Finite Group Databasebeta

← #28402092

Subgroups — #28402092

Order 14464.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813646C211yesmaximal, characteristic, complemented
2C2×#16813642C211yesmaximal, characteristic, complemented
3#20299247C211yesmaximal, characteristic, complemented
4#20299245C211yesmaximal, characteristic, complemented
5#20298989C211yesmaximal, characteristic, complemented
6#20298855C211yesmaximal, characteristic, complemented
7#20298825C211yesmaximal, characteristic, complemented
8#20298811C211yesmaximal, characteristic, complemented
9#20298802C211yesmaximal, characteristic, complemented
10#20298762C211yesmaximal, characteristic, complemented
11#20298761C211yesmaximal, characteristic, complemented
12#20298747C211yesmaximal, characteristic, complemented
13#20298707C211yesmaximal, characteristic, complemented
14#20298666C211yesmaximal, characteristic, complemented
15#449×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×D4×D113C2211yescharacteristic
19#16813646—24no—
20#16813642—24no—
21C2×Dic452C2211yescharacteristic, complemented
22C2×#14268637C2211yescharacteristic, complemented
23C2×#14268636C2211yescharacteristic
24C2×#14268635C2211yescharacteristic
25C2×#14268635C2211yescharacteristic, complemented
26C2×#14268634C2211yescharacteristic
27C2×#14268632C2211yescharacteristic
28C2×#14268630C2211yescharacteristic
29C22×#11744751C2211yescharacteristic, complemented
30#16813620C2211yescharacteristic, complemented
31#16813609C2211yescharacteristic
32#16813605—21no—
33#16813604—21no—
34#16813603—21no—
35#16813602C2211yescharacteristic
36#16813601C2211yescharacteristic, complemented
37#16813598C2211yescharacteristic
38#16813594—21no—
39#16813593—21no—
40#16813590—21no—
41D4×Dic113C2211yescharacteristic, complemented
42#16813584C2211yescharacteristic
43C4×C22⋊D113C2211yescharacteristic
44C2×#14268626—21no—
45C22⋊C4×D113—21no—
46#16813553C2211yescharacteristic, complemented
47#16813551C2211yescharacteristic, complemented
48#16813547C2211yescharacteristic, complemented
49#16813545C2211yescharacteristic, complemented
50#16813544C2211yescharacteristic
51#16813543C2211yescharacteristic
52#16813534C2211yescharacteristic
53#16813532C2211yescharacteristic, complemented
54C2×#41×C113C2211yescharacteristic, complemented
55C2×SD16×C113C2211yescharacteristic
56C2×D8×C113C2211yescharacteristic
57#121×C113C2211yescharacteristic
58#103×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60C22⋊C8×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268647—22no—
63#14268647—41no—
64#14268646—22no—
65#14268646—41no—
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C2×C22⋊D113—21no—
72C2×C22⋊D113D411yescharacteristic
73D4×D113—22no—
74D4×D113—41no—
75C22×Dic113—21no—
76C22×Dic113—21no—
77C2×C4×D113—21no—
78C2×C4×D113—21no—
79C2×C4×D113C2311yescharacteristic
80Dic452—41no—
81#14268637—22no—
82#14268636—22no—
83#14268635—22no—
84#14268635—22no—
85#14268634—22no—
86#14268632D414yescomplemented
87#14268630—22no—
88C2×#11744751—22no—
89C2×#11744751C2311yescharacteristic
90C2×#11744751C2311yescharacteristic
91C4⋊Dic113—21no—
92C4⋊Dic113C2311yescharacteristic
93#14268626—21no—
94#14268626—21no—
95#14268626—21no—
96#14268626—21no—
97#14268626D411yescharacteristic
98C22⋊Dic113—21no—
99C22⋊Dic113—21no—
100C22⋊Dic113—21no—
101C22⋊Dic113—21no—
102C22⋊Dic113D411yescharacteristic
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624D411yescharacteristic
107C4×Dic113C2311yescharacteristic
108#41×C113—22no—
109#41×C113—41no—
110C2×Q8×C113C2311yescharacteristic
111C2×D4×C113—21no—
112C2×D4×C113—21no—
113C2×D4×C113C2311yescharacteristic
114C2×D4×C113C2311yescharacteristic
115C22×C4×C113—21no—
116C22×C4×C113C2311yescharacteristic
117SD16×C113—41no—
118D8×C113—22no—
119C2×C8×C113C2311yescharacteristic
120C2×C8×C113C2311yescharacteristic
121C4⋊C4×C113C2311yescharacteristic
122C22⋊C4×C113—21no—
123C23×C113—21no—
124C23×C113—21no—
125C23×C113C2×D411yescharacteristic
126C22×D113—21no—
127C22×D113—42no—
128C22×D113—42no—
129C22×D113—81no—
130C22×D113C2×D411yescharacteristic
131Q8×C113—21no—
132Q8×C113—21no—
133D4×C113—21no—
134D4×C113—21no—
135D4×C113—21no—
136D4×C113—42no—
137D4×C113—81no—
138D4×C113C2×D412yes—
139C2×C4×C113—21no—
140C2×C4×C113—21no—
141C2×C4×C113—21no—
142C2×C4×C113—21no—
143C2×C4×C113—42no—
144C2×C4×C113C2×D411yescharacteristic
145C2×C4×C113C2411yescharacteristic
146C22⋊D113—41no—
147C22⋊D113—42no—
148C22⋊D113—42no—
149C22⋊D113—42no—
150C2×Dic113—21no—
151C2×Dic113—21no—
152C2×Dic113—21no—
153C2×Dic113—42no—
154C2×Dic113—42no—
155C2×Dic113C2×D411yescharacteristic
156C2×Dic113C2×D411yescharacteristic
157C2×Dic113C2×D411yescharacteristic
158D452—21no—
159D452C2×D412yes—
160C4×D113—21no—
161C4×D113—21no—
162C4×D113—42no—
163C4×D113—81no—
164Dic226—21no—
165Dic226—21no—
166Dic226—21no—
167Dic226—21no—
168C8×C113—21no—
169C8×C113—21no—
170#11744751—21no—
171#11744751C2×D412yes—
172C22×C113—22no—
173C22×C113—21no—
174C22×C113—21no—
175C22×C113—21no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113C22×D411yescharacteristic
182C2×D113—21no—
183C2×D113—22no—
184C2×D113—21no—
185C2×D113—21no—
186C2×D113—41no—
187C2×D113—41no—
188C2×D113—84no—
189C4×C113—21no—
190C4×C113—41no—
191C4×C113—41no—
192C4×C113C22×D411yescharacteristic
193C4×C113H(5,𝔽2)11yescharacteristic
194Dic113—21no—
195Dic113—21no—
196Dic113—21no—
197Dic113—41no—
198Dic113—41no—
199Dic113—41no—
200C2×C113—41no—
201C2×C113—42no—
202C2×C113—81no—
203C2×C113D4211yescharacteristic
204C2×C113#57511yescharacteristic
205C2×C113#57711yescharacteristic
206D113—41no—
207D113—42no—
208#3267—1131nomaximal, Sylow
209C113#326711yescharacteristic, complemented, Sylow
210C2×AGL(1,ℤ/8)—1131no—
211C2×#135—1131no—
212#547—1131no—
213#546—1131no—
214#497—1131no—
215#470—1131no—
216#465—1131no—
217#463—1131no—
218#461—1131no—
219#452—1131no—
220#452—1131no—
221#450—1131no—
222#449D11311yescharacteristic, complemented
223#442—1131no—
224#435—1131no—
225C2×#41—1131no—
226C2×#41—1131no—
227C2×#41C2×D11311yescharacteristic, complemented
228C22×D4—1131no—
229AGL(1,ℤ/8)—2264no—
230#135—2264no—
231C2×Q16—1131no—
232C2×Q16—1131no—
233C2×SD16—1131no—
234C2×SD16—1131no—
235C2×SD16—1131no—
236C2×SD16—1131no—
237C2×SD16C2×D11311yescharacteristic
238C2×D8—1131no—
239C2×D8C2×D11311yescharacteristic
240C2×M16—1131no—
241C22×C8—1131no—
242C4⋊Q8—1131no—
243#124—1131no—
244#123—2261no—
245#123—2261no—
246#123—2261no—
247C22⋊Q8—1131no—
248C22⋊Q8—1131no—
249C22⋊Q8—1131no—
250#121—2261no—
251#121—2261no—
252#121C2×D11311yescharacteristic
253#120—2261no—
254C4×D4—1131no—
255C4×D4—1131no—
256C4×D4—1131no—
257C2×C4⋊C4—2261no—
258C2×C22⋊C4—2261no—
259#106—1131no—
260C4⋊C8—1131no—
261#103—1131no—
262#103—1131no—
263#103C2×D11311yescharacteristic, complemented
264#102—1131no—
265#102—1131no—
266#102C2×D11311yescharacteristic, complemented
267C22⋊C8—1131no—
268C22⋊C8C2×D11311yescharacteristic, complemented
269#97—1131no—
270C24—2261no—
271#41—22no—
272#41—41no—
273#41—4521no—
274#41—4521no—
275#41—2262no—
276#41—2262no—
277C2×Q8—1131no—
278C2×Q8—1131no—
279C2×Q8C22×D11311yescharacteristic
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—1131no—
283C2×D4—1131no—
284C2×D4—4521no—
285C2×D4—2261no—
286C2×D4—2262no—
287C2×D4—2261no—
288C2×D4—2261no—
289C2×D4C22×D11311yescharacteristic
290C2×D4C22×D11311yescharacteristic
291C22×C4—21no—
292C22×C4—1131no—
293C22×C4—2261no—
294C22×C4—2261no—
295C22×C4—2261no—
296C22×C4—2261no—
297C22×C4C22×D11311yescharacteristic
298Q16—4521no—
299Q16—2262no—
300SD16—41no—
301SD16—2262no—
302SD16—2262no—
303SD16—2262no—
304SD16—2262no—
305D8—22no—
306D8—1134no—
307M16—2262no—
308C2×C8—1131no—
309C2×C8—1131no—
310C2×C8—2262no—
311C2×C8C22×D11311yescharacteristic
312C2×C8C22×D11311yescharacteristic
313C4⋊C4—1131no—
314C4⋊C4—1131no—
315C4⋊C4—2261no—
316C4⋊C4—2261no—
317C4⋊C4—2261no—
318C4⋊C4—2261no—
319C4⋊C4—2261no—
320C4⋊C4C22×D11311yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—1131no—
323C22⋊C4—1131no—
324C22⋊C4—2261no—
325C22⋊C4—2261no—
326C22⋊C4—2261no—
327C22⋊C4—2261no—
328C22⋊C4—2261no—
329C22⋊C4—2261no—
330C22⋊C4—2261no—
331C42—1131no—
332C23—21no—
333C23—21no—
334C23—1131no—
335C23—9041no—
336C23—4522no—
337C23—4522no—
338C23—2261no—
339C23D4×D11311yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—2261no—
343Q8—2261no—
344Q8—2261no—
345Q8—2261no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—81no—
351D4—1132no—
352D4—4522no—
353D4—4522no—
354D4—4521no—
355D4—4522no—
356D4—2261no—
357D4D4×D11312yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—1131no—
364C2×C4—1131no—
365C2×C4—1131no—
366C2×C4—9041no—
367C2×C4—4522no—
368C2×C4—4522no—
369C2×C4—4522no—
370C2×C4—2261no—
371C2×C4—2261no—
372C2×C4—2261no—
373C2×C4—2261no—
374C2×C4—2261no—
375C2×C4D4×D11311yescharacteristic
376C2×C4C23×D11311yescharacteristic
377C8—21no—
378C8—21no—
379C8—1132no—
380C8—2261no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—9044no—
391C22—4521no—
392C22—4521no—
393C22—2261no—
394C22—2261no—
395C22—2262no—
396C22—2261no—
397C22C2×D4×D11311yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—4521no—
402C4—4521no—
403C4—4521no—
404C4—2261no—
405C4—2261no—
406C4—2261no—
407C4C2×D4×D11311yescharacteristic
408C4#1681366711yescharacteristic
409C2—41no—
410C2—42no—
411C2—81no—
412C2—4521no—
413C2—4522no—
414C2#2029923011yescharacteristic
415C2#2029939511yescharacteristic
416C2#2029940811yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#449×C113C2
socleC22×C113C22×D4
hypercenter#449D113
hypocenterC113#3267
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. C2×#16813646C2semidirect
2. C2×#16813642C2semidirect
3. #20299247C2semidirect
4. #20299245C2semidirect
5. #20298989C2semidirect
6. #20298855C2semidirect
7. #20298825C2semidirect
8. #20298811C2semidirect
9. #20298802C2semidirect
10. #20298762C2semidirect
11. #20298761C2semidirect
12. #20298747C2semidirect
13. #20298707C2semidirect
14. #20298666C2semidirect
15. #449×C113C2semidirect
21. C2×Dic452C22semidirect
22. C2×#14268637C22semidirect
25. C2×#14268635C22semidirect
29. C22×#11744751C22semidirect
30. #16813620C22semidirect
36. #16813601C22semidirect
41. D4×Dic113C22semidirect
46. #16813553C22semidirect
47. #16813551C22semidirect
48. #16813547C22semidirect
49. #16813545C22semidirect
53. #16813532C22semidirect
54. C2×#41×C113C22semidirect
58. #103×C113C22semidirect
59. #102×C113C22semidirect
60. C22⋊C8×C113C22semidirect
86. #14268632D4semidirect
209. C113#3267semidirect
222. #449D113semidirect
227. C2×#41C2×D113semidirect
263. #103C2×D113semidirect
266. #102C2×D113semidirect
268. C22⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
C2×#168136422
#202992472
#202992452
#202989892
#202988552
#202988252
#202988112
#202988022
#202987622
#202987612
#202987472
#202987072
#202986662
#449×C1132
#3267113