Finite Group Databasebeta

← #46819690

Subgroups — #46819690

Order 34432.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#22575480C211yesmaximal, characteristic
2C4×#16864403C211yesmaximal, characteristic, complemented
3C4×D4×D269C211yesmaximal, characteristic, complemented
4#31770718C211yesmaximal, characteristic, complemented
5#31770715C211yesmaximal, characteristic, complemented
6#31770703C211yesmaximal, characteristic, complemented
7SD16×Dic269C211yesmaximal, characteristic, complemented
8#31770690C211yesmaximal, characteristic, complemented
9#31770687C211yesmaximal, characteristic, complemented
10#31770685C211yesmaximal, characteristic, complemented
11#31770646C211yesmaximal, characteristic, complemented
12#31770608C211yesmaximal, characteristic, complemented
13#31770605C211yesmaximal, characteristic, complemented
14#31770557C211yesmaximal, characteristic, complemented
15#440×C269C211yesmaximal, characteristic, complemented
16C2×#16864403C2211yescharacteristic
17C2×D4×D269C2211yescharacteristic
18C22×C4×D269—21no—
19#22575480C418yescomplemented
20C2×#16864389C2211yescharacteristic
21C2×D2152C2211yescharacteristic
22C2×#16864387C2211yescharacteristic
23C2×#16864385C2211yescharacteristic
24C2×#16864385C2211yescharacteristic
25Q8×Dic269C2211yescharacteristic, complemented
26C4×D1076—21no—
27C4×D1076C2211yescharacteristic
28C4×D1076C2211yescharacteristic, complemented
29D4×Dic269C2211yescharacteristic
30#22575415—21no—
31#22575415C2211yescharacteristic
32#22575415C2211yescharacteristic, complemented
33C4×C22⋊D269—21no—
34#22575413—21no—
35#22575411—21no—
36#22575411C2211yescharacteristic
37C4⋊C4×D269C2211yescharacteristic
38C22⋊C4×D269—21no—
39C42×D269—21no—
40C42×D269C2211yescharacteristic
41#22575386C2211yescharacteristic, complemented
42#22575385C2211yescharacteristic, complemented
43#22575384C2211yescharacteristic, complemented
44#22575377C2211yescharacteristic, complemented
45#22575375C2211yescharacteristic
46#22575375C2211yescharacteristic, complemented
47#22575374C2211yescharacteristic
48#22575373C2211yescharacteristic
49#22575373C2211yescharacteristic, complemented
50#22575364C2211yescharacteristic, complemented
51C8×Dic269C2211yescharacteristic, complemented
52C8×Dic269C2211yescharacteristic, complemented
53C2×SD16×C269C2211yescharacteristic
54C4×Q8×C269C2211yescharacteristic, complemented
55C4×D4×C269C2211yescharacteristic
56#107×C269C2211yescharacteristic, complemented
57#103×C269C2211yescharacteristic, complemented
58#102×C269C2211yescharacteristic
59#97×C269C2211yescharacteristic, complemented
60C23×D269—21no—
61#16864403—22no—
62#16864403C2×C414yescomplemented
63C2×D1076—21no—
64C2×D1076C2311yescharacteristic
65C2×D1076C2311yescharacteristic
66C2×C22⋊D269—21no—
67D4×D269—22no—
68D4×D269C2×C414yescomplemented
69C22×Dic269—21no—
70C2×C4×D269—21no—
71C2×C4×D269—21no—
72C2×C4×D269—21no—
73C2×C4×D269—21no—
74C2×C4×D269—21no—
75C2×C4×D269—21no—
76C2×C4×D269—44no—
77C2×C4×D269D411yescharacteristic
78C2×C4×D269D411yescharacteristic
79C2×C4×D269C2311yescharacteristic
80#16864389C2×C414yescomplemented
81D2152C2×C414yescomplemented
82#16864387C2×C414yescomplemented
83#16864385—22no—
84#16864385C2×C414yescomplemented
85C2×#14524130C2311yescharacteristic
86C2×#14524130C2311yescharacteristic
87C4⋊Dic269—21no—
88C4⋊Dic269C2311yescharacteristic
89C4⋊Dic269C2311yescharacteristic
90#16864381—21no—
91C22⋊Dic269—21no—
92#16864379—21no—
93#16864379—21no—
94#16864379—21no—
95#16864379—21no—
96#16864379—21no—
97C4×Dic269—21no—
98C4×Dic269—21no—
99C4×Dic269D411yescharacteristic
100C4×Dic269D411yescharacteristic
101C4×Dic269C2311yescharacteristic
102C2×Q8×C269C2311yescharacteristic
103C2×D4×C269C2311yescharacteristic
104C22×C4×C269—21no—
105SD16×C269C2×C414yescomplemented
106C2×C8×C269C2311yescharacteristic
107C2×C8×C269C2311yescharacteristic
108C4⋊C4×C269—21no—
109C4⋊C4×C269C2311yescharacteristic
110C4⋊C4×C269C2311yescharacteristic
111C22⋊C4×C269—21no—
112C42×C269—21no—
113C42×C269C2311yescharacteristic
114C22×D269—21no—
115C22×D269—21no—
116C22×D269—24no—
117C22×D269—42no—
118C22×D269—42no—
119C22×D269C2×D411yescharacteristic
120D1076—24no—
121D1076—21no—
122D1076—21no—
123D1076C22×C412yes—
124D1076C22×C412yescomplemented
125C22⋊D269—24no—
126C2×Dic269—21no—
127C2×Dic269—21no—
128C2×Dic269—42no—
129C2×Dic269C2×D411yescharacteristic
130C2×Dic269C2×D411yescharacteristic
131C2×Dic269C2×D411yescharacteristic
132C4×D269—24no—
133C4×D269—22no—
134C4×D269—41no—
135C4×D269—42no—
136C4×D269—42no—
137C4×D269—42no—
138C4×D269—42no—
139C4×D269—42no—
140C4×D269C22×C412yes—
141C4×D269#4112yes—
142#14524130—21no—
143#14524130C22×C412yescomplemented
144C23×C269—21no—
145Q8×C269—21no—
146Q8×C269C22×C412yescomplemented
147D4×C269—21no—
148D4×C269C22×C412yes—
149C2×C4×C269—21no—
150C2×C4×C269—21no—
151C2×C4×C269—21no—
152C2×C4×C269—42no—
153C2×C4×C269C2×D411yescharacteristic
154C2×C4×C269C2×D411yescharacteristic
155C2×C4×C269C2411yescharacteristic
156C8×C269—21no—
157C8×C269C22×C412yescomplemented
158C22×C269—22no—
159C22×C269—41no—
160C22×C269—41no—
161C22×C269C22×D411yescharacteristic
162C2×D269—21no—
163C2×D269—21no—
164C2×D269—22no—
165C2×D269—22no—
166C2×D269—48no—
167C2×D269—41no—
168C2×D269—41no—
169C2×D269—41no—
170C2×D269—41no—
171C2×D269C4×D412yes—
172C4×C269—22no—
173C4×C269—21no—
174C4×C269—21no—
175C4×C269—41no—
176C4×C269—41no—
177C4×C269C23×C411yescharacteristic
178C4×C269C2×#4111yescharacteristic
179Dic269—21no—
180Dic269—41no—
181Dic269—41no—
182Dic269C4×D412yes—
183Dic269AGL(1,ℤ/8)12yescomplemented
184C2×C269—42no—
185C2×C269C2×C4×D411yescharacteristic
186C2×C269C2×AGL(1,ℤ/8)11yescharacteristic
187C2×C269#57511yescharacteristic
188D269—22no—
189D269—42no—
190D269—42no—
191C269C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
192C4×AGL(1,ℤ/8)—2691nomaximal, Sylow
193C2×AGL(1,ℤ/8)—2691no—
194C4×#41—2691no—
195C2×C4×D4—2691no—
196#442—2691no—
197#442—2691no—
198#440—2691no—
199#440D26911yescharacteristic, complemented
200C4×SD16—2691no—
201C4×SD16—2691no—
202C4×D8—2691no—
203C4×D8—2691no—
204#428—2691no—
205#418—2691no—
206#417—2691no—
207C4×M16—2691no—
208C2×#41—2691no—
209C22×D4—2691no—
210C23×C4—5381no—
211AGL(1,ℤ/8)—2698no—
212C2×SD16—2691no—
213C2×SD16C2×D26911yescharacteristic
214C2×D8—2691no—
215C2×D8—2691no—
216C2×M16—2691no—
217C2×M16—2691no—
218C4×Q8—2691no—
219C4×Q8C2×D26911yescharacteristic, complemented
220C4×D4—2691no—
221C4×D4—2691no—
222C4×D4—2691no—
223C4×D4—2691no—
224C4×D4—2691no—
225C4×D4—5381no—
226C4×D4—5381no—
227C4×D4—5381no—
228C4×D4—5381no—
229C4×D4C2×D26911yescharacteristic
230#117—2691no—
231#117—5381no—
232C2×C4⋊C4—2691no—
233C2×C22⋊C4—5381no—
234C2×C42—2691no—
235C2×C42—5381no—
236#107—2691no—
237#107C2×D26911yescharacteristic, complemented
238#106—2691no—
239#106—2691no—
240#103—2691no—
241#103C2×D26911yescharacteristic, complemented
242#102—2691no—
243#102—2691no—
244#102—2691no—
245#102—2691no—
246#102—2691no—
247#102C2×D26911yescharacteristic
248#97—2691no—
249#97C2×D26911yescharacteristic, complemented
250C4×C8—2691no—
251C4×C8—2691no—
252C24—5381no—
253#41—2694no—
254#41—5382no—
255C2×Q8C22×D26911yescharacteristic
256C2×D4—2694no—
257C2×D4—2691no—
258C2×D4—2691no—
259C2×D4—5381no—
260C2×D4—5382no—
261C2×D4—5381no—
262C2×D4C22×D26911yescharacteristic
263C22×C4—21no—
264C22×C4—2691no—
265C22×C4—2691no—
266C22×C4—2691no—
267C22×C4—5381no—
268C22×C4—5381no—
269C22×C4—5381no—
270C22×C4—5381no—
271C22×C4—5381no—
272C22×C4—5381no—
273C22×C4—5381no—
274C22×C4—10764no—
275SD16—2694no—
276SD16C4×D26914yescomplemented
277D8—2694no—
278D8—2694no—
279M16—2694no—
280M16—5382no—
281C2×C8—2691no—
282C2×C8—2691no—
283C2×C8C22×D26911yescharacteristic
284C2×C8C22×D26911yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—2691no—
287C4⋊C4—2691no—
288C4⋊C4—5381no—
289C4⋊C4—5381no—
290C4⋊C4C22×D26911yescharacteristic
291C4⋊C4C22×D26911yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—5381no—
294C22⋊C4—5381no—
295C22⋊C4—5381no—
296C22⋊C4—5381no—
297C22⋊C4—5381no—
298C22⋊C4—5381no—
299C42—21no—
300C42—2691no—
301C42—2691no—
302C42—2691no—
303C42—5381no—
304C42—5381no—
305C42C22×D26911yescharacteristic
306C23—21no—
307C23—2691no—
308C23—5384no—
309C23—5381no—
310C23—5381no—
311C23—10762no—
312C23—10762no—
313Q8—21no—
314Q8C2×C4×D26912yescomplemented
315D4—21no—
316D4—2692no—
317D4—2692no—
318D4—5384no—
319D4—5384no—
320D4—5381no—
321D4—5381no—
322D4C2×C4×D26912yes—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—2691no—
328C2×C4—2691no—
329C2×C4—2692no—
330C2×C4—2692no—
331C2×C4—2691no—
332C2×C4—5382no—
333C2×C4—5384no—
334C2×C4—5381no—
335C2×C4—5381no—
336C2×C4—10761no—
337C2×C4—10762no—
338C2×C4—10762no—
339C2×C4—10762no—
340C2×C4—10762no—
341C2×C4—10762no—
342C2×C4—10762no—
343C2×C4D4×D26911yescharacteristic
344C2×C4D4×D26911yescharacteristic
345C2×C4C23×D26911yescharacteristic
346C8—21no—
347C8—2692no—
348C8—5381no—
349C8C2×C4×D26912yescomplemented
350C22—22no—
351C22—41no—
352C22—41no—
353C22—2692no—
354C22—5381no—
355C22—5381no—
356C22—5382no—
357C22—5382no—
358C22—10768no—
359C22—10761no—
360C22—10761no—
361C22—10761no—
362C22—10761no—
363C22C2×D4×D26911yescharacteristic
364C4—21no—
365C4—22no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—2692no—
370C4—2692no—
371C4—5381no—
372C4—10761no—
373C4—10761no—
374C4C22×C4×D26911yescharacteristic
375C4#41×D26911yescharacteristic
376C2—42no—
377C2—5382no—
378C2—10762no—
379C2—10762no—
380C2C4×D4×D26911yescharacteristic
381C2AGL(1,ℤ/8)×D26911yescharacteristic
382C2#3177140411yescharacteristic
subgroupG/H
centerC22C2×D4×D269
commutatorC4×C269C23×C4
FrattiniC2×C4C23×D269
Fitting#440×C269C2
socleC22×C269C22×D4
prime radicalC2×#22575480C2
cosocleC2×C4×C269C24
hypercenter#440D269
hypocenterC269C4×AGL(1,ℤ/8)
LCSG ▷ C4×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×#16864403C2semidirect
3. C4×D4×D269C2semidirect
4. #31770718C2semidirect
5. #31770715C2semidirect
6. #31770703C2semidirect
7. SD16×Dic269C2semidirect
8. #31770690C2semidirect
9. #31770687C2semidirect
10. #31770685C2semidirect
11. #31770646C2semidirect
12. #31770608C2semidirect
13. #31770605C2semidirect
14. #31770557C2semidirect
15. #440×C269C2semidirect
19. #22575480C4semidirect
25. Q8×Dic269C22semidirect
28. C4×D1076C22semidirect
32. #22575415C22semidirect
41. #22575386C22semidirect
42. #22575385C22semidirect
43. #22575384C22semidirect
44. #22575377C22semidirect
46. #22575375C22semidirect
49. #22575373C22semidirect
50. #22575364C22semidirect
51. C8×Dic269C22semidirect
52. C8×Dic269C22semidirect
54. C4×Q8×C269C22semidirect
56. #107×C269C22semidirect
57. #103×C269C22semidirect
59. #97×C269C22semidirect
62. #16864403C2×C4semidirect
68. D4×D269C2×C4semidirect
80. #16864389C2×C4semidirect
81. D2152C2×C4semidirect
82. #16864387C2×C4semidirect
84. #16864385C2×C4semidirect
105. SD16×C269C2×C4semidirect
124. D1076C22×C4semidirect
143. #14524130C22×C4semidirect
146. Q8×C269C22×C4semidirect
157. C8×C269C22×C4semidirect
183. Dic269AGL(1,ℤ/8)semidirect
191. C269C4×AGL(1,ℤ/8)semidirect
199. #440D269semidirect
219. C4×Q8C2×D269semidirect
237. #107C2×D269semidirect
241. #103C2×D269semidirect
249. #97C2×D269semidirect
276. SD16C4×D269semidirect
314. Q8C2×C4×D269semidirect
349. C8C2×C4×D269semidirect

Maximal subgroups

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

subgroupindex
C2×#225754802
C4×#168644032
C4×D4×D2692
#317707182
#317707152
#317707032
SD16×Dic2692
#317706902
#317706872
#317706852
#317706462
#317706082
#317706052
#317705572
#440×C2692
C4×AGL(1,ℤ/8)269