Finite Group Databasebeta

← C139×#26012 #48020608

Subgroups — C139×#26012 #48020608

Order 35584.

732 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
1#2441×C139C211yesmaximal, characteristic
2#2344×C139C211yesmaximal, characteristic
3#2099×C139C211yesmaximal, characteristic, complemented
4#2088×C139C211yesmaximal, characteristic, complemented
5#2087×C139C211yesmaximal, characteristic, complemented
6#2059×C139C211yesmaximal, characteristic, complemented
7#1989×C139C211yesmaximal, characteristic, complemented
8#1947×C139C211yesmaximal, characteristic, complemented
9#1920×C139C211yesmaximal, characteristic, complemented
10#1919×C139C211yesmaximal, characteristic, complemented
11#1854×C139C211yesmaximal, characteristic
12#1851×C139C211yesmaximal, characteristic
13#1824×C139C211yesmaximal, characteristic
14#1809×C139C211yesmaximal, characteristic
15#1736×C139C211yesmaximal, characteristic
16C22×M16×C139C2211yescharacteristic
17C2×#125×C139C2211yescharacteristic
18C2×#117×C139—21no—
19C2×#117×C139C2211yescharacteristic
20C22×C4⋊C4×C139C2211yescharacteristic
21C2×#107×C139C2211yescharacteristic
22C2×#107×C139C2211yescharacteristic
23C2×#106×C139C2211yescharacteristic
24C2×#106×C139C2211yescharacteristic
25C2×C4⋊C8×C139C2211yescharacteristic
26C2×C4⋊C8×C139C2211yescharacteristic
27C2×C22⋊C8×C139C2211yescharacteristic
28#399×C139—21no—
29#396×C139—21no—
30#389×C139—21no—
31#389×C139C2211yescharacteristic
32#389×C139C2211yescharacteristic
33#389×C139C2211yescharacteristic
34#389×C139C2211yescharacteristic
35#387×C139—21no—
36#387×C139—21no—
37#387×C139—21no—
38#384×C139C2211yescharacteristic
39#381×C139—21no—
40#380×C139C2211yescharacteristic
41#380×C139C2211yescharacteristic
42C4×C4⋊C4×C139C2211yescharacteristic
43C4×C4⋊C4×C139C2211yescharacteristic
44C4×C22⋊C4×C139C2211yescharacteristic
45#340×C139C2211yescharacteristic
46#340×C139C2211yescharacteristic
47#340×C139C2211yescharacteristic
48#340×C139C2211yescharacteristic
49#340×C139C2211yescharacteristic
50#340×C139C2211yescharacteristic
51#340×C139C2211yescharacteristic
52#340×C139C2211yescharacteristic
53#340×C139C2211yescharacteristic
54#340×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#336×C139C2211yescharacteristic
58#336×C139C2211yescharacteristic
59C23×C4×C139—21no—
60C23×C4×C139C2311yescharacteristic
61C2×M16×C139—22no—
62C2×M16×C139—22no—
63C2×M16×C139—41no—
64C22×C8×C139C2311yescharacteristic
65C22×C8×C139C2311yescharacteristic
66C22×C8×C139C2311yescharacteristic
67C22×C8×C139C2311yescharacteristic
68#125×C139—22no—
69#125×C139—41no—
70#117×C139—22no—
71#117×C139—44no—
72#117×C139—41no—
73C2×C4⋊C4×C139—21no—
74C2×C4⋊C4×C139—22no—
75C2×C4⋊C4×C139—21no—
76C2×C4⋊C4×C139—21no—
77C2×C4⋊C4×C139—21no—
78C2×C4⋊C4×C139—21no—
79C2×C4⋊C4×C139—21no—
80C2×C4⋊C4×C139—21no—
81C2×C4⋊C4×C139—21no—
82C2×C4⋊C4×C139—21no—
83C2×C4⋊C4×C139Q814yes—
84C2×C4⋊C4×C139C2311yescharacteristic
85C2×C4⋊C4×C139C2311yescharacteristic
86C2×C4⋊C4×C139C2311yescharacteristic
87C2×C4⋊C4×C139C2311yescharacteristic
88C2×C4⋊C4×C139C2311yescharacteristic
89C2×C4⋊C4×C139C2311yescharacteristic
90C2×C4⋊C4×C139C2311yescharacteristic
91C2×C4⋊C4×C139C2311yescharacteristic
92C2×C22⋊C4×C139—21no—
93C2×C22⋊C4×C139—21no—
94C2×C22⋊C4×C139—21no—
95C2×C22⋊C4×C139D411yescharacteristic
96C2×C22⋊C4×C139D411yescharacteristic
97C2×C42×C139—21no—
98C2×C42×C139—21no—
99C2×C42×C139—21no—
100C2×C42×C139C2311yescharacteristic
101C2×C42×C139C2311yescharacteristic
102#107×C139—41no—
103#107×C139—41no—
104#106×C139—22no—
105#106×C139—22no—
106C4⋊C8×C139—22no—
107C4⋊C8×C139—41no—
108C22⋊C8×C139—22no—
109#95×C139—21no—
110#95×C139—21no—
111#95×C139—21no—
112#95×C139—21no—
113#95×C139—21no—
114#95×C139—21no—
115#95×C139—21no—
116#95×C139—21no—
117#95×C139D411yescharacteristic
118#95×C139D411yescharacteristic
119C24×C139C2×D411yescharacteristic
120C22×C4×C139—21no—
121C22×C4×C139—21no—
122C22×C4×C139—21no—
123C22×C4×C139—21no—
124C22×C4×C139—24no—
125C22×C4×C139—21no—
126C22×C4×C139—21no—
127C22×C4×C139—21no—
128C22×C4×C139—21no—
129C22×C4×C139—21no—
130C22×C4×C139—21no—
131C22×C4×C139—21no—
132C22×C4×C139—21no—
133C22×C4×C139—42no—
134C22×C4×C139—42no—
135C22×C4×C139C2×D411yescharacteristic
136C22×C4×C139C2×D411yescharacteristic
137C22×C4×C139C2×D411yescharacteristic
138C22×C4×C139C2×D411yescharacteristic
139C22×C4×C139C2×D411yescharacteristic
140C22×C4×C139C2×Q812yes—
141C22×C4×C139#4112yes—
142C22×C4×C139C2411yescharacteristic
143M16×C139—44no—
144C2×C8×C139—21no—
145C2×C8×C139—21no—
146C2×C8×C139—21no—
147C2×C8×C139—21no—
148C2×C8×C139—21no—
149C2×C8×C139—21no—
150C2×C8×C139—21no—
151C2×C8×C139—21no—
152C2×C8×C139—21no—
153C2×C8×C139—21no—
154C2×C8×C139—21no—
155C2×C8×C139#4112yes—
156C4⋊C4×C139—24no—
157C4⋊C4×C139—21no—
158C4⋊C4×C139—21no—
159C4⋊C4×C139—21no—
160C4⋊C4×C139—21no—
161C4⋊C4×C139—21no—
162C4⋊C4×C139—21no—
163C4⋊C4×C139—21no—
164C4⋊C4×C139—21no—
165C4⋊C4×C139—21no—
166C4⋊C4×C139—21no—
167C4⋊C4×C139—21no—
168C4⋊C4×C139—21no—
169C4⋊C4×C139—21no—
170C4⋊C4×C139—42no—
171C4⋊C4×C139—42no—
172C4⋊C4×C139—42no—
173C4⋊C4×C139—42no—
174C4⋊C4×C139—42no—
175C4⋊C4×C139—42no—
176C4⋊C4×C139—81no—
177C4⋊C4×C139—81no—
178C4⋊C4×C139C2×Q812yes—
179C4⋊C4×C139C2×Q812yes—
180C4⋊C4×C139#4112yes—
181C22⋊C4×C139—22no—
182C22⋊C4×C139—41no—
183C22⋊C4×C139—42no—
184C22⋊C4×C139—42no—
185C22⋊C4×C139—81no—
186C42×C139—21no—
187C42×C139—21no—
188C42×C139—21no—
189C42×C139—21no—
190C42×C139—42no—
191C42×C139—42no—
192C42×C139—42no—
193C23×C139—21no—
194C23×C139—21no—
195C23×C139—21no—
196C23×C139—21no—
197C23×C139—21no—
198C23×C139—21no—
199C23×C139C22⋊Q812yes—
200C23×C139C22×D411yescharacteristic
201C2×C4×C139—21no—
202C2×C4×C139—21no—
203C2×C4×C139—21no—
204C2×C4×C139—21no—
205C2×C4×C139—22no—
206C2×C4×C139—22no—
207C2×C4×C139—22no—
208C2×C4×C139—22no—
209C2×C4×C139—22no—
210C2×C4×C139—22no—
211C2×C4×C139—21no—
212C2×C4×C139—21no—
213C2×C4×C139—22no—
214C2×C4×C139—21no—
215C2×C4×C139—21no—
216C2×C4×C139—21no—
217C2×C4×C139—21no—
218C2×C4×C139—21no—
219C2×C4×C139—21no—
220C2×C4×C139—21no—
221C2×C4×C139—48no—
222C2×C4×C139—41no—
223C2×C4×C139—41no—
224C2×C4×C139—41no—
225C2×C4×C139—41no—
226C2×C4×C139—41no—
227C2×C4×C139—41no—
228C2×C4×C139—41no—
229C2×C4×C139—41no—
230C2×C4×C139—41no—
231C2×C4×C139—41no—
232C2×C4×C139—41no—
233C2×C4×C139—41no—
234C2×C4×C139—41no—
235C2×C4×C139—41no—
236C2×C4×C139—41no—
237C2×C4×C139—41no—
238C2×C4×C139—41no—
239C2×C4×C139—41no—
240C2×C4×C139—41no—
241C2×C4×C139—41no—
242C2×C4×C139—41no—
243C2×C4×C139C22⋊Q812yes—
244C2×C4×C139AGL(1,ℤ/8)12yes—
245C2×C4×C139C22×Q811yescharacteristic
246C2×C4×C139C2×#4111yescharacteristic
247C2×C4×C139C2×#4111yescharacteristic
248C2×C4×C139C2×#4111yescharacteristic
249C2×C4×C139H(5,𝔽2)11yescharacteristic
250C2×C4×C1392−1+411yescharacteristic
251C8×C139—22no—
252C8×C139—41no—
253C8×C139—41no—
254C8×C139—41no—
255C22×C139—22no—
256C22×C139—22no—
257C22×C139—22no—
258C22×C139—41no—
259C22×C139—41no—
260C22×C139—41no—
261C22×C139—41no—
262C22×C139C2×C22⋊Q811yescharacteristic
263C22×C139#54611yescharacteristic
264C22×C139#54711yescharacteristic
265C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
266C22×C139#57511yescharacteristic
267C22×C139#57711yescharacteristic
268C22×C139#57811yescharacteristic
269C4×C139—22no—
270C4×C139—22no—
271C4×C139—41no—
272C4×C139—42no—
273C4×C139—42no—
274C4×C139—41no—
275C4×C139—41no—
276C4×C139—42no—
277C4×C139—81no—
278C4×C139—81no—
279C4×C139—81no—
280C4×C139—81no—
281C4×C139—81no—
282C4×C139#53311yescharacteristic
283C4×C139#54411yescharacteristic
284C4×C139#55111yescharacteristic
285C4×C139#55211yescharacteristic
286C2×C139—42no—
287C2×C139#243811yescharacteristic
288C2×C139#307711yescharacteristic
289C2×C139#308211yescharacteristic
290C2×C139#331511yescharacteristic
291C2×C139#333211yescharacteristic
292C2×C139#334311yescharacteristic
293C2×C139#335111yescharacteristic
294#26012C13911yesmaximal, characteristic, direct product factor, Sylow
295C139#2601211yescharacteristic, direct product factor, Sylow
296#2441C2×C13911yescharacteristic
297#2344C2×C13911yescharacteristic
298#2099C2×C13911yescharacteristic, complemented
299#2088C2×C13911yescharacteristic, complemented
300#2087C2×C13911yescharacteristic, complemented
301#2059C2×C13911yescharacteristic, complemented
302#1989C2×C13911yescharacteristic, complemented
303#1947C2×C13911yescharacteristic, complemented
304#1920C2×C13911yescharacteristic, complemented
305#1919C2×C13911yescharacteristic, complemented
306#1854C2×C13911yescharacteristic
307#1851C2×C13911yescharacteristic
308#1824C2×C13911yescharacteristic
309#1809C2×C13911yescharacteristic
310#1736C2×C13911yescharacteristic
311C22×M16C22×C13911yescharacteristic
312C2×#125C22×C13911yescharacteristic
313C2×#117—21no—
314C2×#117C22×C13911yescharacteristic
315C22×C4⋊C4C22×C13911yescharacteristic
316C2×#107C22×C13911yescharacteristic
317C2×#107C22×C13911yescharacteristic
318C2×#106C22×C13911yescharacteristic
319C2×#106C22×C13911yescharacteristic
320C2×C4⋊C8C22×C13911yescharacteristic
321C2×C4⋊C8C22×C13911yescharacteristic
322C2×C22⋊C8C22×C13911yescharacteristic
323#399—21no—
324#396—21no—
325#389—21no—
326#389C22×C13911yescharacteristic
327#389C22×C13911yescharacteristic
328#389C22×C13911yescharacteristic
329#389C22×C13911yescharacteristic
330#387—21no—
331#387—21no—
332#387—21no—
333#384C22×C13911yescharacteristic
334#381—21no—
335#380C22×C13911yescharacteristic
336#380C22×C13911yescharacteristic
337C4×C4⋊C4C22×C13911yescharacteristic
338C4×C4⋊C4C22×C13911yescharacteristic
339C4×C22⋊C4C22×C13911yescharacteristic
340#340C22×C13911yescharacteristic
341#340C22×C13911yescharacteristic
342#340C22×C13911yescharacteristic
343#340C22×C13911yescharacteristic
344#340C22×C13911yescharacteristic
345#340C22×C13911yescharacteristic
346#340C22×C13911yescharacteristic
347#340C22×C13911yescharacteristic
348#340C22×C13911yescharacteristic
349#340C22×C13911yescharacteristic
350#340C22×C13911yescharacteristic
351#340C22×C13911yescharacteristic
352#336C22×C13911yescharacteristic
353#336C22×C13911yescharacteristic
354C23×C4—21no—
355C23×C4C23×C13911yescharacteristic
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—41no—
359C22×C8C23×C13911yescharacteristic
360C22×C8C23×C13911yescharacteristic
361C22×C8C23×C13911yescharacteristic
362C22×C8C23×C13911yescharacteristic
363#125—22no—
364#125—41no—
365#117—22no—
366#117—44no—
367#117—41no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4Q8×C13914yes—
379C2×C4⋊C4C23×C13911yescharacteristic
380C2×C4⋊C4C23×C13911yescharacteristic
381C2×C4⋊C4C23×C13911yescharacteristic
382C2×C4⋊C4C23×C13911yescharacteristic
383C2×C4⋊C4C23×C13911yescharacteristic
384C2×C4⋊C4C23×C13911yescharacteristic
385C2×C4⋊C4C23×C13911yescharacteristic
386C2×C4⋊C4C23×C13911yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4D4×C13911yescharacteristic
391C2×C22⋊C4D4×C13911yescharacteristic
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42C23×C13911yescharacteristic
396C2×C42C23×C13911yescharacteristic
397#107—41no—
398#107—41no—
399#106—22no—
400#106—22no—
401C4⋊C8—22no—
402C4⋊C8—41no—
403C22⋊C8—22no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95D4×C13911yescharacteristic
413#95D4×C13911yescharacteristic
414C24C2×D4×C13911yescharacteristic
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4C2×D4×C13911yescharacteristic
431C22×C4C2×D4×C13911yescharacteristic
432C22×C4C2×D4×C13911yescharacteristic
433C22×C4C2×D4×C13911yescharacteristic
434C22×C4C2×D4×C13911yescharacteristic
435C22×C4C2×Q8×C13912yes—
436C22×C4#41×C13912yes—
437C22×C4C24×C13911yescharacteristic
438M16—44no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8#41×C13912yes—
451C4⋊C4—24no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—42no—
468C4⋊C4—42no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4C2×Q8×C13912yes—
474C4⋊C4C2×Q8×C13912yes—
475C4⋊C4#41×C13912yes—
476C22⋊C4—22no—
477C22⋊C4—41no—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C22⋊C4—81no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—42no—
486C42—42no—
487C42—42no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23C22⋊Q8×C13912yes—
495C23C22×D4×C13911yescharacteristic
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—48no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4C22⋊Q8×C13912yes—
539C2×C4AGL(1,ℤ/8)×C13912yes—
540C2×C4C22×Q8×C13911yescharacteristic
541C2×C4C2×#41×C13911yescharacteristic
542C2×C4C2×#41×C13911yescharacteristic
543C2×C4C2×#41×C13911yescharacteristic
544C2×C4H(5,𝔽2)×C13911yescharacteristic
545C2×C42−1+4×C13911yescharacteristic
546C8—22no—
547C8—41no—
548C8—41no—
549C8—41no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22C2×C22⋊Q8×C13911yescharacteristic
558C22#546×C13911yescharacteristic
559C22#547×C13911yescharacteristic
560C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
561C22#575×C13911yescharacteristic
562C22#577×C13911yescharacteristic
563C22#578×C13911yescharacteristic
564C4—22no—
565C4—22no—
566C4—41no—
567C4—42no—
568C4—41no—
569C4—42no—
570C4—42no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4#533×C13911yescharacteristic
578C4#544×C13911yescharacteristic
579C4#551×C13911yescharacteristic
580C4#552×C13911yescharacteristic
581C2—42no—
582C2#2438×C13911yescharacteristic
583C2#3077×C13911yescharacteristic
584C2#3082×C13911yescharacteristic
585C2#3315×C13911yescharacteristic
586C2#3332×C13911yescharacteristic
587C2#3343×C13911yescharacteristic
588C2#3351×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC24×C139C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2099×C139C2semidirect
4. #2088×C139C2semidirect
5. #2087×C139C2semidirect
6. #2059×C139C2semidirect
7. #1989×C139C2semidirect
8. #1947×C139C2semidirect
9. #1920×C139C2semidirect
10. #1919×C139C2semidirect
294. #26012C139direct (N × H)
295. C139#26012direct (N × H)
298. #2099C2×C139semidirect
299. #2088C2×C139semidirect
300. #2087C2×C139semidirect
301. #2059C2×C139semidirect
302. #1989C2×C139semidirect
303. #1947C2×C139semidirect
304. #1920C2×C139semidirect
305. #1919C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2441×C1392
#2344×C1392
#2099×C1392
#2088×C1392
#2087×C1392
#2059×C1392
#1989×C1392
#1947×C1392
#1920×C1392
#1919×C1392
#1854×C1392
#1851×C1392
#1824×C1392
#1809×C1392
#1736×C1392
#26012139