Finite Group Databasebeta

← #28400759

Subgroups — #28400759

Order 14464.

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#20299221C211yesmaximal, characteristic, complemented
2#20299073C211yesmaximal, characteristic, complemented
3#20298936C211yesmaximal, characteristic, complemented
4#20298923C211yesmaximal, characteristic, complemented
5#20298886C211yesmaximal, characteristic, complemented
6#20298876C211yesmaximal, characteristic, complemented
7#20298815C211yesmaximal, characteristic, complemented
8#20298815C211yesmaximal, characteristic, complemented
9#20298732C211yesmaximal, characteristic
10#20298707C211yesmaximal, characteristic, complemented
11#20298699C211yesmaximal, characteristic, complemented
12SD16×Dic113C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#450×C113C211yesmaximal, characteristic, complemented
16C2×#14268632C2211yescharacteristic
17C2×#14268632C2211yescharacteristic
18#16813621C2211yescharacteristic, complemented
19#16813617—21no—
20#16813611C2211yescharacteristic, complemented
21#16813608—21no—
22#16813604—21no—
23#16813602—21no—
24#16813596C2211yescharacteristic
25Q8×Dic113C2211yescharacteristic, complemented
26D4×Dic113—21no—
27D4×Dic113—21no—
28D4×Dic113C2211yescharacteristic
29D4×Dic113C2211yescharacteristic
30D4×Dic113C2211yescharacteristic
31D4×Dic113C2211yescharacteristic
32#16813584C2211yescharacteristic, complemented
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#16813546C2211yescharacteristic, complemented
44#16813546C2211yescharacteristic, complemented
45#16813544C2211yescharacteristic, complemented
46#16813544C2211yescharacteristic, 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×Dic226—21no—
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
62C22×Dic113—21no—
63C22×Dic113—21no—
64C22×Dic113—21no—
65C22×Dic113—21no—
66C2×C4×D113—21no—
67#14268632—22no—
68#14268632—22no—
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C4⋊Dic113—21no—
72C4⋊Dic113D411yescharacteristic
73C4⋊Dic113D411yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77#14268626—21no—
78C22⋊Dic113—21no—
79C22⋊Dic113—21no—
80C22⋊Dic113—21no—
81C22⋊Dic113—21no—
82C22⋊Dic113—21no—
83C22⋊Dic113D411yescharacteristic
84C22⋊Dic113D411yescharacteristic
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—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
114C22×D113—21no—
115Q8×C113—21no—
116Q8×C113—21no—
117D4×C113—24no—
118D4×C113—21no—
119D4×C113—21no—
120D4×C113#4112yes—
121D4×C113#4112yes—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—81no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—81no—
133C2×Dic113—81no—
134C2×Dic113—81no—
135C2×Dic113—81no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139C2×Dic113C2×D411yescharacteristic
140D452—21no—
141D452—21no—
142C4×D113—81no—
143Dic226—81no—
144C8×C113—21no—
145C8×C113—21no—
146#11744751—21no—
147#11744751—21no—
148C22×C113—21no—
149C22×C113—22no—
150C22×C113—22no—
151C22×C113—21no—
152C22×C113—21no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113—84no—
158C22×C113C22×D411yescharacteristic
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—41no—
162C4×C113—21no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113C2×#4111yescharacteristic
166C4×C113C2×#4111yescharacteristic
167Dic113—21no—
168Dic113—21no—
169Dic113—21no—
170Dic113—21no—
171Dic113—41no—
172Dic113—41no—
173Dic113—41no—
174C2×C113—41no—
175C2×C113—42no—
176C2×C113—42no—
177C2×C113#52511yescharacteristic
178C2×C113#57611yescharacteristic
179C2×C113#57711yescharacteristic
180D113—81no—
181#3118—1131nomaximal, Sylow
182C113#311811yescharacteristic, complemented, Sylow
183#542—1131no—
184#518—1131no—
185#485—1131no—
186#482—1131no—
187#476—1131no—
188#474—1131no—
189#463—1131no—
190#463—1131no—
191#450D11311yescharacteristic, complemented
192#447—1131no—
193#442—1131no—
194#440—1131no—
195C4×SD16—1131no—
196C4×D8—1131no—
197#433—1131no—
198C22×D4C2×D11311yescharacteristic
199C2×SD16C2×D11311yescharacteristic
200C2×SD16C2×D11311yescharacteristic
201C2×D8—1131no—
202C2×D8—1131no—
203C4⋊Q8—1131no—
204#126—2261no—
205#124—1131no—
206#124—2261no—
207#123—2261no—
208C22⋊Q8—2261no—
209C22⋊Q8C2×D11311yescharacteristic
210#121—1131no—
211C4×Q8—1131no—
212C4×D4—1131no—
213C4×D4—1131no—
214C4×D4—1131no—
215C4×D4—1131no—
216C4×D4—1131no—
217C4×D4—2261no—
218C4×D4—2261no—
219#117—1131no—
220#117—1131no—
221C2×C22⋊C4—2261no—
222C2×C22⋊C4—2261no—
223#107—1131no—
224#107—1131no—
225#106—1131no—
226#106—1131no—
227C4⋊C8—1131no—
228C4⋊C8—1131no—
229#103—1131no—
230#103—1131no—
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235#102C2×D11311yescharacteristic
236#102C2×D11311yescharacteristic
237C22⋊C8—1131no—
238C22⋊C8C2×D11311yescharacteristic
239#97—1131no—
240C4×C8—1131no—
241C24—21no—
242C2×Q8—2261no—
243C2×Q8C22×D11311yescharacteristic
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—1131no—
248C2×D4—2261no—
249C2×D4C22×D11311yescharacteristic
250C2×D4C22×D11311yescharacteristic
251C22×C4—2261no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4C22×D11311yescharacteristic
257SD16—22no—
258SD16—22no—
259D8—2262no—
260D8—2262no—
261C2×C8—1131no—
262C2×C8—1131no—
263C2×C8C22×D11311yescharacteristic
264C2×C8C22×D11311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—1131no—
270C4⋊C4—1131no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4C22×D11311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—1131no—
276C22⋊C4—1131no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—1131no—
287C42—1131no—
288C42—2261no—
289C42—2261no—
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—2261no—
296C23D4×D11311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—9041no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—9041no—
304D4—2261no—
305D4—2261no—
306D4#1426864612yes—
307D4#1426864612yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—1131no—
313C2×C4—1131no—
314C2×C4—1131no—
315C2×C4—1131no—
316C2×C4—9041no—
317C2×C4—9041no—
318C2×C4—9041no—
319C2×C4—9041no—
320C2×C4—9041no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4D4×D11311yescharacteristic
325C2×C4C23×D11311yescharacteristic
326C8—21no—
327C8—21no—
328C8—2261no—
329C8—2261no—
330C22—21no—
331C22—22no—
332C22—22no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—84no—
340C22—4521no—
341C22—4521no—
342C22—4521no—
343C22C2×D4×D11311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—4521no—
348C4—4521no—
349C4—4521no—
350C4—2261no—
351C4—2261no—
352C4—2261no—
353C4—2261no—
354C4C2×#1426864611yescharacteristic
355C4C2×#1426864611yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—9041no—
360C2#2029910411yescharacteristic
361C2#2029940211yescharacteristic
362C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#450×C113C2
socleC22×C113C22×D4
prime radical#20298732C2
hypercenter#450D113
hypocenterC113#3118
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. #20299221C2semidirect
2. #20299073C2semidirect
3. #20298936C2semidirect
4. #20298923C2semidirect
5. #20298886C2semidirect
6. #20298876C2semidirect
7. #20298815C2semidirect
8. #20298815C2semidirect
10. #20298707C2semidirect
11. #20298699C2semidirect
12. SD16×Dic113C2semidirect
13. #20298678C2semidirect
14. #20298656C2semidirect
15. #450×C113C2semidirect
18. #16813621C22semidirect
20. #16813611C22semidirect
25. Q8×Dic113C22semidirect
32. #16813584C22semidirect
37. #16813556C22semidirect
38. #16813555C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813551C22semidirect
43. #16813546C22semidirect
44. #16813546C22semidirect
45. #16813544C22semidirect
46. #16813544C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
182. C113#3118semidirect
191. #450D113semidirect

Maximal subgroups

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

subgroupindex
#202992212
#202990732
#202989362
#202989232
#202988862
#202988762
#202988152
#202987322
#202987072
#202986992
SD16×Dic1132
#202986782
#202986562
#450×C1132
#3118113