Finite Group Databasebeta

← #385×D101 #27173540

Subgroups — #385×D101 #27173540

Order 12928.

1232 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D101C211yesmaximal, characteristic
2C2×C4⋊C4×D101C212yesmaximal, complemented
3C2×C22⋊C4×D101C211yesmaximal, characteristic
4C2×C22⋊C4×D101C211yesmaximal, characteristic
5#20265052C211yesmaximal, characteristic, complemented
6#20265051C212yesmaximal, complemented
7#20265050C211yesmaximal, characteristic, complemented
8#20265049C211yesmaximal, characteristic, complemented
9#20265048C212yesmaximal, complemented
10#95×D101C212yesmaximal, complemented
11#385×C101C211yesmaximal, characteristic, complemented
12C24×D101C2211yescharacteristic
13C23×Dic101C2211yescharacteristic
14C22×C4×D101—24no—
15C22×C4×D101—28no—
16C22×C4×D101C2212yes—
17C22×C4×D101C2211yescharacteristic
18C22×C4×D101C2211yescharacteristic
19C22×C4×D101C2212yes—
20C22×C4×D101C2212yes—
21C2×C4⋊Dic101C2212yescomplemented
22C2×#13108053C2212yescomplemented
23C2×#13108053C2212yescomplemented
24C4⋊C4×D101—28no—
25C2×C22⋊Dic101C2211yescharacteristic
26C2×C22⋊Dic101C2211yescharacteristic
27C2×#13108051C2211yescharacteristic
28C2×#13108051C2211yescharacteristic
29C2×#13108051C2212yes—
30C22⋊C4×D101—24no—
31C22⋊C4×D101C418yescomplemented
32#15692162C2212yescomplemented
33#15692162C2212yescomplemented
34#15692162C2212yescomplemented
35C23×C4×C101C2211yescharacteristic
36C2×C4⋊C4×C101C2212yescomplemented
37C2×C22⋊C4×C101C2211yescharacteristic
38C2×C22⋊C4×C101C2211yescharacteristic
39#95×C101C2212yescomplemented
40C23×D101—24no—
41C23×D101—24no—
42C23×D101C2×C414yes—
43C23×D101D414yes—
44C23×D101Q814yes—
45C23×D101C2311yescharacteristic
46C23×D101C2311yescharacteristic
47C22×Dic101—22no—
48C22×Dic101—24no—
49C22×Dic101C2311yescharacteristic
50C22×Dic101C2311yescharacteristic
51C22×Dic101C2312yes—
52C22×Dic101C2312yes—
53C2×C4×D101—232no—
54C2×C4×D101—24no—
55C2×C4×D101—24no—
56C2×C4×D101—24no—
57C2×C4×D101—24no—
58C2×C4×D101—24no—
59C2×C4×D101—24no—
60C2×C4×D101—24no—
61C2×C4×D101—22no—
62C2×C4×D101—22no—
63C2×C4×D101—24no—
64C2×C4×D101—24no—
65C2×C4×D101C2×C418yescomplemented
66C2×C4×D101D418yes—
67C4⋊Dic101—24no—
68#13108053—24no—
69#13108053—24no—
70C22⋊Dic101—22no—
71C22⋊Dic101C2×C414yescomplemented
72#13108051—22no—
73#13108051—22no—
74#13108051C2×C418yescomplemented
75C24×C101C2311yescharacteristic
76C22×C4×C101—22no—
77C22×C4×C101—24no—
78C22×C4×C101C2311yescharacteristic
79C22×C4×C101C2311yescharacteristic
80C22×C4×C101C2312yes—
81C22×C4×C101C2312yes—
82C4⋊C4×C101—24no—
83C22⋊C4×C101—22no—
84C22⋊C4×C101C2×C414yescomplemented
85C23×C101—22no—
86C23×C101—22no—
87C23×C101C22×C412yes—
88C23×C101C2×D412yes—
89C23×C101C2×Q812yes—
90C23×C101C2411yescharacteristic
91C22×D101—22no—
92C22×D101—22no—
93C22×D101—216no—
94C22×D101—28no—
95C22×D101—216no—
96C22×D101—28no—
97C22×D101C4⋊C4116yescomplemented
98C22×D101C22×C412yes—
99C22×D101C22×C412yes—
100C22×D101C2×D412yes—
101C22×D101C2×D412yes—
102C22×D101C2×D414yes—
103C22×D101C2×Q812yes—
104C22×D101C2×Q812yes—
105C22×D101#4114yes—
106C2×C4×C101—28no—
107C2×C4×C101—22no—
108C2×C4×C101—22no—
109C2×C4×C101—22no—
110C2×C4×C101—22no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—22no—
114C2×C4×C101—22no—
115C2×C4×C101C22×C414yescomplemented
116C2×C4×C101C2×D414yes—
117C2×Dic101—28no—
118C2×Dic101—22no—
119C2×Dic101—22no—
120C2×Dic101—22no—
121C2×Dic101—22no—
122C2×Dic101—21no—
123C2×Dic101—21no—
124C2×Dic101—22no—
125C2×Dic101—22no—
126C2×Dic101C22×C414yescomplemented
127C2×Dic101C2×D414yes—
128C4×D101—216no—
129C4×D101—216no—
130C4×D101—216no—
131C4×D101—44no—
132C4×D101—44no—
133C22×C101—24no—
134C22×C101—22no—
135C22×C101—24no—
136C22×C101—22no—
137C22×C101C2×C4⋊C414yescomplemented
138C22×C101C23×C411yescharacteristic
139C22×C101C22×D411yescharacteristic
140C22×C101C22×D412yes—
141C22×C101C22×Q811yescharacteristic
142C22×C101C2×#4112yes—
143C2×D101—24no—
144C2×D101—22no—
145C2×D101—24no—
146C2×D101—22no—
147C2×D101—232no—
148C2×D101C2×C4⋊C414yes—
149C2×D101C2×C4⋊C414yescomplemented
150C2×D101C4×D418yes—
151C2×D101#12014yes—
152C2×D101C22⋊Q818yes—
153C2×D101#12314yes—
154C4×C101—24no—
155C4×C101—24no—
156C4×C101—41no—
157C4×C101—41no—
158Dic101—24no—
159Dic101—24no—
160Dic101—41no—
161Dic101—41no—
162C2×C101—24no—
163C2×C101C22×C4⋊C411yescharacteristic
164C2×C101C2×C4×D412yes—
165C2×C101C2×#12011yescharacteristic
166C2×C101C2×C22⋊Q812yes—
167C2×C101C2×#12311yescharacteristic
168D101—24no—
169D101#38518yesdirect product factor
170C2×#385—1011nomaximal, Sylow
171C101C2×#38511yescharacteristic, complemented, Sylow
172C24×C4—1011no—
173C22×C4⋊C4—1012no—
174C22×C22⋊C4—1011no—
175C22×C22⋊C4—1011no—
176#385—1011no—
177#385—1012no—
178#385—1011no—
179#385—1011no—
180#385—1012no—
181#385D10111yescharacteristic, direct product factor
182C2×#95—1012no—
183C25—1011no—
184C23×C4—1012no—
185C23×C4—1012no—
186C23×C4—1011no—
187C23×C4—1011no—
188C23×C4—1011no—
189C23×C4—1012no—
190C23×C4—2028no—
191C23×C4—2024no—
192C23×C4C2×D10111yescharacteristic
193C2×C4⋊C4—1012no—
194C2×C4⋊C4—1012no—
195C2×C4⋊C4—1012no—
196C2×C4⋊C4—2028no—
197C2×C4⋊C4C2×D10112yescomplemented
198C2×C22⋊C4—1011no—
199C2×C22⋊C4—1012no—
200C2×C22⋊C4—1018no—
201C2×C22⋊C4—1011no—
202C2×C22⋊C4—1011no—
203C2×C22⋊C4—1011no—
204C2×C22⋊C4—2024no—
205C2×C22⋊C4C2×D10111yescharacteristic
206C2×C22⋊C4C2×D10111yescharacteristic
207#95—1012no—
208#95—1012no—
209#95—1012no—
210#95C2×D10112yescomplemented
211C24—1011no—
212C24—1014no—
213C24—1014no—
214C24—1014no—
215C24—1011no—
216C24—2024no—
217C24—2024no—
218C24C22×D10111yescharacteristic
219C22×C4—22no—
220C22×C4—24no—
221C22×C4—1012no—
222C22×C4—1012no—
223C22×C4—1018no—
224C22×C4—1018no—
225C22×C4—1011no—
226C22×C4—1011no—
227C22×C4—2024no—
228C22×C4—2022no—
229C22×C4—2022no—
230C22×C4—2024no—
231C22×C4—2024no—
232C22×C4—2024no—
233C22×C4—2024no—
234C22×C4—2024no—
235C22×C4—2024no—
236C22×C4—2024no—
237C22×C4—20232no—
238C22×C4—2024no—
239C22×C4—2022no—
240C22×C4—2024no—
241C22×C4C22×D10111yescharacteristic
242C22×C4C22×D10111yescharacteristic
243C22×C4C22×D10112yes—
244C22×C4C22×D10112yes—
245C4⋊C4—24no—
246C4⋊C4—2024no—
247C4⋊C4—2024no—
248C4⋊C4—2024no—
249C22⋊C4—22no—
250C22⋊C4—1014no—
251C22⋊C4—1018no—
252C22⋊C4—2022no—
253C22⋊C4—2022no—
254C22⋊C4—2022no—
255C22⋊C4C4×D10114yescomplemented
256C23—22no—
257C23—22no—
258C23—1012no—
259C23—1014no—
260C23—1012no—
261C23—1012no—
262C23—1014no—
263C23—1012no—
264C23—1012no—
265C23—1012no—
266C23—10116no—
267C23—2028no—
268C23—20216no—
269C23—20216no—
270C23—2028no—
271C23—2022no—
272C23—2022no—
273C23C2×C4×D10112yes—
274C23D4×D10112yes—
275C23Q8×D10112yes—
276C23C23×D10111yescharacteristic
277C2×C4—28no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—1014no—
287C2×C4—1014no—
288C2×C4—4044no—
289C2×C4—4044no—
290C2×C4—20216no—
291C2×C4—20216no—
292C2×C4—20216no—
293C2×C4—2021no—
294C2×C4—2021no—
295C2×C4—2022no—
296C2×C4—2022no—
297C2×C4—2028no—
298C2×C4—2022no—
299C2×C4—2022no—
300C2×C4—2022no—
301C2×C4—2022no—
302C2×C4C2×C4×D10114yescomplemented
303C2×C4D4×D10114yes—
304C22—24no—
305C22—22no—
306C22—24no—
307C22—22no—
308C22—1014no—
309C22—1018no—
310C22—1014no—
311C22—1018no—
312C22—1014no—
313C22—1014no—
314C22—20232no—
315C22—2024no—
316C22—2022no—
317C22—2024no—
318C22—2022no—
319C22C4⋊C4×D10114yescomplemented
320C22C22×C4×D10111yescharacteristic
321C22C2×D4×D10111yescharacteristic
322C22C2×D4×D10112yes—
323C22C2×Q8×D10111yescharacteristic
324C22#41×D10112yes—
325C4—24no—
326C4—24no—
327C4—41no—
328C4—41no—
329C4—4041no—
330C4—4041no—
331C4—2024no—
332C4—2024no—
333C2—24no—
334C2—1018no—
335C2—2024no—
336C2C2×C4⋊C4×D10111yescharacteristic
337C2C4×D4×D10112yes—
338C2#120×D10111yescharacteristic
339C2C22⋊Q8×D10112yes—
340C2#123×D10111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#385×C101C2
socle, cosocleC23×C101C24
prime radicalC24×D101C22
hypercenter#385D101
hypocenterC101C2×#385
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D101C2semidirect
5. #20265052C2semidirect
6. #20265051C2semidirect
7. #20265050C2semidirect
8. #20265049C2semidirect
9. #20265048C2semidirect
10. #95×D101C2semidirect
11. #385×C101C2semidirect
21. C2×C4⋊Dic101C22semidirect
22. C2×#13108053C22semidirect
23. C2×#13108053C22semidirect
31. C22⋊C4×D101C4semidirect
32. #15692162C22semidirect
33. #15692162C22semidirect
34. #15692162C22semidirect
36. C2×C4⋊C4×C101C22semidirect
39. #95×C101C22semidirect
65. C2×C4×D101C2×C4semidirect
71. C22⋊Dic101C2×C4semidirect
74. #13108051C2×C4semidirect
84. C22⋊C4×C101C2×C4semidirect
97. C22×D101C4⋊C4semidirect
115. C2×C4×C101C22×C4semidirect
126. C2×Dic101C22×C4semidirect
137. C22×C101C2×C4⋊C4semidirect
149. C2×D101C2×C4⋊C4semidirect
169. D101#385direct (N × H)
171. C101C2×#385semidirect
181. #385D101direct (N × H)
197. C2×C4⋊C4C2×D101semidirect
210. #95C2×D101semidirect
255. C22⋊C4C4×D101semidirect
302. C2×C4C2×C4×D101semidirect
319. C22C4⋊C4×D101semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1012
C2×C4⋊C4×D1012
C2×C22⋊C4×D1012
#202650522
#202650512
#202650502
#202650492
#202650482
#95×D1012
#385×C1012
C2×#385101