Finite Group Databasebeta

← #28400758

Subgroups — #28400758

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#20299219C211yesmaximal, characteristic, complemented
2#20298939C211yesmaximal, characteristic, complemented
3#20298922C211yesmaximal, characteristic, complemented
4#20298888C211yesmaximal, characteristic, complemented
5#20298878C211yesmaximal, characteristic, complemented
6#20298813C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298749C211yesmaximal, characteristic, complemented
9#20298732C211yesmaximal, characteristic
10#20298708C211yesmaximal, characteristic, complemented
11#20298698C211yesmaximal, characteristic, complemented
12C4×#14268635C211yesmaximal, characteristic, complemented
13C4×#14268632C211yesmaximal, characteristic, complemented
14#20298659C211yesmaximal, characteristic, complemented
15#518×C113C211yesmaximal, characteristic, complemented
16C2×#14268635C2211yescharacteristic
17C2×#14268635C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20#16813622C2211yescharacteristic, complemented
21#16813617—21no—
22#16813610C2211yescharacteristic, complemented
23#16813608—21no—
24#16813604—21no—
25#16813601C2211yescharacteristic
26#16813600—21no—
27#16813596C2211yescharacteristic
28C4×Dic226C2211yescharacteristic, complemented
29C4×D452C2211yescharacteristic, complemented
30#16813555C2211yescharacteristic, complemented
31#16813555C2211yescharacteristic, complemented
32#16813553C2211yescharacteristic, complemented
33#16813553C2211yescharacteristic, complemented
34C4⋊#11744751C2211yescharacteristic, complemented
35C4⋊#11744751C2211yescharacteristic, complemented
36#16813545C2211yescharacteristic, complemented
37#16813545C2211yescharacteristic, complemented
38#16813543C2211yescharacteristic
39#16813543C2211yescharacteristic
40#16813543C2211yescharacteristic
41#16813543C2211yescharacteristic
42#16813542C2211yescharacteristic, complemented
43#16813542C2211yescharacteristic, complemented
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46#16813533C2211yescharacteristic, complemented
47C4×#11744751C2211yescharacteristic, complemented
48C22×D4×C113C2211yescharacteristic
49C4×D4×C113—21no—
50C4×D4×C113—21no—
51C4×D4×C113C2211yescharacteristic
52C4×D4×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54C4×D4×C113C2211yescharacteristic
55#117×C113C2211yescharacteristic
56#117×C113C2211yescharacteristic
57C2×C22⋊C4×C113—21no—
58C2×C22⋊C4×C113—21no—
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×D452C2311yescharacteristic
62C2×C22⋊D113—21no—
63C2×C4×D113—21no—
64#14268635—22no—
65#14268635—22no—
66#14268632—22no—
67#14268632—22no—
68C2×#11744751C2311yescharacteristic
69C2×#11744751C2311yescharacteristic
70C2×#11744751C2311yescharacteristic
71C2×#11744751C2311yescharacteristic
72C4⋊Dic113—21no—
73C4⋊Dic113C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75#14268626—21no—
76#14268626—21no—
77C22⋊Dic113—21no—
78#14268624—21no—
79#14268624—21no—
80#14268624—21no—
81#14268624—21no—
82C4×Dic113—21no—
83C24×C113—21no—
84C2×D4×C113—22no—
85C2×D4×C113—22no—
86C2×D4×C113—21no—
87C2×D4×C113C2311yescharacteristic
88C2×D4×C113C2311yescharacteristic
89C22×C4×C113—21no—
90C22×C4×C113—21no—
91C22×C4×C113—21no—
92C22×C4×C113—21no—
93C22×C4×C113C2311yescharacteristic
94C4⋊C4×C113D411yescharacteristic
95C4⋊C4×C113D411yescharacteristic
96C4⋊C4×C113C2311yescharacteristic
97C4⋊C4×C113C2311yescharacteristic
98C22⋊C4×C113—21no—
99C22⋊C4×C113—21no—
100C22⋊C4×C113—21no—
101C22⋊C4×C113—21no—
102C22⋊C4×C113—21no—
103C22⋊C4×C113D411yescharacteristic
104C22⋊C4×C113D411yescharacteristic
105C42×C113—21no—
106C42×C113C2311yescharacteristic
107C42×C113C2311yescharacteristic
108C23×C113—24no—
109C23×C113—21no—
110C23×C113—21no—
111C23×C113—81no—
112C23×C113—81no—
113C23×C113C2×D411yescharacteristic
114C22×D113—21no—
115D4×C113—24no—
116D4×C113—21no—
117D4×C113—21no—
118D4×C113#4112yes—
119D4×C113#4112yes—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—81no—
125C2×C4×C113—81no—
126C2×C4×C113—81no—
127C2×C4×C113—81no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2×D411yescharacteristic
131C2×C4×C113C2×D411yescharacteristic
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2411yescharacteristic
134C22⋊D113—81no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138D452—21no—
139D452—21no—
140C4×D113—81no—
141Dic226—21no—
142Dic226—21no—
143Dic226—81no—
144#11744751—21no—
145#11744751—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—21no—
164C4×C113—21no—
165C4×C113—21no—
166C4×C113—21no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113C2×#4111yescharacteristic
170C4×C113C2×#4111yescharacteristic
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#518D11311yescharacteristic, complemented
185#485—1131no—
186#482—1131no—
187#476—1131no—
188#474—1131no—
189#463—1131no—
190#463—1131no—
191#450—1131no—
192#447—1131no—
193#442—1131no—
194#440—1131no—
195C4×SD16—1131no—
196C4×D8—1131no—
197#433—1131no—
198C22×D4C2×D11311yescharacteristic
199C2×SD16—1131no—
200C2×SD16—1131no—
201C2×D8—1131no—
202C2×D8—1131no—
203C4⋊Q8—1131no—
204#126—2261no—
205#124—1131no—
206#124—2261no—
207#123—2261no—
208C22⋊Q8—1131no—
209C22⋊Q8—2261no—
210#121—1131no—
211C4×Q8—1131no—
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—1131no—
215C4×D4C2×D11311yescharacteristic
216C4×D4C2×D11311yescharacteristic
217C4×D4C2×D11311yescharacteristic
218C4×D4C2×D11311yescharacteristic
219#117C2×D11311yescharacteristic
220#117C2×D11311yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
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#102—1131no—
236#102—1131no—
237C22⋊C8—1131no—
238C22⋊C8—1131no—
239#97—1131no—
240C4×C8—1131no—
241C24—21no—
242C2×Q8—1131no—
243C2×Q8—2261no—
244C2×D4—22no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—1131no—
248C2×D4—2261no—
249C2×D4C22×D11311yescharacteristic
250C2×D4C22×D11311yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2261no—
256C22×C4C22×D11311yescharacteristic
257SD16—2262no—
258SD16—2262no—
259D8—2262no—
260D8—2262no—
261C2×C8—1131no—
262C2×C8—1131no—
263C2×C8—1131no—
264C2×C8—1131no—
265C4⋊C4—1131no—
266C4⋊C4—1131no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4C22⋊D11311yescharacteristic
271C4⋊C4C22⋊D11311yescharacteristic
272C4⋊C4C22×D11311yescharacteristic
273C4⋊C4C22×D11311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4C22⋊D11311yescharacteristic
285C22⋊C4C22⋊D11311yescharacteristic
286C42—21no—
287C42—2261no—
288C42C22×D11311yescharacteristic
289C42C22×D11311yescharacteristic
290C23—24no—
291C23—21no—
292C23—21no—
293C23—81no—
294C23—81no—
295C23—2261no—
296C23C2×C22⋊D11311yescharacteristic
297Q8—9041no—
298Q8—2261no—
299Q8—2261no—
300D4—24no—
301D4—21no—
302D4—21no—
303D4—9041no—
304D4—2261no—
305D4—2261no—
306D4#1426864712yes—
307D4#1426864712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—9041no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4C2×C22⋊D11311yescharacteristic
321C2×C4C2×C22⋊D11311yescharacteristic
322C2×C4C2×C22⋊D11311yescharacteristic
323C2×C4C2×C22⋊D11311yescharacteristic
324C2×C4C2×C22⋊D11311yescharacteristic
325C2×C4C23×D11311yescharacteristic
326C8—2261no—
327C8—2261no—
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—
343C22C22×C22⋊D11311yescharacteristic
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—41no—
350C4—41no—
351C4—4521no—
352C4—4521no—
353C4—4521no—
354C4C2×#1426864711yescharacteristic
355C4C2×#1426864711yescharacteristic
356C2—41no—
357C2—42no—
358C2—42no—
359C2—9041no—
360C2#2029910911yescharacteristic
361C2#2029940111yescharacteristic
362C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#518×C113C2
socleC22×C113C22×D4
prime radical#20298732C2
hypercenter#518D113
hypocenterC113#3118
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #20299219C2semidirect
2. #20298939C2semidirect
3. #20298922C2semidirect
4. #20298888C2semidirect
5. #20298878C2semidirect
6. #20298813C2semidirect
7. #20298813C2semidirect
8. #20298749C2semidirect
10. #20298708C2semidirect
11. #20298698C2semidirect
12. C4×#14268635C2semidirect
13. C4×#14268632C2semidirect
14. #20298659C2semidirect
15. #518×C113C2semidirect
20. #16813622C22semidirect
22. #16813610C22semidirect
28. C4×Dic226C22semidirect
29. C4×D452C22semidirect
30. #16813555C22semidirect
31. #16813555C22semidirect
32. #16813553C22semidirect
33. #16813553C22semidirect
34. C4⋊#11744751C22semidirect
35. C4⋊#11744751C22semidirect
36. #16813545C22semidirect
37. #16813545C22semidirect
42. #16813542C22semidirect
43. #16813542C22semidirect
46. #16813533C22semidirect
47. C4×#11744751C22semidirect
182. C113#3118semidirect
184. #518D113semidirect

Maximal subgroups

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

subgroupindex
#202992192
#202989392
#202989222
#202988882
#202988782
#202988132
#202987492
#202987322
#202987082
#202986982
C4×#142686352
C4×#142686322
#202986592
#518×C1132
#3118113