Finite Group Databasebeta

← #28401425

Subgroups — #28401425

Order 14464.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299176C211yesmaximal, characteristic, complemented
2#20299164C211yesmaximal, characteristic, complemented
3#20298937C211yesmaximal, characteristic, complemented
4#20298921C211yesmaximal, characteristic, complemented
5#20298917C211yesmaximal, characteristic, complemented
6#20298909C211yesmaximal, characteristic, complemented
7#20298848C211yesmaximal, characteristic, complemented
8#20298847C211yesmaximal, characteristic, complemented
9#20298833C211yesmaximal, characteristic, complemented
10#20298824C211yesmaximal, characteristic, complemented
11#20298747C211yesmaximal, characteristic, complemented
12#20298743C211yesmaximal, characteristic, complemented
13#20298730C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C2×#14268634C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268630C2211yescharacteristic, complemented
21C2×C8×D113C2211yescharacteristic, complemented
22#16813618—21no—
23#16813608—21no—
24#16813601—21no—
25#16813598C2211yescharacteristic
26#16813598C2211yescharacteristic, complemented
27#16813597C2211yescharacteristic
28#16813596—21no—
29#16813596C2211yescharacteristic
30#16813594—21no—
31#16813594—21no—
32#16813593C2211yescharacteristic
33#16813593C2211yescharacteristic
34#16813593C2211yescharacteristic, complemented
35#16813592—21no—
36#16813590—21no—
37#16813580C2211yescharacteristic
38C2×C4⋊Dic113C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813554C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813543C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic, complemented
53C2×SD16×C113C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#103×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60#14268647—41no—
61#14268647—41no—
62C2×Dic226D411yescharacteristic
63C2×D452—21no—
64C2×D452D411yescharacteristic
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C2×C22⋊D113—21no—
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113D411yescharacteristic
72C2×C22⋊D113D411yescharacteristic
73D4×D113—41no—
74D4×D113—41no—
75C22×Dic113—21no—
76C2×C4×D113C2311yescharacteristic
77C2×C4×D113C2311yescharacteristic
78#14268634—41no—
79#14268632—41no—
80#14268630—41no—
81C2×#11744751C2311yescharacteristic
82C2×#11744751C2311yescharacteristic
83C8×D113—41no—
84C4⋊Dic113—21no—
85C4⋊Dic113C2311yescharacteristic
86C4⋊Dic113C2311yescharacteristic
87C4⋊Dic113C2311yescharacteristic
88#14268626—21no—
89#14268626—21no—
90C22⋊Dic113—21no—
91C22⋊Dic113—21no—
92C22⋊Dic113—21no—
93#14268624—21no—
94#14268624—21no—
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98C4×Dic113—21no—
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—42no—
119C22×D113—81no—
120C22×D113—81no—
121C22×D113C2×D411yescharacteristic
122C22×D113C2×D411yescharacteristic
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—41no—
139C22⋊D113—41no—
140C22⋊D113—42no—
141C22⋊D113—81no—
142C22⋊D113—81no—
143C22⋊D113—81no—
144C22⋊D113—81no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—81no—
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151D452—21no—
152D452—21no—
153D452—41no—
154D452—81no—
155C4×D113—21no—
156C4×D113—21no—
157C4×D113—21no—
158C4×D113—21no—
159Dic226—41no—
160C8×C113—21no—
161C8×C113—21no—
162#11744751—21no—
163#11744751—21no—
164C22×C113—21no—
165C22×C113—21no—
166C22×C113—21no—
167C22×C113—41no—
168C22×C113—41no—
169C22×C113—41no—
170C22×C113—41no—
171C22×C113—41no—
172C22×C113—41no—
173C22×C113C22×D411yescharacteristic
174C2×D113—21no—
175C2×D113—21no—
176C2×D113—21no—
177C2×D113—21no—
178C2×D113—21no—
179C2×D113—21no—
180C2×D113—41no—
181C2×D113—41no—
182C2×D113—41no—
183C2×D113—84no—
184C4×C113—21no—
185C4×C113—41no—
186C4×C113—41no—
187C4×C113H(5,𝔽2)11yescharacteristic
188C4×C113H(5,𝔽2)11yescharacteristic
189Dic113—21no—
190Dic113—21no—
191Dic113—41no—
192Dic113—41no—
193Dic113—41no—
194C2×C113—41no—
195C2×C113—81no—
196C2×C113—81no—
197C2×C113#53411yescharacteristic
198C2×C113#57611yescharacteristic
199C2×C113#57711yescharacteristic
200D113—41no—
201D113—41no—
202D113—81no—
203#3198—1131nomaximal, Sylow
204C113#319811yescharacteristic, complemented, Sylow
205#537—1131no—
206#535—1131no—
207#485—1131no—
208#482—1131no—
209#481—1131no—
210#480—1131no—
211#469—1131no—
212#468—1131no—
213#466—1131no—
214#465—1131no—
215#450—1131no—
216#449—1131no—
217#449D11311yescharacteristic, complemented
218#447—1131no—
219#408—1131no—
220C2×#41—1131no—
221C2×#41C2×D11311yescharacteristic, complemented
222C22×D4—1131no—
223C2×SD16—1131no—
224C2×SD16C2×D11311yescharacteristic
225C2×D8—1131no—
226C2×D8C2×D11311yescharacteristic
227C2×M16—1131no—
228C22×C8—1131no—
229#127—2261no—
230#124—2261no—
231C22⋊Q8—1131no—
232C22⋊Q8—1131no—
233C22⋊Q8—2261no—
234#121—1131no—
235#121—1131no—
236#121—1131no—
237#121—1131no—
238#121—1131no—
239#121—2261no—
240#121—2261no—
241#121—2261no—
242#121C2×D11311yescharacteristic
243#120—2261no—
244#120—2261no—
245#117—1131no—
246C2×C4⋊C4—1131no—
247#107—1131no—
248#107—1131no—
249#106—1131no—
250#106—1131no—
251#103—1131no—
252#103C2×D11311yescharacteristic, complemented
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102—1131no—
257#102—1131no—
258#102C2×D11311yescharacteristic, complemented
259C22⋊C8—1131no—
260C22⋊C8—1131no—
261C22⋊C8—1131no—
262C22⋊C8C2×D11311yescharacteristic, complemented
263C24—2261no—
264#41—41no—
265#41—41no—
266#41—4521no—
267#41—4521no—
268C2×Q8—1131no—
269C2×Q8C22×D11311yescharacteristic
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—1131no—
273C2×D4—1131no—
274C2×D4—1131no—
275C2×D4—1131no—
276C2×D4—4521no—
277C2×D4—4521no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4—2261no—
282C2×D4—2261no—
283C2×D4—2261no—
284C2×D4C22×D11311yescharacteristic
285C2×D4C22×D11311yescharacteristic
286C22×C4—21no—
287C22×C4—1131no—
288C22×C4—1131no—
289C22×C4—2261no—
290C22×C4C22×D11311yescharacteristic
291SD16—41no—
292SD16—4521no—
293D8—41no—
294D8—4521no—
295M16—4521no—
296C2×C8—1131no—
297C2×C8—1131no—
298C2×C8—4521no—
299C2×C8C22×D11311yescharacteristic
300C2×C8C22×D11311yescharacteristic
301C4⋊C4—1131no—
302C4⋊C4—1131no—
303C4⋊C4—1131no—
304C4⋊C4—2261no—
305C4⋊C4—2261no—
306C4⋊C4—2261no—
307C4⋊C4C22×D11311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—2261no—
310C22⋊C4—2261no—
311C22⋊C4—2261no—
312C22⋊C4—2261no—
313C22⋊C4—2261no—
314C22⋊C4—2261no—
315C22⋊C4—2261no—
316C22⋊C4—2261no—
317C42—2261no—
318C23—21no—
319C23—21no—
320C23—1131no—
321C23—1131no—
322C23—9041no—
323C23—9041no—
324C23—4522no—
325C23—2261no—
326C23D4×D11311yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—4521no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—81no—
336D4—9041no—
337D4—9041no—
338D4—9041no—
339D4—9041no—
340D4—9041no—
341D4—4521no—
342D4—4521no—
343D4—4521no—
344D4—4522no—
345D4—2261no—
346D4—2261no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—1131no—
353C2×C4—1131no—
354C2×C4—9041no—
355C2×C4—2261no—
356C2×C4—2261no—
357C2×C4—2261no—
358C2×C4—2261no—
359C2×C4—2261no—
360C2×C4—2261no—
361C2×C4—2261no—
362C2×C4D4×D11311yescharacteristic
363C2×C4C23×D11311yescharacteristic
364C8—21no—
365C8—21no—
366C8—2261no—
367C8—2261no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—9044no—
378C22—4521no—
379C22—4521no—
380C22—4521no—
381C22—2261no—
382C22—2261no—
383C22—2261no—
384C22—2261no—
385C22—2261no—
386C22—2261no—
387C22C2×D4×D11311yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—4521no—
392C4—4521no—
393C4—4521no—
394C4—2261no—
395C4—2261no—
396C4#1681366711yescharacteristic
397C4#1681366711yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—9041no—
402C2—4521no—
403C2—4521no—
404C2#2029915811yescharacteristic
405C2#2029940211yescharacteristic
406C2#2029940511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3198
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. #20299176C2semidirect
2. #20299164C2semidirect
3. #20298937C2semidirect
4. #20298921C2semidirect
5. #20298917C2semidirect
6. #20298909C2semidirect
7. #20298848C2semidirect
8. #20298847C2semidirect
9. #20298833C2semidirect
10. #20298824C2semidirect
11. #20298747C2semidirect
12. #20298743C2semidirect
13. #20298730C2semidirect
14. #20298563C2semidirect
15. #449×C113C2semidirect
20. C2×#14268630C22semidirect
21. C2×C8×D113C22semidirect
26. #16813598C22semidirect
34. #16813593C22semidirect
38. C2×C4⋊Dic113C22semidirect
39. #16813555C22semidirect
40. #16813555C22semidirect
41. #16813554C22semidirect
42. #16813554C22semidirect
43. #16813546C22semidirect
48. #16813543C22semidirect
49. C22⋊#11744751C22semidirect
52. C2×#41×C113C22semidirect
56. #103×C113C22semidirect
57. #102×C113C22semidirect
58. C22⋊C8×C113C22semidirect
204. C113#3198semidirect
217. #449D113semidirect
221. C2×#41C2×D113semidirect
252. #103C2×D113semidirect
258. #102C2×D113semidirect
262. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991762
#202991642
#202989372
#202989212
#202989172
#202989092
#202988482
#202988472
#202988332
#202988242
#202987472
#202987432
#202987302
#202985632
#449×C1132
#3198113