Finite Group Databasebeta

← #28401422

Subgroups — #28401422

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#20299177C211yesmaximal, characteristic, complemented
2#20299165C211yesmaximal, characteristic, complemented
3#20298940C211yesmaximal, characteristic, complemented
4#20298919C211yesmaximal, characteristic, complemented
5#20298915C211yesmaximal, characteristic, complemented
6#20298910C211yesmaximal, characteristic, complemented
7#20298848C211yesmaximal, characteristic, complemented
8#20298843C211yesmaximal, characteristic, complemented
9#20298831C211yesmaximal, characteristic, complemented
10#20298826C211yesmaximal, characteristic, complemented
11#20298749C211yesmaximal, characteristic, complemented
12#20298740C211yesmaximal, characteristic, complemented
13#20298740C211yesmaximal, characteristic, complemented
14#20298563C211yesmaximal, characteristic, complemented
15#447×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268646C2211yescharacteristic, complemented
18C2×#14268635C2211yescharacteristic
19C2×#14268635C2211yescharacteristic
20C2×#14268630C2211yescharacteristic, complemented
21C2×C8×D113C2211yescharacteristic, complemented
22#16813618—21no—
23#16813609—21no—
24#16813602C2211yescharacteristic, complemented
25#16813601C2211yescharacteristic
26#16813599—21no—
27#16813595—21no—
28#16813594—21no—
29#16813593—21no—
30#16813593C2211yescharacteristic
31#16813593C2211yescharacteristic
32#16813593C2211yescharacteristic
33#16813593C2211yescharacteristic
34#16813593C2211yescharacteristic, complemented
35#16813591—21no—
36#16813591—21no—
37#16813581C2211yescharacteristic
38C4⋊C4×D113C2211yescharacteristic, complemented
39#16813556C2211yescharacteristic, complemented
40#16813555C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic, complemented
48#16813543C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic, complemented
51#16813534C2211yescharacteristic, complemented
52C22×D4×C113C2211yescharacteristic
53C2×D8×C113C2211yescharacteristic
54C2×D8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58C22⋊C8×C113C2211yescharacteristic
59#14268647—41no—
60#14268647—41no—
61#14268646—41no—
62#14268646—41no—
63C2×Dic226D411yescharacteristic
64C2×Dic226C2311yescharacteristic
65C2×D452D411yescharacteristic
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⋊D113D411yescharacteristic
73C2×C22⋊D113D411yescharacteristic
74C22×Dic113—21no—
75C2×C4×D113—21no—
76C2×C4×D113C2311yescharacteristic
77C2×C4×D113C2311yescharacteristic
78#14268635—41no—
79#14268635—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—
93C22⋊Dic113—21no—
94C22⋊Dic113—21no—
95C22⋊Dic113—21no—
96C22⋊Dic113—21no—
97#14268624—21no—
98C4×Dic113—21no—
99C24×C113—21no—
100C2×D4×C113—21no—
101C2×D4×C113—21no—
102C2×D4×C113—41no—
103C2×D4×C113—41no—
104C2×D4×C113C2311yescharacteristic
105C2×D4×C113C2311yescharacteristic
106C2×D4×C113C2311yescharacteristic
107C22×C4×C113C2311yescharacteristic
108D8×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×C113—21no—
117C23×C113—42no—
118C23×C113—81no—
119C23×C113—81no—
120C23×C113C2×D411yescharacteristic
121C22×D113C2×D411yescharacteristic
122C22×D113C2×D411yescharacteristic
123D4×C113—21no—
124D4×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×C113C2×D411yescharacteristic
135C2×C4×C113C2411yescharacteristic
136C22⋊D113—41no—
137C22⋊D113—41no—
138C22⋊D113—42no—
139C22⋊D113—81no—
140C22⋊D113—81no—
141C22⋊D113—81no—
142C22⋊D113—81no—
143C22⋊D113—81no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—42no—
149C2×Dic113C2×D411yescharacteristic
150C2×Dic113C2×D411yescharacteristic
151D452—41no—
152C4×D113—21no—
153C4×D113—21no—
154C4×D113—21no—
155C4×D113—21no—
156C4×D113—81no—
157Dic226—21no—
158Dic226—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×C113—41no—
174C22×C113—41no—
175C22×C113—41no—
176C22×C113—84no—
177C22×C113C22×D411yescharacteristic
178C2×D113—21no—
179C2×D113—21no—
180C2×D113—21no—
181C2×D113—21no—
182C2×D113—21no—
183C2×D113—21no—
184C4×C113—21no—
185C4×C113—41no—
186C4×C113H(5,𝔽2)11yescharacteristic
187C4×C113H(5,𝔽2)11yescharacteristic
188Dic113—21no—
189Dic113—21no—
190Dic113—41no—
191Dic113—41no—
192Dic113—41no—
193Dic113—41no—
194C2×C113—41no—
195C2×C113—81no—
196C2×C113—81no—
197C2×C113—81no—
198C2×C113#53411yescharacteristic
199C2×C113#57611yescharacteristic
200C2×C113#57711yescharacteristic
201D113—41no—
202D113—41no—
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#449—1131no—
218#447D11311yescharacteristic, complemented
219#408—1131no—
220C2×#41—1131no—
221C2×#41—1131no—
222C22×D4C2×D11311yescharacteristic
223C2×SD16—1131no—
224C2×SD16—1131no—
225C2×D8C2×D11311yescharacteristic
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#103—1131no—
253#102—1131no—
254#102—1131no—
255#102—1131no—
256#102—1131no—
257#102C2×D11311yescharacteristic
258#102C2×D11311yescharacteristic
259C22⋊C8—1131no—
260C22⋊C8—1131no—
261C22⋊C8—1131no—
262C22⋊C8C2×D11311yescharacteristic
263C24—21no—
264#41—4521no—
265#41—4521no—
266#41—4521no—
267#41—4521no—
268C2×Q8—1131no—
269C2×Q8—1131no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—1131no—
275C2×D4—1131no—
276C2×D4—1131no—
277C2×D4—2261no—
278C2×D4—2261no—
279C2×D4—2261no—
280C2×D4—2261no—
281C2×D4—2261no—
282C2×D4—2261no—
283C2×D4C22×D11311yescharacteristic
284C2×D4C22×D11311yescharacteristic
285C2×D4C22×D11311yescharacteristic
286C22×C4—1131no—
287C22×C4—1131no—
288C22×C4—2261no—
289C22×C4—2261no—
290C22×C4C22×D11311yescharacteristic
291SD16—4521no—
292SD16—4521no—
293D8—41no—
294D8—41no—
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—21no—
321C23—42no—
322C23—81no—
323C23—81no—
324C23—1131no—
325C23—1131no—
326C23D4×D11311yescharacteristic
327Q8—4521no—
328Q8—2261no—
329Q8—2261no—
330D4—21no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—81no—
338D4—9041no—
339D4—9041no—
340D4—9041no—
341D4—9041no—
342D4—9041no—
343D4—4521no—
344D4—4522no—
345D4—4521no—
346D4—4521no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—1131no—
351C2×C4—1131no—
352C2×C4—9041no—
353C2×C4—4522no—
354C2×C4—2261no—
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—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—2261no—
382C22—2261no—
383C22—2261no—
384C22—2261no—
385C22—2261no—
386C22—2261no—
387C22C2×D4×D11311yescharacteristic
388C4—21no—
389C4—41no—
390C4—4521no—
391C4—4521no—
392C4—4521no—
393C4—4521no—
394C4—2261no—
395C4—2261no—
396C4#1681366711yescharacteristic
397C4#1681366711yescharacteristic
398C2—41no—
399C2—81no—
400C2—81no—
401C2—81no—
402C2—4521no—
403C2—4521no—
404C2#2029915811yescharacteristic
405C2#2029939911yescharacteristic
406C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113#3198
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20299177C2semidirect
2. #20299165C2semidirect
3. #20298940C2semidirect
4. #20298919C2semidirect
5. #20298915C2semidirect
6. #20298910C2semidirect
7. #20298848C2semidirect
8. #20298843C2semidirect
9. #20298831C2semidirect
10. #20298826C2semidirect
11. #20298749C2semidirect
12. #20298740C2semidirect
13. #20298740C2semidirect
14. #20298563C2semidirect
15. #447×C113C2semidirect
17. C2×#14268646C22semidirect
20. C2×#14268630C22semidirect
21. C2×C8×D113C22semidirect
24. #16813602C22semidirect
34. #16813593C22semidirect
38. C4⋊C4×D113C22semidirect
39. #16813556C22semidirect
40. #16813555C22semidirect
41. #16813554C22semidirect
42. #16813553C22semidirect
43. #16813547C22semidirect
44. #16813547C22semidirect
47. #16813543C22semidirect
48. #16813543C22semidirect
50. #16813534C22semidirect
51. #16813534C22semidirect
204. C113#3198semidirect
218. #447D113semidirect

Maximal subgroups

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

subgroupindex
#202991772
#202991652
#202989402
#202989192
#202989152
#202989102
#202988482
#202988432
#202988312
#202988262
#202987492
#202987402
#202985632
#447×C1132
#3198113