Finite Group Databasebeta

← C139×#9262 #48003858

Subgroups — C139×#9262 #48003858

Order 35584.

750 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#448×C139C211yesmaximal, characteristic
2Q8×C22⋊C4×C139C211yesmaximal, characteristic, complemented
3#1964×C139C211yesmaximal, characteristic
4#1787×C139C211yesmaximal, characteristic, complemented
5#1519×C139C211yesmaximal, characteristic
6#1289×C139C211yesmaximal, characteristic, complemented
7#1282×C139C211yesmaximal, characteristic, complemented
8C23×Q8×C139C2211yescharacteristic
9C22×SD16×C139C412yescomplemented
10C2×#121×C139C2211yescharacteristic
11C2×C4×Q8×C139—21no—
12#448×C139—21no—
13#448×C139—22no—
14#448×C139—21no—
15C2×#103×C139—22no—
16C2×#103×C139C412yescomplemented
17C2×#99×C139—21no—
18C2×#99×C139—21no—
19C2×C22⋊C8×C139C2211yescharacteristic
20C2×C22⋊C8×C139C2211yescharacteristic
21#391×C139—21no—
22#391×C139—22no—
23#380×C139—21no—
24#380×C139C2211yescharacteristic
25#380×C139C2211yescharacteristic
26C4×C22⋊C4×C139—21no—
27C4×C22⋊C4×C139C2211yescharacteristic
28#327×C139—22no—
29C22×Q8×C139—21no—
30C22×Q8×C139—21no—
31C22×Q8×C139—21no—
32C22×Q8×C139—44no—
33C22×Q8×C139C2×C412yes—
34C22×Q8×C139D411yescharacteristic
35C22×Q8×C139D412yes—
36C22×Q8×C139D411yescharacteristic
37C22×D4×C139—21no—
38C22×D4×C139C2×C411yescharacteristic
39C23×C4×C139—21no—
40C23×C4×C139C2311yescharacteristic
41C2×SD16×C139—22no—
42C2×SD16×C139—22no—
43C2×SD16×C139—44no—
44C22×C8×C139—21no—
45C22×C8×C139C2×C412yes—
46#121×C139—21no—
47#121×C139—21no—
48#121×C139—21no—
49#121×C139—21no—
50C4×Q8×C139—44no—
51C2×C4⋊C4×C139—22no—
52C2×C4⋊C4×C139—21no—
53C2×C4⋊C4×C139—21no—
54C2×C4⋊C4×C139C2×C411yescharacteristic
55C2×C22⋊C4×C139—21no—
56C2×C22⋊C4×C139—21no—
57C2×C22⋊C4×C139—21no—
58C2×C22⋊C4×C139D411yescharacteristic
59C2×C22⋊C4×C139D411yescharacteristic
60C2×C42×C139—22no—
61C2×C42×C139—21no—
62#103×C139—22no—
63#103×C139—22no—
64#103×C139—44no—
65#99×C139—42no—
66#99×C139—42no—
67C22⋊C8×C139—21no—
68C22⋊C8×C139—21no—
69C22⋊C8×C139—21no—
70C22⋊C8×C139—21no—
71#95×C139—22no—
72#95×C139—22no—
73#95×C139—21no—
74#95×C139—21no—
75#95×C139D412yes—
76C24×C139—21no—
77C24×C139C2×D411yescharacteristic
78C2×Q8×C139—24no—
79C2×Q8×C139—22no—
80C2×Q8×C139—22no—
81C2×Q8×C139—21no—
82C2×Q8×C139—21no—
83C2×Q8×C139—24no—
84C2×Q8×C139—24no—
85C2×Q8×C139—42no—
86C2×Q8×C139—42no—
87C2×Q8×C139—42no—
88C2×Q8×C139—44no—
89C2×Q8×C139—44no—
90C2×Q8×C139—44no—
91C2×Q8×C139C22⋊C412yes—
92C2×Q8×C139C22⋊C412yes—
93C2×D4×C139—21no—
94C2×D4×C139—21no—
95C2×D4×C139—42no—
96C2×D4×C139—41no—
97C2×D4×C139—41no—
98C2×D4×C139—41no—
99C2×D4×C139—41no—
100C2×D4×C139—41no—
101C2×D4×C139—41no—
102C22×C4×C139—21no—
103C22×C4×C139—22no—
104C22×C4×C139—21no—
105C22×C4×C139—21no—
106C22×C4×C139—22no—
107C22×C4×C139—21no—
108C22×C4×C139—21no—
109C22×C4×C139—22no—
110C22×C4×C139—42no—
111C22×C4×C139—44no—
112C22×C4×C139—41no—
113C22×C4×C139C22×C411yescharacteristic
114C22×C4×C139C2×D411yescharacteristic
115C22×C4×C139C2×D411yescharacteristic
116C22×C4×C139C2×D411yescharacteristic
117C22×C4×C139#4111yescharacteristic
118C22×C4×C139#4111yescharacteristic
119SD16×C139—44no—
120SD16×C139—44no—
121C2×C8×C139—22no—
122C2×C8×C139—42no—
123C2×C8×C139—42no—
124C2×C8×C139—41no—
125C4⋊C4×C139—21no—
126C4⋊C4×C139—21no—
127C4⋊C4×C139—44no—
128C4⋊C4×C139—42no—
129C4⋊C4×C139—42no—
130C22⋊C4×C139—21no—
131C22⋊C4×C139—21no—
132C22⋊C4×C139—21no—
133C22⋊C4×C139—41no—
134C22⋊C4×C139—41no—
135C22⋊C4×C139—41no—
136C22⋊C4×C139—41no—
137C22⋊C4×C139—41no—
138C22⋊C4×C139—41no—
139C22⋊C4×C139SD1612yescomplemented
140C42×C139—44no—
141C42×C139—42no—
142C23×C139—41no—
143C23×C139—41no—
144C23×C139—41no—
145C23×C139—41no—
146C23×C139—41no—
147C23×C139—81no—
148C23×C139—81no—
149C23×C139C4×D411yescharacteristic
150C23×C139#12011yescharacteristic
151C23×C139#12111yescharacteristic
152C23×C139C2×SD1611yescharacteristic
153C23×C139#13511yescharacteristic
154C23×C139AGL(1,ℤ/8)11yescharacteristic
155C23×C139#13711yescharacteristic
156Q8×C139—24no—
157Q8×C139—22no—
158Q8×C139—22no—
159Q8×C139—22no—
160Q8×C139—44no—
161Q8×C139—44no—
162Q8×C139—42no—
163Q8×C139#9914yescomplemented
164D4×C139—42no—
165D4×C139—81no—
166D4×C139—81no—
167D4×C139—81no—
168D4×C139—81no—
169D4×C139—81no—
170C2×C4×C139—24no—
171C2×C4×C139—22no—
172C2×C4×C139—22no—
173C2×C4×C139—22no—
174C2×C4×C139—22no—
175C2×C4×C139—22no—
176C2×C4×C139—22no—
177C2×C4×C139—41no—
178C2×C4×C139—41no—
179C2×C4×C139—41no—
180C2×C4×C139—44no—
181C2×C4×C139—44no—
182C2×C4×C139—41no—
183C2×C4×C139—41no—
184C2×C4×C139—42no—
185C2×C4×C139—41no—
186C2×C4×C139—42no—
187C2×C4×C139—41no—
188C2×C4×C139—42no—
189C2×C4×C139—41no—
190C2×C4×C139—41no—
191C2×C4×C139—41no—
192C2×C4×C139—41no—
193C2×C4×C139—42no—
194C2×C4×C139—81no—
195C2×C4×C139—81no—
196C2×C4×C139—81no—
197C2×C4×C139C2×C22⋊C411yescharacteristic
198C2×C4×C139C4×D411yescharacteristic
199C2×C4×C139#12111yescharacteristic
200C2×C4×C139#12311yescharacteristic
201C8×C139—42no—
202C8×C139—81no—
203C22×C139—21no—
204C22×C139—21no—
205C22×C139—21no—
206C22×C139—21no—
207C22×C139—21no—
208C22×C139—21no—
209C22×C139—41no—
210C22×C139—41no—
211C22×C139—41no—
212C22×C139—41no—
213C22×C139—81no—
214C22×C139—81no—
215C22×C139—81no—
216C22×C139—161no—
217C22×C139—161no—
218C22×C139#38611yescharacteristic
219C22×C139C4×SD1611yescharacteristic
220C22×C139#44011yescharacteristic
221C22×C139#44811yescharacteristic
222C22×C139#44911yescharacteristic
223C22×C139#46011yescharacteristic
224C22×C139#46411yescharacteristic
225C4×C139—21no—
226C4×C139—24no—
227C4×C139—21no—
228C4×C139—21no—
229C4×C139—42no—
230C4×C139—42no—
231C4×C139—81no—
232C4×C139—82no—
233C4×C139—81no—
234C4×C139—161no—
235C4×C139C2×#9912yes—
236C2×C139—21no—
237C2×C139—21no—
238C2×C139—21no—
239C2×C139—21no—
240C2×C139—21no—
241C2×C139—21no—
242C2×C139—161no—
243C2×C139#188011yescharacteristic
244C2×C139#189811yescharacteristic
245C2×C139#190511yescharacteristic
246#9262C13911yesmaximal, characteristic, direct product factor, Sylow
247C139#926211yescharacteristic, direct product factor, Sylow
248C2×#448C2×C13911yescharacteristic
249Q8×C22⋊C4C2×C13911yescharacteristic, complemented
250#1964C2×C13911yescharacteristic
251#1787C2×C13911yescharacteristic, complemented
252#1519C2×C13911yescharacteristic
253#1289C2×C13911yescharacteristic, complemented
254#1282C2×C13911yescharacteristic, complemented
255C23×Q8C22×C13911yescharacteristic
256C22×SD16C4×C13912yescomplemented
257C2×#121C22×C13911yescharacteristic
258C2×C4×Q8—21no—
259#448—21no—
260#448—22no—
261#448—21no—
262C2×#103—22no—
263C2×#103C4×C13912yescomplemented
264C2×#99—21no—
265C2×#99—21no—
266C2×C22⋊C8C22×C13911yescharacteristic
267C2×C22⋊C8C22×C13911yescharacteristic
268#391—21no—
269#391—22no—
270#380—21no—
271#380C22×C13911yescharacteristic
272#380C22×C13911yescharacteristic
273C4×C22⋊C4—21no—
274C4×C22⋊C4C22×C13911yescharacteristic
275#327—22no—
276C22×Q8—21no—
277C22×Q8—21no—
278C22×Q8—21no—
279C22×Q8—44no—
280C22×Q8C2×C4×C13912yes—
281C22×Q8D4×C13911yescharacteristic
282C22×Q8D4×C13912yes—
283C22×Q8D4×C13911yescharacteristic
284C22×D4—21no—
285C22×D4C2×C4×C13911yescharacteristic
286C23×C4—21no—
287C23×C4C23×C13911yescharacteristic
288C2×SD16—22no—
289C2×SD16—22no—
290C2×SD16—44no—
291C22×C8—21no—
292C22×C8C2×C4×C13912yes—
293#121—21no—
294#121—21no—
295#121—21no—
296#121—21no—
297C4×Q8—44no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4C2×C4×C13911yescharacteristic
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4D4×C13911yescharacteristic
306C2×C22⋊C4D4×C13911yescharacteristic
307C2×C42—22no—
308C2×C42—21no—
309#103—22no—
310#103—22no—
311#103—44no—
312#99—42no—
313#99—42no—
314C22⋊C8—21no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318#95—22no—
319#95—22no—
320#95—21no—
321#95—21no—
322#95D4×C13912yes—
323C24—21no—
324C24C2×D4×C13911yescharacteristic
325C2×Q8—24no—
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8—21no—
329C2×Q8—21no—
330C2×Q8—24no—
331C2×Q8—24no—
332C2×Q8—42no—
333C2×Q8—42no—
334C2×Q8—42no—
335C2×Q8—44no—
336C2×Q8—44no—
337C2×Q8—44no—
338C2×Q8C22⋊C4×C13912yes—
339C2×Q8C22⋊C4×C13912yes—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—42no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—22no—
357C22×C4—42no—
358C22×C4—44no—
359C22×C4—41no—
360C22×C4C22×C4×C13911yescharacteristic
361C22×C4C2×D4×C13911yescharacteristic
362C22×C4C2×D4×C13911yescharacteristic
363C22×C4C2×D4×C13911yescharacteristic
364C22×C4#41×C13911yescharacteristic
365C22×C4#41×C13911yescharacteristic
366SD16—44no—
367SD16—44no—
368C2×C8—22no—
369C2×C8—42no—
370C2×C8—42no—
371C2×C8—41no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—44no—
375C4⋊C4—42no—
376C4⋊C4—42no—
377C22⋊C4—21no—
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4SD16×C13912yescomplemented
387C42—44no—
388C42—42no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—81no—
395C23—81no—
396C23C4×D4×C13911yescharacteristic
397C23#120×C13911yescharacteristic
398C23#121×C13911yescharacteristic
399C23C2×SD16×C13911yescharacteristic
400C23#135×C13911yescharacteristic
401C23AGL(1,ℤ/8)×C13911yescharacteristic
402C23#137×C13911yescharacteristic
403Q8—24no—
404Q8—22no—
405Q8—22no—
406Q8—22no—
407Q8—44no—
408Q8—44no—
409Q8—42no—
410Q8#99×C13914yescomplemented
411D4—42no—
412D4—81no—
413D4—81no—
414D4—81no—
415D4—81no—
416D4—81no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—44no—
428C2×C4—44no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4C2×C22⋊C4×C13911yescharacteristic
445C2×C4C4×D4×C13911yescharacteristic
446C2×C4#121×C13911yescharacteristic
447C2×C4#123×C13911yescharacteristic
448C8—42no—
449C8—81no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—81no—
461C22—81no—
462C22—81no—
463C22—161no—
464C22—161no—
465C22#386×C13911yescharacteristic
466C22C4×SD16×C13911yescharacteristic
467C22#440×C13911yescharacteristic
468C22#448×C13911yescharacteristic
469C22#449×C13911yescharacteristic
470C22#460×C13911yescharacteristic
471C22#464×C13911yescharacteristic
472C4—21no—
473C4—24no—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—42no—
478C4—81no—
479C4—82no—
480C4—81no—
481C4—161no—
482C4C2×#99×C13912yes—
483C2—21no—
484C2—21no—
485C2—21no—
486C2—21no—
487C2—21no—
488C2—21no—
489C2—161no—
490C2#1880×C13911yescharacteristic
491C2#1898×C13911yescharacteristic
492C2#1905×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC2×#121×C139C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×C22⋊C4×C139C2semidirect
4. #1787×C139C2semidirect
6. #1289×C139C2semidirect
7. #1282×C139C2semidirect
9. C22×SD16×C139C4semidirect
16. C2×#103×C139C4semidirect
139. C22⋊C4×C139SD16semidirect
163. Q8×C139#99semidirect
246. #9262C139direct (N × H)
247. C139#9262direct (N × H)
249. Q8×C22⋊C4C2×C139semidirect
251. #1787C2×C139semidirect
253. #1289C2×C139semidirect
254. #1282C2×C139semidirect
256. C22×SD16C4×C139semidirect
263. C2×#103C4×C139semidirect
386. C22⋊C4SD16×C139semidirect
410. Q8#99×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#448×C1392
Q8×C22⋊C4×C1392
#1964×C1392
#1787×C1392
#1519×C1392
#1289×C1392
#1282×C1392
#9262139