Finite Group Databasebeta

← C139×#37208 #48031804

Subgroups — C139×#37208 #48031804

Order 35584.

1492 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2863×C139C212yesmaximal, complemented
2#2811×C139C211yesmaximal, characteristic, complemented
3#2808×C139C212yesmaximal
4#2789×C139C212yesmaximal, complemented
5#2775×C139C214yesmaximal, complemented
6#2759×C139C214yesmaximal, complemented
7#2734×C139C211yesmaximal, characteristic, complemented
8#2731×C139C212yesmaximal
9#2638×C139C212yesmaximal
10#2527×C139C214yesmaximal, complemented
11#2465×C139C214yesmaximal, complemented
12#2327×C139C212yesmaximal, complemented
13C4×#124×C139C211yesmaximal, characteristic
14C2×C4⋊Q8×C139C2212yes—
15C2×#124×C139C2211yescharacteristic
16C2×C22⋊Q8×C139C2212yes—
17C2×C4×Q8×C139C2211yescharacteristic
18C2×C4×Q8×C139C2212yes—
19C2×C4×D4×C139C2211yescharacteristic
20#401×C139C2214yes—
21#400×C139C2214yes—
22#398×C139C2212yes—
23#397×C139C2214yes—
24#397×C139C2214yes—
25#397×C139C2212yes—
26#396×C139C2214yes—
27#395×C139C2214yes—
28#395×C139C2212yes—
29#395×C139C2214yes—
30#394×C139C2214yes—
31#393×C139C2212yes—
32#393×C139C2214yes—
33#393×C139C2214yes—
34#391×C139C2214yes—
35#391×C139C2212yes—
36#391×C139C2214yes—
37#391×C139C2212yes—
38#391×C139C2211yescharacteristic
39#391×C139C2212yes—
40#391×C139C2212yes—
41#391×C139C2212yes—
42#390×C139C2211yescharacteristic
43#389×C139C2212yes—
44#389×C139C2212yes—
45#389×C139C2212yes—
46#388×C139C2214yes—
47#388×C139C2214yes—
48#388×C139C2214yes—
49#388×C139C2214yes—
50#388×C139C2214yes—
51#387×C139C2214yes—
52#387×C139C2214yes—
53#387×C139C2214yes—
54#387×C139C2214yes—
55#387×C139C2214yes—
56#387×C139C2214yes—
57#387×C139C2214yes—
58#387×C139C2214yes—
59#385×C139C2214yes—
60#383×C139C2214yes—
61#382×C139C2212yes—
62#382×C139C2211yescharacteristic
63#381×C139C2212yes—
64C4×C22⋊C4×C139C2214yes—
65#376×C139C2212yes—
66C43×C139C2211yescharacteristic
67C22×Q8×C139C2312yes—
68C22×Q8×C139C2312yes—
69C22×Q8×C139C2312yes—
70C22×Q8×C139C2311yescharacteristic
71C22×D4×C139C2311yescharacteristic
72C23×C4×C139C2312yes—
73C4⋊Q8×C139—28no—
74#124×C139—24no—
75C22⋊Q8×C139—44no—
76C4×Q8×C139—42no—
77C4×Q8×C139—44no—
78C4×D4×C139—42no—
79C2×C4⋊C4×C139C2314yes—
80C2×C4⋊C4×C139C2312yes—
81C2×C4⋊C4×C139C2314yes—
82C2×C4⋊C4×C139C2314yes—
83C2×C4⋊C4×C139C2312yes—
84C2×C4⋊C4×C139C2312yes—
85C2×C4⋊C4×C139C2314yes—
86C2×C4⋊C4×C139C2311yescharacteristic
87C2×C4⋊C4×C139C2312yes—
88C2×C4⋊C4×C139C2312yes—
89C2×C4⋊C4×C139C2314yes—
90C2×C4⋊C4×C139C2311yescharacteristic
91C2×C4⋊C4×C139C2312yes—
92C2×C22⋊C4×C139C2314yes—
93C2×C22⋊C4×C139C2314yes—
94C2×C22⋊C4×C139C2314yes—
95C2×C22⋊C4×C139C2314yes—
96C2×C22⋊C4×C139C2312yes—
97C2×C22⋊C4×C139C2314yes—
98C2×C22⋊C4×C139C2314yes—
99C2×C42×C139C2311yescharacteristic
100C2×C42×C139C2312yes—
101C2×C42×C139C2311yescharacteristic
102C2×C42×C139C2312yes—
103C2×C42×C139C2312yes—
104C2×C42×C139C2314yes—
105C2×C42×C139C2312yes—
106C2×C42×C139C2311yescharacteristic
107C2×C42×C139C2312yes—
108#95×C139C2314yes—
109#95×C139C2314yes—
110#95×C139C2312yes—
111#95×C139C2314yes—
112#95×C139C2314yes—
113#95×C139C2314yes—
114#95×C139C2314yes—
115#95×C139C2314yes—
116#95×C139C2314yes—
117#95×C139C2314yes—
118#95×C139C2314yes—
119#95×C139C2314yes—
120#95×C139C2312yes—
121#95×C139C2314yes—
122#95×C139C2314yes—
123#95×C139C2314yes—
124#95×C139C2314yes—
125#95×C139C2314yes—
126C24×C139C2412yes—
127C2×Q8×C139—24no—
128C2×Q8×C139—24no—
129C2×Q8×C139—41no—
130C2×Q8×C139—42no—
131C2×Q8×C139—41no—
132C2×Q8×C139—42no—
133C2×Q8×C139—42no—
134C2×Q8×C139—42no—
135C2×Q8×C139—42no—
136C2×Q8×C139—44no—
137C2×Q8×C139#4114yes—
138C2×D4×C139—22no—
139C2×D4×C139—41no—
140C2×D4×C139—41no—
141C22×C4×C139—24no—
142C22×C4×C139—44no—
143C22×C4×C139C2414yes—
144C22×C4×C139C2412yes—
145C22×C4×C139C2412yes—
146C22×C4×C139C2411yescharacteristic
147C22×C4×C139C2414yes—
148C22×C4×C139C2412yes—
149C22×C4×C139C2414yes—
150C22×C4×C139C2414yes—
151C22×C4×C139C2412yes—
152C22×C4×C139C2411yescharacteristic
153C22×C4×C139C2411yescharacteristic
154C22×C4×C139C2412yes—
155C4⋊C4×C139—28no—
156C4⋊C4×C139—28no—
157C4⋊C4×C139—28no—
158C4⋊C4×C139—24no—
159C4⋊C4×C139—42no—
160C4⋊C4×C139—42no—
161C4⋊C4×C139—44no—
162C4⋊C4×C139—44no—
163C4⋊C4×C139—41no—
164C4⋊C4×C139—41no—
165C4⋊C4×C139—42no—
166C4⋊C4×C139—42no—
167C4⋊C4×C139—42no—
168C22⋊C4×C139—28no—
169C22⋊C4×C139—28no—
170C22⋊C4×C139—44no—
171C22⋊C4×C139—44no—
172C22⋊C4×C139—44no—
173C22⋊C4×C139—42no—
174C22⋊C4×C139—44no—
175C42×C139—22no—
176C42×C139—24no—
177C42×C139—22no—
178C42×C139—24no—
179C42×C139—24no—
180C42×C139—41no—
181C42×C139—42no—
182C42×C139—42no—
183C42×C139—44no—
184C23×C139—22no—
185C23×C139—22no—
186C23×C139—24no—
187C23×C139—24no—
188C23×C139—22no—
189C23×C139C2511yescharacteristic
190Q8×C139—44no—
191Q8×C139—48no—
192Q8×C139—84no—
193Q8×C139—84no—
194D4×C139—44no—
195C2×C4×C139—21no—
196C2×C4×C139—22no—
197C2×C4×C139—22no—
198C2×C4×C139—22no—
199C2×C4×C139—22no—
200C2×C4×C139—21no—
201C2×C4×C139—22no—
202C2×C4×C139—22no—
203C2×C4×C139—24no—
204C2×C4×C139—24no—
205C2×C4×C139—22no—
206C2×C4×C139—21no—
207C2×C4×C139—24no—
208C2×C4×C139—24no—
209C2×C4×C139—22no—
210C2×C4×C139—22no—
211C2×C4×C139—22no—
212C2×C4×C139—24no—
213C2×C4×C139—24no—
214C2×C4×C139—24no—
215C2×C4×C139—24no—
216C2×C4×C139—22no—
217C2×C4×C139—24no—
218C2×C4×C139—24no—
219C2×C4×C139—24no—
220C2×C4×C139—24no—
221C2×C4×C139—24no—
222C2×C4×C139—24no—
223C2×C4×C139—84no—
224C2×C4×C139C2×#4114yes—
225C2×C4×C139C2×#4112yes—
226C2×C4×C139H(5,𝔽2)12yes—
227C2×C4×C1392−1+414yes—
228C22×C139—42no—
229C22×C139—44no—
230C22×C139—42no—
231C22×C139—42no—
232C22×C139—44no—
233C22×C139C22×#4111yescharacteristic
234C22×C139C2×H(5,𝔽2)11yescharacteristic
235C22×C139C2×2−1+412yes—
236C22×C139#58511yescharacteristic
237C22×C139#58512yes—
238C4×C139—22no—
239C4×C139—24no—
240C4×C139—22no—
241C4×C139—24no—
242C4×C139—44no—
243C4×C139—42no—
244C4×C139—44no—
245C4×C139—42no—
246C4×C139—44no—
247C4×C139—42no—
248C4×C139—41no—
249C4×C139—44no—
250C2×C139—82no—
251C2×C139#345911yescharacteristic
252C2×C139#351812yes—
253C2×C139#354511yescharacteristic
254C2×C139#355011yescharacteristic
255C2×C139#356412yes—
256#37208C13911yesmaximal, characteristic, direct product factor, Sylow
257C139#3720811yescharacteristic, direct product factor, Sylow
258#2863C2×C13912yescomplemented
259#2811C2×C13911yescharacteristic, complemented
260#2808C2×C13912yes—
261#2789C2×C13912yescomplemented
262#2775C2×C13914yescomplemented
263#2759C2×C13914yescomplemented
264#2734C2×C13911yescharacteristic, complemented
265#2731C2×C13912yes—
266#2638C2×C13912yes—
267#2527C2×C13914yescomplemented
268#2465C2×C13914yescomplemented
269#2327C2×C13912yescomplemented
270C4×#124C2×C13911yescharacteristic
271C2×C4⋊Q8C22×C13912yes—
272C2×#124C22×C13911yescharacteristic
273C2×C22⋊Q8C22×C13912yes—
274C2×C4×Q8C22×C13911yescharacteristic
275C2×C4×Q8C22×C13912yes—
276C2×C4×D4C22×C13911yescharacteristic
277#401C22×C13914yes—
278#400C22×C13914yes—
279#398C22×C13912yes—
280#397C22×C13912yes—
281#397C22×C13914yes—
282#397C22×C13914yes—
283#396C22×C13914yes—
284#395C22×C13912yes—
285#395C22×C13914yes—
286#395C22×C13914yes—
287#394C22×C13914yes—
288#393C22×C13912yes—
289#393C22×C13914yes—
290#393C22×C13914yes—
291#391C22×C13912yes—
292#391C22×C13912yes—
293#391C22×C13912yes—
294#391C22×C13912yes—
295#391C22×C13912yes—
296#391C22×C13914yes—
297#391C22×C13911yescharacteristic
298#391C22×C13914yes—
299#390C22×C13911yescharacteristic
300#389C22×C13912yes—
301#389C22×C13912yes—
302#389C22×C13912yes—
303#388C22×C13914yes—
304#388C22×C13914yes—
305#388C22×C13914yes—
306#388C22×C13914yes—
307#388C22×C13914yes—
308#387C22×C13914yes—
309#387C22×C13914yes—
310#387C22×C13914yes—
311#387C22×C13914yes—
312#387C22×C13914yes—
313#387C22×C13914yes—
314#387C22×C13914yes—
315#387C22×C13914yes—
316#385C22×C13914yes—
317#383C22×C13914yes—
318#382C22×C13912yes—
319#382C22×C13911yescharacteristic
320#381C22×C13912yes—
321C4×C22⋊C4C22×C13914yes—
322#376C22×C13912yes—
323C43C22×C13911yescharacteristic
324C22×Q8C23×C13912yes—
325C22×Q8C23×C13912yes—
326C22×Q8C23×C13912yes—
327C22×Q8C23×C13911yescharacteristic
328C22×D4C23×C13911yescharacteristic
329C23×C4C23×C13912yes—
330C4⋊Q8—28no—
331#124—24no—
332C22⋊Q8—44no—
333C4×Q8—42no—
334C4×Q8—44no—
335C4×D4—42no—
336C2×C4⋊C4C23×C13914yes—
337C2×C4⋊C4C23×C13914yes—
338C2×C4⋊C4C23×C13914yes—
339C2×C4⋊C4C23×C13912yes—
340C2×C4⋊C4C23×C13911yescharacteristic
341C2×C4⋊C4C23×C13911yescharacteristic
342C2×C4⋊C4C23×C13912yes—
343C2×C4⋊C4C23×C13912yes—
344C2×C4⋊C4C23×C13912yes—
345C2×C4⋊C4C23×C13914yes—
346C2×C4⋊C4C23×C13914yes—
347C2×C4⋊C4C23×C13912yes—
348C2×C4⋊C4C23×C13912yes—
349C2×C22⋊C4C23×C13914yes—
350C2×C22⋊C4C23×C13914yes—
351C2×C22⋊C4C23×C13912yes—
352C2×C22⋊C4C23×C13914yes—
353C2×C22⋊C4C23×C13914yes—
354C2×C22⋊C4C23×C13914yes—
355C2×C22⋊C4C23×C13914yes—
356C2×C42C23×C13911yescharacteristic
357C2×C42C23×C13912yes—
358C2×C42C23×C13911yescharacteristic
359C2×C42C23×C13912yes—
360C2×C42C23×C13912yes—
361C2×C42C23×C13914yes—
362C2×C42C23×C13912yes—
363C2×C42C23×C13911yescharacteristic
364C2×C42C23×C13912yes—
365#95C23×C13914yes—
366#95C23×C13914yes—
367#95C23×C13914yes—
368#95C23×C13914yes—
369#95C23×C13912yes—
370#95C23×C13912yes—
371#95C23×C13914yes—
372#95C23×C13914yes—
373#95C23×C13914yes—
374#95C23×C13914yes—
375#95C23×C13914yes—
376#95C23×C13914yes—
377#95C23×C13914yes—
378#95C23×C13914yes—
379#95C23×C13914yes—
380#95C23×C13914yes—
381#95C23×C13914yes—
382#95C23×C13914yes—
383C24C24×C13912yes—
384C2×Q8—24no—
385C2×Q8—24no—
386C2×Q8—41no—
387C2×Q8—42no—
388C2×Q8—41no—
389C2×Q8—42no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×Q8—42no—
393C2×Q8—44no—
394C2×Q8#41×C13914yes—
395C2×D4—22no—
396C2×D4—41no—
397C2×D4—41no—
398C22×C4—24no—
399C22×C4—44no—
400C22×C4C24×C13914yes—
401C22×C4C24×C13912yes—
402C22×C4C24×C13912yes—
403C22×C4C24×C13911yescharacteristic
404C22×C4C24×C13914yes—
405C22×C4C24×C13912yes—
406C22×C4C24×C13914yes—
407C22×C4C24×C13914yes—
408C22×C4C24×C13912yes—
409C22×C4C24×C13911yescharacteristic
410C22×C4C24×C13911yescharacteristic
411C22×C4C24×C13912yes—
412C4⋊C4—28no—
413C4⋊C4—28no—
414C4⋊C4—28no—
415C4⋊C4—24no—
416C4⋊C4—42no—
417C4⋊C4—42no—
418C4⋊C4—44no—
419C4⋊C4—44no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—42no—
423C4⋊C4—42no—
424C4⋊C4—42no—
425C22⋊C4—28no—
426C22⋊C4—28no—
427C22⋊C4—44no—
428C22⋊C4—44no—
429C22⋊C4—44no—
430C22⋊C4—42no—
431C22⋊C4—44no—
432C42—22no—
433C42—24no—
434C42—22no—
435C42—24no—
436C42—24no—
437C42—41no—
438C42—42no—
439C42—42no—
440C42—44no—
441C23—22no—
442C23—22no—
443C23—24no—
444C23—24no—
445C23—22no—
446C23C25×C13911yescharacteristic
447Q8—44no—
448Q8—48no—
449Q8—84no—
450Q8—84no—
451D4—44no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—21no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—84no—
481C2×C4C2×#41×C13914yes—
482C2×C4C2×#41×C13912yes—
483C2×C4H(5,𝔽2)×C13912yes—
484C2×C42−1+4×C13914yes—
485C22—42no—
486C22—42no—
487C22—44no—
488C22—42no—
489C22—44no—
490C22C22×#41×C13911yescharacteristic
491C22C2×H(5,𝔽2)×C13911yescharacteristic
492C22C2×2−1+4×C13912yes—
493C22#585×C13912yes—
494C22#585×C13911yescharacteristic
495C4—22no—
496C4—24no—
497C4—22no—
498C4—24no—
499C4—42no—
500C4—44no—
501C4—42no—
502C4—41no—
503C4—44no—
504C4—44no—
505C4—42no—
506C4—44no—
507C2—82no—
508C2#3459×C13911yescharacteristic
509C2#3518×C13912yes—
510C2#3545×C13911yescharacteristic
511C2#3550×C13911yescharacteristic
512C2#3564×C13912yes—
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC22×D4×C139C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2863×C139C2semidirect
2. #2811×C139C2semidirect
4. #2789×C139C2semidirect
5. #2775×C139C2semidirect
6. #2759×C139C2semidirect
7. #2734×C139C2semidirect
10. #2527×C139C2semidirect
11. #2465×C139C2semidirect
12. #2327×C139C2semidirect
256. #37208C139direct (N × H)
257. C139#37208direct (N × H)
258. #2863C2×C139semidirect
259. #2811C2×C139semidirect
261. #2789C2×C139semidirect
262. #2775C2×C139semidirect
263. #2759C2×C139semidirect
264. #2734C2×C139semidirect
267. #2527C2×C139semidirect
268. #2465C2×C139semidirect
269. #2327C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2863×C1392
#2811×C1392
#2808×C1392
#2789×C1392
#2775×C1392
#2759×C1392
#2734×C1392
#2731×C1392
#2638×C1392
#2527×C1392
#2465×C1392
#2327×C1392
C4×#124×C1392
#37208139