Finite Group Databasebeta

← C139×#22185 #48016781

Subgroups — C139×#22185 #48016781

Order 35584.

978 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C139C211yesmaximal, characteristic
2C4×C22⋊Q8×C139C211yesmaximal, characteristic, complemented
3C4×#121×C139C211yesmaximal, characteristic
4#1928×C139C211yesmaximal, characteristic, complemented
5#1925×C139C211yesmaximal, characteristic, complemented
6#1920×C139C211yesmaximal, characteristic, complemented
7#1919×C139C211yesmaximal, characteristic, complemented
8#1893×C139C211yesmaximal, characteristic
9#1892×C139C211yesmaximal, characteristic, complemented
10#1880×C139C211yesmaximal, characteristic, complemented
11#1877×C139C211yesmaximal, characteristic, complemented
12#1863×C139C211yesmaximal, characteristic, complemented
13#1862×C139C211yesmaximal, characteristic, complemented
14#1808×C139C211yesmaximal, characteristic, complemented
15C2×#336×C139C211yesmaximal, characteristic, complemented
16C22×SD16×C139C2211yescharacteristic
17C23×C8×C139C2211yescharacteristic
18C23×C8×C139C2211yescharacteristic
19C2×C22⋊Q8×C139C2211yescharacteristic
20C2×#121×C139C2211yescharacteristic
21C2×C4×Q8×C139C2211yescharacteristic
22C2×C4×D4×C139—21no—
23C2×C4×D4×C139C2211yescharacteristic
24C22×C42×C139C2211yescharacteristic
25#465×C139C418yescomplemented
26C2×#107×C139C2211yescharacteristic
27C2×#107×C139C2211yescharacteristic
28C2×#106×C139C2211yescharacteristic
29C2×#103×C139C2211yescharacteristic
30C2×#103×C139C2211yescharacteristic
31C2×#103×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35#391×C139C2211yescharacteristic
36#390×C139C2211yescharacteristic
37#389×C139C2211yescharacteristic
38#389×C139C2211yescharacteristic
39#388×C139—21no—
40#387×C139—21no—
41#386×C139—21no—
42#385×C139—21no—
43#380×C139C2211yescharacteristic
44#380×C139C2211yescharacteristic
45C4×C4⋊C4×C139—21no—
46C4×C4⋊C4×C139C2211yescharacteristic
47C4×C4⋊C4×C139C2211yescharacteristic
48C4×C22⋊C4×C139—21no—
49C4×C22⋊C4×C139—21no—
50#340×C139C2211yescharacteristic
51#340×C139C2211yescharacteristic
52#340×C139C2211yescharacteristic
53#340×C139C2211yescharacteristic
54#340×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#336×C139C2211yescharacteristic
57#336×C139C2211yescharacteristic
58#336×C139C2211yescharacteristic
59#336×C139C2211yescharacteristic
60C22×Q8×C139C2311yescharacteristic
61C22×D4×C139—21no—
62C22×D4×C139C2311yescharacteristic
63C23×C4×C139—21no—
64C23×C4×C139D411yescharacteristic
65C23×C4×C139D411yescharacteristic
66C23×C4×C139C2311yescharacteristic
67C2×SD16×C139—41no—
68C2×SD16×C139—41no—
69C2×SD16×C139C2×C414yescomplemented
70C22×C8×C139—22no—
71C22×C8×C139—41no—
72C22×C8×C139—41no—
73C22×C8×C139—41no—
74C22×C8×C139—41no—
75C22×C8×C139C2×C414yescomplemented
76C22×C8×C139C2311yescharacteristic
77C22×C8×C139C2311yescharacteristic
78C22×C8×C139C2311yescharacteristic
79C22×C8×C139C2311yescharacteristic
80C22⋊Q8×C139—22no—
81C22⋊Q8×C139C2×C414yescomplemented
82#121×C139—22no—
83#121×C139C2×C414yes—
84C4×Q8×C139—41no—
85C4×Q8×C139—41no—
86C4×D4×C139—41no—
87C4×D4×C139—41no—
88C4×D4×C139—44no—
89C2×C4⋊C4×C139—21no—
90C2×C4⋊C4×C139—21no—
91C2×C4⋊C4×C139—21no—
92C2×C4⋊C4×C139—21no—
93C2×C4⋊C4×C139C2311yescharacteristic
94C2×C4⋊C4×C139C2311yescharacteristic
95C2×C4⋊C4×C139C2311yescharacteristic
96C2×C4⋊C4×C139C2311yescharacteristic
97C2×C4⋊C4×C139C2311yescharacteristic
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C22⋊C4×C139—21no—
100C2×C22⋊C4×C139—21no—
101C2×C22⋊C4×C139—21no—
102C2×C22⋊C4×C139—21no—
103C2×C22⋊C4×C139—21no—
104C2×C22⋊C4×C139—21no—
105C2×C22⋊C4×C139—21no—
106C2×C42×C139—21no—
107C2×C42×C139—21no—
108C2×C42×C139—21no—
109C2×C42×C139—41no—
110C2×C42×C139—41no—
111C2×C42×C139D411yescharacteristic
112C2×C42×C139D411yescharacteristic
113C2×C42×C139C2311yescharacteristic
114C2×C42×C139C2311yescharacteristic
115#107×C139—41no—
116#107×C139—41no—
117#106×C139C2×C414yescomplemented
118#103×C139—41no—
119#103×C139—41no—
120#103×C139C2×C414yescomplemented
121#102×C139—41no—
122#102×C139—41no—
123#102×C139C2×C414yescomplemented
124#95×C139—21no—
125#95×C139—21no—
126#95×C139—21no—
127#95×C139—21no—
128#95×C139—21no—
129#95×C139—21no—
130#95×C139—21no—
131#95×C139—21no—
132C24×C139—21no—
133C24×C139C2×D411yescharacteristic
134C2×Q8×C139—21no—
135C2×Q8×C139—21no—
136C2×Q8×C139—21no—
137C2×Q8×C139—21no—
138C2×Q8×C139—21no—
139C2×Q8×C139C22×C412yes—
140C2×D4×C139—24no—
141C2×D4×C139—21no—
142C2×D4×C139—21no—
143C2×D4×C139—21no—
144C2×D4×C139—21no—
145C2×D4×C139—21no—
146C2×D4×C139—42no—
147C2×D4×C139—42no—
148C2×D4×C139C22×C412yes—
149C22×C4×C139—21no—
150C22×C4×C139—21no—
151C22×C4×C139—21no—
152C22×C4×C139—21no—
153C22×C4×C139—22no—
154C22×C4×C139—22no—
155C22×C4×C139—21no—
156C22×C4×C139—21no—
157C22×C4×C139—21no—
158C22×C4×C139—22no—
159C22×C4×C139—22no—
160C22×C4×C139—21no—
161C22×C4×C139—21no—
162C22×C4×C139—21no—
163C22×C4×C139—21no—
164C22×C4×C139—41no—
165C22×C4×C139—41no—
166C22×C4×C139—42no—
167C22×C4×C139—42no—
168C22×C4×C139—42no—
169C22×C4×C139C22×C412yes—
170C22×C4×C139C2×D411yescharacteristic
171C22×C4×C139C2×D411yescharacteristic
172C22×C4×C139C2×D411yescharacteristic
173C22×C4×C139C2×D411yescharacteristic
174C22×C4×C139C2×D411yescharacteristic
175C22×C4×C139#4112yes—
176C22×C4×C139C2411yescharacteristic
177SD16×C139—44no—
178C2×C8×C139—21no—
179C2×C8×C139—21no—
180C2×C8×C139—21no—
181C2×C8×C139—21no—
182C2×C8×C139—21no—
183C2×C8×C139—21no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139—21no—
188C2×C8×C139—44no—
189C2×C8×C139—44no—
190C2×C8×C139C22×C412yes—
191C2×C8×C139C22×C412yes—
192C4⋊C4×C139—24no—
193C4⋊C4×C139—21no—
194C4⋊C4×C139—21no—
195C4⋊C4×C139—21no—
196C4⋊C4×C139—21no—
197C4⋊C4×C139—21no—
198C4⋊C4×C139—21no—
199C4⋊C4×C139—21no—
200C4⋊C4×C139—21no—
201C4⋊C4×C139—21no—
202C4⋊C4×C139—21no—
203C4⋊C4×C139—42no—
204C4⋊C4×C139—42no—
205C4⋊C4×C139—42no—
206C4⋊C4×C139C22×C412yes—
207C4⋊C4×C139C22×C412yes—
208C22⋊C4×C139—24no—
209C22⋊C4×C139—24no—
210C22⋊C4×C139—42no—
211C22⋊C4×C139—42no—
212C22⋊C4×C139—42no—
213C22⋊C4×C139—42no—
214C22⋊C4×C139—42no—
215C42×C139—21no—
216C42×C139—21no—
217C42×C139—21no—
218C42×C139—21no—
219C42×C139—41no—
220C42×C139—41no—
221C42×C139—42no—
222C42×C139—42no—
223C42×C139—42no—
224C23×C139—21no—
225C23×C139—21no—
226C23×C139—21no—
227C23×C139—21no—
228C23×C139—22no—
229C23×C139—41no—
230C23×C139—41no—
231C23×C139—41no—
232C23×C139—41no—
233C23×C139—41no—
234C23×C139—41no—
235C23×C139C4×D412yes—
236C23×C139AGL(1,ℤ/8)12yes—
237C23×C139#13712yes—
238C23×C139C22×D411yescharacteristic
239Q8×C139—22no—
240Q8×C139—22no—
241Q8×C139—41no—
242Q8×C139—41no—
243D4×C139—22no—
244D4×C139—22no—
245D4×C139—48no—
246D4×C139—41no—
247D4×C139—41no—
248C2×C4×C139—21no—
249C2×C4×C139—21no—
250C2×C4×C139—21no—
251C2×C4×C139—21no—
252C2×C4×C139—21no—
253C2×C4×C139—21no—
254C2×C4×C139—22no—
255C2×C4×C139—22no—
256C2×C4×C139—22no—
257C2×C4×C139—22no—
258C2×C4×C139—22no—
259C2×C4×C139—22no—
260C2×C4×C139—22no—
261C2×C4×C139—21no—
262C2×C4×C139—21no—
263C2×C4×C139—21no—
264C2×C4×C139—21no—
265C2×C4×C139—21no—
266C2×C4×C139—21no—
267C2×C4×C139—44no—
268C2×C4×C139—44no—
269C2×C4×C139—41no—
270C2×C4×C139—41no—
271C2×C4×C139—41no—
272C2×C4×C139—41no—
273C2×C4×C139—41no—
274C2×C4×C139—41no—
275C2×C4×C139—41no—
276C2×C4×C139—41no—
277C2×C4×C139—41no—
278C2×C4×C139—41no—
279C2×C4×C139—41no—
280C2×C4×C139—41no—
281C2×C4×C139—41no—
282C2×C4×C139—41no—
283C2×C4×C139—41no—
284C2×C4×C139—41no—
285C2×C4×C139—41no—
286C2×C4×C139—41no—
287C2×C4×C139—84no—
288C2×C4×C139C4×D412yes—
289C2×C4×C139#13512yes—
290C2×C4×C139#13512yes—
291C2×C4×C139C23×C411yescharacteristic
292C2×C4×C139C2×#4111yescharacteristic
293C2×C4×C139H(5,𝔽2)11yescharacteristic
294C2×C4×C139H(5,𝔽2)11yescharacteristic
295C2×C4×C139H(5,𝔽2)11yescharacteristic
296C2×C4×C1392−1+411yescharacteristic
297C8×C139—22no—
298C8×C139—22no—
299C8×C139—41no—
300C8×C139—41no—
301C22×C139—22no—
302C22×C139—22no—
303C22×C139—22no—
304C22×C139—22no—
305C22×C139—22no—
306C22×C139—22no—
307C22×C139—42no—
308C22×C139—42no—
309C22×C139—42no—
310C22×C139—81no—
311C22×C139—81no—
312C22×C139—81no—
313C22×C139—81no—
314C22×C139#44014yes—
315C22×C139C2×C4×D411yescharacteristic
316C22×C139#53411yescharacteristic
317C22×C139#53711yescharacteristic
318C22×C139C2×#13511yescharacteristic
319C22×C139C2×#13511yescharacteristic
320C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C139C2×#13711yescharacteristic
322C4×C139—22no—
323C4×C139—22no—
324C4×C139—22no—
325C4×C139—42no—
326C4×C139—41no—
327C4×C139—41no—
328C4×C139—42no—
329C4×C139—42no—
330C4×C139—81no—
331C4×C139—81no—
332C4×C139—81no—
333C4×C139—81no—
334C4×C139#51811yescharacteristic
335C4×C139#52011yescharacteristic
336C4×C139#53811yescharacteristic
337C4×C139#53911yescharacteristic
338C2×C139—24no—
339C2×C139—82no—
340C2×C139#232511yescharacteristic
341C2×C139C4×#13511yescharacteristic
342C2×C139C2×#44011yescharacteristic
343C2×C139#318811yescharacteristic
344C2×C139#319011yescharacteristic
345C2×C139#324711yescharacteristic
346C2×C139#324811yescharacteristic
347#22185C13911yesmaximal, characteristic, direct product factor, Sylow
348C139#2218511yescharacteristic, direct product factor, Sylow
349C2×#465C2×C13911yescharacteristic
350C4×C22⋊Q8C2×C13911yescharacteristic, complemented
351C4×#121C2×C13911yescharacteristic
352#1928C2×C13911yescharacteristic, complemented
353#1925C2×C13911yescharacteristic, complemented
354#1920C2×C13911yescharacteristic, complemented
355#1919C2×C13911yescharacteristic, complemented
356#1893C2×C13911yescharacteristic
357#1892C2×C13911yescharacteristic, complemented
358#1880C2×C13911yescharacteristic, complemented
359#1877C2×C13911yescharacteristic, complemented
360#1863C2×C13911yescharacteristic, complemented
361#1862C2×C13911yescharacteristic, complemented
362#1808C2×C13911yescharacteristic, complemented
363C2×#336C2×C13911yescharacteristic, complemented
364C22×SD16C22×C13911yescharacteristic
365C23×C8C22×C13911yescharacteristic
366C23×C8C22×C13911yescharacteristic
367C2×C22⋊Q8C22×C13911yescharacteristic
368C2×#121C22×C13911yescharacteristic
369C2×C4×Q8C22×C13911yescharacteristic
370C2×C4×D4—21no—
371C2×C4×D4C22×C13911yescharacteristic
372C22×C42C22×C13911yescharacteristic
373#465C4×C13918yescomplemented
374C2×#107C22×C13911yescharacteristic
375C2×#107C22×C13911yescharacteristic
376C2×#106C22×C13911yescharacteristic
377C2×#103C22×C13911yescharacteristic
378C2×#103C22×C13911yescharacteristic
379C2×#103C22×C13911yescharacteristic
380C2×#102C22×C13911yescharacteristic
381C2×#102C22×C13911yescharacteristic
382C2×#102C22×C13911yescharacteristic
383#391C22×C13911yescharacteristic
384#390C22×C13911yescharacteristic
385#389C22×C13911yescharacteristic
386#389C22×C13911yescharacteristic
387#388—21no—
388#387—21no—
389#386—21no—
390#385—21no—
391#380C22×C13911yescharacteristic
392#380C22×C13911yescharacteristic
393C4×C4⋊C4—21no—
394C4×C4⋊C4C22×C13911yescharacteristic
395C4×C4⋊C4C22×C13911yescharacteristic
396C4×C22⋊C4—21no—
397C4×C22⋊C4—21no—
398#340C22×C13911yescharacteristic
399#340C22×C13911yescharacteristic
400#340C22×C13911yescharacteristic
401#340C22×C13911yescharacteristic
402#340C22×C13911yescharacteristic
403#340C22×C13911yescharacteristic
404#336C22×C13911yescharacteristic
405#336C22×C13911yescharacteristic
406#336C22×C13911yescharacteristic
407#336C22×C13911yescharacteristic
408C22×Q8C23×C13911yescharacteristic
409C22×D4—21no—
410C22×D4C23×C13911yescharacteristic
411C23×C4—21no—
412C23×C4D4×C13911yescharacteristic
413C23×C4D4×C13911yescharacteristic
414C23×C4C23×C13911yescharacteristic
415C2×SD16—41no—
416C2×SD16—41no—
417C2×SD16C2×C4×C13914yescomplemented
418C22×C8—22no—
419C22×C8—41no—
420C22×C8—41no—
421C22×C8—41no—
422C22×C8—41no—
423C22×C8C2×C4×C13914yescomplemented
424C22×C8C23×C13911yescharacteristic
425C22×C8C23×C13911yescharacteristic
426C22×C8C23×C13911yescharacteristic
427C22×C8C23×C13911yescharacteristic
428C22⋊Q8—22no—
429C22⋊Q8C2×C4×C13914yescomplemented
430#121—22no—
431#121C2×C4×C13914yes—
432C4×Q8—41no—
433C4×Q8—41no—
434C4×D4—41no—
435C4×D4—41no—
436C4×D4—44no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4C23×C13911yescharacteristic
442C2×C4⋊C4C23×C13911yescharacteristic
443C2×C4⋊C4C23×C13911yescharacteristic
444C2×C4⋊C4C23×C13911yescharacteristic
445C2×C4⋊C4C23×C13911yescharacteristic
446C2×C4⋊C4C23×C13911yescharacteristic
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42—41no—
458C2×C42—41no—
459C2×C42D4×C13911yescharacteristic
460C2×C42D4×C13911yescharacteristic
461C2×C42C23×C13911yescharacteristic
462C2×C42C23×C13911yescharacteristic
463#107—41no—
464#107—41no—
465#106C2×C4×C13914yescomplemented
466#103—41no—
467#103—41no—
468#103C2×C4×C13914yescomplemented
469#102—41no—
470#102—41no—
471#102C2×C4×C13914yescomplemented
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480C24—21no—
481C24C2×D4×C13911yescharacteristic
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8C22×C4×C13912yes—
488C2×D4—24no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4C22×C4×C13912yes—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4C22×C4×C13912yes—
518C22×C4C2×D4×C13911yescharacteristic
519C22×C4C2×D4×C13911yescharacteristic
520C22×C4C2×D4×C13911yescharacteristic
521C22×C4C2×D4×C13911yescharacteristic
522C22×C4C2×D4×C13911yescharacteristic
523C22×C4#41×C13912yes—
524C22×C4C24×C13911yescharacteristic
525SD16—44no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—44no—
537C2×C8—44no—
538C2×C8C22×C4×C13912yes—
539C2×C8C22×C4×C13912yes—
540C4⋊C4—24no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4C22×C4×C13912yes—
555C4⋊C4C22×C4×C13912yes—
556C22⋊C4—24no—
557C22⋊C4—24no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—41no—
568C42—41no—
569C42—42no—
570C42—42no—
571C42—42no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—22no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23C4×D4×C13912yes—
584C23AGL(1,ℤ/8)×C13912yes—
585C23#137×C13912yes—
586C23C22×D4×C13911yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—41no—
590Q8—41no—
591D4—22no—
592D4—22no—
593D4—48no—
594D4—41no—
595D4—41no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—84no—
636C2×C4C4×D4×C13912yes—
637C2×C4#135×C13912yes—
638C2×C4#135×C13912yes—
639C2×C4C23×C4×C13911yescharacteristic
640C2×C4C2×#41×C13911yescharacteristic
641C2×C4H(5,𝔽2)×C13911yescharacteristic
642C2×C4H(5,𝔽2)×C13911yescharacteristic
643C2×C4H(5,𝔽2)×C13911yescharacteristic
644C2×C42−1+4×C13911yescharacteristic
645C8—22no—
646C8—22no—
647C8—41no—
648C8—41no—
649C22—22no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22#440×C13914yes—
663C22C2×C4×D4×C13911yescharacteristic
664C22#534×C13911yescharacteristic
665C22#537×C13911yescharacteristic
666C22C2×#135×C13911yescharacteristic
667C22C2×#135×C13911yescharacteristic
668C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
669C22C2×#137×C13911yescharacteristic
670C4—22no—
671C4—22no—
672C4—22no—
673C4—42no—
674C4—41no—
675C4—41no—
676C4—42no—
677C4—42no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4#518×C13911yescharacteristic
683C4#520×C13911yescharacteristic
684C4#538×C13911yescharacteristic
685C4#539×C13911yescharacteristic
686C2—24no—
687C2—82no—
688C2#2325×C13911yescharacteristic
689C2C4×#135×C13911yescharacteristic
690C2C2×#440×C13911yescharacteristic
691C2#3188×C13911yescharacteristic
692C2#3190×C13911yescharacteristic
693C2#3247×C13911yescharacteristic
694C2#3248×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC2×#121×C139C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊Q8×C139C2semidirect
4. #1928×C139C2semidirect
5. #1925×C139C2semidirect
6. #1920×C139C2semidirect
7. #1919×C139C2semidirect
9. #1892×C139C2semidirect
10. #1880×C139C2semidirect
11. #1877×C139C2semidirect
12. #1863×C139C2semidirect
13. #1862×C139C2semidirect
14. #1808×C139C2semidirect
15. C2×#336×C139C2semidirect
25. #465×C139C4semidirect
69. C2×SD16×C139C2×C4semidirect
75. C22×C8×C139C2×C4semidirect
81. C22⋊Q8×C139C2×C4semidirect
117. #106×C139C2×C4semidirect
120. #103×C139C2×C4semidirect
123. #102×C139C2×C4semidirect
347. #22185C139direct (N × H)
348. C139#22185direct (N × H)
350. C4×C22⋊Q8C2×C139semidirect
352. #1928C2×C139semidirect
353. #1925C2×C139semidirect
354. #1920C2×C139semidirect
355. #1919C2×C139semidirect
357. #1892C2×C139semidirect
358. #1880C2×C139semidirect
359. #1877C2×C139semidirect
360. #1863C2×C139semidirect
361. #1862C2×C139semidirect
362. #1808C2×C139semidirect
363. C2×#336C2×C139semidirect
373. #465C4×C139semidirect
417. C2×SD16C2×C4×C139semidirect
423. C22×C8C2×C4×C139semidirect
429. C22⋊Q8C2×C4×C139semidirect
465. #106C2×C4×C139semidirect
468. #103C2×C4×C139semidirect
471. #102C2×C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#465×C1392
C4×C22⋊Q8×C1392
C4×#121×C1392
#1928×C1392
#1925×C1392
#1920×C1392
#1919×C1392
#1893×C1392
#1892×C1392
#1880×C1392
#1877×C1392
#1863×C1392
#1862×C1392
#1808×C1392
C2×#336×C1392
#22185139