Finite Group Databasebeta

← C139×#33881 #48028477

Subgroups — C139×#33881 #48028477

Order 35584.

570 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3338×C139C211yesmaximal, characteristic, complemented
2#3280×C139C211yesmaximal, characteristic
3#2243×C139C211yesmaximal, characteristic, complemented
4#2236×C139C211yesmaximal, characteristic, complemented
5#2232×C139C211yesmaximal, characteristic, complemented
6#2224×C139C211yesmaximal, characteristic, complemented
7#2220×C139C211yesmaximal, characteristic, complemented
8#2216×C139C211yesmaximal, characteristic, complemented
9#2211×C139C211yesmaximal, characteristic, complemented
10#2189×C139C211yesmaximal, characteristic, complemented
11#2187×C139C211yesmaximal, characteristic, complemented
12#2175×C139C211yesmaximal, characteristic, complemented
13#2168×C139C211yesmaximal, characteristic, complemented
14#2139×C139C211yesmaximal, characteristic, complemented
15C2×#357×C139C211yesmaximal, characteristic, complemented
16C2×#135×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18#554×C139—21no—
19#546×C139—21no—
20C2×Q32×C139C2211yescharacteristic, complemented
21C2×SD32×C139C2211yescharacteristic
22C2×SD32×C139C2211yescharacteristic
23C2×M32×C139C2211yescharacteristic, complemented
24C22×C16×C139C2211yescharacteristic
25#500×C139C2211yescharacteristic, complemented
26#495×C139C2211yescharacteristic
27#484×C139—21no—
28#484×C139—21no—
29#477×C139—21no—
30#467×C139C2211yescharacteristic
31#467×C139C2211yescharacteristic
32#467×C139C2211yescharacteristic, complemented
33#466×C139C2211yescharacteristic
34#463×C139—21no—
35#450×C139—21no—
36#449×C139—21no—
37C4×Q16×C139C2211yescharacteristic, complemented
38C4×D8×C139C2211yescharacteristic
39C8×D4×C139C2211yescharacteristic
40C2×#107×C139C2211yescharacteristic
41C2×#107×C139C2211yescharacteristic, complemented
42#366×C139C2211yescharacteristic, complemented
43#366×C139C2211yescharacteristic, complemented
44#366×C139C2211yescharacteristic, complemented
45C4⋊C16×C139C2211yescharacteristic, complemented
46#358×C139C2211yescharacteristic, complemented
47#358×C139C2211yescharacteristic, complemented
48#358×C139C2211yescharacteristic, complemented
49#358×C139C2211yescharacteristic, complemented
50#357×C139C2211yescharacteristic
51#357×C139C2211yescharacteristic
52#357×C139C2211yescharacteristic
53#357×C139C2211yescharacteristic
54#357×C139C2211yescharacteristic
55#357×C139C2211yescharacteristic
56C22⋊C16×C139C2211yescharacteristic
57C22⋊C16×C139C2211yescharacteristic, complemented
58#346×C139C2211yescharacteristic, complemented
59C2×#41×C139—21no—
60C22×D4×C139—21no—
61#135×C139—22no—
62#135×C139—41no—
63C2×Q16×C139C2311yescharacteristic
64C2×Q16×C139C2311yescharacteristic
65C2×SD16×C139—21no—
66C2×SD16×C139—21no—
67C2×D8×C139—22no—
68C2×D8×C139—21no—
69C2×D8×C139—41no—
70C2×D8×C139C2311yescharacteristic
71C2×D8×C139C2311yescharacteristic
72C22×C8×C139C2311yescharacteristic
73C22×C8×C139C2311yescharacteristic
74C4⋊Q8×C139—21no—
75#125×C139—41no—
76#124×C139—21no—
77#123×C139—41no—
78C22⋊Q8×C139—21no—
79C22⋊Q8×C139—21no—
80C22⋊Q8×C139—21no—
81C22⋊Q8×C139—41no—
82C22⋊Q8×C139—41no—
83#121×C139—21no—
84#121×C139—41no—
85#120×C139—41no—
86C4×Q8×C139—21no—
87C4×D4×C139—21no—
88C4×D4×C139—41no—
89C4×D4×C139D411yescharacteristic
90C2×C4⋊C4×C139—21no—
91C2×C4⋊C4×C139—21no—
92C2×C22⋊C4×C139—41no—
93Q32×C139—41no—
94SD32×C139—22no—
95SD32×C139—41no—
96M32×C139—41no—
97C2×C16×C139—41no—
98C2×C16×C139C2311yescharacteristic
99C2×C16×C139C2311yescharacteristic
100C2×C16×C139C2311yescharacteristic
101C2×C16×C139C2311yescharacteristic
102#107×C139—21no—
103#107×C139—21no—
104#107×C139—21no—
105#107×C139C2311yescharacteristic
106#107×C139C2311yescharacteristic
107#107×C139C2311yescharacteristic
108#107×C139C2311yescharacteristic
109C4⋊C8×C139D411yescharacteristic
110#103×C139—21no—
111#103×C139—21no—
112#103×C139—21no—
113#103×C139—21no—
114#102×C139—21no—
115#102×C139—21no—
116C22⋊C8×C139D411yescharacteristic
117C22⋊C8×C139D411yescharacteristic
118C4×C8×C139C2311yescharacteristic
119C24×C139—41no—
120#41×C139—42no—
121#41×C139—81no—
122C2×Q8×C139—21no—
123C2×Q8×C139—21no—
124C2×Q8×C139—41no—
125C2×D4×C139—21no—
126C2×D4×C139—21no—
127C2×D4×C139—42no—
128C2×D4×C139—41no—
129C2×D4×C139—41no—
130C2×D4×C139—41no—
131C2×D4×C139—81no—
132C2×D4×C139D811yescharacteristic
133C22×C4×C139—41no—
134C22×C4×C139—41no—
135C22×C4×C139—41no—
136C22×C4×C139—41no—
137C22×C4×C139C2×D411yescharacteristic
138C22×C4×C139C2×D411yescharacteristic
139Q16×C139—21no—
140Q16×C139—21no—
141Q16×C139—21no—
142Q16×C139—21no—
143SD16×C139—42no—
144SD16×C139—81no—
145D8×C139—21no—
146D8×C139—21no—
147D8×C139—21no—
148D8×C139—42no—
149D8×C139#4112yes—
150C2×C8×C139—21no—
151C2×C8×C139—21no—
152C2×C8×C139—21no—
153C2×C8×C139—21no—
154C2×C8×C139C2×D411yescharacteristic
155C2×C8×C139C2×D411yescharacteristic
156C2×C8×C139C2×D411yescharacteristic
157C2×C8×C139C2411yescharacteristic
158C4⋊C4×C139—21no—
159C4⋊C4×C139—21no—
160C4⋊C4×C139—21no—
161C4⋊C4×C139—21no—
162C4⋊C4×C139—41no—
163C4⋊C4×C139—41no—
164C4⋊C4×C139—41no—
165C4⋊C4×C139—41no—
166C4⋊C4×C139—41no—
167C4⋊C4×C139—41no—
168C4⋊C4×C139—41no—
169C4⋊C4×C139D811yescharacteristic
170C22⋊C4×C139—41no—
171C22⋊C4×C139—41no—
172C22⋊C4×C139—41no—
173C22⋊C4×C139—41no—
174C22⋊C4×C139—41no—
175C22⋊C4×C139—41no—
176C22⋊C4×C139—41no—
177C22⋊C4×C139D811yescharacteristic
178C22⋊C4×C139D811yescharacteristic
179C42×C139—41no—
180C42×C139C2×D411yescharacteristic
181C16×C139—21no—
182C16×C139—21no—
183C16×C139—21no—
184C16×C139—21no—
185C23×C139—41no—
186C23×C139—41no—
187C23×C139—82no—
188C23×C139—82no—
189C23×C139—161no—
190C23×C139C2×D811yescharacteristic
191C23×C139C2×D811yescharacteristic
192Q8×C139—41no—
193Q8×C139—41no—
194Q8×C139—41no—
195Q8×C139—41no—
196Q8×C139—161no—
197D4×C139—22no—
198D4×C139—22no—
199D4×C139—41no—
200D4×C139—41no—
201D4×C139—41no—
202D4×C139—82no—
203D4×C139—82no—
204D4×C139—161no—
205C2×C4×C139—21no—
206C2×C4×C139—21no—
207C2×C4×C139—21no—
208C2×C4×C139—21no—
209C2×C4×C139—41no—
210C2×C4×C139—41no—
211C2×C4×C139—41no—
212C2×C4×C139—41no—
213C2×C4×C139—41no—
214C2×C4×C139—41no—
215C2×C4×C139—82no—
216C2×C4×C139—161no—
217C2×C4×C139—161no—
218C2×C4×C139—161no—
219C2×C4×C139C2×D811yescharacteristic
220C2×C4×C139C2×D811yescharacteristic
221C2×C4×C139C2×D811yescharacteristic
222C2×C4×C139C2×D811yescharacteristic
223C2×C4×C139C22×D411yescharacteristic
224C8×C139—21no—
225C8×C139—21no—
226C8×C139—21no—
227C8×C139C2×#4111yescharacteristic
228C8×C139H(5,𝔽2)11yescharacteristic
229C22×C139—21no—
230C22×C139—21no—
231C22×C139—21no—
232C22×C139—21no—
233C22×C139—21no—
234C22×C139—42no—
235C22×C139—81no—
236C22×C139—81no—
237C22×C139—81no—
238C22×C139—81no—
239C22×C139—81no—
240C22×C139—164no—
241C22×C139#51012yes—
242C22×C139C22×D811yescharacteristic
243C4×C139—21no—
244C4×C139—21no—
245C4×C139—21no—
246C4×C139—21no—
247C4×C139—81no—
248C4×C139—81no—
249C4×C139—81no—
250C4×C139—81no—
251C4×C139—81no—
252C4×C139—81no—
253C4×C139#54611yescharacteristic
254C4×C139#57711yescharacteristic
255C2×C139—22no—
256C2×C139—41no—
257C2×C139—82no—
258C2×C139—161no—
259C2×C139#329411yescharacteristic
260C2×C139C2×#51011yescharacteristic
261C2×C139#341511yescharacteristic
262#33881C13911yesmaximal, characteristic, direct product factor, Sylow
263C139#3388111yescharacteristic, direct product factor, Sylow
264#3338C2×C13911yescharacteristic, complemented
265#3280C2×C13911yescharacteristic
266#2243C2×C13911yescharacteristic, complemented
267#2236C2×C13911yescharacteristic, complemented
268#2232C2×C13911yescharacteristic, complemented
269#2224C2×C13911yescharacteristic, complemented
270#2220C2×C13911yescharacteristic, complemented
271#2216C2×C13911yescharacteristic, complemented
272#2211C2×C13911yescharacteristic, complemented
273#2189C2×C13911yescharacteristic, complemented
274#2187C2×C13911yescharacteristic, complemented
275#2175C2×C13911yescharacteristic, complemented
276#2168C2×C13911yescharacteristic, complemented
277#2139C2×C13911yescharacteristic, complemented
278C2×#357C2×C13911yescharacteristic, complemented
279C2×#135C22×C13911yescharacteristic
280C22×D8C22×C13911yescharacteristic
281#554—21no—
282#546—21no—
283C2×Q32C22×C13911yescharacteristic, complemented
284C2×SD32C22×C13911yescharacteristic
285C2×SD32C22×C13911yescharacteristic
286C2×M32C22×C13911yescharacteristic, complemented
287C22×C16C22×C13911yescharacteristic
288#500C22×C13911yescharacteristic, complemented
289#495C22×C13911yescharacteristic
290#484—21no—
291#484—21no—
292#477—21no—
293#467C22×C13911yescharacteristic
294#467C22×C13911yescharacteristic
295#467C22×C13911yescharacteristic, complemented
296#466C22×C13911yescharacteristic
297#463—21no—
298#450—21no—
299#449—21no—
300C4×Q16C22×C13911yescharacteristic, complemented
301C4×D8C22×C13911yescharacteristic
302C8×D4C22×C13911yescharacteristic
303C2×#107C22×C13911yescharacteristic
304C2×#107C22×C13911yescharacteristic, complemented
305#366C22×C13911yescharacteristic, complemented
306#366C22×C13911yescharacteristic, complemented
307#366C22×C13911yescharacteristic, complemented
308C4⋊C16C22×C13911yescharacteristic, complemented
309#358C22×C13911yescharacteristic, complemented
310#358C22×C13911yescharacteristic, complemented
311#358C22×C13911yescharacteristic, complemented
312#358C22×C13911yescharacteristic, complemented
313#357C22×C13911yescharacteristic
314#357C22×C13911yescharacteristic
315#357C22×C13911yescharacteristic
316#357C22×C13911yescharacteristic
317#357C22×C13911yescharacteristic
318#357C22×C13911yescharacteristic
319C22⋊C16C22×C13911yescharacteristic
320C22⋊C16C22×C13911yescharacteristic, complemented
321#346C22×C13911yescharacteristic, complemented
322C2×#41—21no—
323C22×D4—21no—
324#135—22no—
325#135—41no—
326C2×Q16C23×C13911yescharacteristic
327C2×Q16C23×C13911yescharacteristic
328C2×SD16—21no—
329C2×SD16—21no—
330C2×D8—22no—
331C2×D8—21no—
332C2×D8—41no—
333C2×D8C23×C13911yescharacteristic
334C2×D8C23×C13911yescharacteristic
335C22×C8C23×C13911yescharacteristic
336C22×C8C23×C13911yescharacteristic
337C4⋊Q8—21no—
338#125—41no—
339#124—21no—
340#123—41no—
341C22⋊Q8—21no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344C22⋊Q8—41no—
345C22⋊Q8—41no—
346#121—21no—
347#121—41no—
348#120—41no—
349C4×Q8—21no—
350C4×D4—21no—
351C4×D4—41no—
352C4×D4D4×C13911yescharacteristic
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C22⋊C4—41no—
356Q32—41no—
357SD32—22no—
358SD32—41no—
359M32—41no—
360C2×C16—41no—
361C2×C16C23×C13911yescharacteristic
362C2×C16C23×C13911yescharacteristic
363C2×C16C23×C13911yescharacteristic
364C2×C16C23×C13911yescharacteristic
365#107—21no—
366#107—21no—
367#107—21no—
368#107C23×C13911yescharacteristic
369#107C23×C13911yescharacteristic
370#107C23×C13911yescharacteristic
371#107C23×C13911yescharacteristic
372C4⋊C8D4×C13911yescharacteristic
373#103—21no—
374#103—21no—
375#103—21no—
376#103—21no—
377#102—21no—
378#102—21no—
379C22⋊C8D4×C13911yescharacteristic
380C22⋊C8D4×C13911yescharacteristic
381C4×C8C23×C13911yescharacteristic
382C24—41no—
383#41—42no—
384#41—81no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—41no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—42no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—81no—
395C2×D4D8×C13911yescharacteristic
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4C2×D4×C13911yescharacteristic
401C22×C4C2×D4×C13911yescharacteristic
402Q16—21no—
403Q16—21no—
404Q16—21no—
405Q16—21no—
406SD16—42no—
407SD16—81no—
408D8—21no—
409D8—21no—
410D8—21no—
411D8—42no—
412D8#41×C13912yes—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8C2×D4×C13911yescharacteristic
418C2×C8C2×D4×C13911yescharacteristic
419C2×C8C2×D4×C13911yescharacteristic
420C2×C8C24×C13911yescharacteristic
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4D8×C13911yescharacteristic
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4D8×C13911yescharacteristic
441C22⋊C4D8×C13911yescharacteristic
442C42—41no—
443C42C2×D4×C13911yescharacteristic
444C16—21no—
445C16—21no—
446C16—21no—
447C16—21no—
448C23—41no—
449C23—41no—
450C23—82no—
451C23—82no—
452C23—161no—
453C23C2×D8×C13911yescharacteristic
454C23C2×D8×C13911yescharacteristic
455Q8—41no—
456Q8—41no—
457Q8—41no—
458Q8—41no—
459Q8—161no—
460D4—22no—
461D4—22no—
462D4—41no—
463D4—41no—
464D4—41no—
465D4—82no—
466D4—82no—
467D4—161no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—82no—
479C2×C4—161no—
480C2×C4—161no—
481C2×C4—161no—
482C2×C4C2×D8×C13911yescharacteristic
483C2×C4C2×D8×C13911yescharacteristic
484C2×C4C2×D8×C13911yescharacteristic
485C2×C4C2×D8×C13911yescharacteristic
486C2×C4C22×D4×C13911yescharacteristic
487C8—21no—
488C8—21no—
489C8—21no—
490C8C2×#41×C13911yescharacteristic
491C8H(5,𝔽2)×C13911yescharacteristic
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—42no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—164no—
504C22#510×C13912yes—
505C22C22×D8×C13911yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—81no—
511C4—81no—
512C4—81no—
513C4—81no—
514C4—81no—
515C4—81no—
516C4#546×C13911yescharacteristic
517C4#577×C13911yescharacteristic
518C2—22no—
519C2—41no—
520C2—82no—
521C2—161no—
522C2#3294×C13911yescharacteristic
523C2C2×#510×C13911yescharacteristic
524C2#3415×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C22×D8
commutator, Frattini, cosocleC2×C8C24×C139
prime radical#3280×C139C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C4×D4×C139 ◁ C8×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3338×C139C2semidirect
3. #2243×C139C2semidirect
4. #2236×C139C2semidirect
5. #2232×C139C2semidirect
6. #2224×C139C2semidirect
7. #2220×C139C2semidirect
8. #2216×C139C2semidirect
9. #2211×C139C2semidirect
10. #2189×C139C2semidirect
11. #2187×C139C2semidirect
12. #2175×C139C2semidirect
13. #2168×C139C2semidirect
14. #2139×C139C2semidirect
15. C2×#357×C139C2semidirect
20. C2×Q32×C139C22semidirect
23. C2×M32×C139C22semidirect
25. #500×C139C22semidirect
32. #467×C139C22semidirect
37. C4×Q16×C139C22semidirect
41. C2×#107×C139C22semidirect
42. #366×C139C22semidirect
43. #366×C139C22semidirect
44. #366×C139C22semidirect
45. C4⋊C16×C139C22semidirect
46. #358×C139C22semidirect
47. #358×C139C22semidirect
48. #358×C139C22semidirect
49. #358×C139C22semidirect
57. C22⋊C16×C139C22semidirect
58. #346×C139C22semidirect
262. #33881C139direct (N × H)
263. C139#33881direct (N × H)
264. #3338C2×C139semidirect
266. #2243C2×C139semidirect
267. #2236C2×C139semidirect
268. #2232C2×C139semidirect
269. #2224C2×C139semidirect
270. #2220C2×C139semidirect
271. #2216C2×C139semidirect
272. #2211C2×C139semidirect
273. #2189C2×C139semidirect
274. #2187C2×C139semidirect
275. #2175C2×C139semidirect
276. #2168C2×C139semidirect
277. #2139C2×C139semidirect
278. C2×#357C2×C139semidirect
283. C2×Q32C22×C139semidirect
286. C2×M32C22×C139semidirect
288. #500C22×C139semidirect
295. #467C22×C139semidirect
300. C4×Q16C22×C139semidirect
304. C2×#107C22×C139semidirect
305. #366C22×C139semidirect
306. #366C22×C139semidirect
307. #366C22×C139semidirect
308. C4⋊C16C22×C139semidirect
309. #358C22×C139semidirect
310. #358C22×C139semidirect
311. #358C22×C139semidirect
312. #358C22×C139semidirect
320. C22⋊C16C22×C139semidirect
321. #346C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3338×C1392
#3280×C1392
#2243×C1392
#2236×C1392
#2232×C1392
#2224×C1392
#2220×C1392
#2216×C1392
#2211×C1392
#2189×C1392
#2187×C1392
#2175×C1392
#2168×C1392
#2139×C1392
C2×#357×C1392
#33881139