Finite Group Databasebeta

← #440×D101 #27179907

Subgroups — #440×D101 #27179907

Order 12928.

544 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D101C211yesmaximal, characteristic
2C4×Q8×D101C211yesmaximal, characteristic, complemented
3C4×D4×D101C211yesmaximal, characteristic
4#20265280C211yesmaximal, characteristic, complemented
5#20265279C211yesmaximal, characteristic, complemented
6#20265278C211yesmaximal, characteristic, complemented
7#20265277C211yesmaximal, characteristic, complemented
8#20265276C211yesmaximal, characteristic, complemented
9#20265275C211yesmaximal, characteristic, complemented
10#20265274C211yesmaximal, characteristic, complemented
11#107×D101C211yesmaximal, characteristic, complemented
12#103×D101C211yesmaximal, characteristic, complemented
13#102×D101C211yesmaximal, characteristic
14#97×D101C211yesmaximal, characteristic, complemented
15#440×C101C211yesmaximal, characteristic, complemented
16C2×Q8×D101C2211yescharacteristic
17C2×D4×D101C2211yescharacteristic
18C22×C4×D101—21no—
19C2×#13108063C2211yescharacteristic
20C2×#13108062C2211yescharacteristic
21C2×#13108061C2211yescharacteristic
22SD16×D101C418yescomplemented
23C2×C8×D101C2211yescharacteristic
24C2×C8×D101C2211yescharacteristic
25Q8×Dic101C2211yescharacteristic, complemented
26C4×Dic202—21no—
27C4×Dic202C2211yescharacteristic, complemented
28#15692220—21no—
29#15692220C2211yescharacteristic, complemented
30C4×D404C2211yescharacteristic
31D4×Dic101C2211yescharacteristic
32#15692217C2211yescharacteristic
33C4×C22⋊D101—21no—
34#15692215—21no—
35C4⋊C4×D101—21no—
36C4⋊C4×D101C2211yescharacteristic
37C4⋊C4×D101C2211yescharacteristic
38C22⋊C4×D101—21no—
39C42×D101—21no—
40C42×D101C2211yescharacteristic
41#15692189C2211yescharacteristic, complemented
42#15692188C2211yescharacteristic, complemented
43#15692188C2211yescharacteristic, complemented
44#15692180C2211yescharacteristic, complemented
45#15692179C2211yescharacteristic, complemented
46#15692178C2211yescharacteristic, complemented
47#15692177C2211yescharacteristic
48#15692176C2211yescharacteristic
49#15692175C2211yescharacteristic
50#15692166C2211yescharacteristic, complemented
51#15692165C2211yescharacteristic, complemented
52#15692165C2211yescharacteristic, complemented
53C2×SD16×C101C2211yescharacteristic
54C4×Q8×C101C2211yescharacteristic, complemented
55C4×D4×C101C2211yescharacteristic
56#107×C101C2211yescharacteristic, complemented
57#103×C101C2211yescharacteristic, complemented
58#102×C101C2211yescharacteristic
59#97×C101C2211yescharacteristic, complemented
60C23×D101—21no—
61C2×Dic202—21no—
62C2×Dic202C2311yescharacteristic
63Q8×D101—22no—
64Q8×D101C2×C414yescomplemented
65C2×D404C2311yescharacteristic
66C2×C22⋊D101—21no—
67D4×D101—22no—
68D4×D101C2×C414yes—
69C22×Dic101—21no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101—21no—
74C2×C4×D101—21no—
75C2×C4×D101—44no—
76C2×C4×D101D411yescharacteristic
77C2×C4×D101D411yescharacteristic
78C2×C4×D101C2311yescharacteristic
79#13108063C2×C414yescomplemented
80#13108062C2×C414yescomplemented
81#13108061C2×C414yescomplemented
82C2×#11717579C2311yescharacteristic
83C2×#11717579C2311yescharacteristic
84C8×D101—22no—
85C8×D101C2×C414yescomplemented
86C4⋊Dic101—21no—
87C4⋊Dic101C2311yescharacteristic
88C4⋊Dic101C2311yescharacteristic
89#13108053—21no—
90#13108053—21no—
91#13108053—21no—
92#13108053—21no—
93C22⋊Dic101—21no—
94#13108051—21no—
95#13108051—21no—
96C4×Dic101—21no—
97C4×Dic101—21no—
98C4×Dic101—21no—
99C4×Dic101D411yescharacteristic
100C4×Dic101D411yescharacteristic
101C4×Dic101C2311yescharacteristic
102C2×Q8×C101C2311yescharacteristic
103C2×D4×C101C2311yescharacteristic
104C22×C4×C101—21no—
105SD16×C101C2×C414yescomplemented
106C2×C8×C101C2311yescharacteristic
107C2×C8×C101C2311yescharacteristic
108C4⋊C4×C101—21no—
109C4⋊C4×C101C2311yescharacteristic
110C4⋊C4×C101C2311yescharacteristic
111C22⋊C4×C101—21no—
112C42×C101—21no—
113C42×C101C2311yescharacteristic
114C23×C101—21no—
115C22×D101—21no—
116C22×D101—24no—
117C22×D101—42no—
118C22×D101—42no—
119C22×D101C2×D411yescharacteristic
120Q8×C101—21no—
121Q8×C101C22×C412yescomplemented
122D4×C101—21no—
123D4×C101C22×C412yes—
124C2×C4×C101—21no—
125C2×C4×C101—21no—
126C2×C4×C101—21no—
127C2×C4×C101—42no—
128C2×C4×C101C2×D411yescharacteristic
129C2×C4×C101C2×D411yescharacteristic
130C2×C4×C101C2411yescharacteristic
131C22⋊D101—24no—
132C2×Dic101—21no—
133C2×Dic101—21no—
134C2×Dic101—21no—
135C2×Dic101—42no—
136C2×Dic101C2×D411yescharacteristic
137C2×Dic101C2×D411yescharacteristic
138C2×Dic101C2×D411yescharacteristic
139D404—21no—
140D404C22×C412yes—
141C4×D101—24no—
142C4×D101—22no—
143C4×D101—22no—
144C4×D101—42no—
145C4×D101—42no—
146C4×D101—42no—
147C4×D101—42no—
148C4×D101C22×C412yes—
149C4×D101#4112yes—
150Dic202—21no—
151Dic202—24no—
152Dic202C22×C412yescomplemented
153C8×C101—21no—
154C8×C101C22×C412yescomplemented
155#11717579—21no—
156#11717579C22×C412yescomplemented
157C22×C101—22no—
158C22×C101—41no—
159C22×C101—41no—
160C22×C101C22×D411yescharacteristic
161C2×D101—22no—
162C2×D101—41no—
163C2×D101—41no—
164C2×D101—48no—
165C2×D101C4×D412yes—
166C2×D101AGL(1,ℤ/8)12yes—
167C2×D101#13712yes—
168C4×C101—22no—
169C4×C101—21no—
170C4×C101—21no—
171C4×C101—41no—
172C4×C101—41no—
173C4×C101C23×C411yescharacteristic
174C4×C101C2×#4111yescharacteristic
175Dic101—22no—
176Dic101—21no—
177Dic101—21no—
178Dic101—41no—
179Dic101—41no—
180Dic101C4×D412yes—
181C2×C101—42no—
182C2×C101C2×C4×D411yescharacteristic
183C2×C101C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C101C2×#13711yescharacteristic
185D101—42no—
186D101#44014yesdirect product factor
187C2×#440—1011nomaximal, Sylow
188C101C2×#44011yescharacteristic, complemented, Sylow
189C22×SD16—1011no—
190C2×C4×Q8—1011no—
191C2×C4×D4—1011no—
192#440—1011no—
193#440—1011no—
194#440—1011no—
195#440—1011no—
196#440—1011no—
197#440—1011no—
198#440—1011no—
199#440D10111yescharacteristic, direct product factor
200C2×#107—1011no—
201C2×#103—1011no—
202C2×#102—1011no—
203C2×#97—1011no—
204C22×Q8—1011no—
205C22×D4—1011no—
206C23×C4—2021no—
207C2×SD16—1011no—
208C2×SD16—1011no—
209C2×SD16—1018no—
210C2×SD16—1011no—
211C2×SD16C2×D10111yescharacteristic
212C22×C8—1011no—
213C22×C8—1011no—
214C4×Q8—1011no—
215C4×Q8—1011no—
216C4×Q8—1011no—
217C4×Q8—2021no—
218C4×Q8—2021no—
219C4×Q8C2×D10111yescharacteristic, complemented
220C4×D4—1011no—
221C4×D4—1011no—
222C4×D4—1011no—
223C4×D4—2021no—
224C4×D4—2021no—
225C4×D4C2×D10111yescharacteristic
226C2×C4⋊C4—1011no—
227C2×C4⋊C4—1011no—
228C2×C4⋊C4—2021no—
229C2×C22⋊C4—2021no—
230C2×C42—1011no—
231C2×C42—2021no—
232#107—1011no—
233#107—1011no—
234#107—1011no—
235#107C2×D10111yescharacteristic, complemented
236#103—1011no—
237#103—1011no—
238#103—1011no—
239#103C2×D10111yescharacteristic, complemented
240#102—1011no—
241#102—1011no—
242#102—1011no—
243#102C2×D10111yescharacteristic
244#97—1011no—
245#97—1011no—
246#97—1011no—
247#97C2×D10111yescharacteristic, complemented
248C24—2021no—
249C2×Q8—1014no—
250C2×Q8—1011no—
251C2×Q8—2021no—
252C2×Q8—2022no—
253C2×Q8C22×D10111yescharacteristic
254C2×D4—1014no—
255C2×D4—1011no—
256C2×D4—2022no—
257C2×D4—2021no—
258C2×D4C22×D10111yescharacteristic
259C22×C4—21no—
260C22×C4—1011no—
261C22×C4—1011no—
262C22×C4—1011no—
263C22×C4—4044no—
264C22×C4—2021no—
265C22×C4—2021no—
266C22×C4—2021no—
267C22×C4—2021no—
268C22×C4—2021no—
269C22×C4—2021no—
270SD16—1014no—
271SD16—1014no—
272SD16—1014no—
273SD16C4×D10114yescomplemented
274C2×C8—1011no—
275C2×C8—1014no—
276C2×C8—1011no—
277C2×C8—2022no—
278C2×C8C22×D10111yescharacteristic
279C2×C8C22×D10111yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—1011no—
282C4⋊C4—1011no—
283C4⋊C4—2021no—
284C4⋊C4—2021no—
285C4⋊C4—2021no—
286C4⋊C4—2021no—
287C4⋊C4—2021no—
288C4⋊C4C22×D10111yescharacteristic
289C4⋊C4C22×D10111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2021no—
292C22⋊C4—2021no—
293C22⋊C4—2021no—
294C42—21no—
295C42—1011no—
296C42—1011no—
297C42—1011no—
298C42—2021no—
299C42—2021no—
300C42—2021no—
301C42C22×D10111yescharacteristic
302C23—21no—
303C23—1011no—
304C23—4042no—
305C23—4042no—
306C23—2024no—
307C23—2021no—
308Q8—21no—
309Q8—1012no—
310Q8—2024no—
311Q8—2021no—
312Q8C2×C4×D10112yescomplemented
313D4—21no—
314D4—1012no—
315D4—2024no—
316D4—2021no—
317D4C2×C4×D10112yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—1011no—
323C2×C4—1012no—
324C2×C4—1012no—
325C2×C4—1011no—
326C2×C4—1011no—
327C2×C4—4042no—
328C2×C4—4042no—
329C2×C4—4042no—
330C2×C4—4042no—
331C2×C4—4042no—
332C2×C4—2022no—
333C2×C4—2022no—
334C2×C4—2024no—
335C2×C4—2021no—
336C2×C4—2021no—
337C2×C4—2021no—
338C2×C4D4×D10111yescharacteristic
339C2×C4D4×D10111yescharacteristic
340C2×C4C23×D10111yescharacteristic
341C8—21no—
342C8—1012no—
343C8—2021no—
344C8C2×C4×D10112yescomplemented
345C22—22no—
346C22—41no—
347C22—41no—
348C22—1012no—
349C22—1012no—
350C22—1012no—
351C22—4048no—
352C22—4041no—
353C22—4041no—
354C22—2022no—
355C22C2×D4×D10111yescharacteristic
356C4—22no—
357C4—21no—
358C4—21no—
359C4—41no—
360C4—41no—
361C4—1012no—
362C4—4041no—
363C4—4041no—
364C4—2022no—
365C4—2021no—
366C4—2021no—
367C4C22×C4×D10111yescharacteristic
368C4#41×D10111yescharacteristic
369C2—42no—
370C2—1014no—
371C2—4042no—
372C2C4×D4×D10111yescharacteristic
373C2AGL(1,ℤ/8)×D10111yescharacteristic
374C2#137×D10111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutatorC4×C101C23×C4
FrattiniC2×C4C23×D101
Fitting#440×C101C2
socleC22×C101C22×D4
prime radicalC2×D4×D101C22
cosocleC2×C4×C101C24
hypercenter#440D101
hypocenterC101C2×#440
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D101C2semidirect
4. #20265280C2semidirect
5. #20265279C2semidirect
6. #20265278C2semidirect
7. #20265277C2semidirect
8. #20265276C2semidirect
9. #20265275C2semidirect
10. #20265274C2semidirect
11. #107×D101C2semidirect
12. #103×D101C2semidirect
14. #97×D101C2semidirect
15. #440×C101C2semidirect
22. SD16×D101C4semidirect
25. Q8×Dic101C22semidirect
27. C4×Dic202C22semidirect
29. #15692220C22semidirect
41. #15692189C22semidirect
42. #15692188C22semidirect
43. #15692188C22semidirect
44. #15692180C22semidirect
45. #15692179C22semidirect
46. #15692178C22semidirect
50. #15692166C22semidirect
51. #15692165C22semidirect
52. #15692165C22semidirect
54. C4×Q8×C101C22semidirect
56. #107×C101C22semidirect
57. #103×C101C22semidirect
59. #97×C101C22semidirect
64. Q8×D101C2×C4semidirect
79. #13108063C2×C4semidirect
80. #13108062C2×C4semidirect
81. #13108061C2×C4semidirect
85. C8×D101C2×C4semidirect
105. SD16×C101C2×C4semidirect
121. Q8×C101C22×C4semidirect
152. Dic202C22×C4semidirect
154. C8×C101C22×C4semidirect
156. #11717579C22×C4semidirect
186. D101#440direct (N × H)
188. C101C2×#440semidirect
199. #440D101direct (N × H)
219. C4×Q8C2×D101semidirect
235. #107C2×D101semidirect
239. #103C2×D101semidirect
247. #97C2×D101semidirect
273. SD16C4×D101semidirect
312. Q8C2×C4×D101semidirect
344. C8C2×C4×D101semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×D1012
C4×Q8×D1012
C4×D4×D1012
#202652802
#202652792
#202652782
#202652772
#202652762
#202652752
#202652742
#107×D1012
#103×D1012
#102×D1012
#97×D1012
#440×C1012
C2×#440101