Finite Group Databasebeta

← #28400485

Subgroups — #28400485

Order 14464.

420 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299105C211yesmaximal, characteristic
2#117×D113C211yesmaximal, characteristic, complemented
3#20298938C211yesmaximal, characteristic, complemented
4#20298937C211yesmaximal, characteristic, complemented
5#20298932C211yesmaximal, characteristic, complemented
6#20298927C211yesmaximal, characteristic, complemented
7#20298921C211yesmaximal, characteristic, complemented
8#20298920C211yesmaximal, characteristic, complemented
9#20298915C211yesmaximal, characteristic, complemented
10#20298910C211yesmaximal, characteristic, complemented
11#20298636C211yesmaximal, characteristic, complemented
12#20298634C211yesmaximal, characteristic, complemented
13#20298594C211yesmaximal, characteristic, complemented
14C2×#16813534C211yesmaximal, characteristic, complemented
15#416×C113C211yesmaximal, characteristic, complemented
16C22×C4×D113C2211yescharacteristic
17C22×#11744751C2211yescharacteristic
18#16813603—21no—
19#16813598C2211yescharacteristic
20#16813598C2211yescharacteristic
21#16813593C2211yescharacteristic
22#16813593C2211yescharacteristic
23#16813590—21no—
24C4×C22⋊D113—21no—
25C4×C22⋊D113—21no—
26#16813581C2211yescharacteristic
27#16813581C2211yescharacteristic
28#16813580C2211yescharacteristic
29#16813580C2211yescharacteristic
30#16813579—21no—
31#16813578—21no—
32C4⋊C4×D113C2211yescharacteristic
33C4⋊C4×D113C2211yescharacteristic
34C22⋊C4×D113—21no—
35C42×D113—21no—
36#16813556C2211yescharacteristic, complemented
37#16813556C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813554C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813553C2211yescharacteristic, complemented
44#16813546C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic, complemented
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C2×#41×C113C2211yescharacteristic
53C22×C8×C113C2211yescharacteristic
54#117×C113C2211yescharacteristic
55#103×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59C23×D113D411yescharacteristic
60C2×C22⋊D113—21no—
61C2×C22⋊D113—21no—
62C22×Dic113D411yescharacteristic
63C2×C4×D113—22no—
64C2×C4×D113—22no—
65C2×C4×D113—21no—
66C2×C4×D113—21no—
67C2×C4×D113D411yescharacteristic
68C2×C4×D113D411yescharacteristic
69C2×C4×D113C2311yescharacteristic
70C2×C4×D113C2311yescharacteristic
71C2×#11744751—22no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C4⋊Dic113C2311yescharacteristic
75C4⋊Dic113C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626—21no—
82C22⋊Dic113—21no—
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90C4×Dic113—21no—
91C4×Dic113—21no—
92C4×Dic113—21no—
93C4×Dic113—21no—
94#41×C113—22no—
95#41×C113—22no—
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100C22×C4×C113C2311yescharacteristic
101C2×C8×C113—22no—
102C2×C8×C113C2311yescharacteristic
103C2×C8×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C23×C113—21no—
109C23×C113C2×D411yescharacteristic
110C22×D113—22no—
111C22×D113—22no—
112C22×D113—41no—
113C22×D113C2×D411yescharacteristic
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113—42no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—42no—
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113#4112yes—
126C2×C4×C113#4112yes—
127C2×C4×C113C2411yescharacteristic
128C22⋊D113—42no—
129C22⋊D113—42no—
130C2×Dic113—22no—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113C2×D411yescharacteristic
136C2×Dic113C2×D411yescharacteristic
137C4×D113—22no—
138C4×D113—22no—
139C4×D113—21no—
140C4×D113—21no—
141C4×D113—21no—
142C4×D113—21no—
143C4×D113—42no—
144C4×D113—42no—
145C8×C113—21no—
146C8×C113—21no—
147#11744751—21no—
148#11744751—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113#12312yes—
155C22×C113C22×D411yescharacteristic
156C2×D113—21no—
157C2×D113—21no—
158C2×D113—21no—
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—44no—
162C2×D113#13512yes—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113#12312yes—
167C4×C113C2×#4111yescharacteristic
168C4×C113C2×#4111yescharacteristic
169Dic113—21no—
170Dic113—21no—
171Dic113—41no—
172Dic113—41no—
173Dic113—41no—
174Dic113—41no—
175C2×C113—22no—
176C2×C113—81no—
177C2×C113C2×#12311yescharacteristic
178C2×C113C2×#13511yescharacteristic
179C2×C113#57511yescharacteristic
180D113—22no—
181D113—41no—
182#3091—1131nomaximal, Sylow
183C113#309111yescharacteristic, complemented, Sylow
184#525—1131no—
185C2×#117—1131no—
186#485—1131no—
187#485—1131no—
188#484—1131no—
189#483—1131no—
190#482—1131no—
191#482—1131no—
192#481—1131no—
193#480—1131no—
194#427—1131no—
195#427—1131no—
196#416—1131no—
197#416D11311yescharacteristic, complemented
198C2×C22⋊C8—1131no—
199C2×#41C2×D11311yescharacteristic
200C23×C4—1131no—
201C22×C8—1131no—
202C22×C8C2×D11311yescharacteristic
203#123—2261no—
204C22⋊Q8—1131no—
205C22⋊Q8—1131no—
206#121—1131no—
207#121—1131no—
208#120—2261no—
209C4×D4—2261no—
210C4×D4—2261no—
211#117—1131no—
212#117—1131no—
213#117—1131no—
214#117—1131no—
215#117—2261no—
216#117—2261no—
217#117C2×D11311yescharacteristic
218C2×C4⋊C4—1131no—
219C2×C4⋊C4—1131no—
220C2×C22⋊C4—2261no—
221C2×C42—2261no—
222#107—1131no—
223#107—1131no—
224#107—1131no—
225#107—1131no—
226#106—1131no—
227#106—1131no—
228#106—1131no—
229#106—1131no—
230#103—1131no—
231#103—1131no—
232#103C2×D11311yescharacteristic, complemented
233#103C2×D11311yescharacteristic, complemented
234#102—1131no—
235#102—1131no—
236#102C2×D11311yescharacteristic, complemented
237#102C2×D11311yescharacteristic, complemented
238C22⋊C8—1131no—
239C22⋊C8—1131no—
240C22⋊C8—1131no—
241C22⋊C8—1131no—
242C24—1131no—
243#41—22no—
244#41—22no—
245C2×Q8C22×D11311yescharacteristic
246C2×D4—21no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4C22×D11311yescharacteristic
250C22×C4—21no—
251C22×C4—1131no—
252C22×C4—1131no—
253C22×C4—1131no—
254C22×C4—1131no—
255C22×C4—1131no—
256C22×C4—2261no—
257C22×C4—2261no—
258C22×C4—2262no—
259C22×C4—2262no—
260C22×C4C22×D11311yescharacteristic
261C2×C8—22no—
262C2×C8—1131no—
263C2×C8—1131no—
264C2×C8—2262no—
265C2×C8C22×D11311yescharacteristic
266C2×C8C22×D11311yescharacteristic
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—1131no—
270C4⋊C4—1131no—
271C4⋊C4—2261no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—21no—
287C42—2261no—
288C42—2261no—
289C42—2261no—
290C42—2261no—
291C23—21no—
292C23—1131no—
293C23—1131no—
294C23—4521no—
295C23—2262no—
296C23—2262no—
297C23D4×D11311yescharacteristic
298Q8—21no—
299Q8—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—4522no—
304D4—4522no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—4522no—
312C2×C4—4522no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2262no—
318C2×C4—2262no—
319C2×C4—2262no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4D4×D11311yescharacteristic
325C2×C4#1426864612yes—
326C2×C4#1426864712yes—
327C2×C4C23×D11311yescharacteristic
328C8—21no—
329C8—21no—
330C8—2261no—
331C8—2261no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—1132no—
338C22—4524no—
339C22—2261no—
340C22—2261no—
341C22—2261no—
342C22—2261no—
343C22—2261no—
344C22#1681360412yes—
345C22C2×D4×D11311yescharacteristic
346C4—41no—
347C4—41no—
348C4—41no—
349C4—4521no—
350C4—4521no—
351C4—4521no—
352C4—4521no—
353C4—2261no—
354C4—2261no—
355C4#1681360412yes—
356C4C2×#1426864611yescharacteristic
357C4C2×#1426864711yescharacteristic
358C2—22no—
359C2—81no—
360C2—4521no—
361C2—2262no—
362C2C2×#1681360411yescharacteristic
363C2#135×D11311yescharacteristic
364C2#2029939511yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#416×C113C2
socleC22×C113C22×D4
prime radical#20299105C2
hypercenter#416D113
hypocenterC113#3091
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #117×D113C2semidirect
3. #20298938C2semidirect
4. #20298937C2semidirect
5. #20298932C2semidirect
6. #20298927C2semidirect
7. #20298921C2semidirect
8. #20298920C2semidirect
9. #20298915C2semidirect
10. #20298910C2semidirect
11. #20298636C2semidirect
12. #20298634C2semidirect
13. #20298594C2semidirect
14. C2×#16813534C2semidirect
15. #416×C113C2semidirect
36. #16813556C22semidirect
37. #16813556C22semidirect
38. #16813555C22semidirect
39. #16813555C22semidirect
40. #16813554C22semidirect
41. #16813554C22semidirect
42. #16813553C22semidirect
43. #16813553C22semidirect
44. #16813546C22semidirect
45. #16813546C22semidirect
46. #16813543C22semidirect
47. #16813543C22semidirect
55. #103×C113C22semidirect
56. #103×C113C22semidirect
57. #102×C113C22semidirect
58. #102×C113C22semidirect
183. C113#3091semidirect
197. #416D113semidirect
232. #103C2×D113semidirect
233. #103C2×D113semidirect
236. #102C2×D113semidirect
237. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202991052
#117×D1132
#202989382
#202989372
#202989322
#202989272
#202989212
#202989202
#202989152
#202989102
#202986362
#202986342
#202985942
C2×#168135342
#416×C1132
#3091113