Finite Group Databasebeta

← C139×#36431 #48031027

Subgroups — C139×#36431 #48031027

Order 35584.

2376 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C139C211yesmaximal, characteristic, complemented
2C2×C4×#41×C139C211yesmaximal, characteristic
3#2851×C139C213yesmaximal, complemented
4#2580×C139C213yesmaximal, complemented
5#2566×C139C213yesmaximal, complemented
6#2454×C139C213yesmaximal, complemented
7#2452×C139C213yesmaximal, complemented
8#2441×C139C213yesmaximal, complemented
9#2439×C139C213yesmaximal, complemented
10#2351×C139C211yesmaximal, characteristic, complemented
11#2351×C139C211yesmaximal, characteristic, complemented
12Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
13#2341×C139C211yesmaximal, characteristic
14#2341×C139C211yesmaximal, characteristic
15C4×C22⋊Q8×C139C213yesmaximal, complemented
16C22×#41×C139C2211yescharacteristic
17#557×C139—28no—
18C2×C4⋊Q8×C139C2213yes—
19C2×#125×C139C2213yes—
20C2×#125×C139C2213yes—
21C2×C22⋊Q8×C139C2213yes—
22C4×#41×C139—28no—
23C2×C4×Q8×C139C2213yes—
24C2×C4×Q8×C139C2211yescharacteristic
25C2×C4×Q8×C139C2211yescharacteristic
26C2×C4×Q8×C139C2211yescharacteristic
27C2×C4×Q8×C139C2211yescharacteristic
28C2×C4×Q8×C139C2211yescharacteristic
29C2×C4×Q8×C139C2211yescharacteristic
30C2×C4×D4×C139C2213yes—
31C2×C4×D4×C139C2213yes—
32C2×#117×C139C2213yes—
33C22×C42×C139C2213yes—
34#399×C139C2216yes—
35#396×C139C2216yes—
36#396×C139C2216yes—
37#393×C139C2216yes—
38#391×C139C2213yes—
39#390×C139C2213yes—
40#390×C139C2213yes—
41#390×C139C2213yes—
42#390×C139C2213yes—
43#389×C139C2213yes—
44#389×C139C2213yes—
45#389×C139C2213yes—
46#389×C139C2213yes—
47#389×C139C2213yes—
48#389×C139C2213yes—
49#389×C139C2213yes—
50#387×C139C2211yescharacteristic
51#387×C139C2213yes—
52#387×C139C2216yes—
53#385×C139C2213yes—
54#385×C139C2213yes—
55#385×C139C2216yes—
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—
68C2×#41×C139—24no—
69C2×#41×C139—24no—
70C2×#41×C139Q818yescomplemented
71C22×Q8×C139C2313yes—
72C22×Q8×C139C2311yescharacteristic
73C22×D4×C139C2313yes—
74C23×C4×C139C2313yes—
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×C139D418yes—
88C4×D4×C139—212no—
89C4×D4×C139—212no—
90#117×C139—212no—
91C2×C4⋊C4×C139C2313yes—
92C2×C4⋊C4×C139C2316yes—
93C2×C4⋊C4×C139C2313yes—
94C2×C4⋊C4×C139C2313yes—
95C2×C4⋊C4×C139C2311yescharacteristic
96C2×C4⋊C4×C139C2313yes—
97C2×C4⋊C4×C139C2313yes—
98C2×C4⋊C4×C139C2313yes—
99C2×C4⋊C4×C139C2313yes—
100C2×C4⋊C4×C139C2313yes—
101C2×C4⋊C4×C139C2313yes—
102C2×C4⋊C4×C139C2313yes—
103C2×C4⋊C4×C139C2313yes—
104C2×C4⋊C4×C139C2316yes—
105C2×C4⋊C4×C139C2313yes—
106C2×C4⋊C4×C139C2313yes—
107C2×C4⋊C4×C139C2311yescharacteristic
108C2×C22⋊C4×C139C2316yes—
109C2×C22⋊C4×C139C2313yes—
110C2×C22⋊C4×C139C2313yes—
111C2×C22⋊C4×C139C2313yes—
112C2×C22⋊C4×C139C2316yes—
113C2×C22⋊C4×C139C2316yes—
114C2×C22⋊C4×C139C2313yes—
115C2×C42×C139—212no—
116C2×C42×C139C2311yescharacteristic
117C2×C42×C139C2313yes—
118C2×C42×C139C2313yes—
119C2×C42×C139C2313yes—
120C2×C42×C139C2313yes—
121C2×C42×C139C2313yes—
122C2×C42×C139C2313yes—
123C2×C42×C139C2313yes—
124#95×C139C2313yes—
125#95×C139C2316yes—
126#95×C139C2316yes—
127#95×C139C2311yescharacteristic
128#95×C139C2311yescharacteristic
129#95×C139C2313yes—
130#95×C139C2313yes—
131#95×C139C2311yescharacteristic
132#95×C139C2311yescharacteristic
133#95×C139C2313yes—
134#95×C139C2313yes—
135#95×C139C2313yes—
136C24×C139C2413yes—
137#41×C139—232no—
138C2×Q8×C139—26no—
139C2×Q8×C139—26no—
140C2×Q8×C139—43no—
141C2×Q8×C139C2×D414yes—
142C2×Q8×C139C2×Q814yes—
143C2×Q8×C139#4114yes—
144C2×D4×C139—26no—
145C2×D4×C139—26no—
146C2×D4×C139C2×Q8112yes—
147C22×C4×C139—26no—
148C22×C4×C139—26no—
149C22×C4×C139—26no—
150C22×C4×C139—26no—
151C22×C4×C139—26no—
152C22×C4×C139—43no—
153C22×C4×C139—43no—
154C22×C4×C139—43no—
155C22×C4×C139C2×Q8112yes—
156C22×C4×C139C2411yescharacteristic
157C22×C4×C139C2413yes—
158C22×C4×C139C2413yes—
159C22×C4×C139C2413yes—
160C22×C4×C139C2413yes—
161C22×C4×C139C2411yescharacteristic
162C22×C4×C139C2413yes—
163C22×C4×C139C2411yescharacteristic
164C22×C4×C139C2413yes—
165C22×C4×C139C2411yescharacteristic
166C22×C4×C139C2411yescharacteristic
167C22×C4×C139C2411yescharacteristic
168C22×C4×C139C2411yescharacteristic
169C22×C4×C139C2413yes—
170C4⋊C4×C139—26no—
171C4⋊C4×C139—22no—
172C4⋊C4×C139—26no—
173C4⋊C4×C139—26no—
174C4⋊C4×C139—26no—
175C4⋊C4×C139—26no—
176C4⋊C4×C139—212no—
177C4⋊C4×C139—26no—
178C4⋊C4×C139—26no—
179C4⋊C4×C139—26no—
180C4⋊C4×C139—26no—
181C4⋊C4×C139—43no—
182C4⋊C4×C139—43no—
183C4⋊C4×C139—43no—
184C4⋊C4×C139—46no—
185C4⋊C4×C139C2×D4112yes—
186C4⋊C4×C139#4114yescomplemented
187C22⋊C4×C139—212no—
188C22⋊C4×C139—26no—
189C22⋊C4×C139—26no—
190C22⋊C4×C139—43no—
191C22⋊C4×C139—43no—
192C22⋊C4×C139—46no—
193C22⋊C4×C139—46no—
194C42×C139—22no—
195C42×C139—26no—
196C42×C139—26no—
197C42×C139—26no—
198C42×C139—26no—
199C42×C139—26no—
200C42×C139—26no—
201C42×C139C2×D4112yes—
202C23×C139—23no—
203C23×C139—23no—
204C23×C139—23no—
205C23×C139—23no—
206C23×C139—23no—
207C23×C139—23no—
208C23×C139C22×Q816yes—
209C23×C139C2511yescharacteristic
210Q8×C139—412no—
211Q8×C139C22⋊Q8116yescomplemented
212D4×C139—224no—
213C2×C4×C139—21no—
214C2×C4×C139—21no—
215C2×C4×C139—21no—
216C2×C4×C139—21no—
217C2×C4×C139—23no—
218C2×C4×C139—21no—
219C2×C4×C139—21no—
220C2×C4×C139—23no—
221C2×C4×C139—21no—
222C2×C4×C139—21no—
223C2×C4×C139—21no—
224C2×C4×C139—21no—
225C2×C4×C139—224no—
226C2×C4×C139—21no—
227C2×C4×C139—23no—
228C2×C4×C139—23no—
229C2×C4×C139—23no—
230C2×C4×C139—21no—
231C2×C4×C139—23no—
232C2×C4×C139—23no—
233C2×C4×C139—23no—
234C2×C4×C139—23no—
235C2×C4×C139—21no—
236C2×C4×C139—21no—
237C2×C4×C139—23no—
238C2×C4×C139—23no—
239C2×C4×C139—23no—
240C2×C4×C139—23no—
241C2×C4×C139—23no—
242C2×C4×C139—23no—
243C2×C4×C139—21no—
244C2×C4×C139—21no—
245C2×C4×C139—23no—
246C2×C4×C139—23no—
247C2×C4×C139—412no—
248C2×C4×C139—412no—
249C2×C4×C139C22×D412yes—
250C2×C4×C139C22×D416yes—
251C2×C4×C139C22×D416yes—
252C2×C4×C139C22×Q812yes—
253C2×C4×C139C22×Q816yes—
254C2×C4×C139C2×#4112yes—
255C2×C4×C139C2×#4112yes—
256C2×C4×C139C2×#4112yes—
257C2×C4×C139C2×#4116yes—
258C22×C139—26no—
259C22×C139—26no—
260C22×C139—26no—
261C22×C139—43no—
262C22×C139—43no—
263C22×C139—43no—
264C22×C139—43no—
265C22×C139C23×D411yescharacteristic
266C22×C139C23×Q811yescharacteristic
267C22×C139C22×#4111yescharacteristic
268C22×C139C22×#4111yescharacteristic
269C22×C139#58511yescharacteristic
270C22×C139#58511yescharacteristic
271C22×C139#58511yescharacteristic
272C4×C139—22no—
273C4×C139—22no—
274C4×C139—26no—
275C4×C139—22no—
276C4×C139—22no—
277C4×C139—22no—
278C4×C139—43no—
279C4×C139—43no—
280C4×C139—41no—
281C4×C139—43no—
282C4×C139—43no—
283C4×C139—41no—
284C4×C139—43no—
285C4×C139C2×C22⋊Q8112yes—
286C2×C139—46no—
287C2×C139C22×C22⋊Q811yescharacteristic
288C2×C139D4×#4111yescharacteristic
289C2×C139Q8×#4111yescharacteristic
290C2×C139#348011yescharacteristic
291C2×C139#348711yescharacteristic
292C2×C139#350411yescharacteristic
293C2×C139#352411yescharacteristic
294#36431C13911yesmaximal, characteristic, direct product factor, Sylow
295C139#3643111yescharacteristic, direct product factor, Sylow
296C2×#557C2×C13911yescharacteristic, complemented
297C2×C4×#41C2×C13911yescharacteristic
298#2851C2×C13913yescomplemented
299#2580C2×C13913yescomplemented
300#2566C2×C13913yescomplemented
301#2454C2×C13913yescomplemented
302#2452C2×C13913yescomplemented
303#2441C2×C13913yescomplemented
304#2439C2×C13913yescomplemented
305#2351C2×C13911yescharacteristic, complemented
306#2351C2×C13911yescharacteristic, complemented
307Q8×C4⋊C4C2×C13911yescharacteristic, complemented
308#2341C2×C13911yescharacteristic
309#2341C2×C13911yescharacteristic
310C4×C22⋊Q8C2×C13913yescomplemented
311C22×#41C22×C13911yescharacteristic
312#557—28no—
313C2×C4⋊Q8C22×C13913yes—
314C2×#125C22×C13913yes—
315C2×#125C22×C13913yes—
316C2×C22⋊Q8C22×C13913yes—
317C4×#41—28no—
318C2×C4×Q8C22×C13913yes—
319C2×C4×Q8C22×C13911yescharacteristic
320C2×C4×Q8C22×C13911yescharacteristic
321C2×C4×Q8C22×C13911yescharacteristic
322C2×C4×Q8C22×C13911yescharacteristic
323C2×C4×Q8C22×C13911yescharacteristic
324C2×C4×Q8C22×C13911yescharacteristic
325C2×C4×D4C22×C13913yes—
326C2×C4×D4C22×C13913yes—
327C2×#117C22×C13913yes—
328C22×C42C22×C13913yes—
329#399C22×C13916yes—
330#396C22×C13916yes—
331#396C22×C13916yes—
332#393C22×C13916yes—
333#391C22×C13913yes—
334#390C22×C13913yes—
335#390C22×C13913yes—
336#390C22×C13913yes—
337#390C22×C13913yes—
338#389C22×C13913yes—
339#389C22×C13913yes—
340#389C22×C13913yes—
341#389C22×C13913yes—
342#389C22×C13913yes—
343#389C22×C13913yes—
344#389C22×C13913yes—
345#387C22×C13913yes—
346#387C22×C13916yes—
347#387C22×C13911yescharacteristic
348#385C22×C13913yes—
349#385C22×C13916yes—
350#385C22×C13913yes—
351#385C22×C13916yes—
352#384C22×C13913yes—
353#382C22×C13913yes—
354#382C22×C13913yes—
355#380C22×C13913yes—
356#380C22×C13913yes—
357#380C22×C13913yes—
358C4×C4⋊C4C22×C13913yes—
359C4×C4⋊C4C22×C13913yes—
360C4×C4⋊C4C22×C13913yes—
361C4×C22⋊C4C22×C13913yes—
362C4×C22⋊C4C22×C13913yes—
363C2×#41—24no—
364C2×#41—24no—
365C2×#41Q8×C13918yescomplemented
366C22×Q8C23×C13913yes—
367C22×Q8C23×C13911yescharacteristic
368C22×D4C23×C13913yes—
369C23×C4C23×C13913yes—
370C23×C4C23×C13913yes—
371C23×C4C23×C13913yes—
372C4⋊Q8—212no—
373#125—212no—
374#125—212no—
375C22⋊Q8—212no—
376C4×Q8—24no—
377C4×Q8—24no—
378C4×Q8—24no—
379C4×Q8—24no—
380C4×Q8—24no—
381C4×Q8—212no—
382C4×Q8D4×C13918yes—
383C4×D4—212no—
384C4×D4—212no—
385#117—212no—
386C2×C4⋊C4C23×C13913yes—
387C2×C4⋊C4C23×C13911yescharacteristic
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×C13913yes—
398C2×C4⋊C4C23×C13913yes—
399C2×C4⋊C4C23×C13913yes—
400C2×C4⋊C4C23×C13916yes—
401C2×C4⋊C4C23×C13913yes—
402C2×C4⋊C4C23×C13911yescharacteristic
403C2×C22⋊C4C23×C13916yes—
404C2×C22⋊C4C23×C13913yes—
405C2×C22⋊C4C23×C13913yes—
406C2×C22⋊C4C23×C13913yes—
407C2×C22⋊C4C23×C13913yes—
408C2×C22⋊C4C23×C13916yes—
409C2×C22⋊C4C23×C13916yes—
410C2×C42—212no—
411C2×C42C23×C13913yes—
412C2×C42C23×C13913yes—
413C2×C42C23×C13913yes—
414C2×C42C23×C13913yes—
415C2×C42C23×C13913yes—
416C2×C42C23×C13913yes—
417C2×C42C23×C13911yescharacteristic
418C2×C42C23×C13913yes—
419#95C23×C13911yescharacteristic
420#95C23×C13911yescharacteristic
421#95C23×C13913yes—
422#95C23×C13913yes—
423#95C23×C13911yescharacteristic
424#95C23×C13911yescharacteristic
425#95C23×C13913yes—
426#95C23×C13913yes—
427#95C23×C13913yes—
428#95C23×C13913yes—
429#95C23×C13916yes—
430#95C23×C13916yes—
431C24C24×C13913yes—
432#41—232no—
433C2×Q8—26no—
434C2×Q8—26no—
435C2×Q8—43no—
436C2×Q8C2×D4×C13914yes—
437C2×Q8C2×Q8×C13914yes—
438C2×Q8#41×C13914yes—
439C2×D4—26no—
440C2×D4—26no—
441C2×D4C2×Q8×C139112yes—
442C22×C4—26no—
443C22×C4—26no—
444C22×C4—26no—
445C22×C4—26no—
446C22×C4—26no—
447C22×C4—43no—
448C22×C4—43no—
449C22×C4—43no—
450C22×C4C2×Q8×C139112yes—
451C22×C4C24×C13911yescharacteristic
452C22×C4C24×C13913yes—
453C22×C4C24×C13913yes—
454C22×C4C24×C13913yes—
455C22×C4C24×C13913yes—
456C22×C4C24×C13911yescharacteristic
457C22×C4C24×C13913yes—
458C22×C4C24×C13911yescharacteristic
459C22×C4C24×C13913yes—
460C22×C4C24×C13911yescharacteristic
461C22×C4C24×C13911yescharacteristic
462C22×C4C24×C13911yescharacteristic
463C22×C4C24×C13911yescharacteristic
464C22×C4C24×C13913yes—
465C4⋊C4—26no—
466C4⋊C4—22no—
467C4⋊C4—26no—
468C4⋊C4—26no—
469C4⋊C4—26no—
470C4⋊C4—26no—
471C4⋊C4—212no—
472C4⋊C4—26no—
473C4⋊C4—26no—
474C4⋊C4—26no—
475C4⋊C4—26no—
476C4⋊C4—43no—
477C4⋊C4—43no—
478C4⋊C4—43no—
479C4⋊C4—46no—
480C4⋊C4C2×D4×C139112yes—
481C4⋊C4#41×C13914yescomplemented
482C22⋊C4—212no—
483C22⋊C4—26no—
484C22⋊C4—26no—
485C22⋊C4—43no—
486C22⋊C4—43no—
487C22⋊C4—46no—
488C22⋊C4—46no—
489C42—22no—
490C42—26no—
491C42—26no—
492C42—26no—
493C42—26no—
494C42—26no—
495C42—26no—
496C42C2×D4×C139112yes—
497C23—23no—
498C23—23no—
499C23—23no—
500C23—23no—
501C23—23no—
502C23—23no—
503C23C22×Q8×C13916yes—
504C23C25×C13911yescharacteristic
505Q8—412no—
506Q8C22⋊Q8×C139116yescomplemented
507D4—224no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—23no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—23no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—224no—
521C2×C4—21no—
522C2×C4—23no—
523C2×C4—23no—
524C2×C4—23no—
525C2×C4—21no—
526C2×C4—23no—
527C2×C4—23no—
528C2×C4—23no—
529C2×C4—23no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—23no—
533C2×C4—23no—
534C2×C4—23no—
535C2×C4—23no—
536C2×C4—23no—
537C2×C4—23no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—23no—
541C2×C4—23no—
542C2×C4—412no—
543C2×C4—412no—
544C2×C4C22×D4×C13912yes—
545C2×C4C22×D4×C13916yes—
546C2×C4C22×D4×C13916yes—
547C2×C4C22×Q8×C13912yes—
548C2×C4C22×Q8×C13916yes—
549C2×C4C2×#41×C13912yes—
550C2×C4C2×#41×C13912yes—
551C2×C4C2×#41×C13912yes—
552C2×C4C2×#41×C13916yes—
553C22—26no—
554C22—26no—
555C22—26no—
556C22—43no—
557C22—43no—
558C22—43no—
559C22—43no—
560C22C23×D4×C13911yescharacteristic
561C22C23×Q8×C13911yescharacteristic
562C22C22×#41×C13911yescharacteristic
563C22C22×#41×C13911yescharacteristic
564C22#585×C13911yescharacteristic
565C22#585×C13911yescharacteristic
566C22#585×C13911yescharacteristic
567C4—22no—
568C4—22no—
569C4—26no—
570C4—22no—
571C4—22no—
572C4—22no—
573C4—43no—
574C4—43no—
575C4—43no—
576C4—41no—
577C4—43no—
578C4—41no—
579C4—43no—
580C4C2×C22⋊Q8×C139112yes—
581C2—46no—
582C2C22×C22⋊Q8×C13911yescharacteristic
583C2D4×#41×C13911yescharacteristic
584C2Q8×#41×C13911yescharacteristic
585C2#3480×C13911yescharacteristic
586C2#3487×C13911yescharacteristic
587C2#3504×C13911yescharacteristic
588C2#3524×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC22×#41×C139C22
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
3. #2851×C139C2semidirect
4. #2580×C139C2semidirect
5. #2566×C139C2semidirect
6. #2454×C139C2semidirect
7. #2452×C139C2semidirect
8. #2441×C139C2semidirect
9. #2439×C139C2semidirect
10. #2351×C139C2semidirect
11. #2351×C139C2semidirect
12. Q8×C4⋊C4×C139C2semidirect
15. C4×C22⋊Q8×C139C2semidirect
70. C2×#41×C139Q8semidirect
186. C4⋊C4×C139#41semidirect
211. Q8×C139C22⋊Q8semidirect
294. #36431C139direct (N × H)
295. C139#36431direct (N × H)
296. C2×#557C2×C139semidirect
298. #2851C2×C139semidirect
299. #2580C2×C139semidirect
300. #2566C2×C139semidirect
301. #2454C2×C139semidirect
302. #2452C2×C139semidirect
303. #2441C2×C139semidirect
304. #2439C2×C139semidirect
305. #2351C2×C139semidirect
306. #2351C2×C139semidirect
307. Q8×C4⋊C4C2×C139semidirect
310. C4×C22⋊Q8C2×C139semidirect
365. C2×#41Q8×C139semidirect
481. C4⋊C4#41×C139semidirect
506. Q8C22⋊Q8×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1392
C2×C4×#41×C1392
#2851×C1392
#2580×C1392
#2566×C1392
#2454×C1392
#2452×C1392
#2441×C1392
#2439×C1392
#2351×C1392
Q8×C4⋊C4×C1392
#2341×C1392
C4×C22⋊Q8×C1392
#36431139