Finite Group Databasebeta

← C4×#14579188 #23772209

Subgroups — C4×#14579188 #23772209

Order 10112.

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×#14579188C211yesmaximal, characteristic
2C4×#11929625C211yesmaximal, characteristic, complemented
3C4×D4×D79C211yesmaximal, characteristic, complemented
4#19098674C211yesmaximal, characteristic, complemented
5#19098672C211yesmaximal, characteristic, complemented
6#19098666C211yesmaximal, characteristic, complemented
7#19098664C211yesmaximal, characteristic, complemented
8C4×#11929611C211yesmaximal, characteristic, complemented
9C4×D632C211yesmaximal, characteristic, complemented
10C4×#11929609C211yesmaximal, characteristic, complemented
11#19098602C211yesmaximal, characteristic, complemented
12#19098566C211yesmaximal, characteristic, complemented
13#19098563C211yesmaximal, characteristic, complemented
14C4×#11929607C211yesmaximal, characteristic, complemented
15C4×SD16×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×D4×D79C2211yescharacteristic
18C22×C4×D79—21no—
19#14579188C418yesdirect product factor
20C2×#11929611C2211yescharacteristic
21C2×D632C2211yescharacteristic
22C2×#11929609C2211yescharacteristic
23C2×#11929607C2211yescharacteristic
24C2×#11929607C2211yescharacteristic
25Q8×Dic79C2211yescharacteristic, complemented
26C4×D316—21no—
27C4×D316C2211yescharacteristic
28C4×D316C2211yescharacteristic, complemented
29D4×Dic79C2211yescharacteristic
30#14579123—21no—
31#14579123C2211yescharacteristic
32#14579123C2211yescharacteristic, complemented
33C4×C22⋊D79—21no—
34(C22⋊D79)⋊C4—21no—
35#14579119—21no—
36#14579119C2211yescharacteristic
37C4⋊C4×D79C2211yescharacteristic
38C22⋊C4×D79—21no—
39C42×D79—21no—
40C42×D79C2211yescharacteristic
41#14579095C2211yescharacteristic, complemented
42#14579094C2211yescharacteristic, complemented
43#14579092C2211yescharacteristic, complemented
44#14579085C2211yescharacteristic, complemented
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic, complemented
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49#14579081C2211yescharacteristic, complemented
50#14579071C2211yescharacteristic, complemented
51#14579071C2211yescharacteristic, complemented
52C4×C79⋊C8C2211yescharacteristic, complemented
53C2×SD16×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic, complemented
55C4×D4×C79C2211yescharacteristic
56#106×C79C2211yescharacteristic, complemented
57#103×C79C2211yescharacteristic, complemented
58#102×C79C2211yescharacteristic
59C4×C8×C79C2211yescharacteristic, complemented
60C23×D79—21no—
61#11929625—22no—
62#11929625C2×C414yescomplemented
63C2×D316—21no—
64C2×D316C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67D4×D79—22no—
68D4×D79C2×C414yescomplemented
69C22×Dic79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74C2×C4×D79—21no—
75C2×C4×D79—21no—
76C2×C4×D79—44no—
77C2×C4×D79D411yescharacteristic
78C2×C4×D79D411yescharacteristic
79C2×C4×D79C2311yescharacteristic
80#11929611C2×C414yescomplemented
81D632C2×C414yescomplemented
82#11929609C2×C414yescomplemented
83#11929607—22no—
84#11929607C2×C414yescomplemented
85C2×C79⋊C8C2311yescharacteristic
86C2×C79⋊C8C2311yescharacteristic
87C4⋊Dic79—21no—
88C4⋊Dic79C2311yescharacteristic
89C4⋊Dic79C2311yescharacteristic
90Dic79⋊C4—21no—
91C22⋊Dic79—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97C4×Dic79—21no—
98C4×Dic79—21no—
99C4×Dic79D411yescharacteristic
100C4×Dic79D411yescharacteristic
101C4×Dic79C2311yescharacteristic
102C2×Q8×C79C2311yescharacteristic
103C2×D4×C79C2311yescharacteristic
104C22×C4×C79—21no—
105SD16×C79C2×C414yescomplemented
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79—21no—
109C4⋊C4×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
111C22⋊C4×C79—21no—
112C42×C79—21no—
113C42×C79C2311yescharacteristic
114C23×C79—21no—
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—24no—
118C22×D79—42no—
119C22×D79—42no—
120C22×D79C2×D411yescharacteristic
121Q8×C79—21no—
122Q8×C79C22×C412yescomplemented
123D4×C79—21no—
124D4×C79C22×C412yes—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—42no—
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2411yescharacteristic
132C22⋊D79—24no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—42no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139D316—24no—
140D316—21no—
141D316—21no—
142D316C22×C412yes—
143D316C22×C412yescomplemented
144C4×D79—22no—
145C4×D79—24no—
146C4×D79—41no—
147C4×D79—42no—
148C4×D79—42no—
149C4×D79—42no—
150C4×D79—42no—
151C4×D79—42no—
152C4×D79C22×C412yes—
153C4×D79#4112yes—
154C8×C79—21no—
155C8×C79C22×C412yescomplemented
156C79⋊C8—21no—
157C79⋊C8C22×C412yescomplemented
158C22×C79—22no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79C22×D411yescharacteristic
162C2×D79—21no—
163C2×D79—21no—
164C2×D79—22no—
165C2×D79—22no—
166C2×D79—48no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79C4×D412yes—
172C4×C79—22no—
173C4×C79—21no—
174C4×C79—41no—
175C4×C79—41no—
176C4×C79AGL(1,ℤ/8)12yescomplemented
177C4×C79C23×C411yescharacteristic
178C4×C79C2×#4111yescharacteristic
179Dic79—21no—
180Dic79—21no—
181Dic79—41no—
182Dic79—41no—
183Dic79C4×D412yes—
184C2×C79—42no—
185C2×C79C2×C4×D411yescharacteristic
186C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
187C2×C79#57511yescharacteristic
188D79—22no—
189D79—42no—
190D79—42no—
191C4×AGL(1,ℤ/8)—791nomaximal, Sylow
192C79C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
193C2×AGL(1,ℤ/8)—791no—
194C4×#41—791no—
195C2×C4×D4—791no—
196#442—791no—
197#442—791no—
198#440—791no—
199#440—791no—
200C4×SD16—791no—
201C4×SD16D7911yescharacteristic, complemented
202C4×D8—791no—
203C4×D8—791no—
204#428—791no—
205#418—791no—
206#417—791no—
207C4×M16—791no—
208C2×#41—791no—
209C22×D4—791no—
210C23×C4—1581no—
211AGL(1,ℤ/8)—798no—
212C2×SD16—791no—
213C2×SD16C2×D7911yescharacteristic
214C2×D8—791no—
215C2×D8—791no—
216C2×M16—791no—
217C2×M16—791no—
218C4×Q8—791no—
219C4×Q8C2×D7911yescharacteristic, complemented
220C4×D4—791no—
221C4×D4—791no—
222C4×D4—791no—
223C4×D4—791no—
224C4×D4—791no—
225C4×D4—1581no—
226C4×D4—1581no—
227C4×D4—1581no—
228C4×D4—1581no—
229C4×D4C2×D7911yescharacteristic
230#117—791no—
231#117—1581no—
232C2×C4⋊C4—791no—
233C2×C22⋊C4—1581no—
234C2×C42—791no—
235C2×C42—1581no—
236#107—791no—
237#107—791no—
238#106—791no—
239#106C2×D7911yescharacteristic, complemented
240#103—791no—
241#103C2×D7911yescharacteristic, complemented
242#102—791no—
243#102—791no—
244#102—791no—
245#102—791no—
246#102—791no—
247#102C2×D7911yescharacteristic
248#97—791no—
249#97—791no—
250C4×C8—791no—
251C4×C8C2×D7911yescharacteristic, complemented
252C24—1581no—
253#41—794no—
254#41—1582no—
255C2×Q8C22×D7911yescharacteristic
256C2×D4—794no—
257C2×D4—791no—
258C2×D4—791no—
259C2×D4—1581no—
260C2×D4—1582no—
261C2×D4—1581no—
262C2×D4C22×D7911yescharacteristic
263C22×C4—21no—
264C22×C4—3164no—
265C22×C4—791no—
266C22×C4—791no—
267C22×C4—791no—
268C22×C4—1581no—
269C22×C4—1581no—
270C22×C4—1581no—
271C22×C4—1581no—
272C22×C4—1581no—
273C22×C4—1581no—
274C22×C4—1581no—
275SD16—794no—
276SD16C4×D7914yescomplemented
277D8—794no—
278D8—794no—
279M16—794no—
280M16—1582no—
281C2×C8—791no—
282C2×C8—791no—
283C2×C8C22×D7911yescharacteristic
284C2×C8C22×D7911yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—791no—
287C4⋊C4—791no—
288C4⋊C4—1581no—
289C4⋊C4—1581no—
290C4⋊C4C22×D7911yescharacteristic
291C4⋊C4C22×D7911yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C22⋊C4—1581no—
299C42—21no—
300C42—791no—
301C42—791no—
302C42—791no—
303C42—1581no—
304C42—1581no—
305C42C22×D7911yescharacteristic
306C23—21no—
307C23—3162no—
308C23—3162no—
309C23—791no—
310C23—1584no—
311C23—1581no—
312C23—1581no—
313Q8—21no—
314Q8C2×C4×D7912yescomplemented
315D4—21no—
316D4—792no—
317D4—792no—
318D4—1584no—
319D4—1584no—
320D4—1581no—
321D4—1581no—
322D4C2×C4×D7912yes—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—3161no—
328C2×C4—3162no—
329C2×C4—3162no—
330C2×C4—3162no—
331C2×C4—3162no—
332C2×C4—3162no—
333C2×C4—3162no—
334C2×C4—791no—
335C2×C4—792no—
336C2×C4—792no—
337C2×C4—791no—
338C2×C4—791no—
339C2×C4—1584no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1582no—
343C2×C4D4×D7911yescharacteristic
344C2×C4D4×D7911yescharacteristic
345C2×C4C23×D7911yescharacteristic
346C8—21no—
347C8—792no—
348C8—1581no—
349C8C2×C4×D7912yescomplemented
350C22—22no—
351C22—41no—
352C22—41no—
353C22—3168no—
354C22—3161no—
355C22—3161no—
356C22—3161no—
357C22—3161no—
358C22—792no—
359C22—1582no—
360C22—1582no—
361C22—1581no—
362C22—1581no—
363C22C2×D4×D7911yescharacteristic
364C4—22no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—3161no—
369C4—3161no—
370C4—792no—
371C4—1581no—
372C4—1581no—
373C4#1457918812yesdirect product factor
374C4C22×C4×D7911yescharacteristic
375C4#41×D7911yescharacteristic
376C2—42no—
377C2—3162no—
378C2—3162no—
379C2—1582no—
380C2C4×D4×D7911yescharacteristic
381C2C2×#1457918811yescharacteristic
382C2#1909936011yescharacteristic
subgroupG/H
centerC2×C4D4×D79
commutatorC4×C79C23×C4
FrattiniC2×C4C23×D79
FittingC4×SD16×C79C2
socleC22×C79C22×D4
prime radicalC2×#14579188C2
cosocleC2×C4×C79C24
hypercenterC4×SD16D79
hypocenterC79C4×AGL(1,ℤ/8)
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×#11929625C2semidirect
3. C4×D4×D79C2semidirect
4. #19098674C2semidirect
5. #19098672C2semidirect
6. #19098666C2semidirect
7. #19098664C2semidirect
8. C4×#11929611C2semidirect
9. C4×D632C2semidirect
10. C4×#11929609C2semidirect
11. #19098602C2semidirect
12. #19098566C2semidirect
13. #19098563C2semidirect
14. C4×#11929607C2semidirect
15. C4×SD16×C79C2semidirect
19. #14579188C4direct (N × H)
25. Q8×Dic79C22semidirect
28. C4×D316C22semidirect
32. #14579123C22semidirect
41. #14579095C22semidirect
42. #14579094C22semidirect
43. #14579092C22semidirect
44. #14579085C22semidirect
46. #14579083C22semidirect
49. #14579081C22semidirect
50. #14579071C22semidirect
51. #14579071C22semidirect
52. C4×C79⋊C8C22semidirect
54. C4×Q8×C79C22semidirect
56. #106×C79C22semidirect
57. #103×C79C22semidirect
59. C4×C8×C79C22semidirect
62. #11929625C2×C4semidirect
68. D4×D79C2×C4semidirect
80. #11929611C2×C4semidirect
81. D632C2×C4semidirect
82. #11929609C2×C4semidirect
84. #11929607C2×C4semidirect
105. SD16×C79C2×C4semidirect
122. Q8×C79C22×C4semidirect
143. D316C22×C4semidirect
155. C8×C79C22×C4semidirect
157. C79⋊C8C22×C4semidirect
176. C4×C79AGL(1,ℤ/8)semidirect
192. C79C4×AGL(1,ℤ/8)semidirect
201. C4×SD16D79semidirect
219. C4×Q8C2×D79semidirect
239. #106C2×D79semidirect
241. #103C2×D79semidirect
251. C4×C8C2×D79semidirect
276. SD16C4×D79semidirect
314. Q8C2×C4×D79semidirect
349. C8C2×C4×D79semidirect
373. C4#14579188direct (N × H)