Finite Group Databasebeta

← C139×#36652 #48031248

Subgroups — C139×#36652 #48031248

Order 35584.

2570 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C139C212yesmaximal, complemented
2#2817×C139C211yesmaximal, characteristic, complemented
3#2816×C139C212yesmaximal, complemented
4#2815×C139C211yesmaximal, characteristic, complemented
5#2814×C139C214yesmaximal, complemented
6#2813×C139C214yesmaximal, complemented
7#2812×C139C214yesmaximal, complemented
8#2395×C139C214yesmaximal, complemented
9#2392×C139C214yesmaximal, complemented
10#2388×C139C214yesmaximal, complemented
11#2280×C139C211yesmaximal, characteristic, complemented
12C22×#41×C139C2212yes—
13C24×C4×C139C2211yescharacteristic
14#525×C139—216no—
15C2×#123×C139C2214yes—
16C2×C22⋊Q8×C139C2212yes—
17C2×C22⋊Q8×C139C2212yes—
18C2×#121×C139C2212yes—
19C2×#121×C139C2212yes—
20C2×#120×C139C2214yes—
21C2×C4×D4×C139C2214yes—
22C2×C4×D4×C139C2214yes—
23C2×C4×D4×C139C2214yescomplemented
24C2×#117×C139C2212yes—
25C2×#117×C139C2212yes—
26#400×C139C2214yescomplemented
27#399×C139C2214yescomplemented
28#398×C139C2214yescomplemented
29#398×C139C2214yescomplemented
30#397×C139C2218yes—
31#397×C139C2214yes—
32#397×C139C2214yescomplemented
33#396×C139C2218yescomplemented
34#395×C139C2214yescomplemented
35#394×C139C2218yes—
36#394×C139C2218yes—
37#394×C139C2218yes—
38#394×C139C2214yescomplemented
39#394×C139C2214yescomplemented
40#393×C139C2214yescomplemented
41#392×C139C2218yes—
42#392×C139C2214yes—
43#392×C139C2214yescomplemented
44#381×C139C2211yescharacteristic
45#381×C139C2211yescharacteristic
46#380×C139C2214yes—
47#379×C139C2212yes—
48C4×C4⋊C4×C139C2214yescomplemented
49C4×C22⋊C4×C139C2214yes—
50C4×C22⋊C4×C139C2218yescomplemented
51C25×C139C2311yescharacteristic
52C2×#41×C139—28no—
53C2×#41×C139—48no—
54C22×Q8×C139C2312yes—
55C22×D4×C139C2314yes—
56C22×D4×C139C2314yes—
57C22×D4×C139C2314yes—
58C22×D4×C139C2312yes—
59C22×D4×C139C2314yes—
60C23×C4×C139—44no—
61C23×C4×C139D418yescomplemented
62C23×C4×C139C2314yes—
63C23×C4×C139C2311yescharacteristic
64C23×C4×C139C2312yes—
65C23×C4×C139C2311yescharacteristic
66C23×C4×C139C2312yes—
67#123×C139—216no—
68C22⋊Q8×C139—28no—
69C22⋊Q8×C139—28no—
70#121×C139—28no—
71#121×C139—28no—
72#120×C139—216no—
73C4×D4×C139—216no—
74C4×D4×C139—216no—
75C4×D4×C139—48no—
76#117×C139—28no—
77#117×C139—44no—
78C2×C4⋊C4×C139C2314yes—
79C2×C4⋊C4×C139C2314yes—
80C2×C4⋊C4×C139C2312yes—
81C2×C4⋊C4×C139C2312yes—
82C2×C4⋊C4×C139C2314yes—
83C2×C4⋊C4×C139C2314yes—
84C2×C4⋊C4×C139C2318yes—
85C2×C22⋊C4×C139C2314yes—
86C2×C22⋊C4×C139C2314yes—
87C2×C22⋊C4×C139C2314yes—
88C2×C22⋊C4×C139C2314yes—
89C2×C22⋊C4×C139C2314yes—
90C2×C22⋊C4×C139C2318yes—
91C2×C22⋊C4×C139C2318yes—
92C2×C22⋊C4×C139C2312yes—
93C2×C22⋊C4×C139C2318yes—
94C2×C22⋊C4×C139C2318yes—
95C2×C22⋊C4×C139C2312yes—
96C2×C42×C139C2314yes—
97C2×C42×C139C2314yes—
98#95×C139C2318yes—
99#95×C139C2314yes—
100#95×C139C2314yes—
101#95×C139C2318yes—
102#95×C139C2314yes—
103#95×C139C2314yes—
104C24×C139—42no—
105C24×C139—44no—
106C24×C139C2×D414yes—
107C24×C139C2414yes—
108C24×C139C2411yescharacteristic
109C24×C139C2412yes—
110#41×C139—432no—
111C2×Q8×C139—24no—
112C2×Q8×C139—44no—
113C2×D4×C139—28no—
114C2×D4×C139—28no—
115C2×D4×C139—28no—
116C2×D4×C139—24no—
117C2×D4×C139—44no—
118C2×D4×C139—44no—
119C2×D4×C139—48no—
120C2×D4×C139—48no—
121C2×D4×C139—44no—
122C2×D4×C139—44no—
123C2×D4×C139—48no—
124C22×C4×C139—24no—
125C22×C4×C139—28no—
126C22×C4×C139—28no—
127C22×C4×C139—216no—
128C22×C4×C139—416no—
129C22×C4×C139—44no—
130C22×C4×C139—42no—
131C22×C4×C139C2×D418yes—
132C22×C4×C139C2×D414yes—
133C22×C4×C139C2×D414yes—
134C22×C4×C139C2×D418yes—
135C22×C4×C139C2414yes—
136C22×C4×C139C2414yes—
137C22×C4×C139C2414yes—
138C22×C4×C139C2414yes—
139C22×C4×C139C2414yes—
140C22×C4×C139C2412yes—
141C22×C4×C139C2411yescharacteristic
142C22×C4×C139C2411yescharacteristic
143C4⋊C4×C139—24no—
144C4⋊C4×C139—24no—
145C4⋊C4×C139—28no—
146C4⋊C4×C139—28no—
147C4⋊C4×C139—48no—
148C4⋊C4×C139—44no—
149C4⋊C4×C139—44no—
150C22⋊C4×C139—28no—
151C22⋊C4×C139—28no—
152C22⋊C4×C139—28no—
153C22⋊C4×C139—28no—
154C22⋊C4×C139—28no—
155C22⋊C4×C139—48no—
156C22⋊C4×C139—48no—
157C22⋊C4×C139—48no—
158C22⋊C4×C139—42no—
159C22⋊C4×C139—42no—
160C22⋊C4×C139—48no—
161C42×C139—28no—
162C42×C139—28no—
163C23×C139—22no—
164C23×C139—24no—
165C23×C139—24no—
166C23×C139—24no—
167C23×C139—24no—
168C23×C139—24no—
169C23×C139—28no—
170C23×C139—24no—
171C23×C139—28no—
172C23×C139—24no—
173C23×C139—44no—
174C23×C139—48no—
175C23×C139—416no—
176C23×C139C22×D414yes—
177C23×C139C22×D412yes—
178C23×C139C2511yescharacteristic
179Q8×C139—48no—
180D4×C139—48no—
181D4×C139—416no—
182D4×C139—416no—
183D4×C139—416no—
184D4×C139—416no—
185C2×C4×C139—22no—
186C2×C4×C139—24no—
187C2×C4×C139—28no—
188C2×C4×C139—216no—
189C2×C4×C139—24no—
190C2×C4×C139—24no—
191C2×C4×C139—24no—
192C2×C4×C139—24no—
193C2×C4×C139—24no—
194C2×C4×C139—28no—
195C2×C4×C139—28no—
196C2×C4×C139—24no—
197C2×C4×C139—28no—
198C2×C4×C139—28no—
199C2×C4×C139—24no—
200C2×C4×C139—48no—
201C2×C4×C139—44no—
202C2×C4×C139—416no—
203C2×C4×C139C22×D412yes—
204C2×C4×C139C22×D414yes—
205C2×C4×C139C22×D412yes—
206C2×C4×C139H(5,𝔽2)14yes—
207C22×C139—24no—
208C22×C139—22no—
209C22×C139—24no—
210C22×C139—24no—
211C22×C139—24no—
212C22×C139—416no—
213C22×C139—44no—
214C22×C139—48no—
215C22×C139—44no—
216C22×C139—44no—
217C22×C139—44no—
218C22×C139—48no—
219C22×C139—48no—
220C22×C139C23×D411yescharacteristic
221C22×C139C2×H(5,𝔽2)12yes—
222C22×C139#58514yes—
223C4×C139—22no—
224C4×C139—24no—
225C4×C139—44no—
226C4×C139—44no—
227C4×C139—44no—
228C4×C139—44no—
229C4×C139—44no—
230C4×C139#53414yes—
231C2×C139—44no—
232C2×C139—42no—
233C2×C139—84no—
234C2×C139C2×#53411yescharacteristic
235C2×C139#344912yes—
236C2×C139#352914yes—
237#36652C13911yesmaximal, characteristic, direct product factor, Sylow
238C139#3665211yescharacteristic, direct product factor, Sylow
239C2×#525C2×C13912yescomplemented
240#2817C2×C13911yescharacteristic, complemented
241#2816C2×C13912yescomplemented
242#2815C2×C13911yescharacteristic, complemented
243#2814C2×C13914yescomplemented
244#2813C2×C13914yescomplemented
245#2812C2×C13914yescomplemented
246#2395C2×C13914yescomplemented
247#2392C2×C13914yescomplemented
248#2388C2×C13914yescomplemented
249#2280C2×C13911yescharacteristic, complemented
250C22×#41C22×C13912yes—
251C24×C4C22×C13911yescharacteristic
252#525—216no—
253C2×#123C22×C13914yes—
254C2×C22⋊Q8C22×C13912yes—
255C2×C22⋊Q8C22×C13912yes—
256C2×#121C22×C13912yes—
257C2×#121C22×C13912yes—
258C2×#120C22×C13914yes—
259C2×C4×D4C22×C13914yes—
260C2×C4×D4C22×C13914yes—
261C2×C4×D4C22×C13914yescomplemented
262C2×#117C22×C13912yes—
263C2×#117C22×C13912yes—
264#400C22×C13914yescomplemented
265#399C22×C13914yescomplemented
266#398C22×C13914yescomplemented
267#398C22×C13914yescomplemented
268#397C22×C13914yes—
269#397C22×C13918yes—
270#397C22×C13914yescomplemented
271#396C22×C13918yescomplemented
272#395C22×C13914yescomplemented
273#394C22×C13918yes—
274#394C22×C13918yes—
275#394C22×C13918yes—
276#394C22×C13914yescomplemented
277#394C22×C13914yescomplemented
278#393C22×C13914yescomplemented
279#392C22×C13918yes—
280#392C22×C13914yes—
281#392C22×C13914yescomplemented
282#381C22×C13911yescharacteristic
283#381C22×C13911yescharacteristic
284#380C22×C13914yes—
285#379C22×C13912yes—
286C4×C4⋊C4C22×C13914yescomplemented
287C4×C22⋊C4C22×C13914yes—
288C4×C22⋊C4C22×C13918yescomplemented
289C25C23×C13911yescharacteristic
290C2×#41—28no—
291C2×#41—48no—
292C22×Q8C23×C13912yes—
293C22×D4C23×C13914yes—
294C22×D4C23×C13914yes—
295C22×D4C23×C13914yes—
296C22×D4C23×C13912yes—
297C22×D4C23×C13914yes—
298C23×C4—44no—
299C23×C4D4×C13918yescomplemented
300C23×C4C23×C13914yes—
301C23×C4C23×C13911yescharacteristic
302C23×C4C23×C13912yes—
303C23×C4C23×C13911yescharacteristic
304C23×C4C23×C13912yes—
305#123—216no—
306C22⋊Q8—28no—
307C22⋊Q8—28no—
308#121—28no—
309#121—28no—
310#120—216no—
311C4×D4—216no—
312C4×D4—216no—
313C4×D4—48no—
314#117—28no—
315#117—44no—
316C2×C4⋊C4C23×C13912yes—
317C2×C4⋊C4C23×C13912yes—
318C2×C4⋊C4C23×C13914yes—
319C2×C4⋊C4C23×C13914yes—
320C2×C4⋊C4C23×C13914yes—
321C2×C4⋊C4C23×C13914yes—
322C2×C4⋊C4C23×C13918yes—
323C2×C22⋊C4C23×C13914yes—
324C2×C22⋊C4C23×C13914yes—
325C2×C22⋊C4C23×C13914yes—
326C2×C22⋊C4C23×C13914yes—
327C2×C22⋊C4C23×C13914yes—
328C2×C22⋊C4C23×C13912yes—
329C2×C22⋊C4C23×C13912yes—
330C2×C22⋊C4C23×C13918yes—
331C2×C22⋊C4C23×C13918yes—
332C2×C22⋊C4C23×C13918yes—
333C2×C22⋊C4C23×C13918yes—
334C2×C42C23×C13914yes—
335C2×C42C23×C13914yes—
336#95C23×C13914yes—
337#95C23×C13914yes—
338#95C23×C13918yes—
339#95C23×C13918yes—
340#95C23×C13914yes—
341#95C23×C13914yes—
342C24—42no—
343C24—44no—
344C24C2×D4×C13914yes—
345C24C24×C13914yes—
346C24C24×C13911yescharacteristic
347C24C24×C13912yes—
348#41—432no—
349C2×Q8—24no—
350C2×Q8—44no—
351C2×D4—28no—
352C2×D4—28no—
353C2×D4—28no—
354C2×D4—24no—
355C2×D4—44no—
356C2×D4—44no—
357C2×D4—48no—
358C2×D4—48no—
359C2×D4—44no—
360C2×D4—44no—
361C2×D4—48no—
362C22×C4—24no—
363C22×C4—28no—
364C22×C4—28no—
365C22×C4—216no—
366C22×C4—416no—
367C22×C4—44no—
368C22×C4—42no—
369C22×C4C2×D4×C13918yes—
370C22×C4C2×D4×C13914yes—
371C22×C4C2×D4×C13914yes—
372C22×C4C2×D4×C13918yes—
373C22×C4C24×C13914yes—
374C22×C4C24×C13914yes—
375C22×C4C24×C13914yes—
376C22×C4C24×C13914yes—
377C22×C4C24×C13914yes—
378C22×C4C24×C13912yes—
379C22×C4C24×C13911yescharacteristic
380C22×C4C24×C13911yescharacteristic
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—28no—
384C4⋊C4—28no—
385C4⋊C4—48no—
386C4⋊C4—44no—
387C4⋊C4—44no—
388C22⋊C4—28no—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—48no—
394C22⋊C4—48no—
395C22⋊C4—48no—
396C22⋊C4—42no—
397C22⋊C4—42no—
398C22⋊C4—48no—
399C42—28no—
400C42—28no—
401C23—22no—
402C23—24no—
403C23—24no—
404C23—24no—
405C23—24no—
406C23—24no—
407C23—28no—
408C23—24no—
409C23—28no—
410C23—24no—
411C23—44no—
412C23—48no—
413C23—416no—
414C23C22×D4×C13914yes—
415C23C22×D4×C13912yes—
416C23C25×C13911yescharacteristic
417Q8—48no—
418D4—48no—
419D4—416no—
420D4—416no—
421D4—416no—
422D4—416no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—216no—
426C2×C4—28no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—28no—
433C2×C4—28no—
434C2×C4—24no—
435C2×C4—28no—
436C2×C4—28no—
437C2×C4—24no—
438C2×C4—44no—
439C2×C4—48no—
440C2×C4—416no—
441C2×C4C22×D4×C13912yes—
442C2×C4C22×D4×C13914yes—
443C2×C4C22×D4×C13912yes—
444C2×C4H(5,𝔽2)×C13914yes—
445C22—24no—
446C22—22no—
447C22—24no—
448C22—24no—
449C22—24no—
450C22—416no—
451C22—44no—
452C22—48no—
453C22—44no—
454C22—44no—
455C22—44no—
456C22—48no—
457C22—48no—
458C22C23×D4×C13911yescharacteristic
459C22C2×H(5,𝔽2)×C13912yes—
460C22#585×C13914yes—
461C4—24no—
462C4—22no—
463C4—44no—
464C4—44no—
465C4—44no—
466C4—44no—
467C4—44no—
468C4#534×C13914yes—
469C2—44no—
470C2—42no—
471C2—84no—
472C2C2×#534×C13911yescharacteristic
473C2#3449×C13912yes—
474C2#3529×C13914yes—
subgroupG/H
centerC22×C4×C139C24
commutator, Frattini, cosocleC23C25×C139
socleC23×C139C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#525×C139C2semidirect
2. #2817×C139C2semidirect
3. #2816×C139C2semidirect
4. #2815×C139C2semidirect
5. #2814×C139C2semidirect
6. #2813×C139C2semidirect
7. #2812×C139C2semidirect
8. #2395×C139C2semidirect
9. #2392×C139C2semidirect
10. #2388×C139C2semidirect
11. #2280×C139C2semidirect
23. C2×C4×D4×C139C22semidirect
26. #400×C139C22semidirect
27. #399×C139C22semidirect
28. #398×C139C22semidirect
29. #398×C139C22semidirect
32. #397×C139C22semidirect
33. #396×C139C22semidirect
34. #395×C139C22semidirect
38. #394×C139C22semidirect
39. #394×C139C22semidirect
40. #393×C139C22semidirect
43. #392×C139C22semidirect
48. C4×C4⋊C4×C139C22semidirect
50. C4×C22⋊C4×C139C22semidirect
61. C23×C4×C139D4semidirect
237. #36652C139direct (N × H)
238. C139#36652direct (N × H)
239. C2×#525C2×C139semidirect
240. #2817C2×C139semidirect
241. #2816C2×C139semidirect
242. #2815C2×C139semidirect
243. #2814C2×C139semidirect
244. #2813C2×C139semidirect
245. #2812C2×C139semidirect
246. #2395C2×C139semidirect
247. #2392C2×C139semidirect
248. #2388C2×C139semidirect
249. #2280C2×C139semidirect
261. C2×C4×D4C22×C139semidirect
264. #400C22×C139semidirect
265. #399C22×C139semidirect
266. #398C22×C139semidirect
267. #398C22×C139semidirect
270. #397C22×C139semidirect
271. #396C22×C139semidirect
272. #395C22×C139semidirect
276. #394C22×C139semidirect
277. #394C22×C139semidirect
278. #393C22×C139semidirect
281. #392C22×C139semidirect
286. C4×C4⋊C4C22×C139semidirect
288. C4×C22⋊C4C22×C139semidirect
299. C23×C4D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1392
#2817×C1392
#2816×C1392
#2815×C1392
#2814×C1392
#2813×C1392
#2812×C1392
#2395×C1392
#2392×C1392
#2388×C1392
#2280×C1392
#36652139