Finite Group Databasebeta

← #28401662

Subgroups — #28401662

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#20299167C211yesmaximal, characteristic, complemented
2#20298988C211yesmaximal, characteristic, complemented
3#20298980C211yesmaximal, characteristic, complemented
4#20298960C211yesmaximal, characteristic, complemented
5#20298946C211yesmaximal, characteristic, complemented
6#20298820C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298798C211yesmaximal, characteristic, complemented
9#20298793C211yesmaximal, characteristic, complemented
10#20298758C211yesmaximal, characteristic, complemented
11#20298748C211yesmaximal, characteristic, complemented
12#20298741C211yesmaximal, characteristic, complemented
13#20298731C211yesmaximal, characteristic, complemented
14#20298659C211yesmaximal, characteristic, complemented
15#542×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C22×D452C2211yescharacteristic
18C2×#14268637C2211yescharacteristic, complemented
19C2×#14268635C2211yescharacteristic, complemented
20C2×#14268634C2211yescharacteristic
21C2×#14268634C2211yescharacteristic
22C2×#14268634C2211yescharacteristic, complemented
23C2×#14268632C2211yescharacteristic
24C2×#14268632C2211yescharacteristic
25C2×#14268632C2211yescharacteristic, complemented
26#16813619C2211yescharacteristic
27#16813619C2211yescharacteristic
28#16813610C2211yescharacteristic
29#16813610C2211yescharacteristic
30#16813597—21no—
31#16813597—21no—
32#16813592—21no—
33#16813592—21no—
34C4⋊#11744751C2211yescharacteristic, complemented
35C4⋊#11744751C2211yescharacteristic, complemented
36#16813545C2211yescharacteristic, complemented
37#16813545C2211yescharacteristic, complemented
38#16813542C2211yescharacteristic
39#16813542C2211yescharacteristic
40#16813542C2211yescharacteristic
41#16813542C2211yescharacteristic
42#16813542C2211yescharacteristic, complemented
43#16813542C2211yescharacteristic, complemented
44C22⋊#11744751C2211yescharacteristic
45C22⋊#11744751C2211yescharacteristic
46#16813533C2211yescharacteristic, complemented
47C4×#11744751C2211yescharacteristic, complemented
48C4⋊Q8×C113C2211yescharacteristic, complemented
49#126×C113—21no—
50#124×C113—21no—
51#124×C113C2211yescharacteristic, complemented
52#123×C113—21no—
53C22⋊Q8×C113—21no—
54C22⋊Q8×C113C2211yescharacteristic
55#121×C113C2211yescharacteristic
56C4×Q8×C113C2211yescharacteristic, complemented
57C4×D4×C113C2211yescharacteristic, complemented
58#117×C113C2211yescharacteristic
59C23×D113—21no—
60#14268647—41no—
61#14268647—41no—
62C2×Dic226C2311yescharacteristic
63C2×D452—21no—
64C2×D452—21no—
65C2×D452—21no—
66C2×D452—21no—
67C2×D452—21no—
68C2×D452—41no—
69C2×D452—41no—
70C2×D452C2311yescharacteristic
71C2×D452C2311yescharacteristic
72C2×D452C2311yescharacteristic
73C2×C22⋊D113—21no—
74C2×C4×D113—21no—
75#14268637—41no—
76#14268635—41no—
77#14268634—41no—
78#14268634—41no—
79#14268634—41no—
80#14268632—41no—
81#14268632—41no—
82#14268632—41no—
83C2×#11744751C2311yescharacteristic
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C2×#11744751C2311yescharacteristic
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91C2×Q8×C113—21no—
92C2×Q8×C113C2311yescharacteristic
93C2×D4×C113—21no—
94C2×D4×C113C2311yescharacteristic
95C22×C4×C113—21no—
96C22×C4×C113C2311yescharacteristic
97C4⋊C4×C113—21no—
98C4⋊C4×C113—21no—
99C4⋊C4×C113—21no—
100C4⋊C4×C113D411yescharacteristic
101C4⋊C4×C113D411yescharacteristic
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C22⋊C4×C113—21no—
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C22⋊C4×C113—21no—
108C22⋊C4×C113—21no—
109C22⋊C4×C113D411yescharacteristic
110C22⋊C4×C113D411yescharacteristic
111C42×C113—21no—
112C42×C113C2311yescharacteristic
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C23×C113C2×D411yescharacteristic
116C22×D113—21no—
117C22×D113—21no—
118C22×D113—21no—
119C22×D113—42no—
120C22×D113—81no—
121C22×D113—81no—
122Q8×C113—21no—
123Q8×C113—21no—
124Q8×C113—81no—
125D4×C113—21no—
126D4×C113—21no—
127D4×C113—81no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—21no—
132C2×C4×C113—21no—
133C2×C4×C113—81no—
134C2×C4×C113C2×D411yescharacteristic
135C2×C4×C113C2×D411yescharacteristic
136C2×C4×C113C2×D411yescharacteristic
137C2×C4×C113C2×D411yescharacteristic
138C2×C4×C113C2×D411yescharacteristic
139C2×C4×C113C2411yescharacteristic
140C22⋊D113—42no—
141C2×Dic113—21no—
142D452—21no—
143D452—21no—
144D452—21no—
145D452—21no—
146D452—21no—
147D452—21no—
148D452—42no—
149D452—81no—
150D452—81no—
151D452—81no—
152D452—81no—
153C4×D113—42no—
154Dic226—21no—
155Dic226—21no—
156#11744751—21no—
157#11744751—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×C113C22×D411yescharacteristic
167C2×D113—41no—
168C2×D113—41no—
169C2×D113—41no—
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—21no—
179C4×C113—21no—
180C4×C113—21no—
181C4×C113—21no—
182C4×C113—41no—
183C4×C113—41no—
184C4×C113—41no—
185C4×C113H(5,𝔽2)11yescharacteristic
186C4×C113H(5,𝔽2)11yescharacteristic
187Dic113—41no—
188C2×C113—41no—
189C2×C113—81no—
190C2×C113#53511yescharacteristic
191C2×C113#57611yescharacteristic
192C2×C113#57711yescharacteristic
193D113—81no—
194D113—81no—
195D113—81no—
196#3224—1131nomaximal, Sylow
197C113#322411yescharacteristic, complemented, Sylow
198#542D11311yescharacteristic, complemented
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#449—1131no—
211#447—1131no—
212#433—1131no—
213C2×#41—1131no—
214C22×D4—1131no—
215C2×Q16—1131no—
216C2×SD16—1131no—
217C2×SD16—1131no—
218C2×SD16—1131no—
219C2×SD16—1131no—
220C2×D8—1131no—
221C2×D8—1131no—
222C2×D8—1131no—
223C4⋊Q8C2×D11311yescharacteristic, complemented
224#127—1131no—
225#127—1131no—
226#126—21no—
227#124—21no—
228#124—1131no—
229#124—1131no—
230#124C2×D11311yescharacteristic, complemented
231#123—21no—
232C22⋊Q8—21no—
233C22⋊Q8C2×D11311yescharacteristic
234#121—2261no—
235#121—2261no—
236#121C2×D11311yescharacteristic
237#120—2261no—
238#120—2261no—
239C4×Q8C2×D11311yescharacteristic, complemented
240C4×D4C2×D11311yescharacteristic, complemented
241#117C2×D11311yescharacteristic
242C4⋊C8—1131no—
243C4⋊C8—1131no—
244#103—1131no—
245#103—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251#102—1131no—
252C22⋊C8—1131no—
253C22⋊C8—1131no—
254#97—1131no—
255C4×C8—1131no—
256C24—2261no—
257#41—4521no—
258#41—4521no—
259C2×Q8—21no—
260C2×Q8—1131no—
261C2×Q8C22×D11311yescharacteristic
262C2×D4—21no—
263C2×D4—1131no—
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×D4—2261no—
274C2×D4C22×D11311yescharacteristic
275C22×C4—21no—
276C22×C4—2261no—
277C22×C4C22×D11311yescharacteristic
278Q16—4521no—
279SD16—4521no—
280SD16—4521no—
281SD16—4521no—
282SD16—4521no—
283D8—4521no—
284D8—4521no—
285D8—4521no—
286C2×C8—1131no—
287C2×C8—1131no—
288C2×C8—1131no—
289C2×C8—1131no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C22⋊D11311yescharacteristic
294C4⋊C4C22⋊D11311yescharacteristic
295C4⋊C4C22×D11311yescharacteristic
296C4⋊C4C22×D11311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—2261no—
303C22⋊C4—2261no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4C22⋊D11311yescharacteristic
307C22⋊C4C22⋊D11311yescharacteristic
308C42—21no—
309C42C22×D11311yescharacteristic
310C42C22×D11311yescharacteristic
311C23—21no—
312C23—9041no—
313C23—9041no—
314C23—4522no—
315C23—2261no—
316C23—2261no—
317C23—2261no—
318C23C2×C22⋊D11311yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—81no—
322Q8—2261no—
323Q8—2261no—
324D4—21no—
325D4—21no—
326D4—81no—
327D4—9041no—
328D4—9041no—
329D4—9041no—
330D4—9041no—
331D4—4522no—
332D4—4522no—
333D4—2261no—
334D4—2261no—
335D4—2261no—
336D4—2261no—
337D4—2261no—
338D4—2261no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—81no—
345C2×C4—4522no—
346C2×C4—2261no—
347C2×C4C2×C22⋊D11311yescharacteristic
348C2×C4C2×C22⋊D11311yescharacteristic
349C2×C4C2×C22⋊D11311yescharacteristic
350C2×C4C2×C22⋊D11311yescharacteristic
351C2×C4C2×C22⋊D11311yescharacteristic
352C2×C4C23×D11311yescharacteristic
353C8—2261no—
354C8—2261no—
355C8—2261no—
356C8—2261no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—9044no—
364C22—4521no—
365C22—4521no—
366C22—4521no—
367C22—4521no—
368C22—4521no—
369C22—4521no—
370C22—4521no—
371C22—4521no—
372C22—4521no—
373C22C22×C22⋊D11311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—4521no—
383C4#1681366811yescharacteristic
384C4#1681366811yescharacteristic
385C2—41no—
386C2—81no—
387C2—9041no—
388C2—9041no—
389C2—9041no—
390C2#2029916211yescharacteristic
391C2#2029940111yescharacteristic
392C2#2029940611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#542×C113C2
socleC22×C113C22×D4
hypercenter#542D113
hypocenterC113#3224
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #20299167C2semidirect
2. #20298988C2semidirect
3. #20298980C2semidirect
4. #20298960C2semidirect
5. #20298946C2semidirect
6. #20298820C2semidirect
7. #20298813C2semidirect
8. #20298798C2semidirect
9. #20298793C2semidirect
10. #20298758C2semidirect
11. #20298748C2semidirect
12. #20298741C2semidirect
13. #20298731C2semidirect
14. #20298659C2semidirect
15. #542×C113C2semidirect
18. C2×#14268637C22semidirect
19. C2×#14268635C22semidirect
22. C2×#14268634C22semidirect
25. C2×#14268632C22semidirect
34. C4⋊#11744751C22semidirect
35. C4⋊#11744751C22semidirect
36. #16813545C22semidirect
37. #16813545C22semidirect
42. #16813542C22semidirect
43. #16813542C22semidirect
46. #16813533C22semidirect
47. C4×#11744751C22semidirect
48. C4⋊Q8×C113C22semidirect
51. #124×C113C22semidirect
56. C4×Q8×C113C22semidirect
57. C4×D4×C113C22semidirect
197. C113#3224semidirect
198. #542D113semidirect
223. C4⋊Q8C2×D113semidirect
230. #124C2×D113semidirect
239. C4×Q8C2×D113semidirect
240. C4×D4C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991672
#202989882
#202989802
#202989602
#202989462
#202988202
#202988132
#202987982
#202987932
#202987582
#202987482
#202987412
#202987312
#202986592
#542×C1132
#3224113