Finite Group Databasebeta

← C139×#24142 #48018738

Subgroups — C139×#24142 #48018738

Order 35584.

1292 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3505×C139C211yesmaximal, characteristic, complemented
2#2626×C139C211yesmaximal, characteristic, complemented
3#2617×C139C211yesmaximal, characteristic, complemented
4#2321×C139C211yesmaximal, characteristic, complemented
5#2044×C139C212yesmaximal, complemented
6#2021×C139C212yesmaximal, complemented
7#1996×C139C211yesmaximal, characteristic, complemented
8#1964×C139C211yesmaximal, characteristic, complemented
9#1889×C139C212yesmaximal, complemented
10#1867×C139C212yesmaximal, complemented
11#1799×C139C211yesmaximal, characteristic, complemented
12#553×C139—22no—
13#553×C139—21no—
14#552×C139—21no—
15#551×C139—22no—
16#548×C139—21no—
17#546×C139—21no—
18#539×C139—21no—
19#538×C139—21no—
20#534×C139C2212yes—
21#529×C139—21no—
22#525×C139—21no—
23C2×C22⋊Q8×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#120×C139C2211yescharacteristic
26C2×#120×C139C2212yes—
27#518×C139C2212yes—
28C2×C4×D4×C139C2211yescharacteristic
29C22×C22⋊C4×C139C2211yescharacteristic
30C2×#99×C139C2212yes—
31C2×#99×C139C2212yes—
32C2×#99×C139C2212yes—
33#399×C139—21no—
34#397×C139—21no—
35#396×C139—22no—
36#394×C139—22no—
37#393×C139—21no—
38#392×C139—21no—
39#390×C139—21no—
40#388×C139—21no—
41#388×C139—21no—
42#386×C139—21no—
43#386×C139C2211yescharacteristic
44#386×C139C2212yes—
45#385×C139C2212yes—
46#385×C139C2211yescharacteristic
47#380×C139C2211yescharacteristic
48#380×C139C2211yescharacteristic
49#379×C139C2212yes—
50#379×C139C2211yescharacteristic
51C4×C22⋊C4×C139C2211yescharacteristic
52#342×C139C2212yes—
53#342×C139C2212yes—
54#342×C139C2212yes—
55C25×C139C2311yescharacteristic
56C2×#41×C139—21no—
57C22×Q8×C139D411yescharacteristic, complemented
58C22×D4×C139—21no—
59C22×D4×C139—22no—
60C22×D4×C139D411yescharacteristic, complemented
61C22×D4×C139C2311yescharacteristic
62C22×D4×C139C2312yes—
63C23×C4×C139D411yescharacteristic, complemented
64C23×C4×C139C2311yescharacteristic
65C23×C4×C139C2311yescharacteristic
66#126×C139—22no—
67#126×C139—22no—
68#126×C139—22no—
69#125×C139—21no—
70#125×C139—22no—
71#124×C139—21no—
72#124×C139—22no—
73#123×C139—22no—
74#123×C139—22no—
75#123×C139—22no—
76#123×C139—22no—
77#123×C139—22no—
78C22⋊Q8×C139—21no—
79C22⋊Q8×C139—22no—
80C22⋊Q8×C139—21no—
81C22⋊Q8×C139—21no—
82C22⋊Q8×C139—21no—
83C22⋊Q8×C139—21no—
84#121×C139—21no—
85#121×C139—22no—
86#121×C139—21no—
87#121×C139—21no—
88#121×C139—21no—
89#121×C139—21no—
90#121×C139—22no—
91#121×C139—22no—
92#120×C139—22no—
93#120×C139—22no—
94#120×C139—22no—
95#120×C139—22no—
96#120×C139—24no—
97#120×C139—42no—
98C4×Q8×C139—21no—
99C4×D4×C139—22no—
100C4×D4×C139—21no—
101C4×D4×C139—21no—
102C4×D4×C139—21no—
103C4×D4×C139—21no—
104C4×D4×C139—21no—
105C4×D4×C139—22no—
106C4×D4×C139—22no—
107C4×D4×C139—22no—
108C4×D4×C139—22no—
109#117×C139—21no—
110#117×C139—22no—
111#117×C139—22no—
112C2×C4⋊C4×C139—21no—
113C2×C4⋊C4×C139—22no—
114C2×C4⋊C4×C139—21no—
115C2×C4⋊C4×C139—21no—
116C2×C4⋊C4×C139D412yescomplemented
117C2×C4⋊C4×C139D411yescharacteristic, complemented
118C2×C4⋊C4×C139D411yescharacteristic, complemented
119C2×C4⋊C4×C139D411yescharacteristic, complemented
120C2×C22⋊C4×C139—22no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—21no—
124C2×C22⋊C4×C139—22no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—21no—
129C2×C22⋊C4×C139—21no—
130C2×C22⋊C4×C139—22no—
131C2×C22⋊C4×C139—22no—
132C2×C22⋊C4×C139—22no—
133C2×C22⋊C4×C139—21no—
134C2×C22⋊C4×C139—21no—
135C2×C22⋊C4×C139D411yescharacteristic, complemented
136C2×C22⋊C4×C139D412yescomplemented
137C2×C22⋊C4×C139C2312yes—
138C2×C22⋊C4×C139C2311yescharacteristic
139C2×C22⋊C4×C139C2312yes—
140C2×C22⋊C4×C139C2311yescharacteristic
141C2×C22⋊C4×C139C2312yes—
142C2×C22⋊C4×C139C2311yescharacteristic
143C2×C42×C139—21no—
144C2×C42×C139D411yescharacteristic, complemented
145#99×C139—24no—
146#99×C139—42no—
147#99×C139—42no—
148#95×C139—22no—
149#95×C139—21no—
150#95×C139—22no—
151#95×C139—21no—
152#95×C139—21no—
153#95×C139—21no—
154#95×C139—21no—
155C24×C139—21no—
156C24×C139—21no—
157C24×C139—21no—
158C24×C139—21no—
159C24×C139—21no—
160C24×C139—21no—
161C24×C139—81no—
162C24×C139—81no—
163C24×C139C2×D412yes—
164C24×C139C2×D411yescharacteristic
165C24×C139#4112yescomplemented
166C24×C139C2411yescharacteristic
167#41×C139—82no—
168C2×Q8×C139—21no—
169C2×Q8×C139—21no—
170C2×Q8×C139—81no—
171C2×D4×C139—21no—
172C2×D4×C139—22no—
173C2×D4×C139—21no—
174C2×D4×C139—22no—
175C2×D4×C139—22no—
176C2×D4×C139—21no—
177C2×D4×C139—21no—
178C2×D4×C139—22no—
179C2×D4×C139—21no—
180C2×D4×C139—22no—
181C2×D4×C139—21no—
182C2×D4×C139—22no—
183C2×D4×C139—22no—
184C2×D4×C139—22no—
185C2×D4×C139—24no—
186C2×D4×C139—21no—
187C2×D4×C139—21no—
188C2×D4×C139—44no—
189C2×D4×C139—81no—
190C2×D4×C139—81no—
191C2×D4×C139—81no—
192C2×D4×C139—82no—
193C2×D4×C139—82no—
194C22×C4×C139—21no—
195C22×C4×C139—22no—
196C22×C4×C139—22no—
197C22×C4×C139—21no—
198C22×C4×C139—21no—
199C22×C4×C139—21no—
200C22×C4×C139—21no—
201C22×C4×C139—21no—
202C22×C4×C139—22no—
203C22×C4×C139—22no—
204C22×C4×C139—21no—
205C22×C4×C139—81no—
206C22×C4×C139—81no—
207C22×C4×C139—81no—
208C22×C4×C139C2×D411yescharacteristic
209C22×C4×C139C2×D412yes—
210C22×C4×C139C2×D411yescharacteristic
211C22×C4×C139C2×D412yes—
212C22×C4×C139C2×D411yescharacteristic
213C22×C4×C139C2×D412yes—
214C22×C4×C139C2×D411yescharacteristic
215C22×C4×C139C2×D411yescharacteristic
216C22×C4×C139C2×D411yescharacteristic
217C22×C4×C139C2×D411yescharacteristic
218C22×C4×C139C2×D411yescharacteristic
219C22×C4×C139C2×D411yescharacteristic
220C4⋊C4×C139—22no—
221C4⋊C4×C139—22no—
222C4⋊C4×C139—22no—
223C4⋊C4×C139—22no—
224C4⋊C4×C139—21no—
225C4⋊C4×C139—22no—
226C4⋊C4×C139—21no—
227C4⋊C4×C139—21no—
228C4⋊C4×C139—21no—
229C4⋊C4×C139—21no—
230C4⋊C4×C139—22no—
231C4⋊C4×C139—21no—
232C4⋊C4×C139—81no—
233C4⋊C4×C139—81no—
234C4⋊C4×C139—81no—
235C4⋊C4×C139—82no—
236C22⋊C4×C139—22no—
237C22⋊C4×C139—22no—
238C22⋊C4×C139—24no—
239C22⋊C4×C139—22no—
240C22⋊C4×C139—22no—
241C22⋊C4×C139—22no—
242C22⋊C4×C139—22no—
243C22⋊C4×C139—21no—
244C22⋊C4×C139—22no—
245C22⋊C4×C139—21no—
246C22⋊C4×C139—22no—
247C22⋊C4×C139—21no—
248C22⋊C4×C139—22no—
249C22⋊C4×C139—21no—
250C22⋊C4×C139—21no—
251C22⋊C4×C139—22no—
252C22⋊C4×C139—22no—
253C22⋊C4×C139—22no—
254C22⋊C4×C139—21no—
255C22⋊C4×C139—22no—
256C22⋊C4×C139—22no—
257C22⋊C4×C139—21no—
258C22⋊C4×C139—44no—
259C22⋊C4×C139—41no—
260C22⋊C4×C139—41no—
261C22⋊C4×C139—41no—
262C22⋊C4×C139—41no—
263C22⋊C4×C139—81no—
264C22⋊C4×C139—82no—
265C22⋊C4×C139—81no—
266C22⋊C4×C139—82no—
267C22⋊C4×C139—81no—
268C22⋊C4×C139—82no—
269C22⋊C4×C139#4112yescomplemented
270C42×C139—22no—
271C42×C139—22no—
272C42×C139—21no—
273C42×C139—21no—
274C42×C139—81no—
275C23×C139—21no—
276C23×C139—22no—
277C23×C139—22no—
278C23×C139—21no—
279C23×C139—22no—
280C23×C139—22no—
281C23×C139—21no—
282C23×C139—22no—
283C23×C139—22no—
284C23×C139—41no—
285C23×C139—41no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139—42no—
289C23×C139—41no—
290C23×C139—42no—
291C23×C139—41no—
292C23×C139—41no—
293C23×C139—42no—
294C23×C139—41no—
295C23×C139—42no—
296C23×C139—42no—
297C23×C139—42no—
298C23×C139—41no—
299C23×C139—41no—
300C23×C139—41no—
301C23×C139—41no—
302C23×C139—82no—
303C23×C139—82no—
304C23×C139—82no—
305C23×C139—82no—
306C23×C139C22×D411yescharacteristic
307C23×C139C22×D411yescharacteristic
308C23×C139C22×D411yescharacteristic
309C23×C139C2×#4111yescharacteristic
310C23×C139C2×#4111yescharacteristic
311C23×C139H(5,𝔽2)11yescharacteristic
312C23×C1392−1+411yescharacteristic
313Q8×C139—42no—
314Q8×C139—81no—
315D4×C139—42no—
316D4×C139—42no—
317D4×C139—42no—
318D4×C139—41no—
319D4×C139—41no—
320D4×C139—41no—
321D4×C139—42no—
322D4×C139—42no—
323D4×C139—41no—
324D4×C139—81no—
325D4×C139—82no—
326D4×C139—84no—
327D4×C139—82no—
328D4×C139—88no—
329C2×C4×C139—21no—
330C2×C4×C139—22no—
331C2×C4×C139—21no—
332C2×C4×C139—21no—
333C2×C4×C139—22no—
334C2×C4×C139—22no—
335C2×C4×C139—21no—
336C2×C4×C139—22no—
337C2×C4×C139—21no—
338C2×C4×C139—22no—
339C2×C4×C139—22no—
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—42no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—42no—
351C2×C4×C139—41no—
352C2×C4×C139—42no—
353C2×C4×C139—41no—
354C2×C4×C139—41no—
355C2×C4×C139—42no—
356C2×C4×C139—42no—
357C2×C4×C139—41no—
358C2×C4×C139—42no—
359C2×C4×C139—42no—
360C2×C4×C139—42no—
361C2×C4×C139—41no—
362C2×C4×C139—42no—
363C2×C4×C139—41no—
364C2×C4×C139—41no—
365C2×C4×C139—42no—
366C2×C4×C139—42no—
367C2×C4×C139—81no—
368C2×C4×C139—82no—
369C2×C4×C139—82no—
370C2×C4×C139#12011yescharacteristic
371C2×C4×C139#12011yescharacteristic
372C2×C4×C139#12011yescharacteristic
373C2×C4×C139#12011yescharacteristic
374C22×C139—21no—
375C22×C139—21no—
376C22×C139—21no—
377C22×C139—21no—
378C22×C139—21no—
379C22×C139—21no—
380C22×C139—41no—
381C22×C139—41no—
382C22×C139—41no—
383C22×C139—41no—
384C22×C139—42no—
385C22×C139—42no—
386C22×C139—44no—
387C22×C139—42no—
388C22×C139—44no—
389C22×C139—41no—
390C22×C139—42no—
391C22×C139—42no—
392C22×C139—41no—
393C22×C139—42no—
394C22×C139—42no—
395C22×C139—41no—
396C22×C139—82no—
397C22×C139—81no—
398C22×C139—82no—
399C22×C139—82no—
400C22×C139—81no—
401C22×C139—81no—
402C22×C139—82no—
403C22×C139—81no—
404C22×C139—81no—
405C22×C139C2×#12011yescharacteristic
406C22×C139#52511yescharacteristic
407C22×C139#53711yescharacteristic
408C22×C139#54611yescharacteristic
409C22×C139#54711yescharacteristic
410C22×C139#54811yescharacteristic
411C22×C139#55011yescharacteristic
412C4×C139—21no—
413C4×C139—21no—
414C4×C139—21no—
415C4×C139—21no—
416C4×C139—42no—
417C4×C139—41no—
418C4×C139—42no—
419C4×C139—41no—
420C4×C139—42no—
421C4×C139—41no—
422C4×C139—42no—
423C4×C139—82no—
424C4×C139—81no—
425C4×C139—82no—
426C4×C139—81no—
427C2×C139—21no—
428C2×C139—21no—
429C2×C139—21no—
430C2×C139—21no—
431C2×C139—21no—
432C2×C139—21no—
433C2×C139—82no—
434C2×C139—81no—
435C2×C139—82no—
436C2×C139#240711yescharacteristic
437C2×C139#302611yescharacteristic
438C2×C139#302711yescharacteristic
439#24142C13911yesmaximal, characteristic, direct product factor, Sylow
440C139#2414211yescharacteristic, direct product factor, Sylow
441#3505C2×C13911yescharacteristic, complemented
442#2626C2×C13911yescharacteristic, complemented
443#2617C2×C13911yescharacteristic, complemented
444#2321C2×C13911yescharacteristic, complemented
445#2044C2×C13912yescomplemented
446#2021C2×C13912yescomplemented
447#1996C2×C13911yescharacteristic, complemented
448#1964C2×C13911yescharacteristic, complemented
449#1889C2×C13912yescomplemented
450#1867C2×C13912yescomplemented
451#1799C2×C13911yescharacteristic, complemented
452#553—22no—
453#553—21no—
454#552—21no—
455#551—22no—
456#548—21no—
457#546—21no—
458#539—21no—
459#538—21no—
460#534C22×C13912yes—
461#529—21no—
462#525—21no—
463C2×C22⋊Q8C22×C13911yescharacteristic
464C2×#121C22×C13911yescharacteristic
465C2×#120C22×C13911yescharacteristic
466C2×#120C22×C13912yes—
467#518C22×C13912yes—
468C2×C4×D4C22×C13911yescharacteristic
469C22×C22⋊C4C22×C13911yescharacteristic
470C2×#99C22×C13912yes—
471C2×#99C22×C13912yes—
472C2×#99C22×C13912yes—
473#399—21no—
474#397—21no—
475#396—22no—
476#394—22no—
477#393—21no—
478#392—21no—
479#390—21no—
480#388—21no—
481#388—21no—
482#386—21no—
483#386C22×C13911yescharacteristic
484#386C22×C13912yes—
485#385C22×C13911yescharacteristic
486#385C22×C13912yes—
487#380C22×C13911yescharacteristic
488#380C22×C13911yescharacteristic
489#379C22×C13911yescharacteristic
490#379C22×C13912yes—
491C4×C22⋊C4C22×C13911yescharacteristic
492#342C22×C13912yes—
493#342C22×C13912yes—
494#342C22×C13912yes—
495C25C23×C13911yescharacteristic
496C2×#41—21no—
497C22×Q8D4×C13911yescharacteristic, complemented
498C22×D4—21no—
499C22×D4—22no—
500C22×D4D4×C13911yescharacteristic, complemented
501C22×D4C23×C13911yescharacteristic
502C22×D4C23×C13912yes—
503C23×C4D4×C13911yescharacteristic, complemented
504C23×C4C23×C13911yescharacteristic
505C23×C4C23×C13911yescharacteristic
506#126—22no—
507#126—22no—
508#126—22no—
509#125—21no—
510#125—22no—
511#124—21no—
512#124—22no—
513#123—22no—
514#123—22no—
515#123—22no—
516#123—22no—
517#123—22no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524#121—21no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—22no—
531#121—22no—
532#120—22no—
533#120—22no—
534#120—22no—
535#120—22no—
536#120—24no—
537#120—42no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549#117—21no—
550#117—22no—
551#117—22no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4D4×C13911yescharacteristic, complemented
557C2×C4⋊C4D4×C13911yescharacteristic, complemented
558C2×C4⋊C4D4×C13912yescomplemented
559C2×C4⋊C4D4×C13911yescharacteristic, complemented
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C13911yescharacteristic, complemented
576C2×C22⋊C4D4×C13912yescomplemented
577C2×C22⋊C4C23×C13912yes—
578C2×C22⋊C4C23×C13911yescharacteristic
579C2×C22⋊C4C23×C13912yes—
580C2×C22⋊C4C23×C13911yescharacteristic
581C2×C22⋊C4C23×C13912yes—
582C2×C22⋊C4C23×C13911yescharacteristic
583C2×C42—21no—
584C2×C42D4×C13911yescharacteristic, complemented
585#99—24no—
586#99—42no—
587#99—42no—
588#95—21no—
589#95—21no—
590#95—21no—
591#95—21no—
592#95—22no—
593#95—21no—
594#95—22no—
595C24—21no—
596C24—21no—
597C24—21no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—81no—
602C24—81no—
603C24C2×D4×C13912yes—
604C24C2×D4×C13911yescharacteristic
605C24#41×C13912yescomplemented
606C24C24×C13911yescharacteristic
607#41—82no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—81no—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—44no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—82no—
633C2×D4—82no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—21no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4C2×D4×C13911yescharacteristic
649C22×C4C2×D4×C13912yes—
650C22×C4C2×D4×C13911yescharacteristic
651C22×C4C2×D4×C13912yes—
652C22×C4C2×D4×C13911yescharacteristic
653C22×C4C2×D4×C13912yes—
654C22×C4C2×D4×C13911yescharacteristic
655C22×C4C2×D4×C13911yescharacteristic
656C22×C4C2×D4×C13911yescharacteristic
657C22×C4C2×D4×C13911yescharacteristic
658C22×C4C2×D4×C13911yescharacteristic
659C22×C4C2×D4×C13911yescharacteristic
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—22no—
671C4⋊C4—21no—
672C4⋊C4—81no—
673C4⋊C4—81no—
674C4⋊C4—81no—
675C4⋊C4—82no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—21no—
684C22⋊C4—22no—
685C22⋊C4—21no—
686C22⋊C4—22no—
687C22⋊C4—21no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—21no—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—21no—
698C22⋊C4—44no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C22⋊C4—41no—
702C22⋊C4—41no—
703C22⋊C4—81no—
704C22⋊C4—82no—
705C22⋊C4—81no—
706C22⋊C4—82no—
707C22⋊C4—81no—
708C22⋊C4—82no—
709C22⋊C4#41×C13912yescomplemented
710C42—22no—
711C42—22no—
712C42—21no—
713C42—21no—
714C42—81no—
715C23—21no—
716C23—22no—
717C23—22no—
718C23—21no—
719C23—22no—
720C23—22no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—82no—
743C23—82no—
744C23—82no—
745C23—82no—
746C23C22×D4×C13911yescharacteristic
747C23C22×D4×C13911yescharacteristic
748C23C22×D4×C13911yescharacteristic
749C23C2×#41×C13911yescharacteristic
750C23C2×#41×C13911yescharacteristic
751C23H(5,𝔽2)×C13911yescharacteristic
752C232−1+4×C13911yescharacteristic
753Q8—42no—
754Q8—81no—
755D4—42no—
756D4—42no—
757D4—42no—
758D4—41no—
759D4—41no—
760D4—41no—
761D4—42no—
762D4—42no—
763D4—41no—
764D4—81no—
765D4—84no—
766D4—82no—
767D4—82no—
768D4—88no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—81no—
808C2×C4—82no—
809C2×C4—82no—
810C2×C4#120×C13911yescharacteristic
811C2×C4#120×C13911yescharacteristic
812C2×C4#120×C13911yescharacteristic
813C2×C4#120×C13911yescharacteristic
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—41no—
830C22—42no—
831C22—42no—
832C22—41no—
833C22—41no—
834C22—42no—
835C22—42no—
836C22—82no—
837C22—81no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C2×#120×C13911yescharacteristic
846C22#525×C13911yescharacteristic
847C22#537×C13911yescharacteristic
848C22#546×C13911yescharacteristic
849C22#547×C13911yescharacteristic
850C22#548×C13911yescharacteristic
851C22#550×C13911yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—41no—
858C4—42no—
859C4—41no—
860C4—42no—
861C4—41no—
862C4—42no—
863C4—82no—
864C4—82no—
865C4—81no—
866C4—81no—
867C2—21no—
868C2—21no—
869C2—21no—
870C2—21no—
871C2—21no—
872C2—21no—
873C2—82no—
874C2—81no—
875C2—82no—
876C2#2407×C13911yescharacteristic
877C2#3026×C13911yescharacteristic
878C2#3027×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC24C24×C139
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3505×C139C2semidirect
2. #2626×C139C2semidirect
3. #2617×C139C2semidirect
4. #2321×C139C2semidirect
5. #2044×C139C2semidirect
6. #2021×C139C2semidirect
7. #1996×C139C2semidirect
8. #1964×C139C2semidirect
9. #1889×C139C2semidirect
10. #1867×C139C2semidirect
11. #1799×C139C2semidirect
57. C22×Q8×C139D4semidirect
60. C22×D4×C139D4semidirect
63. C23×C4×C139D4semidirect
116. C2×C4⋊C4×C139D4semidirect
117. C2×C4⋊C4×C139D4semidirect
118. C2×C4⋊C4×C139D4semidirect
119. C2×C4⋊C4×C139D4semidirect
135. C2×C22⋊C4×C139D4semidirect
136. C2×C22⋊C4×C139D4semidirect
144. C2×C42×C139D4semidirect
165. C24×C139#41semidirect
269. C22⋊C4×C139#41semidirect
439. #24142C139direct (N × H)
440. C139#24142direct (N × H)
441. #3505C2×C139semidirect
442. #2626C2×C139semidirect
443. #2617C2×C139semidirect
444. #2321C2×C139semidirect
445. #2044C2×C139semidirect
446. #2021C2×C139semidirect
447. #1996C2×C139semidirect
448. #1964C2×C139semidirect
449. #1889C2×C139semidirect
450. #1867C2×C139semidirect
451. #1799C2×C139semidirect
497. C22×Q8D4×C139semidirect
500. C22×D4D4×C139semidirect
503. C23×C4D4×C139semidirect
556. C2×C4⋊C4D4×C139semidirect
557. C2×C4⋊C4D4×C139semidirect
558. C2×C4⋊C4D4×C139semidirect
559. C2×C4⋊C4D4×C139semidirect
575. C2×C22⋊C4D4×C139semidirect
576. C2×C22⋊C4D4×C139semidirect
584. C2×C42D4×C139semidirect
605. C24#41×C139semidirect
709. C22⋊C4#41×C139semidirect

Maximal subgroups

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

subgroupindex
#3505×C1392
#2626×C1392
#2617×C1392
#2321×C1392
#2044×C1392
#2021×C1392
#1996×C1392
#1964×C1392
#1889×C1392
#1867×C1392
#1799×C1392
#24142139