Finite Group Databasebeta

← C139×#20207 #48014803

Subgroups — C139×#20207 #48014803

Order 35584.

592 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3384×C139C211yesmaximal, characteristic
2#3367×C139C211yesmaximal, characteristic
3#3328×C139C211yesmaximal, characteristic, complemented
4#3299×C139C211yesmaximal, characteristic, complemented
5#1718×C139C211yesmaximal, characteristic, complemented
6#1703×C139C211yesmaximal, characteristic, complemented
7#1700×C139C211yesmaximal, characteristic, complemented
8#1692×C139C211yesmaximal, characteristic, complemented
9#1679×C139C211yesmaximal, characteristic, complemented
10#1649×C139C211yesmaximal, characteristic, complemented
11#1649×C139C211yesmaximal, characteristic, complemented
12#1643×C139C211yesmaximal, characteristic, complemented
13#1638×C139C211yesmaximal, characteristic, complemented
14#1593×C139C211yesmaximal, characteristic, complemented
15#1581×C139C211yesmaximal, characteristic
16#556×C139C2211yescharacteristic
17#554×C139C2211yescharacteristic
18D4×Q8×C139C2211yescharacteristic
19D4×Q8×C139C2211yescharacteristic
20#501×C139—21no—
21#500×C139C2211yescharacteristic
22#498×C139C2211yescharacteristic
23#489×C139—21no—
24#487×C139C2211yescharacteristic
25#487×C139C2211yescharacteristic
26#487×C139C2211yescharacteristic
27#487×C139C2211yescharacteristic
28#485×C139—21no—
29#484×C139—21no—
30#478×C139—21no—
31#477×C139—21no—
32#477×C139C2211yescharacteristic
33#476×C139—21no—
34#476×C139C2211yescharacteristic
35#475×C139C2211yescharacteristic
36#474×C139C2211yescharacteristic
37#474×C139C2211yescharacteristic
38#470×C139—21no—
39#467×C139—21no—
40#463×C139—21no—
41#462×C139C2211yescharacteristic
42#462×C139C2211yescharacteristic
43#461×C139C2211yescharacteristic
44#451×C139—21no—
45#451×C139—21no—
46#446×C139C2211yescharacteristic
47#446×C139C2211yescharacteristic
48#442×C139—21no—
49#440×C139—21no—
50C4×Q16×C139C2211yescharacteristic
51C4×D8×C139C2211yescharacteristic
52#436×C139C2211yescharacteristic
53C8×D4×C139C2211yescharacteristic
54#419×C139—21no—
55C2×#103×C139—21no—
56#335×C139C2211yescharacteristic
57#334×C139C2211yescharacteristic
58#333×C139C2211yescharacteristic
59#332×C139C2211yescharacteristic
60#332×C139C2211yescharacteristic
61#332×C139C2211yescharacteristic
62Q8⋊C8×C139C2211yescharacteristic
63Q8⋊C8×C139C2211yescharacteristic
64D4⋊C8×C139C2211yescharacteristic
65D4⋊C8×C139C2211yescharacteristic
66#322×C139C2211yescharacteristic
67C22×Q8×C139—21no—
68C22×Q8×C139—21no—
69C2×Q16×C139—21no—
70C2×Q16×C139—21no—
71C2×Q16×C139D411yescharacteristic
72C2×SD16×C139—21no—
73C2×D8×C139D411yescharacteristic
74C2×M16×C139—21no—
75C22×C8×C139—21no—
76C4⋊Q8×C139—21no—
77C4⋊Q8×C139—21no—
78C4⋊Q8×C139C2311yescharacteristic
79C4⋊Q8×C139C2311yescharacteristic
80C4⋊Q8×C139C2311yescharacteristic
81C4⋊Q8×C139C2311yescharacteristic
82#126×C139—41no—
83#125×C139—21no—
84#124×C139—21no—
85C22⋊Q8×C139—21no—
86C22⋊Q8×C139—21no—
87C22⋊Q8×C139—21no—
88C22⋊Q8×C139—21no—
89C22⋊Q8×C139—41no—
90C22⋊Q8×C139—41no—
91C22⋊Q8×C139—41no—
92C4×Q8×C139—21no—
93C4×Q8×C139C2311yescharacteristic
94C4×Q8×C139C2311yescharacteristic
95C4×D4×C139—21no—
96C4×D4×C139—21no—
97C4×D4×C139—21no—
98C4×D4×C139C2311yescharacteristic
99C4×D4×C139C2311yescharacteristic
100#117×C139—21no—
101C2×C4⋊C4×C139—21no—
102#107×C139—21no—
103#107×C139—21no—
104#107×C139—21no—
105#107×C139—41no—
106#107×C139D411yescharacteristic
107#107×C139D411yescharacteristic
108#106×C139—21no—
109#106×C139—21no—
110#106×C139—21no—
111#106×C139—21no—
112C4⋊C8×C139—21no—
113C4⋊C8×C139—21no—
114C4⋊C8×C139C2311yescharacteristic
115C4⋊C8×C139C2311yescharacteristic
116C4⋊C8×C139C2311yescharacteristic
117C4⋊C8×C139C2311yescharacteristic
118#103×C139—21no—
119#103×C139—21no—
120#103×C139—21no—
121#103×C139—21no—
122#103×C139—21no—
123#103×C139—21no—
124#103×C139—21no—
125#103×C139—21no—
126#103×C139—21no—
127#103×C139—21no—
128#103×C139—21no—
129#103×C139—41no—
130#103×C139D411yescharacteristic
131#103×C139D411yescharacteristic
132#102×C139—21no—
133#102×C139—21no—
134#102×C139—21no—
135#102×C139D411yescharacteristic
136#102×C139D411yescharacteristic
137C22⋊C8×C139—21no—
138C22⋊C8×C139—21no—
139#97×C139—21no—
140#97×C139—21no—
141C4×C8×C139C2311yescharacteristic
142C4×C8×C139C2311yescharacteristic
143C4×C8×C139C2311yescharacteristic
144C2×Q8×C139—21no—
145C2×Q8×C139—21no—
146C2×Q8×C139—21no—
147C2×Q8×C139—21no—
148C2×Q8×C139—41no—
149C2×Q8×C139—41no—
150C2×Q8×C139—42no—
151C2×Q8×C139—42no—
152C2×Q8×C139—81no—
153C2×Q8×C139—81no—
154C2×Q8×C139C2×D411yescharacteristic
155C2×Q8×C139C2×D411yescharacteristic
156C2×D4×C139C2×D411yescharacteristic
157C2×D4×C139C2×D411yescharacteristic
158C22×C4×C139—21no—
159C22×C4×C139—21no—
160C22×C4×C139—41no—
161C22×C4×C139—41no—
162C22×C4×C139—41no—
163Q16×C139—41no—
164Q16×C139—81no—
165Q16×C139—81no—
166SD16×C139—42no—
167D8×C139—22no—
168M16×C139—81no—
169C2×C8×C139—21no—
170C2×C8×C139—21no—
171C2×C8×C139—21no—
172C2×C8×C139—21no—
173C2×C8×C139—21no—
174C2×C8×C139—81no—
175C2×C8×C139C2×D411yescharacteristic
176C2×C8×C139C2×D411yescharacteristic
177C2×C8×C139C2×D411yescharacteristic
178C2×C8×C139C2×D411yescharacteristic
179C4⋊C4×C139—21no—
180C4⋊C4×C139—21no—
181C4⋊C4×C139—21no—
182C4⋊C4×C139—21no—
183C4⋊C4×C139—21no—
184C4⋊C4×C139—21no—
185C4⋊C4×C139—21no—
186C4⋊C4×C139—21no—
187C4⋊C4×C139—21no—
188C4⋊C4×C139—21no—
189C4⋊C4×C139—41no—
190C4⋊C4×C139—41no—
191C4⋊C4×C139—41no—
192C4⋊C4×C139—41no—
193C4⋊C4×C139—41no—
194C4⋊C4×C139C2×D411yescharacteristic
195C4⋊C4×C139C2×D411yescharacteristic
196C4⋊C4×C139C2×D411yescharacteristic
197C4⋊C4×C139C2×D411yescharacteristic
198C22⋊C4×C139—21no—
199C22⋊C4×C139—21no—
200C22⋊C4×C139—41no—
201C22⋊C4×C139—41no—
202C22⋊C4×C139—41no—
203C22⋊C4×C139—41no—
204C22⋊C4×C139—41no—
205C42×C139—21no—
206C42×C139—21no—
207C42×C139—41no—
208C42×C139C2411yescharacteristic
209C23×C139—21no—
210C23×C139—21no—
211Q8×C139—21no—
212Q8×C139—21no—
213Q8×C139—21no—
214Q8×C139—21no—
215Q8×C139—41no—
216Q8×C139—41no—
217Q8×C139—41no—
218Q8×C139—41no—
219Q8×C139—41no—
220Q8×C139—41no—
221Q8×C139—81no—
222Q8×C139—82no—
223Q8×C139—82no—
224D4×C139—21no—
225D4×C139—21no—
226D4×C139—21no—
227D4×C139#13712yes—
228C2×C4×C139—21no—
229C2×C4×C139—21no—
230C2×C4×C139—21no—
231C2×C4×C139—21no—
232C2×C4×C139—21no—
233C2×C4×C139—21no—
234C2×C4×C139—41no—
235C2×C4×C139—41no—
236C2×C4×C139—41no—
237C2×C4×C139—41no—
238C2×C4×C139—41no—
239C2×C4×C139—41no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—82no—
243C2×C4×C139—82no—
244C2×C4×C139—161no—
245C2×C4×C139C22×D411yescharacteristic
246C2×C4×C139C22×D411yescharacteristic
247C2×C4×C139H(5,𝔽2)11yescharacteristic
248C8×C139—21no—
249C8×C139—21no—
250C8×C139—21no—
251C8×C139—21no—
252C8×C139—41no—
253C8×C139—41no—
254C8×C139—41no—
255C8×C139—41no—
256C8×C139—41no—
257C22×C139—22no—
258C22×C139—41no—
259C22×C139—41no—
260C22×C139—41no—
261C22×C139—41no—
262C22×C139—41no—
263C22×C139D4211yescharacteristic
264C4×C139—21no—
265C4×C139—41no—
266C4×C139—41no—
267C4×C139—41no—
268C4×C139—41no—
269C4×C139—41no—
270C4×C139—41no—
271C4×C139—81no—
272C4×C139—81no—
273C4×C139—81no—
274C4×C139—81no—
275C4×C139C2×#13711yescharacteristic
276C4×C139#57511yescharacteristic
277C4×C139#57611yescharacteristic
278C4×C139#57811yescharacteristic
279C2×C139—42no—
280C2×C139—81no—
281C2×C139#327011yescharacteristic
282C2×C139#327311yescharacteristic
283C2×C139#328911yescharacteristic
284#20207C13911yesmaximal, characteristic, direct product factor, Sylow
285C139#2020711yescharacteristic, direct product factor, Sylow
286#3384C2×C13911yescharacteristic
287#3367C2×C13911yescharacteristic
288#3328C2×C13911yescharacteristic, complemented
289#3299C2×C13911yescharacteristic, complemented
290#1718C2×C13911yescharacteristic, complemented
291#1703C2×C13911yescharacteristic, complemented
292#1700C2×C13911yescharacteristic, complemented
293#1692C2×C13911yescharacteristic, complemented
294#1679C2×C13911yescharacteristic, complemented
295#1649C2×C13911yescharacteristic, complemented
296#1649C2×C13911yescharacteristic, complemented
297#1643C2×C13911yescharacteristic, complemented
298#1638C2×C13911yescharacteristic, complemented
299#1593C2×C13911yescharacteristic, complemented
300#1581C2×C13911yescharacteristic
301#556C22×C13911yescharacteristic
302#554C22×C13911yescharacteristic
303D4×Q8C22×C13911yescharacteristic
304D4×Q8C22×C13911yescharacteristic
305#501—21no—
306#500C22×C13911yescharacteristic
307#498C22×C13911yescharacteristic
308#489—21no—
309#487C22×C13911yescharacteristic
310#487C22×C13911yescharacteristic
311#487C22×C13911yescharacteristic
312#487C22×C13911yescharacteristic
313#485—21no—
314#484—21no—
315#478—21no—
316#477—21no—
317#477C22×C13911yescharacteristic
318#476—21no—
319#476C22×C13911yescharacteristic
320#475C22×C13911yescharacteristic
321#474C22×C13911yescharacteristic
322#474C22×C13911yescharacteristic
323#470—21no—
324#467—21no—
325#463—21no—
326#462C22×C13911yescharacteristic
327#462C22×C13911yescharacteristic
328#461C22×C13911yescharacteristic
329#451—21no—
330#451—21no—
331#446C22×C13911yescharacteristic
332#446C22×C13911yescharacteristic
333#442—21no—
334#440—21no—
335C4×Q16C22×C13911yescharacteristic
336C4×D8C22×C13911yescharacteristic
337#436C22×C13911yescharacteristic
338C8×D4C22×C13911yescharacteristic
339#419—21no—
340C2×#103—21no—
341#335C22×C13911yescharacteristic
342#334C22×C13911yescharacteristic
343#333C22×C13911yescharacteristic
344#332C22×C13911yescharacteristic
345#332C22×C13911yescharacteristic
346#332C22×C13911yescharacteristic
347Q8⋊C8C22×C13911yescharacteristic
348Q8⋊C8C22×C13911yescharacteristic
349D4⋊C8C22×C13911yescharacteristic
350D4⋊C8C22×C13911yescharacteristic
351#322C22×C13911yescharacteristic
352C22×Q8—21no—
353C22×Q8—21no—
354C2×Q16—21no—
355C2×Q16—21no—
356C2×Q16D4×C13911yescharacteristic
357C2×SD16—21no—
358C2×D8D4×C13911yescharacteristic
359C2×M16—21no—
360C22×C8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8C23×C13911yescharacteristic
364C4⋊Q8C23×C13911yescharacteristic
365C4⋊Q8C23×C13911yescharacteristic
366C4⋊Q8C23×C13911yescharacteristic
367#126—41no—
368#125—21no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375C22⋊Q8—41no—
376C22⋊Q8—41no—
377C4×Q8—21no—
378C4×Q8C23×C13911yescharacteristic
379C4×Q8C23×C13911yescharacteristic
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C23×C13911yescharacteristic
384C4×D4C23×C13911yescharacteristic
385#117—21no—
386C2×C4⋊C4—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—41no—
391#107D4×C13911yescharacteristic
392#107D4×C13911yescharacteristic
393#106—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8C23×C13911yescharacteristic
400C4⋊C8C23×C13911yescharacteristic
401C4⋊C8C23×C13911yescharacteristic
402C4⋊C8C23×C13911yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—41no—
415#103D4×C13911yescharacteristic
416#103D4×C13911yescharacteristic
417#102—21no—
418#102—21no—
419#102—21no—
420#102D4×C13911yescharacteristic
421#102D4×C13911yescharacteristic
422C22⋊C8—21no—
423C22⋊C8—21no—
424#97—21no—
425#97—21no—
426C4×C8C23×C13911yescharacteristic
427C4×C8C23×C13911yescharacteristic
428C4×C8C23×C13911yescharacteristic
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—42no—
436C2×Q8—42no—
437C2×Q8—81no—
438C2×Q8—81no—
439C2×Q8C2×D4×C13911yescharacteristic
440C2×Q8C2×D4×C13911yescharacteristic
441C2×D4C2×D4×C13911yescharacteristic
442C2×D4C2×D4×C13911yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448Q16—41no—
449Q16—81no—
450Q16—81no—
451SD16—42no—
452D8—22no—
453M16—81no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8C2×D4×C13911yescharacteristic
461C2×C8C2×D4×C13911yescharacteristic
462C2×C8C2×D4×C13911yescharacteristic
463C2×C8C2×D4×C13911yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C13911yescharacteristic
480C4⋊C4C2×D4×C13911yescharacteristic
481C4⋊C4C2×D4×C13911yescharacteristic
482C4⋊C4C2×D4×C13911yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42C24×C13911yescharacteristic
494C23—21no—
495C23—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—82no—
508Q8—82no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4#137×C13912yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—161no—
530C2×C4C22×D4×C13911yescharacteristic
531C2×C4C22×D4×C13911yescharacteristic
532C2×C4H(5,𝔽2)×C13911yescharacteristic
533C8—21no—
534C8—21no—
535C8—21no—
536C8—21no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22D42×C13911yescharacteristic
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4—81no—
560C4C2×#137×C13911yescharacteristic
561C4#575×C13911yescharacteristic
562C4#576×C13911yescharacteristic
563C4#578×C13911yescharacteristic
564C2—42no—
565C2—81no—
566C2#3270×C13911yescharacteristic
567C2#3273×C13911yescharacteristic
568C2#3289×C13911yescharacteristic
subgroupG/H
center, socleC22×C139D42
commutator, Frattini, cosocleC42C24×C139
prime radicalC2×D8×C139D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #3328×C139C2semidirect
4. #3299×C139C2semidirect
5. #1718×C139C2semidirect
6. #1703×C139C2semidirect
7. #1700×C139C2semidirect
8. #1692×C139C2semidirect
9. #1679×C139C2semidirect
10. #1649×C139C2semidirect
11. #1649×C139C2semidirect
12. #1643×C139C2semidirect
13. #1638×C139C2semidirect
14. #1593×C139C2semidirect
284. #20207C139direct (N × H)
285. C139#20207direct (N × H)
288. #3328C2×C139semidirect
289. #3299C2×C139semidirect
290. #1718C2×C139semidirect
291. #1703C2×C139semidirect
292. #1700C2×C139semidirect
293. #1692C2×C139semidirect
294. #1679C2×C139semidirect
295. #1649C2×C139semidirect
296. #1649C2×C139semidirect
297. #1643C2×C139semidirect
298. #1638C2×C139semidirect
299. #1593C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3384×C1392
#3367×C1392
#3328×C1392
#3299×C1392
#1718×C1392
#1703×C1392
#1700×C1392
#1692×C1392
#1679×C1392
#1649×C1392
#1643×C1392
#1638×C1392
#1593×C1392
#1581×C1392
#20207139