2691no—
229#106—2691no—
230#106—2691no—
231C4⋊C8—2691no—
232#103—2691no—
233#103—2691no—
234#103—2691no—
235#103C2×D26911yescharacteristic, complemented
236#102—2691no—
237#102—2691no—
238#102—2691no—
239#102—2691no—
240#102—2691no—
241#102C2×D26911yescharacteristic
242C22⋊C8—2691no—
243C22⋊C8C2×D26911yescharacteristic, complemented
244#97—2691no—
245C24—5381no—
246#41—22no—
247#41—41no—
248C2×Q8—5381no—
249C2×Q8C22×D26911yescharacteristic
250C2×Q8C22×D26911yescharacteristic
251C2×D4—21no—
252C2×D4—2691no—
253C2×D4—2691no—
254C2×D4—5381no—
255C2×D4—5382no—
256C2×D4—5381no—
257C2×D4—10761no—
258C2×D4C22×D26911yescharacteristic
259C22×C4—21no—
260C22×C4—2691no—
261C22×C4—5381no—
262C22×C4C22×D26911yescharacteristic
263Q16—41no—
264SD16—22no—
265SD16—10761no—
266M16—10761no—
267C2×C8—2691no—
268C2×C8—2691no—
269C2×C8—10761no—
270C2×C8C22×D26911yescharacteristic
271C2×C8C22×D26911yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—2691no—
274C4⋊C4—2691no—
275C4⋊C4—2691no—
276C4⋊C4—2691no—
277C4⋊C4—5381no—
278C4⋊C4—5381no—
279C4⋊C4—5381no—
280C4⋊C4—5381no—
281C4⋊C4C22×D26911yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—2691no—
284C22⋊C4—2691no—
285C22⋊C4—5381no—
286C22⋊C4—5381no—
287C22⋊C4—5381no—
288C22⋊C4—5381no—
289C22⋊C4—5381no—
290C22⋊C4—5381no—
291C22⋊C4—5381no—
292C22⋊C4—5381no—
293C42—2691no—
294C42—5381no—
295C42—5381no—
296C42—5381no—
297C23—21no—
298C23—2691no—
299C23—5381no—
300C23—10762no—
301C23—10762no—
302C23—21521no—
303C23D4×D26911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—10762no—
309D4—21no—
310D4—42no—
311D4—5381no—
312D4—5381no—
313D4—10761no—
314D4—10762no—
315D4—21521no—
316D4#1686440112yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—2691no—
324C2×C4—2691no—
325C2×C4—2691no—
326C2×C4—5381no—
327C2×C4—5381no—
328C2×C4—5381no—
329C2×C4—5381no—
330C2×C4—5381no—
331C2×C4—21521no—
332C2×C4D4×D26911yescharacteristic
333C2×C4C23×D26911yescharacteristic
334C8—21no—
335C8—21no—
336C8—5381no—
337C8—5381no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—5381no—
345C22—5381no—
346C22—5381no—
347C22—10761no—
348C22—10761no—
349C22—10761no—
350C22—21524no—
351C22C2×D4×D26911yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—5381no—
357C4—5381no—
358C4—5381no—
359C4—10761no—
360C4—10761no—
361C4—10761no—
362C4C2×#1686440111yescharacteristic
363C4#2257549811yescharacteristic
364C2—41no—
365C2—42no—
366C2—10761no—
367C2—21521no—
368C2#3177124211yescharacteristic
369C2#3177140211yescharacteristic
370C2#3177141411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#452×C269C2
socleC22×C269C22×D4
prime radical#31771243C2
hypercenter#452D269
hypocenterC269#3311
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #31771326C2semidirect
3. #31770966C2semidirect
4. #31770945C2semidirect
5. #31770930C2semidirect
6. #31770893C2semidirect
7. #31770860C2semidirect
8. #31770836C2semidirect
9. #31770829C2semidirect
10. #31770754C2semidirect
11. #31770706C2semidirect
12. #31770673C2semidirect
13. #31770608C2semidirect
14. #31770601C2semidirect
15. #452×C269C2semidirect
19. C22×#14524130C22semidirect
20. #22575452C22semidirect
31. Q8×Dic269C22semidirect
35. #22575412C22semidirect
38. #22575387C22semidirect
39. #22575385C22semidirect
40. #22575384C22semidirect
41. #22575382C22semidirect
42. #22575377C22semidirect
43. #22575377C22semidirect
44. #22575377C22semidirect
51. #22575363C22semidirect
53. C2×Q16×C269C22semidirect
55. C22⋊Q8×C269C22semidirect
56. #103×C269C22semidirect
58. C22⋊C8×C269C22semidirect
185. C269#3311semidirect
196. #452D269semidirect
204. C2×Q16C2×D269semidirect
217. C22⋊Q8C2×D269semidirect
235. #103C2×D269semidirect
243. C22⋊C8C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317713262
#317712432
#317709662
#317709452
#317709302
#317708932
#317708602
#317708362
#317708292
#317707542
#317707062
#317706732
#317706082
#317706012
#452×C2692
#3311269