Finite Group Databasebeta

← C4×#14519801 #21454622

Subgroups — C4×#14519801 #21454622

Order 7808.

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×#14519801C211yesmaximal, characteristic
2C4×#11758224C211yesmaximal, characteristic, complemented
3C4×D4×D61C211yesmaximal, characteristic, complemented
4#16839874C211yesmaximal, characteristic, complemented
5#16839871C211yesmaximal, characteristic, complemented
6#16839861C211yesmaximal, characteristic, complemented
7#16839859C211yesmaximal, characteristic, complemented
8C4×#11758190C211yesmaximal, characteristic, complemented
9C4×#11758200C211yesmaximal, characteristic, complemented
10C4×#11758199C211yesmaximal, characteristic, complemented
11#16839803C211yesmaximal, characteristic, complemented
12#16839765C211yesmaximal, characteristic, complemented
13#16839760C211yesmaximal, characteristic, complemented
14C4×#11758189C211yesmaximal, characteristic, complemented
15C4×D8×C61C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C22×C4×D61—21no—
19#14519801C418yesdirect product factor
20C2×#11758190C2211yescharacteristic
21C2×#11758200C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23C2×#11758189C2211yescharacteristic
24C2×#11758189C2211yescharacteristic
25C4×Dic122C2211yescharacteristic, complemented
26#14519742C2211yescharacteristic, complemented
27C4×D244C2211yescharacteristic
28D4×Dic61C2211yescharacteristic
29D4×Dic61C2211yescharacteristic, complemented
30#14519739C2211yescharacteristic
31C4×C22⋊D61—21no—
32C4×C22⋊D61—21no—
33#14519737—21no—
34#14519737—21no—
35#14519735C2211yescharacteristic
36#14519733—21no—
37C4⋊C4×D61C2211yescharacteristic
38C22⋊C4×D61—21no—
39C2×C4×Dic61—21no—
40C42×D61C2211yescharacteristic
41#14519710C2211yescharacteristic, complemented
42#14519709C2211yescharacteristic, complemented
43#14519708C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51#14519687C2211yescharacteristic, complemented
52C4×#92418C2211yescharacteristic, complemented
53C2×D8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic, complemented
56#107×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic, complemented
59C4×C8×C61C2211yescharacteristic, complemented
60C23×D61—21no—
61C2×D4×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70#11758224—22no—
71#11758224C2×C414yescomplemented
72D4×D61—22no—
73D4×D61C2×C414yescomplemented
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—44no—
79C2×C4×D61D411yescharacteristic
80C2×C4×D61D411yescharacteristic
81C2×C4×D61C2311yescharacteristic
82C2×Dic122C2311yescharacteristic
83D8×C61C2×C414yescomplemented
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C22⋊C4×C61—21no—
89C22⋊C4×C61—21no—
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93#11758200C2×C414yescomplemented
94#11758199C2×C414yescomplemented
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61D411yescharacteristic
107C4×Dic61D411yescharacteristic
108C4×Dic61C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111#11758190C2×C414yescomplemented
112#11758189—22no—
113#11758189C2×C414yescomplemented
114C23×C61—21no—
115C23×C61—21no—
116C22×D61—21no—
117C22×D61—24no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61C2×D411yescharacteristic
121D4×C61—21no—
122D4×C61—21no—
123D4×C61C22×C412yes—
124D4×C61C22×C412yescomplemented
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2411yescharacteristic
132C22⋊D61—24no—
133C22⋊D61—24no—
134C2×Dic61—21no—
135C2×Dic61—24no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—42no—
139C2×Dic61—42no—
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143D244—21no—
144D244C22×C412yes—
145C4×D61—22no—
146C4×D61—41no—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61—42no—
150C4×D61C22×C412yes—
151C4×D61#4112yes—
152Dic122—21no—
153Dic122C22×C412yescomplemented
154C8×C61—21no—
155C8×C61C22×C412yescomplemented
156#92418—21no—
157#92418C22×C412yescomplemented
158C22×C61—22no—
159C22×C61—22no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—22no—
168C2×D61—48no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61C4×D412yes—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61AGL(1,ℤ/8)12yescomplemented
176C4×C61C23×C411yescharacteristic
177C4×C61C2×#4111yescharacteristic
178Dic61—22no—
179Dic61—21no—
180Dic61—21no—
181Dic61—41no—
182Dic61—41no—
183Dic61C4×D412yes—
184C4×AGL(1,ℤ/8)—611nomaximal, Sylow
185C2×C61—42no—
186C2×C61—42no—
187C2×C61C2×C4×D411yescharacteristic
188C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
189C2×C61#57511yescharacteristic
190D61—22no—
191D61—42no—
192C2×AGL(1,ℤ/8)—611no—
193C4×#41—611no—
194C2×C4×D4—611no—
195#442—611no—
196#442—611no—
197#440—611no—
198#440—611no—
199C4×SD16—611no—
200C4×SD16—611no—
201C4×D8—611no—
202C4×D8D6111yescharacteristic, complemented
203#428—611no—
204#418—611no—
205#417—611no—
206C4×M16—611no—
207C61C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
208C2×#41—611no—
209C22×D4—611no—
210C23×C4—1221no—
211AGL(1,ℤ/8)—618no—
212C2×SD16—611no—
213C2×SD16—611no—
214C2×D8—611no—
215C2×D8C2×D6111yescharacteristic
216C2×M16—611no—
217C2×M16—611no—
218C4×Q8—611no—
219C4×Q8—611no—
220C4×D4—611no—
221C4×D4—611no—
222C4×D4—611no—
223C4×D4—611no—
224C4×D4—1221no—
225C4×D4—1221no—
226C4×D4—1221no—
227C4×D4—1221no—
228C4×D4C2×D6111yescharacteristic
229C4×D4C2×D6111yescharacteristic, complemented
230#117—611no—
231#117—1221no—
232C2×C4⋊C4—611no—
233C2×C22⋊C4—1221no—
234C2×C42—611no—
235C2×C42—1221no—
236#107—611no—
237#107C2×D6111yescharacteristic, complemented
238#106—611no—
239#106—611no—
240#103—611no—
241#103—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102C2×D6111yescharacteristic
247#102C2×D6111yescharacteristic, complemented
248#97—611no—
249#97—611no—
250C4×C8—611no—
251C4×C8C2×D6111yescharacteristic, complemented
252C24—1221no—
253#41—614no—
254#41—1222no—
255C2×Q8—611no—
256C2×D4—614no—
257C2×D4—611no—
258C2×D4—1222no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4C22×D6111yescharacteristic
262C2×D4C22×D6111yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—611no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—2444no—
275SD16—614no—
276SD16—614no—
277D8—614no—
278D8C4×D6114yescomplemented
279M16—614no—
280M16—1222no—
281C2×C8—611no—
282C2×C8—611no—
283C2×C8C22×D6111yescharacteristic
284C2×C8C22×D6111yescharacteristic
285C4⋊C4—611no—
286C4⋊C4—611no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4C22×D6111yescharacteristic
291C4⋊C4C22×D6111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C42—611no—
300C42—611no—
301C42—611no—
302C42—1221no—
303C42—1221no—
304C42—1221no—
305C42C22×D6111yescharacteristic
306C23—21no—
307C23—21no—
308C23—611no—
309C23—1224no—
310C23—1221no—
311C23—2442no—
312C23—2442no—
313Q8—612no—
314Q8—1221no—
315D4—21no—
316D4—21no—
317D4—612no—
318D4—1224no—
319D4—1224no—
320D4—1221no—
321D4C2×C4×D6112yes—
322D4C2×C4×D6112yescomplemented
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—611no—
328C2×C4—612no—
329C2×C4—612no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—1224no—
333C2×C4—1221no—
334C2×C4—1222no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—2441no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4D4×D6111yescharacteristic
344C2×C4D4×D6111yescharacteristic
345C2×C4C23×D6111yescharacteristic
346C8—21no—
347C8—612no—
348C8—1221no—
349C8C2×C4×D6112yescomplemented
350C22—22no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—612no—
357C22—1221no—
358C22—1221no—
359C22—1222no—
360C22—2448no—
361C22—2441no—
362C22—2441no—
363C22C2×D4×D6111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—612no—
368C4—1222no—
369C4—1221no—
370C4—1221no—
371C4—2441no—
372C4—2441no—
373C4#1451980112yesdirect product factor
374C4C22×C4×D6111yescharacteristic
375C4#41×D6111yescharacteristic
376C2—42no—
377C2—42no—
378C2—1222no—
379C2—2442no—
380C2C4×D4×D6111yescharacteristic
381C2C2×#1451980111yescharacteristic
382C2#1684055911yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC4×D8×C61C2
socleC22×C61C22×D4
hypercenterC4×D8D61
hypocenterC61C4×AGL(1,ℤ/8)
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
2. C4×#11758224C2semidirect
3. C4×D4×D61C2semidirect
4. #16839874C2semidirect
5. #16839871C2semidirect
6. #16839861C2semidirect
7. #16839859C2semidirect
8. C4×#11758190C2semidirect
9. C4×#11758200C2semidirect
10. C4×#11758199C2semidirect
11. #16839803C2semidirect
12. #16839765C2semidirect
13. #16839760C2semidirect
14. C4×#11758189C2semidirect
15. C4×D8×C61C2semidirect
19. #14519801C4direct (N × H)
25. C4×Dic122C22semidirect
26. #14519742C22semidirect
29. D4×Dic61C22semidirect
41. #14519710C22semidirect
42. #14519709C22semidirect
43. #14519708C22semidirect
44. #14519702C22semidirect
45. #14519700C22semidirect
48. #14519698C22semidirect
50. #14519687C22semidirect
51. #14519687C22semidirect
52. C4×#92418C22semidirect
55. C4×D4×C61C22semidirect
56. #107×C61C22semidirect
58. #102×C61C22semidirect
59. C4×C8×C61C22semidirect
71. #11758224C2×C4semidirect
73. D4×D61C2×C4semidirect
83. D8×C61C2×C4semidirect
93. #11758200C2×C4semidirect
94. #11758199C2×C4semidirect
111. #11758190C2×C4semidirect
113. #11758189C2×C4semidirect
124. D4×C61C22×C4semidirect
153. Dic122C22×C4semidirect
155. C8×C61C22×C4semidirect
157. #92418C22×C4semidirect
175. C4×C61AGL(1,ℤ/8)semidirect
202. C4×D8D61semidirect
207. C61C4×AGL(1,ℤ/8)semidirect
229. C4×D4C2×D61semidirect
237. #107C2×D61semidirect
247. #102C2×D61semidirect
251. C4×C8C2×D61semidirect
278. D8C4×D61semidirect
322. D4C2×C4×D61semidirect
349. C8C2×C4×D61semidirect
373. C4#14519801direct (N × H)