Finite Group Databasebeta

← C139×#25142 #48019738

Subgroups — C139×#25142 #48019738

Order 35584.

986 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#473×C139C211yesmaximal, characteristic, complemented
2#3056×C139C211yesmaximal, characteristic
3#3004×C139C211yesmaximal, characteristic
4C2×#451×C139C211yesmaximal, characteristic, complemented
5#2933×C139C211yesmaximal, characteristic
6C22×#101×C139C211yesmaximal, characteristic, complemented
7#2064×C139C211yesmaximal, characteristic, complemented
8#2052×C139C211yesmaximal, characteristic, complemented
9#2047×C139C211yesmaximal, characteristic, complemented
10#2020×C139C211yesmaximal, characteristic, complemented
11#1979×C139C211yesmaximal, characteristic, complemented
12#1930×C139C211yesmaximal, characteristic, complemented
13#1908×C139C211yesmaximal, characteristic, complemented
14#1901×C139C211yesmaximal, characteristic, complemented
15#1855×C139C211yesmaximal, characteristic, complemented
16C23×Q8×C139C2211yescharacteristic
17C2×#137×C139C2211yescharacteristic
18C2×#137×C139C2211yescharacteristic
19C2×#137×C139C2211yescharacteristic
20C22×Q16×C139C2211yescharacteristic
21C22×Q16×C139C2211yescharacteristic
22C2×#131×C139C2211yescharacteristic
23C22×M16×C139C2211yescharacteristic
24C22×M16×C139C2211yescharacteristic
25#525×C139C2211yescharacteristic
26C2×C22⋊Q8×C139C2211yescharacteristic
27#473×C139—24no—
28#470×C139—21no—
29#468×C139—21no—
30#467×C139—21no—
31#465×C139—21no—
32#451×C139—21no—
33#451×C139—21no—
34#451×C139—21no—
35#451×C139—21no—
36#451×C139—21no—
37#451×C139—21no—
38#448×C139—21no—
39#448×C139—21no—
40#436×C139—21no—
41#435×C139—21no—
42#435×C139—21no—
43C8×D4×C139—21no—
44C2×#108×C139C2211yescharacteristic
45C2×#108×C139C2211yescharacteristic
46#428×C139C2211yescharacteristic
47#424×C139C2211yescharacteristic
48#419×C139C2211yescharacteristic
49#419×C139C2211yescharacteristic
50#419×C139C2211yescharacteristic
51#417×C139C2211yescharacteristic
52C2×#103×C139C2211yescharacteristic
53C2×#103×C139C2211yescharacteristic
54C2×#101×C139—24no—
55C2×#101×C139C2211yescharacteristic
56C2×#101×C139C2211yescharacteristic
57C2×#101×C139C2211yescharacteristic
58C2×#101×C139C2211yescharacteristic
59C2×#101×C139C2211yescharacteristic
60C2×#101×C139C2211yescharacteristic
61#408×C139C2211yescharacteristic
62#407×C139C2211yescharacteristic
63C2×C22⋊C8×C139C2211yescharacteristic
64#405×C139C2211yescharacteristic
65#343×C139C2211yescharacteristic
66#343×C139C2211yescharacteristic
67#341×C139C2211yescharacteristic
68#341×C139C2211yescharacteristic
69C2×#41×C139C2311yescharacteristic
70C22×Q8×C139—22no—
71C22×Q8×C139—22no—
72C22×Q8×C139—21no—
73C22×Q8×C139—21no—
74C22×Q8×C139—21no—
75C22×Q8×C139—21no—
76C22×Q8×C139—21no—
77C22×Q8×C139—41no—
78C22×Q8×C139—41no—
79C22×Q8×C139C2311yescharacteristic
80C22×Q8×C139C2311yescharacteristic
81C22×Q8×C139C2311yescharacteristic
82C23×C4×C139—21no—
83C23×C4×C139C2311yescharacteristic
84#137×C139—22no—
85#137×C139—22no—
86#137×C139—22no—
87#137×C139—41no—
88#137×C139—41no—
89#137×C139—41no—
90C2×Q16×C139—21no—
91C2×Q16×C139—21no—
92C2×Q16×C139—21no—
93C2×Q16×C139—22no—
94C2×Q16×C139—22no—
95C2×Q16×C139—21no—
96C2×Q16×C139—21no—
97C2×Q16×C139—21no—
98C2×Q16×C139—21no—
99C2×Q16×C139—41no—
100C2×Q16×C139—41no—
101C2×SD16×C139—21no—
102C2×SD16×C139—21no—
103C2×SD16×C139—21no—
104#131×C139—22no—
105#131×C139—41no—
106C2×M16×C139—21no—
107C2×M16×C139—21no—
108C2×M16×C139—21no—
109C2×M16×C139—22no—
110C2×M16×C139—22no—
111C2×M16×C139—41no—
112C2×M16×C139—41no—
113C2×M16×C139C2311yescharacteristic
114C2×M16×C139C2311yescharacteristic
115C2×M16×C139C2311yescharacteristic
116C2×M16×C139C2311yescharacteristic
117C2×M16×C139C2311yescharacteristic
118C2×M16×C139C2311yescharacteristic
119C22×C8×C139—21no—
120C22×C8×C139—21no—
121C22×C8×C139—21no—
122C22×C8×C139C2311yescharacteristic
123C22×C8×C139C2311yescharacteristic
124#123×C139—21no—
125C22⋊Q8×C139—21no—
126C22⋊Q8×C139—21no—
127C22⋊Q8×C139—21no—
128C22⋊Q8×C139—21no—
129C22⋊Q8×C139D411yescharacteristic
130C22⋊Q8×C139D411yescharacteristic
131#121×C139D411yescharacteristic
132#121×C139D411yescharacteristic
133#120×C139—21no—
134C4×D4×C139—21no—
135C4×D4×C139—21no—
136#117×C139C2311yescharacteristic
137C2×C4⋊C4×C139—21no—
138C2×C4⋊C4×C139C2311yescharacteristic
139C2×C22⋊C4×C139—21no—
140#108×C139—22no—
141#108×C139—41no—
142#107×C139—21no—
143#106×C139—21no—
144C4⋊C8×C139—21no—
145C4⋊C8×C139—21no—
146#103×C139—21no—
147#103×C139—21no—
148#103×C139—21no—
149#103×C139—21no—
150#103×C139—21no—
151#103×C139—21no—
152#103×C139—21no—
153#103×C139—21no—
154#103×C139—21no—
155#103×C139—21no—
156#103×C139—21no—
157#102×C139—21no—
158#101×C139—22no—
159#101×C139—22no—
160#101×C139—22no—
161#101×C139—22no—
162#101×C139—41no—
163#101×C139D414yescomplemented
164C22⋊C8×C139—21no—
165C22⋊C8×C139—21no—
166C22⋊C8×C139—21no—
167C22⋊C8×C139—21no—
168C22⋊C8×C139D411yescharacteristic
169C22⋊C8×C139D411yescharacteristic
170C22⋊C8×C139D411yescharacteristic
171C22⋊C8×C139D411yescharacteristic
172#97×C139—21no—
173C4×C8×C139—21no—
174C24×C139#4111yescharacteristic
175#41×C139—21no—
176#41×C139—21no—
177#41×C139—21no—
178#41×C139—21no—
179C2×Q8×C139—24no—
180C2×Q8×C139—21no—
181C2×Q8×C139—21no—
182C2×Q8×C139—21no—
183C2×Q8×C139—21no—
184C2×Q8×C139—21no—
185C2×Q8×C139—21no—
186C2×Q8×C139—21no—
187C2×Q8×C139—21no—
188C2×Q8×C139—21no—
189C2×Q8×C139—21no—
190C2×Q8×C139—21no—
191C2×Q8×C139—21no—
192C2×Q8×C139—21no—
193C2×Q8×C139—21no—
194C2×Q8×C139—21no—
195C2×Q8×C139—21no—
196C2×Q8×C139—42no—
197C2×Q8×C139—42no—
198C2×Q8×C139—42no—
199C2×Q8×C139—42no—
200C2×Q8×C139—42no—
201C2×Q8×C139—42no—
202C2×Q8×C139—42no—
203C2×Q8×C139—42no—
204C2×Q8×C139—42no—
205C2×Q8×C139—41no—
206C2×Q8×C139—41no—
207C2×Q8×C139C2×D412yes—
208C2×Q8×C139C2×D411yescharacteristic
209C2×Q8×C139#4112yes—
210C2×D4×C139—21no—
211C2×D4×C139—21no—
212C2×D4×C139—21no—
213C2×D4×C139C2×D411yescharacteristic
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139—24no—
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—21no—
224C22×C4×C139—42no—
225C22×C4×C139—41no—
226C22×C4×C139—41no—
227C22×C4×C139C2×D411yescharacteristic
228C22×C4×C139C2×D411yescharacteristic
229C22×C4×C139C2×D411yescharacteristic
230C22×C4×C139C2×D411yescharacteristic
231C22×C4×C139#4111yescharacteristic
232C22×C4×C139C2411yescharacteristic
233Q16×C139—42no—
234Q16×C139—42no—
235Q16×C139—42no—
236Q16×C139—42no—
237Q16×C139—42no—
238Q16×C139—42no—
239Q16×C139—42no—
240SD16×C139—42no—
241SD16×C139—42no—
242SD16×C139—42no—
243M16×C139—21no—
244M16×C139—21no—
245M16×C139—21no—
246M16×C139—21no—
247M16×C139—21no—
248M16×C139—21no—
249M16×C139—21no—
250M16×C139—21no—
251M16×C139—21no—
252M16×C139—21no—
253M16×C139—42no—
254M16×C139—42no—
255M16×C139—42no—
256M16×C139C2×D412yes—
257M16×C139C2×D412yes—
258C2×C8×C139—21no—
259C2×C8×C139—21no—
260C2×C8×C139—21no—
261C2×C8×C139—21no—
262C2×C8×C139—21no—
263C2×C8×C139—21no—
264C2×C8×C139—21no—
265C2×C8×C139—21no—
266C2×C8×C139—21no—
267C2×C8×C139—21no—
268C2×C8×C139—42no—
269C2×C8×C139—42no—
270C2×C8×C139—42no—
271C2×C8×C139C2×D411yescharacteristic
272C2×C8×C139C2×D411yescharacteristic
273C2×C8×C139C2×D411yescharacteristic
274C2×C8×C139C2×D411yescharacteristic
275C4⋊C4×C139—21no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139—21no—
278C4⋊C4×C139—21no—
279C4⋊C4×C139—41no—
280C4⋊C4×C139—41no—
281C4⋊C4×C139C2×D411yescharacteristic
282C4⋊C4×C139C2×D411yescharacteristic
283C22⋊C4×C139—21no—
284C22⋊C4×C139—21no—
285C22⋊C4×C139—21no—
286C22⋊C4×C139—21no—
287C22⋊C4×C139—21no—
288C22⋊C4×C139—41no—
289C22⋊C4×C139—41no—
290C42×C139—21no—
291C23×C139—21no—
292C23×C139—21no—
293C23×C139—22no—
294C23×C139—21no—
295C23×C139—41no—
296C23×C139#12111yescharacteristic
297C23×C139#12111yescharacteristic
298C23×C139C2×#4111yescharacteristic
299Q8×C139—22no—
300Q8×C139—21no—
301Q8×C139—22no—
302Q8×C139—22no—
303Q8×C139—22no—
304Q8×C139—21no—
305Q8×C139—44no—
306Q8×C139—44no—
307Q8×C139—41no—
308Q8×C139—41no—
309Q8×C139—41no—
310Q8×C139—41no—
311Q8×C139—41no—
312Q8×C139—41no—
313Q8×C139—41no—
314Q8×C139—41no—
315D4×C139—21no—
316D4×C139—21no—
317D4×C139—41no—
318D4×C139—41no—
319D4×C139—42no—
320D4×C139—81no—
321C2×C4×C139—21no—
322C2×C4×C139—21no—
323C2×C4×C139—21no—
324C2×C4×C139—21no—
325C2×C4×C139—21no—
326C2×C4×C139—21no—
327C2×C4×C139—21no—
328C2×C4×C139—21no—
329C2×C4×C139—21no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—21no—
333C2×C4×C139—21no—
334C2×C4×C139—22no—
335C2×C4×C139—22no—
336C2×C4×C139—44no—
337C2×C4×C139—44no—
338C2×C4×C139—41no—
339C2×C4×C139—41no—
340C2×C4×C139—41no—
341C2×C4×C139—41no—
342C2×C4×C139—41no—
343C2×C4×C139—41no—
344C2×C4×C139—41no—
345C2×C4×C139—41no—
346C2×C4×C139—41no—
347C2×C4×C139—41no—
348C2×C4×C139—81no—
349C2×C4×C139#12111yescharacteristic
350C2×C4×C139#12111yescharacteristic
351C2×C4×C139C22×D411yescharacteristic
352C2×C4×C139C22×D411yescharacteristic
353C2×C4×C139C22×D411yescharacteristic
354C2×C4×C139C2×#4111yescharacteristic
355C2×C4×C139H(5,𝔽2)11yescharacteristic
356C2×C4×C139H(5,𝔽2)11yescharacteristic
357C8×C139—21no—
358C8×C139—21no—
359C8×C139—22no—
360C8×C139—22no—
361C8×C139—21no—
362C8×C139—21no—
363C8×C139—41no—
364C8×C139—41no—
365C8×C139—41no—
366C8×C139—41no—
367C22×C139—21no—
368C22×C139—21no—
369C22×C139—21no—
370C22×C139—21no—
371C22×C139—21no—
372C22×C139—21no—
373C22×C139—21no—
374C22×C139—42no—
375C22×C139—42no—
376C22×C139—41no—
377C22×C139—41no—
378C22×C139—41no—
379C22×C139#47312yescomplemented
380C22×C139C2×#12111yescharacteristic
381C22×C139#52511yescharacteristic
382C22×C139#53811yescharacteristic
383C4×C139—21no—
384C4×C139—21no—
385C4×C139—42no—
386C4×C139—42no—
387C4×C139—41no—
388C4×C139—41no—
389C4×C139—41no—
390C4×C139—81no—
391C4×C139—81no—
392C4×C139D4211yescharacteristic
393C4×C139D4211yescharacteristic
394C4×C139#54611yescharacteristic
395C4×C139#54611yescharacteristic
396C2×C139—21no—
397C2×C139—21no—
398C2×C139—22no—
399C2×C139—41no—
400C2×C139—81no—
401C2×C139#242411yescharacteristic
402C2×C139C2×#47311yescharacteristic
403C2×C139#306911yescharacteristic
404#25142C13911yesmaximal, characteristic, direct product factor, Sylow
405C139#2514211yescharacteristic, direct product factor, Sylow
406C2×#473C2×C13911yescharacteristic, complemented
407#3056C2×C13911yescharacteristic
408#3004C2×C13911yescharacteristic
409C2×#451C2×C13911yescharacteristic, complemented
410#2933C2×C13911yescharacteristic
411C22×#101C2×C13911yescharacteristic, complemented
412#2064C2×C13911yescharacteristic, complemented
413#2052C2×C13911yescharacteristic, complemented
414#2047C2×C13911yescharacteristic, complemented
415#2020C2×C13911yescharacteristic, complemented
416#1979C2×C13911yescharacteristic, complemented
417#1930C2×C13911yescharacteristic, complemented
418#1908C2×C13911yescharacteristic, complemented
419#1901C2×C13911yescharacteristic, complemented
420#1855C2×C13911yescharacteristic, complemented
421C23×Q8C22×C13911yescharacteristic
422C2×#137C22×C13911yescharacteristic
423C2×#137C22×C13911yescharacteristic
424C2×#137C22×C13911yescharacteristic
425C22×Q16C22×C13911yescharacteristic
426C22×Q16C22×C13911yescharacteristic
427C2×#131C22×C13911yescharacteristic
428C22×M16C22×C13911yescharacteristic
429C22×M16C22×C13911yescharacteristic
430#525C22×C13911yescharacteristic
431C2×C22⋊Q8C22×C13911yescharacteristic
432#473—24no—
433#470—21no—
434#468—21no—
435#467—21no—
436#465—21no—
437#451—21no—
438#451—21no—
439#451—21no—
440#451—21no—
441#451—21no—
442#451—21no—
443#448—21no—
444#448—21no—
445#436—21no—
446#435—21no—
447#435—21no—
448C8×D4—21no—
449C2×#108C22×C13911yescharacteristic
450C2×#108C22×C13911yescharacteristic
451#428C22×C13911yescharacteristic
452#424C22×C13911yescharacteristic
453#419C22×C13911yescharacteristic
454#419C22×C13911yescharacteristic
455#419C22×C13911yescharacteristic
456#417C22×C13911yescharacteristic
457C2×#103C22×C13911yescharacteristic
458C2×#103C22×C13911yescharacteristic
459C2×#101—24no—
460C2×#101C22×C13911yescharacteristic
461C2×#101C22×C13911yescharacteristic
462C2×#101C22×C13911yescharacteristic
463C2×#101C22×C13911yescharacteristic
464C2×#101C22×C13911yescharacteristic
465C2×#101C22×C13911yescharacteristic
466#408C22×C13911yescharacteristic
467#407C22×C13911yescharacteristic
468C2×C22⋊C8C22×C13911yescharacteristic
469#405C22×C13911yescharacteristic
470#343C22×C13911yescharacteristic
471#343C22×C13911yescharacteristic
472#341C22×C13911yescharacteristic
473#341C22×C13911yescharacteristic
474C2×#41C23×C13911yescharacteristic
475C22×Q8—22no—
476C22×Q8—22no—
477C22×Q8—21no—
478C22×Q8—21no—
479C22×Q8—21no—
480C22×Q8—21no—
481C22×Q8—21no—
482C22×Q8—41no—
483C22×Q8—41no—
484C22×Q8C23×C13911yescharacteristic
485C22×Q8C23×C13911yescharacteristic
486C22×Q8C23×C13911yescharacteristic
487C23×C4—21no—
488C23×C4C23×C13911yescharacteristic
489#137—22no—
490#137—22no—
491#137—22no—
492#137—41no—
493#137—41no—
494#137—41no—
495C2×Q16—22no—
496C2×Q16—21no—
497C2×Q16—21no—
498C2×Q16—21no—
499C2×Q16—22no—
500C2×Q16—21no—
501C2×Q16—21no—
502C2×Q16—21no—
503C2×Q16—21no—
504C2×Q16—41no—
505C2×Q16—41no—
506C2×SD16—21no—
507C2×SD16—21no—
508C2×SD16—21no—
509#131—22no—
510#131—41no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C2×M16C23×C13911yescharacteristic
519C2×M16C23×C13911yescharacteristic
520C2×M16C23×C13911yescharacteristic
521C2×M16C23×C13911yescharacteristic
522C2×M16C23×C13911yescharacteristic
523C2×M16C23×C13911yescharacteristic
524C22×C8—21no—
525C22×C8—21no—
526C22×C8—21no—
527C22×C8C23×C13911yescharacteristic
528C22×C8C23×C13911yescharacteristic
529#123—21no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8D4×C13911yescharacteristic
535C22⋊Q8D4×C13911yescharacteristic
536#121D4×C13911yescharacteristic
537#121D4×C13911yescharacteristic
538#120—21no—
539C4×D4—21no—
540C4×D4—21no—
541#117C23×C13911yescharacteristic
542C2×C4⋊C4—21no—
543C2×C4⋊C4C23×C13911yescharacteristic
544C2×C22⋊C4—21no—
545#108—22no—
546#108—41no—
547#107—21no—
548#106—21no—
549C4⋊C8—21no—
550C4⋊C8—21no—
551#103—21no—
552#103—21no—
553#103—21no—
554#103—21no—
555#103—21no—
556#103—21no—
557#103—21no—
558#103—21no—
559#103—21no—
560#103—21no—
561#103—21no—
562#102—21no—
563#101—22no—
564#101—22no—
565#101—22no—
566#101—22no—
567#101—41no—
568#101D4×C13914yescomplemented
569C22⋊C8—21no—
570C22⋊C8—21no—
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8D4×C13911yescharacteristic
574C22⋊C8D4×C13911yescharacteristic
575C22⋊C8D4×C13911yescharacteristic
576C22⋊C8D4×C13911yescharacteristic
577#97—21no—
578C4×C8—21no—
579C24#41×C13911yescharacteristic
580#41—21no—
581#41—21no—
582#41—21no—
583#41—21no—
584C2×Q8—24no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—42no—
602C2×Q8—42no—
603C2×Q8—42no—
604C2×Q8—42no—
605C2×Q8—42no—
606C2×Q8—42no—
607C2×Q8—42no—
608C2×Q8—42no—
609C2×Q8—42no—
610C2×Q8—41no—
611C2×Q8—41no—
612C2×Q8C2×D4×C13912yes—
613C2×Q8C2×D4×C13911yescharacteristic
614C2×Q8#41×C13912yes—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4C2×D4×C13911yescharacteristic
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—42no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4C2×D4×C13911yescharacteristic
633C22×C4C2×D4×C13911yescharacteristic
634C22×C4C2×D4×C13911yescharacteristic
635C22×C4C2×D4×C13911yescharacteristic
636C22×C4#41×C13911yescharacteristic
637C22×C4C24×C13911yescharacteristic
638Q16—42no—
639Q16—42no—
640Q16—42no—
641Q16—42no—
642Q16—42no—
643Q16—42no—
644Q16—42no—
645SD16—42no—
646SD16—42no—
647SD16—42no—
648M16—21no—
649M16—21no—
650M16—21no—
651M16—21no—
652M16—21no—
653M16—21no—
654M16—21no—
655M16—21no—
656M16—21no—
657M16—21no—
658M16—42no—
659M16—42no—
660M16—42no—
661M16C2×D4×C13912yes—
662M16C2×D4×C13912yes—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—42no—
674C2×C8—42no—
675C2×C8—42no—
676C2×C8C2×D4×C13911yescharacteristic
677C2×C8C2×D4×C13911yescharacteristic
678C2×C8C2×D4×C13911yescharacteristic
679C2×C8C2×D4×C13911yescharacteristic
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—41no—
685C4⋊C4—41no—
686C4⋊C4C2×D4×C13911yescharacteristic
687C4⋊C4C2×D4×C13911yescharacteristic
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—41no—
694C22⋊C4—41no—
695C42—21no—
696C23—22no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—41no—
701C23#121×C13911yescharacteristic
702C23#121×C13911yescharacteristic
703C23C2×#41×C13911yescharacteristic
704Q8—22no—
705Q8—21no—
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—21no—
710Q8—44no—
711Q8—44no—
712Q8—41no—
713Q8—41no—
714Q8—41no—
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719Q8—41no—
720D4—21no—
721D4—21no—
722D4—42no—
723D4—41no—
724D4—41no—
725D4—81no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—81no—
754C2×C4#121×C13911yescharacteristic
755C2×C4#121×C13911yescharacteristic
756C2×C4C22×D4×C13911yescharacteristic
757C2×C4C22×D4×C13911yescharacteristic
758C2×C4C22×D4×C13911yescharacteristic
759C2×C4C2×#41×C13911yescharacteristic
760C2×C4H(5,𝔽2)×C13911yescharacteristic
761C2×C4H(5,𝔽2)×C13911yescharacteristic
762C8—21no—
763C8—21no—
764C8—22no—
765C8—22no—
766C8—21no—
767C8—21no—
768C8—41no—
769C8—41no—
770C8—41no—
771C8—41no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—42no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22#473×C13912yescomplemented
785C22C2×#121×C13911yescharacteristic
786C22#525×C13911yescharacteristic
787C22#538×C13911yescharacteristic
788C4—21no—
789C4—21no—
790C4—41no—
791C4—41no—
792C4—42no—
793C4—42no—
794C4—41no—
795C4—81no—
796C4—81no—
797C4D42×C13911yescharacteristic
798C4D42×C13911yescharacteristic
799C4#546×C13911yescharacteristic
800C4#546×C13911yescharacteristic
801C2—22no—
802C2—21no—
803C2—21no—
804C2—41no—
805C2—81no—
806C2#2424×C13911yescharacteristic
807C2C2×#473×C13911yescharacteristic
808C2#3069×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#121
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#525×C139C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#473×C139C2semidirect
4. C2×#451×C139C2semidirect
6. C22×#101×C139C2semidirect
7. #2064×C139C2semidirect
8. #2052×C139C2semidirect
9. #2047×C139C2semidirect
10. #2020×C139C2semidirect
11. #1979×C139C2semidirect
12. #1930×C139C2semidirect
13. #1908×C139C2semidirect
14. #1901×C139C2semidirect
15. #1855×C139C2semidirect
163. #101×C139D4semidirect
379. C22×C139#473semidirect
404. #25142C139direct (N × H)
405. C139#25142direct (N × H)
406. C2×#473C2×C139semidirect
409. C2×#451C2×C139semidirect
411. C22×#101C2×C139semidirect
412. #2064C2×C139semidirect
413. #2052C2×C139semidirect
414. #2047C2×C139semidirect
415. #2020C2×C139semidirect
416. #1979C2×C139semidirect
417. #1930C2×C139semidirect
418. #1908C2×C139semidirect
419. #1901C2×C139semidirect
420. #1855C2×C139semidirect
568. #101D4×C139semidirect
784. C22#473×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#473×C1392
#3056×C1392
#3004×C1392
C2×#451×C1392
#2933×C1392
C22×#101×C1392
#2064×C1392
#2052×C1392
#2047×C1392
#2020×C1392
#1979×C1392
#1930×C1392
#1908×C1392
#1901×C1392
#1855×C1392
#25142139