Finite Group Databasebeta

← #21454624

Subgroups — #21454624

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×#14519804C211yesmaximal, characteristic
2C4×#11758226C211yesmaximal, characteristic, complemented
3C4×D4×D61C211yesmaximal, characteristic, complemented
4#16839875C211yesmaximal, characteristic, complemented
5#16839872C211yesmaximal, characteristic, complemented
6#16839860C211yesmaximal, characteristic, complemented
7SD16×Dic61C211yesmaximal, characteristic, complemented
8#16839847C211yesmaximal, characteristic, complemented
9#16839844C211yesmaximal, characteristic, complemented
10#16839842C211yesmaximal, characteristic, complemented
11#16839803C211yesmaximal, characteristic, complemented
12#16839765C211yesmaximal, characteristic, complemented
13#16839762C211yesmaximal, characteristic, complemented
14#16839714C211yesmaximal, characteristic, complemented
15C61×#440C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C22×C4×D61—21no—
19#14519804C418yescomplemented
20C2×#11758201C2211yescharacteristic
21C2×D488C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23C2×#11758189C2211yescharacteristic
24C2×#11758189C2211yescharacteristic
25Q8×Dic61C2211yescharacteristic, complemented
26C4×D244—21no—
27C4×D244C2211yescharacteristic
28C4×D244C2211yescharacteristic, complemented
29D4×Dic61C2211yescharacteristic
30#14519739—21no—
31#14519739C2211yescharacteristic
32#14519739C2211yescharacteristic, complemented
33C4×C22⋊D61—21no—
34#14519737—21no—
35#14519735—21no—
36#14519735C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic
38C22⋊C4×D61—21no—
39C42×D61—21no—
40C42×D61C2211yescharacteristic
41#14519710C2211yescharacteristic, complemented
42#14519709C2211yescharacteristic, complemented
43#14519708C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic, complemented
50#14519688C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C8×Dic61C2211yescharacteristic, complemented
53C2×SD16×C61C2211yescharacteristic
54C4×Q8×C61C2211yescharacteristic, complemented
55C4×D4×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic
59#97×C61C2211yescharacteristic, complemented
60C23×D61—21no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C22×Dic61—21no—
66#11758226—22no—
67#11758226C2×C414yescomplemented
68D4×D61—22no—
69D4×D61C2×C414yescomplemented
70C2×D244—21no—
71C2×D244C2311yescharacteristic
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—44no—
80C2×C4×D61D411yescharacteristic
81C2×C4×D61D411yescharacteristic
82C2×C4×D61C2311yescharacteristic
83SD16×C61C2×C414yescomplemented
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C4⋊C4×C61—21no—
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C42×C61—21no—
91C42×C61C2311yescharacteristic
92C22⋊Dic61—21no—
93#11758201C2×C414yescomplemented
94#11758199C2×C414yescomplemented
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104C4×Dic61—21no—
105C4×Dic61—21no—
106C4×Dic61D411yescharacteristic
107C4×Dic61D411yescharacteristic
108C4×Dic61C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111D488C2×C414yescomplemented
112#11758189—22no—
113#11758189C2×C414yescomplemented
114C23×C61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—24no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61C2×D411yescharacteristic
121Q8×C61—21no—
122Q8×C61C22×C412yescomplemented
123D4×C61—21no—
124D4×C61C22×C412yes—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—42no—
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2411yescharacteristic
132C22⋊D61—24no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—42no—
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138C2×Dic61C2×D411yescharacteristic
139D244—24no—
140D244—21no—
141D244—21no—
142D244C22×C412yes—
143D244C22×C412yescomplemented
144C4×D61—24no—
145C4×D61—22no—
146C4×D61—41no—
147C4×D61—42no—
148C4×D61—42no—
149C4×D61—42no—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61C22×C412yes—
153C4×D61#4112yes—
154C8×C61—21no—
155C8×C61C22×C412yescomplemented
156#92418—21no—
157#92418C22×C412yescomplemented
158C22×C61—22no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61C22×D411yescharacteristic
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—22no—
165C2×D61—22no—
166C2×D61—48no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61C4×D412yes—
172C4×C61—22no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61C23×C411yescharacteristic
178C4×C61C2×#4111yescharacteristic
179Dic61—21no—
180Dic61—41no—
181Dic61—41no—
182Dic61C4×D412yes—
183Dic61AGL(1,ℤ/8)12yescomplemented
184C4×AGL(1,ℤ/8)—611nomaximal, Sylow
185C2×C61—42no—
186C2×C61C2×C4×D411yescharacteristic
187C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
188C2×C61#57511yescharacteristic
189D61—22no—
190D61—42no—
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#440D6111yescharacteristic, complemented
199C4×SD16—611no—
200C4×SD16—611no—
201C4×D8—611no—
202C4×D8—611no—
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×SD16C2×D6111yescharacteristic
214C2×D8—611no—
215C2×D8—611no—
216C2×M16—611no—
217C2×M16—611no—
218C4×Q8—611no—
219C4×Q8C2×D6111yescharacteristic, complemented
220C4×D4—611no—
221C4×D4—611no—
222C4×D4—611no—
223C4×D4—611no—
224C4×D4—611no—
225C4×D4—1221no—
226C4×D4—1221no—
227C4×D4—1221no—
228C4×D4—1221no—
229C4×D4C2×D6111yescharacteristic
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#103C2×D6111yescharacteristic, complemented
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102C2×D6111yescharacteristic
248#97—611no—
249#97C2×D6111yescharacteristic, complemented
250C4×C8—611no—
251C4×C8—611no—
252C24—1221no—
253#41—614no—
254#41—1222no—
255C2×Q8C22×D6111yescharacteristic
256C2×D4—614no—
257C2×D4—611no—
258C2×D4—611no—
259C2×D4—1221no—
260C2×D4—1222no—
261C2×D4—1221no—
262C2×D4C22×D6111yescharacteristic
263C22×C4—21no—
264C22×C4—611no—
265C22×C4—611no—
266C22×C4—611no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—2444no—
275SD16—614no—
276SD16C4×D6114yescomplemented
277D8—614no—
278D8—614no—
279M16—614no—
280M16—1222no—
281C2×C8—611no—
282C2×C8—611no—
283C2×C8C22×D6111yescharacteristic
284C2×C8C22×D6111yescharacteristic
285C4⋊C4—21no—
286C4⋊C4—611no—
287C4⋊C4—611no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4C22×D6111yescharacteristic
291C4⋊C4C22×D6111yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C42—21no—
300C42—611no—
301C42—611no—
302C42—611no—
303C42—1221no—
304C42—1221no—
305C42C22×D6111yescharacteristic
306C23—21no—
307C23—611no—
308C23—1224no—
309C23—1221no—
310C23—1221no—
311C23—2442no—
312C23—2442no—
313Q8—21no—
314Q8C2×C4×D6112yescomplemented
315D4—21no—
316D4—612no—
317D4—612no—
318D4—1224no—
319D4—1224no—
320D4—1221no—
321D4—1221no—
322D4C2×C4×D6112yes—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—611no—
328C2×C4—611no—
329C2×C4—612no—
330C2×C4—612no—
331C2×C4—611no—
332C2×C4—1222no—
333C2×C4—1224no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—2441no—
337C2×C4—2442no—
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—41no—
352C22—41no—
353C22—612no—
354C22—1221no—
355C22—1221no—
356C22—1222no—
357C22—1222no—
358C22—2448no—
359C22—2441no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22C2×D4×D6111yescharacteristic
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—612no—
370C4—612no—
371C4—1221no—
372C4—2441no—
373C4—2441no—
374C4C22×C4×D6111yescharacteristic
375C4#41×D6111yescharacteristic
376C2—42no—
377C2—1222no—
378C2—2442no—
379C2—2442no—
380C2C4×D4×D6111yescharacteristic
381C2AGL(1,ℤ/8)×D6111yescharacteristic
382C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC4×C61C23×C4
FrattiniC2×C4C23×D61
FittingC61×#440C2
socleC22×C61C22×D4
hypercenter#440D61
hypocenterC61C4×AGL(1,ℤ/8)
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. C4×#11758226C2semidirect
3. C4×D4×D61C2semidirect
4. #16839875C2semidirect
5. #16839872C2semidirect
6. #16839860C2semidirect
7. SD16×Dic61C2semidirect
8. #16839847C2semidirect
9. #16839844C2semidirect
10. #16839842C2semidirect
11. #16839803C2semidirect
12. #16839765C2semidirect
13. #16839762C2semidirect
14. #16839714C2semidirect
15. C61×#440C2semidirect
19. #14519804C4semidirect
25. Q8×Dic61C22semidirect
28. C4×D244C22semidirect
32. #14519739C22semidirect
41. #14519710C22semidirect
42. #14519709C22semidirect
43. #14519708C22semidirect
44. #14519701C22semidirect
46. #14519699C22semidirect
49. #14519697C22semidirect
50. #14519688C22semidirect
51. C8×Dic61C22semidirect
52. C8×Dic61C22semidirect
54. C4×Q8×C61C22semidirect
56. #107×C61C22semidirect
57. #103×C61C22semidirect
59. #97×C61C22semidirect
67. #11758226C2×C4semidirect
69. D4×D61C2×C4semidirect
83. SD16×C61C2×C4semidirect
93. #11758201C2×C4semidirect
94. #11758199C2×C4semidirect
111. D488C2×C4semidirect
113. #11758189C2×C4semidirect
122. Q8×C61C22×C4semidirect
143. D244C22×C4semidirect
155. C8×C61C22×C4semidirect
157. #92418C22×C4semidirect
183. Dic61AGL(1,ℤ/8)semidirect
198. #440D61semidirect
207. C61C4×AGL(1,ℤ/8)semidirect
219. C4×Q8C2×D61semidirect
237. #107C2×D61semidirect
241. #103C2×D61semidirect
249. #97C2×D61semidirect
276. SD16C4×D61semidirect
314. Q8C2×C4×D61semidirect
349. C8C2×C4×D61semidirect