Finite Group Databasebeta

← C139×#35723 #48030319

Subgroups — C139×#35723 #48030319

Order 35584.

2284 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C139C211yesmaximal, characteristic
2C2×#519×C139C211yesmaximal, characteristic, complemented
3#2625×C139C213yesmaximal, complemented
4#2499×C139C213yesmaximal, complemented
5#2485×C139C213yesmaximal
6#2446×C139C213yesmaximal, complemented
7#2446×C139C213yesmaximal, complemented
8#2423×C139C213yesmaximal, complemented
9#2421×C139C213yesmaximal, complemented
10#2395×C139C213yesmaximal
11#2351×C139C211yesmaximal, characteristic, complemented
12Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
13Q8×C22⋊C4×C139C211yesmaximal, characteristic, complemented
14Q8×C22⋊C4×C139C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C139C211yesmaximal, characteristic, complemented
16C23×Q8×C139C2211yescharacteristic
17C23×Q8×C139C2211yescharacteristic
18D4×Q8×C139—28no—
19C2×C4⋊Q8×C139C2213yes—
20C2×C22⋊Q8×C139C2213yes—
21C2×C22⋊Q8×C139C2213yes—
22#519×C139—28no—
23C2×C4×Q8×C139C2211yescharacteristic
24C2×C4×Q8×C139C2211yescharacteristic
25C2×C4×Q8×C139C2211yescharacteristic
26C2×C4×Q8×C139C2211yescharacteristic
27C2×C4×Q8×C139C2211yescharacteristic
28C2×C4×Q8×C139C2213yes—
29C2×C4×Q8×C139C2213yes—
30C2×C4×D4×C139C2213yes—
31C2×#117×C139C2213yes—
32C2×#117×C139C2213yes—
33#400×C139C2216yes—
34#400×C139C2213yes—
35#399×C139C2213yes—
36#398×C139C2216yes—
37#398×C139C2213yes—
38#397×C139C2213yes—
39#397×C139C2216yes—
40#397×C139C2213yes—
41#397×C139C2213yes—
42#394×C139C2211yescharacteristic
43#394×C139C2213yes—
44#391×C139C2213yes—
45#391×C139C2213yes—
46#391×C139C2213yes—
47#391×C139C2213yes—
48#391×C139C2213yes—
49#391×C139C2213yes—
50#389×C139C2213yes—
51#389×C139C2213yes—
52#389×C139C2213yes—
53#389×C139C2213yes—
54#388×C139C2216yes—
55#387×C139C2216yes—
56#387×C139C2216yes—
57#387×C139C2216yes—
58#384×C139C2213yes—
59#382×C139C2213yes—
60#380×C139C2213yes—
61#380×C139C2213yes—
62#380×C139C2213yes—
63C4×C4⋊C4×C139C2213yes—
64C4×C4⋊C4×C139C2213yes—
65C4×C22⋊C4×C139C2213yes—
66C4×C22⋊C4×C139C2213yes—
67C4×C22⋊C4×C139C2213yes—
68C22×Q8×C139—24no—
69C22×Q8×C139—24no—
70C22×Q8×C139—24no—
71C22×Q8×C139—24no—
72C22×Q8×C139—24no—
73C22×Q8×C139D418yes—
74C22×Q8×C139C2313yes—
75C22×Q8×C139C2313yes—
76C22×Q8×C139C2311yescharacteristic
77C22×D4×C139C2311yescharacteristic
78C23×C4×C139C2313yes—
79C23×C4×C139C2313yes—
80C4⋊Q8×C139—212no—
81C22⋊Q8×C139—212no—
82C22⋊Q8×C139—212no—
83C4×Q8×C139—212no—
84C4×Q8×C139—212no—
85C4×Q8×C139—24no—
86C4×Q8×C139—24no—
87C4×Q8×C139—24no—
88C4×Q8×C139—24no—
89C4×Q8×C139—24no—
90C4×D4×C139—212no—
91#117×C139—212no—
92#117×C139—212no—
93C2×C4⋊C4×C139C2313yes—
94C2×C4⋊C4×C139C2313yes—
95C2×C4⋊C4×C139C2311yescharacteristic
96C2×C4⋊C4×C139C2313yes—
97C2×C4⋊C4×C139C2313yes—
98C2×C4⋊C4×C139C2316yes—
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×C139C2313yes—
106C2×C4⋊C4×C139C2316yes—
107C2×C22⋊C4×C139C2313yes—
108C2×C22⋊C4×C139C2311yescharacteristic
109C2×C22⋊C4×C139C2313yes—
110C2×C22⋊C4×C139C2311yescharacteristic
111C2×C22⋊C4×C139C2311yescharacteristic
112C2×C22⋊C4×C139C2313yes—
113C2×C22⋊C4×C139C2313yes—
114C2×C22⋊C4×C139C2311yescharacteristic
115C2×C22⋊C4×C139C2313yes—
116C2×C22⋊C4×C139C2313yes—
117C2×C42×C139C2313yes—
118C2×C42×C139C2313yes—
119C2×C42×C139C2316yes—
120C2×C42×C139C2313yes—
121C2×C42×C139C2313yes—
122C2×C42×C139C2313yes—
123#95×C139C2313yes—
124#95×C139C2313yes—
125#95×C139C2313yes—
126#95×C139C2313yes—
127#95×C139C2313yes—
128#95×C139C2316yes—
129#95×C139C2313yes—
130#95×C139C2313yes—
131#95×C139C2316yes—
132#95×C139C2316yes—
133#95×C139C2313yes—
134#95×C139C2316yes—
135#95×C139C2311yescharacteristic
136#95×C139C2313yes—
137C24×C139C2411yescharacteristic
138C24×C139C2411yescharacteristic
139C2×Q8×C139—232no—
140C2×Q8×C139—26no—
141C2×Q8×C139—26no—
142C2×Q8×C139—26no—
143C2×Q8×C139—26no—
144C2×Q8×C139—26no—
145C2×Q8×C139—416no—
146C2×Q8×C139C2×D4112yes—
147C2×Q8×C139C2×D414yes—
148C2×Q8×C139#4114yes—
149C2×Q8×C139#4114yes—
150C2×D4×C139—22no—
151C2×D4×C139—22no—
152C2×D4×C139—22no—
153C22×C4×C139—26no—
154C22×C4×C139—26no—
155C22×C4×C139—26no—
156C22×C4×C139—26no—
157C22×C4×C139—26no—
158C22×C4×C139C2×D4112yes—
159C22×C4×C139C2411yescharacteristic
160C22×C4×C139C2413yes—
161C22×C4×C139C2413yes—
162C22×C4×C139C2413yes—
163C22×C4×C139C2411yescharacteristic
164C22×C4×C139C2413yes—
165C22×C4×C139C2411yescharacteristic
166C22×C4×C139C2413yes—
167C22×C4×C139C2413yes—
168C22×C4×C139C2413yes—
169C22×C4×C139C2411yescharacteristic
170C22×C4×C139C2411yescharacteristic
171C22×C4×C139C2413yes—
172C4⋊C4×C139—26no—
173C4⋊C4×C139—26no—
174C4⋊C4×C139—26no—
175C4⋊C4×C139—26no—
176C4⋊C4×C139—26no—
177C4⋊C4×C139—26no—
178C4⋊C4×C139—212no—
179C4⋊C4×C139—26no—
180C4⋊C4×C139—26no—
181C4⋊C4×C139—22no—
182C4⋊C4×C139—26no—
183C4⋊C4×C139—26no—
184C4⋊C4×C139—43no—
185C4⋊C4×C139—46no—
186C22⋊C4×C139—22no—
187C22⋊C4×C139—26no—
188C22⋊C4×C139—26no—
189C22⋊C4×C139—22no—
190C22⋊C4×C139—26no—
191C22⋊C4×C139—26no—
192C22⋊C4×C139—22no—
193C22⋊C4×C139—22no—
194C22⋊C4×C139—43no—
195C22⋊C4×C139—43no—
196C42×C139—212no—
197C42×C139—26no—
198C42×C139—26no—
199C42×C139—26no—
200C42×C139—26no—
201C42×C139—26no—
202C23×C139—21no—
203C23×C139—21no—
204C23×C139—21no—
205C23×C139—21no—
206C23×C139—21no—
207C23×C139—21no—
208C23×C139—21no—
209C23×C139—21no—
210C23×C139—21no—
211C23×C139—21no—
212C23×C139—21no—
213C23×C139—21no—
214C23×C139C22×D412yes—
215C23×C1392−1+412yes—
216C23×C139C2511yescharacteristic
217Q8×C139—224no—
218Q8×C139—412no—
219Q8×C139#123116yes—
220D4×C139—28no—
221C2×C4×C139—21no—
222C2×C4×C139—21no—
223C2×C4×C139—23no—
224C2×C4×C139—23no—
225C2×C4×C139—21no—
226C2×C4×C139—21no—
227C2×C4×C139—224no—
228C2×C4×C139—23no—
229C2×C4×C139—21no—
230C2×C4×C139—21no—
231C2×C4×C139—23no—
232C2×C4×C139—23no—
233C2×C4×C139—23no—
234C2×C4×C139—21no—
235C2×C4×C139—23no—
236C2×C4×C139—23no—
237C2×C4×C139—23no—
238C2×C4×C139—23no—
239C2×C4×C139—21no—
240C2×C4×C139—23no—
241C2×C4×C139—21no—
242C2×C4×C139—23no—
243C2×C4×C139—21no—
244C2×C4×C139—21no—
245C2×C4×C139—21no—
246C2×C4×C139—23no—
247C2×C4×C139—23no—
248C2×C4×C139—23no—
249C2×C4×C139—23no—
250C2×C4×C139—23no—
251C2×C4×C139—23no—
252C2×C4×C139—23no—
253C2×C4×C139—21no—
254C2×C4×C139—23no—
255C2×C4×C139—412no—
256C2×C4×C139C22×D416yes—
257C2×C4×C139C22×D416yes—
258C2×C4×C139C2×#4116yes—
259C2×C4×C139C2×#4116yes—
260C2×C4×C1392−1+412yes—
261C2×C4×C1392−1+412yes—
262C22×C139—22no—
263C22×C139—22no—
264C22×C139—22no—
265C22×C139—22no—
266C22×C139—22no—
267C22×C139—22no—
268C22×C139—41no—
269C22×C139—41no—
270C22×C139—41no—
271C22×C139—41no—
272C22×C139—41no—
273C22×C139—41no—
274C22×C139—41no—
275C22×C139—41no—
276C22×C139C23×D411yescharacteristic
277C22×C139C22×#4111yescharacteristic
278C22×C139C22×#4111yescharacteristic
279C22×C139C2×2−1+411yescharacteristic
280C22×C139C2×2−1+411yescharacteristic
281C22×C139C2×2−1+411yescharacteristic
282C22×C139#58511yescharacteristic
283C4×C139—26no—
284C4×C139—22no—
285C4×C139—22no—
286C4×C139—43no—
287C4×C139—43no—
288C4×C139—41no—
289C4×C139—41no—
290C4×C139—43no—
291C4×C139—43no—
292C4×C139—43no—
293C4×C139—43no—
294C4×C139—41no—
295C4×C139C2×#123112yes—
296C2×C139—42no—
297C2×C139—42no—
298C2×C139C22×#12311yescharacteristic
299C2×C139#348611yescharacteristic
300C2×C139#349711yescharacteristic
301C2×C139#351611yescharacteristic
302C2×C139#351811yescharacteristic
303C2×C139#352311yescharacteristic
304C2×C139#352311yescharacteristic
305#35723C13911yesmaximal, characteristic, direct product factor, Sylow
306C139#3572311yescharacteristic, direct product factor, Sylow
307C2×D4×Q8C2×C13911yescharacteristic
308C2×#519C2×C13911yescharacteristic, complemented
309#2625C2×C13913yescomplemented
310#2499C2×C13913yescomplemented
311#2485C2×C13913yes—
312#2446C2×C13913yescomplemented
313#2446C2×C13913yescomplemented
314#2423C2×C13913yescomplemented
315#2421C2×C13913yescomplemented
316#2395C2×C13913yes—
317#2351C2×C13911yescharacteristic, complemented
318Q8×C4⋊C4C2×C13911yescharacteristic, complemented
319Q8×C22⋊C4C2×C13911yescharacteristic, complemented
320Q8×C22⋊C4C2×C13911yescharacteristic, complemented
321Q8×C22⋊C4C2×C13911yescharacteristic, complemented
322C23×Q8C22×C13911yescharacteristic
323C23×Q8C22×C13911yescharacteristic
324D4×Q8—28no—
325C2×C4⋊Q8C22×C13913yes—
326C2×C22⋊Q8C22×C13913yes—
327C2×C22⋊Q8C22×C13913yes—
328#519—28no—
329C2×C4×Q8C22×C13911yescharacteristic
330C2×C4×Q8C22×C13911yescharacteristic
331C2×C4×Q8C22×C13911yescharacteristic
332C2×C4×Q8C22×C13911yescharacteristic
333C2×C4×Q8C22×C13911yescharacteristic
334C2×C4×Q8C22×C13913yes—
335C2×C4×Q8C22×C13913yes—
336C2×C4×D4C22×C13913yes—
337C2×#117C22×C13913yes—
338C2×#117C22×C13913yes—
339#400C22×C13916yes—
340#400C22×C13913yes—
341#399C22×C13913yes—
342#398C22×C13916yes—
343#398C22×C13913yes—
344#397C22×C13913yes—
345#397C22×C13916yes—
346#397C22×C13913yes—
347#397C22×C13913yes—
348#394C22×C13911yescharacteristic
349#394C22×C13913yes—
350#391C22×C13913yes—
351#391C22×C13913yes—
352#391C22×C13913yes—
353#391C22×C13913yes—
354#391C22×C13913yes—
355#391C22×C13913yes—
356#389C22×C13913yes—
357#389C22×C13913yes—
358#389C22×C13913yes—
359#389C22×C13913yes—
360#388C22×C13916yes—
361#387C22×C13916yes—
362#387C22×C13916yes—
363#387C22×C13916yes—
364#384C22×C13913yes—
365#382C22×C13913yes—
366#380C22×C13913yes—
367#380C22×C13913yes—
368#380C22×C13913yes—
369C4×C4⋊C4C22×C13913yes—
370C4×C4⋊C4C22×C13913yes—
371C4×C22⋊C4C22×C13913yes—
372C4×C22⋊C4C22×C13913yes—
373C4×C22⋊C4C22×C13913yes—
374C22×Q8—24no—
375C22×Q8—24no—
376C22×Q8—24no—
377C22×Q8—24no—
378C22×Q8—24no—
379C22×Q8D4×C13918yes—
380C22×Q8C23×C13913yes—
381C22×Q8C23×C13913yes—
382C22×Q8C23×C13911yescharacteristic
383C22×D4C23×C13911yescharacteristic
384C23×C4C23×C13913yes—
385C23×C4C23×C13913yes—
386C4⋊Q8—212no—
387C22⋊Q8—212no—
388C22⋊Q8—212no—
389C4×Q8—212no—
390C4×Q8—212no—
391C4×Q8—24no—
392C4×Q8—24no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×Q8—24no—
396C4×D4—212no—
397#117—212no—
398#117—212no—
399C2×C4⋊C4C23×C13913yes—
400C2×C4⋊C4C23×C13913yes—
401C2×C4⋊C4C23×C13913yes—
402C2×C4⋊C4C23×C13913yes—
403C2×C4⋊C4C23×C13913yes—
404C2×C4⋊C4C23×C13913yes—
405C2×C4⋊C4C23×C13913yes—
406C2×C4⋊C4C23×C13913yes—
407C2×C4⋊C4C23×C13916yes—
408C2×C4⋊C4C23×C13911yescharacteristic
409C2×C4⋊C4C23×C13913yes—
410C2×C4⋊C4C23×C13913yes—
411C2×C4⋊C4C23×C13913yes—
412C2×C4⋊C4C23×C13916yes—
413C2×C22⋊C4C23×C13911yescharacteristic
414C2×C22⋊C4C23×C13913yes—
415C2×C22⋊C4C23×C13913yes—
416C2×C22⋊C4C23×C13913yes—
417C2×C22⋊C4C23×C13911yescharacteristic
418C2×C22⋊C4C23×C13911yescharacteristic
419C2×C22⋊C4C23×C13911yescharacteristic
420C2×C22⋊C4C23×C13913yes—
421C2×C22⋊C4C23×C13913yes—
422C2×C22⋊C4C23×C13913yes—
423C2×C42C23×C13913yes—
424C2×C42C23×C13913yes—
425C2×C42C23×C13916yes—
426C2×C42C23×C13913yes—
427C2×C42C23×C13913yes—
428C2×C42C23×C13913yes—
429#95C23×C13913yes—
430#95C23×C13913yes—
431#95C23×C13913yes—
432#95C23×C13913yes—
433#95C23×C13913yes—
434#95C23×C13913yes—
435#95C23×C13911yescharacteristic
436#95C23×C13913yes—
437#95C23×C13913yes—
438#95C23×C13913yes—
439#95C23×C13916yes—
440#95C23×C13916yes—
441#95C23×C13916yes—
442#95C23×C13916yes—
443C24C24×C13911yescharacteristic
444C24C24×C13911yescharacteristic
445C2×Q8—232no—
446C2×Q8—26no—
447C2×Q8—26no—
448C2×Q8—26no—
449C2×Q8—26no—
450C2×Q8—26no—
451C2×Q8—416no—
452C2×Q8C2×D4×C139112yes—
453C2×Q8C2×D4×C13914yes—
454C2×Q8#41×C13914yes—
455C2×Q8#41×C13914yes—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C22×C4—26no—
460C22×C4—26no—
461C22×C4—26no—
462C22×C4—26no—
463C22×C4—26no—
464C22×C4C2×D4×C139112yes—
465C22×C4C24×C13911yescharacteristic
466C22×C4C24×C13913yes—
467C22×C4C24×C13913yes—
468C22×C4C24×C13913yes—
469C22×C4C24×C13913yes—
470C22×C4C24×C13911yescharacteristic
471C22×C4C24×C13911yescharacteristic
472C22×C4C24×C13913yes—
473C22×C4C24×C13913yes—
474C22×C4C24×C13913yes—
475C22×C4C24×C13911yescharacteristic
476C22×C4C24×C13911yescharacteristic
477C22×C4C24×C13913yes—
478C4⋊C4—26no—
479C4⋊C4—26no—
480C4⋊C4—26no—
481C4⋊C4—26no—
482C4⋊C4—26no—
483C4⋊C4—26no—
484C4⋊C4—212no—
485C4⋊C4—26no—
486C4⋊C4—26no—
487C4⋊C4—22no—
488C4⋊C4—26no—
489C4⋊C4—26no—
490C4⋊C4—43no—
491C4⋊C4—46no—
492C22⋊C4—22no—
493C22⋊C4—26no—
494C22⋊C4—26no—
495C22⋊C4—22no—
496C22⋊C4—26no—
497C22⋊C4—26no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—43no—
501C22⋊C4—43no—
502C42—212no—
503C42—26no—
504C42—26no—
505C42—26no—
506C42—26no—
507C42—26no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23C22×D4×C13912yes—
521C232−1+4×C13912yes—
522C23C25×C13911yescharacteristic
523Q8—224no—
524Q8—412no—
525Q8#123×C139116yes—
526D4—28no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—23no—
530C2×C4—23no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—224no—
534C2×C4—23no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—23no—
538C2×C4—23no—
539C2×C4—23no—
540C2×C4—21no—
541C2×C4—23no—
542C2×C4—23no—
543C2×C4—23no—
544C2×C4—23no—
545C2×C4—21no—
546C2×C4—23no—
547C2×C4—21no—
548C2×C4—23no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—23no—
553C2×C4—23no—
554C2×C4—23no—
555C2×C4—23no—
556C2×C4—23no—
557C2×C4—23no—
558C2×C4—23no—
559C2×C4—21no—
560C2×C4—23no—
561C2×C4—412no—
562C2×C4C22×D4×C13916yes—
563C2×C4C22×D4×C13916yes—
564C2×C4C2×#41×C13916yes—
565C2×C4C2×#41×C13916yes—
566C2×C42−1+4×C13912yes—
567C2×C42−1+4×C13912yes—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22C23×D4×C13911yescharacteristic
583C22C22×#41×C13911yescharacteristic
584C22C22×#41×C13911yescharacteristic
585C22C2×2−1+4×C13911yescharacteristic
586C22C2×2−1+4×C13911yescharacteristic
587C22C2×2−1+4×C13911yescharacteristic
588C22#585×C13911yescharacteristic
589C4—26no—
590C4—22no—
591C4—22no—
592C4—43no—
593C4—43no—
594C4—41no—
595C4—41no—
596C4—43no—
597C4—43no—
598C4—43no—
599C4—43no—
600C4—41no—
601C4C2×#123×C139112yes—
602C2—42no—
603C2—42no—
604C2C22×#123×C13911yescharacteristic
605C2#3486×C13911yescharacteristic
606C2#3497×C13911yescharacteristic
607C2#3516×C13911yescharacteristic
608C2#3518×C13911yescharacteristic
609C2#3523×C13911yescharacteristic
610C2#3523×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC22×D4×C139C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#519×C139C2semidirect
3. #2625×C139C2semidirect
4. #2499×C139C2semidirect
6. #2446×C139C2semidirect
7. #2446×C139C2semidirect
8. #2423×C139C2semidirect
9. #2421×C139C2semidirect
11. #2351×C139C2semidirect
12. Q8×C4⋊C4×C139C2semidirect
13. Q8×C22⋊C4×C139C2semidirect
14. Q8×C22⋊C4×C139C2semidirect
15. Q8×C22⋊C4×C139C2semidirect
305. #35723C139direct (N × H)
306. C139#35723direct (N × H)
308. C2×#519C2×C139semidirect
309. #2625C2×C139semidirect
310. #2499C2×C139semidirect
312. #2446C2×C139semidirect
313. #2446C2×C139semidirect
314. #2423C2×C139semidirect
315. #2421C2×C139semidirect
317. #2351C2×C139semidirect
318. Q8×C4⋊C4C2×C139semidirect
319. Q8×C22⋊C4C2×C139semidirect
320. Q8×C22⋊C4C2×C139semidirect
321. Q8×C22⋊C4C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1392
C2×#519×C1392
#2625×C1392
#2499×C1392
#2485×C1392
#2446×C1392
#2423×C1392
#2421×C1392
#2395×C1392
#2351×C1392
Q8×C4⋊C4×C1392
Q8×C22⋊C4×C1392
#35723139