Finite Group Databasebeta

← #28401666

Subgroups — #28401666

Order 14464.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299215C211yesmaximal, characteristic, complemented
2#20299162C211yesmaximal, characteristic, complemented
3#20298986C211yesmaximal, characteristic, complemented
4#20298979C211yesmaximal, characteristic, complemented
5#20298959C211yesmaximal, characteristic, complemented
6#20298943C211yesmaximal, characteristic, complemented
7#20298823C211yesmaximal, characteristic, complemented
8#20298815C211yesmaximal, characteristic, complemented
9#20298797C211yesmaximal, characteristic, complemented
10#20298791C211yesmaximal, characteristic, complemented
11#20298760C211yesmaximal, characteristic, complemented
12#20298751C211yesmaximal, characteristic, complemented
13#20298731C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic
17C2×#14268637C2211yescharacteristic, complemented
18C2×#14268636C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268635C2211yescharacteristic, complemented
21C2×#14268632C2211yescharacteristic
22C2×#14268632C2211yescharacteristic
23#16813621C2211yescharacteristic, complemented
24#16813618C2211yescharacteristic
25#16813618C2211yescharacteristic
26#16813615—21no—
27#16813611C2211yescharacteristic
28#16813611C2211yescharacteristic
29#16813609—21no—
30#16813609C2211yescharacteristic, complemented
31#16813603—21no—
32#16813601C2211yescharacteristic
33#16813599—21no—
34#16813596—21no—
35#16813596—21no—
36#16813590—21no—
37#16813590—21no—
38#16813587C2211yescharacteristic, complemented
39D4×Dic113C2211yescharacteristic, complemented
40#16813581C2211yescharacteristic
41#16813551C2211yescharacteristic, complemented
42#16813551C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic
49C22⋊#11744751C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×#41×C113C2211yescharacteristic
53C2×SD16×C113C2211yescharacteristic, complemented
54C2×D8×C113C2211yescharacteristic, complemented
55#121×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C23×D113—21no—
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62C2×D452—21no—
63C2×D452—41no—
64C2×D452—41no—
65C2×D452C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C22×Dic113—21no—
72#14268637—41no—
73#14268636—41no—
74#14268636—41no—
75#14268635—41no—
76#14268632—41no—
77#14268632—41no—
78C2×#11744751C2311yescharacteristic
79C2×#11744751C2311yescharacteristic
80C4⋊Dic113D411yescharacteristic
81C4⋊Dic113D411yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90C22⋊Dic113D411yescharacteristic
91C22⋊Dic113D411yescharacteristic
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96C4×Dic113—21no—
97C4×Dic113C2311yescharacteristic
98C4×Dic113C2311yescharacteristic
99#41×C113—41no—
100#41×C113—41no—
101C2×Q8×C113C2311yescharacteristic
102C2×D4×C113—21no—
103C2×D4×C113—21no—
104C2×D4×C113C2311yescharacteristic
105C2×D4×C113C2311yescharacteristic
106C22×C4×C113—21no—
107C22×C4×C113C2311yescharacteristic
108SD16×C113—41no—
109D8×C113—41no—
110C2×C8×C113C2311yescharacteristic
111C2×C8×C113C2311yescharacteristic
112C4⋊C4×C113C2311yescharacteristic
113C22⋊C4×C113—21no—
114C23×C113—21no—
115C23×C113—21no—
116C23×C113C2×D411yescharacteristic
117C22×D113—21no—
118C22×D113—21no—
119C22×D113—42no—
120C22×D113—81no—
121C22×D113—81no—
122Q8×C113—21no—
123Q8×C113—21no—
124D4×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—42no—
129D4×C113—81no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—42no—
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2411yescharacteristic
137C22⋊D113—81no—
138C22⋊D113—81no—
139C22⋊D113—81no—
140C22⋊D113—81no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113—81no—
144C2×Dic113C2×D411yescharacteristic
145C2×Dic113C2×D411yescharacteristic
146C2×Dic113C2×D411yescharacteristic
147C2×Dic113C2×D411yescharacteristic
148D452—21no—
149D452—21no—
150D452—21no—
151D452—21no—
152D452—42no—
153Dic226—21no—
154Dic226—21no—
155Dic226—81no—
156C8×C113—21no—
157C8×C113—21no—
158#11744751—21no—
159#11744751—21no—
160C22×C113—21no—
161C22×C113—21no—
162C22×C113—21no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113—41no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113C22×D411yescharacteristic
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—84no—
177C4×C113—21no—
178C4×C113—41no—
179C4×C113—41no—
180C4×C113H(5,𝔽2)11yescharacteristic
181C4×C113H(5,𝔽2)11yescharacteristic
182Dic113—21no—
183Dic113—21no—
184Dic113—21no—
185Dic113—21no—
186Dic113—41no—
187Dic113—41no—
188C2×C113—41no—
189C2×C113—81no—
190C2×C113—81no—
191C2×C113#53511yescharacteristic
192C2×C113#57611yescharacteristic
193C2×C113#57711yescharacteristic
194D113—81no—
195D113—81no—
196#3224—1131nomaximal, Sylow
197C113#322411yescharacteristic, complemented, Sylow
198#542—1131no—
199#535—1131no—
200#496—1131no—
201#495—1131no—
202#489—1131no—
203#486—1131no—
204#464—1131no—
205#463—1131no—
206#460—1131no—
207#459—1131no—
208#452—1131no—
209#450—1131no—
210#449D11311yescharacteristic, complemented
211#447—1131no—
212#433—1131no—
213C2×#41C2×D11311yescharacteristic
214C22×D4—1131no—
215C2×Q16—1131no—
216C2×SD16—1131no—
217C2×SD16—1131no—
218C2×SD16—1131no—
219C2×SD16C2×D11311yescharacteristic, complemented
220C2×D8—1131no—
221C2×D8—1131no—
222C2×D8C2×D11311yescharacteristic, complemented
223C4⋊Q8—1131no—
224#127—1131no—
225#127—1131no—
226#126—2261no—
227#124—1131no—
228#124—1131no—
229#124—1131no—
230#124—2261no—
231#123—2261no—
232C22⋊Q8—1131no—
233C22⋊Q8—2261no—
234#121—2261no—
235#121—2261no—
236#121C2×D11311yescharacteristic
237#120—2261no—
238#120—2261no—
239C4×Q8—1131no—
240C4×D4—1131no—
241#117—1131no—
242C4⋊C8—1131no—
243C4⋊C8—1131no—
244#103—1131no—
245#103C2×D11311yescharacteristic, complemented
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251#102C2×D11311yescharacteristic, complemented
252C22⋊C8—1131no—
253C22⋊C8C2×D11311yescharacteristic
254#97—1131no—
255C4×C8—1131no—
256C24—2261no—
257#41—41no—
258#41—41no—
259C2×Q8—1131no—
260C2×Q8—2261no—
261C2×Q8C22×D11311yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—1131no—
265C2×D4—1131no—
266C2×D4—4521no—
267C2×D4—4521no—
268C2×D4—2261no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4—2261no—
272C2×D4—2261no—
273C2×D4C22×D11311yescharacteristic
274C2×D4C22×D11311yescharacteristic
275C22×C4—21no—
276C22×C4—2261no—
277C22×C4C22×D11311yescharacteristic
278Q16—4521no—
279SD16—41no—
280SD16—4521no—
281SD16—4521no—
282SD16—4521no—
283D8—41no—
284D8—4521no—
285D8—4521no—
286C2×C8—1131no—
287C2×C8—1131no—
288C2×C8C22×D11311yescharacteristic
289C2×C8C22×D11311yescharacteristic
290C4⋊C4—1131no—
291C4⋊C4—1131no—
292C4⋊C4—1131no—
293C4⋊C4—2261no—
294C4⋊C4—2261no—
295C4⋊C4—2261no—
296C4⋊C4C22×D11311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—1131no—
299C22⋊C4—1131no—
300C22⋊C4—2261no—
301C22⋊C4—2261no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C42—1131no—
309C42—1131no—
310C42—2261no—
311C23—21no—
312C23—21no—
313C23—9041no—
314C23—9041no—
315C23—4522no—
316C23—2261no—
317C23—2261no—
318C23D4×D11311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—9041no—
322Q8—2261no—
323Q8—2261no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—81no—
330D4—9041no—
331D4—9041no—
332D4—9041no—
333D4—9041no—
334D4—4522no—
335D4—2261no—
336D4—2261no—
337D4—2261no—
338D4—2261no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—1131no—
345C2×C4—1131no—
346C2×C4—1131no—
347C2×C4—1131no—
348C2×C4—9041no—
349C2×C4—2261no—
350C2×C4—2261no—
351C2×C4D4×D11311yescharacteristic
352C2×C4C23×D11311yescharacteristic
353C8—21no—
354C8—21no—
355C8—2261no—
356C8—2261no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—9044no—
367C22—4521no—
368C22—4521no—
369C22—4521no—
370C22—4521no—
371C22—4521no—
372C22—4521no—
373C22C2×D4×D11311yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—4521no—
378C4—4521no—
379C4—2261no—
380C4—2261no—
381C4—2261no—
382C4—2261no—
383C4#1681366711yescharacteristic
384C4#1681366711yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—9041no—
389C2—9041no—
390C2#2029916311yescharacteristic
391C2#2029940211yescharacteristic
392C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3224
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #20299215C2semidirect
2. #20299162C2semidirect
3. #20298986C2semidirect
4. #20298979C2semidirect
5. #20298959C2semidirect
6. #20298943C2semidirect
7. #20298823C2semidirect
8. #20298815C2semidirect
9. #20298797C2semidirect
10. #20298791C2semidirect
11. #20298760C2semidirect
12. #20298751C2semidirect
13. #20298731C2semidirect
14. #20298656C2semidirect
15. #449×C113C2semidirect
17. C2×#14268637C22semidirect
20. C2×#14268635C22semidirect
23. #16813621C22semidirect
30. #16813609C22semidirect
38. #16813587C22semidirect
39. D4×Dic113C22semidirect
41. #16813551C22semidirect
42. #16813551C22semidirect
43. #16813546C22semidirect
46. #16813543C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
53. C2×SD16×C113C22semidirect
54. C2×D8×C113C22semidirect
56. #103×C113C22semidirect
57. #102×C113C22semidirect
197. C113#3224semidirect
210. #449D113semidirect
219. C2×SD16C2×D113semidirect
222. C2×D8C2×D113semidirect
245. #103C2×D113semidirect
251. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992152
#202991622
#202989862
#202989792
#202989592
#202989432
#202988232
#202988152
#202987972
#202987912
#202987602
#202987512
#202987312
#202986562
#449×C1132
#3224113