Finite Group Databasebeta

← #468×D61 #21455403

Subgroups — #468×D61 #21455403

Order 7808.

544 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×D61C211yesmaximal, characteristic, complemented
2C2×M16×D61C211yesmaximal, characteristic, complemented
3C22⋊Q8×D61C211yesmaximal, characteristic, complemented
4#121×D61C211yesmaximal, characteristic
5#16840011C211yesmaximal, characteristic, complemented
6#16840010C211yesmaximal, characteristic, complemented
7#16840009C211yesmaximal, characteristic, complemented
8#16840008C211yesmaximal, characteristic, complemented
9#16840007C211yesmaximal, characteristic, complemented
10#16840006C211yesmaximal, characteristic, complemented
11#16840005C211yesmaximal, characteristic, complemented
12#107×D61C211yesmaximal, characteristic, complemented
13#103×D61C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×D4×D61—21no—
18C2×D4×D61C2211yescharacteristic
19C22×C4×D61C2211yescharacteristic
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758200C2211yescharacteristic, complemented
22C2×#11758201C2211yescharacteristic, complemented
23SD16×D61—24no—
24C2×#11758194C2211yescharacteristic, complemented
25C2×#11758189C2211yescharacteristic, complemented
26C2×#11758189C2211yescharacteristic, complemented
27M16×D61—24no—
28C2×C8×D61C2211yescharacteristic
29C2×C8×D61C2211yescharacteristic
30#14519757C2211yescharacteristic, complemented
31#14519756C2211yescharacteristic, complemented
32#14519755—21no—
33#14519754—21no—
34#14519753C2211yescharacteristic, complemented
35#14519752C2211yescharacteristic
36#14519751C2211yescharacteristic
37#14519750—21no—
38#14519749—21no—
39#14519748C2211yescharacteristic
40C4⋊C4×D61—21no—
41C4⋊C4×D61C2211yescharacteristic
42C4⋊C4×D61C2211yescharacteristic
43C22⋊C4×D61—21no—
44C22⋊C4×D61—21no—
45#14519711C2211yescharacteristic, complemented
46#14519710C2211yescharacteristic, complemented
47#14519710C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519701C2211yescharacteristic, complemented
50#14519700C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic, complemented
52#14519698C2211yescharacteristic, complemented
53#14519697C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×M16×C61C2211yescharacteristic, complemented
56C22⋊Q8×C61C2211yescharacteristic, complemented
57#121×C61C2211yescharacteristic
58#107×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic, complemented
61C23×D61—21no—
62C23×D61D411yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C22×Dic61D411yescharacteristic
71Q8×D61—22no—
72Q8×D61—22no—
73D4×D61—22no—
74D4×D61—22no—
75D4×D61—44no—
76C2×D244—21no—
77C2×D244C2311yescharacteristic
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61D411yescharacteristic
84C2×C4×D61D411yescharacteristic
85C2×C4×D61C2311yescharacteristic
86C2×C4×D61C2311yescharacteristic
87C2×Dic122—21no—
88C2×Dic122C2311yescharacteristic
89SD16×C61—22no—
90M16×C61—22no—
91C2×C8×C61C2311yescharacteristic
92C2×C8×C61C2311yescharacteristic
93C4⋊C4×C61—21no—
94C4⋊C4×C61C2311yescharacteristic
95C4⋊C4×C61C2311yescharacteristic
96C22⋊C4×C61—21no—
97C22⋊C4×C61—21no—
98C22⋊Dic61—21no—
99C22⋊Dic61—21no—
100#11758201—22no—
101#11758200—22no—
102#11758198—21no—
103#11758198—21no—
104#11758198—21no—
105#11758198—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61C2311yescharacteristic
108C4⋊Dic61C2311yescharacteristic
109#11758196—21no—
110#11758196—21no—
111#11758196—21no—
112#11758196—21no—
113#11758194—22no—
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116#11758190—22no—
117#11758189—22no—
118#11758189—22no—
119C8×D61—22no—
120C8×D61D414yescomplemented
121C23×C61—21no—
122C23×C61C2×D411yescharacteristic
123C22×D61—22no—
124C22×D61—22no—
125C22×D61—22no—
126C22×D61—21no—
127C22×D61—42no—
128C22×D61—42no—
129C22×D61—42no—
130C22×D61C2×D411yescharacteristic
131C22×D61C2×D411yescharacteristic
132Q8×C61—21no—
133Q8×C61—21no—
134D4×C61—21no—
135D4×C61—21no—
136D4×C61—42no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61C2×D411yescharacteristic
143C2×C4×C61C2411yescharacteristic
144C22⋊D61—42no—
145C22⋊D61—42no—
146C22⋊D61—42no—
147C2×Dic61—22no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61C2×D411yescharacteristic
152C2×Dic61C2×D411yescharacteristic
153D244—21no—
154D244—21no—
155D244—42no—
156C4×D61—22no—
157C4×D61—21no—
158C4×D61—21no—
159C4×D61—22no—
160C4×D61—42no—
161C4×D61—42no—
162C4×D61—42no—
163C4×D61C2×D412yes—
164C4×D61#4112yes—
165Dic122—21no—
166Dic122—21no—
167Dic122—42no—
168C8×C61—21no—
169C8×C61C2×D412yescomplemented
170#92418—21no—
171#92418C2×D412yescomplemented
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61C22×D411yescharacteristic
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—44no—
183C2×D61—41no—
184C2×D61—41no—
185C2×D61—41no—
186C2×D61—84no—
187C2×D61#12112yes—
188C2×D61AGL(1,ℤ/8)12yes—
189C2×D61#13712yes—
190C4×C61—21no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61—41no—
194C4×C61C22×D411yescharacteristic
195C4×C61C2×#4111yescharacteristic
196Dic61—21no—
197Dic61—41no—
198Dic61—41no—
199Dic61—41no—
200Dic61#12112yes—
201C2×#468—611nomaximal, Sylow
202C2×C61—41no—
203C2×C61—81no—
204C2×C61C2×#12111yescharacteristic
205C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
206C2×C61C2×#13711yescharacteristic
207D61—41no—
208D61—81no—
209D61#46814yesdirect product factor
210C22×SD16—611no—
211C22×M16—611no—
212C2×C22⋊Q8—611no—
213C2×#121—611no—
214#468—611no—
215#468—611no—
216#468—611no—
217#468—611no—
218#468—611no—
219#468—611no—
220#468—611no—
221#468D6111yescharacteristic, direct product factor
222C2×#107—611no—
223C2×#103—611no—
224C2×#102—611no—
225C61C2×#46811yescharacteristic, complemented, Sylow
226C22×Q8—611no—
227C22×D4—611no—
228C22×D4—1221no—
229C23×C4—611no—
230C2×SD16—611no—
231C2×SD16—611no—
232C2×SD16—611no—
233C2×SD16—1224no—
234C2×SD16C2×D6111yescharacteristic, complemented
235C2×M16—611no—
236C2×M16—611no—
237C2×M16—611no—
238C2×M16—1224no—
239C2×M16C2×D6111yescharacteristic, complemented
240C22×C8—611no—
241C22×C8—611no—
242C22⋊Q8—611no—
243C22⋊Q8—611no—
244C22⋊Q8—611no—
245C22⋊Q8—1221no—
246C22⋊Q8—1221no—
247C22⋊Q8C2×D6111yescharacteristic, complemented
248#121—611no—
249#121—611no—
250#121—611no—
251#121—1221no—
252#121—1221no—
253#121C2×D6111yescharacteristic
254C2×C4⋊C4—611no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—1221no—
257C2×C22⋊C4—1221no—
258C2×C22⋊C4—1221no—
259#107—611no—
260#107—611no—
261#107—611no—
262#107C2×D6111yescharacteristic, complemented
263#103—611no—
264#103—611no—
265#103—611no—
266#103C2×D6111yescharacteristic, complemented
267#102—611no—
268#102—611no—
269#102—611no—
270#102C2×D6111yescharacteristic, complemented
271C24—611no—
272C24—1221no—
273C2×Q8—611no—
274C2×Q8—1221no—
275C2×Q8—1222no—
276C2×Q8—1222no—
277C2×Q8C22×D6111yescharacteristic
278C2×D4—21no—
279C2×D4—611no—
280C2×D4—1221no—
281C2×D4—1222no—
282C2×D4—1222no—
283C2×D4—1221no—
284C2×D4—1221no—
285C2×D4—1221no—
286C2×D4—2444no—
287C2×D4C22×D6111yescharacteristic
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—1222no—
294C22×C4—1222no—
295C22×C4—1221no—
296C22×C4—1221no—
297C22×C4—1221no—
298C22×C4C22×D6111yescharacteristic
299SD16—22no—
300SD16—1222no—
301SD16—1222no—
302SD16—1222no—
303M16—22no—
304M16—1222no—
305M16—1222no—
306M16—1222no—
307C2×C8—611no—
308C2×C8—614no—
309C2×C8—611no—
310C2×C8—1222no—
311C2×C8C22×D6111yescharacteristic
312C2×C8C22×D6111yescharacteristic
313C4⋊C4—21no—
314C4⋊C4—611no—
315C4⋊C4—611no—
316C4⋊C4—1221no—
317C4⋊C4—1221no—
318C4⋊C4—1221no—
319C4⋊C4—1221no—
320C4⋊C4—1221no—
321C4⋊C4C22×D6111yescharacteristic
322C4⋊C4C22×D6111yescharacteristic
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—1221no—
326C22⋊C4—1221no—
327C22⋊C4—1221no—
328C22⋊C4—1221no—
329C22⋊C4—1221no—
330C22⋊C4—1221no—
331C23—21no—
332C23—611no—
333C23—611no—
334C23—1222no—
335C23—1222no—
336C23—1222no—
337C23—1221no—
338C23—2442no—
339C23—2442no—
340C23—2442no—
341C23D4×D6111yescharacteristic
342Q8—21no—
343Q8—21no—
344Q8—1221no—
345Q8—1221no—
346Q8—2442no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—1221no—
351D4—1221no—
352D4—2442no—
353D4—2442no—
354D4—2442no—
355D4—2442no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—611no—
362C2×C4—612no—
363C2×C4—612no—
364C2×C4—611no—
365C2×C4—1222no—
366C2×C4—1222no—
367C2×C4—1222no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—1221no—
373C2×C4—2442no—
374C2×C4—2442no—
375C2×C4—2442no—
376C2×C4D4×D6111yescharacteristic
377C2×C4C23×D6111yescharacteristic
378C8—21no—
379C8—612no—
380C8—1221no—
381C8D4×D6112yescomplemented
382C22—21no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—612no—
389C22—612no—
390C22—612no—
391C22—1221no—
392C22—1221no—
393C22—1221no—
394C22—4884no—
395C22—2444no—
396C22—2441no—
397C22—2441no—
398C22—2441no—
399C22C2×D4×D6111yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—612no—
405C4—1221no—
406C4—2441no—
407C4—2441no—
408C4—2441no—
409C4C2×D4×D6111yescharacteristic
410C4#41×D6111yescharacteristic
411C2—41no—
412C2—81no—
413C2—614no—
414C2—4881no—
415C2—2441no—
416C2#121×D6111yescharacteristic
417C2AGL(1,ℤ/8)×D6111yescharacteristic
418C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61C2×#468
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×SD16×D61C2semidirect
2. C2×M16×D61C2semidirect
3. C22⋊Q8×D61C2semidirect
5. #16840011C2semidirect
6. #16840010C2semidirect
7. #16840009C2semidirect
8. #16840008C2semidirect
9. #16840007C2semidirect
10. #16840006C2semidirect
11. #16840005C2semidirect
12. #107×D61C2semidirect
13. #103×D61C2semidirect
14. #102×D61C2semidirect
15. C61×#468C2semidirect
20. C2×#11758190C22semidirect
21. C2×#11758200C22semidirect
22. C2×#11758201C22semidirect
24. C2×#11758194C22semidirect
25. C2×#11758189C22semidirect
26. C2×#11758189C22semidirect
30. #14519757C22semidirect
31. #14519756C22semidirect
34. #14519753C22semidirect
45. #14519711C22semidirect
46. #14519710C22semidirect
47. #14519710C22semidirect
48. #14519702C22semidirect
49. #14519701C22semidirect
50. #14519700C22semidirect
51. #14519699C22semidirect
52. #14519698C22semidirect
53. #14519697C22semidirect
54. C2×SD16×C61C22semidirect
55. C2×M16×C61C22semidirect
56. C22⋊Q8×C61C22semidirect
58. #107×C61C22semidirect
59. #103×C61C22semidirect
60. #102×C61C22semidirect
120. C8×D61D4semidirect
169. C8×C61C2×D4semidirect
171. #92418C2×D4semidirect
209. D61#468direct (N × H)
221. #468D61direct (N × H)
225. C61C2×#468semidirect
234. C2×SD16C2×D61semidirect
239. C2×M16C2×D61semidirect
247. C22⋊Q8C2×D61semidirect
262. #107C2×D61semidirect
266. #103C2×D61semidirect
270. #102C2×D61semidirect
381. C8D4×D61semidirect