Finite Group Databasebeta

← C139×#29309 #48023905

Subgroups — C139×#29309 #48023905

Order 35584.

702 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2629×C139C211yesmaximal, characteristic
2#2317×C139C211yesmaximal, characteristic
3#2084×C139C211yesmaximal, characteristic, complemented
4#2083×C139C211yesmaximal, characteristic, complemented
5#2059×C139C211yesmaximal, characteristic, complemented
6#2059×C139C211yesmaximal, characteristic, complemented
7#1944×C139C211yesmaximal, characteristic, complemented
8#1943×C139C211yesmaximal, characteristic, complemented
9#1942×C139C211yesmaximal, characteristic, complemented
10#1941×C139C211yesmaximal, characteristic, complemented
11#1854×C139C211yesmaximal, characteristic
12#1854×C139C211yesmaximal, characteristic
13#1853×C139C211yesmaximal, characteristic
14#1852×C139C211yesmaximal, characteristic
15#1750×C139C211yesmaximal, characteristic
16C2×#125×C139C2211yescharacteristic
17C2×#117×C139C2211yescharacteristic
18C2×#117×C139C2211yescharacteristic
19C22×C4⋊C4×C139C2211yescharacteristic
20C2×#107×C139C2211yescharacteristic
21C2×#107×C139C2211yescharacteristic
22C2×#107×C139C2211yescharacteristic
23C2×#107×C139C2211yescharacteristic
24C2×#106×C139C2211yescharacteristic
25C2×#106×C139C2211yescharacteristic
26C2×#106×C139C2211yescharacteristic
27C2×#106×C139C2211yescharacteristic
28C2×C22⋊C8×C139C2211yescharacteristic
29C2×C22⋊C8×C139C2211yescharacteristic
30C2×#97×C139C2211yescharacteristic
31C2×C4×C8×C139C2211yescharacteristic
32#398×C139—21no—
33#398×C139—21no—
34#396×C139—21no—
35#396×C139—21no—
36#389×C139C2211yescharacteristic
37#389×C139C2211yescharacteristic
38#389×C139C2211yescharacteristic
39#389×C139C2211yescharacteristic
40#389×C139C2211yescharacteristic
41#389×C139C2211yescharacteristic
42#385×C139—21no—
43#385×C139—21no—
44#384×C139—21no—
45#384×C139C2211yescharacteristic
46#382×C139—21no—
47#380×C139C2211yescharacteristic
48#380×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
61C22×C8×C139C2311yescharacteristic
62C22×C8×C139C2311yescharacteristic
63C22×C8×C139C2311yescharacteristic
64C22×C8×C139C2311yescharacteristic
65#125×C139—41no—
66#125×C139—41no—
67#117×C139—22no—
68#117×C139—22no—
69#117×C139—41no—
70#117×C139—41no—
71C2×C4⋊C4×C139—21no—
72C2×C4⋊C4×C139—21no—
73C2×C4⋊C4×C139—21no—
74C2×C4⋊C4×C139—21no—
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—41no—
83C2×C4⋊C4×C139—41no—
84C2×C4⋊C4×C139D411yescharacteristic
85C2×C4⋊C4×C139D411yescharacteristic
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×C4⋊C4×C139C2311yescharacteristic
93C2×C4⋊C4×C139C2311yescharacteristic
94C2×C22⋊C4×C139—21no—
95C2×C22⋊C4×C139—21no—
96C2×C22⋊C4×C139—21no—
97C2×C22⋊C4×C139D411yescharacteristic
98C2×C22⋊C4×C139D411yescharacteristic
99C2×C42×C139—21no—
100C2×C42×C139C2311yescharacteristic
101C2×C42×C139C2311yescharacteristic
102#107×C139—22no—
103#107×C139—22no—
104#107×C139—41no—
105#107×C139—41no—
106#106×C139—22no—
107#106×C139—22no—
108#106×C139—41no—
109#106×C139—41no—
110C22⋊C8×C139Q814yes—
111C22⋊C8×C139Q814yes—
112#97×C139—41no—
113C4×C8×C139—41no—
114#95×C139—21no—
115#95×C139—21no—
116#95×C139—21no—
117#95×C139—21no—
118#95×C139—21no—
119#95×C139—21no—
120#95×C139—21no—
121#95×C139—21no—
122C24×C139C2×D411yescharacteristic
123C22×C4×C139—21no—
124C22×C4×C139—21no—
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—21no—
134C22×C4×C139—21no—
135C22×C4×C139—42no—
136C22×C4×C139—81no—
137C22×C4×C139—81no—
138C22×C4×C139C2×D411yescharacteristic
139C22×C4×C139C2×D411yescharacteristic
140C22×C4×C139C2×D411yescharacteristic
141C22×C4×C139C2×D411yescharacteristic
142C22×C4×C139C2×D411yescharacteristic
143C22×C4×C139C2×Q812yes—
144C22×C4×C139C2×Q812yes—
145C22×C4×C139C2411yescharacteristic
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×C139C2×Q812yes—
155C2×C8×C139C2×Q812yes—
156C2×C8×C139C2×Q812yes—
157C2×C8×C139C2×Q812yes—
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—21no—
171C4⋊C4×C139—21no—
172C4⋊C4×C139—41no—
173C4⋊C4×C139—41no—
174C4⋊C4×C139—42no—
175C4⋊C4×C139—42no—
176C4⋊C4×C139—42no—
177C4⋊C4×C139—81no—
178C4⋊C4×C139—81no—
179C4⋊C4×C139—81no—
180C4⋊C4×C139—81no—
181C4⋊C4×C139—81no—
182C4⋊C4×C139—81no—
183C4⋊C4×C139—81no—
184C4⋊C4×C139—81no—
185C4⋊C4×C139#4112yes—
186C4⋊C4×C139#4112yes—
187C22⋊C4×C139—24no—
188C22⋊C4×C139—41no—
189C22⋊C4×C139—41no—
190C22⋊C4×C139—81no—
191C22⋊C4×C139—81no—
192C42×C139—24no—
193C42×C139—21no—
194C42×C139—21no—
195C42×C139—21no—
196C42×C139—21no—
197C23×C139—21no—
198C23×C139—21no—
199C23×C139—21no—
200C23×C139—21no—
201C23×C139—21no—
202C23×C139—21no—
203C23×C139C4⋊Q812yes—
204C23×C139C22×D411yescharacteristic
205C2×C4×C139—21no—
206C2×C4×C139—21no—
207C2×C4×C139—22no—
208C2×C4×C139—22no—
209C2×C4×C139—22no—
210C2×C4×C139—22no—
211C2×C4×C139—22no—
212C2×C4×C139—22no—
213C2×C4×C139—21no—
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—21no—
222C2×C4×C139—21no—
223C2×C4×C139—21no—
224C2×C4×C139—21no—
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×C139—41no—
244C2×C4×C139—41no—
245C2×C4×C139—41no—
246C2×C4×C139—41no—
247C2×C4×C139—84no—
248C2×C4×C139C4⋊Q812yes—
249C2×C4×C139C22×Q811yescharacteristic
250C2×C4×C139C22×Q811yescharacteristic
251C2×C4×C139C2×#4111yescharacteristic
252C2×C4×C139C2×#4111yescharacteristic
253C2×C4×C139H(5,𝔽2)11yescharacteristic
254C2×C4×C139H(5,𝔽2)11yescharacteristic
255C8×C139—22no—
256C8×C139—22no—
257C8×C139—22no—
258C8×C139—22no—
259C22×C139—22no—
260C22×C139—22no—
261C22×C139—22no—
262C22×C139—41no—
263C22×C139—41no—
264C22×C139—41no—
265C22×C139—41no—
266C22×C139#52511yescharacteristic
267C22×C139C2×C4⋊Q811yescharacteristic
268C22×C139#53411yescharacteristic
269C22×C139#57611yescharacteristic
270C22×C139#57711yescharacteristic
271C22×C139#57711yescharacteristic
272C22×C139#57811yescharacteristic
273C4×C139—22no—
274C4×C139—42no—
275C4×C139—42no—
276C4×C139—41no—
277C4×C139—41no—
278C4×C139—41no—
279C4×C139—41no—
280C4×C139—81no—
281C4×C139—81no—
282C4×C139—81no—
283C4×C139—81no—
284C4×C139—81no—
285C4×C139—81no—
286C4×C139#55411yescharacteristic
287C4×C139#55411yescharacteristic
288C4×C139#55411yescharacteristic
289C4×C139#55411yescharacteristic
290C2×C139—42no—
291C2×C139#258311yescharacteristic
292C2×C139#311911yescharacteristic
293C2×C139#312011yescharacteristic
294C2×C139#316311yescharacteristic
295C2×C139#316411yescharacteristic
296C2×C139#319811yescharacteristic
297C2×C139#320111yescharacteristic
298#29309C13911yesmaximal, characteristic, direct product factor, Sylow
299C139#2930911yescharacteristic, direct product factor, Sylow
300#2629C2×C13911yescharacteristic
301#2317C2×C13911yescharacteristic
302#2084C2×C13911yescharacteristic, complemented
303#2083C2×C13911yescharacteristic, complemented
304#2059C2×C13911yescharacteristic, complemented
305#2059C2×C13911yescharacteristic, complemented
306#1944C2×C13911yescharacteristic, complemented
307#1943C2×C13911yescharacteristic, complemented
308#1942C2×C13911yescharacteristic, complemented
309#1941C2×C13911yescharacteristic, complemented
310#1854C2×C13911yescharacteristic
311#1854C2×C13911yescharacteristic
312#1853C2×C13911yescharacteristic
313#1852C2×C13911yescharacteristic
314#1750C2×C13911yescharacteristic
315C2×#125C22×C13911yescharacteristic
316C2×#117C22×C13911yescharacteristic
317C2×#117C22×C13911yescharacteristic
318C22×C4⋊C4C22×C13911yescharacteristic
319C2×#107C22×C13911yescharacteristic
320C2×#107C22×C13911yescharacteristic
321C2×#107C22×C13911yescharacteristic
322C2×#107C22×C13911yescharacteristic
323C2×#106C22×C13911yescharacteristic
324C2×#106C22×C13911yescharacteristic
325C2×#106C22×C13911yescharacteristic
326C2×#106C22×C13911yescharacteristic
327C2×C22⋊C8C22×C13911yescharacteristic
328C2×C22⋊C8C22×C13911yescharacteristic
329C2×#97C22×C13911yescharacteristic
330C2×C4×C8C22×C13911yescharacteristic
331#398—21no—
332#398—21no—
333#396—21no—
334#396—21no—
335#389C22×C13911yescharacteristic
336#389C22×C13911yescharacteristic
337#389C22×C13911yescharacteristic
338#389C22×C13911yescharacteristic
339#389C22×C13911yescharacteristic
340#389C22×C13911yescharacteristic
341#385—21no—
342#385—21no—
343#384—21no—
344#384C22×C13911yescharacteristic
345#382—21no—
346#380C22×C13911yescharacteristic
347#380C22×C13911yescharacteristic
348#340C22×C13911yescharacteristic
349#340C22×C13911yescharacteristic
350#340C22×C13911yescharacteristic
351#340C22×C13911yescharacteristic
352#340C22×C13911yescharacteristic
353#340C22×C13911yescharacteristic
354#340C22×C13911yescharacteristic
355#340C22×C13911yescharacteristic
356#336C22×C13911yescharacteristic
357#336C22×C13911yescharacteristic
358C23×C4—21no—
359C23×C4C23×C13911yescharacteristic
360C22×C8C23×C13911yescharacteristic
361C22×C8C23×C13911yescharacteristic
362C22×C8C23×C13911yescharacteristic
363C22×C8C23×C13911yescharacteristic
364#125—41no—
365#125—41no—
366#117—22no—
367#117—22no—
368#117—41no—
369#117—41no—
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⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—41no—
383C2×C4⋊C4D4×C13911yescharacteristic
384C2×C4⋊C4D4×C13911yescharacteristic
385C2×C4⋊C4C23×C13911yescharacteristic
386C2×C4⋊C4C23×C13911yescharacteristic
387C2×C4⋊C4C23×C13911yescharacteristic
388C2×C4⋊C4C23×C13911yescharacteristic
389C2×C4⋊C4C23×C13911yescharacteristic
390C2×C4⋊C4C23×C13911yescharacteristic
391C2×C4⋊C4C23×C13911yescharacteristic
392C2×C4⋊C4C23×C13911yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4D4×C13911yescharacteristic
397C2×C22⋊C4D4×C13911yescharacteristic
398C2×C42—21no—
399C2×C42C23×C13911yescharacteristic
400C2×C42C23×C13911yescharacteristic
401#107—22no—
402#107—22no—
403#107—41no—
404#107—41no—
405#106—22no—
406#106—22no—
407#106—41no—
408#106—41no—
409C22⋊C8Q8×C13914yes—
410C22⋊C8Q8×C13914yes—
411#97—41no—
412C4×C8—41no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421C24C2×D4×C13911yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—42no—
435C22×C4—81no—
436C22×C4—81no—
437C22×C4C2×D4×C13911yescharacteristic
438C22×C4C2×D4×C13911yescharacteristic
439C22×C4C2×D4×C13911yescharacteristic
440C22×C4C2×D4×C13911yescharacteristic
441C22×C4C2×D4×C13911yescharacteristic
442C22×C4C2×Q8×C13912yes—
443C22×C4C2×Q8×C13912yes—
444C22×C4C24×C13911yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8C2×Q8×C13912yes—
454C2×C8C2×Q8×C13912yes—
455C2×C8C2×Q8×C13912yes—
456C2×C8C2×Q8×C13912yes—
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—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4#41×C13912yes—
485C4⋊C4#41×C13912yes—
486C22⋊C4—24no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—81no—
490C22⋊C4—81no—
491C42—24no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23C4⋊Q8×C13912yes—
503C23C22×D4×C13911yescharacteristic
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
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×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—84no—
547C2×C4C4⋊Q8×C13912yes—
548C2×C4C22×Q8×C13911yescharacteristic
549C2×C4C22×Q8×C13911yescharacteristic
550C2×C4C2×#41×C13911yescharacteristic
551C2×C4C2×#41×C13911yescharacteristic
552C2×C4H(5,𝔽2)×C13911yescharacteristic
553C2×C4H(5,𝔽2)×C13911yescharacteristic
554C8—22no—
555C8—22no—
556C8—22no—
557C8—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22#525×C13911yescharacteristic
566C22C2×C4⋊Q8×C13911yescharacteristic
567C22#534×C13911yescharacteristic
568C22#576×C13911yescharacteristic
569C22#577×C13911yescharacteristic
570C22#577×C13911yescharacteristic
571C22#578×C13911yescharacteristic
572C4—22no—
573C4—42no—
574C4—42no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4#554×C13911yescharacteristic
586C4#554×C13911yescharacteristic
587C4#554×C13911yescharacteristic
588C4#554×C13911yescharacteristic
589C2—42no—
590C2#2583×C13911yescharacteristic
591C2#3119×C13911yescharacteristic
592C2#3120×C13911yescharacteristic
593C2#3163×C13911yescharacteristic
594C2#3164×C13911yescharacteristic
595C2#3198×C13911yescharacteristic
596C2#3201×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC24×C139C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×#117×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2084×C139C2semidirect
4. #2083×C139C2semidirect
5. #2059×C139C2semidirect
6. #2059×C139C2semidirect
7. #1944×C139C2semidirect
8. #1943×C139C2semidirect
9. #1942×C139C2semidirect
10. #1941×C139C2semidirect
298. #29309C139direct (N × H)
299. C139#29309direct (N × H)
302. #2084C2×C139semidirect
303. #2083C2×C139semidirect
304. #2059C2×C139semidirect
305. #2059C2×C139semidirect
306. #1944C2×C139semidirect
307. #1943C2×C139semidirect
308. #1942C2×C139semidirect
309. #1941C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2629×C1392
#2317×C1392
#2084×C1392
#2083×C1392
#2059×C1392
#1944×C1392
#1943×C1392
#1942×C1392
#1941×C1392
#1854×C1392
#1853×C1392
#1852×C1392
#1750×C1392
#29309139