Finite Group Databasebeta

← C139×#36978 #48031574

Subgroups — C139×#36978 #48031574

Order 35584.

1726 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2854×C139C212yesmaximal, complemented
2#2777×C139C214yesmaximal, complemented
3#2756×C139C214yesmaximal, complemented
4#2749×C139C214yesmaximal, complemented
5#2738×C139C214yesmaximal, complemented
6#2656×C139C211yesmaximal, characteristic
7#2646×C139C211yesmaximal, characteristic, complemented
8#2444×C139C214yesmaximal, complemented
9#2425×C139C214yesmaximal, complemented
10#2325×C139C212yesmaximal, complemented
11C2×#383×C139C211yesmaximal, characteristic, complemented
12C2×#123×C139C2214yes—
13C2×#121×C139C2212yes—
14C2×#121×C139C2214yes—
15C2×C4×D4×C139C2214yes—
16C22×C42×C139C2211yescharacteristic
17#400×C139C2214yes—
18#400×C139C2214yes—
19#399×C139C2214yes—
20#398×C139C2214yes—
21#398×C139C2214yes—
22#397×C139C2214yes—
23#397×C139C2214yes—
24#397×C139C2214yes—
25#396×C139C2214yes—
26#394×C139C2214yes—
27#394×C139C2214yes—
28#392×C139C2214yes—
29#390×C139C2212yes—
30#390×C139C2212yes—
31#389×C139C2212yes—
32#389×C139C2214yes—
33#389×C139C2212yes—
34#388×C139C2214yes—
35#388×C139C2214yes—
36#388×C139C2214yes—
37#388×C139C2214yes—
38#388×C139C2214yes—
39#387×C139C2214yes—
40#387×C139C2214yes—
41#386×C139C2214yes—
42#386×C139C2214yes—
43#386×C139C2214yes—
44#386×C139C2214yes—
45#386×C139C2214yes—
46#385×C139C2214yes—
47#385×C139C2214yes—
48#383×C139C2214yes—
49#383×C139C2214yes—
50#381×C139C2214yes—
51#380×C139C2212yes—
52#380×C139C2214yes—
53C2×#95×C139C2211yescharacteristic
54C2×#95×C139C2211yescharacteristic
55C2×#95×C139C2212yes—
56C2×#95×C139C2212yes—
57C22×D4×C139C2314yes—
58C22×D4×C139C2312yes—
59C22×D4×C139C2314yes—
60C23×C4×C139C2311yescharacteristic
61C23×C4×C139C2311yescharacteristic
62C23×C4×C139C2312yes—
63C23×C4×C139C2312yes—
64C23×C4×C139C2314yes—
65C23×C4×C139C2311yescharacteristic
66#123×C139—48no—
67#121×C139—28no—
68#121×C139—48no—
69C4×D4×C139—48no—
70C2×C4⋊C4×C139C2312yes—
71C2×C4⋊C4×C139C2314yes—
72C2×C4⋊C4×C139C2314yes—
73C2×C4⋊C4×C139C2314yes—
74C2×C4⋊C4×C139C2314yes—
75C2×C4⋊C4×C139C2314yes—
76C2×C4⋊C4×C139C2312yes—
77C2×C4⋊C4×C139C2314yes—
78C2×C4⋊C4×C139C2312yes—
79C2×C22⋊C4×C139C2314yes—
80C2×C22⋊C4×C139C2314yes—
81C2×C22⋊C4×C139C2314yes—
82C2×C22⋊C4×C139C2314yes—
83C2×C22⋊C4×C139C2314yes—
84C2×C22⋊C4×C139C2314yes—
85C2×C22⋊C4×C139C2314yes—
86C2×C22⋊C4×C139C2314yes—
87C2×C22⋊C4×C139C2314yes—
88C2×C22⋊C4×C139C2314yes—
89C2×C22⋊C4×C139C2314yes—
90C2×C42×C139—24no—
91C2×C42×C139C2312yes—
92C2×C42×C139C2312yes—
93C2×C42×C139C2314yes—
94#95×C139C2314yes—
95#95×C139C2314yes—
96#95×C139C2314yes—
97#95×C139C2314yes—
98#95×C139C2314yes—
99#95×C139C2314yes—
100#95×C139C2314yes—
101#95×C139C2314yes—
102#95×C139C2314yes—
103#95×C139C2314yes—
104#95×C139C2314yes—
105#95×C139C2314yes—
106#95×C139C2314yes—
107C24×C139C2414yes—
108C24×C139C2411yescharacteristic
109C2×D4×C139—28no—
110C2×D4×C139—28no—
111C2×D4×C139—28no—
112C2×D4×C139—24no—
113C2×D4×C139—44no—
114C2×D4×C139—42no—
115C2×D4×C139—42no—
116C2×D4×C139—44no—
117C2×D4×C139—44no—
118C22×C4×C139—22no—
119C22×C4×C139—22no—
120C22×C4×C139—24no—
121C22×C4×C139—24no—
122C22×C4×C139—24no—
123C22×C4×C139—42no—
124C22×C4×C139—41no—
125C22×C4×C139—41no—
126C22×C4×C139—44no—
127C22×C4×C139—44no—
128C22×C4×C139—42no—
129C22×C4×C139—42no—
130C22×C4×C139—44no—
131C22×C4×C139—42no—
132C22×C4×C139—42no—
133C22×C4×C139#4114yes—
134C22×C4×C139C2412yes—
135C22×C4×C139C2414yes—
136C22×C4×C139C2414yes—
137C22×C4×C139C2414yes—
138C22×C4×C139C2411yescharacteristic
139C22×C4×C139C2411yescharacteristic
140C22×C4×C139C2414yes—
141C22×C4×C139C2414yes—
142C22×C4×C139C2412yes—
143C4⋊C4×C139—24no—
144C4⋊C4×C139—42no—
145C4⋊C4×C139—42no—
146C4⋊C4×C139—44no—
147C4⋊C4×C139—44no—
148C4⋊C4×C139—44no—
149C4⋊C4×C139—44no—
150C4⋊C4×C139—44no—
151C4⋊C4×C139—44no—
152C22⋊C4×C139—28no—
153C22⋊C4×C139—28no—
154C22⋊C4×C139—44no—
155C22⋊C4×C139—44no—
156C22⋊C4×C139—44no—
157C22⋊C4×C139—44no—
158C22⋊C4×C139—44no—
159C22⋊C4×C139—44no—
160C22⋊C4×C139—44no—
161C22⋊C4×C139—44no—
162C22⋊C4×C139—44no—
163C42×C139—24no—
164C42×C139—24no—
165C42×C139—44no—
166C23×C139—22no—
167C23×C139—21no—
168C23×C139—21no—
169C23×C139—24no—
170C23×C139—24no—
171C23×C139—24no—
172C23×C139—24no—
173C23×C139—24no—
174C23×C139—24no—
175C23×C139—24no—
176C23×C139C2×#4112yes—
177C23×C139H(5,𝔽2)14yes—
178C23×C139C2511yescharacteristic
179D4×C139—416no—
180D4×C139—84no—
181D4×C139—88no—
182C2×C4×C139—22no—
183C2×C4×C139—22no—
184C2×C4×C139—21no—
185C2×C4×C139—21no—
186C2×C4×C139—22no—
187C2×C4×C139—24no—
188C2×C4×C139—24no—
189C2×C4×C139—24no—
190C2×C4×C139—24no—
191C2×C4×C139—24no—
192C2×C4×C139—22no—
193C2×C4×C139—22no—
194C2×C4×C139—24no—
195C2×C4×C139—24no—
196C2×C4×C139—22no—
197C2×C4×C139—22no—
198C2×C4×C139—24no—
199C2×C4×C139—24no—
200C2×C4×C139—24no—
201C2×C4×C139—24no—
202C2×C4×C139—24no—
203C2×C4×C139—24no—
204C2×C4×C139—24no—
205C2×C4×C139—24no—
206C2×C4×C139—44no—
207C2×C4×C139—44no—
208C2×C4×C139—44no—
209C2×C4×C139—84no—
210C2×C4×C139—84no—
211C2×C4×C139—88no—
212C2×C4×C139C2×#4114yes—
213C22×C139—22no—
214C22×C139—22no—
215C22×C139—24no—
216C22×C139—24no—
217C22×C139—44no—
218C22×C139—44no—
219C22×C139—44no—
220C22×C139—44no—
221C22×C139—44no—
222C22×C139—44no—
223C22×C139—44no—
224C22×C139#54014yes—
225C22×C139C22×#4111yescharacteristic
226C22×C139C2×H(5,𝔽2)12yes—
227C22×C139#58512yes—
228C22×C139#58511yescharacteristic
229C22×C139#58511yescharacteristic
230C4×C139—24no—
231C4×C139—41no—
232C4×C139—41no—
233C4×C139—44no—
234C4×C139—42no—
235C4×C139—44no—
236C4×C139—44no—
237C4×C139—44no—
238C4×C139—44no—
239C2×C139—24no—
240C2×C139—84no—
241C2×C139C2×#54011yescharacteristic
242C2×C139#349111yescharacteristic
243C2×C139#349311yescharacteristic
244C2×C139#356012yes—
245C2×C139#356012yes—
246#36978C13911yesmaximal, characteristic, direct product factor, Sylow
247C139#3697811yescharacteristic, direct product factor, Sylow
248#2854C2×C13912yescomplemented
249#2777C2×C13914yescomplemented
250#2756C2×C13914yescomplemented
251#2749C2×C13914yescomplemented
252#2738C2×C13914yescomplemented
253#2656C2×C13911yescharacteristic
254#2646C2×C13911yescharacteristic, complemented
255#2444C2×C13914yescomplemented
256#2425C2×C13914yescomplemented
257#2325C2×C13912yescomplemented
258C2×#383C2×C13911yescharacteristic, complemented
259C2×#123C22×C13914yes—
260C2×#121C22×C13912yes—
261C2×#121C22×C13914yes—
262C2×C4×D4C22×C13914yes—
263C22×C42C22×C13911yescharacteristic
264#400C22×C13914yes—
265#400C22×C13914yes—
266#399C22×C13914yes—
267#398C22×C13914yes—
268#398C22×C13914yes—
269#397C22×C13914yes—
270#397C22×C13914yes—
271#397C22×C13914yes—
272#396C22×C13914yes—
273#394C22×C13914yes—
274#394C22×C13914yes—
275#392C22×C13914yes—
276#390C22×C13912yes—
277#390C22×C13912yes—
278#389C22×C13912yes—
279#389C22×C13912yes—
280#389C22×C13914yes—
281#388C22×C13914yes—
282#388C22×C13914yes—
283#388C22×C13914yes—
284#388C22×C13914yes—
285#388C22×C13914yes—
286#387C22×C13914yes—
287#387C22×C13914yes—
288#386C22×C13914yes—
289#386C22×C13914yes—
290#386C22×C13914yes—
291#386C22×C13914yes—
292#386C22×C13914yes—
293#385C22×C13914yes—
294#385C22×C13914yes—
295#383C22×C13914yes—
296#383C22×C13914yes—
297#381C22×C13914yes—
298#380C22×C13912yes—
299#380C22×C13914yes—
300C2×#95C22×C13911yescharacteristic
301C2×#95C22×C13911yescharacteristic
302C2×#95C22×C13912yes—
303C2×#95C22×C13912yes—
304C22×D4C23×C13914yes—
305C22×D4C23×C13912yes—
306C22×D4C23×C13914yes—
307C23×C4C23×C13911yescharacteristic
308C23×C4C23×C13912yes—
309C23×C4C23×C13912yes—
310C23×C4C23×C13911yescharacteristic
311C23×C4C23×C13914yes—
312C23×C4C23×C13911yescharacteristic
313#123—48no—
314#121—28no—
315#121—48no—
316C4×D4—48no—
317C2×C4⋊C4C23×C13912yes—
318C2×C4⋊C4C23×C13914yes—
319C2×C4⋊C4C23×C13914yes—
320C2×C4⋊C4C23×C13914yes—
321C2×C4⋊C4C23×C13914yes—
322C2×C4⋊C4C23×C13912yes—
323C2×C4⋊C4C23×C13914yes—
324C2×C4⋊C4C23×C13912yes—
325C2×C4⋊C4C23×C13914yes—
326C2×C22⋊C4C23×C13914yes—
327C2×C22⋊C4C23×C13914yes—
328C2×C22⋊C4C23×C13914yes—
329C2×C22⋊C4C23×C13914yes—
330C2×C22⋊C4C23×C13914yes—
331C2×C22⋊C4C23×C13914yes—
332C2×C22⋊C4C23×C13914yes—
333C2×C22⋊C4C23×C13914yes—
334C2×C22⋊C4C23×C13914yes—
335C2×C22⋊C4C23×C13914yes—
336C2×C22⋊C4C23×C13914yes—
337C2×C42—24no—
338C2×C42C23×C13912yes—
339C2×C42C23×C13912yes—
340C2×C42C23×C13914yes—
341#95C23×C13914yes—
342#95C23×C13914yes—
343#95C23×C13914yes—
344#95C23×C13914yes—
345#95C23×C13914yes—
346#95C23×C13914yes—
347#95C23×C13914yes—
348#95C23×C13914yes—
349#95C23×C13914yes—
350#95C23×C13914yes—
351#95C23×C13914yes—
352#95C23×C13914yes—
353#95C23×C13914yes—
354C24C24×C13914yes—
355C24C24×C13911yescharacteristic
356C2×D4—28no—
357C2×D4—28no—
358C2×D4—28no—
359C2×D4—24no—
360C2×D4—44no—
361C2×D4—42no—
362C2×D4—42no—
363C2×D4—44no—
364C2×D4—44no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—42no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—44no—
374C22×C4—44no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—44no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4#41×C13914yes—
381C22×C4C24×C13912yes—
382C22×C4C24×C13914yes—
383C22×C4C24×C13914yes—
384C22×C4C24×C13914yes—
385C22×C4C24×C13911yescharacteristic
386C22×C4C24×C13911yescharacteristic
387C22×C4C24×C13914yes—
388C22×C4C24×C13914yes—
389C22×C4C24×C13912yes—
390C4⋊C4—24no—
391C4⋊C4—42no—
392C4⋊C4—42no—
393C4⋊C4—44no—
394C4⋊C4—44no—
395C4⋊C4—44no—
396C4⋊C4—44no—
397C4⋊C4—44no—
398C4⋊C4—44no—
399C22⋊C4—28no—
400C22⋊C4—28no—
401C22⋊C4—44no—
402C22⋊C4—44no—
403C22⋊C4—44no—
404C22⋊C4—44no—
405C22⋊C4—44no—
406C22⋊C4—44no—
407C22⋊C4—44no—
408C22⋊C4—44no—
409C22⋊C4—44no—
410C42—24no—
411C42—24no—
412C42—44no—
413C23—22no—
414C23—21no—
415C23—21no—
416C23—24no—
417C23—24no—
418C23—24no—
419C23—24no—
420C23—24no—
421C23—24no—
422C23—24no—
423C23C2×#41×C13912yes—
424C23H(5,𝔽2)×C13914yes—
425C23C25×C13911yescharacteristic
426D4—416no—
427D4—84no—
428D4—88no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—24no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—84no—
457C2×C4—84no—
458C2×C4—88no—
459C2×C4C2×#41×C13914yes—
460C22—24no—
461C22—24no—
462C22—22no—
463C22—22no—
464C22—44no—
465C22—44no—
466C22—44no—
467C22—44no—
468C22—44no—
469C22—44no—
470C22—44no—
471C22#540×C13914yes—
472C22C22×#41×C13911yescharacteristic
473C22C2×H(5,𝔽2)×C13912yes—
474C22#585×C13912yes—
475C22#585×C13911yescharacteristic
476C22#585×C13911yescharacteristic
477C4—24no—
478C4—44no—
479C4—44no—
480C4—44no—
481C4—44no—
482C4—41no—
483C4—41no—
484C4—44no—
485C4—42no—
486C2—24no—
487C2—84no—
488C2C2×#540×C13911yescharacteristic
489C2#3491×C13911yescharacteristic
490C2#3493×C13911yescharacteristic
491C2#3560×C13912yes—
492C2#3560×C13912yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radical#2656×C139C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2854×C139C2semidirect
2. #2777×C139C2semidirect
3. #2756×C139C2semidirect
4. #2749×C139C2semidirect
5. #2738×C139C2semidirect
7. #2646×C139C2semidirect
8. #2444×C139C2semidirect
9. #2425×C139C2semidirect
10. #2325×C139C2semidirect
11. C2×#383×C139C2semidirect
246. #36978C139direct (N × H)
247. C139#36978direct (N × H)
248. #2854C2×C139semidirect
249. #2777C2×C139semidirect
250. #2756C2×C139semidirect
251. #2749C2×C139semidirect
252. #2738C2×C139semidirect
254. #2646C2×C139semidirect
255. #2444C2×C139semidirect
256. #2425C2×C139semidirect
257. #2325C2×C139semidirect
258. C2×#383C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2854×C1392
#2777×C1392
#2756×C1392
#2749×C1392
#2738×C1392
#2656×C1392
#2646×C1392
#2444×C1392
#2425×C1392
#2325×C1392
C2×#383×C1392
#36978139