Finite Group Databasebeta

← #464×D101 #27180572

Subgroups — #464×D101 #27180572

Order 12928.

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×D101C211yesmaximal, characteristic, complemented
2C2×SD16×D101C211yesmaximal, characteristic
3#124×D101C211yesmaximal, characteristic
4C4×Q8×D101C211yesmaximal, characteristic, complemented
5#20265402C211yesmaximal, characteristic, complemented
6#20265401C211yesmaximal, characteristic, complemented
7#20265400C211yesmaximal, characteristic, complemented
8#20265399C211yesmaximal, characteristic, complemented
9#20265398C211yesmaximal, characteristic, complemented
10#20265397C211yesmaximal, characteristic, complemented
11#20265396C211yesmaximal, characteristic, complemented
12C4⋊C8×D101C211yesmaximal, characteristic, complemented
13#103×D101C211yesmaximal, characteristic, complemented
14#102×D101C211yesmaximal, characteristic
15#464×C101C211yesmaximal, characteristic, complemented
16C2×Q8×D101C2211yescharacteristic
17C2×Q8×D101C2211yescharacteristic
18C2×D4×D101C2211yescharacteristic
19C2×Dic404C2211yescharacteristic, complemented
20C2×#13108064C2211yescharacteristic, complemented
21C2×#13108064C2211yescharacteristic, complemented
22Q16×D101—24no—
23C2×#13108063C2211yescharacteristic
24C2×#13108062C2211yescharacteristic
25C2×#13108061C2211yescharacteristic
26SD16×D101—24no—
27C2×C8×D101C2211yescharacteristic
28C2×C8×D101C2211yescharacteristic
29#15692244C2211yescharacteristic
30#15692243C2211yescharacteristic
31#15692242C2211yescharacteristic
32#15692241—21no—
33#15692241—21no—
34Q8×Dic101C2211yescharacteristic, complemented
35C4×Dic202—21no—
36C4×Dic202C2211yescharacteristic, complemented
37#15692220—21no—
38#15692220C2211yescharacteristic, complemented
39C4⋊C4×D101—21no—
40C4⋊C4×D101C2211yescharacteristic
41C22⋊C4×D101—21no—
42C22⋊C4×D101—21no—
43C42×D101—21no—
44C42×D101C2211yescharacteristic
45C4⋊#11717579C2211yescharacteristic, complemented
46#15692184C2211yescharacteristic, complemented
47#15692184C2211yescharacteristic, complemented
48#15692180C2211yescharacteristic, complemented
49#15692179C2211yescharacteristic, complemented
50#15692178C2211yescharacteristic, complemented
51#15692177C2211yescharacteristic
52#15692176C2211yescharacteristic
53#15692175C2211yescharacteristic
54C2×Q16×C101C2211yescharacteristic, complemented
55C2×SD16×C101C2211yescharacteristic
56#124×C101C2211yescharacteristic
57C4×Q8×C101C2211yescharacteristic, complemented
58C4⋊C8×C101C2211yescharacteristic, complemented
59#103×C101C2211yescharacteristic, complemented
60#102×C101C2211yescharacteristic
61C23×D101—21no—
62C2×Dic202—21no—
63C2×Dic202—21no—
64C2×Dic202C2311yescharacteristic
65C2×Dic202C2311yescharacteristic
66Q8×D101—22no—
67Q8×D101—22no—
68Q8×D101—22no—
69Q8×D101D414yes—
70C2×D404C2311yescharacteristic
71C2×C22⋊D101—21no—
72D4×D101—22no—
73D4×D101—22no—
74C2×C4×D101—21no—
75C2×C4×D101—21no—
76C2×C4×D101—21no—
77C2×C4×D101D411yescharacteristic
78C2×C4×D101D411yescharacteristic
79C2×C4×D101C2311yescharacteristic
80Dic404—22no—
81#13108064—22no—
82#13108064—22no—
83#13108063—22no—
84#13108062—22no—
85#13108061—22no—
86C2×#11717579C2311yescharacteristic
87C2×#11717579C2311yescharacteristic
88C8×D101—22no—
89C8×D101—22no—
90C4⋊Dic101—21no—
91C4⋊Dic101C2311yescharacteristic
92#13108053—21no—
93#13108053—21no—
94#13108053—21no—
95C22⋊Dic101—21no—
96C22⋊Dic101—21no—
97#13108051—21no—
98#13108051—21no—
99#13108051—21no—
100#13108051—21no—
101C4×Dic101—21no—
102C4×Dic101—21no—
103C4×Dic101—21no—
104C4×Dic101D411yescharacteristic
105C4×Dic101D411yescharacteristic
106C4×Dic101C2311yescharacteristic
107C2×Q8×C101C2311yescharacteristic
108C2×Q8×C101C2311yescharacteristic
109C2×D4×C101C2311yescharacteristic
110Q16×C101—22no—
111SD16×C101—22no—
112C2×C8×C101C2311yescharacteristic
113C2×C8×C101C2311yescharacteristic
114C4⋊C4×C101—21no—
115C4⋊C4×C101C2311yescharacteristic
116C22⋊C4×C101—21no—
117C22⋊C4×C101—21no—
118C42×C101—21no—
119C42×C101C2311yescharacteristic
120C23×C101—21no—
121C22×D101—21no—
122C22×D101—42no—
123C22×D101—42no—
124C22×D101—42no—
125C22×D101C2×D411yescharacteristic
126Q8×C101—21no—
127Q8×C101—21no—
128Q8×C101—21no—
129Q8×C101C2×D412yes—
130D4×C101—21no—
131D4×C101—21no—
132C2×C4×C101—21no—
133C2×C4×C101—21no—
134C2×C4×C101—21no—
135C2×C4×C101C2×D411yescharacteristic
136C2×C4×C101C2×D411yescharacteristic
137C2×C4×C101C2411yescharacteristic
138C22⋊D101—42no—
139C2×Dic101—21no—
140C2×Dic101—21no—
141C2×Dic101—21no—
142C2×Dic101C2×D411yescharacteristic
143C2×Dic101C2×D411yescharacteristic
144C2×Dic101C2×D411yescharacteristic
145D404—21no—
146D404—21no—
147C4×D101—24no—
148C4×D101—22no—
149C4×D101—22no—
150C4×D101—42no—
151C4×D101—42no—
152C4×D101C2×D412yes—
153C4×D101#4112yes—
154Dic202—21no—
155Dic202—24no—
156Dic202—21no—
157Dic202—21no—
158Dic202—42no—
159Dic202C2×D412yes—
160C8×C101—21no—
161C8×C101—21no—
162#11717579—21no—
163#11717579—21no—
164C22×C101—41no—
165C22×C101—41no—
166C22×C101—41no—
167C22×C101C22×D411yescharacteristic
168C2×D101—41no—
169C2×D101—41no—
170C2×D101—41no—
171C2×D101—84no—
172C2×D101#12112yes—
173C2×D101#13512yes—
174C2×D101#13712yes—
175C4×C101—22no—
176C4×C101—21no—
177C4×C101—21no—
178C4×C101—41no—
179C4×C101—41no—
180C4×C101C22×D411yescharacteristic
181C4×C101C2×#4111yescharacteristic
182Dic101—22no—
183Dic101—21no—
184Dic101—21no—
185Dic101—41no—
186Dic101—41no—
187Dic101#12112yes—
188C2×C101—81no—
189C2×C101C2×#12111yescharacteristic
190C2×C101C2×#13511yescharacteristic
191C2×C101C2×#13711yescharacteristic
192D101—81no—
193D101#46414yesdirect product factor
194C2×#464—1011nomaximal, Sylow
195C101C2×#46411yescharacteristic, complemented, Sylow
196C22×Q16—1011no—
197C22×SD16—1011no—
198C2×#124—1011no—
199C2×C4×Q8—1011no—
200#464—1011no—
201#464—1011no—
202#464—1011no—
203#464—1011no—
204#464—1011no—
205#464—1011no—
206#464—1011no—
207#464D10111yescharacteristic, direct product factor
208C2×C4⋊C8—1011no—
209C2×#103—1011no—
210C2×#102—1011no—
211C22×Q8—1011no—
212C22×Q8—1011no—
213C22×D4—1011no—
214C2×Q16—1011no—
215C2×Q16—1011no—
216C2×Q16—1011no—
217C2×Q16—2024no—
218C2×Q16C2×D10111yescharacteristic, complemented
219C2×SD16—1011no—
220C2×SD16—1011no—
221C2×SD16—1011no—
222C2×SD16—2024no—
223C2×SD16C2×D10111yescharacteristic
224C22×C8—1011no—
225C22×C8—1011no—
226#124—1011no—
227#124—1011no—
228#124—1011no—
229#124—2021no—
230#124—2021no—
231#124C2×D10111yescharacteristic
232C4×Q8—1011no—
233C4×Q8—1011no—
234C4×Q8—1011no—
235C4×Q8—2021no—
236C4×Q8—2021no—
237C4×Q8C2×D10111yescharacteristic, complemented
238C2×C4⋊C4—1011no—
239C2×C4⋊C4—2021no—
240C2×C22⋊C4—2021no—
241C2×C22⋊C4—2021no—
242C2×C42—1011no—
243C2×C42—2021no—
244C4⋊C8—1011no—
245C4⋊C8—1011no—
246C4⋊C8—1011no—
247C4⋊C8C2×D10111yescharacteristic, complemented
248#103—1011no—
249#103—1011no—
250#103—1011no—
251#103C2×D10111yescharacteristic, complemented
252#102—1011no—
253#102—1011no—
254#102—1011no—
255#102C2×D10111yescharacteristic
256C24—2021no—
257C2×Q8—1014no—
258C2×Q8—1011no—
259C2×Q8—1011no—
260C2×Q8—2021no—
261C2×Q8—2021no—
262C2×Q8—2022no—
263C2×Q8—2022no—
264C2×Q8—2022no—
265C2×Q8C22×D10111yescharacteristic
266C2×Q8C22×D10111yescharacteristic
267C2×D4—1011no—
268C2×D4—2022no—
269C2×D4—2022no—
270C2×D4—2021no—
271C2×D4C22×D10111yescharacteristic
272C22×C4—1011no—
273C22×C4—1011no—
274C22×C4—1011no—
275C22×C4—2021no—
276C22×C4—2021no—
277C22×C4—2021no—
278Q16—22no—
279Q16—2022no—
280Q16—2022no—
281Q16—2022no—
282SD16—22no—
283SD16—2022no—
284SD16—2022no—
285SD16—2022no—
286C2×C8—1011no—
287C2×C8—1011no—
288C2×C8—2022no—
289C2×C8—2022no—
290C2×C8C22×D10111yescharacteristic
291C2×C8C22×D10111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—1011no—
294C4⋊C4—2021no—
295C4⋊C4—2021no—
296C4⋊C4—2021no—
297C4⋊C4—2021no—
298C4⋊C4C22×D10111yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—2021no—
302C22⋊C4—2021no—
303C22⋊C4—2021no—
304C22⋊C4—2021no—
305C22⋊C4—2021no—
306C22⋊C4—2021no—
307C42—21no—
308C42—1011no—
309C42—1011no—
310C42—1011no—
311C42—2021no—
312C42—2021no—
313C42—2021no—
314C42C22×D10111yescharacteristic
315C23—21no—
316C23—1011no—
317C23—4042no—
318C23—4042no—
319C23—4042no—
320C23—2021no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324Q8—1012no—
325Q8—4042no—
326Q8—2024no—
327Q8—2021no—
328Q8—2021no—
329Q8—2021no—
330Q8D4×D10112yes—
331D4—21no—
332D4—21no—
333D4—4042no—
334D4—2021no—
335D4—2021no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—1011no—
340C2×C4—1012no—
341C2×C4—1012no—
342C2×C4—1011no—
343C2×C4—1011no—
344C2×C4—4042no—
345C2×C4—4042no—
346C2×C4—2022no—
347C2×C4—2022no—
348C2×C4—2024no—
349C2×C4—2021no—
350C2×C4—2021no—
351C2×C4—2021no—
352C2×C4D4×D10111yescharacteristic
353C2×C4D4×D10111yescharacteristic
354C2×C4C23×D10111yescharacteristic
355C8—21no—
356C8—21no—
357C8—2021no—
358C8—2021no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—8084no—
363C22—1012no—
364C22—1012no—
365C22—1012no—
366C22—4041no—
367C22—4041no—
368C22—4041no—
369C22C2×D4×D10111yescharacteristic
370C4—22no—
371C4—21no—
372C4—21no—
373C4—41no—
374C4—41no—
375C4—1012no—
376C4—4041no—
377C4—4041no—
378C4—2022no—
379C4—2021no—
380C4—2021no—
381C4C2×D4×D10111yescharacteristic
382C4#41×D10111yescharacteristic
383C2—81no—
384C2—8081no—
385C2—1014no—
386C2#121×D10111yescharacteristic
387C2#135×D10111yescharacteristic
388C2#137×D10111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#464×C101C2
socleC22×C101C22×D4
prime radicalC2×D4×D101C22
hypercenter#464D101
hypocenterC101C2×#464
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D101C2semidirect
4. C4×Q8×D101C2semidirect
5. #20265402C2semidirect
6. #20265401C2semidirect
7. #20265400C2semidirect
8. #20265399C2semidirect
9. #20265398C2semidirect
10. #20265397C2semidirect
11. #20265396C2semidirect
12. C4⋊C8×D101C2semidirect
13. #103×D101C2semidirect
15. #464×C101C2semidirect
19. C2×Dic404C22semidirect
20. C2×#13108064C22semidirect
21. C2×#13108064C22semidirect
34. Q8×Dic101C22semidirect
36. C4×Dic202C22semidirect
38. #15692220C22semidirect
45. C4⋊#11717579C22semidirect
46. #15692184C22semidirect
47. #15692184C22semidirect
48. #15692180C22semidirect
49. #15692179C22semidirect
50. #15692178C22semidirect
54. C2×Q16×C101C22semidirect
57. C4×Q8×C101C22semidirect
58. C4⋊C8×C101C22semidirect
59. #103×C101C22semidirect
193. D101#464direct (N × H)
195. C101C2×#464semidirect
207. #464D101direct (N × H)
218. C2×Q16C2×D101semidirect
237. C4×Q8C2×D101semidirect
247. C4⋊C8C2×D101semidirect
251. #103C2×D101semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×Q16×D1012
C2×SD16×D1012
#124×D1012
C4×Q8×D1012
#202654022
#202654012
#202654002
#202653992
#202653982
#202653972
#202653962
C4⋊C8×D1012
#103×D1012
#102×D1012
#464×C1012
C2×#464101