Finite Group Databasebeta

← #485×D101 #27181020

Subgroups — #485×D101 #27181020

Order 12928.

416 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D101C211yesmaximal, characteristic
2#117×D101C211yesmaximal, characteristic
3#20265521C211yesmaximal, characteristic, complemented
4#20265520C211yesmaximal, characteristic, complemented
5#20265519C211yesmaximal, characteristic, complemented
6#20265518C211yesmaximal, characteristic, complemented
7#20265517C211yesmaximal, characteristic, complemented
8#20265516C211yesmaximal, characteristic, complemented
9#20265515C211yesmaximal, characteristic, complemented
10#107×D101C211yesmaximal, characteristic, complemented
11#106×D101C211yesmaximal, characteristic, complemented
12#103×D101C211yesmaximal, characteristic, complemented
13#103×D101C211yesmaximal, characteristic, complemented
14C22⋊C8×D101C211yesmaximal, characteristic
15#485×C101C211yesmaximal, characteristic, complemented
16C2×Q8×D101C2211yescharacteristic
17C22×C4×D101C2211yescharacteristic
18C2×C8×D101C2211yescharacteristic
19C2×C8×D101C2211yescharacteristic
20#15692235C2211yescharacteristic
21#15692234C2211yescharacteristic
22#15692233—21no—
23#15692232—21no—
24#15692231C2211yescharacteristic
25#15692214C2211yescharacteristic
26#15692213C2211yescharacteristic
27#15692213C2211yescharacteristic
28#15692212—21no—
29#15692211—21no—
30C4⋊C4×D101—21no—
31C4⋊C4×D101C2211yescharacteristic
32C4⋊C4×D101C2211yescharacteristic
33C4⋊C4×D101C2211yescharacteristic
34C22⋊C4×D101—21no—
35C22⋊C4×D101—21no—
36C42×D101—21no—
37#15692189C2211yescharacteristic, complemented
38#15692188C2211yescharacteristic, complemented
39#15692188C2211yescharacteristic, complemented
40#15692187C2211yescharacteristic, complemented
41#15692186C2211yescharacteristic, complemented
42#15692186C2211yescharacteristic, complemented
43#15692180C2211yescharacteristic, complemented
44#15692180C2211yescharacteristic, complemented
45#15692179C2211yescharacteristic, complemented
46#15692179C2211yescharacteristic, complemented
47#15692178C2211yescharacteristic, complemented
48#15692178C2211yescharacteristic, complemented
49C22⋊#11717579C2211yescharacteristic
50#15692167C2211yescharacteristic
51#15692167C2211yescharacteristic
52C22⋊Q8×C101C2211yescharacteristic
53#117×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic, complemented
55#106×C101C2211yescharacteristic, complemented
56#103×C101C2211yescharacteristic, complemented
57#103×C101C2211yescharacteristic, complemented
58C22⋊C8×C101C2211yescharacteristic
59C23×D101D411yescharacteristic
60C2×Dic202—21no—
61C2×Dic202C2311yescharacteristic
62Q8×D101—22no—
63Q8×D101—22no—
64C22×Dic101D411yescharacteristic
65C2×C4×D101—22no—
66C2×C4×D101—22no—
67C2×C4×D101—21no—
68C2×C4×D101—21no—
69C2×C4×D101—21no—
70C2×C4×D101—21no—
71C2×C4×D101D411yescharacteristic
72C2×C4×D101D411yescharacteristic
73C2×C4×D101C2311yescharacteristic
74C2×C4×D101C2311yescharacteristic
75C2×#11717579C2311yescharacteristic
76C2×#11717579C2311yescharacteristic
77C8×D101—22no—
78C8×D101—22no—
79C4⋊Dic101—21no—
80C4⋊Dic101C2311yescharacteristic
81C4⋊Dic101C2311yescharacteristic
82C4⋊Dic101C2311yescharacteristic
83#13108053—21no—
84#13108053—21no—
85#13108053—21no—
86#13108053—21no—
87#13108053—21no—
88C22⋊Dic101—21no—
89C22⋊Dic101—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93#13108051—21no—
94C4×Dic101—21no—
95C4×Dic101—21no—
96C4×Dic101—21no—
97C2×Q8×C101C2311yescharacteristic
98C22×C4×C101C2311yescharacteristic
99C2×C8×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C4⋊C4×C101—21no—
102C4⋊C4×C101C2311yescharacteristic
103C4⋊C4×C101C2311yescharacteristic
104C4⋊C4×C101C2311yescharacteristic
105C22⋊C4×C101—21no—
106C22⋊C4×C101—21no—
107C42×C101—21no—
108C23×C101C2×D411yescharacteristic
109C22×D101—22no—
110C22×D101—22no—
111C22×D101—22no—
112C22×D101C2×D411yescharacteristic
113C22×D101C2×D411yescharacteristic
114Q8×C101—21no—
115Q8×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
121C2×C4×C101—21no—
122C2×C4×C101C2×D411yescharacteristic
123C2×C4×C101C2411yescharacteristic
124C2×Dic101—22no—
125C2×Dic101—21no—
126C2×Dic101—21no—
127C2×Dic101—21no—
128C2×Dic101—21no—
129C2×Dic101C2×D411yescharacteristic
130C2×Dic101C2×D411yescharacteristic
131C4×D101—22no—
132C4×D101—21no—
133C4×D101—21no—
134C4×D101—22no—
135C4×D101—42no—
136C4×D101—42no—
137C4×D101—42no—
138C4×D101—42no—
139C4×D101#4112yes—
140C4×D101#4112yes—
141Dic202—21no—
142Dic202—21no—
143Dic202—42no—
144C8×C101—21no—
145C8×C101—21no—
146#11717579—21no—
147#11717579—21no—
148C22×C101—21no—
149C22×C101—21no—
150C22×C101—21no—
151C22×C101C22×D411yescharacteristic
152C2×D101—21no—
153C2×D101—21no—
154C2×D101—21no—
155C2×D101—44no—
156C2×D101#12312yes—
157C2×D101#13512yes—
158C2×D101#13712yes—
159C4×C101—21no—
160C4×C101—41no—
161C4×C101—41no—
162C4×C101—41no—
163C4×C101—41no—
164C4×C101C2×#4111yescharacteristic
165C4×C101C2×#4111yescharacteristic
166Dic101—21no—
167Dic101—41no—
168Dic101—41no—
169Dic101—41no—
170Dic101—41no—
171Dic101#12312yes—
172C2×C101—41no—
173C2×C101C2×#12311yescharacteristic
174C2×C101C2×#13511yescharacteristic
175C2×C101C2×#13711yescharacteristic
176D101—41no—
177D101#48514yesdirect product factor
178C2×#485—1011nomaximal, Sylow
179C101C2×#48511yescharacteristic, complemented, Sylow
180C2×C22⋊Q8—1011no—
181C2×#117—1011no—
182#485—1011no—
183#485—1011no—
184#485—1011no—
185#485—1011no—
186#485—1011no—
187#485—1011no—
188#485—1011no—
189#485D10111yescharacteristic, direct product factor
190C2×#107—1011no—
191C2×#106—1011no—
192C2×#103—1011no—
193C2×#103—1011no—
194C2×C22⋊C8—1011no—
195C22×Q8—1011no—
196C23×C4—1011no—
197C22×C8—1011no—
198C22×C8—1011no—
199C22⋊Q8—1011no—
200C22⋊Q8—1011no—
201C22⋊Q8—1011no—
202C22⋊Q8—2021no—
203C22⋊Q8—2021no—
204C22⋊Q8C2×D10111yescharacteristic
205#117—1011no—
206#117—1011no—
207#117—1011no—
208#117—2021no—
209#117—2021no—
210#117C2×D10111yescharacteristic
211C2×C4⋊C4—1011no—
212C2×C4⋊C4—1011no—
213C2×C4⋊C4—1011no—
214C2×C4⋊C4—2021no—
215C2×C22⋊C4—2021no—
216C2×C22⋊C4—2021no—
217C2×C42—2021no—
218#107—1011no—
219#107—1011no—
220#107—1011no—
221#107C2×D10111yescharacteristic, complemented
222#106—1011no—
223#106—1011no—
224#106—1011no—
225#106C2×D10111yescharacteristic, complemented
226#103—1011no—
227#103—1011no—
228#103—1011no—
229#103—1011no—
230#103—1011no—
231#103—1011no—
232#103C2×D10111yescharacteristic, complemented
233#103C2×D10111yescharacteristic, complemented
234C22⋊C8—1011no—
235C22⋊C8—1011no—
236C22⋊C8—1011no—
237C22⋊C8C2×D10111yescharacteristic
238C24—1011no—
239C2×Q8—1011no—
240C2×Q8—2021no—
241C2×Q8—2022no—
242C2×Q8—2022no—
243C2×Q8C22×D10111yescharacteristic
244C22×C4—1011no—
245C22×C4—1011no—
246C22×C4—1011no—
247C22×C4—1011no—
248C22×C4—1011no—
249C22×C4—2022no—
250C22×C4—2022no—
251C22×C4—2021no—
252C22×C4—2021no—
253C22×C4—2021no—
254C22×C4—2021no—
255C22×C4C22×D10111yescharacteristic
256C2×C8—1011no—
257C2×C8—1011no—
258C2×C8—2022no—
259C2×C8—2022no—
260C2×C8C22×D10111yescharacteristic
261C2×C8C22×D10111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—1011no—
264C4⋊C4—1011no—
265C4⋊C4—1011no—
266C4⋊C4—2021no—
267C4⋊C4—2021no—
268C4⋊C4—2021no—
269C4⋊C4—2021no—
270C4⋊C4—2021no—
271C4⋊C4—2021no—
272C4⋊C4C22×D10111yescharacteristic
273C4⋊C4C22×D10111yescharacteristic
274C4⋊C4C22×D10111yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2021no—
278C22⋊C4—2021no—
279C22⋊C4—2021no—
280C22⋊C4—2021no—
281C22⋊C4—2021no—
282C22⋊C4—2021no—
283C42—21no—
284C42—2021no—
285C42—2021no—
286C42—2021no—
287C23—1011no—
288C23—1011no—
289C23—2022no—
290C23—2022no—
291C23—2022no—
292C23D4×D10111yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—4042no—
296Q8—2021no—
297Q8—2021no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—1011no—
305C2×C4—1012no—
306C2×C4—1012no—
307C2×C4—1011no—
308C2×C4—4042no—
309C2×C4—4042no—
310C2×C4—4042no—
311C2×C4—4042no—
312C2×C4—2022no—
313C2×C4—2022no—
314C2×C4—2022no—
315C2×C4—2021no—
316C2×C4—2021no—
317C2×C4—2021no—
318C2×C4—2021no—
319C2×C4—2021no—
320C2×C4—2021no—
321C2×C4D4×D10111yescharacteristic
322C2×C4C23×D10111yescharacteristic
323C8—21no—
324C8—21no—
325C8—2021no—
326C8—2021no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—1012no—
331C22—1012no—
332C22—1012no—
333C22—4044no—
334C22—2021no—
335C22—2021no—
336C22—2021no—
337C22C2×D4×D10111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1012no—
344C4—4041no—
345C4—4041no—
346C4—4041no—
347C4—4041no—
348C4—2021no—
349C4#41×D10111yescharacteristic
350C4#41×D10111yescharacteristic
351C2—41no—
352C2—1014no—
353C2—4041no—
354C2#123×D10111yescharacteristic
355C2#135×D10111yescharacteristic
356C2#137×D10111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#485×C101C2
socleC22×C101C22×D4
prime radicalC23×D101D4
hypercenter#485D101
hypocenterC101C2×#485
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #20265521C2semidirect
4. #20265520C2semidirect
5. #20265519C2semidirect
6. #20265518C2semidirect
7. #20265517C2semidirect
8. #20265516C2semidirect
9. #20265515C2semidirect
10. #107×D101C2semidirect
11. #106×D101C2semidirect
12. #103×D101C2semidirect
13. #103×D101C2semidirect
15. #485×C101C2semidirect
37. #15692189C22semidirect
38. #15692188C22semidirect
39. #15692188C22semidirect
40. #15692187C22semidirect
41. #15692186C22semidirect
42. #15692186C22semidirect
43. #15692180C22semidirect
44. #15692180C22semidirect
45. #15692179C22semidirect
46. #15692179C22semidirect
47. #15692178C22semidirect
48. #15692178C22semidirect
54. #107×C101C22semidirect
55. #106×C101C22semidirect
56. #103×C101C22semidirect
57. #103×C101C22semidirect
177. D101#485direct (N × H)
179. C101C2×#485semidirect
189. #485D101direct (N × H)
221. #107C2×D101semidirect
225. #106C2×D101semidirect
232. #103C2×D101semidirect
233. #103C2×D101semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1012
#117×D1012
#202655212
#202655202
#202655192
#202655182
#202655172
#202655162
#202655152
#107×D1012
#106×D1012
#103×D1012
C22⋊C8×D1012
#485×C1012
C2×#485101