Finite Group Databasebeta

← #28402065

Subgroups — #28402065

Order 14464.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813648C211yesmaximal, characteristic, complemented
2C22×#14268635C211yesmaximal, characteristic, complemented
3#20299257C211yesmaximal, characteristic, complemented
4#20298985C211yesmaximal, characteristic, complemented
5#20298842C211yesmaximal, characteristic, complemented
6#20298832C211yesmaximal, characteristic, complemented
7#20298813C211yesmaximal, characteristic, complemented
8#20298795C211yesmaximal, characteristic, complemented
9#20298749C211yesmaximal, characteristic, complemented
10#20298741C211yesmaximal, characteristic, complemented
11#20298736C211yesmaximal, characteristic, complemented
12#20298732C211yesmaximal, characteristic, complemented
13#20298698C211yesmaximal, characteristic, complemented
14#20298670C211yesmaximal, characteristic, complemented
15D42×C113C211yesmaximal, characteristic, complemented
16C2×#14268647C2211yescharacteristic, complemented
17C22×Dic226C2211yescharacteristic, complemented
18#16813648—24no—
19C2×#14268635—24no—
20C2×#14268635C2211yescharacteristic
21C2×#14268635C2211yescharacteristic
22C2×#14268635C2211yescharacteristic, complemented
23C2×#14268635C2211yescharacteristic, complemented
24C2×#14268635C2211yescharacteristic, complemented
25C2×#14268635C2211yescharacteristic, complemented
26C2×#14268632C2211yescharacteristic
27C2×#14268632C2211yescharacteristic, complemented
28C2×#14268632C2211yescharacteristic, complemented
29C2×#14268631C2211yescharacteristic, complemented
30C22×#11744751C2211yescharacteristic, complemented
31#16813610C2211yescharacteristic, complemented
32#16813608—21no—
33#16813601C2211yescharacteristic, complemented
34#16813600—21no—
35#16813596C2211yescharacteristic, complemented
36#16813594—21no—
37C4×Dic226C2211yescharacteristic, complemented
38#16813582—21no—
39#16813555C2211yescharacteristic, complemented
40C4⋊#11744751C2211yescharacteristic, complemented
41#16813545C2211yescharacteristic, complemented
42#16813545C2211yescharacteristic, complemented
43#16813543C2211yescharacteristic
44#16813543C2211yescharacteristic, complemented
45#16813543C2211yescharacteristic, complemented
46#16813542C2211yescharacteristic, complemented
47C22⋊#11744751C2211yescharacteristic, complemented
48C22⋊#11744751C2211yescharacteristic, complemented
49#16813533C2211yescharacteristic, complemented
50C22×D4×C113—21no—
51C22×D4×C113C2211yescharacteristic
52C22×D4×C113C2211yescharacteristic
53#127×C113C2211yescharacteristic
54#121×C113—21no—
55#121×C113C2211yescharacteristic
56#121×C113C2211yescharacteristic
57#120×C113—21no—
58#120×C113—21no—
59C4×D4×C113C2211yescharacteristic
60C4×D4×C113C2211yescharacteristic
61#14268647—22no—
62#14268647—41no—
63C2×Dic226—22no—
64C2×Dic226—21no—
65C2×Dic226—41no—
66C2×Dic226C2311yescharacteristic
67C2×Dic226C2311yescharacteristic
68C2×D452C2311yescharacteristic
69C2×C22⋊D113—21no—
70C2×C22⋊D113—21no—
71C22×Dic113—21no—
72C2×C4×D113—21no—
73#14268635—22no—
74#14268635—22no—
75#14268635—22no—
76#14268635—22no—
77#14268635—41no—
78#14268635D414yescomplemented
79#14268632—22no—
80#14268632—22no—
81#14268632—41no—
82#14268631—22no—
83C2×#11744751—22no—
84C2×#11744751C2311yescharacteristic
85C2×#11744751C2311yescharacteristic
86C2×#11744751C2311yescharacteristic
87C2×#11744751C2311yescharacteristic
88C4⋊Dic113C2311yescharacteristic
89#14268626—21no—
90#14268626—21no—
91C22⋊Dic113—21no—
92#14268624—21no—
93#14268624—21no—
94#14268624—21no—
95C4×Dic113—21no—
96C24×C113—21no—
97C24×C113—21no—
98C2×D4×C113—22no—
99C2×D4×C113—22no—
100C2×D4×C113—21no—
101C2×D4×C113—21no—
102C2×D4×C113—21no—
103C2×D4×C113—21no—
104C2×D4×C113—21no—
105C2×D4×C113—21no—
106C2×D4×C113—41no—
107C2×D4×C113—41no—
108C2×D4×C113—44no—
109C2×D4×C113D411yescharacteristic
110C2×D4×C113C2311yescharacteristic
111C2×D4×C113C2311yescharacteristic
112C2×D4×C113C2311yescharacteristic
113C22×C4×C113—21no—
114C22×C4×C113C2311yescharacteristic
115C22×C4×C113C2311yescharacteristic
116C4⋊C4×C113D411yescharacteristic
117C4⋊C4×C113C2311yescharacteristic
118C22⋊C4×C113—21no—
119C22⋊C4×C113—21no—
120C22⋊C4×C113—21no—
121C22⋊C4×C113D411yescharacteristic
122C22⋊C4×C113D411yescharacteristic
123C42×C113C2311yescharacteristic
124C23×C113—21no—
125C23×C113—21no—
126C23×C113—21no—
127C23×C113—42no—
128C23×C113—42no—
129C23×C113—42no—
130C23×C113—42no—
131C23×C113—81no—
132C23×C113—81no—
133C23×C113C2×D411yescharacteristic
134C23×C113C2×D411yescharacteristic
135C22×D113—21no—
136D4×C113—22no—
137D4×C113—21no—
138D4×C113—21no—
139D4×C113—21no—
140D4×C113—21no—
141D4×C113—21no—
142D4×C113—42no—
143D4×C113—42no—
144D4×C113—42no—
145D4×C113—42no—
146D4×C113—42no—
147D4×C113—81no—
148D4×C113C2×D412yes—
149C2×C4×C113—21no—
150C2×C4×C113—21no—
151C2×C4×C113—21no—
152C2×C4×C113—21no—
153C2×C4×C113—21no—
154C2×C4×C113—42no—
155C2×C4×C113C2×D411yescharacteristic
156C2×C4×C113C2×D411yescharacteristic
157C2×C4×C113C2×D411yescharacteristic
158C2×C4×C113C2×D411yescharacteristic
159C2×C4×C113C2411yescharacteristic
160C22⋊D113—42no—
161C22⋊D113—42no—
162C2×Dic113—21no—
163C2×Dic113—21no—
164C2×Dic113—21no—
165C2×Dic113—42no—
166D452—21no—
167D452—21no—
168C4×D113—42no—
169Dic226—21no—
170Dic226—21no—
171Dic226—21no—
172Dic226—42no—
173Dic226C2×D412yescomplemented
174#11744751—21no—
175#11744751—21no—
176#11744751—21no—
177#11744751C2×D412yescomplemented
178C22×C113—21no—
179C22×C113—21no—
180C22×C113—21no—
181C22×C113—22no—
182C22×C113—21no—
183C22×C113—21no—
184C22×C113—41no—
185C22×C113—41no—
186C22×C113—41no—
187C22×C113—41no—
188C22×C113—41no—
189C22×C113—41no—
190C22×C113—41no—
191C22×C113—41no—
192C22×C113—84no—
193C22×C113—84no—
194C22×C113AGL(1,ℤ/8)12yescomplemented
195C22×C113C22×D411yescharacteristic
196C2×D113—41no—
197C2×D113—41no—
198C2×D113—41no—
199C4×C113—21no—
200C4×C113—21no—
201C4×C113—21no—
202C4×C113—21no—
203C4×C113—41no—
204C4×C113C22×D411yescharacteristic
205C4×C113H(5,𝔽2)11yescharacteristic
206Dic113—22no—
207Dic113—41no—
208Dic113—41no—
209C2×C113—22no—
210C2×C113—41no—
211C2×C113—42no—
212C2×C113—81no—
213C2×C113—81no—
214C2×C113D4211yescharacteristic
215C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
216C2×C113#57711yescharacteristic
217D113—81no—
218#3265—1131nomaximal, Sylow
219C113#326511yescharacteristic, complemented, Sylow
220C2×AGL(1,ℤ/8)—1131no—
221C22×SD16—1131no—
222#548—1131no—
223D42D11311yescharacteristic, complemented
224#496—1131no—
225#468—1131no—
226#466—1131no—
227#463—1131no—
228#460—1131no—
229#450—1131no—
230#449—1131no—
231#448—1131no—
232#447—1131no—
233#440—1131no—
234#435—1131no—
235C2×#41—1131no—
236C22×Q8—1131no—
237C22×D4—21no—
238C22×D4C2×D11311yescharacteristic
239C22×D4C2×D11311yescharacteristic
240AGL(1,ℤ/8)—2264no—
241C2×SD16—1131no—
242C2×SD16—1131no—
243C2×SD16—1131no—
244C2×SD16—1131no—
245C2×SD16—1131no—
246C2×SD16—1131no—
247C2×SD16—2264no—
248C2×D8—1131no—
249C2×D8—1131no—
250C2×D8—1131no—
251C2×M16—1131no—
252C22×C8—1131no—
253#127C2×D11311yescharacteristic
254#124—1131no—
255#124—2261no—
256C22⋊Q8—1131no—
257C22⋊Q8—2261no—
258#121—21no—
259#121—1131no—
260#121—2261no—
261#121C2×D11311yescharacteristic
262#121C2×D11311yescharacteristic
263#120—21no—
264#120—21no—
265C4×Q8—1131no—
266C4×D4—2261no—
267C4×D4C2×D11311yescharacteristic
268C4×D4C2×D11311yescharacteristic
269#107—1131no—
270C4⋊C8—1131no—
271#103—1131no—
272#103—1131no—
273#102—1131no—
274#102—1131no—
275#102—1131no—
276#102—1131no—
277C22⋊C8—1131no—
278C22⋊C8—1131no—
279#97—1131no—
280C24—21no—
281C24—21no—
282#41—4521no—
283#41—2262no—
284C2×Q8—1131no—
285C2×Q8—1131no—
286C2×Q8—4521no—
287C2×Q8—2262no—
288C2×Q8—2261no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—44no—
300C2×D4—1131no—
301C2×D4—2261no—
302C2×D4—2261no—
303C2×D4C22⋊D11311yescharacteristic
304C2×D4C22×D11311yescharacteristic
305C2×D4C22×D11311yescharacteristic
306C2×D4C22×D11311yescharacteristic
307C22×C4—21no—
308C22×C4—2261no—
309C22×C4—2261no—
310C22×C4C22×D11311yescharacteristic
311C22×C4C22×D11311yescharacteristic
312SD16—1134no—
313SD16—4521no—
314SD16—2262no—
315SD16—2262no—
316SD16—2262no—
317SD16—2262no—
318D8—4521no—
319D8—2262no—
320D8—2262no—
321M16—2262no—
322C2×C8—1131no—
323C2×C8—1131no—
324C2×C8—1131no—
325C2×C8—1131no—
326C2×C8—2262no—
327C4⋊C4—1131no—
328C4⋊C4—2261no—
329C4⋊C4—2261no—
330C4⋊C4C22⋊D11311yescharacteristic
331C4⋊C4C22×D11311yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—2261no—
336C22⋊C4—2261no—
337C22⋊C4—2261no—
338C22⋊C4—2261no—
339C22⋊C4C22⋊D11311yescharacteristic
340C22⋊C4C22⋊D11311yescharacteristic
341C42—2261no—
342C42C22×D11311yescharacteristic
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23—42no—
350C23—81no—
351C23—81no—
352C23—2261no—
353C23C2×C22⋊D11311yescharacteristic
354C23C2×C22⋊D11311yescharacteristic
355Q8—1132no—
356Q8—4522no—
357Q8—2261no—
358Q8—2261no—
359Q8—2261no—
360D4—22no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—21no—
366D4—42no—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—42no—
371D4—81no—
372D4—4522no—
373D4—4522no—
374D4—2261no—
375D4—2261no—
376D4D4×D11312yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—4522no—
384C2×C4—4522no—
385C2×C4—2261no—
386C2×C4—2261no—
387C2×C4—2261no—
388C2×C4C2×C22⋊D11311yescharacteristic
389C2×C4C2×C22⋊D11311yescharacteristic
390C2×C4C2×C22⋊D11311yescharacteristic
391C2×C4C2×C22⋊D11311yescharacteristic
392C2×C4C23×D11311yescharacteristic
393C8—1132no—
394C8—2261no—
395C8—2261no—
396C8—2261no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—84no—
412C22—84no—
413C22—4521no—
414C22—4521no—
415C22—4521no—
416C22#1681364812yescomplemented
417C22C22×C22⋊D11311yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—41no—
423C4—4521no—
424C4—4521no—
425C4—2262no—
426C4C2×D4×D11311yescharacteristic
427C4#1681366711yescharacteristic
428C2—22no—
429C2—41no—
430C2—42no—
431C2—81no—
432C2—81no—
433C2—9041no—
434C2D4×C22⋊D11311yescharacteristic
435C2C2×#1681364811yescharacteristic
436C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingD42×C113C2
socleC22×C113C22×D4
hypercenterD42D113
hypocenterC113#3265
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. C22×#14268635C2semidirect
3. #20299257C2semidirect
4. #20298985C2semidirect
5. #20298842C2semidirect
6. #20298832C2semidirect
7. #20298813C2semidirect
8. #20298795C2semidirect
9. #20298749C2semidirect
10. #20298741C2semidirect
11. #20298736C2semidirect
12. #20298732C2semidirect
13. #20298698C2semidirect
14. #20298670C2semidirect
15. D42×C113C2semidirect
16. C2×#14268647C22semidirect
17. C22×Dic226C22semidirect
22. C2×#14268635C22semidirect
23. C2×#14268635C22semidirect
24. C2×#14268635C22semidirect
25. C2×#14268635C22semidirect
27. C2×#14268632C22semidirect
28. C2×#14268632C22semidirect
29. C2×#14268631C22semidirect
30. C22×#11744751C22semidirect
31. #16813610C22semidirect
33. #16813601C22semidirect
35. #16813596C22semidirect
37. C4×Dic226C22semidirect
39. #16813555C22semidirect
40. C4⋊#11744751C22semidirect
41. #16813545C22semidirect
42. #16813545C22semidirect
44. #16813543C22semidirect
45. #16813543C22semidirect
46. #16813542C22semidirect
47. C22⋊#11744751C22semidirect
48. C22⋊#11744751C22semidirect
49. #16813533C22semidirect
78. #14268635D4semidirect
173. Dic226C2×D4semidirect
177. #11744751C2×D4semidirect
194. C22×C113AGL(1,ℤ/8)semidirect
219. C113#3265semidirect
223. D42D113semidirect
416. C22#16813648semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
C22×#142686352
#202992572
#202989852
#202988422
#202988322
#202988132
#202987952
#202987492
#202987412
#202987362
#202987322
#202986982
#202986702
D42×C1132
#3265113