Finite Group Databasebeta

← C139×#26977 #48021573

Subgroups — C139×#26977 #48021573

Order 35584.

1028 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C139C211yesmaximal, characteristic, complemented
2C2×#442×C139C211yesmaximal, characteristic, complemented
3#2428×C139C211yesmaximal, characteristic, complemented
4#2420×C139C211yesmaximal, characteristic, complemented
5#2085×C139C211yesmaximal, characteristic, complemented
6#2034×C139C211yesmaximal, characteristic, complemented
7#2011×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1961×C139C211yesmaximal, characteristic, complemented
10#1936×C139C211yesmaximal, characteristic, complemented
11#1936×C139C211yesmaximal, characteristic, complemented
12#1893×C139C211yesmaximal, characteristic, complemented
13#1879×C139C211yesmaximal, characteristic, complemented
14#1862×C139C211yesmaximal, characteristic, complemented
15#1752×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C23×C8×C139C2211yescharacteristic
19C2×#127×C139C2211yescharacteristic
20C2×#121×C139—21no—
21C2×#121×C139C2211yescharacteristic
22C2×#121×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×C4×D4×C139C2211yescharacteristic
25C2×C4×D4×C139C2211yescharacteristic
26#466×C139—24no—
27#442×C139—24no—
28C2×#107×C139C2211yescharacteristic
29C2×#106×C139C2211yescharacteristic
30C2×#102×C139C2211yescharacteristic
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×C22⋊C8×C139C2211yescharacteristic
39C2×#97×C139C2211yescharacteristic
40C2×#97×C139C2211yescharacteristic
41#397×C139—21no—
42#394×C139—21no—
43#394×C139—21no—
44#392×C139—21no—
45#390×C139C2211yescharacteristic
46#390×C139C2211yescharacteristic
47#389×C139C2211yescharacteristic
48#389×C139C2211yescharacteristic
49#386×C139—21no—
50#386×C139—21no—
51#382×C139C2211yescharacteristic
52#381×C139—21no—
53#380×C139C2211yescharacteristic
54C4×C22⋊C4×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#336×C139C2211yescharacteristic
60#336×C139C2211yescharacteristic
61C22×D4×C139—21no—
62C22×D4×C139—21no—
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139C2311yescharacteristic
67C22×D4×C139C2311yescharacteristic
68C22×D4×C139C2311yescharacteristic
69C23×C4×C139—21no—
70C23×C4×C139—21no—
71C23×C4×C139C2311yescharacteristic
72C2×D8×C139—22no—
73C2×D8×C139—22no—
74C2×D8×C139—22no—
75C2×D8×C139—22no—
76C2×D8×C139—22no—
77C2×D8×C139—41no—
78C22×C8×C139—22no—
79C22×C8×C139—22no—
80C22×C8×C139—41no—
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83C22×C8×C139C2311yescharacteristic
84C22×C8×C139C2311yescharacteristic
85#127×C139—22no—
86#127×C139—41no—
87#121×C139—22no—
88#121×C139—22no—
89#121×C139—22no—
90#121×C139—44no—
91#121×C139—41no—
92#121×C139—41no—
93#121×C139—41no—
94C4×D4×C139—22no—
95C4×D4×C139—22no—
96C4×D4×C139—41no—
97C4×D4×C139—41no—
98C2×C4⋊C4×C139—21no—
99C2×C4⋊C4×C139—21no—
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C4⋊C4×C139C2311yescharacteristic
102C2×C4⋊C4×C139C2311yescharacteristic
103C2×C4⋊C4×C139C2311yescharacteristic
104C2×C4⋊C4×C139C2311yescharacteristic
105C2×C22⋊C4×C139—21no—
106C2×C22⋊C4×C139—21no—
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
109C2×C22⋊C4×C139—21no—
110C2×C22⋊C4×C139—21no—
111C2×C22⋊C4×C139—21no—
112C2×C22⋊C4×C139—21no—
113C2×C22⋊C4×C139—21no—
114C2×C22⋊C4×C139—21no—
115C2×C22⋊C4×C139D411yescharacteristic
116C2×C22⋊C4×C139D411yescharacteristic
117C2×C42×C139C2311yescharacteristic
118C2×C42×C139C2311yescharacteristic
119#107×C139—22no—
120#106×C139—22no—
121#102×C139—22no—
122#102×C139—22no—
123#102×C139—22no—
124#102×C139—22no—
125#102×C139—41no—
126#102×C139—41no—
127#102×C139—41no—
128#102×C139D414yescomplemented
129C22⋊C8×C139—22no—
130#97×C139—22no—
131#97×C139—41no—
132#95×C139—21no—
133#95×C139—21no—
134#95×C139—21no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139D411yescharacteristic
138#95×C139D411yescharacteristic
139C24×C139—21no—
140C24×C139—21no—
141C24×C139—21no—
142C24×C139C2×D411yescharacteristic
143C2×D4×C139—21no—
144C2×D4×C139—21no—
145C2×D4×C139—21no—
146C2×D4×C139—21no—
147C2×D4×C139—21no—
148C2×D4×C139—21no—
149C2×D4×C139—21no—
150C2×D4×C139—21no—
151C2×D4×C139—21no—
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—42no—
160C2×D4×C139—42no—
161C2×D4×C139—42no—
162C2×D4×C139—42no—
163C2×D4×C139—42no—
164C2×D4×C139—42no—
165C2×D4×C139—42no—
166C2×D4×C139—42no—
167C2×D4×C139—42no—
168C2×D4×C139—42no—
169C2×D4×C139—81no—
170C2×D4×C139—81no—
171C2×D4×C139—81no—
172C2×D4×C139—81no—
173C2×D4×C139—81no—
174C2×D4×C139C2×D412yes—
175C2×D4×C139#4112yes—
176C22×C4×C139—21no—
177C22×C4×C139—21no—
178C22×C4×C139—21no—
179C22×C4×C139—21no—
180C22×C4×C139—21no—
181C22×C4×C139—21no—
182C22×C4×C139—21no—
183C22×C4×C139—21no—
184C22×C4×C139—21no—
185C22×C4×C139—21no—
186C22×C4×C139—21no—
187C22×C4×C139—42no—
188C22×C4×C139—42no—
189C22×C4×C139—42no—
190C22×C4×C139—42no—
191C22×C4×C139—81no—
192C22×C4×C139—81no—
193C22×C4×C139C2×D411yescharacteristic
194C22×C4×C139C2×D411yescharacteristic
195C22×C4×C139C2×D411yescharacteristic
196C22×C4×C139C2×D411yescharacteristic
197C22×C4×C139C2×D411yescharacteristic
198C22×C4×C139C2411yescharacteristic
199D8×C139—28no—
200D8×C139—44no—
201C2×C8×C139—21no—
202C2×C8×C139—21no—
203C2×C8×C139—21no—
204C2×C8×C139—21no—
205C2×C8×C139—21no—
206C2×C8×C139—21no—
207C2×C8×C139—21no—
208C2×C8×C139—21no—
209C2×C8×C139—21no—
210C2×C8×C139—44no—
211C2×C8×C139C2×D412yes—
212C2×C8×C139#4112yes—
213C2×C8×C139#4112yes—
214C4⋊C4×C139—21no—
215C4⋊C4×C139—21no—
216C4⋊C4×C139—21no—
217C4⋊C4×C139—21no—
218C4⋊C4×C139—21no—
219C4⋊C4×C139—21no—
220C4⋊C4×C139—21no—
221C4⋊C4×C139—21no—
222C4⋊C4×C139—21no—
223C4⋊C4×C139—42no—
224C4⋊C4×C139—81no—
225C4⋊C4×C139C2×D412yes—
226C22⋊C4×C139—22no—
227C22⋊C4×C139—41no—
228C22⋊C4×C139—42no—
229C22⋊C4×C139—42no—
230C22⋊C4×C139—42no—
231C22⋊C4×C139—42no—
232C22⋊C4×C139—42no—
233C22⋊C4×C139—42no—
234C22⋊C4×C139—81no—
235C22⋊C4×C139—81no—
236C22⋊C4×C139—81no—
237C22⋊C4×C139—81no—
238C42×C139—21no—
239C42×C139—21no—
240C42×C139—21no—
241C42×C139—21no—
242C23×C139—21no—
243C23×C139—21no—
244C23×C139—21no—
245C23×C139—21no—
246C23×C139—21no—
247C23×C139—21no—
248C23×C139—22no—
249C23×C139—22no—
250C23×C139—41no—
251C23×C139—41no—
252C23×C139—41no—
253C23×C139—41no—
254C23×C139—41no—
255C23×C139—41no—
256C23×C139—41no—
257C23×C139—41no—
258C23×C139—41no—
259C23×C139—41no—
260C23×C139—41no—
261C23×C139—41no—
262C23×C139—41no—
263C23×C139—41no—
264C23×C139—41no—
265C23×C139—41no—
266C23×C139—41no—
267C23×C139—41no—
268C23×C139—41no—
269C23×C139AGL(1,ℤ/8)12yes—
270C23×C139C22×D411yescharacteristic
271D4×C139—22no—
272D4×C139—22no—
273D4×C139—22no—
274D4×C139—22no—
275D4×C139—41no—
276D4×C139—41no—
277D4×C139—41no—
278D4×C139—41no—
279D4×C139—41no—
280D4×C139—41no—
281D4×C139—41no—
282D4×C139—41no—
283D4×C139—84no—
284D4×C139—84no—
285D4×C139—84no—
286D4×C139—84no—
287D4×C139—84no—
288C2×C4×C139—21no—
289C2×C4×C139—21no—
290C2×C4×C139—21no—
291C2×C4×C139—21no—
292C2×C4×C139—22no—
293C2×C4×C139—21no—
294C2×C4×C139—21no—
295C2×C4×C139—21no—
296C2×C4×C139—21no—
297C2×C4×C139—21no—
298C2×C4×C139—21no—
299C2×C4×C139—21no—
300C2×C4×C139—21no—
301C2×C4×C139—21no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—41no—
305C2×C4×C139—41no—
306C2×C4×C139—41no—
307C2×C4×C139—41no—
308C2×C4×C139—41no—
309C2×C4×C139—41no—
310C2×C4×C139—41no—
311C2×C4×C139—41no—
312C2×C4×C139—41no—
313C2×C4×C139—41no—
314C2×C4×C139—41no—
315C2×C4×C139—41no—
316C2×C4×C139—41no—
317C2×C4×C139—41no—
318C2×C4×C139—41no—
319C2×C4×C139—41no—
320C2×C4×C139—41no—
321C2×C4×C139—41no—
322C2×C4×C139—84no—
323C2×C4×C139—84no—
324C2×C4×C139C22×D411yescharacteristic
325C2×C4×C139C2×#4111yescharacteristic
326C2×C4×C139C2×#4111yescharacteristic
327C2×C4×C139C2×#4111yescharacteristic
328C2×C4×C139H(5,𝔽2)11yescharacteristic
329C2×C4×C139H(5,𝔽2)11yescharacteristic
330C8×C139—22no—
331C8×C139—22no—
332C8×C139—22no—
333C8×C139—41no—
334C22×C139—22no—
335C22×C139—22no—
336C22×C139—22no—
337C22×C139—41no—
338C22×C139—41no—
339C22×C139—41no—
340C22×C139—41no—
341C22×C139—42no—
342C22×C139—42no—
343C22×C139—42no—
344C22×C139—42no—
345C22×C139—42no—
346C22×C139—42no—
347C22×C139—81no—
348C22×C139—81no—
349C22×C139—81no—
350C22×C139—81no—
351C22×C139—81no—
352C22×C139—81no—
353C22×C139—81no—
354C22×C139—81no—
355C22×C139—81no—
356C22×C139—81no—
357C22×C139—81no—
358C22×C139—81no—
359C22×C139—81no—
360C22×C139—81no—
361C22×C139—81no—
362C22×C139#53211yescharacteristic
363C22×C139D4211yescharacteristic
364C22×C139#54611yescharacteristic
365C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C139#57511yescharacteristic
367C22×C139#57611yescharacteristic
368C22×C139#57611yescharacteristic
369C4×C139—41no—
370C4×C139—41no—
371C4×C139—42no—
372C4×C139—41no—
373C4×C139—41no—
374C4×C139—41no—
375C4×C139—81no—
376C4×C139—81no—
377C4×C139—81no—
378C4×C139—81no—
379C4×C139#52511yescharacteristic
380C4×C139#54011yescharacteristic
381C4×C139#54611yescharacteristic
382C4×C139#55311yescharacteristic
383C2×C139—42no—
384C2×C139—82no—
385C2×C139—82no—
386C2×C139—161no—
387C2×C139#246411yescharacteristic
388C2×C139#317611yescharacteristic
389C2×C139#318011yescharacteristic
390C2×C139#326411yescharacteristic
391C2×C139#326811yescharacteristic
392C2×C139#331811yescharacteristic
393C2×C139#331911yescharacteristic
394#26977C13911yesmaximal, characteristic, direct product factor, Sylow
395C139#2697711yescharacteristic, direct product factor, Sylow
396C2×#466C2×C13911yescharacteristic, complemented
397C2×#442C2×C13911yescharacteristic, complemented
398#2428C2×C13911yescharacteristic, complemented
399#2420C2×C13911yescharacteristic, complemented
400#2085C2×C13911yescharacteristic, complemented
401#2034C2×C13911yescharacteristic, complemented
402#2011C2×C13911yescharacteristic, complemented
403#1999C2×C13911yescharacteristic, complemented
404#1961C2×C13911yescharacteristic, complemented
405#1936C2×C13911yescharacteristic, complemented
406#1936C2×C13911yescharacteristic, complemented
407#1893C2×C13911yescharacteristic, complemented
408#1879C2×C13911yescharacteristic, complemented
409#1862C2×C13911yescharacteristic, complemented
410#1752C2×C13911yescharacteristic, complemented
411C22×D8C22×C13911yescharacteristic
412C22×D8C22×C13911yescharacteristic
413C23×C8C22×C13911yescharacteristic
414C2×#127C22×C13911yescharacteristic
415C2×#121—21no—
416C2×#121C22×C13911yescharacteristic
417C2×#121C22×C13911yescharacteristic
418C2×#121C22×C13911yescharacteristic
419C2×C4×D4C22×C13911yescharacteristic
420C2×C4×D4C22×C13911yescharacteristic
421#466—24no—
422#442—24no—
423C2×#107C22×C13911yescharacteristic
424C2×#106C22×C13911yescharacteristic
425C2×#102C22×C13911yescharacteristic
426C2×#102C22×C13911yescharacteristic
427C2×#102C22×C13911yescharacteristic
428C2×#102C22×C13911yescharacteristic
429C2×#102C22×C13911yescharacteristic
430C2×#102C22×C13911yescharacteristic
431C2×#102C22×C13911yescharacteristic
432C2×#102C22×C13911yescharacteristic
433C2×C22⋊C8C22×C13911yescharacteristic
434C2×#97C22×C13911yescharacteristic
435C2×#97C22×C13911yescharacteristic
436#397—21no—
437#394—21no—
438#394—21no—
439#392—21no—
440#390C22×C13911yescharacteristic
441#390C22×C13911yescharacteristic
442#389C22×C13911yescharacteristic
443#389C22×C13911yescharacteristic
444#386—21no—
445#386—21no—
446#382C22×C13911yescharacteristic
447#381—21no—
448#380C22×C13911yescharacteristic
449C4×C22⋊C4C22×C13911yescharacteristic
450#340C22×C13911yescharacteristic
451#340C22×C13911yescharacteristic
452#340C22×C13911yescharacteristic
453#340C22×C13911yescharacteristic
454#336C22×C13911yescharacteristic
455#336C22×C13911yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C23×C13911yescharacteristic
462C22×D4C23×C13911yescharacteristic
463C22×D4C23×C13911yescharacteristic
464C23×C4—21no—
465C23×C4—21no—
466C23×C4C23×C13911yescharacteristic
467C2×D8—22no—
468C2×D8—22no—
469C2×D8—22no—
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—41no—
473C22×C8—22no—
474C22×C8—22no—
475C22×C8—41no—
476C22×C8C23×C13911yescharacteristic
477C22×C8C23×C13911yescharacteristic
478C22×C8C23×C13911yescharacteristic
479C22×C8C23×C13911yescharacteristic
480#127—22no—
481#127—41no—
482#121—22no—
483#121—22no—
484#121—22no—
485#121—44no—
486#121—41no—
487#121—41no—
488#121—41no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—41no—
492C4×D4—41no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4C23×C13911yescharacteristic
496C2×C4⋊C4C23×C13911yescharacteristic
497C2×C4⋊C4C23×C13911yescharacteristic
498C2×C4⋊C4C23×C13911yescharacteristic
499C2×C4⋊C4C23×C13911yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4D4×C13911yescharacteristic
511C2×C22⋊C4D4×C13911yescharacteristic
512C2×C42C23×C13911yescharacteristic
513C2×C42C23×C13911yescharacteristic
514#107—22no—
515#106—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—41no—
521#102—41no—
522#102—41no—
523#102D4×C13914yescomplemented
524C22⋊C8—22no—
525#97—22no—
526#97—41no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95D4×C13911yescharacteristic
533#95D4×C13911yescharacteristic
534C24—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C13911yescharacteristic
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—81no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4C2×D4×C13912yes—
570C2×D4#41×C13912yes—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4C2×D4×C13911yescharacteristic
589C22×C4C2×D4×C13911yescharacteristic
590C22×C4C2×D4×C13911yescharacteristic
591C22×C4C2×D4×C13911yescharacteristic
592C22×C4C2×D4×C13911yescharacteristic
593C22×C4C24×C13911yescharacteristic
594D8—28no—
595D8—44no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—44no—
606C2×C8C2×D4×C13912yes—
607C2×C8#41×C13912yes—
608C2×C8#41×C13912yes—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—81no—
620C4⋊C4C2×D4×C13912yes—
621C22⋊C4—22no—
622C22⋊C4—41no—
623C22⋊C4—42no—
624C22⋊C4—42no—
625C22⋊C4—42no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C42—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—22no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23AGL(1,ℤ/8)×C13912yes—
665C23C22×D4×C13911yescharacteristic
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—41no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682D4—84no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—84no—
718C2×C4—84no—
719C2×C4C22×D4×C13911yescharacteristic
720C2×C4C2×#41×C13911yescharacteristic
721C2×C4C2×#41×C13911yescharacteristic
722C2×C4C2×#41×C13911yescharacteristic
723C2×C4H(5,𝔽2)×C13911yescharacteristic
724C2×C4H(5,𝔽2)×C13911yescharacteristic
725C8—22no—
726C8—22no—
727C8—22no—
728C8—41no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22#532×C13911yescharacteristic
758C22D42×C13911yescharacteristic
759C22#546×C13911yescharacteristic
760C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
761C22#575×C13911yescharacteristic
762C22#576×C13911yescharacteristic
763C22#576×C13911yescharacteristic
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—42no—
769C4—41no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4#525×C13911yescharacteristic
775C4#540×C13911yescharacteristic
776C4#546×C13911yescharacteristic
777C4#553×C13911yescharacteristic
778C2—42no—
779C2—82no—
780C2—82no—
781C2—161no—
782C2#2464×C13911yescharacteristic
783C2#3176×C13911yescharacteristic
784C2#3180×C13911yescharacteristic
785C2#3264×C13911yescharacteristic
786C2#3268×C13911yescharacteristic
787C2#3318×C13911yescharacteristic
788C2#3319×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#466×C139C2semidirect
2. C2×#442×C139C2semidirect
3. #2428×C139C2semidirect
4. #2420×C139C2semidirect
5. #2085×C139C2semidirect
6. #2034×C139C2semidirect
7. #2011×C139C2semidirect
8. #1999×C139C2semidirect
9. #1961×C139C2semidirect
10. #1936×C139C2semidirect
11. #1936×C139C2semidirect
12. #1893×C139C2semidirect
13. #1879×C139C2semidirect
14. #1862×C139C2semidirect
15. #1752×C139C2semidirect
128. #102×C139D4semidirect
394. #26977C139direct (N × H)
395. C139#26977direct (N × H)
396. C2×#466C2×C139semidirect
397. C2×#442C2×C139semidirect
398. #2428C2×C139semidirect
399. #2420C2×C139semidirect
400. #2085C2×C139semidirect
401. #2034C2×C139semidirect
402. #2011C2×C139semidirect
403. #1999C2×C139semidirect
404. #1961C2×C139semidirect
405. #1936C2×C139semidirect
406. #1936C2×C139semidirect
407. #1893C2×C139semidirect
408. #1879C2×C139semidirect
409. #1862C2×C139semidirect
410. #1752C2×C139semidirect
523. #102D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1392
C2×#442×C1392
#2428×C1392
#2420×C1392
#2085×C1392
#2034×C1392
#2011×C1392
#1999×C1392
#1961×C1392
#1936×C1392
#1893×C1392
#1879×C1392
#1862×C1392
#1752×C1392
#26977139