Finite Group Databasebeta

← #28401622

Subgroups — #28401622

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299201C211yesmaximal, characteristic, complemented
2#20299162C211yesmaximal, characteristic, complemented
3#20298984C211yesmaximal, characteristic, complemented
4#20298973C211yesmaximal, characteristic, complemented
5#20298961C211yesmaximal, characteristic, complemented
6#20298954C211yesmaximal, characteristic, complemented
7#20298816C211yesmaximal, characteristic, complemented
8#20298815C211yesmaximal, characteristic, complemented
9#20298792C211yesmaximal, characteristic, complemented
10#20298791C211yesmaximal, characteristic, complemented
11#20298743C211yesmaximal, characteristic, complemented
12#20298734C211yesmaximal, characteristic, complemented
13#20298731C211yesmaximal, characteristic, complemented
14#20298656C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic
17C2×#14268634C2211yescharacteristic, complemented
18C2×D904C2211yescharacteristic
19C2×D904C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21C2×#14268632C2211yescharacteristic
22C2×#14268632C2211yescharacteristic, complemented
23#16813618C2211yescharacteristic
24#16813618C2211yescharacteristic
25#16813618C2211yescharacteristic, complemented
26#16813613C2211yescharacteristic, complemented
27#16813611C2211yescharacteristic
28#16813611C2211yescharacteristic
29#16813606—21no—
30#16813604—21no—
31#16813596—21no—
32#16813596—21no—
33#16813596C2211yescharacteristic
34#16813594—21no—
35#16813593—21no—
36#16813590—21no—
37#16813590—21no—
38D4×Dic113C2211yescharacteristic, complemented
39#16813584C2211yescharacteristic, 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×D452—21no—
61C2×D452—41no—
62C2×D452—41no—
63C2×D452C2311yescharacteristic
64C2×D452C2311yescharacteristic
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113—21no—
73C22×Dic113—21no—
74C2×C4×D113—21no—
75#14268634—41no—
76D904—41no—
77D904—41no—
78#14268632—41no—
79#14268632—41no—
80#14268632—41no—
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2311yescharacteristic
83C4⋊Dic113—21no—
84C4⋊Dic113D411yescharacteristic
85C4⋊Dic113D411yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113D411yescharacteristic
90C22⋊Dic113D411yescharacteristic
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—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—21no—
120C22×D113—42no—
121C22×D113—81no—
122C22×D113—81no—
123Q8×C113—21no—
124Q8×C113—21no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—21no—
128D4×C113—21no—
129D4×C113—42no—
130D4×C113—81no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—21no—
134C2×C4×C113—21no—
135C2×C4×C113—42no—
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2411yescharacteristic
138C22⋊D113—81no—
139C22⋊D113—81no—
140C22⋊D113—81no—
141C22⋊D113—81no—
142C22⋊D113—81no—
143C22⋊D113—81no—
144C22⋊D113—81no—
145C2×Dic113—21no—
146C2×Dic113—81no—
147C2×Dic113C2×D411yescharacteristic
148C2×Dic113C2×D411yescharacteristic
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151D452—21no—
152D452—21no—
153D452—21no—
154D452—21no—
155D452—21no—
156D452—21no—
157D452—42no—
158C4×D113—81no—
159C8×C113—21no—
160C8×C113—21no—
161#11744751—21no—
162#11744751—21no—
163C22×C113—21no—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113—41no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113C22×D411yescharacteristic
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C2×D113—41no—
178C2×D113—41no—
179C2×D113—41no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—84no—
183C4×C113—21no—
184C4×C113—41no—
185C4×C113—41no—
186C4×C113H(5,𝔽2)11yescharacteristic
187C4×C113H(5,𝔽2)11yescharacteristic
188Dic113—21no—
189Dic113—21no—
190Dic113—21no—
191Dic113—21no—
192Dic113—41no—
193C2×C113—41no—
194C2×C113—81no—
195C2×C113—81no—
196C2×C113#53511yescharacteristic
197C2×C113#57611yescharacteristic
198C2×C113#57611yescharacteristic
199D113—81no—
200D113—81no—
201D113—81no—
202#3220—1131nomaximal, Sylow
203C113#322011yescharacteristic, complemented, Sylow
204#540—1131no—
205#535—1131no—
206#496—1131no—
207#493—1131no—
208#490—1131no—
209#488—1131no—
210#463—1131no—
211#463—1131no—
212#459—1131no—
213#459—1131no—
214#449—1131no—
215#449D11311yescharacteristic, complemented
216#447—1131no—
217#447—1131no—
218#433—1131no—
219C2×#41C2×D11311yescharacteristic
220C22×D4—1131no—
221C2×SD16—1131no—
222C2×SD16C2×D11311yescharacteristic, complemented
223C2×D8—1131no—
224C2×D8—1131no—
225C2×D8—1131no—
226C2×D8—1131no—
227C2×D8—1131no—
228C2×D8C2×D11311yescharacteristic, complemented
229#127—1131no—
230#127—1131no—
231#127—1131no—
232#125—1131no—
233#124—1131no—
234#124—1131no—
235#123—2261no—
236#123—2261no—
237#121—1131no—
238#121—2261no—
239#121—2261no—
240#121—2261no—
241#121—2261no—
242#121C2×D11311yescharacteristic
243#120—2261no—
244#120—2261no—
245C4×D4—1131no—
246C4×D4—1131no—
247#117—1131no—
248C4⋊C8—1131no—
249C4⋊C8—1131no—
250#103—1131no—
251#103C2×D11311yescharacteristic, complemented
252#102—1131no—
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102—1131no—
257#102C2×D11311yescharacteristic, complemented
258C22⋊C8—1131no—
259C22⋊C8C2×D11311yescharacteristic
260#97—1131no—
261C4×C8—1131no—
262C24—2261no—
263#41—41no—
264#41—41no—
265C2×Q8C22×D11311yescharacteristic
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—1131no—
269C2×D4—1131no—
270C2×D4—1131no—
271C2×D4—4521no—
272C2×D4—4521no—
273C2×D4—2261no—
274C2×D4—2261no—
275C2×D4—2261no—
276C2×D4—2261no—
277C2×D4—2261no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4C22×D11311yescharacteristic
282C2×D4C22×D11311yescharacteristic
283C22×C4—21no—
284C22×C4—2261no—
285C22×C4—2261no—
286C22×C4C22×D11311yescharacteristic
287SD16—41no—
288SD16—4521no—
289D8—41no—
290D8—4521no—
291D8—4521no—
292D8—4521no—
293D8—4521no—
294D8—4521no—
295C2×C8—1131no—
296C2×C8—1131no—
297C2×C8C22×D11311yescharacteristic
298C2×C8C22×D11311yescharacteristic
299C4⋊C4—1131no—
300C4⋊C4—1131no—
301C4⋊C4—1131no—
302C4⋊C4—2261no—
303C4⋊C4—2261no—
304C4⋊C4C22×D11311yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—1131no—
307C22⋊C4—1131no—
308C22⋊C4—2261no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C42—1131no—
316C42—1131no—
317C23—21no—
318C23—21no—
319C23—9041no—
320C23—9041no—
321C23—4522no—
322C23—2261no—
323C23—2261no—
324C23—2261no—
325C23D4×D11311yescharacteristic
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—81no—
334D4—9041no—
335D4—9041no—
336D4—9041no—
337D4—9041no—
338D4—9041no—
339D4—9041no—
340D4—9041no—
341D4—4522no—
342D4—2261no—
343D4—2261no—
344D4—2261no—
345D4—2261no—
346D4—2261no—
347D4—2261no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—1131no—
354C2×C4—1131no—
355C2×C4—1131no—
356C2×C4—1131no—
357C2×C4—9041no—
358C2×C4—9041no—
359C2×C4—2261no—
360C2×C4D4×D11311yescharacteristic
361C2×C4C23×D11311yescharacteristic
362C8—21no—
363C8—21no—
364C8—2261no—
365C8—2261no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—9044no—
376C22—4521no—
377C22—4521no—
378C22—4521no—
379C22—4521no—
380C22—4521no—
381C22—4521no—
382C22—4521no—
383C22—4521no—
384C22—4521no—
385C22C2×D4×D11311yescharacteristic
386C4—21no—
387C4—41no—
388C4—41no—
389C4—4521no—
390C4—2261no—
391C4—2261no—
392C4—2261no—
393C4—2261no—
394C4#1681366711yescharacteristic
395C4#1681366711yescharacteristic
396C2—41no—
397C2—81no—
398C2—81no—
399C2—9041no—
400C2—9041no—
401C2—9041no—
402C2#2029916311yescharacteristic
403C2#2029940011yescharacteristic
404C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3220
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. #20299201C2semidirect
2. #20299162C2semidirect
3. #20298984C2semidirect
4. #20298973C2semidirect
5. #20298961C2semidirect
6. #20298954C2semidirect
7. #20298816C2semidirect
8. #20298815C2semidirect
9. #20298792C2semidirect
10. #20298791C2semidirect
11. #20298743C2semidirect
12. #20298734C2semidirect
13. #20298731C2semidirect
14. #20298656C2semidirect
15. #449×C113C2semidirect
17. C2×#14268634C22semidirect
22. C2×#14268632C22semidirect
25. #16813618C22semidirect
26. #16813613C22semidirect
38. D4×Dic113C22semidirect
39. #16813584C22semidirect
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
203. C113#3220semidirect
215. #449D113semidirect
222. C2×SD16C2×D113semidirect
228. C2×D8C2×D113semidirect
251. #103C2×D113semidirect
257. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992012
#202991622
#202989842
#202989732
#202989612
#202989542
#202988162
#202988152
#202987922
#202987912
#202987432
#202987342
#202987312
#202986562
#449×C1132
#3220113