Finite Group Databasebeta

← #27181369

Subgroups — #27181369

Order 12928.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265780C211yesmaximal, characteristic, complemented
2#20265652C211yesmaximal, characteristic, complemented
3#20265502C211yesmaximal, characteristic, complemented
4#20265498C211yesmaximal, characteristic, complemented
5#20265479C211yesmaximal, characteristic, complemented
6#20265475C211yesmaximal, characteristic, complemented
7#20265370C211yesmaximal, characteristic, complemented
8#20265370C211yesmaximal, characteristic, complemented
9#20265311C211yesmaximal, characteristic, complemented
10#20265289C211yesmaximal, characteristic, complemented
11#20265286C211yesmaximal, characteristic, complemented
12D8×Dic101C211yesmaximal, characteristic, complemented
13#20265257C211yesmaximal, characteristic, complemented
14#20265235C211yesmaximal, characteristic, complemented
15#447×C101C211yesmaximal, characteristic, complemented
16C2×#13108059C2211yescharacteristic
17C2×#13108059C2211yescharacteristic
18#15692251C2211yescharacteristic, complemented
19#15692246C2211yescharacteristic, complemented
20#15692239—21no—
21#15692237—21no—
22#15692229C2211yescharacteristic
23#15692227—21no—
24#15692226—21no—
25D4×Dic101—21no—
26D4×Dic101—21no—
27D4×Dic101C2211yescharacteristic
28D4×Dic101C2211yescharacteristic
29D4×Dic101C2211yescharacteristic
30D4×Dic101C2211yescharacteristic
31D4×Dic101C2211yescharacteristic, complemented
32#15692217C2211yescharacteristic, complemented
33#15692214C2211yescharacteristic
34#15692214C2211yescharacteristic
35C2×C22⋊Dic101—21no—
36C2×C22⋊Dic101—21no—
37#15692189C2211yescharacteristic, complemented
38#15692188C2211yescharacteristic, complemented
39#15692187C2211yescharacteristic, complemented
40#15692186C2211yescharacteristic, complemented
41#15692184C2211yescharacteristic, complemented
42#15692184C2211yescharacteristic, complemented
43#15692177C2211yescharacteristic, complemented
44#15692177C2211yescharacteristic, complemented
45#15692176C2211yescharacteristic
46#15692176C2211yescharacteristic
47#15692176C2211yescharacteristic, complemented
48#15692176C2211yescharacteristic, complemented
49C22⋊#11717579C2211yescharacteristic
50#15692165C2211yescharacteristic, complemented
51C8×Dic101C2211yescharacteristic, complemented
52C22×D4×C101C2211yescharacteristic
53C2×D8×C101C2211yescharacteristic
54C2×D8×C101C2211yescharacteristic
55#121×C101C2211yescharacteristic
56#102×C101C2211yescharacteristic
57#102×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic
59C2×D404C2311yescharacteristic
60C2×C22⋊D101—21no—
61C2×C22⋊D101—21no—
62C2×C22⋊D101—21no—
63C22×Dic101—21no—
64C22×Dic101—21no—
65C22×Dic101—21no—
66C22×Dic101—21no—
67C22×Dic101—21no—
68C2×C4×D101—21no—
69#13108059—22no—
70#13108059—22no—
71C2×#11717579C2311yescharacteristic
72C2×#11717579C2311yescharacteristic
73C4⋊Dic101—21no—
74C4⋊Dic101D411yescharacteristic
75C4⋊Dic101D411yescharacteristic
76C4⋊Dic101C2311yescharacteristic
77C4⋊Dic101C2311yescharacteristic
78C4⋊Dic101C2311yescharacteristic
79#13108053—21no—
80C22⋊Dic101—21no—
81C22⋊Dic101—21no—
82C22⋊Dic101—21no—
83C22⋊Dic101—21no—
84C22⋊Dic101—21no—
85C22⋊Dic101—21no—
86C22⋊Dic101D411yescharacteristic
87C22⋊Dic101D411yescharacteristic
88#13108051—21no—
89#13108051—21no—
90C4×Dic101—21no—
91C4×Dic101C2311yescharacteristic
92C4×Dic101C2311yescharacteristic
93C24×C101—21no—
94C2×D4×C101—22no—
95C2×D4×C101—22no—
96C2×D4×C101—21no—
97C2×D4×C101—21no—
98C2×D4×C101C2311yescharacteristic
99C2×D4×C101C2311yescharacteristic
100C2×D4×C101C2311yescharacteristic
101C22×C4×C101C2311yescharacteristic
102D8×C101—22no—
103D8×C101—22no—
104C2×C8×C101C2311yescharacteristic
105C2×C8×C101C2311yescharacteristic
106C4⋊C4×C101C2311yescharacteristic
107C22⋊C4×C101—21no—
108C23×C101—24no—
109C23×C101—21no—
110C23×C101—21no—
111C23×C101—21no—
112C23×C101—81no—
113C23×C101—81no—
114C23×C101C2×D411yescharacteristic
115C22×D101—21no—
116D4×C101—24no—
117D4×C101—21no—
118D4×C101—21no—
119D4×C101—21no—
120D4×C101—21no—
121D4×C101—81no—
122D4×C101#4112yes—
123D4×C101#4112yes—
124C2×C4×C101—21no—
125C2×C4×C101—21no—
126C2×C4×C101—21no—
127C2×C4×C101C2×D411yescharacteristic
128C2×C4×C101C2411yescharacteristic
129C22⋊D101—81no—
130C22⋊D101—81no—
131C22⋊D101—81no—
132C2×Dic101—21no—
133C2×Dic101—21no—
134C2×Dic101—21no—
135C2×Dic101—81no—
136C2×Dic101—81no—
137C2×Dic101—81no—
138C2×Dic101—81no—
139C2×Dic101—81no—
140C2×Dic101C2×D411yescharacteristic
141C2×Dic101C2×D411yescharacteristic
142C2×Dic101C2×D411yescharacteristic
143C2×Dic101C2×D411yescharacteristic
144D404—21no—
145D404—21no—
146C4×D101—81no—
147C8×C101—21no—
148C8×C101—21no—
149#11717579—21no—
150#11717579—21no—
151C22×C101—21no—
152C22×C101—22no—
153C22×C101—22no—
154C22×C101—21no—
155C22×C101—21no—
156C22×C101—41no—
157C22×C101—41no—
158C22×C101—41no—
159C22×C101—41no—
160C22×C101—41no—
161C22×C101—41no—
162C22×C101—41no—
163C22×C101—84no—
164C22×C101C22×D411yescharacteristic
165C2×D101—41no—
166C2×D101—41no—
167C2×D101—41no—
168C4×C101—21no—
169C4×C101—41no—
170C4×C101C2×#4111yescharacteristic
171C4×C101C2×#4111yescharacteristic
172Dic101—21no—
173Dic101—21no—
174Dic101—21no—
175Dic101—21no—
176Dic101—41no—
177Dic101—41no—
178Dic101—41no—
179C2×C101—41no—
180C2×C101—42no—
181C2×C101—42no—
182C2×C101—81no—
183C2×C101#52511yescharacteristic
184C2×C101#57611yescharacteristic
185C2×C101#57611yescharacteristic
186D101—81no—
187#3122—1011nomaximal, Sylow
188C101#312211yescharacteristic, complemented, Sylow
189#540—1011no—
190#518—1011no—
191#482—1011no—
192#482—1011no—
193#478—1011no—
194#478—1011no—
195#459—1011no—
196#459—1011no—
197#447—1011no—
198#447D10111yescharacteristic, complemented
199#442—1011no—
200#442—1011no—
201C4×D8—1011no—
202C4×D8—1011no—
203#433—1011no—
204C22×D4C2×D10111yescharacteristic
205C2×D8—1011no—
206C2×D8—1011no—
207C2×D8C2×D10111yescharacteristic
208C2×D8C2×D10111yescharacteristic
209#127—1011no—
210#125—1011no—
211#123—2021no—
212#123—2021no—
213#121—1011no—
214#121—2021no—
215#121—2021no—
216#121C2×D10111yescharacteristic
217C4×D4—1011no—
218C4×D4—1011no—
219C4×D4—1011no—
220C4×D4—1011no—
221C4×D4—1011no—
222C4×D4—1011no—
223C4×D4—2021no—
224C4×D4—2021no—
225#117—1011no—
226#117—1011no—
227C2×C22⋊C4—2021no—
228C2×C22⋊C4—2021no—
229#107—1011no—
230#107—1011no—
231#106—1011no—
232#106—1011no—
233C4⋊C8—1011no—
234C4⋊C8—1011no—
235#102—1011no—
236#102—1011no—
237#102—1011no—
238#102—1011no—
239#102—1011no—
240#102—1011no—
241#102C2×D10111yescharacteristic
242#102C2×D10111yescharacteristic
243C22⋊C8—1011no—
244C22⋊C8C2×D10111yescharacteristic
245#97—1011no—
246C4×C8—1011no—
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—1011no—
253C2×D4—2021no—
254C2×D4—2021no—
255C2×D4—2021no—
256C2×D4C22×D10111yescharacteristic
257C2×D4C22×D10111yescharacteristic
258C2×D4C22×D10111yescharacteristic
259C22×C4—2021no—
260C22×C4—2021no—
261C22×C4—2021no—
262C22×C4—2021no—
263C22×C4—2021no—
264C22×C4—2021no—
265C22×C4C22×D10111yescharacteristic
266D8—22no—
267D8—22no—
268D8—2022no—
269D8—2022no—
270C2×C8—1011no—
271C2×C8—1011no—
272C2×C8C22×D10111yescharacteristic
273C2×C8C22×D10111yescharacteristic
274C4⋊C4—1011no—
275C4⋊C4—1011no—
276C4⋊C4—1011no—
277C4⋊C4—1011no—
278C4⋊C4—1011no—
279C4⋊C4—2021no—
280C4⋊C4—2021no—
281C4⋊C4C22×D10111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—1011no—
284C22⋊C4—1011no—
285C22⋊C4—2021no—
286C22⋊C4—2021no—
287C22⋊C4—2021no—
288C22⋊C4—2021no—
289C22⋊C4—2021no—
290C22⋊C4—2021no—
291C22⋊C4—2021no—
292C22⋊C4—2021no—
293C42—1011no—
294C42—1011no—
295C42—2021no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—2021no—
303C23D4×D10111yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—8081no—
311D4—8081no—
312D4—8081no—
313D4—2021no—
314D4—2021no—
315D4#1310807312yes—
316D4#1310807312yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—8081no—
321C2×C4—8081no—
322C2×C4—8081no—
323C2×C4—8081no—
324C2×C4—8081no—
325C2×C4—8081no—
326C2×C4—1011no—
327C2×C4—1011no—
328C2×C4—1011no—
329C2×C4—1011no—
330C2×C4—2021no—
331C2×C4—2021no—
332C2×C4—2021no—
333C2×C4D4×D10111yescharacteristic
334C2×C4C23×D10111yescharacteristic
335C8—21no—
336C8—21no—
337C8—2021no—
338C8—2021no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—4041no—
353C22—4041no—
354C22—4041no—
355C22C2×D4×D10111yescharacteristic
356C4—21no—
357C4—41no—
358C4—4041no—
359C4—4041no—
360C4—4041no—
361C4—2021no—
362C4—2021no—
363C4—2021no—
364C4—2021no—
365C4C2×#1310807311yescharacteristic
366C4C2×#1310807311yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—8081no—
372C2#2026568311yescharacteristic
373C2#2026597811yescharacteristic
374C2#2026598111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#447×C101C2
socleC22×C101C22×D4
hypercenter#447D101
hypocenterC101#3122
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20265780C2semidirect
2. #20265652C2semidirect
3. #20265502C2semidirect
4. #20265498C2semidirect
5. #20265479C2semidirect
6. #20265475C2semidirect
7. #20265370C2semidirect
8. #20265370C2semidirect
9. #20265311C2semidirect
10. #20265289C2semidirect
11. #20265286C2semidirect
12. D8×Dic101C2semidirect
13. #20265257C2semidirect
14. #20265235C2semidirect
15. #447×C101C2semidirect
18. #15692251C22semidirect
19. #15692246C22semidirect
31. D4×Dic101C22semidirect
32. #15692217C22semidirect
37. #15692189C22semidirect
38. #15692188C22semidirect
39. #15692187C22semidirect
40. #15692186C22semidirect
41. #15692184C22semidirect
42. #15692184C22semidirect
43. #15692177C22semidirect
44. #15692177C22semidirect
47. #15692176C22semidirect
48. #15692176C22semidirect
50. #15692165C22semidirect
51. C8×Dic101C22semidirect
188. C101#3122semidirect
198. #447D101semidirect

Maximal subgroups

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

subgroupindex
#202657802
#202656522
#202655022
#202654982
#202654792
#202654752
#202653702
#202653112
#202652892
#202652862
D8×Dic1012
#202652572
#202652352
#447×C1012
#3122101