Finite Group Databasebeta

← #27181309

Subgroups — #27181309

Order 12928.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265794C211yesmaximal, characteristic, complemented
2#20265652C211yesmaximal, characteristic, complemented
3#20265519C211yesmaximal, characteristic, complemented
4#20265498C211yesmaximal, characteristic, complemented
5#20265465C211yesmaximal, characteristic, complemented
6#20265455C211yesmaximal, characteristic, complemented
7#20265390C211yesmaximal, characteristic, complemented
8#20265390C211yesmaximal, characteristic, complemented
9#20265328C211yesmaximal, characteristic, complemented
10#20265289C211yesmaximal, characteristic, complemented
11#20265274C211yesmaximal, characteristic, complemented
12#20265268C211yesmaximal, characteristic, complemented
13D8×Dic101C211yesmaximal, characteristic, complemented
14#20265235C211yesmaximal, characteristic, complemented
15#447×C101C211yesmaximal, characteristic
16C2×#13108062C2211yescharacteristic
17C2×#13108062C2211yescharacteristic
18#15692254C2211yescharacteristic, complemented
19#15692248—21no—
20#15692242—21no—
21#15692242C2211yescharacteristic, complemented
22#15692236—21no—
23#15692234C2211yescharacteristic
24#15692232—21no—
25#15692220C2211yescharacteristic, complemented
26D4×Dic101—21no—
27D4×Dic101—21no—
28D4×Dic101C2211yescharacteristic
29D4×Dic101C2211yescharacteristic
30D4×Dic101C2211yescharacteristic
31D4×Dic101C2211yescharacteristic
32D4×Dic101C2211yescharacteristic, 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#15692180C2211yescharacteristic, complemented
44#15692180C2211yescharacteristic, 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×Dic202—21no—
60C2×Dic202C2311yescharacteristic
61C22×Dic101—21no—
62C22×Dic101—21no—
63C22×Dic101—21no—
64C22×Dic101—21no—
65C22×Dic101—21no—
66#13108062—22no—
67#13108062—22no—
68C2×#11717579C2311yescharacteristic
69C2×#11717579C2311yescharacteristic
70C4⋊Dic101D411yescharacteristic
71C4⋊Dic101D411yescharacteristic
72C4⋊Dic101C2311yescharacteristic
73C4⋊Dic101C2311yescharacteristic
74C4⋊Dic101C2311yescharacteristic
75#13108053—21no—
76#13108053—21no—
77#13108053—21no—
78C22⋊Dic101—21no—
79C22⋊Dic101—21no—
80C22⋊Dic101—21no—
81C22⋊Dic101—21no—
82C22⋊Dic101—21no—
83C22⋊Dic101—21no—
84C22⋊Dic101—21no—
85C22⋊Dic101—21no—
86C22⋊Dic101—21no—
87C22⋊Dic101D411yescharacteristic
88C22⋊Dic101D411yescharacteristic
89C4×Dic101—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
115D4×C101—24no—
116D4×C101—21no—
117D4×C101—21no—
118D4×C101—21no—
119D4×C101—21no—
120D4×C101—81no—
121D4×C101#4112yes—
122D4×C101#4112yes—
123C2×C4×C101—21no—
124C2×C4×C101—21no—
125C2×C4×C101—21no—
126C2×C4×C101C2×D411yescharacteristic
127C2×C4×C101C2411yescharacteristic
128C2×Dic101—21no—
129C2×Dic101—21no—
130C2×Dic101—21no—
131C2×Dic101—21no—
132C2×Dic101—81no—
133C2×Dic101—81no—
134C2×Dic101—81no—
135C2×Dic101—81no—
136C2×Dic101—81no—
137C2×Dic101C2×D411yescharacteristic
138C2×Dic101C2×D411yescharacteristic
139C2×Dic101C2×D411yescharacteristic
140C2×Dic101C2×D411yescharacteristic
141Dic202—21no—
142Dic202—21no—
143Dic202—81no—
144C8×C101—21no—
145C8×C101—21no—
146#11717579—21no—
147#11717579—21no—
148C22×C101—21no—
149C22×C101—22no—
150C22×C101—22no—
151C22×C101—21no—
152C22×C101—21no—
153C22×C101—41no—
154C22×C101—41no—
155C22×C101—41no—
156C22×C101—41no—
157C22×C101—41no—
158C22×C101—41no—
159C22×C101—41no—
160C22×C101—84no—
161C22×C101C22×D411yescharacteristic
162C4×C101—21no—
163C4×C101—41no—
164C4×C101C2×#4111yescharacteristic
165C4×C101C2×#4111yescharacteristic
166Dic101—21no—
167Dic101—21no—
168Dic101—21no—
169Dic101—21no—
170Dic101—41no—
171Dic101—41no—
172Dic101—41no—
173Dic101—41no—
174C2×C101—41no—
175C2×C101—42no—
176C2×C101—42no—
177C2×C101—81no—
178C2×C101#52511yescharacteristic
179C2×C101#57611yescharacteristic
180C2×C101#57711yescharacteristic
181#3118—1011nomaximal, Sylow
182C101#311811yescharacteristic, complemented, Sylow
183#542—1011no—
184#518—1011no—
185#485—1011no—
186#482—1011no—
187#476—1011no—
188#474—1011no—
189#463—1011no—
190#463—1011no—
191#450—1011no—
192#447D10111yescharacteristic
193#442—1011no—
194#440—1011no—
195C4×SD16—1011no—
196C4×D8—1011no—
197#433—1011no—
198C22×D4C2×D10111yescharacteristic
199C2×SD16—1011no—
200C2×SD16—1011no—
201C2×D8C2×D10111yescharacteristic
202C2×D8C2×D10111yescharacteristic
203C4⋊Q8—1011no—
204#126—2021no—
205#124—1011no—
206#124—2021no—
207#123—2021no—
208C22⋊Q8—1011no—
209C22⋊Q8—2021no—
210#121C2×D10111yescharacteristic
211C4×Q8—1011no—
212C4×D4—1011no—
213C4×D4—1011no—
214C4×D4—1011no—
215C4×D4—1011no—
216C4×D4—1011no—
217C4×D4—2021no—
218C4×D4—2021no—
219#117—1011no—
220#117—1011no—
221C2×C22⋊C4—2021no—
222C2×C22⋊C4—2021no—
223#107—1011no—
224#107—1011no—
225#106—1011no—
226#106—1011no—
227C4⋊C8—1011no—
228C4⋊C8—1011no—
229#103—1011no—
230#103—1011no—
231#102—1011no—
232#102—1011no—
233#102—1011no—
234#102—1011no—
235#102C2×D10111yescharacteristic
236#102C2×D10111yescharacteristic
237C22⋊C8—1011no—
238C22⋊C8C2×D10111yescharacteristic
239#97—1011no—
240C4×C8—1011no—
241C24—21no—
242C2×Q8—1011no—
243C2×Q8—2021no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4C22×D10111yescharacteristic
249C2×D4C22×D10111yescharacteristic
250C2×D4C22×D10111yescharacteristic
251C22×C4—2021no—
252C22×C4—2021no—
253C22×C4—2021no—
254C22×C4—2021no—
255C22×C4—2021no—
256C22×C4C22×D10111yescharacteristic
257SD16—2022no—
258SD16—2022no—
259D8—22no—
260D8—22no—
261C2×C8—1011no—
262C2×C8—1011no—
263C2×C8C22×D10111yescharacteristic
264C2×C8C22×D10111yescharacteristic
265C4⋊C4—1011no—
266C4⋊C4—1011no—
267C4⋊C4—1011no—
268C4⋊C4—1011no—
269C4⋊C4—1011no—
270C4⋊C4—2021no—
271C4⋊C4—2021no—
272C4⋊C4—2021no—
273C4⋊C4C22×D10111yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—1011no—
276C22⋊C4—1011no—
277C22⋊C4—2021no—
278C22⋊C4—2021no—
279C22⋊C4—2021no—
280C22⋊C4—2021no—
281C22⋊C4—2021no—
282C22⋊C4—2021no—
283C22⋊C4—2021no—
284C22⋊C4—2021no—
285C22⋊C4—2021no—
286C42—1011no—
287C42—1011no—
288C42—2021no—
289C42—2021no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—81no—
295C23—81no—
296C23D4×D10111yescharacteristic
297Q8—8081no—
298Q8—2021no—
299Q8—2021no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—81no—
306D4#1310807312yes—
307D4#1310807312yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—8081no—
312C2×C4—8081no—
313C2×C4—8081no—
314C2×C4—8081no—
315C2×C4—8081no—
316C2×C4—1011no—
317C2×C4—1011no—
318C2×C4—1011no—
319C2×C4—1011no—
320C2×C4—2021no—
321C2×C4—2021no—
322C2×C4—2021no—
323C2×C4—2021no—
324C2×C4D4×D10111yescharacteristic
325C2×C4C23×D10111yescharacteristic
326C8—21no—
327C8—21no—
328C8—2021no—
329C8—2021no—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—22no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—84no—
343C22C2×D4×D10111yescharacteristic
344C4—21no—
345C4—41no—
346C4—4041no—
347C4—4041no—
348C4—4041no—
349C4—4041no—
350C4—2021no—
351C4—2021no—
352C4—2021no—
353C4—2021no—
354C4C2×#1310807311yescharacteristic
355C4C2×#1310807311yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—81no—
360C2#2026568311yescharacteristic
361C2#2026597811yescharacteristic
362C2#2026598711yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting, prime radical#447×C101C2
socleC22×C101C22×D4
hypercenter#447D101
hypocenterC101#3118
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. #20265794C2semidirect
2. #20265652C2semidirect
3. #20265519C2semidirect
4. #20265498C2semidirect
5. #20265465C2semidirect
6. #20265455C2semidirect
7. #20265390C2semidirect
8. #20265390C2semidirect
9. #20265328C2semidirect
10. #20265289C2semidirect
11. #20265274C2semidirect
12. #20265268C2semidirect
13. D8×Dic101C2semidirect
14. #20265235C2semidirect
18. #15692254C22semidirect
21. #15692242C22semidirect
25. #15692220C22semidirect
32. D4×Dic101C22semidirect
37. #15692189C22semidirect
38. #15692188C22semidirect
39. #15692187C22semidirect
40. #15692186C22semidirect
41. #15692184C22semidirect
42. #15692184C22semidirect
43. #15692180C22semidirect
44. #15692180C22semidirect
47. #15692176C22semidirect
48. #15692176C22semidirect
50. #15692165C22semidirect
51. C8×Dic101C22semidirect
182. C101#3118semidirect

Maximal subgroups

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

subgroupindex
#202657942
#202656522
#202655192
#202654982
#202654652
#202654552
#202653902
#202653282
#202652892
#202652742
#202652682
D8×Dic1012
#202652352
#447×C1012
#3118101