Finite Group Databasebeta

← #46821022

Subgroups — #46821022

Order 34432.

450 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#31771134C211yesmaximal, characteristic, complemented
2C4×D4×D269C211yesmaximal, characteristic, complemented
3#31770934C211yesmaximal, characteristic, complemented
4#31770917C211yesmaximal, characteristic, complemented
5#31770906C211yesmaximal, characteristic, complemented
6#31770905C211yesmaximal, characteristic, complemented
7#31770817C211yesmaximal, characteristic, complemented
8#31770754C211yesmaximal, characteristic, complemented
9#31770737C211yesmaximal, characteristic
10#31770717C211yesmaximal, characteristic, complemented
11#31770714C211yesmaximal, characteristic, complemented
12#31770708C211yesmaximal, characteristic, complemented
13#31770706C211yesmaximal, characteristic, complemented
14#31770661C211yesmaximal, characteristic, complemented
15#463×C269C211yesmaximal, characteristic, complemented
16C2×D4×D269C2211yescharacteristic
17C22×C4×D269—21no—
18C2×#16864389C2211yescharacteristic
19C2×#16864387C2211yescharacteristic
20#22575446—21no—
21#22575445C2211yescharacteristic, complemented
22#22575435—21no—
23#22575429C2211yescharacteristic
24#22575424C2211yescharacteristic
25Q8×Dic269C2211yescharacteristic, complemented
26C4×D1076C2211yescharacteristic
27D4×Dic269C2211yescharacteristic
28D4×Dic269C2211yescharacteristic, complemented
29#22575415C2211yescharacteristic
30C4×C22⋊D269—21no—
31#22575413—21no—
32#22575413—21no—
33#22575409—21no—
34C4⋊C4×D269C2211yescharacteristic
35C22⋊C4×D269—21no—
36C42×D269C2211yescharacteristic
37#22575387C2211yescharacteristic, complemented
38#22575386C2211yescharacteristic, complemented
39#22575385C2211yescharacteristic, complemented
40#22575384C2211yescharacteristic, complemented
41C4⋊#14524130C2211yescharacteristic, complemented
42#22575377C2211yescharacteristic, complemented
43#22575375C2211yescharacteristic
44#22575375C2211yescharacteristic
45#22575374C2211yescharacteristic
46#22575374C2211yescharacteristic
47#22575374C2211yescharacteristic, complemented
48#22575365C2211yescharacteristic
49#22575365C2211yescharacteristic
50#22575363C2211yescharacteristic, complemented
51#22575363C2211yescharacteristic, complemented
52C2×SD16×C269C2211yescharacteristic
53C2×D8×C269C2211yescharacteristic
54#124×C269C2211yescharacteristic, complemented
55C4×D4×C269C2211yescharacteristic
56C4⋊C8×C269C2211yescharacteristic, complemented
57#103×C269C2211yescharacteristic, complemented
58#102×C269C2211yescharacteristic, complemented
59C23×D269—21no—
60C2×D1076C2311yescharacteristic
61C2×C22⋊D269—21no—
62C2×C22⋊D269—21no—
63D4×D269—22no—
64D4×D269—22no—
65C22×Dic269—21no—
66C22×Dic269—21no—
67C2×C4×D269—21no—
68C2×C4×D269—21no—
69C2×C4×D269—21no—
70C2×C4×D269—44no—
71C2×C4×D269D411yescharacteristic
72C2×C4×D269D411yescharacteristic
73C2×C4×D269C2311yescharacteristic
74#16864389—22no—
75#16864387—22no—
76C2×#14524130C2311yescharacteristic
77C2×#14524130C2311yescharacteristic
78C4⋊Dic269—21no—
79C4⋊Dic269C2311yescharacteristic
80C4⋊Dic269C2311yescharacteristic
81C4⋊Dic269C2311yescharacteristic
82#16864381—21no—
83#16864381—21no—
84#16864381—21no—
85#16864381—21no—
86C22⋊Dic269—21no—
87C22⋊Dic269—21no—
88C22⋊Dic269—21no—
89#16864379—21no—
90#16864379—21no—
91#16864379—21no—
92C4×Dic269—21no—
93C4×Dic269D411yescharacteristic
94C4×Dic269D411yescharacteristic
95C4×Dic269C2311yescharacteristic
96C2×Q8×C269C2311yescharacteristic
97C2×D4×C269C2311yescharacteristic
98C2×D4×C269C2311yescharacteristic
99C22×C4×C269—21no—
100SD16×C269—22no—
101D8×C269—22no—
102C2×C8×C269C2311yescharacteristic
103C2×C8×C269C2311yescharacteristic
104C4⋊C4×C269C2311yescharacteristic
105C22⋊C4×C269—21no—
106C22⋊C4×C269—21no—
107C22⋊C4×C269—21no—
108C42×C269C2311yescharacteristic
109C22×D269—24no—
110C22×D269—21no—
111C22×D269—42no—
112C22×D269—42no—
113C22×D269C2×D411yescharacteristic
114D1076—21no—
115D1076#4112yes—
116C22⋊D269—24no—
117C22⋊D269—42no—
118C2×Dic269—21no—
119C2×Dic269—21no—
120C2×Dic269—21no—
121C2×Dic269—42no—
122C2×Dic269—42no—
123C2×Dic269C2×D411yescharacteristic
124C2×Dic269C2×D411yescharacteristic
125C2×Dic269C2×D411yescharacteristic
126C4×D269—22no—
127C4×D269—21no—
128C4×D269—21no—
129C4×D269—41no—
130C4×D269—42no—
131C4×D269—42no—
132C4×D269—42no—
133#14524130—21no—
134#14524130—21no—
135C23×C269—21no—
136C23×C269—21no—
137Q8×C269—21no—
138Q8×C269—21no—
139D4×C269—21no—
140D4×C269—21no—
141D4×C269—21no—
142D4×C269#4112yes—
143C2×C4×C269—21no—
144C2×C4×C269—21no—
145C2×C4×C269—42no—
146C2×C4×C269C2×D411yescharacteristic
147C2×C4×C269C2×D411yescharacteristic
148C2×C4×C269C2411yescharacteristic
149C8×C269—21no—
150C8×C269—21no—
151C22×C269—22no—
152C22×C269—41no—
153C22×C269—41no—
154C22×C269—41no—
155C22×C269—41no—
156C22×C269—41no—
157C22×C269C22×D411yescharacteristic
158C2×D269—21no—
159C2×D269—21no—
160C2×D269—22no—
161C2×D269—48no—
162C2×D269—41no—
163C2×D269—41no—
164C2×D269AGL(1,ℤ/8)12yes—
165C4×C269—21no—
166C4×C269—21no—
167C4×C269—41no—
168C4×C269—41no—
169C4×C269C2×#4111yescharacteristic
170C4×C269C2×#4111yescharacteristic
171Dic269—21no—
172Dic269—21no—
173Dic269—21no—
174Dic269—41no—
175Dic269—41no—
176Dic269—41no—
177C2×C269—42no—
178C2×C269—81no—
179C2×C269#52511yescharacteristic
180C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C269#57511yescharacteristic
182D269—22no—
183D269—42no—
184C269#311411yescharacteristic, complemented, Sylow
185#3114—2691nomaximal, Sylow
186#529—2691no—
187C2×C4×D4—2691no—
188#483—2691no—
189#480—2691no—
190#478—2691no—
191#478—2691no—
192#463—2691no—
193#463D26911yescharacteristic, complemented
194#450—2691no—
195#447—2691no—
196#442—2691no—
197#442—2691no—
198#440—2691no—
199#440—2691no—
200#432—2691no—
201C22×D4—2691no—
202C23×C4—5381no—
203C2×SD16—2691no—
204C2×SD16C2×D26911yescharacteristic
205C2×D8—2691no—
206C2×D8C2×D26911yescharacteristic
207#126—5381no—
208#125—2691no—
209#124C2×D26911yescharacteristic, complemented
210#123—5381no—
211C22⋊Q8—2691no—
212#121—2691no—
213C4×Q8—2691no—
214C4×D4—2691no—
215C4×D4—2691no—
216C4×D4—2691no—
217C4×D4—2691no—
218C4×D4—5381no—
219C4×D4—5381no—
220C4×D4—5381no—
221C4×D4C2×D26911yescharacteristic
222#117—5381no—
223C2×C4⋊C4—2691no—
224C2×C22⋊C4—5381no—
225C2×C42—2691no—
226#107—2691no—
227#107—2691no—
228#106—2691no—
229#106—2691no—
230C4⋊C8—2691no—
231C4⋊C8C2×D26911yescharacteristic, complemented
232#103—2691no—
233#103C2×D26911yescharacteristic, complemented
234#102—2691no—
235#102—2691no—
236#102—2691no—
237#102—2691no—
238#102—2691no—
239#102C2×D26911yescharacteristic, complemented
240C22⋊C8—2691no—
241C22⋊C8—2691no—
242#97—2691no—
243#97—2691no—
244C24—5381no—
245C2×Q8C22×D26911yescharacteristic
246C2×D4—2691no—
247C2×D4—5381no—
248C2×D4—5382no—
249C2×D4—5382no—
250C2×D4—5381no—
251C2×D4C22×D26911yescharacteristic
252C2×D4C22×D26911yescharacteristic
253C22×C4—21no—
254C22×C4—2691no—
255C22×C4—2691no—
256C22×C4—2691no—
257C22×C4—5381no—
258C22×C4—5381no—
259C22×C4—5381no—
260C22×C4—5381no—
261C22×C4—5381no—
262C22×C4—10764no—
263SD16—22no—
264SD16—5382no—
265D8—22no—
266D8—5382no—
267C2×C8—2691no—
268C2×C8—2691no—
269C2×C8C22×D26911yescharacteristic
270C2×C8C22×D26911yescharacteristic
271C4⋊C4—2691no—
272C4⋊C4—2691no—
273C4⋊C4—2691no—
274C4⋊C4—5381no—
275C4⋊C4—5381no—
276C4⋊C4—5381no—
277C4⋊C4—5381no—
278C4⋊C4—5381no—
279C4⋊C4C22×D26911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—5381no—
284C22⋊C4—5381no—
285C22⋊C4—5381no—
286C22⋊C4—5381no—
287C22⋊C4—5381no—
288C22⋊C4—5381no—
289C42—2691no—
290C42—2691no—
291C42—2691no—
292C42—5381no—
293C42C22×D26911yescharacteristic
294C23—21no—
295C23—21no—
296C23—2691no—
297C23—5384no—
298C23—5381no—
299C23—10762no—
300C23—10762no—
301Q8—21no—
302Q8—21no—
303D4—21no—
304D4—21no—
305D4—21no—
306D4—2692no—
307D4—5384no—
308D4—5381no—
309D4—10762no—
310D4#1686440112yes—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—2691no—
315C2×C4—2691no—
316C2×C4—2691no—
317C2×C4—5382no—
318C2×C4—5381no—
319C2×C4—5381no—
320C2×C4—5381no—
321C2×C4—5381no—
322C2×C4—5381no—
323C2×C4—10761no—
324C2×C4—10762no—
325C2×C4—10762no—
326C2×C4—10762no—
327C2×C4—10762no—
328C2×C4—10762no—
329C2×C4D4×D26911yescharacteristic
330C2×C4D4×D26911yescharacteristic
331C2×C4C23×D26911yescharacteristic
332C8—21no—
333C8—21no—
334C8—5381no—
335C8—5381no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—2692no—
343C22—5381no—
344C22—5381no—
345C22—5382no—
346C22—10768no—
347C22—10761no—
348C22—10761no—
349C22C2×D4×D26911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—5381no—
355C4—5381no—
356C4—5381no—
357C4—10761no—
358C4—10761no—
359C4—10761no—
360C4#41×D26911yescharacteristic
361C4C2×#1686440111yescharacteristic
362C2—42no—
363C2—81no—
364C2—5382no—
365C2—10762no—
366C2#3177111511yescharacteristic
367C2AGL(1,ℤ/8)×D26911yescharacteristic
368C2#3177140211yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutator, cosocleC2×C4×C269C24
FrattiniC2×C4C23×D269
Fitting#463×C269C2
socleC22×C269C22×D4
prime radical#31770737C2
hypercenter#463D269
hypocenterC269#3114
LCSG ▷ C2×C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #31771134C2semidirect
2. C4×D4×D269C2semidirect
3. #31770934C2semidirect
4. #31770917C2semidirect
5. #31770906C2semidirect
6. #31770905C2semidirect
7. #31770817C2semidirect
8. #31770754C2semidirect
10. #31770717C2semidirect
11. #31770714C2semidirect
12. #31770708C2semidirect
13. #31770706C2semidirect
14. #31770661C2semidirect
15. #463×C269C2semidirect
21. #22575445C22semidirect
25. Q8×Dic269C22semidirect
28. D4×Dic269C22semidirect
37. #22575387C22semidirect
38. #22575386C22semidirect
39. #22575385C22semidirect
40. #22575384C22semidirect
41. C4⋊#14524130C22semidirect
42. #22575377C22semidirect
47. #22575374C22semidirect
50. #22575363C22semidirect
51. #22575363C22semidirect
54. #124×C269C22semidirect
56. C4⋊C8×C269C22semidirect
57. #103×C269C22semidirect
58. #102×C269C22semidirect
184. C269#3114semidirect
193. #463D269semidirect
209. #124C2×D269semidirect
231. C4⋊C8C2×D269semidirect
233. #103C2×D269semidirect
239. #102C2×D269semidirect

Maximal subgroups

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

subgroupindex
#317711342
C4×D4×D2692
#317709342
#317709172
#317709062
#317709052
#317708172
#317707542
#317707372
#317707172
#317707142
#317707082
#317707062
#317706612
#463×C2692
#3114269