Finite Group Databasebeta

← #28402120

Subgroups — #28402120

Order 14464.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813646C211yesmaximal, characteristic, complemented
2C2×#16813641C211yesmaximal, characteristic, complemented
3#20299268C211yesmaximal, characteristic, complemented
4#20299243C211yesmaximal, characteristic, complemented
5#20298985C211yesmaximal, characteristic, complemented
6#20298843C211yesmaximal, characteristic, complemented
7#20298833C211yesmaximal, characteristic, complemented
8#20298821C211yesmaximal, characteristic, complemented
9#20298761C211yesmaximal, characteristic, complemented
10#20298744C211yesmaximal, characteristic, complemented
11#20298740C211yesmaximal, characteristic, complemented
12#20298730C211yesmaximal, characteristic, complemented
13#20298698C211yesmaximal, characteristic, complemented
14#20298668C211yesmaximal, characteristic, complemented
15#459×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18C2×#14268646C2211yescharacteristic, complemented
19C2×D4×D113C2211yescharacteristic
20#16813646—24no—
21#16813641—24no—
22C2×Dic452C2211yescharacteristic, complemented
23C2×#14268636C2211yescharacteristic
24C2×#14268635C2211yescharacteristic
25C2×#14268635C2211yescharacteristic, complemented
26C2×#14268635C2211yescharacteristic, complemented
27C2×#14268632C2211yescharacteristic
28C2×#14268632C2211yescharacteristic
29C2×#14268630C2211yescharacteristic
30C2×C8×D113C2211yescharacteristic, complemented
31#16813618—21no—
32#16813610C2211yescharacteristic
33#16813606—21no—
34#16813602C2211yescharacteristic
35#16813597C2211yescharacteristic
36#16813596—21no—
37#16813594—21no—
38#16813594—21no—
39#16813593C2211yescharacteristic
40#16813593C2211yescharacteristic, complemented
41#16813592—21no—
42C4×Dic226C2211yescharacteristic, complemented
43C4×D452C2211yescharacteristic
44D4×Dic113—21no—
45C2×#14268624—21no—
46#16813555C2211yescharacteristic, complemented
47#16813547C2211yescharacteristic, complemented
48#16813545C2211yescharacteristic, complemented
49#16813544C2211yescharacteristic
50#16813543C2211yescharacteristic
51#16813534C2211yescharacteristic
52#16813534C2211yescharacteristic, complemented
53#16813533C2211yescharacteristic, complemented
54C2×D8×C113C2211yescharacteristic
55C2×D8×C113C2211yescharacteristic
56#127×C113C2211yescharacteristic, complemented
57C4×D4×C113C2211yescharacteristic
58C4⋊C8×C113C2211yescharacteristic, complemented
59#102×C113C2211yescharacteristic, complemented
60#102×C113C2211yescharacteristic, complemented
61C23×D113—21no—
62#14268646—22no—
63#14268646—22no—
64#14268646—22no—
65#14268646—41no—
66#14268646—41no—
67#14268646—41no—
68C2×Dic226C2311yescharacteristic
69C2×Dic226C2311yescharacteristic
70C2×D452—21no—
71C2×D452D411yescharacteristic
72C2×D452C2311yescharacteristic
73C2×C22⋊D113—21no—
74C2×C22⋊D113—21no—
75C2×C22⋊D113—21no—
76C2×C22⋊D113—21no—
77C2×C22⋊D113—21no—
78C2×C22⋊D113—21no—
79D4×D113—22no—
80D4×D113—41no—
81C22×Dic113—21no—
82C22×Dic113—21no—
83C22×Dic113—21no—
84C2×C4×D113C2311yescharacteristic
85C2×C4×D113C2311yescharacteristic
86Dic452—22no—
87#14268636—22no—
88#14268635—22no—
89#14268635—41no—
90#14268635D414yescomplemented
91#14268632—22no—
92#14268632—41no—
93#14268630—22no—
94C2×#11744751C2311yescharacteristic
95C2×#11744751C2311yescharacteristic
96C8×D113—22no—
97C4⋊Dic113—21no—
98C4⋊Dic113D411yescharacteristic
99C4⋊Dic113C2311yescharacteristic
100#14268626—21no—
101C22⋊Dic113—21no—
102C22⋊Dic113—21no—
103#14268624—21no—
104#14268624—21no—
105#14268624—21no—
106#14268624—21no—
107#14268624D411yescharacteristic
108#14268624D411yescharacteristic
109C4×Dic113—21no—
110C2×D4×C113—21no—
111C2×D4×C113—21no—
112C2×D4×C113C2311yescharacteristic
113C2×D4×C113C2311yescharacteristic
114C2×D4×C113C2311yescharacteristic
115C22×C4×C113—21no—
116D8×C113—22no—
117D8×C113—22no—
118C2×C8×C113C2311yescharacteristic
119C2×C8×C113C2311yescharacteristic
120C4⋊C4×C113C2311yescharacteristic
121C22⋊C4×C113—21no—
122C42×C113C2311yescharacteristic
123C23×C113—21no—
124C23×C113—21no—
125C23×C113—21no—
126C22×D113—21no—
127C22×D113—42no—
128C22×D113—42no—
129C22×D113—81no—
130C22×D113C2×D411yescharacteristic
131C22×D113C2×D411yescharacteristic
132D4×C113—21no—
133D4×C113—21no—
134D4×C113—21no—
135D4×C113—21no—
136D4×C113—21no—
137D4×C113—42no—
138D4×C113—81no—
139D4×C113C2×D412yes—
140C2×C4×C113—21no—
141C2×C4×C113—81no—
142C2×C4×C113C2×D411yescharacteristic
143C2×C4×C113C2×D411yescharacteristic
144C2×C4×C113C2411yescharacteristic
145C22⋊D113—42no—
146C22⋊D113—42no—
147C22⋊D113—42no—
148C22⋊D113—42no—
149C22⋊D113—81no—
150C22⋊D113—81no—
151C2×Dic113—21no—
152C2×Dic113—21no—
153C2×Dic113—21no—
154C2×Dic113—42no—
155C2×Dic113—42no—
156C2×Dic113—42no—
157C2×Dic113C2×D411yescharacteristic
158C2×Dic113C2×D411yescharacteristic
159D452—21no—
160D452—21no—
161D452—41no—
162D452—81no—
163C4×D113—21no—
164C4×D113—21no—
165C4×D113—21no—
166C4×D113—21no—
167Dic226—21no—
168Dic226—21no—
169Dic226—21no—
170Dic226C2×D412yes—
171C8×C113—21no—
172C8×C113—21no—
173#11744751—21no—
174#11744751C2×D412yes—
175C22×C113—22no—
176C22×C113—41no—
177C22×C113—41no—
178C22×C113—41no—
179C22×C113—41no—
180C22×C113—41no—
181C22×C113—41no—
182C22×C113—41no—
183C22×C113—41no—
184C22×C113C22×D411yescharacteristic
185C2×D113—21no—
186C2×D113—21no—
187C2×D113—21no—
188C2×D113—21no—
189C2×D113—21no—
190C2×D113—21no—
191C2×D113—41no—
192C2×D113—41no—
193C2×D113—41no—
194C2×D113—84no—
195C4×C113—21no—
196C4×C113—21no—
197C4×C113—41no—
198C4×C113C22×D411yescharacteristic
199C4×C113H(5,𝔽2)11yescharacteristic
200Dic113—22no—
201Dic113—21no—
202Dic113—21no—
203Dic113—41no—
204Dic113—41no—
205C2×C113—42no—
206C2×C113—81no—
207C2×C113—81no—
208C2×C113D4211yescharacteristic
209C2×C113#57511yescharacteristic
210C2×C113#57611yescharacteristic
211D113—41no—
212D113—41no—
213D113—81no—
214#3268—1131nomaximal, Sylow
215C113#326811yescharacteristic, complemented, Sylow
216C2×AGL(1,ℤ/8)—1131no—
217C2×#135—1131no—
218#550—1131no—
219#546—1131no—
220#496—1131no—
221#468—1131no—
222#466—1131no—
223#464—1131no—
224#459D11311yescharacteristic, complemented
225#452—1131no—
226#449—1131no—
227#449—1131no—
228#447—1131no—
229#440—1131no—
230#435—1131no—
231C2×#41—1131no—
232C2×#41—1131no—
233C2×#41—1131no—
234C22×D4—1131no—
235AGL(1,ℤ/8)—2264no—
236#135—2264no—
237C2×Q16—1131no—
238C2×SD16—1131no—
239C2×SD16—1131no—
240C2×SD16—1131no—
241C2×SD16—1131no—
242C2×D8—1131no—
243C2×D8—1131no—
244C2×D8C2×D11311yescharacteristic
245C2×D8C2×D11311yescharacteristic
246C2×M16—1131no—
247C22×C8—1131no—
248#127—2261no—
249#127C2×D11311yescharacteristic, complemented
250#124—1131no—
251#123—2261no—
252C22⋊Q8—1131no—
253#121—1131no—
254#121—1131no—
255#121—1131no—
256#121—2261no—
257#121—2261no—
258#121—2261no—
259#120—2261no—
260C4×Q8—1131no—
261C4×D4—1131no—
262C4×D4—2261no—
263C4×D4C2×D11311yescharacteristic
264C2×C22⋊C4—2261no—
265#107—1131no—
266C4⋊C8C2×D11311yescharacteristic, complemented
267#103—1131no—
268#103—1131no—
269#102—1131no—
270#102—1131no—
271#102C2×D11311yescharacteristic, complemented
272#102C2×D11311yescharacteristic, complemented
273C22⋊C8—1131no—
274C22⋊C8—1131no—
275#97—1131no—
276C24—2261no—
277#41—4521no—
278#41—4521no—
279#41—4521no—
280#41—2262no—
281#41—2262no—
282#41—2262no—
283C2×Q8—1131no—
284C2×Q8—1131no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—1131no—
288C2×D4—1131no—
289C2×D4—4521no—
290C2×D4—2261no—
291C2×D4—2261no—
292C2×D4—2261no—
293C2×D4—2261no—
294C2×D4—2261no—
295C2×D4—2261no—
296C2×D4—2261no—
297C2×D4—2262no—
298C2×D4C22×D11311yescharacteristic
299C2×D4C22×D11311yescharacteristic
300C2×D4C22×D11311yescharacteristic
301C22×C4—21no—
302C22×C4—1131no—
303C22×C4—1131no—
304C22×C4—2261no—
305C22×C4—2261no—
306C22×C4—2261no—
307Q16—2262no—
308SD16—1134no—
309SD16—4521no—
310SD16—2262no—
311SD16—2262no—
312D8—22no—
313D8—22no—
314D8—4521no—
315D8—2262no—
316M16—2262no—
317C2×C8—1131no—
318C2×C8—1131no—
319C2×C8—2262no—
320C2×C8C22×D11311yescharacteristic
321C2×C8C22×D11311yescharacteristic
322C4⋊C4—1131no—
323C4⋊C4—1131no—
324C4⋊C4—2261no—
325C4⋊C4—2261no—
326C4⋊C4C22×D11311yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—1131no—
329C22⋊C4—1131no—
330C22⋊C4—2261no—
331C22⋊C4—2261no—
332C22⋊C4—2261no—
333C22⋊C4—2261no—
334C22⋊C4—2261no—
335C22⋊C4—2261no—
336C42—2261no—
337C42C22×D11311yescharacteristic
338C23—21no—
339C23—21no—
340C23—21no—
341C23—1131no—
342C23—1131no—
343C23—9041no—
344C23—4522no—
345C23—4522no—
346C23—2261no—
347Q8—1132no—
348Q8—2261no—
349Q8—2261no—
350Q8—2261no—
351D4—21no—
352D4—21no—
353D4—21no—
354D4—21no—
355D4—21no—
356D4—42no—
357D4—81no—
358D4—9041no—
359D4—9041no—
360D4—9041no—
361D4—4521no—
362D4—4522no—
363D4—4522no—
364D4—4522no—
365D4—4522no—
366D4—2261no—
367D4—2261no—
368D4D4×D11312yes—
369C2×C4—21no—
370C2×C4—81no—
371C2×C4—1131no—
372C2×C4—1131no—
373C2×C4—4522no—
374C2×C4—4522no—
375C2×C4—4522no—
376C2×C4—2261no—
377C2×C4—2261no—
378C2×C4—2261no—
379C2×C4—2261no—
380C2×C4—2261no—
381C2×C4—2261no—
382C2×C4—2261no—
383C2×C4D4×D11311yescharacteristic
384C2×C4D4×D11311yescharacteristic
385C2×C4C23×D11311yescharacteristic
386C8—21no—
387C8—21no—
388C8—1132no—
389C8—2261no—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—41no—
399C22—9044no—
400C22—4521no—
401C22—4521no—
402C22—4521no—
403C22—2261no—
404C22—2261no—
405C22—2261no—
406C22—2261no—
407C22—2261no—
408C22—2261no—
409C22C2×D4×D11311yescharacteristic
410C4—21no—
411C4—21no—
412C4—41no—
413C4—4521no—
414C4—4521no—
415C4—2261no—
416C4—2261no—
417C4—2262no—
418C4C2×D4×D11311yescharacteristic
419C4#1681366811yescharacteristic
420C2—42no—
421C2—81no—
422C2—81no—
423C2—9041no—
424C2—4521no—
425C2—4521no—
426C2#2029923211yescharacteristic
427C2#2029939411yescharacteristic
428C2#2029939911yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3268
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#16813646C2semidirect
2. C2×#16813641C2semidirect
3. #20299268C2semidirect
4. #20299243C2semidirect
5. #20298985C2semidirect
6. #20298843C2semidirect
7. #20298833C2semidirect
8. #20298821C2semidirect
9. #20298761C2semidirect
10. #20298744C2semidirect
11. #20298740C2semidirect
12. #20298730C2semidirect
13. #20298698C2semidirect
14. #20298668C2semidirect
15. #459×C113C2semidirect
18. C2×#14268646C22semidirect
22. C2×Dic452C22semidirect
25. C2×#14268635C22semidirect
26. C2×#14268635C22semidirect
30. C2×C8×D113C22semidirect
40. #16813593C22semidirect
42. C4×Dic226C22semidirect
46. #16813555C22semidirect
47. #16813547C22semidirect
48. #16813545C22semidirect
52. #16813534C22semidirect
53. #16813533C22semidirect
56. #127×C113C22semidirect
58. C4⋊C8×C113C22semidirect
59. #102×C113C22semidirect
60. #102×C113C22semidirect
90. #14268635D4semidirect
215. C113#3268semidirect
224. #459D113semidirect
249. #127C2×D113semidirect
266. C4⋊C8C2×D113semidirect
271. #102C2×D113semidirect
272. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136462
C2×#168136412
#202992682
#202992432
#202989852
#202988432
#202988332
#202988212
#202987612
#202987442
#202987402
#202987302
#202986982
#202986682
#459×C1132
#3268113