Finite Group Databasebeta

← C139×#35898 #48030494

Subgroups — C139×#35898 #48030494

Order 35584.

1748 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2644×C139C213yesmaximal, complemented
2#2513×C139C213yesmaximal, complemented
3#2512×C139C213yesmaximal, complemented
4#2512×C139C213yesmaximal, complemented
5#2497×C139C213yesmaximal, complemented
6#2496×C139C213yesmaximal, complemented
7#2494×C139C213yesmaximal, complemented
8#2401×C139C213yesmaximal, complemented
9#2351×C139C211yesmaximal, characteristic, complemented
10Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
11Q8×C4⋊C4×C139C211yesmaximal, characteristic, complemented
12#2341×C139C211yesmaximal, characteristic
13#2341×C139C211yesmaximal, characteristic
14#2341×C139C211yesmaximal, characteristic
15#2276×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C2×#126×C139C2216yes—
18C2×C4×Q8×C139C2211yescharacteristic
19C2×C4×Q8×C139C2211yescharacteristic
20C2×C4×Q8×C139C2211yescharacteristic
21C2×C4×Q8×C139C2211yescharacteristic
22C2×C4×Q8×C139C2211yescharacteristic
23C2×C4×Q8×C139C2211yescharacteristic
24#401×C139C2213yes—
25#400×C139C2211yescharacteristic
26#400×C139C2213yes—
27#400×C139C2213yes—
28#397×C139C2213yes—
29#397×C139C2216yes—
30#397×C139C2213yes—
31#397×C139C2216yes—
32#397×C139C2213yes—
33#396×C139C2213yes—
34#396×C139C2216yes—
35#390×C139C2213yes—
36#390×C139C2213yes—
37#390×C139C2213yes—
38#390×C139C2213yes—
39#390×C139C2213yes—
40#390×C139C2213yes—
41#389×C139C2213yes—
42#389×C139C2213yes—
43#389×C139C2213yes—
44#389×C139C2213yes—
45#389×C139C2213yes—
46#389×C139C2213yes—
47#388×C139C2216yes—
48#388×C139C2216yes—
49#387×C139C2216yes—
50#384×C139C2213yes—
51#384×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—
65#376×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—412no—
73C4×Q8×C139—24no—
74C4×Q8×C139—24no—
75C4×Q8×C139—24no—
76C4×Q8×C139—24no—
77C4×Q8×C139—24no—
78C4×Q8×C139—24no—
79C2×C4⋊C4×C139C2311yescharacteristic
80C2×C4⋊C4×C139C2313yes—
81C2×C4⋊C4×C139C2311yescharacteristic
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×C139C2313yes—
90C2×C4⋊C4×C139C2316yes—
91C2×C4⋊C4×C139C2316yes—
92C2×C4⋊C4×C139C2313yes—
93C2×C22⋊C4×C139C2313yes—
94C2×C22⋊C4×C139C2313yes—
95C2×C22⋊C4×C139C2313yes—
96C2×C22⋊C4×C139C2313yes—
97C2×C22⋊C4×C139C2316yes—
98C2×C22⋊C4×C139C2316yes—
99C2×C22⋊C4×C139C2313yes—
100C2×C22⋊C4×C139C2316yes—
101C2×C22⋊C4×C139C2313yes—
102C2×C42×C139C2313yes—
103C2×C42×C139C2313yes—
104C2×C42×C139C2313yes—
105C2×C42×C139C2313yes—
106C2×C42×C139C2313yes—
107C2×C42×C139C2313yes—
108C2×C42×C139C2316yes—
109#95×C139C2313yes—
110#95×C139C2313yes—
111#95×C139C2311yescharacteristic
112#95×C139C2313yes—
113#95×C139C2311yescharacteristic
114#95×C139C2313yes—
115#95×C139C2313yes—
116#95×C139C2316yes—
117#95×C139C2313yes—
118#95×C139C2313yes—
119#95×C139C2313yes—
120#95×C139C2311yescharacteristic
121#95×C139C2311yescharacteristic
122#95×C139C2313yes—
123#95×C139C2311yescharacteristic
124#95×C139C2313yes—
125#95×C139C2313yes—
126C24×C139C2413yes—
127#41×C139—416no—
128C2×Q8×C139#4114yes—
129C2×Q8×C139#4114yes—
130C2×Q8×C139#4114yes—
131C2×D4×C139—26no—
132C2×D4×C139—26no—
133C2×D4×C139—26no—
134C22×C4×C139—26no—
135C22×C4×C139—26no—
136C22×C4×C139—26no—
137C22×C4×C139C2411yescharacteristic
138C22×C4×C139C2411yescharacteristic
139C22×C4×C139C2411yescharacteristic
140C22×C4×C139C2411yescharacteristic
141C22×C4×C139C2411yescharacteristic
142C22×C4×C139C2413yes—
143C22×C4×C139C2413yes—
144C22×C4×C139C2413yes—
145C22×C4×C139C2413yes—
146C22×C4×C139C2413yes—
147C22×C4×C139C2413yes—
148C22×C4×C139C2411yescharacteristic
149C22×C4×C139C2411yescharacteristic
150C22×C4×C139C2413yes—
151C4⋊C4×C139—26no—
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—22no—
160C4⋊C4×C139—22no—
161C4⋊C4×C139—43no—
162C4⋊C4×C139—43no—
163C4⋊C4×C139—46no—
164C4⋊C4×C139—46no—
165C22⋊C4×C139—26no—
166C22⋊C4×C139—26no—
167C22⋊C4×C139—43no—
168C22⋊C4×C139—43no—
169C22⋊C4×C139—43no—
170C22⋊C4×C139—43no—
171C22⋊C4×C139—46no—
172C22⋊C4×C139—46no—
173C22⋊C4×C139—46no—
174C42×C139—26no—
175C42×C139—26no—
176C42×C139—26no—
177C42×C139—26no—
178C42×C139—26no—
179C42×C139—26no—
180C42×C139—46no—
181C23×C139—23no—
182C23×C139—23no—
183C23×C139—23no—
184C23×C139—23no—
185C23×C139—23no—
186C23×C139—23no—
187C23×C139—23no—
188C23×C139C2511yescharacteristic
189Q8×C139#126116yescomplemented
190D4×C139—412no—
191C2×C4×C139—21no—
192C2×C4×C139—21no—
193C2×C4×C139—21no—
194C2×C4×C139—21no—
195C2×C4×C139—21no—
196C2×C4×C139—21no—
197C2×C4×C139—21no—
198C2×C4×C139—21no—
199C2×C4×C139—23no—
200C2×C4×C139—23no—
201C2×C4×C139—23no—
202C2×C4×C139—23no—
203C2×C4×C139—23no—
204C2×C4×C139—23no—
205C2×C4×C139—21no—
206C2×C4×C139—21no—
207C2×C4×C139—21no—
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—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—23no—
222C2×C4×C139—23no—
223C2×C4×C139—23no—
224C2×C4×C139—23no—
225C2×C4×C139—23no—
226C2×C4×C139—23no—
227C2×C4×C139—21no—
228C2×C4×C139—412no—
229C2×C4×C139C2×#4116yes—
230C2×C4×C139C2×#4116yes—
231C2×C4×C139C2×#4116yes—
232C2×C4×C139H(5,𝔽2)12yes—
233C2×C4×C1392−1+412yes—
234C22×C139—43no—
235C22×C139—43no—
236C22×C139—43no—
237C22×C139—43no—
238C22×C139—43no—
239C22×C139—43no—
240C22×C139—43no—
241C22×C139C22×#4111yescharacteristic
242C22×C139C22×#4111yescharacteristic
243C22×C139C22×#4111yescharacteristic
244C22×C139C2×H(5,𝔽2)11yescharacteristic
245C22×C139C2×2−1+411yescharacteristic
246C22×C139#58511yescharacteristic
247C22×C139#58511yescharacteristic
248C4×C139—22no—
249C4×C139—22no—
250C4×C139—41no—
251C4×C139—41no—
252C4×C139—43no—
253C4×C139—43no—
254C4×C139—43no—
255C4×C139—43no—
256C4×C139—41no—
257C4×C139—41no—
258C4×C139—43no—
259C4×C139—41no—
260C4×C139—43no—
261C4×C139C2×#126112yes—
262C2×C139—83no—
263C2×C139C22×#12611yescharacteristic
264C2×C139#351611yescharacteristic
265C2×C139#351711yescharacteristic
266C2×C139#351711yescharacteristic
267C2×C139#351811yescharacteristic
268C2×C139#352211yescharacteristic
269C2×C139#352411yescharacteristic
270#35898C13911yesmaximal, characteristic, direct product factor, Sylow
271C139#3589811yescharacteristic, direct product factor, Sylow
272#2644C2×C13913yescomplemented
273#2513C2×C13913yescomplemented
274#2512C2×C13913yescomplemented
275#2512C2×C13913yescomplemented
276#2497C2×C13913yescomplemented
277#2496C2×C13913yescomplemented
278#2494C2×C13913yescomplemented
279#2401C2×C13913yescomplemented
280#2351C2×C13911yescharacteristic, complemented
281Q8×C4⋊C4C2×C13911yescharacteristic, complemented
282Q8×C4⋊C4C2×C13911yescharacteristic, complemented
283#2341C2×C13911yescharacteristic
284#2341C2×C13911yescharacteristic
285#2341C2×C13911yescharacteristic
286#2276C2×C13911yescharacteristic, complemented
287C22×#41C22×C13911yescharacteristic
288C2×#126C22×C13916yes—
289C2×C4×Q8C22×C13911yescharacteristic
290C2×C4×Q8C22×C13911yescharacteristic
291C2×C4×Q8C22×C13911yescharacteristic
292C2×C4×Q8C22×C13911yescharacteristic
293C2×C4×Q8C22×C13911yescharacteristic
294C2×C4×Q8C22×C13911yescharacteristic
295#401C22×C13913yes—
296#400C22×C13911yescharacteristic
297#400C22×C13913yes—
298#400C22×C13913yes—
299#397C22×C13913yes—
300#397C22×C13916yes—
301#397C22×C13916yes—
302#397C22×C13913yes—
303#397C22×C13913yes—
304#396C22×C13916yes—
305#396C22×C13913yes—
306#390C22×C13913yes—
307#390C22×C13913yes—
308#390C22×C13913yes—
309#390C22×C13913yes—
310#390C22×C13913yes—
311#390C22×C13913yes—
312#389C22×C13913yes—
313#389C22×C13913yes—
314#389C22×C13913yes—
315#389C22×C13913yes—
316#389C22×C13913yes—
317#389C22×C13913yes—
318#388C22×C13916yes—
319#388C22×C13916yes—
320#387C22×C13916yes—
321#384C22×C13913yes—
322#384C22×C13913yes—
323#382C22×C13913yes—
324#380C22×C13913yes—
325#380C22×C13913yes—
326#380C22×C13913yes—
327C4×C4⋊C4C22×C13913yes—
328C4×C4⋊C4C22×C13913yes—
329C4×C4⋊C4C22×C13913yes—
330C4×C4⋊C4C22×C13913yes—
331C4×C4⋊C4C22×C13913yes—
332C4×C4⋊C4C22×C13913yes—
333C4×C22⋊C4C22×C13913yes—
334C4×C22⋊C4C22×C13913yes—
335C4×C22⋊C4C22×C13913yes—
336#376C22×C13913yes—
337C2×#41—24no—
338C2×#41—24no—
339C2×#41—24no—
340C22×Q8C23×C13911yescharacteristic
341C22×D4C23×C13913yes—
342C23×C4C23×C13913yes—
343#126—412no—
344C4×Q8—24no—
345C4×Q8—24no—
346C4×Q8—24no—
347C4×Q8—24no—
348C4×Q8—24no—
349C4×Q8—24no—
350C2×C4⋊C4C23×C13913yes—
351C2×C4⋊C4C23×C13913yes—
352C2×C4⋊C4C23×C13913yes—
353C2×C4⋊C4C23×C13913yes—
354C2×C4⋊C4C23×C13913yes—
355C2×C4⋊C4C23×C13913yes—
356C2×C4⋊C4C23×C13913yes—
357C2×C4⋊C4C23×C13913yes—
358C2×C4⋊C4C23×C13911yescharacteristic
359C2×C4⋊C4C23×C13911yescharacteristic
360C2×C4⋊C4C23×C13916yes—
361C2×C4⋊C4C23×C13913yes—
362C2×C4⋊C4C23×C13913yes—
363C2×C4⋊C4C23×C13916yes—
364C2×C22⋊C4C23×C13913yes—
365C2×C22⋊C4C23×C13913yes—
366C2×C22⋊C4C23×C13916yes—
367C2×C22⋊C4C23×C13916yes—
368C2×C22⋊C4C23×C13913yes—
369C2×C22⋊C4C23×C13913yes—
370C2×C22⋊C4C23×C13913yes—
371C2×C22⋊C4C23×C13913yes—
372C2×C22⋊C4C23×C13916yes—
373C2×C42C23×C13913yes—
374C2×C42C23×C13913yes—
375C2×C42C23×C13913yes—
376C2×C42C23×C13913yes—
377C2×C42C23×C13913yes—
378C2×C42C23×C13913yes—
379C2×C42C23×C13916yes—
380#95C23×C13911yescharacteristic
381#95C23×C13913yes—
382#95C23×C13913yes—
383#95C23×C13913yes—
384#95C23×C13911yescharacteristic
385#95C23×C13911yescharacteristic
386#95C23×C13911yescharacteristic
387#95C23×C13913yes—
388#95C23×C13913yes—
389#95C23×C13913yes—
390#95C23×C13911yescharacteristic
391#95C23×C13913yes—
392#95C23×C13913yes—
393#95C23×C13913yes—
394#95C23×C13913yes—
395#95C23×C13913yes—
396#95C23×C13916yes—
397C24C24×C13913yes—
398#41—416no—
399C2×Q8#41×C13914yes—
400C2×Q8#41×C13914yes—
401C2×Q8#41×C13914yes—
402C2×D4—26no—
403C2×D4—26no—
404C2×D4—26no—
405C22×C4—26no—
406C22×C4—26no—
407C22×C4—26no—
408C22×C4C24×C13911yescharacteristic
409C22×C4C24×C13911yescharacteristic
410C22×C4C24×C13911yescharacteristic
411C22×C4C24×C13911yescharacteristic
412C22×C4C24×C13911yescharacteristic
413C22×C4C24×C13913yes—
414C22×C4C24×C13913yes—
415C22×C4C24×C13913yes—
416C22×C4C24×C13913yes—
417C22×C4C24×C13913yes—
418C22×C4C24×C13913yes—
419C22×C4C24×C13911yescharacteristic
420C22×C4C24×C13911yescharacteristic
421C22×C4C24×C13913yes—
422C4⋊C4—26no—
423C4⋊C4—26no—
424C4⋊C4—26no—
425C4⋊C4—26no—
426C4⋊C4—26no—
427C4⋊C4—26no—
428C4⋊C4—26no—
429C4⋊C4—26no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—43no—
433C4⋊C4—43no—
434C4⋊C4—46no—
435C4⋊C4—46no—
436C22⋊C4—26no—
437C22⋊C4—26no—
438C22⋊C4—43no—
439C22⋊C4—43no—
440C22⋊C4—43no—
441C22⋊C4—43no—
442C22⋊C4—46no—
443C22⋊C4—46no—
444C22⋊C4—46no—
445C42—26no—
446C42—26no—
447C42—26no—
448C42—26no—
449C42—26no—
450C42—26no—
451C42—46no—
452C23—23no—
453C23—23no—
454C23—23no—
455C23—23no—
456C23—23no—
457C23—23no—
458C23—23no—
459C23C25×C13911yescharacteristic
460Q8#126×C139116yescomplemented
461D4—412no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—23no—
471C2×C4—23no—
472C2×C4—23no—
473C2×C4—23no—
474C2×C4—23no—
475C2×C4—23no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—23no—
480C2×C4—23no—
481C2×C4—23no—
482C2×C4—23no—
483C2×C4—23no—
484C2×C4—23no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—23no—
493C2×C4—23no—
494C2×C4—23no—
495C2×C4—23no—
496C2×C4—23no—
497C2×C4—23no—
498C2×C4—21no—
499C2×C4—412no—
500C2×C4C2×#41×C13916yes—
501C2×C4C2×#41×C13916yes—
502C2×C4C2×#41×C13916yes—
503C2×C4H(5,𝔽2)×C13912yes—
504C2×C42−1+4×C13912yes—
505C22—43no—
506C22—43no—
507C22—43no—
508C22—43no—
509C22—43no—
510C22—43no—
511C22—43no—
512C22C22×#41×C13911yescharacteristic
513C22C22×#41×C13911yescharacteristic
514C22C22×#41×C13911yescharacteristic
515C22C2×H(5,𝔽2)×C13911yescharacteristic
516C22C2×2−1+4×C13911yescharacteristic
517C22#585×C13911yescharacteristic
518C22#585×C13911yescharacteristic
519C4—22no—
520C4—22no—
521C4—41no—
522C4—41no—
523C4—43no—
524C4—43no—
525C4—43no—
526C4—43no—
527C4—41no—
528C4—41no—
529C4—43no—
530C4—41no—
531C4—43no—
532C4C2×#126×C139112yes—
533C2—83no—
534C2C22×#126×C13911yescharacteristic
535C2#3516×C13911yescharacteristic
536C2#3517×C13911yescharacteristic
537C2#3517×C13911yescharacteristic
538C2#3518×C13911yescharacteristic
539C2#3522×C13911yescharacteristic
540C2#3524×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. #2644×C139C2semidirect
2. #2513×C139C2semidirect
3. #2512×C139C2semidirect
4. #2512×C139C2semidirect
5. #2497×C139C2semidirect
6. #2496×C139C2semidirect
7. #2494×C139C2semidirect
8. #2401×C139C2semidirect
9. #2351×C139C2semidirect
10. Q8×C4⋊C4×C139C2semidirect
11. Q8×C4⋊C4×C139C2semidirect
15. #2276×C139C2semidirect
189. Q8×C139#126semidirect
270. #35898C139direct (N × H)
271. C139#35898direct (N × H)
272. #2644C2×C139semidirect
273. #2513C2×C139semidirect
274. #2512C2×C139semidirect
275. #2512C2×C139semidirect
276. #2497C2×C139semidirect
277. #2496C2×C139semidirect
278. #2494C2×C139semidirect
279. #2401C2×C139semidirect
280. #2351C2×C139semidirect
281. Q8×C4⋊C4C2×C139semidirect
282. Q8×C4⋊C4C2×C139semidirect
286. #2276C2×C139semidirect
460. Q8#126×C139semidirect

Maximal subgroups

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

subgroupindex
#2644×C1392
#2513×C1392
#2512×C1392
#2497×C1392
#2496×C1392
#2494×C1392
#2401×C1392
#2351×C1392
Q8×C4⋊C4×C1392
#2341×C1392
#2276×C1392
#35898139