Finite Group Databasebeta

← C139×#35801 #48030397

Subgroups — C139×#35801 #48030397

Order 35584.

2342 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C139C211yesmaximal, characteristic
2C2×#519×C139C211yesmaximal, characteristic, complemented
3#2624×C139C213yesmaximal, complemented
4#2500×C139C213yesmaximal, complemented
5#2485×C139C213yesmaximal, complemented
6#2448×C139C213yesmaximal, complemented
7#2448×C139C213yesmaximal, complemented
8#2423×C139C213yesmaximal, complemented
9#2421×C139C213yesmaximal, complemented
10#2395×C139C213yesmaximal, complemented
11#2351×C139C211yesmaximal, characteristic, complemented
12Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
13#2341×C139C211yesmaximal, characteristic, complemented
14#2341×C139C211yesmaximal, characteristic, complemented
15Q8×C22⋊C4×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×Q8×C139C2211yescharacteristic
18#548×C139—28no—
19C2×#124×C139C2213yes—
20C2×C22⋊Q8×C139C2213yes—
21C2×#121×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×C139C2213yes—
34#399×C139C2216yes—
35#399×C139C2213yes—
36#398×C139C2213yes—
37#397×C139C2216yes—
38#397×C139C2211yescharacteristic
39#397×C139C2213yes—
40#397×C139C2213yes—
41#394×C139C2213yes—
42#394×C139C2216yes—
43#394×C139C2213yes—
44#391×C139C2213yes—
45#391×C139C2213yes—
46#390×C139C2213yes—
47#390×C139C2213yes—
48#390×C139C2213yes—
49#390×C139C2213yes—
50#389×C139C2213yes—
51#389×C139C2213yes—
52#389×C139C2213yes—
53#389×C139C2213yes—
54#388×C139C2216yes—
55#388×C139C2216yes—
56#388×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—
68C2×#41×C139—24no—
69C2×#41×C139—24no—
70C2×#41×C139—24no—
71C22×Q8×C139—24no—
72C22×Q8×C139—24no—
73C22×Q8×C139D418yes—
74C22×Q8×C139C2313yes—
75C22×Q8×C139C2311yescharacteristic
76C22×D4×C139C2313yes—
77C22×D4×C139C2313yes—
78C23×C4×C139C2313yes—
79C23×C4×C139C2313yes—
80#124×C139—212no—
81C22⋊Q8×C139—212no—
82#121×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×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×C22⋊C4×C139C2311yescharacteristic
107C2×C22⋊C4×C139C2313yes—
108C2×C22⋊C4×C139C2316yes—
109C2×C22⋊C4×C139C2311yescharacteristic
110C2×C22⋊C4×C139C2313yes—
111C2×C22⋊C4×C139C2311yescharacteristic
112C2×C22⋊C4×C139C2313yes—
113C2×C22⋊C4×C139C2313yes—
114C2×C22⋊C4×C139C2313yes—
115C2×C22⋊C4×C139C2313yes—
116C2×C22⋊C4×C139C2313yes—
117C2×C22⋊C4×C139C2316yes—
118C2×C22⋊C4×C139C2316yes—
119C2×C42×C139C2313yes—
120C2×C42×C139C2313yes—
121C2×C42×C139C2316yes—
122C2×C42×C139C2313yes—
123C2×C42×C139C2313yes—
124C2×C42×C139C2313yes—
125#95×C139C2311yescharacteristic
126#95×C139C2313yes—
127#95×C139C2313yes—
128#95×C139C2311yescharacteristic
129#95×C139C2313yes—
130#95×C139C2316yes—
131#95×C139C2311yescharacteristic
132#95×C139C2313yes—
133#95×C139C2313yes—
134#95×C139C2316yes—
135#95×C139C2313yes—
136#95×C139C2313yes—
137C24×C139C2413yes—
138C24×C139C2411yescharacteristic
139#41×C139—416no—
140C2×Q8×C139—232no—
141C2×Q8×C139—26no—
142C2×Q8×C139—26no—
143C2×Q8×C139C2×D4112yes—
144C2×Q8×C139C2×D414yes—
145C2×Q8×C139#4114yes—
146C2×Q8×C139#4114yes—
147C2×D4×C139—26no—
148C2×D4×C139—26no—
149C2×D4×C139—26no—
150C2×D4×C139—26no—
151C2×D4×C139—43no—
152C2×D4×C139—43no—
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×C139C2411yescharacteristic
161C22×C4×C139C2413yes—
162C22×C4×C139C2413yes—
163C22×C4×C139C2411yescharacteristic
164C22×C4×C139C2413yes—
165C22×C4×C139C2411yescharacteristic
166C22×C4×C139C2413yes—
167C22×C4×C139C2411yescharacteristic
168C22×C4×C139C2413yes—
169C22×C4×C139C2413yes—
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—26no—
179C4⋊C4×C139—26no—
180C4⋊C4×C139—22no—
181C4⋊C4×C139—43no—
182C4⋊C4×C139—43no—
183C4⋊C4×C139—43no—
184C4⋊C4×C139—46no—
185C22⋊C4×C139—22no—
186C22⋊C4×C139—26no—
187C22⋊C4×C139—22no—
188C22⋊C4×C139—26no—
189C22⋊C4×C139—212no—
190C22⋊C4×C139—22no—
191C22⋊C4×C139—26no—
192C22⋊C4×C139—43no—
193C22⋊C4×C139—43no—
194C22⋊C4×C139—46no—
195C22⋊C4×C139—43no—
196C22⋊C4×C139—43no—
197C22⋊C4×C139—46no—
198C42×C139—212no—
199C42×C139—26no—
200C42×C139—26no—
201C42×C139—26no—
202C42×C139—26no—
203C42×C139—26no—
204C23×C139—21no—
205C23×C139—21no—
206C23×C139—21no—
207C23×C139—21no—
208C23×C139—21no—
209C23×C139—21no—
210C23×C139—23no—
211C23×C139—23no—
212C23×C139—23no—
213C23×C139—23no—
214C23×C139—23no—
215C23×C139—23no—
216C23×C139—23no—
217C23×C139C22×D412yes—
218C23×C139C2511yescharacteristic
219Q8×C139—224no—
220Q8×C139#123116yes—
221D4×C139—412no—
222D4×C139—412no—
223C2×C4×C139—21no—
224C2×C4×C139—23no—
225C2×C4×C139—23no—
226C2×C4×C139—21no—
227C2×C4×C139—224no—
228C2×C4×C139—21no—
229C2×C4×C139—21no—
230C2×C4×C139—23no—
231C2×C4×C139—23no—
232C2×C4×C139—21no—
233C2×C4×C139—23no—
234C2×C4×C139—21no—
235C2×C4×C139—21no—
236C2×C4×C139—23no—
237C2×C4×C139—23no—
238C2×C4×C139—21no—
239C2×C4×C139—21no—
240C2×C4×C139—23no—
241C2×C4×C139—21no—
242C2×C4×C139—21no—
243C2×C4×C139—21no—
244C2×C4×C139—21no—
245C2×C4×C139—21no—
246C2×C4×C139—21no—
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—23no—
254C2×C4×C139—21no—
255C2×C4×C139—21no—
256C2×C4×C139—23no—
257C2×C4×C139—23no—
258C2×C4×C139—412no—
259C2×C4×C139C22×D416yes—
260C2×C4×C139C22×D416yes—
261C2×C4×C139C2×#4116yes—
262C2×C4×C139C2×#4116yes—
263C2×C4×C1392−1+412yes—
264C22×C139—22no—
265C22×C139—22no—
266C22×C139—22no—
267C22×C139—41no—
268C22×C139—41no—
269C22×C139—41no—
270C22×C139—41no—
271C22×C139—43no—
272C22×C139—43no—
273C22×C139—43no—
274C22×C139—43no—
275C22×C139—43no—
276C22×C139—43no—
277C22×C139—43no—
278C22×C139C23×D411yescharacteristic
279C22×C139C22×#4111yescharacteristic
280C22×C139C22×#4111yescharacteristic
281C22×C139C2×2−1+411yescharacteristic
282C22×C139#58511yescharacteristic
283C22×C139#58511yescharacteristic
284C22×C139#58511yescharacteristic
285C4×C139—26no—
286C4×C139—22no—
287C4×C139—41no—
288C4×C139—41no—
289C4×C139—43no—
290C4×C139—43no—
291C4×C139—41no—
292C4×C139—43no—
293C4×C139—41no—
294C4×C139—41no—
295C4×C139—43no—
296C4×C139—43no—
297C4×C139C2×#123112yes—
298C2×C139—42no—
299C2×C139—83no—
300C2×C139C22×#12311yescharacteristic
301C2×C139#348711yescharacteristic
302C2×C139#349711yescharacteristic
303C2×C139#351611yescharacteristic
304C2×C139#351811yescharacteristic
305C2×C139#352411yescharacteristic
306C2×C139#352411yescharacteristic
307#35801C13911yesmaximal, characteristic, direct product factor, Sylow
308C139#3580111yescharacteristic, direct product factor, Sylow
309C2×#548C2×C13911yescharacteristic
310C2×#519C2×C13911yescharacteristic, complemented
311#2624C2×C13913yescomplemented
312#2500C2×C13913yescomplemented
313#2485C2×C13913yescomplemented
314#2448C2×C13913yescomplemented
315#2448C2×C13913yescomplemented
316#2423C2×C13913yescomplemented
317#2421C2×C13913yescomplemented
318#2395C2×C13913yescomplemented
319#2351C2×C13911yescharacteristic, complemented
320Q8×C4⋊C4C2×C13911yescharacteristic, complemented
321#2341C2×C13911yescharacteristic, complemented
322#2341C2×C13911yescharacteristic, complemented
323Q8×C22⋊C4C2×C13911yescharacteristic, complemented
324C22×#41C22×C13911yescharacteristic
325C23×Q8C22×C13911yescharacteristic
326#548—28no—
327C2×#124C22×C13913yes—
328C2×C22⋊Q8C22×C13913yes—
329C2×#121C22×C13913yes—
330#519—28no—
331C2×C4×Q8C22×C13911yescharacteristic
332C2×C4×Q8C22×C13911yescharacteristic
333C2×C4×Q8C22×C13911yescharacteristic
334C2×C4×Q8C22×C13911yescharacteristic
335C2×C4×Q8C22×C13911yescharacteristic
336C2×C4×Q8C22×C13913yes—
337C2×C4×Q8C22×C13913yes—
338C2×C4×D4C22×C13913yes—
339C2×#117C22×C13913yes—
340C2×#117C22×C13913yes—
341#400C22×C13913yes—
342#399C22×C13916yes—
343#399C22×C13913yes—
344#398C22×C13913yes—
345#397C22×C13916yes—
346#397C22×C13911yescharacteristic
347#397C22×C13913yes—
348#397C22×C13913yes—
349#394C22×C13913yes—
350#394C22×C13916yes—
351#394C22×C13913yes—
352#391C22×C13913yes—
353#391C22×C13913yes—
354#390C22×C13913yes—
355#390C22×C13913yes—
356#390C22×C13913yes—
357#390C22×C13913yes—
358#389C22×C13913yes—
359#389C22×C13913yes—
360#389C22×C13913yes—
361#389C22×C13913yes—
362#388C22×C13916yes—
363#388C22×C13916yes—
364#388C22×C13916yes—
365#387C22×C13916yes—
366#384C22×C13913yes—
367#382C22×C13913yes—
368#380C22×C13913yes—
369#380C22×C13913yes—
370#380C22×C13913yes—
371C4×C4⋊C4C22×C13913yes—
372C4×C4⋊C4C22×C13913yes—
373C4×C22⋊C4C22×C13913yes—
374C4×C22⋊C4C22×C13913yes—
375C4×C22⋊C4C22×C13913yes—
376C2×#41—24no—
377C2×#41—24no—
378C2×#41—24no—
379C22×Q8—24no—
380C22×Q8—24no—
381C22×Q8D4×C13918yes—
382C22×Q8C23×C13913yes—
383C22×Q8C23×C13911yescharacteristic
384C22×D4C23×C13913yes—
385C22×D4C23×C13913yes—
386C23×C4C23×C13913yes—
387C23×C4C23×C13913yes—
388#124—212no—
389C22⋊Q8—212no—
390#121—212no—
391C4×Q8—212no—
392C4×Q8—212no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×Q8—24no—
396C4×Q8—24no—
397C4×Q8—24no—
398C4×D4—212no—
399#117—212no—
400#117—212no—
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×C13913yes—
408C2×C4⋊C4C23×C13913yes—
409C2×C4⋊C4C23×C13911yescharacteristic
410C2×C4⋊C4C23×C13913yes—
411C2×C4⋊C4C23×C13913yes—
412C2×C4⋊C4C23×C13913yes—
413C2×C4⋊C4C23×C13916yes—
414C2×C22⋊C4C23×C13911yescharacteristic
415C2×C22⋊C4C23×C13913yes—
416C2×C22⋊C4C23×C13911yescharacteristic
417C2×C22⋊C4C23×C13913yes—
418C2×C22⋊C4C23×C13916yes—
419C2×C22⋊C4C23×C13911yescharacteristic
420C2×C22⋊C4C23×C13913yes—
421C2×C22⋊C4C23×C13913yes—
422C2×C22⋊C4C23×C13913yes—
423C2×C22⋊C4C23×C13913yes—
424C2×C22⋊C4C23×C13913yes—
425C2×C22⋊C4C23×C13916yes—
426C2×C22⋊C4C23×C13916yes—
427C2×C42C23×C13913yes—
428C2×C42C23×C13913yes—
429C2×C42C23×C13916yes—
430C2×C42C23×C13913yes—
431C2×C42C23×C13913yes—
432C2×C42C23×C13913yes—
433#95C23×C13911yescharacteristic
434#95C23×C13911yescharacteristic
435#95C23×C13913yes—
436#95C23×C13913yes—
437#95C23×C13913yes—
438#95C23×C13913yes—
439#95C23×C13911yescharacteristic
440#95C23×C13913yes—
441#95C23×C13913yes—
442#95C23×C13913yes—
443#95C23×C13916yes—
444#95C23×C13916yes—
445C24C24×C13913yes—
446C24C24×C13911yescharacteristic
447#41—416no—
448C2×Q8—232no—
449C2×Q8—26no—
450C2×Q8—26no—
451C2×Q8C2×D4×C139112yes—
452C2×Q8C2×D4×C13914yes—
453C2×Q8#41×C13914yes—
454C2×Q8#41×C13914yes—
455C2×D4—26no—
456C2×D4—26no—
457C2×D4—26no—
458C2×D4—26no—
459C2×D4—43no—
460C2×D4—43no—
461C22×C4—26no—
462C22×C4—26no—
463C22×C4—26no—
464C22×C4—26no—
465C22×C4—26no—
466C22×C4C2×D4×C139112yes—
467C22×C4C24×C13911yescharacteristic
468C22×C4C24×C13911yescharacteristic
469C22×C4C24×C13913yes—
470C22×C4C24×C13913yes—
471C22×C4C24×C13911yescharacteristic
472C22×C4C24×C13913yes—
473C22×C4C24×C13911yescharacteristic
474C22×C4C24×C13913yes—
475C22×C4C24×C13911yescharacteristic
476C22×C4C24×C13913yes—
477C22×C4C24×C13913yes—
478C22×C4C24×C13911yescharacteristic
479C22×C4C24×C13913yes—
480C4⋊C4—26no—
481C4⋊C4—26no—
482C4⋊C4—26no—
483C4⋊C4—26no—
484C4⋊C4—26no—
485C4⋊C4—26no—
486C4⋊C4—26no—
487C4⋊C4—26no—
488C4⋊C4—22no—
489C4⋊C4—43no—
490C4⋊C4—43no—
491C4⋊C4—43no—
492C4⋊C4—46no—
493C22⋊C4—22no—
494C22⋊C4—26no—
495C22⋊C4—22no—
496C22⋊C4—26no—
497C22⋊C4—212no—
498C22⋊C4—22no—
499C22⋊C4—26no—
500C22⋊C4—43no—
501C22⋊C4—43no—
502C22⋊C4—46no—
503C22⋊C4—43no—
504C22⋊C4—43no—
505C22⋊C4—46no—
506C42—212no—
507C42—26no—
508C42—26no—
509C42—26no—
510C42—26no—
511C42—26no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—23no—
519C23—23no—
520C23—23no—
521C23—23no—
522C23—23no—
523C23—23no—
524C23—23no—
525C23C22×D4×C13912yes—
526C23C25×C13911yescharacteristic
527Q8—224no—
528Q8#123×C139116yes—
529D4—412no—
530D4—412no—
531C2×C4—21no—
532C2×C4—23no—
533C2×C4—23no—
534C2×C4—21no—
535C2×C4—224no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—23no—
539C2×C4—23no—
540C2×C4—21no—
541C2×C4—23no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—23no—
545C2×C4—23no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—23no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—23no—
556C2×C4—23no—
557C2×C4—23no—
558C2×C4—23no—
559C2×C4—23no—
560C2×C4—23no—
561C2×C4—23no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—23no—
565C2×C4—23no—
566C2×C4—412no—
567C2×C4C22×D4×C13916yes—
568C2×C4C22×D4×C13916yes—
569C2×C4C2×#41×C13916yes—
570C2×C4C2×#41×C13916yes—
571C2×C42−1+4×C13912yes—
572C22—22no—
573C22—22no—
574C22—22no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—43no—
580C22—43no—
581C22—43no—
582C22—43no—
583C22—43no—
584C22—43no—
585C22—43no—
586C22C23×D4×C13911yescharacteristic
587C22C22×#41×C13911yescharacteristic
588C22C22×#41×C13911yescharacteristic
589C22C2×2−1+4×C13911yescharacteristic
590C22#585×C13911yescharacteristic
591C22#585×C13911yescharacteristic
592C22#585×C13911yescharacteristic
593C4—26no—
594C4—22no—
595C4—41no—
596C4—43no—
597C4—41no—
598C4—43no—
599C4—41no—
600C4—43no—
601C4—41no—
602C4—41no—
603C4—43no—
604C4—43no—
605C4C2×#123×C139112yes—
606C2—42no—
607C2—83no—
608C2C22×#123×C13911yescharacteristic
609C2#3487×C13911yescharacteristic
610C2#3497×C13911yescharacteristic
611C2#3516×C13911yescharacteristic
612C2#3518×C13911yescharacteristic
613C2#3524×C13911yescharacteristic
614C2#3524×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC2×#548×C139C2
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. #2624×C139C2semidirect
4. #2500×C139C2semidirect
5. #2485×C139C2semidirect
6. #2448×C139C2semidirect
7. #2448×C139C2semidirect
8. #2423×C139C2semidirect
9. #2421×C139C2semidirect
10. #2395×C139C2semidirect
11. #2351×C139C2semidirect
12. Q8×C4⋊C4×C139C2semidirect
13. #2341×C139C2semidirect
14. #2341×C139C2semidirect
15. Q8×C22⋊C4×C139C2semidirect
307. #35801C139direct (N × H)
308. C139#35801direct (N × H)
310. C2×#519C2×C139semidirect
311. #2624C2×C139semidirect
312. #2500C2×C139semidirect
313. #2485C2×C139semidirect
314. #2448C2×C139semidirect
315. #2448C2×C139semidirect
316. #2423C2×C139semidirect
317. #2421C2×C139semidirect
318. #2395C2×C139semidirect
319. #2351C2×C139semidirect
320. Q8×C4⋊C4C2×C139semidirect
321. #2341C2×C139semidirect
322. #2341C2×C139semidirect
323. 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×#548×C1392
C2×#519×C1392
#2624×C1392
#2500×C1392
#2485×C1392
#2448×C1392
#2423×C1392
#2421×C1392
#2395×C1392
#2351×C1392
Q8×C4⋊C4×C1392
#2341×C1392
Q8×C22⋊C4×C1392
#35801139