Finite Group Databasebeta

← C139×#8534 #48003130

Subgroups — C139×#8534 #48003130

Order 35584.

1408 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3484×C139C211yesmaximal, characteristic
2#1898×C139C214yesmaximal, complemented
3#1781×C139C211yesmaximal, characteristic, complemented
4#1438×C139C211yesmaximal, characteristic, complemented
5C2×H(5,𝔽2)×C139C411yescharacteristic, complemented
6C23×D4×C139C2211yescharacteristic
7#546×C139—24no—
8D42×C139—24no—
9#535×C139—21no—
10#534×C139—21no—
11#534×C139C412yescomplemented
12#525×C139—21no—
13C2×#120×C139—21no—
14C2×#120×C139C2212yes—
15#518×C139C411yescharacteristic, complemented
16C22×C22⋊C4×C139—21no—
17C22×C22⋊C4×C139C2212yescomplemented
18C2×#99×C139—21no—
19C2×#99×C139—21no—
20C2×#99×C139—24no—
21#379×C139C2212yescomplemented
22C2×#95×C139—21no—
23#342×C139—24no—
24C25×C139D411yescharacteristic
25C25×C139C2311yescharacteristic
26H(5,𝔽2)×C139—42no—
27H(5,𝔽2)×C139—42no—
28C2×#41×C139—21no—
29C2×#41×C139—22no—
30C22×D4×C139—21no—
31C22×D4×C139—22no—
32C22×D4×C139—24no—
33C22×D4×C139—22no—
34C22×D4×C139—42no—
35C22×D4×C139—42no—
36C22×D4×C139C2×C411yescharacteristic
37C22×D4×C139C2×C411yescharacteristic
38C22×D4×C139C2×C412yes—
39C22×D4×C139D411yescharacteristic
40C22×D4×C139D411yescharacteristic
41C22×D4×C139D414yes—
42C23×C4×C139—22no—
43C23×C4×C139D411yescharacteristic
44#127×C139—22no—
45#124×C139—22no—
46#123×C139—22no—
47#123×C139—22no—
48#123×C139—22no—
49C22⋊Q8×C139—22no—
50#121×C139—22no—
51#121×C139—24no—
52#121×C139—24no—
53#121×C139—24no—
54#120×C139—24no—
55#120×C139—22no—
56#120×C139—22no—
57#120×C139—22no—
58#120×C139—22no—
59#120×C139—22no—
60#120×C139—24no—
61C4×D4×C139—24no—
62C4×D4×C139—24no—
63#117×C139—21no—
64C2×C22⋊C4×C139—22no—
65C2×C22⋊C4×C139—21no—
66C2×C22⋊C4×C139—24no—
67C2×C22⋊C4×C139—22no—
68C2×C22⋊C4×C139—24no—
69C2×C22⋊C4×C139—44no—
70C2×C22⋊C4×C139—44no—
71C2×C22⋊C4×C139—42no—
72C2×C22⋊C4×C139C2×C412yes—
73C2×C22⋊C4×C139D414yes—
74#99×C139—48no—
75#99×C139—42no—
76#99×C139—42no—
77#95×C139—42no—
78C24×C139—21no—
79C24×C139—22no—
80C24×C139—22no—
81C24×C139—42no—
82C24×C139—41no—
83C24×C139—41no—
84C24×C139—41no—
85C24×C139—42no—
86C24×C139—42no—
87C24×C139—42no—
88C24×C139C22⋊C411yescharacteristic
89C24×C139C22⋊C411yescharacteristic
90C24×C139C22⋊C412yescomplemented
91C24×C139C22×C411yescharacteristic
92C24×C139C2×D411yescharacteristic
93C24×C139C2×D414yes—
94C24×C139C2×D411yescharacteristic
95#41×C139—42no—
96#41×C139—48no—
97#41×C139—42no—
98C2×Q8×C139—21no—
99C2×D4×C139—22no—
100C2×D4×C139—22no—
101C2×D4×C139—22no—
102C2×D4×C139—21no—
103C2×D4×C139—22no—
104C2×D4×C139—22no—
105C2×D4×C139—22no—
106C2×D4×C139—22no—
107C2×D4×C139—24no—
108C2×D4×C139—22no—
109C2×D4×C139—22no—
110C2×D4×C139—24no—
111C2×D4×C139—24no—
112C2×D4×C139—22no—
113C2×D4×C139—22no—
114C2×D4×C139—41no—
115C2×D4×C139—41no—
116C2×D4×C139—41no—
117C2×D4×C139—41no—
118C2×D4×C139—416no—
119C2×D4×C139—48no—
120C2×D4×C139—42no—
121C2×D4×C139—42no—
122C2×D4×C139—42no—
123C2×D4×C139—42no—
124C2×D4×C139—44no—
125C2×D4×C139—44no—
126C2×D4×C139—82no—
127C2×D4×C139—82no—
128C22×C4×C139—21no—
129C22×C4×C139—22no—
130C22×C4×C139—22no—
131C22×C4×C139—22no—
132C22×C4×C139—22no—
133C22×C4×C139—24no—
134C22×C4×C139—41no—
135C22×C4×C139—42no—
136C22×C4×C139—42no—
137C22×C4×C139—42no—
138C22×C4×C139—42no—
139C22×C4×C139—42no—
140C22×C4×C139—42no—
141C22×C4×C139—42no—
142C22×C4×C139C22⋊C411yescharacteristic
143C22×C4×C139C22⋊C411yescharacteristic
144C22×C4×C139C22⋊C414yescomplemented
145C22×C4×C139C22⋊C412yescomplemented
146C4⋊C4×C139—22no—
147C4⋊C4×C139—24no—
148C22⋊C4×C139—22no—
149C22⋊C4×C139—24no—
150C22⋊C4×C139—24no—
151C22⋊C4×C139—22no—
152C22⋊C4×C139—22no—
153C22⋊C4×C139—24no—
154C22⋊C4×C139—24no—
155C22⋊C4×C139—28no—
156C22⋊C4×C139—44no—
157C22⋊C4×C139—48no—
158C22⋊C4×C139—42no—
159C22⋊C4×C139—42no—
160C22⋊C4×C139—44no—
161C22⋊C4×C139—44no—
162C42×C139—22no—
163C23×C139—21no—
164C23×C139—21no—
165C23×C139—22no—
166C23×C139—22no—
167C23×C139—21no—
168C23×C139—21no—
169C23×C139—21no—
170C23×C139—21no—
171C23×C139—21no—
172C23×C139—21no—
173C23×C139—24no—
174C23×C139—24no—
175C23×C139—21no—
176C23×C139—22no—
177C23×C139—21no—
178C23×C139—21no—
179C23×C139—44no—
180C23×C139—42no—
181C23×C139—44no—
182C23×C139—42no—
183C23×C139—44no—
184C23×C139—42no—
185C23×C139—42no—
186C23×C139—42no—
187C23×C139—44no—
188C23×C139—42no—
189C23×C139—42no—
190C23×C139—42no—
191C23×C139—44no—
192C23×C139—42no—
193C23×C139—42no—
194C23×C139—82no—
195C23×C139—81no—
196C23×C139—82no—
197C23×C139—82no—
198C23×C139—81no—
199C23×C139—81no—
200C23×C139—82no—
201C23×C139—81no—
202C23×C139—81no—
203C23×C139—81no—
204C23×C139—82no—
205C23×C139#9912yescomplemented
206C23×C139C2×C22⋊C412yes—
207C23×C139C2×C22⋊C411yescharacteristic
208C23×C139#12012yes—
209C23×C139#12012yes—
210Q8×C139—42no—
211D4×C139—28no—
212D4×C139—44no—
213D4×C139—42no—
214D4×C139—44no—
215D4×C139—44no—
216D4×C139—44no—
217D4×C139—44no—
218D4×C139—42no—
219D4×C139—42no—
220D4×C139—44no—
221D4×C139—44no—
222D4×C139—84no—
223D4×C139—84no—
224C2×C4×C139—21no—
225C2×C4×C139—21no—
226C2×C4×C139—24no—
227C2×C4×C139—22no—
228C2×C4×C139—21no—
229C2×C4×C139—21no—
230C2×C4×C139—21no—
231C2×C4×C139—44no—
232C2×C4×C139—44no—
233C2×C4×C139—42no—
234C2×C4×C139—44no—
235C2×C4×C139—42no—
236C2×C4×C139—44no—
237C2×C4×C139—44no—
238C2×C4×C139—44no—
239C2×C4×C139—82no—
240C2×C4×C139—82no—
241C2×C4×C139—82no—
242C2×C4×C139—82no—
243C2×C4×C139—82no—
244C2×C4×C139—82no—
245C2×C4×C139—84no—
246C2×C4×C139#9912yescomplemented
247C22×C139—21no—
248C22×C139—22no—
249C22×C139—21no—
250C22×C139—22no—
251C22×C139—21no—
252C22×C139—21no—
253C22×C139—22no—
254C22×C139—22no—
255C22×C139—22no—
256C22×C139—22no—
257C22×C139—22no—
258C22×C139—22no—
259C22×C139—24no—
260C22×C139—24no—
261C22×C139—42no—
262C22×C139—42no—
263C22×C139—42no—
264C22×C139—42no—
265C22×C139—41no—
266C22×C139—44no—
267C22×C139—42no—
268C22×C139—84no—
269C22×C139—81no—
270C22×C139—81no—
271C22×C139—81no—
272C22×C139—81no—
273C22×C139—81no—
274C22×C139—84no—
275C22×C139—84no—
276C22×C139—84no—
277C22×C139—81no—
278C22×C139—162no—
279C22×C139—162no—
280C22×C139#37911yescharacteristic
281C22×C139C2×#9911yescharacteristic
282C22×C139C2×#9911yescharacteristic
283C22×C139B(4,𝔽2)12yes—
284C22×C139#45812yes—
285C4×C139—22no—
286C4×C139—41no—
287C4×C139—42no—
288C4×C139—44no—
289C4×C139—84no—
290C4×C139—162no—
291C2×C139—22no—
292C2×C139—21no—
293C2×C139—21no—
294C2×C139—22no—
295C2×C139—42no—
296C2×C139—42no—
297C2×C139—42no—
298C2×C139—81no—
299C2×C139—82no—
300C2×C139#178111yescharacteristic
301C2×C139#179012yes—
302#8534C13911yesmaximal, characteristic, direct product factor, Sylow
303C139#853411yescharacteristic, direct product factor, Sylow
304#3484C2×C13911yescharacteristic
305#1898C2×C13914yescomplemented
306#1781C2×C13911yescharacteristic, complemented
307#1438C2×C13911yescharacteristic, complemented
308C2×H(5,𝔽2)C4×C13911yescharacteristic, complemented
309C23×D4C22×C13911yescharacteristic
310#546—24no—
311D42—24no—
312#535—21no—
313#534—21no—
314#534C4×C13912yescomplemented
315#525—21no—
316C2×#120—21no—
317C2×#120C22×C13912yes—
318#518C4×C13911yescharacteristic, complemented
319C22×C22⋊C4—21no—
320C22×C22⋊C4C22×C13912yescomplemented
321C2×#99—24no—
322C2×#99—21no—
323C2×#99—21no—
324#379C22×C13912yescomplemented
325C2×#95—21no—
326#342—24no—
327C25D4×C13911yescharacteristic
328C25C23×C13911yescharacteristic
329H(5,𝔽2)—42no—
330H(5,𝔽2)—42no—
331C2×#41—21no—
332C2×#41—22no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4C2×C4×C13911yescharacteristic
340C22×D4C2×C4×C13911yescharacteristic
341C22×D4C2×C4×C13912yes—
342C22×D4D4×C13911yescharacteristic
343C22×D4D4×C13911yescharacteristic
344C22×D4D4×C13914yes—
345C23×C4—22no—
346C23×C4D4×C13911yescharacteristic
347#127—22no—
348#124—22no—
349#123—22no—
350#123—22no—
351#123—22no—
352C22⋊Q8—22no—
353#121—22no—
354#121—24no—
355#121—24no—
356#121—24no—
357#120—24no—
358#120—22no—
359#120—22no—
360#120—22no—
361#120—22no—
362#120—22no—
363#120—24no—
364C4×D4—24no—
365C4×D4—24no—
366#117—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4C2×C4×C13912yes—
376C2×C22⋊C4D4×C13914yes—
377#99—48no—
378#99—42no—
379#99—42no—
380#95—42no—
381C24—21no—
382C24—22no—
383C24—22no—
384C24—42no—
385C24—41no—
386C24—41no—
387C24—41no—
388C24—42no—
389C24—42no—
390C24—42no—
391C24C22⋊C4×C13911yescharacteristic
392C24C22⋊C4×C13911yescharacteristic
393C24C22⋊C4×C13912yescomplemented
394C24C22×C4×C13911yescharacteristic
395C24C2×D4×C13911yescharacteristic
396C24C2×D4×C13914yes—
397C24C2×D4×C13911yescharacteristic
398#41—42no—
399#41—48no—
400#41—42no—
401C2×Q8—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—21no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—416no—
422C2×D4—48no—
423C2×D4—42no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—82no—
430C2×D4—82no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—41no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4C22⋊C4×C13911yescharacteristic
446C22×C4C22⋊C4×C13911yescharacteristic
447C22×C4C22⋊C4×C13914yescomplemented
448C22×C4C22⋊C4×C13912yescomplemented
449C4⋊C4—22no—
450C4⋊C4—24no—
451C22⋊C4—22no—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—28no—
459C22⋊C4—44no—
460C22⋊C4—48no—
461C22⋊C4—42no—
462C22⋊C4—42no—
463C22⋊C4—44no—
464C22⋊C4—44no—
465C42—22no—
466C23—21no—
467C23—21no—
468C23—22no—
469C23—22no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—24no—
477C23—24no—
478C23—21no—
479C23—21no—
480C23—22no—
481C23—21no—
482C23—44no—
483C23—42no—
484C23—44no—
485C23—42no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—44no—
495C23—42no—
496C23—42no—
497C23—82no—
498C23—81no—
499C23—82no—
500C23—82no—
501C23—81no—
502C23—81no—
503C23—82no—
504C23—81no—
505C23—81no—
506C23—81no—
507C23—82no—
508C23#99×C13912yescomplemented
509C23C2×C22⋊C4×C13912yes—
510C23C2×C22⋊C4×C13911yescharacteristic
511C23#120×C13912yes—
512C23#120×C13912yes—
513Q8—42no—
514D4—28no—
515D4—44no—
516D4—42no—
517D4—44no—
518D4—44no—
519D4—44no—
520D4—44no—
521D4—42no—
522D4—42no—
523D4—44no—
524D4—44no—
525D4—84no—
526D4—84no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—44no—
535C2×C4—44no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—44no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—82no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—82no—
548C2×C4—84no—
549C2×C4#99×C13912yescomplemented
550C22—21no—
551C22—22no—
552C22—21no—
553C22—22no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—24no—
563C22—24no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—41no—
569C22—44no—
570C22—42no—
571C22—84no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—84no—
578C22—84no—
579C22—84no—
580C22—81no—
581C22—162no—
582C22—162no—
583C22#379×C13911yescharacteristic
584C22C2×#99×C13911yescharacteristic
585C22C2×#99×C13911yescharacteristic
586C22B(4,𝔽2)×C13912yes—
587C22#458×C13912yes—
588C4—22no—
589C4—41no—
590C4—42no—
591C4—44no—
592C4—84no—
593C4—162no—
594C2—22no—
595C2—21no—
596C2—21no—
597C2—22no—
598C2—42no—
599C2—42no—
600C2—42no—
601C2—81no—
602C2—82no—
603C2#1781×C13911yescharacteristic
604C2#1790×C13912yes—
subgroupG/H
center, socleC22×C139#379
commutatorC24C22×C4×C139
Frattini, cosocleC25C23×C139
prime radical#3484×C139C2
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C25×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1898×C139C2semidirect
3. #1781×C139C2semidirect
4. #1438×C139C2semidirect
5. C2×H(5,𝔽2)×C139C4semidirect
11. #534×C139C4semidirect
15. #518×C139C4semidirect
17. C22×C22⋊C4×C139C22semidirect
21. #379×C139C22semidirect
90. C24×C139C22⋊C4semidirect
144. C22×C4×C139C22⋊C4semidirect
145. C22×C4×C139C22⋊C4semidirect
205. C23×C139#99semidirect
246. C2×C4×C139#99semidirect
302. #8534C139direct (N × H)
303. C139#8534direct (N × H)
305. #1898C2×C139semidirect
306. #1781C2×C139semidirect
307. #1438C2×C139semidirect
308. C2×H(5,𝔽2)C4×C139semidirect
314. #534C4×C139semidirect
318. #518C4×C139semidirect
320. C22×C22⋊C4C22×C139semidirect
324. #379C22×C139semidirect
393. C24C22⋊C4×C139semidirect
447. C22×C4C22⋊C4×C139semidirect
448. C22×C4C22⋊C4×C139semidirect
508. C23#99×C139semidirect
549. C2×C4#99×C139semidirect

Maximal subgroups

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

subgroupindex
#3484×C1392
#1898×C1392
#1781×C1392
#1438×C1392
#8534139