Finite Group Databasebeta

← C139×#36435 #48031031

Subgroups — C139×#36435 #48031031

Order 35584.

2312 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C139C211yesmaximal, characteristic, complemented
2C22×C4×Q8×C139C211yesmaximal, characteristic
3#2851×C139C213yesmaximal
4#2581×C139C213yesmaximal, complemented
5#2565×C139C213yesmaximal, complemented
6#2453×C139C213yesmaximal, complemented
7#2451×C139C213yesmaximal, complemented
8#2442×C139C213yesmaximal
9#2440×C139C213yesmaximal
10#2351×C139C211yesmaximal, characteristic, complemented
11#2351×C139C211yesmaximal, characteristic, complemented
12Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
13Q8×C22⋊C4×C139C211yesmaximal, characteristic
14Q8×C22⋊C4×C139C211yesmaximal, characteristic
15C4×C22⋊Q8×C139C213yesmaximal
16C23×Q8×C139C2211yescharacteristic
17#557×C139—28no—
18C2×C4⋊Q8×C139C2213yes—
19C2×#125×C139C2213yes—
20C2×#125×C139C2213yes—
21C2×C22⋊Q8×C139C2213yes—
22C2×C4×Q8×C139—28no—
23C2×C4×Q8×C139C2213yes—
24C2×C4×Q8×C139C2213yes—
25C2×C4×Q8×C139C2211yescharacteristic
26C2×C4×Q8×C139C2211yescharacteristic
27C2×C4×Q8×C139C2211yescharacteristic
28C2×C4×Q8×C139C2211yescharacteristic
29C2×C4×Q8×C139C2211yescharacteristic
30C2×C4×Q8×C139C2213yes—
31C2×C4×Q8×C139C2211yescharacteristic
32C22×C4⋊C4×C139C2213yes—
33C22×C42×C139C2213yes—
34#400×C139C2216yes—
35#398×C139C2216yes—
36#398×C139C2216yes—
37#395×C139C2216yes—
38#391×C139C2213yes—
39#391×C139C2213yes—
40#391×C139C2213yes—
41#391×C139C2213yes—
42#391×C139C2213yes—
43#389×C139C2213yes—
44#389×C139C2213yes—
45#389×C139C2213yes—
46#389×C139C2213yes—
47#389×C139C2213yes—
48#389×C139C2213yes—
49#389×C139C2213yes—
50#387×C139C2213yes—
51#387×C139C2213yes—
52#387×C139C2216yes—
53#387×C139C2216yes—
54#385×C139C2211yescharacteristic
55#385×C139C2213yes—
56#385×C139C2216yes—
57#384×C139C2213yes—
58#382×C139C2213yes—
59#382×C139C2213yes—
60#380×C139C2213yes—
61#380×C139C2213yes—
62#380×C139C2213yes—
63C4×C4⋊C4×C139C2213yes—
64C4×C4⋊C4×C139C2213yes—
65C4×C4⋊C4×C139C2213yes—
66C4×C22⋊C4×C139C2213yes—
67C4×C22⋊C4×C139C2213yes—
68C22×Q8×C139—24no—
69C22×Q8×C139—24no—
70C22×Q8×C139Q818yescomplemented
71C22×Q8×C139C2313yes—
72C22×Q8×C139C2313yes—
73C22×Q8×C139C2311yescharacteristic
74C23×C4×C139C2311yescharacteristic
75C23×C4×C139C2313yes—
76C23×C4×C139C2313yes—
77C4⋊Q8×C139—212no—
78#125×C139—212no—
79#125×C139—212no—
80C22⋊Q8×C139—212no—
81C4×Q8×C139—24no—
82C4×Q8×C139—24no—
83C4×Q8×C139—24no—
84C4×Q8×C139—24no—
85C4×Q8×C139—24no—
86C4×Q8×C139—212no—
87C4×Q8×C139—212no—
88C4×Q8×C139—212no—
89C4×Q8×C139D418yes—
90C2×C4⋊C4×C139—212no—
91C2×C4⋊C4×C139C2313yes—
92C2×C4⋊C4×C139C2316yes—
93C2×C4⋊C4×C139C2313yes—
94C2×C4⋊C4×C139C2313yes—
95C2×C4⋊C4×C139C2316yes—
96C2×C4⋊C4×C139C2313yes—
97C2×C4⋊C4×C139C2313yes—
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C4⋊C4×C139C2313yes—
100C2×C4⋊C4×C139C2313yes—
101C2×C4⋊C4×C139C2313yes—
102C2×C4⋊C4×C139C2313yes—
103C2×C4⋊C4×C139C2313yes—
104C2×C4⋊C4×C139C2311yescharacteristic
105C2×C4⋊C4×C139C2313yes—
106C2×C4⋊C4×C139C2316yes—
107C2×C4⋊C4×C139C2313yes—
108C2×C4⋊C4×C139C2313yes—
109C2×C22⋊C4×C139C2313yes—
110C2×C22⋊C4×C139C2311yescharacteristic
111C2×C22⋊C4×C139C2313yes—
112C2×C22⋊C4×C139C2311yescharacteristic
113C2×C42×C139—212no—
114C2×C42×C139C2313yes—
115C2×C42×C139C2313yes—
116C2×C42×C139C2313yes—
117C2×C42×C139C2313yes—
118C2×C42×C139C2313yes—
119C2×C42×C139C2313yes—
120C2×C42×C139C2313yes—
121C2×C42×C139C2313yes—
122#95×C139C2313yes—
123#95×C139C2316yes—
124#95×C139C2316yes—
125#95×C139C2313yes—
126#95×C139C2313yes—
127#95×C139C2313yes—
128#95×C139C2316yes—
129#95×C139C2316yes—
130#95×C139C2313yes—
131#95×C139C2313yes—
132#95×C139C2311yescharacteristic
133#95×C139C2311yescharacteristic
134#95×C139C2313yes—
135#95×C139C2313yes—
136C24×C139C2411yescharacteristic
137C2×Q8×C139—232no—
138C2×Q8×C139—26no—
139C2×Q8×C139—26no—
140C2×Q8×C139—26no—
141C2×Q8×C139—26no—
142C2×Q8×C139—43no—
143C2×Q8×C139C2×D414yes—
144C2×Q8×C139C2×Q8112yes—
145C2×Q8×C139C2×Q814yes—
146C2×Q8×C139#4114yes—
147C22×C4×C139—22no—
148C22×C4×C139—22no—
149C22×C4×C139—26no—
150C22×C4×C139—26no—
151C22×C4×C139—22no—
152C22×C4×C139—26no—
153C22×C4×C139—26no—
154C22×C4×C139—43no—
155C22×C4×C139C2×Q8112yes—
156C22×C4×C139C2411yescharacteristic
157C22×C4×C139C2413yes—
158C22×C4×C139C2413yes—
159C22×C4×C139C2411yescharacteristic
160C22×C4×C139C2413yes—
161C22×C4×C139C2413yes—
162C22×C4×C139C2413yes—
163C22×C4×C139C2411yescharacteristic
164C22×C4×C139C2413yes—
165C22×C4×C139C2413yes—
166C22×C4×C139C2411yescharacteristic
167C22×C4×C139C2411yescharacteristic
168C22×C4×C139C2411yescharacteristic
169C22×C4×C139C2413yes—
170C4⋊C4×C139—212no—
171C4⋊C4×C139—26no—
172C4⋊C4×C139—22no—
173C4⋊C4×C139—26no—
174C4⋊C4×C139—26no—
175C4⋊C4×C139—26no—
176C4⋊C4×C139—26no—
177C4⋊C4×C139—212no—
178C4⋊C4×C139—26no—
179C4⋊C4×C139—26no—
180C4⋊C4×C139—26no—
181C4⋊C4×C139—26no—
182C4⋊C4×C139—26no—
183C4⋊C4×C139—22no—
184C4⋊C4×C139—26no—
185C4⋊C4×C139—43no—
186C4⋊C4×C139—46no—
187C4⋊C4×C139C2×D4112yes—
188C22⋊C4×C139—26no—
189C22⋊C4×C139—22no—
190C22⋊C4×C139—26no—
191C22⋊C4×C139#4114yes—
192C42×C139—26no—
193C42×C139—26no—
194C42×C139—26no—
195C42×C139—26no—
196C42×C139—26no—
197C42×C139—26no—
198C42×C139—26no—
199C42×C139C2×D4112yes—
200C23×C139—21no—
201C23×C139—21no—
202C23×C139—21no—
203C23×C139—21no—
204C23×C139C22×Q812yes—
205C23×C139C2×#4112yes—
206C23×C1392−1+412yes—
207C23×C139C2511yescharacteristic
208Q8×C139—224no—
209Q8×C139—412no—
210Q8×C139C22⋊Q8116yescomplemented
211C2×C4×C139—28no—
212C2×C4×C139—21no—
213C2×C4×C139—21no—
214C2×C4×C139—23no—
215C2×C4×C139—21no—
216C2×C4×C139—23no—
217C2×C4×C139—23no—
218C2×C4×C139—21no—
219C2×C4×C139—21no—
220C2×C4×C139—21no—
221C2×C4×C139—21no—
222C2×C4×C139—23no—
223C2×C4×C139—21no—
224C2×C4×C139—224no—
225C2×C4×C139—21no—
226C2×C4×C139—23no—
227C2×C4×C139—23no—
228C2×C4×C139—23no—
229C2×C4×C139—21no—
230C2×C4×C139—23no—
231C2×C4×C139—23no—
232C2×C4×C139—23no—
233C2×C4×C139—23no—
234C2×C4×C139—23no—
235C2×C4×C139—21no—
236C2×C4×C139—23no—
237C2×C4×C139—21no—
238C2×C4×C139—23no—
239C2×C4×C139—23no—
240C2×C4×C139—21no—
241C2×C4×C139—23no—
242C2×C4×C139—21no—
243C2×C4×C139—23no—
244C2×C4×C139—23no—
245C2×C4×C139—23no—
246C2×C4×C139—412no—
247C2×C4×C139C22×D412yes—
248C2×C4×C139C22×D416yes—
249C2×C4×C139C22×D416yes—
250C2×C4×C139C22×Q816yes—
251C2×C4×C139C22×Q816yes—
252C2×C4×C139C2×#4112yes—
253C2×C4×C139C2×#4112yes—
254C2×C4×C139C2×#4116yes—
255C2×C4×C1392−1+412yes—
256C22×C139—22no—
257C22×C139—22no—
258C22×C139—22no—
259C22×C139—22no—
260C22×C139—22no—
261C22×C139—22no—
262C22×C139#55714yescomplemented
263C22×C139C23×D411yescharacteristic
264C22×C139C23×Q811yescharacteristic
265C22×C139C22×#4111yescharacteristic
266C22×C139C22×#4111yescharacteristic
267C22×C139C2×2−1+411yescharacteristic
268C22×C139C2×2−1+411yescharacteristic
269C22×C139#58511yescharacteristic
270C4×C139—26no—
271C4×C139—26no—
272C4×C139—22no—
273C4×C139—22no—
274C4×C139—22no—
275C4×C139—22no—
276C4×C139—43no—
277C4×C139—43no—
278C4×C139—43no—
279C4×C139—41no—
280C4×C139—43no—
281C4×C139—41no—
282C4×C139—43no—
283C4×C139C2×C22⋊Q8112yes—
284C2×C139—24no—
285C2×C139C22×C22⋊Q811yescharacteristic
286C2×C139D4×#4111yescharacteristic
287C2×C139C2×#55711yescharacteristic
288C2×C139#348211yescharacteristic
289C2×C139#348611yescharacteristic
290C2×C139#350211yescharacteristic
291C2×C139#351611yescharacteristic
292#36435C13911yesmaximal, characteristic, direct product factor, Sylow
293C139#3643511yescharacteristic, direct product factor, Sylow
294C2×#557C2×C13911yescharacteristic, complemented
295C22×C4×Q8C2×C13911yescharacteristic
296#2851C2×C13913yes—
297#2581C2×C13913yescomplemented
298#2565C2×C13913yescomplemented
299#2453C2×C13913yescomplemented
300#2451C2×C13913yescomplemented
301#2442C2×C13913yes—
302#2440C2×C13913yes—
303#2351C2×C13911yescharacteristic, complemented
304#2351C2×C13911yescharacteristic, complemented
305Q8×C4⋊C4C2×C13911yescharacteristic, complemented
306Q8×C22⋊C4C2×C13911yescharacteristic
307Q8×C22⋊C4C2×C13911yescharacteristic
308C4×C22⋊Q8C2×C13913yes—
309C23×Q8C22×C13911yescharacteristic
310#557—28no—
311C2×C4⋊Q8C22×C13913yes—
312C2×#125C22×C13913yes—
313C2×#125C22×C13913yes—
314C2×C22⋊Q8C22×C13913yes—
315C2×C4×Q8—28no—
316C2×C4×Q8C22×C13913yes—
317C2×C4×Q8C22×C13913yes—
318C2×C4×Q8C22×C13911yescharacteristic
319C2×C4×Q8C22×C13911yescharacteristic
320C2×C4×Q8C22×C13911yescharacteristic
321C2×C4×Q8C22×C13911yescharacteristic
322C2×C4×Q8C22×C13911yescharacteristic
323C2×C4×Q8C22×C13913yes—
324C2×C4×Q8C22×C13911yescharacteristic
325C22×C4⋊C4C22×C13913yes—
326C22×C42C22×C13913yes—
327#400C22×C13916yes—
328#398C22×C13916yes—
329#398C22×C13916yes—
330#395C22×C13916yes—
331#391C22×C13913yes—
332#391C22×C13913yes—
333#391C22×C13913yes—
334#391C22×C13913yes—
335#391C22×C13913yes—
336#389C22×C13913yes—
337#389C22×C13913yes—
338#389C22×C13913yes—
339#389C22×C13913yes—
340#389C22×C13913yes—
341#389C22×C13913yes—
342#389C22×C13913yes—
343#387C22×C13913yes—
344#387C22×C13916yes—
345#387C22×C13913yes—
346#387C22×C13916yes—
347#385C22×C13913yes—
348#385C22×C13916yes—
349#385C22×C13911yescharacteristic
350#384C22×C13913yes—
351#382C22×C13913yes—
352#382C22×C13913yes—
353#380C22×C13913yes—
354#380C22×C13913yes—
355#380C22×C13913yes—
356C4×C4⋊C4C22×C13913yes—
357C4×C4⋊C4C22×C13913yes—
358C4×C4⋊C4C22×C13913yes—
359C4×C22⋊C4C22×C13913yes—
360C4×C22⋊C4C22×C13913yes—
361C22×Q8—24no—
362C22×Q8—24no—
363C22×Q8Q8×C13918yescomplemented
364C22×Q8C23×C13913yes—
365C22×Q8C23×C13913yes—
366C22×Q8C23×C13911yescharacteristic
367C23×C4C23×C13911yescharacteristic
368C23×C4C23×C13913yes—
369C23×C4C23×C13913yes—
370C4⋊Q8—212no—
371#125—212no—
372#125—212no—
373C22⋊Q8—212no—
374C4×Q8—24no—
375C4×Q8—24no—
376C4×Q8—24no—
377C4×Q8—24no—
378C4×Q8—24no—
379C4×Q8—212no—
380C4×Q8—212no—
381C4×Q8—212no—
382C4×Q8D4×C13918yes—
383C2×C4⋊C4—212no—
384C2×C4⋊C4C23×C13913yes—
385C2×C4⋊C4C23×C13916yes—
386C2×C4⋊C4C23×C13911yescharacteristic
387C2×C4⋊C4C23×C13913yes—
388C2×C4⋊C4C23×C13913yes—
389C2×C4⋊C4C23×C13913yes—
390C2×C4⋊C4C23×C13913yes—
391C2×C4⋊C4C23×C13913yes—
392C2×C4⋊C4C23×C13913yes—
393C2×C4⋊C4C23×C13913yes—
394C2×C4⋊C4C23×C13913yes—
395C2×C4⋊C4C23×C13913yes—
396C2×C4⋊C4C23×C13916yes—
397C2×C4⋊C4C23×C13911yescharacteristic
398C2×C4⋊C4C23×C13913yes—
399C2×C4⋊C4C23×C13913yes—
400C2×C4⋊C4C23×C13916yes—
401C2×C4⋊C4C23×C13913yes—
402C2×C22⋊C4C23×C13913yes—
403C2×C22⋊C4C23×C13911yescharacteristic
404C2×C22⋊C4C23×C13913yes—
405C2×C22⋊C4C23×C13911yescharacteristic
406C2×C42—212no—
407C2×C42C23×C13913yes—
408C2×C42C23×C13913yes—
409C2×C42C23×C13913yes—
410C2×C42C23×C13913yes—
411C2×C42C23×C13913yes—
412C2×C42C23×C13913yes—
413C2×C42C23×C13913yes—
414C2×C42C23×C13913yes—
415#95C23×C13913yes—
416#95C23×C13913yes—
417#95C23×C13913yes—
418#95C23×C13913yes—
419#95C23×C13911yescharacteristic
420#95C23×C13911yescharacteristic
421#95C23×C13913yes—
422#95C23×C13913yes—
423#95C23×C13913yes—
424#95C23×C13913yes—
425#95C23×C13916yes—
426#95C23×C13916yes—
427#95C23×C13916yes—
428#95C23×C13916yes—
429C24C24×C13911yescharacteristic
430C2×Q8—232no—
431C2×Q8—26no—
432C2×Q8—26no—
433C2×Q8—26no—
434C2×Q8—26no—
435C2×Q8—43no—
436C2×Q8C2×D4×C13914yes—
437C2×Q8C2×Q8×C139112yes—
438C2×Q8C2×Q8×C13914yes—
439C2×Q8#41×C13914yes—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—26no—
443C22×C4—26no—
444C22×C4—22no—
445C22×C4—26no—
446C22×C4—26no—
447C22×C4—43no—
448C22×C4C2×Q8×C139112yes—
449C22×C4C24×C13911yescharacteristic
450C22×C4C24×C13913yes—
451C22×C4C24×C13913yes—
452C22×C4C24×C13911yescharacteristic
453C22×C4C24×C13913yes—
454C22×C4C24×C13913yes—
455C22×C4C24×C13913yes—
456C22×C4C24×C13911yescharacteristic
457C22×C4C24×C13913yes—
458C22×C4C24×C13913yes—
459C22×C4C24×C13911yescharacteristic
460C22×C4C24×C13911yescharacteristic
461C22×C4C24×C13911yescharacteristic
462C22×C4C24×C13913yes—
463C4⋊C4—212no—
464C4⋊C4—26no—
465C4⋊C4—22no—
466C4⋊C4—26no—
467C4⋊C4—26no—
468C4⋊C4—26no—
469C4⋊C4—26no—
470C4⋊C4—212no—
471C4⋊C4—26no—
472C4⋊C4—26no—
473C4⋊C4—26no—
474C4⋊C4—26no—
475C4⋊C4—26no—
476C4⋊C4—22no—
477C4⋊C4—26no—
478C4⋊C4—43no—
479C4⋊C4—46no—
480C4⋊C4C2×D4×C139112yes—
481C22⋊C4—26no—
482C22⋊C4—22no—
483C22⋊C4—26no—
484C22⋊C4#41×C13914yes—
485C42—26no—
486C42—26no—
487C42—26no—
488C42—26no—
489C42—26no—
490C42—26no—
491C42—26no—
492C42C2×D4×C139112yes—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23C22×Q8×C13912yes—
498C23C2×#41×C13912yes—
499C232−1+4×C13912yes—
500C23C25×C13911yescharacteristic
501Q8—224no—
502Q8—412no—
503Q8C22⋊Q8×C139116yescomplemented
504C2×C4—28no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—23no—
508C2×C4—21no—
509C2×C4—23no—
510C2×C4—23no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—23no—
516C2×C4—21no—
517C2×C4—224no—
518C2×C4—21no—
519C2×C4—23no—
520C2×C4—23no—
521C2×C4—23no—
522C2×C4—21no—
523C2×C4—23no—
524C2×C4—23no—
525C2×C4—23no—
526C2×C4—23no—
527C2×C4—23no—
528C2×C4—21no—
529C2×C4—23no—
530C2×C4—21no—
531C2×C4—23no—
532C2×C4—23no—
533C2×C4—21no—
534C2×C4—23no—
535C2×C4—21no—
536C2×C4—23no—
537C2×C4—23no—
538C2×C4—23no—
539C2×C4—412no—
540C2×C4C22×D4×C13912yes—
541C2×C4C22×D4×C13916yes—
542C2×C4C22×D4×C13916yes—
543C2×C4C22×Q8×C13916yes—
544C2×C4C22×Q8×C13916yes—
545C2×C4C2×#41×C13912yes—
546C2×C4C2×#41×C13912yes—
547C2×C4C2×#41×C13916yes—
548C2×C42−1+4×C13912yes—
549C22—22no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—22no—
555C22#557×C13914yescomplemented
556C22C23×D4×C13911yescharacteristic
557C22C23×Q8×C13911yescharacteristic
558C22C22×#41×C13911yescharacteristic
559C22C22×#41×C13911yescharacteristic
560C22C2×2−1+4×C13911yescharacteristic
561C22C2×2−1+4×C13911yescharacteristic
562C22#585×C13911yescharacteristic
563C4—26no—
564C4—26no—
565C4—22no—
566C4—22no—
567C4—22no—
568C4—22no—
569C4—43no—
570C4—43no—
571C4—43no—
572C4—41no—
573C4—43no—
574C4—41no—
575C4—43no—
576C4C2×C22⋊Q8×C139112yes—
577C2—24no—
578C2C22×C22⋊Q8×C13911yescharacteristic
579C2D4×#41×C13911yescharacteristic
580C2C2×#557×C13911yescharacteristic
581C2#3482×C13911yescharacteristic
582C2#3486×C13911yescharacteristic
583C2#3502×C13911yescharacteristic
584C2#3516×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC24×C139C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#557×C139C2semidirect
4. #2581×C139C2semidirect
5. #2565×C139C2semidirect
6. #2453×C139C2semidirect
7. #2451×C139C2semidirect
10. #2351×C139C2semidirect
11. #2351×C139C2semidirect
12. Q8×C4⋊C4×C139C2semidirect
70. C22×Q8×C139Q8semidirect
210. Q8×C139C22⋊Q8semidirect
262. C22×C139#557semidirect
292. #36435C139direct (N × H)
293. C139#36435direct (N × H)
294. C2×#557C2×C139semidirect
297. #2581C2×C139semidirect
298. #2565C2×C139semidirect
299. #2453C2×C139semidirect
300. #2451C2×C139semidirect
303. #2351C2×C139semidirect
304. #2351C2×C139semidirect
305. Q8×C4⋊C4C2×C139semidirect
363. C22×Q8Q8×C139semidirect
503. Q8C22⋊Q8×C139semidirect
555. C22#557×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1392
C22×C4×Q8×C1392
#2851×C1392
#2581×C1392
#2565×C1392
#2453×C1392
#2451×C1392
#2442×C1392
#2440×C1392
#2351×C1392
Q8×C4⋊C4×C1392
Q8×C22⋊C4×C1392
C4×C22⋊Q8×C1392
#36435139