Finite Group Databasebeta

← C139×#9260 #48003856

Subgroups — C139×#9260 #48003856

Order 35584.

594 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C139C211yesmaximal, characteristic
2#2344×C139C211yesmaximal, characteristic, complemented
3#1964×C139C211yesmaximal, characteristic
4#1823×C139C211yesmaximal, characteristic, complemented
5#1519×C139C211yesmaximal, characteristic
6#1289×C139C211yesmaximal, characteristic, complemented
7#1282×C139C211yesmaximal, characteristic, complemented
8C2×#121×C139C2211yescharacteristic
9C2×#117×C139—21no—
10C22×C4⋊C4×C139C2211yescharacteristic
11#480×C139—22no—
12#480×C139—21no—
13#480×C139—21no—
14C2×#107×C139C412yescomplemented
15C2×#102×C139C412yescomplemented
16C2×#99×C139—21no—
17C2×#99×C139—21no—
18C2×C22⋊C8×C139C2211yescharacteristic
19C2×C22⋊C8×C139C2211yescharacteristic
20#389×C139—21no—
21#387×C139—22no—
22#381×C139—21no—
23#380×C139C2211yescharacteristic
24#380×C139C2211yescharacteristic
25C4×C4⋊C4×C139—21no—
26C4×C22⋊C4×C139C2211yescharacteristic
27#340×C139—22no—
28#327×C139—22no—
29C22×D4×C139—21no—
30C22×D4×C139C2×C411yescharacteristic
31C23×C4×C139—21no—
32C23×C4×C139C2311yescharacteristic
33C22×C8×C139—21no—
34C22×C8×C139C2×C412yes—
35#121×C139—21no—
36#121×C139—21no—
37#121×C139—21no—
38#121×C139—21no—
39#117×C139—42no—
40#117×C139—42no—
41C2×C4⋊C4×C139—21no—
42C2×C4⋊C4×C139—21no—
43C2×C4⋊C4×C139—21no—
44C2×C4⋊C4×C139—22no—
45C2×C4⋊C4×C139—21no—
46C2×C4⋊C4×C139—21no—
47C2×C4⋊C4×C139C2×C411yescharacteristic
48C2×C4⋊C4×C139C2×C412yes—
49C2×C4⋊C4×C139D412yes—
50C2×C4⋊C4×C139D411yescharacteristic
51C2×C4⋊C4×C139D411yescharacteristic
52C2×C22⋊C4×C139—21no—
53C2×C22⋊C4×C139—21no—
54C2×C22⋊C4×C139—21no—
55C2×C22⋊C4×C139D411yescharacteristic
56C2×C22⋊C4×C139D411yescharacteristic
57C2×C42×C139—22no—
58C2×C42×C139—21no—
59#107×C139—22no—
60#107×C139—22no—
61#102×C139—22no—
62#102×C139—22no—
63#99×C139—42no—
64#99×C139—42no—
65C22⋊C8×C139—21no—
66C22⋊C8×C139—21no—
67C22⋊C8×C139—21no—
68C22⋊C8×C139—21no—
69#95×C139—22no—
70#95×C139—22no—
71#95×C139—21no—
72#95×C139—21no—
73#95×C139D412yes—
74C24×C139—21no—
75C24×C139C2×D411yescharacteristic
76C2×D4×C139—21no—
77C2×D4×C139—21no—
78C2×D4×C139—42no—
79C2×D4×C139—41no—
80C2×D4×C139—41no—
81C2×D4×C139—41no—
82C2×D4×C139—41no—
83C2×D4×C139—41no—
84C2×D4×C139—41no—
85C22×C4×C139—22no—
86C22×C4×C139—21no—
87C22×C4×C139—21no—
88C22×C4×C139—21no—
89C22×C4×C139—22no—
90C22×C4×C139—21no—
91C22×C4×C139—21no—
92C22×C4×C139—22no—
93C22×C4×C139—42no—
94C22×C4×C139—41no—
95C22×C4×C139—41no—
96C22×C4×C139—41no—
97C22×C4×C139—41no—
98C22×C4×C139—41no—
99C22×C4×C139C22×C411yescharacteristic
100C22×C4×C139C2×D411yescharacteristic
101C22×C4×C139C2×D411yescharacteristic
102C22×C4×C139C2×D411yescharacteristic
103C22×C4×C139#4111yescharacteristic
104C22×C4×C139#4111yescharacteristic
105C2×C8×C139—22no—
106C2×C8×C139—42no—
107C2×C8×C139—42no—
108C2×C8×C139—41no—
109C4⋊C4×C139—22no—
110C4⋊C4×C139—22no—
111C4⋊C4×C139—21no—
112C4⋊C4×C139—21no—
113C4⋊C4×C139—21no—
114C4⋊C4×C139—21no—
115C4⋊C4×C139—42no—
116C4⋊C4×C139—44no—
117C4⋊C4×C139—42no—
118C4⋊C4×C139C22⋊C412yes—
119C4⋊C4×C139C22⋊C412yes—
120C22⋊C4×C139—21no—
121C22⋊C4×C139—21no—
122C22⋊C4×C139—21no—
123C22⋊C4×C139—41no—
124C22⋊C4×C139—41no—
125C22⋊C4×C139—41no—
126C22⋊C4×C139—41no—
127C22⋊C4×C139—41no—
128C22⋊C4×C139—41no—
129C22⋊C4×C139D812yes—
130C42×C139—42no—
131C42×C139—44no—
132C23×C139—41no—
133C23×C139—41no—
134C23×C139—41no—
135C23×C139—41no—
136C23×C139—41no—
137C23×C139—81no—
138C23×C139—81no—
139C23×C139C4×D411yescharacteristic
140C23×C139#12011yescharacteristic
141C23×C139#12111yescharacteristic
142C23×C139C2×D811yescharacteristic
143C23×C139#13511yescharacteristic
144C23×C139AGL(1,ℤ/8)11yescharacteristic
145C23×C139AGL(1,ℤ/8)11yescharacteristic
146D4×C139—42no—
147D4×C139—81no—
148D4×C139—81no—
149D4×C139—81no—
150D4×C139—81no—
151D4×C139—81no—
152C2×C4×C139—22no—
153C2×C4×C139—22no—
154C2×C4×C139—22no—
155C2×C4×C139—22no—
156C2×C4×C139—22no—
157C2×C4×C139—22no—
158C2×C4×C139—41no—
159C2×C4×C139—41no—
160C2×C4×C139—41no—
161C2×C4×C139—41no—
162C2×C4×C139—41no—
163C2×C4×C139—42no—
164C2×C4×C139—42no—
165C2×C4×C139—41no—
166C2×C4×C139—41no—
167C2×C4×C139—41no—
168C2×C4×C139—41no—
169C2×C4×C139—42no—
170C2×C4×C139—42no—
171C2×C4×C139—41no—
172C2×C4×C139—42no—
173C2×C4×C139—41no—
174C2×C4×C139—42no—
175C2×C4×C139—41no—
176C2×C4×C139—41no—
177C2×C4×C139—41no—
178C2×C4×C139—42no—
179C2×C4×C139—41no—
180C2×C4×C139—81no—
181C2×C4×C139—81no—
182C2×C4×C139—81no—
183C2×C4×C139C2×C22⋊C411yescharacteristic
184C2×C4×C139C4×D411yescharacteristic
185C2×C4×C139#12111yescharacteristic
186C2×C4×C139#12311yescharacteristic
187C8×C139—42no—
188C8×C139—81no—
189C22×C139—21no—
190C22×C139—21no—
191C22×C139—21no—
192C22×C139—21no—
193C22×C139—21no—
194C22×C139—21no—
195C22×C139—41no—
196C22×C139—41no—
197C22×C139—41no—
198C22×C139—41no—
199C22×C139—81no—
200C22×C139—81no—
201C22×C139—81no—
202C22×C139—161no—
203C22×C139—161no—
204C22×C139#38611yescharacteristic
205C22×C139C4×D811yescharacteristic
206C22×C139#44211yescharacteristic
207C22×C139#44711yescharacteristic
208C22×C139#44911yescharacteristic
209C22×C139#45911yescharacteristic
210C22×C139#46311yescharacteristic
211C4×C139—21no—
212C4×C139—21no—
213C4×C139—21no—
214C4×C139—42no—
215C4×C139—42no—
216C4×C139—42no—
217C4×C139—82no—
218C4×C139—81no—
219C4×C139—81no—
220C4×C139—161no—
221C4×C139#41012yes—
222C2×C139—21no—
223C2×C139—21no—
224C2×C139—21no—
225C2×C139—21no—
226C2×C139—21no—
227C2×C139—21no—
228C2×C139—161no—
229C2×C139#187911yescharacteristic
230C2×C139#189911yescharacteristic
231C2×C139#190511yescharacteristic
232#9260C13911yesmaximal, characteristic, direct product factor, Sylow
233C139#926011yescharacteristic, direct product factor, Sylow
234C2×#480C2×C13911yescharacteristic
235#2344C2×C13911yescharacteristic, complemented
236#1964C2×C13911yescharacteristic
237#1823C2×C13911yescharacteristic, complemented
238#1519C2×C13911yescharacteristic
239#1289C2×C13911yescharacteristic, complemented
240#1282C2×C13911yescharacteristic, complemented
241C2×#121C22×C13911yescharacteristic
242C2×#117—21no—
243C22×C4⋊C4C22×C13911yescharacteristic
244#480—22no—
245#480—21no—
246#480—21no—
247C2×#107C4×C13912yescomplemented
248C2×#102C4×C13912yescomplemented
249C2×#99—21no—
250C2×#99—21no—
251C2×C22⋊C8C22×C13911yescharacteristic
252C2×C22⋊C8C22×C13911yescharacteristic
253#389—21no—
254#387—22no—
255#381—21no—
256#380C22×C13911yescharacteristic
257#380C22×C13911yescharacteristic
258C4×C4⋊C4—21no—
259C4×C22⋊C4C22×C13911yescharacteristic
260#340—22no—
261#327—22no—
262C22×D4—21no—
263C22×D4C2×C4×C13911yescharacteristic
264C23×C4—21no—
265C23×C4C23×C13911yescharacteristic
266C22×C8—21no—
267C22×C8C2×C4×C13912yes—
268#121—21no—
269#121—21no—
270#121—21no—
271#121—21no—
272#117—42no—
273#117—42no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4C2×C4×C13911yescharacteristic
281C2×C4⋊C4C2×C4×C13912yes—
282C2×C4⋊C4D4×C13912yes—
283C2×C4⋊C4D4×C13911yescharacteristic
284C2×C4⋊C4D4×C13911yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—21no—
288C2×C22⋊C4D4×C13911yescharacteristic
289C2×C22⋊C4D4×C13911yescharacteristic
290C2×C42—22no—
291C2×C42—21no—
292#107—22no—
293#107—22no—
294#102—22no—
295#102—22no—
296#99—42no—
297#99—42no—
298C22⋊C8—21no—
299C22⋊C8—21no—
300C22⋊C8—21no—
301C22⋊C8—21no—
302#95—22no—
303#95—22no—
304#95—21no—
305#95—21no—
306#95D4×C13912yes—
307C24—21no—
308C24C2×D4×C13911yescharacteristic
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—42no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—42no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4C22×C4×C13911yescharacteristic
333C22×C4C2×D4×C13911yescharacteristic
334C22×C4C2×D4×C13911yescharacteristic
335C22×C4C2×D4×C13911yescharacteristic
336C22×C4#41×C13911yescharacteristic
337C22×C4#41×C13911yescharacteristic
338C2×C8—22no—
339C2×C8—42no—
340C2×C8—42no—
341C2×C8—41no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—42no—
349C4⋊C4—44no—
350C4⋊C4—42no—
351C4⋊C4C22⋊C4×C13912yes—
352C4⋊C4C22⋊C4×C13912yes—
353C22⋊C4—21no—
354C22⋊C4—21no—
355C22⋊C4—21no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—41no—
359C22⋊C4—41no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4D8×C13912yes—
363C42—42no—
364C42—44no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—81no—
371C23—81no—
372C23C4×D4×C13911yescharacteristic
373C23#120×C13911yescharacteristic
374C23#121×C13911yescharacteristic
375C23C2×D8×C13911yescharacteristic
376C23#135×C13911yescharacteristic
377C23AGL(1,ℤ/8)×C13911yescharacteristic
378C23AGL(1,ℤ/8)×C13911yescharacteristic
379D4—42no—
380D4—81no—
381D4—81no—
382D4—81no—
383D4—81no—
384D4—81no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4—81no—
416C2×C4C2×C22⋊C4×C13911yescharacteristic
417C2×C4C4×D4×C13911yescharacteristic
418C2×C4#121×C13911yescharacteristic
419C2×C4#123×C13911yescharacteristic
420C8—42no—
421C8—81no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—161no—
436C22—161no—
437C22#386×C13911yescharacteristic
438C22C4×D8×C13911yescharacteristic
439C22#442×C13911yescharacteristic
440C22#447×C13911yescharacteristic
441C22#449×C13911yescharacteristic
442C22#459×C13911yescharacteristic
443C22#463×C13911yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—82no—
451C4—81no—
452C4—81no—
453C4—161no—
454C4#410×C13912yes—
455C2—21no—
456C2—21no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—161no—
462C2#1879×C13911yescharacteristic
463C2#1899×C13911yescharacteristic
464C2#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. #2344×C139C2semidirect
4. #1823×C139C2semidirect
6. #1289×C139C2semidirect
7. #1282×C139C2semidirect
14. C2×#107×C139C4semidirect
15. C2×#102×C139C4semidirect
232. #9260C139direct (N × H)
233. C139#9260direct (N × H)
235. #2344C2×C139semidirect
237. #1823C2×C139semidirect
239. #1289C2×C139semidirect
240. #1282C2×C139semidirect
247. C2×#107C4×C139semidirect
248. C2×#102C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1392
#2344×C1392
#1964×C1392
#1823×C1392
#1519×C1392
#1289×C1392
#1282×C1392
#9260139