Finite Group Databasebeta

← #464×D61 #21455259

Subgroups — #464×D61 #21455259

Order 7808.

500 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D61C211yesmaximal, characteristic, complemented
2C2×SD16×D61C211yesmaximal, characteristic
3#124×D61C211yesmaximal, characteristic
4C4×Q8×D61C211yesmaximal, characteristic, complemented
5#16839987C211yesmaximal, characteristic, complemented
6#16839986C211yesmaximal, characteristic, complemented
7#16839985C211yesmaximal, characteristic, complemented
8#16839984C211yesmaximal, characteristic, complemented
9#16839983C211yesmaximal, characteristic, complemented
10#16839982C211yesmaximal, characteristic, complemented
11#16839981C211yesmaximal, characteristic, complemented
12C4⋊C8×D61C211yesmaximal, characteristic, complemented
13#103×D61C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic
15C61×#464C211yesmaximal, characteristic, complemented
16C2×Q8×D61C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×D4×D61C2211yescharacteristic
19C2×Dic244C2211yescharacteristic, complemented
20C2×#11758202C2211yescharacteristic, complemented
21C2×#11758202C2211yescharacteristic, complemented
22Q16×D61—24no—
23C2×#11758190C2211yescharacteristic
24C2×#11758200C2211yescharacteristic
25C2×#11758201C2211yescharacteristic
26SD16×D61—24no—
27C2×C8×D61C2211yescharacteristic
28C2×C8×D61C2211yescharacteristic
29#14519766C2211yescharacteristic
30#14519765C2211yescharacteristic
31#14519764C2211yescharacteristic
32#14519763—21no—
33#14519763—21no—
34Q8×Dic61C2211yescharacteristic, complemented
35C4×Dic122—21no—
36C4×Dic122C2211yescharacteristic, complemented
37#14519742—21no—
38#14519742C2211yescharacteristic, complemented
39C4⋊C4×D61—21no—
40C4⋊C4×D61C2211yescharacteristic
41C22⋊C4×D61—21no—
42C22⋊C4×D61—21no—
43C42×D61—21no—
44C42×D61C2211yescharacteristic
45C4⋊#92418C2211yescharacteristic, complemented
46#14519706C2211yescharacteristic, complemented
47#14519706C2211yescharacteristic, complemented
48#14519702C2211yescharacteristic, complemented
49#14519701C2211yescharacteristic, complemented
50#14519700C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic
52#14519698C2211yescharacteristic
53#14519697C2211yescharacteristic
54C2×Q16×C61C2211yescharacteristic, complemented
55C2×SD16×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic
57C4×Q8×C61C2211yescharacteristic, complemented
58C4⋊C8×C61C2211yescharacteristic, complemented
59#103×C61C2211yescharacteristic, complemented
60#102×C61C2211yescharacteristic
61C23×D61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66Q8×D61—22no—
67Q8×D61—22no—
68Q8×D61—22no—
69Q8×D61D414yes—
70D4×D61—22no—
71D4×D61—22no—
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61D411yescharacteristic
77C2×C4×D61D411yescharacteristic
78C2×C4×D61C2311yescharacteristic
79C2×Dic122—21no—
80C2×Dic122—21no—
81C2×Dic122C2311yescharacteristic
82C2×Dic122C2311yescharacteristic
83Q16×C61—22no—
84SD16×C61—22no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61—21no—
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C42×C61—21no—
92C42×C61C2311yescharacteristic
93C22⋊Dic61—21no—
94C22⋊Dic61—21no—
95#11758202—22no—
96#11758202—22no—
97#11758201—22no—
98#11758200—22no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61D411yescharacteristic
112C4×Dic61D411yescharacteristic
113C4×Dic61C2311yescharacteristic
114C2×#92418C2311yescharacteristic
115C2×#92418C2311yescharacteristic
116Dic244—22no—
117#11758190—22no—
118C8×D61—22no—
119C8×D61—22no—
120C23×C61—21no—
121C22×D61—21no—
122C22×D61—42no—
123C22×D61—42no—
124C22×D61—42no—
125C22×D61C2×D411yescharacteristic
126Q8×C61—21no—
127Q8×C61—21no—
128Q8×C61—21no—
129Q8×C61C2×D412yes—
130D4×C61—21no—
131D4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2411yescharacteristic
138C22⋊D61—42no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145D244—21no—
146D244—21no—
147C4×D61—24no—
148C4×D61—22no—
149C4×D61—22no—
150C4×D61—42no—
151C4×D61—42no—
152C4×D61C2×D412yes—
153C4×D61#4112yes—
154Dic122—21no—
155Dic122—24no—
156Dic122—21no—
157Dic122—21no—
158Dic122—42no—
159Dic122C2×D412yes—
160C8×C61—21no—
161C8×C61—21no—
162#92418—21no—
163#92418—21no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61C22×D411yescharacteristic
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—84no—
172C2×D61#12112yes—
173C2×D61#13512yes—
174C2×D61#13712yes—
175C4×C61—22no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61C22×D411yescharacteristic
181C4×C61C2×#4111yescharacteristic
182Dic61—22no—
183Dic61—21no—
184Dic61—21no—
185Dic61—41no—
186Dic61—41no—
187Dic61#12112yes—
188C2×#464—611nomaximal, Sylow
189C2×C61—81no—
190C2×C61C2×#12111yescharacteristic
191C2×C61C2×#13511yescharacteristic
192C2×C61C2×#13711yescharacteristic
193D61—81no—
194D61#46414yesdirect product factor
195C22×Q16—611no—
196C22×SD16—611no—
197C2×#124—611no—
198C2×C4×Q8—611no—
199#464—611no—
200#464—611no—
201#464—611no—
202#464—611no—
203#464—611no—
204#464—611no—
205#464—611no—
206#464D6111yescharacteristic, direct product factor
207C2×C4⋊C8—611no—
208C2×#103—611no—
209C2×#102—611no—
210C61C2×#46411yescharacteristic, complemented, Sylow
211C22×Q8—611no—
212C22×Q8—611no—
213C22×D4—611no—
214C2×Q16—611no—
215C2×Q16—611no—
216C2×Q16—611no—
217C2×Q16—1224no—
218C2×Q16C2×D6111yescharacteristic, complemented
219C2×SD16—611no—
220C2×SD16—611no—
221C2×SD16—611no—
222C2×SD16—1224no—
223C2×SD16C2×D6111yescharacteristic
224C22×C8—611no—
225C22×C8—611no—
226#124—611no—
227#124—611no—
228#124—611no—
229#124—1221no—
230#124—1221no—
231#124C2×D6111yescharacteristic
232C4×Q8—611no—
233C4×Q8—611no—
234C4×Q8—611no—
235C4×Q8—1221no—
236C4×Q8—1221no—
237C4×Q8C2×D6111yescharacteristic, complemented
238C2×C4⋊C4—611no—
239C2×C4⋊C4—1221no—
240C2×C22⋊C4—1221no—
241C2×C22⋊C4—1221no—
242C2×C42—611no—
243C2×C42—1221no—
244C4⋊C8—611no—
245C4⋊C8—611no—
246C4⋊C8—611no—
247C4⋊C8C2×D6111yescharacteristic, complemented
248#103—611no—
249#103—611no—
250#103—611no—
251#103C2×D6111yescharacteristic, complemented
252#102—611no—
253#102—611no—
254#102—611no—
255#102C2×D6111yescharacteristic
256C24—1221no—
257C2×Q8—614no—
258C2×Q8—611no—
259C2×Q8—611no—
260C2×Q8—1221no—
261C2×Q8—1221no—
262C2×Q8—1222no—
263C2×Q8—1222no—
264C2×Q8—1222no—
265C2×Q8C22×D6111yescharacteristic
266C2×Q8C22×D6111yescharacteristic
267C2×D4—611no—
268C2×D4—1222no—
269C2×D4—1222no—
270C2×D4—1221no—
271C2×D4C22×D6111yescharacteristic
272C22×C4—611no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278Q16—22no—
279Q16—1222no—
280Q16—1222no—
281Q16—1222no—
282SD16—22no—
283SD16—1222no—
284SD16—1222no—
285SD16—1222no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—1222no—
289C2×C8—1222no—
290C2×C8C22×D6111yescharacteristic
291C2×C8C22×D6111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—611no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4C22×D6111yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C42—21no—
308C42—611no—
309C42—611no—
310C42—611no—
311C42—1221no—
312C42—1221no—
313C42—1221no—
314C42C22×D6111yescharacteristic
315C23—21no—
316C23—611no—
317C23—1221no—
318C23—2442no—
319C23—2442no—
320C23—2442no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—612no—
325Q8—1224no—
326Q8—1221no—
327Q8—1221no—
328Q8—1221no—
329Q8—2442no—
330Q8D4×D6112yes—
331D4—21no—
332D4—21no—
333D4—1221no—
334D4—1221no—
335D4—2442no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—611no—
340C2×C4—612no—
341C2×C4—612no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—1222no—
345C2×C4—1222no—
346C2×C4—1224no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4D4×D6111yescharacteristic
353C2×C4D4×D6111yescharacteristic
354C2×C4C23×D6111yescharacteristic
355C8—21no—
356C8—21no—
357C8—1221no—
358C8—1221no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—612no—
363C22—612no—
364C22—612no—
365C22—4884no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22C2×D4×D6111yescharacteristic
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—612no—
376C4—1222no—
377C4—1221no—
378C4—1221no—
379C4—2441no—
380C4—2441no—
381C4C2×D4×D6111yescharacteristic
382C4#41×D6111yescharacteristic
383C2—81no—
384C2—614no—
385C2—4881no—
386C2#121×D6111yescharacteristic
387C2#135×D6111yescharacteristic
388C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#464C2
socleC22×C61C22×D4
hypercenter#464D61
hypocenterC61C2×#464
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D61C2semidirect
4. C4×Q8×D61C2semidirect
5. #16839987C2semidirect
6. #16839986C2semidirect
7. #16839985C2semidirect
8. #16839984C2semidirect
9. #16839983C2semidirect
10. #16839982C2semidirect
11. #16839981C2semidirect
12. C4⋊C8×D61C2semidirect
13. #103×D61C2semidirect
15. C61×#464C2semidirect
19. C2×Dic244C22semidirect
20. C2×#11758202C22semidirect
21. C2×#11758202C22semidirect
34. Q8×Dic61C22semidirect
36. C4×Dic122C22semidirect
38. #14519742C22semidirect
45. C4⋊#92418C22semidirect
46. #14519706C22semidirect
47. #14519706C22semidirect
48. #14519702C22semidirect
49. #14519701C22semidirect
50. #14519700C22semidirect
54. C2×Q16×C61C22semidirect
57. C4×Q8×C61C22semidirect
58. C4⋊C8×C61C22semidirect
59. #103×C61C22semidirect
194. D61#464direct (N × H)
206. #464D61direct (N × H)
210. C61C2×#464semidirect
218. C2×Q16C2×D61semidirect
237. C4×Q8C2×D61semidirect
247. C4⋊C8C2×D61semidirect
251. #103C2×D61semidirect