Finite Group Databasebeta

← #28402396

Subgroups — #28402396

Order 14464.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299303C211yesmaximal, characteristic, complemented
2#20299232C211yesmaximal, characteristic
3#20298943C211yesmaximal, characteristic, complemented
4#20298918C211yesmaximal, characteristic, complemented
5#20298887C211yesmaximal, characteristic, complemented
6#20298828C211yesmaximal, characteristic, complemented
7#20298825C211yesmaximal, characteristic, complemented
8#20298797C211yesmaximal, characteristic, complemented
9#20298751C211yesmaximal, characteristic, complemented
10#20298750C211yesmaximal, characteristic, complemented
11#20298685C211yesmaximal, characteristic, complemented
12#20298661C211yesmaximal, characteristic, complemented
13C2×#16813542C211yesmaximal, characteristic, complemented
14#102×D113C211yesmaximal, characteristic, complemented
15#481×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic
17C2×D4×D113—21no—
18C2×D4×D113C2211yescharacteristic
19C2×#14268636C2211yescharacteristic
20C2×#14268636C2211yescharacteristic, complemented
21C2×#14268635C2211yescharacteristic, complemented
22C22×#11744751C2211yescharacteristic, complemented
23C2×C8×D113C2211yescharacteristic, complemented
24#16813621C2211yescharacteristic, complemented
25#16813618C2211yescharacteristic
26#16813612—21no—
27#16813602C2211yescharacteristic, complemented
28#16813601—21no—
29#16813601C2211yescharacteristic, complemented
30#16813600—21no—
31#16813597C2211yescharacteristic
32#16813595—21no—
33#16813592—21no—
34#16813590—21no—
35#16813587C2211yescharacteristic, complemented
36#16813584C2211yescharacteristic
37C4×C22⋊D113—21no—
38C4×C22⋊D113C2211yescharacteristic
39C4⋊C4×D113C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813545C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic
44#16813544C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic, complemented
46#16813542C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic, complemented
49#16813542C2211yescharacteristic, complemented
50#16813534C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52#121×C113C2211yescharacteristic
53C2×C4⋊C4×C113C2211yescharacteristic, complemented
54#106×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#102×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C23×D113—21no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63C2×D452—22no—
64C2×D452—21no—
65C2×D452—21no—
66C2×D452—41no—
67C2×D452C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113D411yescharacteristic
73D4×D113—22no—
74D4×D113—41no—
75D4×D113—44no—
76C2×C4×D113—21no—
77C2×C4×D113—21no—
78C2×C4×D113C2311yescharacteristic
79#14268636—22no—
80#14268636—41no—
81#14268635—41no—
82C2×#11744751—41no—
83C2×#11744751C2311yescharacteristic
84C2×#11744751C2311yescharacteristic
85C8×D113—41no—
86C4⋊Dic113—21no—
87C4⋊Dic113C2311yescharacteristic
88#14268626—21no—
89#14268626—21no—
90#14268626—21no—
91#14268626—21no—
92#14268626D411yescharacteristic
93C22⋊Dic113—21no—
94C22⋊Dic113D411yescharacteristic
95#14268624—21no—
96#14268624—21no—
97#14268624—21no—
98#14268624D411yescharacteristic
99C4×Dic113—21no—
100C4×Dic113C2311yescharacteristic
101C2×D4×C113—21no—
102C2×D4×C113C2311yescharacteristic
103C22×C4×C113—21no—
104C22×C4×C113C2311yescharacteristic
105C2×C8×C113C2311yescharacteristic
106C2×C8×C113C2311yescharacteristic
107C4⋊C4×C113—21no—
108C4⋊C4×C113C2311yescharacteristic
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C23×C113—21no—
113C23×C113C2×D411yescharacteristic
114C22×D113—21no—
115C22×D113—21no—
116C22×D113—42no—
117C22×D113—42no—
118C22×D113—42no—
119C22×D113—42no—
120C22×D113—81no—
121C22×D113—81no—
122C22×D113C2×D411yescharacteristic
123D4×C113—21no—
124D4×C113—21no—
125D4×C113—42no—
126C2×C4×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113—21no—
131C2×C4×C113—81no—
132C2×C4×C113C2×D411yescharacteristic
133C2×C4×C113C2411yescharacteristic
134C22⋊D113—42no—
135C22⋊D113—42no—
136C22⋊D113—81no—
137C22⋊D113SD1614yescomplemented
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113C2×D411yescharacteristic
141C2×Dic113C2×D411yescharacteristic
142C2×Dic113C2×D411yescharacteristic
143D452—21no—
144D452—21no—
145D452—21no—
146D452—42no—
147D452—42no—
148D452#4112yes—
149C4×D113—21no—
150C4×D113—21no—
151C4×D113—42no—
152C4×D113—81no—
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—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113C2×SD1612yes—
166C22×C113C22×D411yescharacteristic
167C2×D113—21no—
168C2×D113—21no—
169C2×D113—22no—
170C2×D113—41no—
171C2×D113—41no—
172C2×D113—41no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—84no—
176C2×D113—84no—
177C2×D113C2×SD1612yes—
178C4×C113—21no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113—41no—
182C4×C113C2×#4111yescharacteristic
183C4×C113H(5,𝔽2)11yescharacteristic
184Dic113—21no—
185Dic113—21no—
186Dic113—41no—
187Dic113—41no—
188Dic113C2×SD1612yes—
189C2×C113—22no—
190C2×C113—81no—
191C2×C113#54611yescharacteristic
192C2×C113C22×SD1611yescharacteristic
193C2×C113#57611yescharacteristic
194D113—22no—
195D113—42no—
196D113—81no—
197#3295—1131nomaximal, Sylow
198C113#329511yescharacteristic, complemented, Sylow
199#554—1131no—
200D42—1131no—
201#486—1131no—
202#481—1131no—
203#481D11311yescharacteristic, complemented
204#476—1131no—
205#465—1131no—
206#465—1131no—
207#460—1131no—
208#450—1131no—
209#450—1131no—
210C4×SD16—1131no—
211C8×D4—1131no—
212C2×#102—1131no—
213C2×#102—1131no—
214C22×D4—1131no—
215C22×D4—1131no—
216C22×D4—2261no—
217C2×SD16—1131no—
218C2×SD16—1131no—
219C2×SD16—1131no—
220C22×C8—1131no—
221C22×C8—1131no—
222C4⋊Q8—1131no—
223#127—1131no—
224#125—2261no—
225C22⋊Q8—1131no—
226C22⋊Q8—1131no—
227C22⋊Q8—2261no—
228C22⋊Q8—2261no—
229#121—1131no—
230#121—2261no—
231#121C2×D11311yescharacteristic
232#120—2261no—
233#120—2261no—
234C4×Q8—1131no—
235C4×D4—1131no—
236C4×D4—1131no—
237C4×D4—2261no—
238C2×C4⋊C4—1131no—
239C2×C4⋊C4C2×D11311yescharacteristic, complemented
240#106—1131no—
241#106C2×D11311yescharacteristic, complemented
242#106C2×D11311yescharacteristic, complemented
243C4⋊C8—1131no—
244#103—1131no—
245#102—1131no—
246#102—1131no—
247#102—1131no—
248#102—1131no—
249#102—1131no—
250#102—1131no—
251#102—1131no—
252#102C2×D11311yescharacteristic, complemented
253#102C2×D11311yescharacteristic, complemented
254C22⋊C8—1131no—
255C22⋊C8C2×D11311yescharacteristic, complemented
256C4×C8—1131no—
257C24—2261no—
258C24—2261no—
259C2×Q8—1131no—
260C2×Q8—2261no—
261C2×D4—21no—
262C2×D4—1131no—
263C2×D4—1131no—
264C2×D4—1131no—
265C2×D4—4521no—
266C2×D4—4524no—
267C2×D4—4521no—
268C2×D4—2262no—
269C2×D4—2261no—
270C2×D4—2261no—
271C2×D4—2261no—
272C2×D4—2261no—
273C2×D4—2262no—
274C2×D4—2261no—
275C2×D4C22×D11311yescharacteristic
276C22×C4—21no—
277C22×C4—1131no—
278C22×C4—2261no—
279C22×C4—2261no—
280C22×C4C22×D11311yescharacteristic
281SD16—4521no—
282SD16—4521no—
283SD16—2262no—
284C2×C8—1131no—
285C2×C8—1131no—
286C2×C8—4521no—
287C2×C8—4521no—
288C2×C8C22×D11311yescharacteristic
289C2×C8C22×D11311yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—1131no—
292C4⋊C4—1131no—
293C4⋊C4—2261no—
294C4⋊C4—2261no—
295C4⋊C4—2261no—
296C4⋊C4—2261no—
297C4⋊C4—2261no—
298C4⋊C4C22×D11311yescharacteristic
299C4⋊C4C22×D11311yescharacteristic
300C4⋊C4C22×D11311yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—1131no—
303C22⋊C4—1131no—
304C22⋊C4—2261no—
305C22⋊C4—2261no—
306C22⋊C4—2261no—
307C22⋊C4—2261no—
308C42—1131no—
309C42—2261no—
310C23—21no—
311C23—1131no—
312C23—9041no—
313C23—9041no—
314C23—4522no—
315C23—4522no—
316C23—4522no—
317C23—4522no—
318C23—2261no—
319C23—2261no—
320C23D4×D11311yescharacteristic
321Q8—9041no—
322Q8—2261no—
323Q8—2261no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—1134no—
328D4—1132no—
329D4—9041no—
330D4—4522no—
331D4—4522no—
332D4—4522no—
333D4—4522no—
334D4—2261no—
335D4—2261no—
336D4—2261no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—81no—
343C2×C4—1131no—
344C2×C4—1131no—
345C2×C4—1131no—
346C2×C4—9041no—
347C2×C4—4522no—
348C2×C4—2261no—
349C2×C4—2261no—
350C2×C4—2261no—
351C2×C4—2261no—
352C2×C4D4×D11311yescharacteristic
353C2×C4C23×D11311yescharacteristic
354C8—21no—
355C8—21no—
356C8—2261no—
357C8—2261no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—1132no—
364C22—9044no—
365C22—9044no—
366C22—4521no—
367C22—4521no—
368C22—4521no—
369C22—4521no—
370C22—4521no—
371C22—2262no—
372C22—2261no—
373C22—2261no—
374C22SD16×D11312yes—
375C22C2×D4×D11311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1132no—
381C4—4521no—
382C4—4521no—
383C4—2261no—
384C4—2261no—
385C4#41×D11311yescharacteristic
386C4#1681366811yescharacteristic
387C2—22no—
388C2—81no—
389C2—9041no—
390C2—4522no—
391C2—2262no—
392C2#2029924011yescharacteristic
393C2C2×SD16×D11311yescharacteristic
394C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#481×C113C2
socleC22×C113C22×D4
prime radical#20299232C2
hypercenter#481D113
hypocenterC113#3295
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #20299303C2semidirect
3. #20298943C2semidirect
4. #20298918C2semidirect
5. #20298887C2semidirect
6. #20298828C2semidirect
7. #20298825C2semidirect
8. #20298797C2semidirect
9. #20298751C2semidirect
10. #20298750C2semidirect
11. #20298685C2semidirect
12. #20298661C2semidirect
13. C2×#16813542C2semidirect
14. #102×D113C2semidirect
15. #481×C113C2semidirect
20. C2×#14268636C22semidirect
21. C2×#14268635C22semidirect
22. C22×#11744751C22semidirect
23. C2×C8×D113C22semidirect
24. #16813621C22semidirect
27. #16813602C22semidirect
29. #16813601C22semidirect
35. #16813587C22semidirect
39. C4⋊C4×D113C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813545C22semidirect
44. #16813544C22semidirect
45. #16813543C22semidirect
48. #16813542C22semidirect
49. #16813542C22semidirect
50. #16813534C22semidirect
51. C8×Dic113C22semidirect
53. C2×C4⋊C4×C113C22semidirect
54. #106×C113C22semidirect
55. #106×C113C22semidirect
56. #102×C113C22semidirect
57. #102×C113C22semidirect
58. C22⋊C8×C113C22semidirect
137. C22⋊D113SD16semidirect
198. C113#3295semidirect
203. #481D113semidirect
239. C2×C4⋊C4C2×D113semidirect
241. #106C2×D113semidirect
242. #106C2×D113semidirect
252. #102C2×D113semidirect
253. #102C2×D113semidirect
255. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993032
#202992322
#202989432
#202989182
#202988872
#202988282
#202988252
#202987972
#202987512
#202987502
#202986852
#202986612
C2×#168135422
#102×D1132
#481×C1132
#3295113