Finite Group Databasebeta

← C139×#35786 #48030382

Subgroups — C139×#35786 #48030382

Order 35584.

2174 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C139C211yesmaximal, characteristic, complemented
2C2×#519×C139C211yesmaximal, characteristic
3#2629×C139C213yesmaximal
4#2582×C139C213yesmaximal, complemented
5#2565×C139C213yesmaximal, complemented
6#2453×C139C213yesmaximal, complemented
7#2451×C139C213yesmaximal, complemented
8#2441×C139C213yesmaximal
9#2439×C139C213yesmaximal
10#2396×C139C213yesmaximal
11#2351×C139C211yesmaximal, characteristic, complemented
12Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
13Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
14Q8×C22⋊C4×C139C211yesmaximal, characteristic
15Q8×C22⋊C4×C139C211yesmaximal, characteristic
16C23×Q8×C139C2211yescharacteristic
17#557×C139—28no—
18C2×C4⋊Q8×C139C2213yes—
19C2×#125×C139C2213yes—
20C2×#125×C139C2213yes—
21#519×C139—28no—
22C2×C4×Q8×C139C2213yes—
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×C139C2213yes—
30C2×C4×Q8×C139C2211yescharacteristic
31C2×#117×C139C2213yes—
32C2×#117×C139C2213yes—
33#400×C139C2213yes—
34#399×C139C2213yes—
35#398×C139C2213yes—
36#398×C139C2216yes—
37#398×C139C2213yes—
38#398×C139C2216yes—
39#396×C139C2213yes—
40#396×C139C2216yes—
41#396×C139C2211yescharacteristic
42#395×C139C2213yes—
43#393×C139C2213yes—
44#391×C139C2213yes—
45#391×C139C2213yes—
46#391×C139C2213yes—
47#391×C139C2213yes—
48#391×C139C2216yes—
49#389×C139C2213yes—
50#389×C139C2213yes—
51#389×C139C2216yes—
52#389×C139C2213yes—
53#389×C139C2213yes—
54#389×C139C2213yes—
55#389×C139C2213yes—
56#387×C139C2216yes—
57#387×C139C2216yes—
58#384×C139C2213yes—
59#384×C139C2213yes—
60#382×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×C139C2313yes—
75C4⋊Q8×C139—212no—
76#125×C139—212no—
77#125×C139—212no—
78C4×Q8×C139—24no—
79C4×Q8×C139—24no—
80C4×Q8×C139—24no—
81C4×Q8×C139—24no—
82C4×Q8×C139—24no—
83C4×Q8×C139—212no—
84C4×Q8×C139—212no—
85C4×Q8×C139—212no—
86C4×Q8×C139D418yes—
87#117×C139—212no—
88#117×C139—212no—
89C2×C4⋊C4×C139C2311yescharacteristic
90C2×C4⋊C4×C139C2313yes—
91C2×C4⋊C4×C139C2311yescharacteristic
92C2×C4⋊C4×C139C2313yes—
93C2×C4⋊C4×C139C2311yescharacteristic
94C2×C4⋊C4×C139C2316yes—
95C2×C4⋊C4×C139C2313yes—
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×C139C2313yes—
105C2×C4⋊C4×C139C2316yes—
106C2×C4⋊C4×C139C2316yes—
107C2×C4⋊C4×C139C2313yes—
108C2×C4⋊C4×C139C2313yes—
109C2×C22⋊C4×C139C2311yescharacteristic
110C2×C22⋊C4×C139C2313yes—
111C2×C22⋊C4×C139C2311yescharacteristic
112C2×C22⋊C4×C139C2311yescharacteristic
113C2×C22⋊C4×C139C2313yes—
114C2×C22⋊C4×C139C2313yes—
115C2×C42×C139C2313yes—
116C2×C42×C139C2316yes—
117C2×C42×C139C2313yes—
118C2×C42×C139C2313yes—
119C2×C42×C139C2313yes—
120C2×C42×C139C2313yes—
121C2×C42×C139C2313yes—
122#95×C139C2313yes—
123#95×C139C2313yes—
124#95×C139C2313yes—
125#95×C139C2313yes—
126#95×C139C2316yes—
127#95×C139C2311yescharacteristic
128#95×C139C2316yes—
129#95×C139C2316yes—
130#95×C139C2313yes—
131#95×C139C2313yes—
132#95×C139C2313yes—
133#95×C139C2313yes—
134#95×C139C2313yes—
135C24×C139C2411yescharacteristic
136C2×Q8×C139—232no—
137C2×Q8×C139—26no—
138C2×Q8×C139—26no—
139C2×Q8×C139—26no—
140C2×Q8×C139—26no—
141C2×Q8×C139—43no—
142C2×Q8×C139C2×D414yes—
143C2×Q8×C139C2×Q8112yes—
144C2×Q8×C139C2×Q814yes—
145C2×Q8×C139#4114yes—
146C22×C4×C139—26no—
147C22×C4×C139—26no—
148C22×C4×C139C2×Q8112yes—
149C22×C4×C139C2411yescharacteristic
150C22×C4×C139C2413yes—
151C22×C4×C139C2413yes—
152C22×C4×C139C2413yes—
153C22×C4×C139C2411yescharacteristic
154C22×C4×C139C2413yes—
155C22×C4×C139C2411yescharacteristic
156C22×C4×C139C2413yes—
157C22×C4×C139C2413yes—
158C22×C4×C139C2411yescharacteristic
159C22×C4×C139C2413yes—
160C22×C4×C139C2411yescharacteristic
161C22×C4×C139C2411yescharacteristic
162C22×C4×C139C2413yes—
163C4⋊C4×C139—26no—
164C4⋊C4×C139—26no—
165C4⋊C4×C139—26no—
166C4⋊C4×C139—22no—
167C4⋊C4×C139—26no—
168C4⋊C4×C139—26no—
169C4⋊C4×C139—26no—
170C4⋊C4×C139—26no—
171C4⋊C4×C139—212no—
172C4⋊C4×C139—26no—
173C4⋊C4×C139—26no—
174C4⋊C4×C139—22no—
175C4⋊C4×C139—22no—
176C4⋊C4×C139—26no—
177C4⋊C4×C139—43no—
178C4⋊C4×C139—46no—
179C4⋊C4×C139—46no—
180C4⋊C4×C139—43no—
181C4⋊C4×C139—43no—
182C4⋊C4×C139C2×D4112yes—
183C22⋊C4×C139—26no—
184C22⋊C4×C139—22no—
185C22⋊C4×C139—22no—
186C22⋊C4×C139—22no—
187C22⋊C4×C139—43no—
188C22⋊C4×C139—43no—
189C42×C139—212no—
190C42×C139—26no—
191C42×C139—26no—
192C42×C139—26no—
193C42×C139—26no—
194C42×C139—26no—
195C42×C139C2×D4112yes—
196C23×C139—21no—
197C23×C139—21no—
198C23×C139—21no—
199C23×C139—21no—
200C23×C139—21no—
201C23×C139—21no—
202C23×C139C22×Q812yes—
203C23×C139C2511yescharacteristic
204Q8×C139—224no—
205Q8×C139—412no—
206Q8×C139C22⋊Q8116yes—
207C2×C4×C139—21no—
208C2×C4×C139—23no—
209C2×C4×C139—21no—
210C2×C4×C139—23no—
211C2×C4×C139—21no—
212C2×C4×C139—21no—
213C2×C4×C139—23no—
214C2×C4×C139—21no—
215C2×C4×C139—23no—
216C2×C4×C139—21no—
217C2×C4×C139—224no—
218C2×C4×C139—21no—
219C2×C4×C139—23no—
220C2×C4×C139—21no—
221C2×C4×C139—23no—
222C2×C4×C139—23no—
223C2×C4×C139—21no—
224C2×C4×C139—23no—
225C2×C4×C139—23no—
226C2×C4×C139—21no—
227C2×C4×C139—21no—
228C2×C4×C139—21no—
229C2×C4×C139—23no—
230C2×C4×C139—23no—
231C2×C4×C139—21no—
232C2×C4×C139—23no—
233C2×C4×C139—23no—
234C2×C4×C139—23no—
235C2×C4×C139—23no—
236C2×C4×C139—23no—
237C2×C4×C139—21no—
238C2×C4×C139—23no—
239C2×C4×C139—21no—
240C2×C4×C139—23no—
241C2×C4×C139—23no—
242C2×C4×C139C22×D416yes—
243C2×C4×C139C22×D412yes—
244C2×C4×C139C22×D416yes—
245C2×C4×C139C22×Q816yes—
246C2×C4×C139C22×Q816yes—
247C2×C4×C139C2×#4116yes—
248C2×C4×C1392−1+412yes—
249C2×C4×C1392−1+412yes—
250C22×C139—22no—
251C22×C139—22no—
252C22×C139—22no—
253C22×C139—41no—
254C22×C139—41no—
255C22×C139—41no—
256C22×C139—41no—
257C22×C139C23×D411yescharacteristic
258C22×C139C23×Q811yescharacteristic
259C22×C139C22×#4111yescharacteristic
260C22×C139C2×2−1+411yescharacteristic
261C22×C139C2×2−1+411yescharacteristic
262C22×C139#58511yescharacteristic
263C22×C139#58511yescharacteristic
264C4×C139—26no—
265C4×C139—26no—
266C4×C139—22no—
267C4×C139—22no—
268C4×C139—22no—
269C4×C139—41no—
270C4×C139—43no—
271C4×C139—43no—
272C4×C139—41no—
273C4×C139—43no—
274C4×C139—41no—
275C4×C139—43no—
276C4×C139—43no—
277C4×C139C2×C22⋊Q8112yes—
278C2×C139—42no—
279C2×C139C22×C22⋊Q811yescharacteristic
280C2×C139#348911yescharacteristic
281C2×C139#349711yescharacteristic
282C2×C139#350211yescharacteristic
283C2×C139#350211yescharacteristic
284C2×C139#352311yescharacteristic
285C2×C139#352411yescharacteristic
286#35786C13911yesmaximal, characteristic, direct product factor, Sylow
287C139#3578611yescharacteristic, direct product factor, Sylow
288C2×#557C2×C13911yescharacteristic, complemented
289C2×#519C2×C13911yescharacteristic
290#2629C2×C13913yes—
291#2582C2×C13913yescomplemented
292#2565C2×C13913yescomplemented
293#2453C2×C13913yescomplemented
294#2451C2×C13913yescomplemented
295#2441C2×C13913yes—
296#2439C2×C13913yes—
297#2396C2×C13913yes—
298#2351C2×C13911yescharacteristic, complemented
299Q8×C4⋊C4C2×C13911yescharacteristic, complemented
300Q8×C4⋊C4C2×C13911yescharacteristic, complemented
301Q8×C22⋊C4C2×C13911yescharacteristic
302Q8×C22⋊C4C2×C13911yescharacteristic
303C23×Q8C22×C13911yescharacteristic
304#557—28no—
305C2×C4⋊Q8C22×C13913yes—
306C2×#125C22×C13913yes—
307C2×#125C22×C13913yes—
308#519—28no—
309C2×C4×Q8C22×C13913yes—
310C2×C4×Q8C22×C13913yes—
311C2×C4×Q8C22×C13911yescharacteristic
312C2×C4×Q8C22×C13911yescharacteristic
313C2×C4×Q8C22×C13911yescharacteristic
314C2×C4×Q8C22×C13911yescharacteristic
315C2×C4×Q8C22×C13911yescharacteristic
316C2×C4×Q8C22×C13913yes—
317C2×C4×Q8C22×C13911yescharacteristic
318C2×#117C22×C13913yes—
319C2×#117C22×C13913yes—
320#400C22×C13913yes—
321#399C22×C13913yes—
322#398C22×C13913yes—
323#398C22×C13916yes—
324#398C22×C13913yes—
325#398C22×C13916yes—
326#396C22×C13913yes—
327#396C22×C13916yes—
328#396C22×C13911yescharacteristic
329#395C22×C13913yes—
330#393C22×C13913yes—
331#391C22×C13913yes—
332#391C22×C13913yes—
333#391C22×C13913yes—
334#391C22×C13913yes—
335#391C22×C13916yes—
336#389C22×C13913yes—
337#389C22×C13913yes—
338#389C22×C13916yes—
339#389C22×C13913yes—
340#389C22×C13913yes—
341#389C22×C13913yes—
342#389C22×C13913yes—
343#387C22×C13916yes—
344#387C22×C13916yes—
345#384C22×C13913yes—
346#384C22×C13913yes—
347#382C22×C13913yes—
348#380C22×C13913yes—
349#380C22×C13913yes—
350C4×C4⋊C4C22×C13913yes—
351C4×C4⋊C4C22×C13913yes—
352C4×C4⋊C4C22×C13913yes—
353C4×C22⋊C4C22×C13913yes—
354C4×C22⋊C4C22×C13913yes—
355C22×Q8—24no—
356C22×Q8—24no—
357C22×Q8Q8×C13918yescomplemented
358C22×Q8C23×C13913yes—
359C22×Q8C23×C13913yes—
360C22×Q8C23×C13911yescharacteristic
361C23×C4C23×C13913yes—
362C4⋊Q8—212no—
363#125—212no—
364#125—212no—
365C4×Q8—24no—
366C4×Q8—24no—
367C4×Q8—24no—
368C4×Q8—24no—
369C4×Q8—24no—
370C4×Q8—212no—
371C4×Q8—212no—
372C4×Q8—212no—
373C4×Q8D4×C13918yes—
374#117—212no—
375#117—212no—
376C2×C4⋊C4C23×C13913yes—
377C2×C4⋊C4C23×C13913yes—
378C2×C4⋊C4C23×C13913yes—
379C2×C4⋊C4C23×C13911yescharacteristic
380C2×C4⋊C4C23×C13913yes—
381C2×C4⋊C4C23×C13913yes—
382C2×C4⋊C4C23×C13913yes—
383C2×C4⋊C4C23×C13913yes—
384C2×C4⋊C4C23×C13913yes—
385C2×C4⋊C4C23×C13913yes—
386C2×C4⋊C4C23×C13916yes—
387C2×C4⋊C4C23×C13911yescharacteristic
388C2×C4⋊C4C23×C13911yescharacteristic
389C2×C4⋊C4C23×C13913yes—
390C2×C4⋊C4C23×C13913yes—
391C2×C4⋊C4C23×C13913yes—
392C2×C4⋊C4C23×C13913yes—
393C2×C4⋊C4C23×C13916yes—
394C2×C4⋊C4C23×C13916yes—
395C2×C4⋊C4C23×C13913yes—
396C2×C22⋊C4C23×C13913yes—
397C2×C22⋊C4C23×C13911yescharacteristic
398C2×C22⋊C4C23×C13911yescharacteristic
399C2×C22⋊C4C23×C13911yescharacteristic
400C2×C22⋊C4C23×C13913yes—
401C2×C22⋊C4C23×C13913yes—
402C2×C42C23×C13913yes—
403C2×C42C23×C13916yes—
404C2×C42C23×C13913yes—
405C2×C42C23×C13913yes—
406C2×C42C23×C13913yes—
407C2×C42C23×C13913yes—
408C2×C42C23×C13913yes—
409#95C23×C13913yes—
410#95C23×C13913yes—
411#95C23×C13913yes—
412#95C23×C13913yes—
413#95C23×C13911yescharacteristic
414#95C23×C13913yes—
415#95C23×C13913yes—
416#95C23×C13913yes—
417#95C23×C13913yes—
418#95C23×C13913yes—
419#95C23×C13916yes—
420#95C23×C13916yes—
421#95C23×C13916yes—
422C24C24×C13911yescharacteristic
423C2×Q8—232no—
424C2×Q8—26no—
425C2×Q8—26no—
426C2×Q8—26no—
427C2×Q8—26no—
428C2×Q8—43no—
429C2×Q8C2×D4×C13914yes—
430C2×Q8C2×Q8×C139112yes—
431C2×Q8C2×Q8×C13914yes—
432C2×Q8#41×C13914yes—
433C22×C4—26no—
434C22×C4—26no—
435C22×C4C2×Q8×C139112yes—
436C22×C4C24×C13911yescharacteristic
437C22×C4C24×C13913yes—
438C22×C4C24×C13913yes—
439C22×C4C24×C13913yes—
440C22×C4C24×C13911yescharacteristic
441C22×C4C24×C13913yes—
442C22×C4C24×C13911yescharacteristic
443C22×C4C24×C13913yes—
444C22×C4C24×C13913yes—
445C22×C4C24×C13911yescharacteristic
446C22×C4C24×C13913yes—
447C22×C4C24×C13911yescharacteristic
448C22×C4C24×C13911yescharacteristic
449C22×C4C24×C13913yes—
450C4⋊C4—26no—
451C4⋊C4—26no—
452C4⋊C4—26no—
453C4⋊C4—22no—
454C4⋊C4—26no—
455C4⋊C4—26no—
456C4⋊C4—26no—
457C4⋊C4—26no—
458C4⋊C4—212no—
459C4⋊C4—26no—
460C4⋊C4—26no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—26no—
464C4⋊C4—43no—
465C4⋊C4—46no—
466C4⋊C4—43no—
467C4⋊C4—46no—
468C4⋊C4—43no—
469C4⋊C4C2×D4×C139112yes—
470C22⋊C4—26no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—43no—
475C22⋊C4—43no—
476C42—212no—
477C42—26no—
478C42—26no—
479C42—26no—
480C42—26no—
481C42—26no—
482C42C2×D4×C139112yes—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23C22×Q8×C13912yes—
490C23C25×C13911yescharacteristic
491Q8—224no—
492Q8—412no—
493Q8C22⋊Q8×C139116yes—
494C2×C4—21no—
495C2×C4—23no—
496C2×C4—21no—
497C2×C4—23no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—23no—
501C2×C4—21no—
502C2×C4—23no—
503C2×C4—21no—
504C2×C4—224no—
505C2×C4—21no—
506C2×C4—23no—
507C2×C4—21no—
508C2×C4—23no—
509C2×C4—23no—
510C2×C4—21no—
511C2×C4—23no—
512C2×C4—23no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—23no—
517C2×C4—23no—
518C2×C4—21no—
519C2×C4—23no—
520C2×C4—23no—
521C2×C4—23no—
522C2×C4—23no—
523C2×C4—23no—
524C2×C4—21no—
525C2×C4—23no—
526C2×C4—21no—
527C2×C4—23no—
528C2×C4—23no—
529C2×C4C22×D4×C13916yes—
530C2×C4C22×D4×C13912yes—
531C2×C4C22×D4×C13916yes—
532C2×C4C22×Q8×C13916yes—
533C2×C4C22×Q8×C13916yes—
534C2×C4C2×#41×C13916yes—
535C2×C42−1+4×C13912yes—
536C2×C42−1+4×C13912yes—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22C23×D4×C13911yescharacteristic
545C22C23×Q8×C13911yescharacteristic
546C22C22×#41×C13911yescharacteristic
547C22C2×2−1+4×C13911yescharacteristic
548C22C2×2−1+4×C13911yescharacteristic
549C22#585×C13911yescharacteristic
550C22#585×C13911yescharacteristic
551C4—26no—
552C4—26no—
553C4—22no—
554C4—22no—
555C4—22no—
556C4—43no—
557C4—41no—
558C4—43no—
559C4—41no—
560C4—43no—
561C4—41no—
562C4—43no—
563C4—43no—
564C4C2×C22⋊Q8×C139112yes—
565C2—42no—
566C2C22×C22⋊Q8×C13911yescharacteristic
567C2#3489×C13911yescharacteristic
568C2#3497×C13911yescharacteristic
569C2#3502×C13911yescharacteristic
570C2#3502×C13911yescharacteristic
571C2#3523×C13911yescharacteristic
572C2#3524×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. #2582×C139C2semidirect
5. #2565×C139C2semidirect
6. #2453×C139C2semidirect
7. #2451×C139C2semidirect
11. #2351×C139C2semidirect
12. Q8×C4⋊C4×C139C2semidirect
13. Q8×C4⋊C4×C139C2semidirect
70. C22×Q8×C139Q8semidirect
286. #35786C139direct (N × H)
287. C139#35786direct (N × H)
288. C2×#557C2×C139semidirect
291. #2582C2×C139semidirect
292. #2565C2×C139semidirect
293. #2453C2×C139semidirect
294. #2451C2×C139semidirect
298. #2351C2×C139semidirect
299. Q8×C4⋊C4C2×C139semidirect
300. Q8×C4⋊C4C2×C139semidirect
357. C22×Q8Q8×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×#519×C1392
#2629×C1392
#2582×C1392
#2565×C1392
#2453×C1392
#2451×C1392
#2441×C1392
#2439×C1392
#2396×C1392
#2351×C1392
Q8×C4⋊C4×C1392
Q8×C22⋊C4×C1392
#35786139