Finite Group Databasebeta

← C139×#33968 #48028564

Subgroups — C139×#33968 #48028564

Order 35584.

516 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3396×C139C211yesmaximal, characteristic, complemented
2#3393×C139C211yesmaximal, characteristic, complemented
3#2251×C139C211yesmaximal, characteristic, complemented
4#2250×C139C211yesmaximal, characteristic
5#2249×C139C211yesmaximal, characteristic, complemented
6#2211×C139C211yesmaximal, characteristic, complemented
7#2211×C139C211yesmaximal, characteristic, complemented
8#2210×C139C211yesmaximal, characteristic, complemented
9#2210×C139C211yesmaximal, characteristic, complemented
10#2208×C139C211yesmaximal, characteristic, complemented
11#2207×C139C211yesmaximal, characteristic, complemented
12#2183×C139C211yesmaximal, characteristic, complemented
13#2177×C139C211yesmaximal, characteristic, complemented
14#2176×C139C211yesmaximal, characteristic, complemented
15C4×SD32×C139C211yesmaximal, characteristic, complemented
16#559×C139—21no—
17#556×C139—21no—
18C2×Q32×C139C2211yescharacteristic
19C2×Q32×C139C2211yescharacteristic
20C2×SD32×C139C2211yescharacteristic
21C2×SD32×C139C2211yescharacteristic
22C2×SD32×C139C2211yescharacteristic
23C2×SD32×C139C2211yescharacteristic
24C2×SD32×C139C2211yescharacteristic
25C2×D16×C139C2211yescharacteristic
26C2×D16×C139C2211yescharacteristic
27#495×C139C2211yescharacteristic
28#495×C139C2211yescharacteristic
29#495×C139C2211yescharacteristic
30#495×C139C2211yescharacteristic
31#494×C139C2211yescharacteristic
32#493×C139C2211yescharacteristic
33#464×C139—21no—
34#464×C139—21no—
35#463×C139—21no—
36#463×C139—21no—
37#461×C139—21no—
38#460×C139—21no—
39C8×Q8×C139C2211yescharacteristic
40C4×Q16×C139C2211yescharacteristic
41C4×Q16×C139C2211yescharacteristic
42C4×Q16×C139C2211yescharacteristic
43C4×D8×C139C2211yescharacteristic
44C4×D8×C139C2211yescharacteristic
45C4×D8×C139C2211yescharacteristic
46#367×C139C2211yescharacteristic
47C4⋊C16×C139C2211yescharacteristic
48C4⋊C16×C139C2211yescharacteristic
49C4⋊C16×C139C2211yescharacteristic
50#358×C139C2211yescharacteristic
51#358×C139C2211yescharacteristic
52#358×C139C2211yescharacteristic
53#357×C139C2211yescharacteristic
54#357×C139C2211yescharacteristic
55#357×C139C2211yescharacteristic
56#346×C139C2211yescharacteristic
57#346×C139C2211yescharacteristic
58C4×C16×C139C2211yescharacteristic
59C2×Q16×C139—21no—
60C2×Q16×C139C2311yescharacteristic
61C2×Q16×C139C2311yescharacteristic
62C2×Q16×C139C2311yescharacteristic
63C2×SD16×C139—21no—
64C2×SD16×C139—21no—
65C2×SD16×C139—21no—
66C2×SD16×C139—21no—
67C2×D8×C139—21no—
68C2×D8×C139C2311yescharacteristic
69C2×D8×C139C2311yescharacteristic
70C2×D8×C139C2311yescharacteristic
71C4⋊Q8×C139—21no—
72#127×C139—21no—
73#126×C139—41no—
74#126×C139—41no—
75#124×C139—21no—
76#124×C139—21no—
77#124×C139—21no—
78#124×C139—21no—
79#124×C139—41no—
80#123×C139—41no—
81#123×C139—41no—
82C22⋊Q8×C139—41no—
83C4×Q8×C139—21no—
84C4×Q8×C139—21no—
85C4×Q8×C139—21no—
86C4×Q8×C139D411yescharacteristic
87C4×D4×C139—21no—
88C4×D4×C139—21no—
89C4×D4×C139—21no—
90C4×D4×C139—41no—
91#117×C139—41no—
92Q32×C139—22no—
93Q32×C139—41no—
94SD32×C139—22no—
95SD32×C139—41no—
96SD32×C139—41no—
97SD32×C139—41no—
98SD32×C139—41no—
99D16×C139—22no—
100D16×C139—41no—
101C2×C16×C139C2311yescharacteristic
102C2×C16×C139C2311yescharacteristic
103C2×C16×C139C2311yescharacteristic
104C2×C16×C139C2311yescharacteristic
105#107×C139C2311yescharacteristic
106#107×C139C2311yescharacteristic
107C4⋊C8×C139D411yescharacteristic
108C4⋊C8×C139D411yescharacteristic
109C4⋊C8×C139D411yescharacteristic
110#103×C139—21no—
111#103×C139—21no—
112#103×C139—21no—
113#102×C139—21no—
114#102×C139—21no—
115#102×C139—21no—
116C4×C8×C139C2311yescharacteristic
117C4×C8×C139C2311yescharacteristic
118C4×C8×C139C2311yescharacteristic
119C2×Q8×C139—21no—
120C2×Q8×C139—21no—
121C2×Q8×C139—21no—
122C2×Q8×C139D811yescharacteristic
123C2×D4×C139—21no—
124C2×D4×C139—21no—
125C2×D4×C139—21no—
126C2×D4×C139—41no—
127C2×D4×C139—41no—
128C22×C4×C139—41no—
129C22×C4×C139—41no—
130C22×C4×C139—41no—
131Q16×C139—21no—
132Q16×C139—21no—
133Q16×C139—21no—
134Q16×C139—21no—
135Q16×C139—21no—
136Q16×C139—21no—
137Q16×C139—81no—
138SD16×C139—81no—
139SD16×C139—81no—
140SD16×C139—81no—
141SD16×C139—81no—
142D8×C139—21no—
143D8×C139—21no—
144D8×C139—21no—
145D8×C139—21no—
146D8×C139—21no—
147D8×C139—21no—
148D8×C139—81no—
149C2×C8×C139C2×D411yescharacteristic
150C2×C8×C139C2×D411yescharacteristic
151C2×C8×C139C2×D411yescharacteristic
152C2×C8×C139C2411yescharacteristic
153C4⋊C4×C139—21no—
154C4⋊C4×C139—21no—
155C4⋊C4×C139—41no—
156C4⋊C4×C139—41no—
157C4⋊C4×C139—41no—
158C4⋊C4×C139—41no—
159C4⋊C4×C139—41no—
160C4⋊C4×C139D811yescharacteristic
161C4⋊C4×C139D811yescharacteristic
162C4⋊C4×C139D811yescharacteristic
163C22⋊C4×C139—41no—
164C22⋊C4×C139—41no—
165C22⋊C4×C139—41no—
166C22⋊C4×C139—41no—
167C22⋊C4×C139—41no—
168C22⋊C4×C139—41no—
169C22⋊C4×C139—41no—
170C22⋊C4×C139—41no—
171C22⋊C4×C139—41no—
172C22⋊C4×C139—41no—
173C22⋊C4×C139—41no—
174C42×C139—41no—
175C42×C139—41no—
176C42×C139—41no—
177C42×C139C2×D411yescharacteristic
178C42×C139C2×D411yescharacteristic
179C42×C139C2×D411yescharacteristic
180C16×C139—21no—
181C16×C139—21no—
182C16×C139—21no—
183C16×C139#4112yes—
184C23×C139—41no—
185C23×C139—41no—
186C23×C139—41no—
187Q8×C139—41no—
188Q8×C139—41no—
189Q8×C139—41no—
190Q8×C139—41no—
191Q8×C139—41no—
192Q8×C139—41no—
193Q8×C139—41no—
194D4×C139—41no—
195D4×C139—41no—
196D4×C139—41no—
197D4×C139—41no—
198D4×C139—41no—
199D4×C139—41no—
200D4×C139—82no—
201D4×C139—161no—
202C2×C4×C139—41no—
203C2×C4×C139—41no—
204C2×C4×C139—41no—
205C2×C4×C139—41no—
206C2×C4×C139—41no—
207C2×C4×C139—82no—
208C2×C4×C139—161no—
209C2×C4×C139—161no—
210C2×C4×C139C2×D811yescharacteristic
211C2×C4×C139C2×D811yescharacteristic
212C2×C4×C139C2×D811yescharacteristic
213C2×C4×C139C2×D811yescharacteristic
214C2×C4×C139C2×D811yescharacteristic
215C2×C4×C139C2×D811yescharacteristic
216C2×C4×C139C22×D411yescharacteristic
217C8×C139—21no—
218C8×C139—21no—
219C8×C139—21no—
220C8×C139C2×#4111yescharacteristic
221C8×C139H(5,𝔽2)11yescharacteristic
222C22×C139—81no—
223C22×C139—81no—
224C22×C139—81no—
225C22×C139—81no—
226C22×C139—81no—
227C22×C139—81no—
228C22×C139—81no—
229C22×C139—81no—
230C22×C139—81no—
231C22×C139C22×D811yescharacteristic
232C4×C139—21no—
233C4×C139—21no—
234C4×C139—21no—
235C4×C139—21no—
236C4×C139—21no—
237C4×C139—21no—
238C4×C139—81no—
239C4×C139—81no—
240C4×C139—81no—
241C4×C139—81no—
242C4×C139—81no—
243C4×C139#55011yescharacteristic
244C4×C139#57611yescharacteristic
245C2×C139—161no—
246C2×C139—161no—
247C2×C139—161no—
248C2×C139#339111yescharacteristic
249C2×C139#341411yescharacteristic
250C2×C139#341611yescharacteristic
251#33968C13911yesmaximal, characteristic, direct product factor, Sylow
252C139#3396811yescharacteristic, direct product factor, Sylow
253#3396C2×C13911yescharacteristic, complemented
254#3393C2×C13911yescharacteristic, complemented
255#2251C2×C13911yescharacteristic, complemented
256#2250C2×C13911yescharacteristic
257#2249C2×C13911yescharacteristic, complemented
258#2211C2×C13911yescharacteristic, complemented
259#2211C2×C13911yescharacteristic, complemented
260#2210C2×C13911yescharacteristic, complemented
261#2210C2×C13911yescharacteristic, complemented
262#2208C2×C13911yescharacteristic, complemented
263#2207C2×C13911yescharacteristic, complemented
264#2183C2×C13911yescharacteristic, complemented
265#2177C2×C13911yescharacteristic, complemented
266#2176C2×C13911yescharacteristic, complemented
267C4×SD32C2×C13911yescharacteristic, complemented
268#559—21no—
269#556—21no—
270C2×Q32C22×C13911yescharacteristic
271C2×Q32C22×C13911yescharacteristic
272C2×SD32C22×C13911yescharacteristic
273C2×SD32C22×C13911yescharacteristic
274C2×SD32C22×C13911yescharacteristic
275C2×SD32C22×C13911yescharacteristic
276C2×SD32C22×C13911yescharacteristic
277C2×D16C22×C13911yescharacteristic
278C2×D16C22×C13911yescharacteristic
279#495C22×C13911yescharacteristic
280#495C22×C13911yescharacteristic
281#495C22×C13911yescharacteristic
282#495C22×C13911yescharacteristic
283#494C22×C13911yescharacteristic
284#493C22×C13911yescharacteristic
285#464—21no—
286#464—21no—
287#463—21no—
288#463—21no—
289#461—21no—
290#460—21no—
291C8×Q8C22×C13911yescharacteristic
292C4×Q16C22×C13911yescharacteristic
293C4×Q16C22×C13911yescharacteristic
294C4×Q16C22×C13911yescharacteristic
295C4×D8C22×C13911yescharacteristic
296C4×D8C22×C13911yescharacteristic
297C4×D8C22×C13911yescharacteristic
298#367C22×C13911yescharacteristic
299C4⋊C16C22×C13911yescharacteristic
300C4⋊C16C22×C13911yescharacteristic
301C4⋊C16C22×C13911yescharacteristic
302#358C22×C13911yescharacteristic
303#358C22×C13911yescharacteristic
304#358C22×C13911yescharacteristic
305#357C22×C13911yescharacteristic
306#357C22×C13911yescharacteristic
307#357C22×C13911yescharacteristic
308#346C22×C13911yescharacteristic
309#346C22×C13911yescharacteristic
310C4×C16C22×C13911yescharacteristic
311C2×Q16—21no—
312C2×Q16C23×C13911yescharacteristic
313C2×Q16C23×C13911yescharacteristic
314C2×Q16C23×C13911yescharacteristic
315C2×SD16—21no—
316C2×SD16—21no—
317C2×SD16—21no—
318C2×SD16—21no—
319C2×D8—21no—
320C2×D8C23×C13911yescharacteristic
321C2×D8C23×C13911yescharacteristic
322C2×D8C23×C13911yescharacteristic
323C4⋊Q8—21no—
324#127—21no—
325#126—41no—
326#126—41no—
327#124—21no—
328#124—21no—
329#124—21no—
330#124—21no—
331#124—41no—
332#123—41no—
333#123—41no—
334C22⋊Q8—41no—
335C4×Q8—21no—
336C4×Q8—21no—
337C4×Q8—21no—
338C4×Q8D4×C13911yescharacteristic
339C4×D4—21no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—41no—
343#117—41no—
344Q32—22no—
345Q32—41no—
346SD32—22no—
347SD32—41no—
348SD32—41no—
349SD32—41no—
350SD32—41no—
351D16—22no—
352D16—41no—
353C2×C16C23×C13911yescharacteristic
354C2×C16C23×C13911yescharacteristic
355C2×C16C23×C13911yescharacteristic
356C2×C16C23×C13911yescharacteristic
357#107C23×C13911yescharacteristic
358#107C23×C13911yescharacteristic
359C4⋊C8D4×C13911yescharacteristic
360C4⋊C8D4×C13911yescharacteristic
361C4⋊C8D4×C13911yescharacteristic
362#103—21no—
363#103—21no—
364#103—21no—
365#102—21no—
366#102—21no—
367#102—21no—
368C4×C8C23×C13911yescharacteristic
369C4×C8C23×C13911yescharacteristic
370C4×C8C23×C13911yescharacteristic
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—21no—
374C2×Q8D8×C13911yescharacteristic
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—41no—
379C2×D4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383Q16—21no—
384Q16—21no—
385Q16—21no—
386Q16—21no—
387Q16—21no—
388Q16—21no—
389Q16—81no—
390SD16—81no—
391SD16—81no—
392SD16—81no—
393SD16—81no—
394D8—21no—
395D8—21no—
396D8—21no—
397D8—21no—
398D8—21no—
399D8—21no—
400D8—81no—
401C2×C8C2×D4×C13911yescharacteristic
402C2×C8C2×D4×C13911yescharacteristic
403C2×C8C2×D4×C13911yescharacteristic
404C2×C8C24×C13911yescharacteristic
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4D8×C13911yescharacteristic
413C4⋊C4D8×C13911yescharacteristic
414C4⋊C4D8×C13911yescharacteristic
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C42—41no—
427C42—41no—
428C42—41no—
429C42C2×D4×C13911yescharacteristic
430C42C2×D4×C13911yescharacteristic
431C42C2×D4×C13911yescharacteristic
432C16—21no—
433C16—21no—
434C16—21no—
435C16#41×C13912yes—
436C23—41no—
437C23—41no—
438C23—41no—
439Q8—41no—
440Q8—41no—
441Q8—41no—
442Q8—41no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446D4—41no—
447D4—41no—
448D4—41no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—82no—
453D4—161no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—82no—
460C2×C4—161no—
461C2×C4—161no—
462C2×C4C2×D8×C13911yescharacteristic
463C2×C4C2×D8×C13911yescharacteristic
464C2×C4C2×D8×C13911yescharacteristic
465C2×C4C2×D8×C13911yescharacteristic
466C2×C4C2×D8×C13911yescharacteristic
467C2×C4C2×D8×C13911yescharacteristic
468C2×C4C22×D4×C13911yescharacteristic
469C8—21no—
470C8—21no—
471C8—21no—
472C8C2×#41×C13911yescharacteristic
473C8H(5,𝔽2)×C13911yescharacteristic
474C22—81no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22C22×D8×C13911yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—81no—
491C4—81no—
492C4—81no—
493C4—81no—
494C4—81no—
495C4#550×C13911yescharacteristic
496C4#576×C13911yescharacteristic
497C2—161no—
498C2—161no—
499C2—161no—
500C2#3391×C13911yescharacteristic
501C2#3414×C13911yescharacteristic
502C2#3416×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C22×D8
commutator, Frattini, cosocleC2×C8C24×C139
prime radical#2250×C139C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C4×Q8×C139 ◁ C8×Q8×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3396×C139C2semidirect
2. #3393×C139C2semidirect
3. #2251×C139C2semidirect
5. #2249×C139C2semidirect
6. #2211×C139C2semidirect
7. #2211×C139C2semidirect
8. #2210×C139C2semidirect
9. #2210×C139C2semidirect
10. #2208×C139C2semidirect
11. #2207×C139C2semidirect
12. #2183×C139C2semidirect
13. #2177×C139C2semidirect
14. #2176×C139C2semidirect
15. C4×SD32×C139C2semidirect
251. #33968C139direct (N × H)
252. C139#33968direct (N × H)
253. #3396C2×C139semidirect
254. #3393C2×C139semidirect
255. #2251C2×C139semidirect
257. #2249C2×C139semidirect
258. #2211C2×C139semidirect
259. #2211C2×C139semidirect
260. #2210C2×C139semidirect
261. #2210C2×C139semidirect
262. #2208C2×C139semidirect
263. #2207C2×C139semidirect
264. #2183C2×C139semidirect
265. #2177C2×C139semidirect
266. #2176C2×C139semidirect
267. C4×SD32C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3396×C1392
#3393×C1392
#2251×C1392
#2250×C1392
#2249×C1392
#2211×C1392
#2210×C1392
#2208×C1392
#2207×C1392
#2183×C1392
#2177×C1392
#2176×C1392
C4×SD32×C1392
#33968139