Finite Group Databasebeta

← #28400820

Subgroups — #28400820

Order 14464.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299208C211yesmaximal, characteristic, complemented
2#20299073C211yesmaximal, characteristic
3#20298940C211yesmaximal, characteristic, complemented
4#20298936C211yesmaximal, characteristic, complemented
5#20298900C211yesmaximal, characteristic, complemented
6#20298896C211yesmaximal, characteristic, complemented
7#20298801C211yesmaximal, characteristic, complemented
8#20298801C211yesmaximal, characteristic, complemented
9#20298749C211yesmaximal, characteristic
10#20298699C211yesmaximal, characteristic, complemented
11#20298695C211yesmaximal, characteristic, complemented
12#20298689C211yesmaximal, characteristic, complemented
13SD16×Dic113C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#450×C113C211yesmaximal, characteristic
16C2×#14268635C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18#16813620C2211yescharacteristic, complemented
19#16813615—21no—
20#16813615—21no—
21#16813613—21no—
22#16813613C2211yescharacteristic, complemented
23#16813612—21no—
24#16813601C2211yescharacteristic
25Q8×Dic113C2211yescharacteristic, complemented
26#16813587C2211yescharacteristic, complemented
27D4×Dic113—21no—
28D4×Dic113—21no—
29D4×Dic113C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31D4×Dic113C2211yescharacteristic
32D4×Dic113C2211yescharacteristic
33#16813581C2211yescharacteristic
34#16813581C2211yescharacteristic
35C2×C22⋊Dic113—21no—
36C2×C22⋊Dic113—21no—
37#16813556C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813551C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813546C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic
54C2×SD16×C113C2211yescharacteristic
55C22⋊Q8×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59C2×Dic226C2311yescharacteristic
60C22×Dic113—21no—
61C22×Dic113—21no—
62C22×Dic113—21no—
63C22×Dic113—21no—
64#14268635—22no—
65#14268635—22no—
66C2×#11744751C2311yescharacteristic
67C2×#11744751C2311yescharacteristic
68C4⋊Dic113—21no—
69C4⋊Dic113—21no—
70C4⋊Dic113D411yescharacteristic
71C4⋊Dic113D411yescharacteristic
72C4⋊Dic113C2311yescharacteristic
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77#14268626—21no—
78#14268626—21no—
79#14268626—21no—
80C22⋊Dic113—21no—
81C22⋊Dic113—21no—
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113D411yescharacteristic
87C22⋊Dic113D411yescharacteristic
88C4×Dic113—21no—
89C4×Dic113—21no—
90C4×Dic113—21no—
91C4×Dic113C2311yescharacteristic
92C4×Dic113C2311yescharacteristic
93C24×C113—21no—
94C2×Q8×C113C2311yescharacteristic
95C2×D4×C113—22no—
96C2×D4×C113—22no—
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C2×D4×C113C2311yescharacteristic
100C22×C4×C113C2311yescharacteristic
101SD16×C113—22no—
102SD16×C113—22no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113—21no—
106C4⋊C4×C113C2311yescharacteristic
107C22⋊C4×C113—21no—
108C23×C113—24no—
109C23×C113—21no—
110C23×C113—21no—
111C23×C113—81no—
112C23×C113—81no—
113C23×C113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116D4×C113—24no—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113#4112yes—
120D4×C113#4112yes—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—81no—
132C2×Dic113—81no—
133C2×Dic113—81no—
134C2×Dic113—81no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139Dic226—21no—
140Dic226—21no—
141C8×C113—21no—
142C8×C113—21no—
143#11744751—21no—
144#11744751—21no—
145C22×C113—21no—
146C22×C113—22no—
147C22×C113—22no—
148C22×C113—21no—
149C22×C113—21no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113—84no—
155C22×C113C22×D411yescharacteristic
156C4×C113—21no—
157C4×C113—41no—
158C4×C113—41no—
159C4×C113C2×#4111yescharacteristic
160C4×C113C2×#4111yescharacteristic
161Dic113—21no—
162Dic113—21no—
163Dic113—21no—
164Dic113—21no—
165Dic113—41no—
166Dic113—41no—
167Dic113—41no—
168Dic113—41no—
169C2×C113—41no—
170C2×C113—42no—
171C2×C113—42no—
172C2×C113#52511yescharacteristic
173C2×C113#57711yescharacteristic
174C2×C113#57711yescharacteristic
175#3123—1131nomaximal, Sylow
176C113#312311yescharacteristic, complemented, Sylow
177#541—1131no—
178#518—1131no—
179#485—1131no—
180#485—1131no—
181#478—1131no—
182#478—1131no—
183#461—1131no—
184#461—1131no—
185#450—1131no—
186#450D11311yescharacteristic
187#440—1131no—
188#440—1131no—
189C4×SD16—1131no—
190C4×SD16—1131no—
191#433—1131no—
192C22×D4C2×D11311yescharacteristic
193C2×SD16—1131no—
194C2×SD16—1131no—
195C2×SD16C2×D11311yescharacteristic
196C2×SD16C2×D11311yescharacteristic
197C4⋊Q8—1131no—
198#126—2261no—
199#126—2261no—
200#125—1131no—
201#125—2261no—
202#125—2261no—
203C22⋊Q8—1131no—
204C22⋊Q8C2×D11311yescharacteristic
205C4×Q8—1131no—
206C4×Q8—1131no—
207C4×D4—1131no—
208C4×D4—1131no—
209C4×D4—1131no—
210C4×D4—1131no—
211C4×D4—2261no—
212C4×D4—2261no—
213#117—1131no—
214#117—1131no—
215C2×C22⋊C4—2261no—
216C2×C22⋊C4—2261no—
217#107—1131no—
218#107—1131no—
219#106—1131no—
220#106—1131no—
221C4⋊C8—1131no—
222C4⋊C8—1131no—
223#103—1131no—
224#103—1131no—
225#103—1131no—
226#103—1131no—
227#102—1131no—
228#102—1131no—
229#102C2×D11311yescharacteristic
230#102C2×D11311yescharacteristic
231C22⋊C8—1131no—
232C22⋊C8C2×D11311yescharacteristic
233#97—1131no—
234C4×C8—1131no—
235C24—21no—
236C2×Q8—1131no—
237C2×Q8C22×D11311yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4C22×D11311yescharacteristic
242C2×D4C22×D11311yescharacteristic
243C22×C4—2261no—
244C22×C4—2261no—
245C22×C4—2261no—
246C22×C4—2261no—
247C22×C4C22×D11311yescharacteristic
248SD16—22no—
249SD16—22no—
250SD16—2262no—
251SD16—2262no—
252C2×C8—1131no—
253C2×C8—1131no—
254C2×C8C22×D11311yescharacteristic
255C2×C8C22×D11311yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—1131no—
258C4⋊C4—1131no—
259C4⋊C4—1131no—
260C4⋊C4—1131no—
261C4⋊C4—1131no—
262C4⋊C4—2261no—
263C4⋊C4—2261no—
264C4⋊C4—2261no—
265C4⋊C4—2261no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4C22×D11311yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—1131no—
272C22⋊C4—1131no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C42—1131no—
280C42—1131no—
281C42—2261no—
282C42—2261no—
283C42—2261no—
284C23—24no—
285C23—21no—
286C23—21no—
287C23—81no—
288C23—81no—
289C23D4×D11311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—2261no—
293Q8—2261no—
294D4—24no—
295D4—21no—
296D4—21no—
297D4#1426864612yes—
298D4#1426864612yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—1131no—
304C2×C4—1131no—
305C2×C4—1131no—
306C2×C4—1131no—
307C2×C4—9041no—
308C2×C4—9041no—
309C2×C4—9041no—
310C2×C4—9041no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4D4×D11311yescharacteristic
316C2×C4C23×D11311yescharacteristic
317C8—21no—
318C8—21no—
319C8—2261no—
320C8—2261no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—84no—
331C22C2×D4×D11311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—4521no—
336C4—4521no—
337C4—4521no—
338C4—4521no—
339C4—2261no—
340C4—2261no—
341C4—2261no—
342C4—2261no—
343C4C2×#1426864611yescharacteristic
344C4C2×#1426864611yescharacteristic
345C2—41no—
346C2—42no—
347C2—42no—
348C2#2029910411yescharacteristic
349C2#2029940411yescharacteristic
350C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
prime radicalC22×D4×C113C22
hypercenter#450D113
hypocenterC113#3123
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #20299208C2semidirect
3. #20298940C2semidirect
4. #20298936C2semidirect
5. #20298900C2semidirect
6. #20298896C2semidirect
7. #20298801C2semidirect
8. #20298801C2semidirect
10. #20298699C2semidirect
11. #20298695C2semidirect
12. #20298689C2semidirect
13. SD16×Dic113C2semidirect
14. #20298656C2semidirect
18. #16813620C22semidirect
22. #16813613C22semidirect
25. Q8×Dic113C22semidirect
26. #16813587C22semidirect
37. #16813556C22semidirect
38. #16813555C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813551C22semidirect
43. #16813547C22semidirect
44. #16813547C22semidirect
45. #16813546C22semidirect
46. #16813546C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
176. C113#3123semidirect

Maximal subgroups

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

subgroupindex
#202992082
#202990732
#202989402
#202989362
#202989002
#202988962
#202988012
#202987492
#202986992
#202986952
#202986892
SD16×Dic1132
#202986562
#450×C1132
#3123113