Finite Group Databasebeta

← C139×#19752 #48014348

Subgroups — C139×#19752 #48014348

Order 35584.

706 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3185×C139C211yesmaximal, characteristic, complemented
2#3182×C139C211yesmaximal, characteristic
3#3182×C139C211yesmaximal, characteristic
4#3165×C139C211yesmaximal, characteristic, complemented
5#3141×C139C211yesmaximal, characteristic
6#3139×C139C211yesmaximal, characteristic, complemented
7#1723×C139C211yesmaximal, characteristic, complemented
8#1720×C139C211yesmaximal, characteristic, complemented
9#1719×C139C211yesmaximal, characteristic, complemented
10#1718×C139C211yesmaximal, characteristic, complemented
11#1718×C139C211yesmaximal, characteristic, complemented
12#1714×C139C211yesmaximal, characteristic, complemented
13#1710×C139C211yesmaximal, characteristic, complemented
14#1708×C139C211yesmaximal, characteristic, complemented
15#1455×C139C211yesmaximal, characteristic, complemented
16#533×C139C2211yescharacteristic
17#533×C139C2211yescharacteristic
18#532×C139C2211yescharacteristic
19C2×C4⋊Q8×C139C2211yescharacteristic
20#501×C139—22no—
21#500×C139C2211yescharacteristic
22#500×C139C2211yescharacteristic
23#500×C139C2211yescharacteristic
24#500×C139C2211yescharacteristic
25#498×C139C2211yescharacteristic
26#498×C139C2211yescharacteristic
27#498×C139C2211yescharacteristic
28#494×C139C2211yescharacteristic
29#492×C139C2211yescharacteristic
30#492×C139C2211yescharacteristic
31#491×C139—22no—
32#489×C139—22no—
33#487×C139C2211yescharacteristic
34#487×C139C2211yescharacteristic
35#487×C139C2211yescharacteristic
36#487×C139C2211yescharacteristic
37#487×C139C2211yescharacteristic
38#487×C139C2211yescharacteristic
39#487×C139C2211yescharacteristic
40#487×C139C2211yescharacteristic
41#487×C139C2211yescharacteristic
42#487×C139C2211yescharacteristic
43#486×C139C2211yescharacteristic
44#486×C139C2211yescharacteristic
45#486×C139C2211yescharacteristic
46#486×C139C2211yescharacteristic
47#470×C139—22no—
48#468×C139—22no—
49#468×C139—22no—
50#441×C139—22no—
51#440×C139—22no—
52#440×C139—22no—
53#428×C139—22no—
54#419×C139—22no—
55#417×C139—22no—
56C4×M16×C139C2211yescharacteristic
57C4×M16×C139C2211yescharacteristic
58C4×M16×C139C2211yescharacteristic
59#322×C139C2211yescharacteristic
60#322×C139C2211yescharacteristic
61#322×C139C2211yescharacteristic
62C82×C139C2211yescharacteristic
63C2×#41×C139—21no—
64C22×Q8×C139—21no—
65C2×Q16×C139—22no—
66C2×SD16×C139—22no—
67C2×SD16×C139—22no—
68C2×M16×C139D412yes—
69C2×M16×C139D412yes—
70C2×M16×C139D412yes—
71C4⋊Q8×C139—21no—
72C4⋊Q8×C139—21no—
73C4⋊Q8×C139—21no—
74C4⋊Q8×C139C2311yescharacteristic
75C4⋊Q8×C139C2311yescharacteristic
76C4⋊Q8×C139C2311yescharacteristic
77C4⋊Q8×C139C2311yescharacteristic
78C4⋊Q8×C139C2311yescharacteristic
79C4⋊Q8×C139C2311yescharacteristic
80C4⋊Q8×C139C2311yescharacteristic
81#127×C139C2311yescharacteristic
82#125×C139—21no—
83#125×C139—21no—
84#124×C139—21no—
85C22⋊Q8×C139—21no—
86C22⋊Q8×C139—21no—
87C22⋊Q8×C139—21no—
88C22⋊Q8×C139—21no—
89#121×C139—21no—
90#121×C139—21no—
91C4×Q8×C139—21no—
92C4×Q8×C139—21no—
93C4×Q8×C139—21no—
94C4×Q8×C139—21no—
95C4×D4×C139—21no—
96C4×D4×C139—21no—
97#117×C139—21no—
98#117×C139—21no—
99C2×C4⋊C4×C139—21no—
100C2×C4⋊C4×C139—21no—
101C2×C42×C139C2311yescharacteristic
102#107×C139—22no—
103#107×C139—22no—
104#107×C139—22no—
105#107×C139—22no—
106#106×C139—22no—
107#106×C139—22no—
108#106×C139—22no—
109#103×C139—22no—
110#103×C139—22no—
111#103×C139—22no—
112#103×C139—22no—
113#103×C139—22no—
114#103×C139—22no—
115#103×C139—22no—
116#103×C139—22no—
117#103×C139—22no—
118#103×C139—22no—
119#102×C139—22no—
120#102×C139—22no—
121#102×C139—22no—
122#102×C139—22no—
123#97×C139D412yes—
124#97×C139D412yes—
125#97×C139D412yes—
126C4×C8×C139C2311yescharacteristic
127C4×C8×C139C2311yescharacteristic
128C4×C8×C139C2311yescharacteristic
129C4×C8×C139C2311yescharacteristic
130C4×C8×C139C2311yescharacteristic
131C4×C8×C139C2311yescharacteristic
132#41×C139—44no—
133C2×Q8×C139—21no—
134C2×Q8×C139—21no—
135C2×Q8×C139—21no—
136C2×Q8×C139—21no—
137C2×Q8×C139—21no—
138C2×Q8×C139—21no—
139C2×Q8×C139—21no—
140C2×Q8×C139—44no—
141C2×Q8×C139—41no—
142C2×D4×C139—21no—
143C2×D4×C139—21no—
144C2×D4×C139—21no—
145C2×D4×C139—41no—
146C22×C4×C139—41no—
147C22×C4×C139—41no—
148C22×C4×C139C2×D411yescharacteristic
149C22×C4×C139C2×D411yescharacteristic
150C22×C4×C139C2×D411yescharacteristic
151Q16×C139—44no—
152SD16×C139—44no—
153SD16×C139—44no—
154M16×C139—24no—
155M16×C139—42no—
156M16×C139—42no—
157C2×C8×C139C2×D412yes—
158C2×C8×C139C2×D412yes—
159C2×C8×C139C2×D412yes—
160C2×C8×C139C2×D412yes—
161C2×C8×C139C2×D412yes—
162C2×C8×C139C2×D412yes—
163C4⋊C4×C139—21no—
164C4⋊C4×C139—21no—
165C4⋊C4×C139—21no—
166C4⋊C4×C139—21no—
167C4⋊C4×C139—21no—
168C4⋊C4×C139—21no—
169C4⋊C4×C139—21no—
170C4⋊C4×C139—21no—
171C4⋊C4×C139—21no—
172C4⋊C4×C139—21no—
173C4⋊C4×C139—21no—
174C4⋊C4×C139—21no—
175C4⋊C4×C139—21no—
176C4⋊C4×C139—21no—
177C4⋊C4×C139—41no—
178C4⋊C4×C139—41no—
179C4⋊C4×C139—41no—
180C4⋊C4×C139—41no—
181C4⋊C4×C139—41no—
182C4⋊C4×C139—41no—
183C22⋊C4×C139—41no—
184C22⋊C4×C139—41no—
185C22⋊C4×C139—41no—
186C22⋊C4×C139—41no—
187C42×C139—41no—
188C42×C139—41no—
189C42×C139C2×D411yescharacteristic
190C42×C139C2×D411yescharacteristic
191C42×C139C2×D411yescharacteristic
192C42×C139C2411yescharacteristic
193C23×C139—41no—
194C23×C139#12711yescharacteristic
195Q8×C139—42no—
196Q8×C139—42no—
197Q8×C139—42no—
198Q8×C139—42no—
199Q8×C139—42no—
200Q8×C139—42no—
201Q8×C139—42no—
202Q8×C139—82no—
203D4×C139—42no—
204D4×C139—42no—
205D4×C139—42no—
206D4×C139—82no—
207C2×C4×C139—22no—
208C2×C4×C139—22no—
209C2×C4×C139—22no—
210C2×C4×C139—41no—
211C2×C4×C139—41no—
212C2×C4×C139—41no—
213C2×C4×C139—41no—
214C2×C4×C139—41no—
215C2×C4×C139—41no—
216C2×C4×C139—41no—
217C2×C4×C139—82no—
218C2×C4×C139—82no—
219C2×C4×C139#12711yescharacteristic
220C2×C4×C139#12711yescharacteristic
221C2×C4×C139#12711yescharacteristic
222C2×C4×C139C22×D411yescharacteristic
223C2×C4×C139C22×D411yescharacteristic
224C2×C4×C139C22×D411yescharacteristic
225C8×C139—22no—
226C8×C139—22no—
227C8×C139—22no—
228C8×C139—22no—
229C8×C139—22no—
230C8×C139#13714yes—
231C22×C139—21no—
232C22×C139—21no—
233C22×C139—21no—
234C22×C139—81no—
235C22×C139—81no—
236C22×C139—81no—
237C22×C139C2×#12711yescharacteristic
238C4×C139—21no—
239C4×C139—21no—
240C4×C139—21no—
241C4×C139—81no—
242C4×C139—81no—
243C4×C139—81no—
244C4×C139—81no—
245C4×C139—81no—
246C4×C139—81no—
247C4×C139—81no—
248C4×C139C2×#13712yes—
249C4×C139#57512yes—
250C4×C139#57512yes—
251C2×C139—41no—
252C2×C139—161no—
253C2×C139#315211yescharacteristic
254C2×C139#315311yescharacteristic
255C2×C139#315311yescharacteristic
256#19752C13911yesmaximal, characteristic, direct product factor, Sylow
257C139#1975211yescharacteristic, direct product factor, Sylow
258#3185C2×C13911yescharacteristic, complemented
259#3182C2×C13911yescharacteristic
260#3182C2×C13911yescharacteristic
261#3165C2×C13911yescharacteristic, complemented
262#3141C2×C13911yescharacteristic
263#3139C2×C13911yescharacteristic, complemented
264#1723C2×C13911yescharacteristic, complemented
265#1720C2×C13911yescharacteristic, complemented
266#1719C2×C13911yescharacteristic, complemented
267#1718C2×C13911yescharacteristic, complemented
268#1718C2×C13911yescharacteristic, complemented
269#1714C2×C13911yescharacteristic, complemented
270#1710C2×C13911yescharacteristic, complemented
271#1708C2×C13911yescharacteristic, complemented
272#1455C2×C13911yescharacteristic, complemented
273#533C22×C13911yescharacteristic
274#533C22×C13911yescharacteristic
275#532C22×C13911yescharacteristic
276C2×C4⋊Q8C22×C13911yescharacteristic
277#501—22no—
278#500C22×C13911yescharacteristic
279#500C22×C13911yescharacteristic
280#500C22×C13911yescharacteristic
281#500C22×C13911yescharacteristic
282#498C22×C13911yescharacteristic
283#498C22×C13911yescharacteristic
284#498C22×C13911yescharacteristic
285#494C22×C13911yescharacteristic
286#492C22×C13911yescharacteristic
287#492C22×C13911yescharacteristic
288#491—22no—
289#489—22no—
290#487C22×C13911yescharacteristic
291#487C22×C13911yescharacteristic
292#487C22×C13911yescharacteristic
293#487C22×C13911yescharacteristic
294#487C22×C13911yescharacteristic
295#487C22×C13911yescharacteristic
296#487C22×C13911yescharacteristic
297#487C22×C13911yescharacteristic
298#487C22×C13911yescharacteristic
299#487C22×C13911yescharacteristic
300#486C22×C13911yescharacteristic
301#486C22×C13911yescharacteristic
302#486C22×C13911yescharacteristic
303#486C22×C13911yescharacteristic
304#470—22no—
305#468—22no—
306#468—22no—
307#441—22no—
308#440—22no—
309#440—22no—
310#428—22no—
311#419—22no—
312#417—22no—
313C4×M16C22×C13911yescharacteristic
314C4×M16C22×C13911yescharacteristic
315C4×M16C22×C13911yescharacteristic
316#322C22×C13911yescharacteristic
317#322C22×C13911yescharacteristic
318#322C22×C13911yescharacteristic
319C82C22×C13911yescharacteristic
320C2×#41—21no—
321C22×Q8—21no—
322C2×Q16—22no—
323C2×SD16—22no—
324C2×SD16—22no—
325C2×M16D4×C13912yes—
326C2×M16D4×C13912yes—
327C2×M16D4×C13912yes—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8C23×C13911yescharacteristic
332C4⋊Q8C23×C13911yescharacteristic
333C4⋊Q8C23×C13911yescharacteristic
334C4⋊Q8C23×C13911yescharacteristic
335C4⋊Q8C23×C13911yescharacteristic
336C4⋊Q8C23×C13911yescharacteristic
337C4⋊Q8C23×C13911yescharacteristic
338#127C23×C13911yescharacteristic
339#125—21no—
340#125—21no—
341#124—21no—
342C22⋊Q8—21no—
343C22⋊Q8—21no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346#121—21no—
347#121—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×D4—21no—
353C4×D4—21no—
354#117—21no—
355#117—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C42C23×C13911yescharacteristic
359#107—22no—
360#107—22no—
361#107—22no—
362#107—22no—
363#106—22no—
364#106—22no—
365#106—22no—
366#103—22no—
367#103—22no—
368#103—22no—
369#103—22no—
370#103—22no—
371#103—22no—
372#103—22no—
373#103—22no—
374#103—22no—
375#103—22no—
376#102—22no—
377#102—22no—
378#102—22no—
379#102—22no—
380#97D4×C13912yes—
381#97D4×C13912yes—
382#97D4×C13912yes—
383C4×C8C23×C13911yescharacteristic
384C4×C8C23×C13911yescharacteristic
385C4×C8C23×C13911yescharacteristic
386C4×C8C23×C13911yescharacteristic
387C4×C8C23×C13911yescharacteristic
388C4×C8C23×C13911yescharacteristic
389#41—44no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—44no—
398C2×Q8—41no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4C2×D4×C13911yescharacteristic
406C22×C4C2×D4×C13911yescharacteristic
407C22×C4C2×D4×C13911yescharacteristic
408Q16—44no—
409SD16—44no—
410SD16—44no—
411M16—24no—
412M16—42no—
413M16—42no—
414C2×C8C2×D4×C13912yes—
415C2×C8C2×D4×C13912yes—
416C2×C8C2×D4×C13912yes—
417C2×C8C2×D4×C13912yes—
418C2×C8C2×D4×C13912yes—
419C2×C8C2×D4×C13912yes—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C42—41no—
445C42—41no—
446C42C2×D4×C13911yescharacteristic
447C42C2×D4×C13911yescharacteristic
448C42C2×D4×C13911yescharacteristic
449C42C24×C13911yescharacteristic
450C23—41no—
451C23#127×C13911yescharacteristic
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—42no—
456Q8—42no—
457Q8—42no—
458Q8—42no—
459Q8—82no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—82no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—82no—
475C2×C4—82no—
476C2×C4#127×C13911yescharacteristic
477C2×C4#127×C13911yescharacteristic
478C2×C4#127×C13911yescharacteristic
479C2×C4C22×D4×C13911yescharacteristic
480C2×C4C22×D4×C13911yescharacteristic
481C2×C4C22×D4×C13911yescharacteristic
482C8—22no—
483C8—22no—
484C8—22no—
485C8—22no—
486C8—22no—
487C8#137×C13914yes—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22C2×#127×C13911yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—81no—
499C4—81no—
500C4—81no—
501C4—81no—
502C4—81no—
503C4—81no—
504C4—81no—
505C4C2×#137×C13912yes—
506C4#575×C13912yes—
507C4#575×C13912yes—
508C2—41no—
509C2—161no—
510C2#3152×C13911yescharacteristic
511C2#3153×C13911yescharacteristic
512C2#3153×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#127
commutator, Frattini, cosocleC42C24×C139
prime radical#532×C139C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3185×C139C2semidirect
4. #3165×C139C2semidirect
6. #3139×C139C2semidirect
7. #1723×C139C2semidirect
8. #1720×C139C2semidirect
9. #1719×C139C2semidirect
10. #1718×C139C2semidirect
11. #1718×C139C2semidirect
12. #1714×C139C2semidirect
13. #1710×C139C2semidirect
14. #1708×C139C2semidirect
15. #1455×C139C2semidirect
256. #19752C139direct (N × H)
257. C139#19752direct (N × H)
258. #3185C2×C139semidirect
261. #3165C2×C139semidirect
263. #3139C2×C139semidirect
264. #1723C2×C139semidirect
265. #1720C2×C139semidirect
266. #1719C2×C139semidirect
267. #1718C2×C139semidirect
268. #1718C2×C139semidirect
269. #1714C2×C139semidirect
270. #1710C2×C139semidirect
271. #1708C2×C139semidirect
272. #1455C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3185×C1392
#3182×C1392
#3165×C1392
#3141×C1392
#3139×C1392
#1723×C1392
#1720×C1392
#1719×C1392
#1718×C1392
#1714×C1392
#1710×C1392
#1708×C1392
#1455×C1392
#19752139