Finite Group Databasebeta

← #27182977

Subgroups — #27182977

Order 12928.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265874C211yesmaximal, characteristic, complemented
2#20265824C211yesmaximal, characteristic, complemented
3#20265530C211yesmaximal, characteristic, complemented
4#20265514C211yesmaximal, characteristic, complemented
5#20265498C211yesmaximal, characteristic, complemented
6#20265480C211yesmaximal, characteristic, complemented
7#20265405C211yesmaximal, characteristic, complemented
8#20265390C211yesmaximal, characteristic, complemented
9#20265320C211yesmaximal, characteristic, complemented
10#20265309C211yesmaximal, characteristic, complemented
11#20265257C211yesmaximal, characteristic, complemented
12C8×C22⋊D101C211yesmaximal, characteristic, complemented
13#20265174C211yesmaximal, characteristic, complemented
14#102×D101C211yesmaximal, characteristic, complemented
15#466×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×D4×D101C2211yescharacteristic
18C2×#13108062C2211yescharacteristic, complemented
19C2×#13108059C2211yescharacteristic
20C2×C8×D101C2211yescharacteristic
21#15692248—21no—
22#15692246C2211yescharacteristic, complemented
23#15692242C2211yescharacteristic
24#15692237—21no—
25#15692236—21no—
26#15692235C2211yescharacteristic
27#15692226—21no—
28#15692226—21no—
29#15692226C2211yescharacteristic
30#15692223—21no—
31D4×Dic101C2211yescharacteristic, complemented
32#15692217C2211yescharacteristic
33C4×C22⋊D101C2211yescharacteristic
34#15692215—21no—
35#15692214C2211yescharacteristic, complemented
36C4⋊C4×D101C2211yescharacteristic
37C22⋊C4×D101—21no—
38#15692188C2211yescharacteristic, complemented
39#15692186C2211yescharacteristic, complemented
40#15692184C2211yescharacteristic, complemented
41#15692180C2211yescharacteristic, complemented
42#15692180C2211yescharacteristic, complemented
43#15692178C2211yescharacteristic, complemented
44#15692177C2211yescharacteristic
45#15692177C2211yescharacteristic
46#15692176C2211yescharacteristic
47#15692176C2211yescharacteristic
48#15692175C2211yescharacteristic
49C22⋊#11717579C2211yescharacteristic, complemented
50#15692167C2211yescharacteristic
51C8×Dic101C2211yescharacteristic, complemented
52C2×D8×C101C2211yescharacteristic
53C22×C8×C101C2211yescharacteristic, complemented
54#121×C101C2211yescharacteristic
55#121×C101C2211yescharacteristic, complemented
56#107×C101C2211yescharacteristic, complemented
57#102×C101C2211yescharacteristic
58#102×C101C2211yescharacteristic, complemented
59C23×D101—21no—
60#13108074—22no—
61#13108074—41no—
62C2×Dic202C2311yescharacteristic
63C2×D404C2311yescharacteristic
64C2×C22⋊D101—21no—
65C2×C22⋊D101—21no—
66C2×C22⋊D101—21no—
67C2×C22⋊D101D411yescharacteristic
68D4×D101—22no—
69D4×D101—41no—
70C22×Dic101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101—21no—
74C2×C4×D101C2311yescharacteristic
75#13108062—41no—
76#13108059—22no—
77C2×#11717579C2311yescharacteristic
78C2×#11717579C2311yescharacteristic
79C8×D101—41no—
80C4⋊Dic101—21no—
81C4⋊Dic101—21no—
82C4⋊Dic101C2311yescharacteristic
83C4⋊Dic101C2311yescharacteristic
84#13108053—21no—
85#13108053—21no—
86#13108053D411yescharacteristic
87C22⋊Dic101—21no—
88C22⋊Dic101—21no—
89C22⋊Dic101—21no—
90C22⋊Dic101—21no—
91C22⋊Dic101—21no—
92C22⋊Dic101D411yescharacteristic
93#13108051—21no—
94#13108051—21no—
95#13108051D411yescharacteristic
96C4×Dic101—21no—
97C4×Dic101C2311yescharacteristic
98C2×D4×C101—21no—
99C2×D4×C101—21no—
100C2×D4×C101C2311yescharacteristic
101C2×D4×C101C2311yescharacteristic
102C22×C4×C101C2311yescharacteristic
103D8×C101—41no—
104C2×C8×C101—41no—
105C2×C8×C101C2311yescharacteristic
106C2×C8×C101C2311yescharacteristic
107C4⋊C4×C101C2311yescharacteristic
108C4⋊C4×C101C2311yescharacteristic
109C22⋊C4×C101—21no—
110C22⋊C4×C101—21no—
111C23×C101—21no—
112C23×C101—21no—
113C23×C101C2×D411yescharacteristic
114C22×D101—21no—
115C22×D101—42no—
116C22×D101—42no—
117C22×D101—81no—
118C22×D101C2×D411yescharacteristic
119D4×C101—21no—
120D4×C101—21no—
121D4×C101—21no—
122D4×C101—21no—
123D4×C101—81no—
124D4×C101—81no—
125C2×C4×C101—21no—
126C2×C4×C101—21no—
127C2×C4×C101—21no—
128C2×C4×C101—21no—
129C2×C4×C101C2×D411yescharacteristic
130C2×C4×C101C2411yescharacteristic
131C22⋊D101—22no—
132C22⋊D101—42no—
133C22⋊D101—42no—
134C22⋊D101—42no—
135C2×Dic101—21no—
136C2×Dic101—21no—
137C2×Dic101—21no—
138C2×Dic101—81no—
139C2×Dic101C2×D411yescharacteristic
140C2×Dic101C2×D411yescharacteristic
141C2×Dic101C2×D411yescharacteristic
142D404—21no—
143D404#4112yes—
144C4×D101—21no—
145C4×D101—21no—
146C4×D101—42no—
147C4×D101—81no—
148C4×D101—81no—
149Dic202—21no—
150Dic202—21no—
151C8×C101—21no—
152C8×C101—21no—
153#11717579—21no—
154#11717579—21no—
155C22×C101—21no—
156C22×C101—21no—
157C22×C101—21no—
158C22×C101—41no—
159C22×C101—41no—
160C22×C101—41no—
161C22×C101—41no—
162C22×C101—41no—
163C22×C101—41no—
164C22×C101C22×D411yescharacteristic
165C2×D101—21no—
166C2×D101—21no—
167C2×D101—22no—
168C2×D101—41no—
169C2×D101—41no—
170C2×D101—84no—
171C2×D101#13512yes—
172C4×C101—21no—
173C4×C101—41no—
174C4×C101—41no—
175C4×C101C2×#4111yescharacteristic
176C4×C101H(5,𝔽2)11yescharacteristic
177Dic101—21no—
178Dic101—21no—
179Dic101—21no—
180Dic101—41no—
181Dic101—41no—
182Dic101—41no—
183C2×C101—41no—
184C2×C101—81no—
185C2×C101—81no—
186C2×C101#54611yescharacteristic
187C2×C101C2×#13511yescharacteristic
188C2×C101#57611yescharacteristic
189D101—22no—
190D101—42no—
191#3297—1011nomaximal, Sylow
192C101#329711yescharacteristic, complemented, Sylow
193#553—1011no—
194#546—1011no—
195#488—1011no—
196#484—1011no—
197#482—1011no—
198#478—1011no—
199#466D10111yescharacteristic, complemented
200#465—1011no—
201#463—1011no—
202#449—1011no—
203#447—1011no—
204C4×D8—1011no—
205C8×D4—1011no—
206#416—1011no—
207C2×#102—1011no—
208C2×#41—1011no—
209C22×D4—1011no—
210C2×SD16—1011no—
211C2×D8—1011no—
212C2×D8C2×D10111yescharacteristic
213C22×C8—1011no—
214C22×C8C2×D10111yescharacteristic, complemented
215#126—2021no—
216#125—1011no—
217#124—1011no—
218#123—2021no—
219#123—2021no—
220C22⋊Q8—1011no—
221#121—1011no—
222#121—2021no—
223#121—2021no—
224#121C2×D10111yescharacteristic
225#121C2×D10111yescharacteristic, complemented
226#120—2021no—
227C4×D4—1011no—
228C4×D4—1011no—
229C4×D4—1011no—
230C4×D4—2021no—
231#117—1011no—
232C2×C4⋊C4—1011no—
233C2×C22⋊C4—2021no—
234#107—1011no—
235#107C2×D10111yescharacteristic, complemented
236#106—1011no—
237C4⋊C8—1011no—
238#103—1011no—
239#103—1011no—
240#103—1011no—
241#102—1011no—
242#102—1011no—
243#102—1011no—
244#102—1011no—
245#102—1011no—
246#102C2×D10111yescharacteristic
247#102C2×D10111yescharacteristic, complemented
248C22⋊C8—1011no—
249C22⋊C8—1011no—
250C4×C8—1011no—
251C24—2021no—
252#41—4041no—
253#41—2022no—
254C2×Q8—1011no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—1011no—
258C2×D4—1011no—
259C2×D4—4041no—
260C2×D4—2021no—
261C2×D4—2022no—
262C2×D4—2021no—
263C2×D4—2021no—
264C2×D4C22×D10111yescharacteristic
265C2×D4C22×D10111yescharacteristic
266C22×C4—1011no—
267C22×C4—2021no—
268C22×C4—2021no—
269C22×C4—2021no—
270C22×C4—2021no—
271C22×C4C22×D10111yescharacteristic
272SD16—4041no—
273D8—41no—
274D8—2022no—
275C2×C8—41no—
276C2×C8—1011no—
277C2×C8—1011no—
278C2×C8—4041no—
279C2×C8C22×D10111yescharacteristic
280C2×C8C22×D10111yescharacteristic
281C4⋊C4—1011no—
282C4⋊C4—1011no—
283C4⋊C4—1011no—
284C4⋊C4—2021no—
285C4⋊C4—2021no—
286C4⋊C4—2021no—
287C4⋊C4—2021no—
288C4⋊C4C22×D10111yescharacteristic
289C4⋊C4C22×D10111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—1011no—
293C22⋊C4—1011no—
294C22⋊C4—2021no—
295C22⋊C4—2021no—
296C22⋊C4—2021no—
297C22⋊C4—2021no—
298C22⋊C4—2021no—
299C22⋊C4—2021no—
300C22⋊C4—2021no—
301C42—1011no—
302C42—2021no—
303C23—21no—
304C23—21no—
305C23—8081no—
306C23—1011no—
307C23—4042no—
308C23—4042no—
309C23—2021no—
310C23D4×D10111yescharacteristic
311Q8—2021no—
312Q8—2021no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—81no—
318D4—81no—
319D4—1012no—
320D4—4042no—
321D4—4042no—
322D4—4042no—
323D4—2022no—
324D4—2021no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—8081no—
330C2×C4—8081no—
331C2×C4—8081no—
332C2×C4—1011no—
333C2×C4—1011no—
334C2×C4—1011no—
335C2×C4—4042no—
336C2×C4—2021no—
337C2×C4—2021no—
338C2×C4—2021no—
339C2×C4—2021no—
340C2×C4—2021no—
341C2×C4D4×D10111yescharacteristic
342C2×C4C23×D10111yescharacteristic
343C8—21no—
344C8—21no—
345C8—2021no—
346C8—2021no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—8084no—
357C22—1012no—
358C22—4041no—
359C22—4041no—
360C22—2022no—
361C22—2021no—
362C22—2021no—
363C22C2×D4×D10111yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—4041no—
368C4—4041no—
369C4—4041no—
370C4—2021no—
371C4—2021no—
372C4—2021no—
373C4#41×D10111yescharacteristic
374C4#1569230011yescharacteristic
375C2—41no—
376C2—81no—
377C2—81no—
378C2—4042no—
379C2—2022no—
380C2#2026581611yescharacteristic
381C2#135×D10111yescharacteristic
382C2#2026597811yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#466×C101C2
socleC22×C101C22×D4
hypercenter#466D101
hypocenterC101#3297
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #20265874C2semidirect
2. #20265824C2semidirect
3. #20265530C2semidirect
4. #20265514C2semidirect
5. #20265498C2semidirect
6. #20265480C2semidirect
7. #20265405C2semidirect
8. #20265390C2semidirect
9. #20265320C2semidirect
10. #20265309C2semidirect
11. #20265257C2semidirect
12. C8×C22⋊D101C2semidirect
13. #20265174C2semidirect
14. #102×D101C2semidirect
15. #466×C101C2semidirect
18. C2×#13108062C22semidirect
22. #15692246C22semidirect
31. D4×Dic101C22semidirect
35. #15692214C22semidirect
38. #15692188C22semidirect
39. #15692186C22semidirect
40. #15692184C22semidirect
41. #15692180C22semidirect
42. #15692180C22semidirect
43. #15692178C22semidirect
49. C22⋊#11717579C22semidirect
51. C8×Dic101C22semidirect
53. C22×C8×C101C22semidirect
55. #121×C101C22semidirect
56. #107×C101C22semidirect
58. #102×C101C22semidirect
192. C101#3297semidirect
199. #466D101semidirect
214. C22×C8C2×D101semidirect
225. #121C2×D101semidirect
235. #107C2×D101semidirect
247. #102C2×D101semidirect

Maximal subgroups

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

subgroupindex
#202658742
#202658242
#202655302
#202655142
#202654982
#202654802
#202654052
#202653902
#202653202
#202653092
#202652572
C8×C22⋊D1012
#202651742
#102×D1012
#466×C1012
#3297101