Finite Group Databasebeta

← C139×#8561 #48003157

Subgroups — C139×#8561 #48003157

Order 35584.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C139C211yesmaximal, characteristic
2#1797×C139C211yesmaximal, characteristic, complemented
3#1797×C139C211yesmaximal, characteristic, complemented
4C2×#323×C139C212yesmaximal
5#1280×C139C212yesmaximal, complemented
6C22×C4⋊C4×C139C411yescharacteristic
7C22×C22⋊C4×C139C411yescharacteristic
8C22×C22⋊C4×C139C411yescharacteristic
9C22×C22⋊C4×C139C2211yescharacteristic
10C22×C42×C139C2211yescharacteristic
11C2×C4⋊C8×C139—21no—
12C2×C4⋊C8×C139—21no—
13C2×C22⋊C8×C139C2212yes—
14C2×C22⋊C8×C139C2212yes—
15#388×C139—21no—
16#388×C139—21no—
17#388×C139—21no—
18#388×C139—21no—
19C2×#95×C139C411yescharacteristic
20C2×#95×C139C2211yescharacteristic
21#336×C139—21no—
22#336×C139—21no—
23#323×C139—24no—
24C25×C139C2×C411yescharacteristic
25C23×C4×C139C2×C411yescharacteristic
26C23×C4×C139C2×C411yescharacteristic
27C23×C4×C139C2×C411yescharacteristic
28C23×C4×C139C2×C411yescharacteristic
29C23×C4×C139C2×C411yescharacteristic
30C23×C4×C139C2311yescharacteristic
31C22×C8×C139—22no—
32C22×C8×C139—22no—
33C2×C4⋊C4×C139—21no—
34C2×C4⋊C4×C139—21no—
35C2×C4⋊C4×C139—42no—
36C2×C22⋊C4×C139—21no—
37C2×C22⋊C4×C139—21no—
38C2×C22⋊C4×C139—21no—
39C2×C22⋊C4×C139—21no—
40C2×C22⋊C4×C139—21no—
41C2×C22⋊C4×C139—21no—
42C2×C22⋊C4×C139—21no—
43C2×C22⋊C4×C139—21no—
44C2×C22⋊C4×C139—42no—
45C2×C22⋊C4×C139—42no—
46C2×C22⋊C4×C139D412yes—
47C2×C22⋊C4×C139Q812yes—
48C2×C42×C139—42no—
49C2×C42×C139D411yescharacteristic
50C2×C42×C139D411yescharacteristic
51C2×C42×C139D411yescharacteristic
52C2×C42×C139D411yescharacteristic
53C4⋊C8×C139—42no—
54C4⋊C8×C139—42no—
55C22⋊C8×C139—22no—
56C22⋊C8×C139—22no—
57C22⋊C8×C139—22no—
58C22⋊C8×C139—22no—
59#95×C139—21no—
60#95×C139—21no—
61#95×C139—21no—
62#95×C139—21no—
63C24×C139—21no—
64C24×C139—21no—
65C24×C139—22no—
66C24×C139—22no—
67C24×C139—41no—
68C24×C139—41no—
69C24×C139—41no—
70C24×C139—41no—
71C24×C139C4⋊C412yes—
72C24×C139C22×C411yescharacteristic
73C22×C4×C139—21no—
74C22×C4×C139—21no—
75C22×C4×C139—22no—
76C22×C4×C139—22no—
77C22×C4×C139—22no—
78C22×C4×C139—22no—
79C22×C4×C139—21no—
80C22×C4×C139—21no—
81C22×C4×C139—22no—
82C22×C4×C139—22no—
83C22×C4×C139—41no—
84C22×C4×C139—41no—
85C22×C4×C139—41no—
86C22×C4×C139—41no—
87C22×C4×C139—41no—
88C22×C4×C139—41no—
89C22×C4×C139—41no—
90C22×C4×C139—41no—
91C22×C4×C139—41no—
92C22×C4×C139—41no—
93C22×C4×C139C22⋊C411yescharacteristic
94C22×C4×C139C22⋊C411yescharacteristic
95C22×C4×C139C22⋊C411yescharacteristic
96C22×C4×C139C22⋊C411yescharacteristic
97C22×C4×C139C4⋊C412yes—
98C22×C4×C139C2×D411yescharacteristic
99C22×C4×C139C2×D411yescharacteristic
100C22×C4×C139C2×D411yescharacteristic
101C22×C4×C139C2×Q811yescharacteristic
102C22×C4×C139#4111yescharacteristic
103C22×C4×C139#4111yescharacteristic
104C2×C8×C139—42no—
105C2×C8×C139—42no—
106C2×C8×C139—42no—
107C2×C8×C139—42no—
108C2×C8×C139—42no—
109C2×C8×C139—42no—
110C4⋊C4×C139—42no—
111C4⋊C4×C139—42no—
112C22⋊C4×C139—22no—
113C22⋊C4×C139—22no—
114C22⋊C4×C139—22no—
115C22⋊C4×C139—22no—
116C22⋊C4×C139—42no—
117C22⋊C4×C139—42no—
118C22⋊C4×C139—42no—
119C22⋊C4×C139—42no—
120C42×C139—22no—
121C42×C139—22no—
122C42×C139—41no—
123C42×C139—41no—
124C23×C139—21no—
125C23×C139—21no—
126C23×C139—21no—
127C23×C139—21no—
128C23×C139—22no—
129C23×C139—24no—
130C23×C139—42no—
131C23×C139—42no—
132C23×C139—42no—
133C23×C139—42no—
134C23×C139—41no—
135C23×C139—41no—
136C23×C139—41no—
137C23×C139—41no—
138C23×C139—41no—
139C23×C139—41no—
140C23×C139—42no—
141C23×C139—82no—
142C23×C139—82no—
143C23×C139—82no—
144C23×C139—82no—
145C23×C139C2×C22⋊C411yescharacteristic
146C23×C139C2×C4⋊C411yescharacteristic
147C23×C139#11711yescharacteristic
148C23×C139#13112yes—
149C23×C139#13112yes—
150C2×C4×C139—21no—
151C2×C4×C139—21no—
152C2×C4×C139—21no—
153C2×C4×C139—21no—
154C2×C4×C139—21no—
155C2×C4×C139—21no—
156C2×C4×C139—21no—
157C2×C4×C139—21no—
158C2×C4×C139—22no—
159C2×C4×C139—21no—
160C2×C4×C139—21no—
161C2×C4×C139—21no—
162C2×C4×C139—21no—
163C2×C4×C139—21no—
164C2×C4×C139—21no—
165C2×C4×C139—41no—
166C2×C4×C139—41no—
167C2×C4×C139—41no—
168C2×C4×C139—41no—
169C2×C4×C139—44no—
170C2×C4×C139—44no—
171C2×C4×C139—42no—
172C2×C4×C139—41no—
173C2×C4×C139—41no—
174C2×C4×C139—42no—
175C2×C4×C139—41no—
176C2×C4×C139—41no—
177C2×C4×C139—41no—
178C2×C4×C139—41no—
179C2×C4×C139—41no—
180C2×C4×C139—41no—
181C2×C4×C139—82no—
182C2×C4×C139—82no—
183C2×C4×C139#9912yes—
184C2×C4×C139#10012yes—
185C2×C4×C139#12111yescharacteristic
186C2×C4×C139#12111yescharacteristic
187C2×C4×C139C22⋊Q811yescharacteristic
188C2×C4×C139C22⋊Q811yescharacteristic
189C8×C139—82no—
190C8×C139—82no—
191C22×C139—21no—
192C22×C139—21no—
193C22×C139—21no—
194C22×C139—21no—
195C22×C139—22no—
196C22×C139—22no—
197C22×C139—22no—
198C22×C139—22no—
199C22×C139—42no—
200C22×C139—42no—
201C22×C139—42no—
202C22×C139—84no—
203C22×C139—84no—
204C22×C139—81no—
205C22×C139—81no—
206C22×C139—81no—
207C22×C139—81no—
208C22×C139#38011yescharacteristic
209C22×C139#40811yescharacteristic
210C22×C139#40811yescharacteristic
211C22×C139C2×#9911yescharacteristic
212C22×C139#41011yescharacteristic
213C22×C139C2×#10011yescharacteristic
214C22×C139#41311yescharacteristic
215C22×C139#42412yes—
216C22×C139#43312yes—
217C4×C139—21no—
218C4×C139—21no—
219C4×C139—21no—
220C4×C139—21no—
221C4×C139—22no—
222C4×C139—22no—
223C4×C139—42no—
224C4×C139—41no—
225C4×C139—41no—
226C4×C139—81no—
227C4×C139—81no—
228C2×C139—22no—
229C2×C139—22no—
230C2×C139—82no—
231C2×C139#146811yescharacteristic
232C2×C139#146911yescharacteristic
233C2×C139#147111yescharacteristic
234C2×C139#147311yescharacteristic
235C2×C139#179811yescharacteristic
236C2×C139#179911yescharacteristic
237C2×C139#180011yescharacteristic
238#8561C13911yesmaximal, characteristic, direct product factor, Sylow
239C139#856111yescharacteristic, direct product factor, Sylow
240C2×#388C2×C13911yescharacteristic
241#1797C2×C13911yescharacteristic, complemented
242#1797C2×C13911yescharacteristic, complemented
243C2×#323C2×C13912yes—
244#1280C2×C13912yescomplemented
245C22×C4⋊C4C4×C13911yescharacteristic
246C22×C22⋊C4C4×C13911yescharacteristic
247C22×C22⋊C4C4×C13911yescharacteristic
248C22×C22⋊C4C22×C13911yescharacteristic
249C22×C42C22×C13911yescharacteristic
250C2×C4⋊C8—21no—
251C2×C4⋊C8—21no—
252C2×C22⋊C8C22×C13912yes—
253C2×C22⋊C8C22×C13912yes—
254#388—21no—
255#388—21no—
256#388—21no—
257#388—21no—
258C2×#95C4×C13911yescharacteristic
259C2×#95C22×C13911yescharacteristic
260#336—21no—
261#336—21no—
262#323—24no—
263C25C2×C4×C13911yescharacteristic
264C23×C4C2×C4×C13911yescharacteristic
265C23×C4C2×C4×C13911yescharacteristic
266C23×C4C2×C4×C13911yescharacteristic
267C23×C4C2×C4×C13911yescharacteristic
268C23×C4C2×C4×C13911yescharacteristic
269C23×C4C23×C13911yescharacteristic
270C22×C8—22no—
271C22×C8—22no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—42no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—42no—
284C2×C22⋊C4—42no—
285C2×C22⋊C4D4×C13912yes—
286C2×C22⋊C4Q8×C13912yes—
287C2×C42—42no—
288C2×C42D4×C13911yescharacteristic
289C2×C42D4×C13911yescharacteristic
290C2×C42D4×C13911yescharacteristic
291C2×C42D4×C13911yescharacteristic
292C4⋊C8—42no—
293C4⋊C8—42no—
294C22⋊C8—22no—
295C22⋊C8—22no—
296C22⋊C8—22no—
297C22⋊C8—22no—
298#95—21no—
299#95—21no—
300#95—21no—
301#95—21no—
302C24—21no—
303C24—21no—
304C24—22no—
305C24—22no—
306C24—41no—
307C24—41no—
308C24—41no—
309C24—41no—
310C24C4⋊C4×C13912yes—
311C24C22×C4×C13911yescharacteristic
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4C22⋊C4×C13911yescharacteristic
333C22×C4C22⋊C4×C13911yescharacteristic
334C22×C4C22⋊C4×C13911yescharacteristic
335C22×C4C22⋊C4×C13911yescharacteristic
336C22×C4C4⋊C4×C13912yes—
337C22×C4C2×D4×C13911yescharacteristic
338C22×C4C2×D4×C13911yescharacteristic
339C22×C4C2×D4×C13911yescharacteristic
340C22×C4C2×Q8×C13911yescharacteristic
341C22×C4#41×C13911yescharacteristic
342C22×C4#41×C13911yescharacteristic
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8—42no—
347C2×C8—42no—
348C2×C8—42no—
349C4⋊C4—42no—
350C4⋊C4—42no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—42no—
358C22⋊C4—42no—
359C42—22no—
360C42—22no—
361C42—41no—
362C42—41no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—22no—
368C23—24no—
369C23—42no—
370C23—42no—
371C23—42no—
372C23—42no—
373C23—41no—
374C23—41no—
375C23—41no—
376C23—41no—
377C23—41no—
378C23—41no—
379C23—42no—
380C23—82no—
381C23—82no—
382C23—82no—
383C23—82no—
384C23C2×C22⋊C4×C13911yescharacteristic
385C23C2×C4⋊C4×C13911yescharacteristic
386C23#117×C13911yescharacteristic
387C23#131×C13912yes—
388C23#131×C13912yes—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4#99×C13912yes—
423C2×C4#100×C13912yes—
424C2×C4#121×C13911yescharacteristic
425C2×C4#121×C13911yescharacteristic
426C2×C4C22⋊Q8×C13911yescharacteristic
427C2×C4C22⋊Q8×C13911yescharacteristic
428C8—82no—
429C8—82no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—84no—
442C22—84no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22#380×C13911yescharacteristic
448C22#408×C13911yescharacteristic
449C22#408×C13911yescharacteristic
450C22C2×#99×C13911yescharacteristic
451C22#410×C13911yescharacteristic
452C22C2×#100×C13911yescharacteristic
453C22#413×C13911yescharacteristic
454C22#424×C13912yes—
455C22#433×C13912yes—
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—22no—
461C4—22no—
462C4—42no—
463C4—41no—
464C4—41no—
465C4—81no—
466C4—81no—
467C2—22no—
468C2—22no—
469C2—82no—
470C2#1468×C13911yescharacteristic
471C2#1469×C13911yescharacteristic
472C2#1471×C13911yescharacteristic
473C2#1473×C13911yescharacteristic
474C2#1798×C13911yescharacteristic
475C2#1799×C13911yescharacteristic
476C2#1800×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC24C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC25×C139C2×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1797×C139C2semidirect
3. #1797×C139C2semidirect
5. #1280×C139C2semidirect
238. #8561C139direct (N × H)
239. C139#8561direct (N × H)
241. #1797C2×C139semidirect
242. #1797C2×C139semidirect
244. #1280C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1392
#1797×C1392
C2×#323×C1392
#1280×C1392
#8561139