Finite Group Databasebeta

← C139×#36458 #48031054

Subgroups — C139×#36458 #48031054

Order 35584.

1834 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2860×C139C213yesmaximal, complemented
2#2513×C139C213yesmaximal, complemented
3#2512×C139C213yesmaximal, complemented
4#2512×C139C213yesmaximal, complemented
5#2497×C139C213yesmaximal, complemented
6#2496×C139C213yesmaximal, complemented
7#2495×C139C213yesmaximal, complemented
8#2351×C139C211yesmaximal, characteristic, complemented
9Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
10Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
11#2341×C139C211yesmaximal, characteristic
12#2341×C139C211yesmaximal, characteristic
13#2341×C139C211yesmaximal, characteristic
14C4×#126×C139C213yesmaximal, complemented
15C42×Q8×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C2×#126×C139C2213yes—
18C2×#126×C139C2216yes—
19C2×C4×Q8×C139C2211yescharacteristic
20C2×C4×Q8×C139C2211yescharacteristic
21C2×C4×Q8×C139C2211yescharacteristic
22C2×C4×Q8×C139C2211yescharacteristic
23C2×C4×Q8×C139C2211yescharacteristic
24C2×C4×Q8×C139C2211yescharacteristic
25#400×C139C2216yes—
26#397×C139C2216yes—
27#397×C139C2216yes—
28#396×C139C2216yes—
29#390×C139C2213yes—
30#390×C139C2213yes—
31#390×C139C2213yes—
32#390×C139C2213yes—
33#390×C139C2213yes—
34#390×C139C2213yes—
35#389×C139C2213yes—
36#389×C139C2213yes—
37#389×C139C2213yes—
38#389×C139C2213yes—
39#389×C139C2213yes—
40#389×C139C2213yes—
41#388×C139C2213yes—
42#388×C139C2216yes—
43#388×C139C2213yes—
44#388×C139C2216yes—
45#388×C139C2213yes—
46#387×C139C2211yescharacteristic
47#387×C139C2213yes—
48#387×C139C2213yes—
49#384×C139C2213yes—
50#384×C139C2213yes—
51#383×C139C2213yes—
52#382×C139C2213yes—
53#380×C139C2213yes—
54#380×C139C2213yes—
55#380×C139C2213yes—
56C4×C4⋊C4×C139C2213yes—
57C4×C4⋊C4×C139C2213yes—
58C4×C4⋊C4×C139C2213yes—
59C4×C4⋊C4×C139C2213yes—
60C4×C4⋊C4×C139C2213yes—
61C4×C4⋊C4×C139C2213yes—
62C4×C22⋊C4×C139C2213yes—
63C4×C22⋊C4×C139C2213yes—
64C4×C22⋊C4×C139C2213yes—
65C43×C139C2213yes—
66C2×#41×C139—24no—
67C2×#41×C139—24no—
68C2×#41×C139—24no—
69C22×Q8×C139C2311yescharacteristic
70C22×D4×C139C2313yes—
71C23×C4×C139C2313yes—
72#126×C139—212no—
73#126×C139—412no—
74C4×Q8×C139—24no—
75C4×Q8×C139—24no—
76C4×Q8×C139—24no—
77C4×Q8×C139—24no—
78C4×Q8×C139—24no—
79C4×Q8×C139—24no—
80C2×C4⋊C4×C139C2313yes—
81C2×C4⋊C4×C139C2313yes—
82C2×C4⋊C4×C139C2313yes—
83C2×C4⋊C4×C139C2313yes—
84C2×C4⋊C4×C139C2313yes—
85C2×C4⋊C4×C139C2313yes—
86C2×C4⋊C4×C139C2313yes—
87C2×C4⋊C4×C139C2313yes—
88C2×C4⋊C4×C139C2313yes—
89C2×C4⋊C4×C139C2311yescharacteristic
90C2×C4⋊C4×C139C2313yes—
91C2×C4⋊C4×C139C2316yes—
92C2×C4⋊C4×C139C2316yes—
93C2×C4⋊C4×C139C2311yescharacteristic
94C2×C22⋊C4×C139C2313yes—
95C2×C22⋊C4×C139C2313yes—
96C2×C22⋊C4×C139C2313yes—
97C2×C22⋊C4×C139C2313yes—
98C2×C22⋊C4×C139C2313yes—
99C2×C22⋊C4×C139C2316yes—
100C2×C22⋊C4×C139C2316yes—
101C2×C22⋊C4×C139C2316yes—
102C2×C22⋊C4×C139C2313yes—
103C2×C42×C139C2313yes—
104C2×C42×C139C2313yes—
105C2×C42×C139C2313yes—
106C2×C42×C139C2313yes—
107C2×C42×C139C2313yes—
108C2×C42×C139C2313yes—
109C2×C42×C139C2313yes—
110C2×C42×C139C2313yes—
111C2×C42×C139C2311yescharacteristic
112C2×C42×C139C2313yes—
113#95×C139C2316yes—
114#95×C139C2313yes—
115#95×C139C2313yes—
116#95×C139C2313yes—
117#95×C139C2316yes—
118#95×C139C2313yes—
119#95×C139C2313yes—
120#95×C139C2313yes—
121#95×C139C2311yescharacteristic
122#95×C139C2311yescharacteristic
123#95×C139C2311yescharacteristic
124#95×C139C2311yescharacteristic
125#95×C139C2313yes—
126#95×C139C2313yes—
127C24×C139C2413yes—
128#41×C139—416no—
129C2×Q8×C139#4114yes—
130C2×Q8×C139#4114yes—
131C2×Q8×C139#4114yes—
132C2×D4×C139—26no—
133C2×D4×C139—26no—
134C2×D4×C139—26no—
135C22×C4×C139—26no—
136C22×C4×C139—26no—
137C22×C4×C139—26no—
138C22×C4×C139C2411yescharacteristic
139C22×C4×C139C2411yescharacteristic
140C22×C4×C139C2413yes—
141C22×C4×C139C2413yes—
142C22×C4×C139C2413yes—
143C22×C4×C139C2413yes—
144C22×C4×C139C2413yes—
145C22×C4×C139C2413yes—
146C22×C4×C139C2411yescharacteristic
147C22×C4×C139C2411yescharacteristic
148C22×C4×C139C2411yescharacteristic
149C22×C4×C139C2411yescharacteristic
150C22×C4×C139C2411yescharacteristic
151C22×C4×C139C2413yes—
152C4⋊C4×C139—26no—
153C4⋊C4×C139—26no—
154C4⋊C4×C139—26no—
155C4⋊C4×C139—26no—
156C4⋊C4×C139—26no—
157C4⋊C4×C139—26no—
158C4⋊C4×C139—26no—
159C4⋊C4×C139—26no—
160C4⋊C4×C139—26no—
161C4⋊C4×C139—22no—
162C4⋊C4×C139—43no—
163C4⋊C4×C139—46no—
164C4⋊C4×C139—46no—
165C4⋊C4×C139#4114yescomplemented
166C22⋊C4×C139—26no—
167C22⋊C4×C139—26no—
168C22⋊C4×C139—26no—
169C22⋊C4×C139—26no—
170C22⋊C4×C139—26no—
171C22⋊C4×C139—46no—
172C22⋊C4×C139—43no—
173C22⋊C4×C139—46no—
174C22⋊C4×C139—46no—
175C42×C139—26no—
176C42×C139—26no—
177C42×C139—26no—
178C42×C139—26no—
179C42×C139—26no—
180C42×C139—26no—
181C42×C139—26no—
182C42×C139—26no—
183C42×C139—22no—
184C42×C139—43no—
185C23×C139—23no—
186C23×C139—23no—
187C23×C139—23no—
188C23×C139—23no—
189C23×C139—23no—
190C23×C139—23no—
191C23×C139—23no—
192C23×C139C2511yescharacteristic
193Q8×C139#126116yescomplemented
194D4×C139—412no—
195C2×C4×C139—21no—
196C2×C4×C139—21no—
197C2×C4×C139—21no—
198C2×C4×C139—21no—
199C2×C4×C139—21no—
200C2×C4×C139—21no—
201C2×C4×C139—21no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—21no—
205C2×C4×C139—21no—
206C2×C4×C139—23no—
207C2×C4×C139—23no—
208C2×C4×C139—23no—
209C2×C4×C139—23no—
210C2×C4×C139—23no—
211C2×C4×C139—23no—
212C2×C4×C139—23no—
213C2×C4×C139—23no—
214C2×C4×C139—23no—
215C2×C4×C139—21no—
216C2×C4×C139—21no—
217C2×C4×C139—21no—
218C2×C4×C139—23no—
219C2×C4×C139—23no—
220C2×C4×C139—23no—
221C2×C4×C139—23no—
222C2×C4×C139—23no—
223C2×C4×C139—23no—
224C2×C4×C139—21no—
225C2×C4×C139—23no—
226C2×C4×C139—23no—
227C2×C4×C139—21no—
228C2×C4×C139—23no—
229C2×C4×C139—412no—
230C2×C4×C139C2×#4112yes—
231C2×C4×C139C2×#4112yes—
232C2×C4×C139C2×#4112yes—
233C2×C4×C139C2×#4116yes—
234C2×C4×C139C2×#4116yes—
235C2×C4×C139C2×#4116yes—
236C2×C4×C139H(5,𝔽2)12yes—
237C2×C4×C1392−1+412yes—
238C22×C139—43no—
239C22×C139—43no—
240C22×C139—43no—
241C22×C139—43no—
242C22×C139—43no—
243C22×C139—43no—
244C22×C139—43no—
245C22×C139C22×#4111yescharacteristic
246C22×C139C22×#4111yescharacteristic
247C22×C139C22×#4111yescharacteristic
248C22×C139C22×#4111yescharacteristic
249C22×C139C2×H(5,𝔽2)11yescharacteristic
250C22×C139C2×2−1+411yescharacteristic
251C22×C139#58511yescharacteristic
252C4×C139—22no—
253C4×C139—22no—
254C4×C139—22no—
255C4×C139—22no—
256C4×C139—22no—
257C4×C139—41no—
258C4×C139—43no—
259C4×C139—43no—
260C4×C139—43no—
261C4×C139—41no—
262C4×C139—43no—
263C4×C139—43no—
264C4×C139—43no—
265C4×C139C2×#126112yes—
266C2×C139—83no—
267C2×C139C22×#12611yescharacteristic
268C2×C139#348011yescharacteristic
269C2×C139#348211yescharacteristic
270C2×C139#348311yescharacteristic
271C2×C139#351611yescharacteristic
272C2×C139#351711yescharacteristic
273C2×C139#352211yescharacteristic
274#36458C13911yesmaximal, characteristic, direct product factor, Sylow
275C139#3645811yescharacteristic, direct product factor, Sylow
276#2860C2×C13913yescomplemented
277#2513C2×C13913yescomplemented
278#2512C2×C13913yescomplemented
279#2512C2×C13913yescomplemented
280#2497C2×C13913yescomplemented
281#2496C2×C13913yescomplemented
282#2495C2×C13913yescomplemented
283#2351C2×C13911yescharacteristic, complemented
284Q8×C4⋊C4C2×C13911yescharacteristic, complemented
285Q8×C4⋊C4C2×C13911yescharacteristic, complemented
286#2341C2×C13911yescharacteristic
287#2341C2×C13911yescharacteristic
288#2341C2×C13911yescharacteristic
289C4×#126C2×C13913yescomplemented
290C42×Q8C2×C13911yescharacteristic, complemented
291C22×#41C22×C13911yescharacteristic
292C2×#126C22×C13913yes—
293C2×#126C22×C13916yes—
294C2×C4×Q8C22×C13911yescharacteristic
295C2×C4×Q8C22×C13911yescharacteristic
296C2×C4×Q8C22×C13911yescharacteristic
297C2×C4×Q8C22×C13911yescharacteristic
298C2×C4×Q8C22×C13911yescharacteristic
299C2×C4×Q8C22×C13911yescharacteristic
300#400C22×C13916yes—
301#397C22×C13916yes—
302#397C22×C13916yes—
303#396C22×C13916yes—
304#390C22×C13913yes—
305#390C22×C13913yes—
306#390C22×C13913yes—
307#390C22×C13913yes—
308#390C22×C13913yes—
309#390C22×C13913yes—
310#389C22×C13913yes—
311#389C22×C13913yes—
312#389C22×C13913yes—
313#389C22×C13913yes—
314#389C22×C13913yes—
315#389C22×C13913yes—
316#388C22×C13913yes—
317#388C22×C13913yes—
318#388C22×C13913yes—
319#388C22×C13916yes—
320#388C22×C13916yes—
321#387C22×C13911yescharacteristic
322#387C22×C13913yes—
323#387C22×C13913yes—
324#384C22×C13913yes—
325#384C22×C13913yes—
326#383C22×C13913yes—
327#382C22×C13913yes—
328#380C22×C13913yes—
329#380C22×C13913yes—
330#380C22×C13913yes—
331C4×C4⋊C4C22×C13913yes—
332C4×C4⋊C4C22×C13913yes—
333C4×C4⋊C4C22×C13913yes—
334C4×C4⋊C4C22×C13913yes—
335C4×C4⋊C4C22×C13913yes—
336C4×C4⋊C4C22×C13913yes—
337C4×C22⋊C4C22×C13913yes—
338C4×C22⋊C4C22×C13913yes—
339C4×C22⋊C4C22×C13913yes—
340C43C22×C13913yes—
341C2×#41—24no—
342C2×#41—24no—
343C2×#41—24no—
344C22×Q8C23×C13911yescharacteristic
345C22×D4C23×C13913yes—
346C23×C4C23×C13913yes—
347#126—212no—
348#126—412no—
349C4×Q8—24no—
350C4×Q8—24no—
351C4×Q8—24no—
352C4×Q8—24no—
353C4×Q8—24no—
354C4×Q8—24no—
355C2×C4⋊C4C23×C13913yes—
356C2×C4⋊C4C23×C13913yes—
357C2×C4⋊C4C23×C13913yes—
358C2×C4⋊C4C23×C13913yes—
359C2×C4⋊C4C23×C13913yes—
360C2×C4⋊C4C23×C13913yes—
361C2×C4⋊C4C23×C13913yes—
362C2×C4⋊C4C23×C13913yes—
363C2×C4⋊C4C23×C13913yes—
364C2×C4⋊C4C23×C13911yescharacteristic
365C2×C4⋊C4C23×C13916yes—
366C2×C4⋊C4C23×C13916yes—
367C2×C4⋊C4C23×C13913yes—
368C2×C4⋊C4C23×C13911yescharacteristic
369C2×C22⋊C4C23×C13913yes—
370C2×C22⋊C4C23×C13913yes—
371C2×C22⋊C4C23×C13913yes—
372C2×C22⋊C4C23×C13913yes—
373C2×C22⋊C4C23×C13913yes—
374C2×C22⋊C4C23×C13916yes—
375C2×C22⋊C4C23×C13916yes—
376C2×C22⋊C4C23×C13913yes—
377C2×C22⋊C4C23×C13916yes—
378C2×C42C23×C13913yes—
379C2×C42C23×C13913yes—
380C2×C42C23×C13913yes—
381C2×C42C23×C13913yes—
382C2×C42C23×C13913yes—
383C2×C42C23×C13913yes—
384C2×C42C23×C13913yes—
385C2×C42C23×C13913yes—
386C2×C42C23×C13911yescharacteristic
387C2×C42C23×C13913yes—
388#95C23×C13911yescharacteristic
389#95C23×C13911yescharacteristic
390#95C23×C13911yescharacteristic
391#95C23×C13913yes—
392#95C23×C13913yes—
393#95C23×C13913yes—
394#95C23×C13911yescharacteristic
395#95C23×C13916yes—
396#95C23×C13913yes—
397#95C23×C13913yes—
398#95C23×C13913yes—
399#95C23×C13913yes—
400#95C23×C13913yes—
401#95C23×C13916yes—
402C24C24×C13913yes—
403#41—416no—
404C2×Q8#41×C13914yes—
405C2×Q8#41×C13914yes—
406C2×Q8#41×C13914yes—
407C2×D4—26no—
408C2×D4—26no—
409C2×D4—26no—
410C22×C4—26no—
411C22×C4—26no—
412C22×C4—26no—
413C22×C4C24×C13911yescharacteristic
414C22×C4C24×C13911yescharacteristic
415C22×C4C24×C13913yes—
416C22×C4C24×C13913yes—
417C22×C4C24×C13913yes—
418C22×C4C24×C13913yes—
419C22×C4C24×C13913yes—
420C22×C4C24×C13913yes—
421C22×C4C24×C13911yescharacteristic
422C22×C4C24×C13911yescharacteristic
423C22×C4C24×C13911yescharacteristic
424C22×C4C24×C13911yescharacteristic
425C22×C4C24×C13911yescharacteristic
426C22×C4C24×C13913yes—
427C4⋊C4—26no—
428C4⋊C4—26no—
429C4⋊C4—26no—
430C4⋊C4—26no—
431C4⋊C4—26no—
432C4⋊C4—26no—
433C4⋊C4—26no—
434C4⋊C4—26no—
435C4⋊C4—26no—
436C4⋊C4—22no—
437C4⋊C4—43no—
438C4⋊C4—46no—
439C4⋊C4—46no—
440C4⋊C4#41×C13914yescomplemented
441C22⋊C4—26no—
442C22⋊C4—26no—
443C22⋊C4—26no—
444C22⋊C4—26no—
445C22⋊C4—26no—
446C22⋊C4—46no—
447C22⋊C4—43no—
448C22⋊C4—46no—
449C22⋊C4—46no—
450C42—26no—
451C42—26no—
452C42—26no—
453C42—26no—
454C42—26no—
455C42—26no—
456C42—26no—
457C42—26no—
458C42—22no—
459C42—43no—
460C23—23no—
461C23—23no—
462C23—23no—
463C23—23no—
464C23—23no—
465C23—23no—
466C23—23no—
467C23C25×C13911yescharacteristic
468Q8#126×C139116yescomplemented
469D4—412no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—23no—
482C2×C4—23no—
483C2×C4—23no—
484C2×C4—23no—
485C2×C4—23no—
486C2×C4—23no—
487C2×C4—23no—
488C2×C4—23no—
489C2×C4—23no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—23no—
494C2×C4—23no—
495C2×C4—23no—
496C2×C4—23no—
497C2×C4—23no—
498C2×C4—23no—
499C2×C4—21no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—21no—
503C2×C4—23no—
504C2×C4—412no—
505C2×C4C2×#41×C13912yes—
506C2×C4C2×#41×C13912yes—
507C2×C4C2×#41×C13912yes—
508C2×C4C2×#41×C13916yes—
509C2×C4C2×#41×C13916yes—
510C2×C4C2×#41×C13916yes—
511C2×C4H(5,𝔽2)×C13912yes—
512C2×C42−1+4×C13912yes—
513C22—43no—
514C22—43no—
515C22—43no—
516C22—43no—
517C22—43no—
518C22—43no—
519C22—43no—
520C22C22×#41×C13911yescharacteristic
521C22C22×#41×C13911yescharacteristic
522C22C22×#41×C13911yescharacteristic
523C22C22×#41×C13911yescharacteristic
524C22C2×H(5,𝔽2)×C13911yescharacteristic
525C22C2×2−1+4×C13911yescharacteristic
526C22#585×C13911yescharacteristic
527C4—22no—
528C4—22no—
529C4—22no—
530C4—22no—
531C4—22no—
532C4—41no—
533C4—43no—
534C4—43no—
535C4—43no—
536C4—41no—
537C4—43no—
538C4—43no—
539C4—43no—
540C4C2×#126×C139112yes—
541C2—83no—
542C2C22×#126×C13911yescharacteristic
543C2#3480×C13911yescharacteristic
544C2#3482×C13911yescharacteristic
545C2#3483×C13911yescharacteristic
546C2#3516×C13911yescharacteristic
547C2#3517×C13911yescharacteristic
548C2#3522×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. #2860×C139C2semidirect
2. #2513×C139C2semidirect
3. #2512×C139C2semidirect
4. #2512×C139C2semidirect
5. #2497×C139C2semidirect
6. #2496×C139C2semidirect
7. #2495×C139C2semidirect
8. #2351×C139C2semidirect
9. Q8×C4⋊C4×C139C2semidirect
10. Q8×C4⋊C4×C139C2semidirect
14. C4×#126×C139C2semidirect
15. C42×Q8×C139C2semidirect
165. C4⋊C4×C139#41semidirect
193. Q8×C139#126semidirect
274. #36458C139direct (N × H)
275. C139#36458direct (N × H)
276. #2860C2×C139semidirect
277. #2513C2×C139semidirect
278. #2512C2×C139semidirect
279. #2512C2×C139semidirect
280. #2497C2×C139semidirect
281. #2496C2×C139semidirect
282. #2495C2×C139semidirect
283. #2351C2×C139semidirect
284. Q8×C4⋊C4C2×C139semidirect
285. Q8×C4⋊C4C2×C139semidirect
289. C4×#126C2×C139semidirect
290. C42×Q8C2×C139semidirect
440. C4⋊C4#41×C139semidirect
468. Q8#126×C139semidirect

Maximal subgroups

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

subgroupindex
#2860×C1392
#2513×C1392
#2512×C1392
#2497×C1392
#2496×C1392
#2495×C1392
#2351×C1392
Q8×C4⋊C4×C1392
#2341×C1392
C4×#126×C1392
C42×Q8×C1392
#36458139