Finite Group Databasebeta

← C139×#25421 #48020017

Subgroups — C139×#25421 #48020017

Order 35584.

1140 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#496×C139C211yesmaximal, characteristic, complemented
2C2×#466×C139C211yesmaximal, characteristic, complemented
3C2×#465×C139C211yesmaximal, characteristic, complemented
4C2×#442×C139C211yesmaximal, characteristic, complemented
5#2428×C139C211yesmaximal, characteristic, complemented
6#2427×C139C211yesmaximal, characteristic, complemented
7#2042×C139C211yesmaximal, characteristic, complemented
8#2041×C139C211yesmaximal, characteristic, complemented
9#2000×C139C211yesmaximal, characteristic, complemented
10#1999×C139C211yesmaximal, characteristic, complemented
11#1973×C139C211yesmaximal, characteristic, complemented
12#1944×C139C211yesmaximal, characteristic, complemented
13#1879×C139C211yesmaximal, characteristic, complemented
14#1877×C139C211yesmaximal, characteristic, complemented
15#1752×C139C211yesmaximal, characteristic, complemented
16C22×SD16×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic
20C23×C8×C139C2211yescharacteristic
21C2×#127×C139C2211yescharacteristic
22C2×#124×C139C2211yescharacteristic
23C2×C22⋊Q8×C139C2211yescharacteristic
24C2×#121×C139—21no—
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×#121×C139C2211yescharacteristic
28C2×C4×D4×C139C2211yescharacteristic
29C2×C4×D4×C139C2211yescharacteristic
30#496×C139—24no—
31#466×C139—24no—
32#465×C139—24no—
33#442×C139—24no—
34C2×#107×C139C2211yescharacteristic
35C2×#106×C139C2211yescharacteristic
36C2×#103×C139C2211yescharacteristic
37C2×#103×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×C22⋊C8×C139C2211yescharacteristic
45C2×#97×C139C2211yescharacteristic
46C2×#97×C139C2211yescharacteristic
47#397×C139—21no—
48#394×C139—21no—
49#394×C139—21no—
50#392×C139—21no—
51#391×C139C2211yescharacteristic
52#390×C139C2211yescharacteristic
53#389×C139C2211yescharacteristic
54#389×C139C2211yescharacteristic
55#386×C139—21no—
56#386×C139—21no—
57#380×C139—21no—
58C4×C22⋊C4×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#336×C139C2211yescharacteristic
62#336×C139C2211yescharacteristic
63C22×Q8×C139C2311yescharacteristic
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139C2311yescharacteristic
70C22×D4×C139C2311yescharacteristic
71C22×D4×C139C2311yescharacteristic
72C23×C4×C139—21no—
73C23×C4×C139—21no—
74C23×C4×C139C2311yescharacteristic
75C2×SD16×C139—22no—
76C2×SD16×C139—22no—
77C2×SD16×C139—22no—
78C2×SD16×C139—22no—
79C2×SD16×C139—22no—
80C2×SD16×C139—41no—
81C2×D8×C139—22no—
82C2×D8×C139—22no—
83C2×D8×C139—22no—
84C2×D8×C139—22no—
85C2×D8×C139—41no—
86C2×D8×C139D414yescomplemented
87C22×C8×C139—22no—
88C22×C8×C139—22no—
89C22×C8×C139—22no—
90C22×C8×C139C2311yescharacteristic
91C22×C8×C139C2311yescharacteristic
92C22×C8×C139C2311yescharacteristic
93C22×C8×C139C2311yescharacteristic
94#127×C139—22no—
95#127×C139—41no—
96#124×C139—22no—
97#124×C139—41no—
98C22⋊Q8×C139—22no—
99C22⋊Q8×C139—41no—
100#121×C139—22no—
101#121×C139—22no—
102#121×C139—22no—
103#121×C139—44no—
104#121×C139—41no—
105#121×C139—41no—
106#121×C139—41no—
107C4×D4×C139—22no—
108C4×D4×C139—22no—
109C4×D4×C139—41no—
110C4×D4×C139—41no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139—21no—
113C2×C4⋊C4×C139—21no—
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C22⋊C4×C139—21no—
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—21no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139D411yescharacteristic
129C2×C22⋊C4×C139D411yescharacteristic
130C2×C42×C139C2311yescharacteristic
131C2×C42×C139C2311yescharacteristic
132#107×C139—22no—
133#106×C139D414yescomplemented
134#103×C139—22no—
135#103×C139—41no—
136#102×C139—22no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—41no—
142C22⋊C8×C139—22no—
143#97×C139—22no—
144#97×C139—22no—
145#95×C139—21no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139—21no—
149#95×C139D411yescharacteristic
150#95×C139D411yescharacteristic
151C24×C139—21no—
152C24×C139—21no—
153C24×C139—21no—
154C24×C139C2×D411yescharacteristic
155C2×Q8×C139—21no—
156C2×Q8×C139—21no—
157C2×Q8×C139—21no—
158C2×Q8×C139—21no—
159C2×Q8×C139—21no—
160C2×Q8×C139—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—21no—
165C2×D4×C139—21no—
166C2×D4×C139—21no—
167C2×D4×C139—21no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139—21no—
176C2×D4×C139—21no—
177C2×D4×C139—42no—
178C2×D4×C139—42no—
179C2×D4×C139—42no—
180C2×D4×C139—42no—
181C2×D4×C139—42no—
182C2×D4×C139—42no—
183C2×D4×C139—42no—
184C2×D4×C139—42no—
185C2×D4×C139—42no—
186C2×D4×C139—42no—
187C2×D4×C139—81no—
188C2×D4×C139—81no—
189C2×D4×C139—81no—
190C2×D4×C139—81no—
191C2×D4×C139—81no—
192C2×D4×C139C2×D412yes—
193C2×D4×C139C2×D412yes—
194C22×C4×C139—21no—
195C22×C4×C139—21no—
196C22×C4×C139—21no—
197C22×C4×C139—21no—
198C22×C4×C139—21no—
199C22×C4×C139—21no—
200C22×C4×C139—21no—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—21no—
205C22×C4×C139—42no—
206C22×C4×C139—42no—
207C22×C4×C139—42no—
208C22×C4×C139—42no—
209C22×C4×C139—81no—
210C22×C4×C139—81no—
211C22×C4×C139C2×D411yescharacteristic
212C22×C4×C139C2×D411yescharacteristic
213C22×C4×C139C2×D411yescharacteristic
214C22×C4×C139C2×D411yescharacteristic
215C22×C4×C139C2×D411yescharacteristic
216C22×C4×C139C2411yescharacteristic
217SD16×C139—44no—
218SD16×C139—44no—
219D8×C139—28no—
220D8×C139—44no—
221C2×C8×C139—21no—
222C2×C8×C139—21no—
223C2×C8×C139—21no—
224C2×C8×C139—21no—
225C2×C8×C139—21no—
226C2×C8×C139—21no—
227C2×C8×C139—21no—
228C2×C8×C139—21no—
229C2×C8×C139—44no—
230C2×C8×C139C2×D412yes—
231C2×C8×C139C2×D412yes—
232C2×C8×C139#4112yes—
233C2×C8×C139#4112yes—
234C4⋊C4×C139—21no—
235C4⋊C4×C139—21no—
236C4⋊C4×C139—21no—
237C4⋊C4×C139—21no—
238C4⋊C4×C139—21no—
239C4⋊C4×C139—21no—
240C4⋊C4×C139—42no—
241C4⋊C4×C139—42no—
242C4⋊C4×C139—81no—
243C4⋊C4×C139C2×D412yes—
244C4⋊C4×C139C2×D412yes—
245C22⋊C4×C139—22no—
246C22⋊C4×C139—41no—
247C22⋊C4×C139—42no—
248C22⋊C4×C139—42no—
249C22⋊C4×C139—42no—
250C22⋊C4×C139—42no—
251C22⋊C4×C139—42no—
252C22⋊C4×C139—42no—
253C22⋊C4×C139—42no—
254C22⋊C4×C139—42no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—81no—
257C42×C139—21no—
258C42×C139—21no—
259C42×C139—21no—
260C42×C139—21no—
261C23×C139—21no—
262C23×C139—21no—
263C23×C139—21no—
264C23×C139—21no—
265C23×C139—21no—
266C23×C139—21no—
267C23×C139—22no—
268C23×C139—22no—
269C23×C139—41no—
270C23×C139—41no—
271C23×C139—41no—
272C23×C139—41no—
273C23×C139—41no—
274C23×C139—41no—
275C23×C139—41no—
276C23×C139—41no—
277C23×C139—41no—
278C23×C139—41no—
279C23×C139—41no—
280C23×C139—41no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—41no—
285C23×C139—41no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139AGL(1,ℤ/8)12yes—
289C23×C139C22×D411yescharacteristic
290Q8×C139—41no—
291Q8×C139—41no—
292Q8×C139—41no—
293Q8×C139—41no—
294D4×C139—22no—
295D4×C139—22no—
296D4×C139—22no—
297D4×C139—22no—
298D4×C139—41no—
299D4×C139—41no—
300D4×C139—41no—
301D4×C139—41no—
302D4×C139—41no—
303D4×C139—41no—
304D4×C139—41no—
305D4×C139—41no—
306D4×C139—84no—
307D4×C139—84no—
308D4×C139—84no—
309D4×C139—84no—
310D4×C139—84no—
311C2×C4×C139—21no—
312C2×C4×C139—21no—
313C2×C4×C139—21no—
314C2×C4×C139—21no—
315C2×C4×C139—21no—
316C2×C4×C139—21no—
317C2×C4×C139—22no—
318C2×C4×C139—22no—
319C2×C4×C139—21no—
320C2×C4×C139—21no—
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—41no—
329C2×C4×C139—41no—
330C2×C4×C139—41no—
331C2×C4×C139—41no—
332C2×C4×C139—41no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139—41no—
336C2×C4×C139—41no—
337C2×C4×C139—41no—
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—84no—
346C2×C4×C139—84no—
347C2×C4×C139C22×D411yescharacteristic
348C2×C4×C139C22×D411yescharacteristic
349C2×C4×C139C2×#4111yescharacteristic
350C2×C4×C139C2×#4111yescharacteristic
351C2×C4×C139H(5,𝔽2)11yescharacteristic
352C2×C4×C139H(5,𝔽2)11yescharacteristic
353C8×C139—22no—
354C8×C139—41no—
355C8×C139—41no—
356C8×C139#12114yescomplemented
357C22×C139—22no—
358C22×C139—22no—
359C22×C139—22no—
360C22×C139—41no—
361C22×C139—41no—
362C22×C139—41no—
363C22×C139—41no—
364C22×C139—42no—
365C22×C139—42no—
366C22×C139—42no—
367C22×C139—42no—
368C22×C139—42no—
369C22×C139—42no—
370C22×C139—81no—
371C22×C139—81no—
372C22×C139—81no—
373C22×C139—81no—
374C22×C139—81no—
375C22×C139—81no—
376C22×C139—81no—
377C22×C139—81no—
378C22×C139—81no—
379C22×C139—81no—
380C22×C139—81no—
381C22×C139—81no—
382C22×C139—81no—
383C22×C139—81no—
384C22×C139—81no—
385C22×C139#53211yescharacteristic
386C22×C139D4211yescharacteristic
387C22×C139D4211yescharacteristic
388C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
389C22×C139#57511yescharacteristic
390C22×C139#57611yescharacteristic
391C22×C139#57711yescharacteristic
392C4×C139—41no—
393C4×C139—41no—
394C4×C139—41no—
395C4×C139—42no—
396C4×C139—41no—
397C4×C139—41no—
398C4×C139—42no—
399C4×C139—81no—
400C4×C139—81no—
401C4×C139—81no—
402C4×C139C2×#12111yescharacteristic
403C4×C139#54011yescharacteristic
404C4×C139#54611yescharacteristic
405C4×C139#55011yescharacteristic
406C2×C139—42no—
407C2×C139—82no—
408C2×C139—82no—
409C2×C139—161no—
410C2×C139#242811yescharacteristic
411C2×C139#317911yescharacteristic
412C2×C139#318011yescharacteristic
413C2×C139#326411yescharacteristic
414C2×C139#326511yescharacteristic
415C2×C139#326711yescharacteristic
416C2×C139#326811yescharacteristic
417#25421C13911yesmaximal, characteristic, direct product factor, Sylow
418C139#2542111yescharacteristic, direct product factor, Sylow
419C2×#496C2×C13911yescharacteristic, complemented
420C2×#466C2×C13911yescharacteristic, complemented
421C2×#465C2×C13911yescharacteristic, complemented
422C2×#442C2×C13911yescharacteristic, complemented
423#2428C2×C13911yescharacteristic, complemented
424#2427C2×C13911yescharacteristic, complemented
425#2042C2×C13911yescharacteristic, complemented
426#2041C2×C13911yescharacteristic, complemented
427#2000C2×C13911yescharacteristic, complemented
428#1999C2×C13911yescharacteristic, complemented
429#1973C2×C13911yescharacteristic, complemented
430#1944C2×C13911yescharacteristic, complemented
431#1879C2×C13911yescharacteristic, complemented
432#1877C2×C13911yescharacteristic, complemented
433#1752C2×C13911yescharacteristic, complemented
434C22×SD16C22×C13911yescharacteristic
435C22×SD16C22×C13911yescharacteristic
436C22×D8C22×C13911yescharacteristic
437C22×D8C22×C13911yescharacteristic
438C23×C8C22×C13911yescharacteristic
439C2×#127C22×C13911yescharacteristic
440C2×#124C22×C13911yescharacteristic
441C2×C22⋊Q8C22×C13911yescharacteristic
442C2×#121—21no—
443C2×#121C22×C13911yescharacteristic
444C2×#121C22×C13911yescharacteristic
445C2×#121C22×C13911yescharacteristic
446C2×C4×D4C22×C13911yescharacteristic
447C2×C4×D4C22×C13911yescharacteristic
448#496—24no—
449#466—24no—
450#465—24no—
451#442—24no—
452C2×#107C22×C13911yescharacteristic
453C2×#106C22×C13911yescharacteristic
454C2×#103C22×C13911yescharacteristic
455C2×#103C22×C13911yescharacteristic
456C2×#102C22×C13911yescharacteristic
457C2×#102C22×C13911yescharacteristic
458C2×#102C22×C13911yescharacteristic
459C2×#102C22×C13911yescharacteristic
460C2×#102C22×C13911yescharacteristic
461C2×#102C22×C13911yescharacteristic
462C2×C22⋊C8C22×C13911yescharacteristic
463C2×#97C22×C13911yescharacteristic
464C2×#97C22×C13911yescharacteristic
465#397—21no—
466#394—21no—
467#394—21no—
468#392—21no—
469#391C22×C13911yescharacteristic
470#390C22×C13911yescharacteristic
471#389C22×C13911yescharacteristic
472#389C22×C13911yescharacteristic
473#386—21no—
474#386—21no—
475#380—21no—
476C4×C22⋊C4C22×C13911yescharacteristic
477#340C22×C13911yescharacteristic
478#340C22×C13911yescharacteristic
479#336C22×C13911yescharacteristic
480#336C22×C13911yescharacteristic
481C22×Q8C23×C13911yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4C23×C13911yescharacteristic
488C22×D4C23×C13911yescharacteristic
489C22×D4C23×C13911yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4C23×C13911yescharacteristic
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—41no—
499C2×D8—22no—
500C2×D8—22no—
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C2×D8D4×C13914yescomplemented
505C22×C8—22no—
506C22×C8—22no—
507C22×C8—22no—
508C22×C8C23×C13911yescharacteristic
509C22×C8C23×C13911yescharacteristic
510C22×C8C23×C13911yescharacteristic
511C22×C8C23×C13911yescharacteristic
512#127—22no—
513#127—41no—
514#124—22no—
515#124—41no—
516C22⋊Q8—22no—
517C22⋊Q8—41no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—44no—
522#121—41no—
523#121—41no—
524#121—41no—
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—41no—
528C4×D4—41no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4C23×C13911yescharacteristic
533C2×C4⋊C4C23×C13911yescharacteristic
534C2×C4⋊C4C23×C13911yescharacteristic
535C2×C4⋊C4C23×C13911yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4D4×C13911yescharacteristic
547C2×C22⋊C4D4×C13911yescharacteristic
548C2×C42C23×C13911yescharacteristic
549C2×C42C23×C13911yescharacteristic
550#107—22no—
551#106D4×C13914yescomplemented
552#103—22no—
553#103—41no—
554#102—22no—
555#102—22no—
556#102—22no—
557#102—22no—
558#102—22no—
559#102—41no—
560C22⋊C8—22no—
561#97—22no—
562#97—22no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95D4×C13911yescharacteristic
568#95D4×C13911yescharacteristic
569C24—21no—
570C24—21no—
571C24—21no—
572C24C2×D4×C13911yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—42no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—81no—
610C2×D4C2×D4×C13912yes—
611C2×D4C2×D4×C13912yes—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—81no—
628C22×C4—81no—
629C22×C4C2×D4×C13911yescharacteristic
630C22×C4C2×D4×C13911yescharacteristic
631C22×C4C2×D4×C13911yescharacteristic
632C22×C4C2×D4×C13911yescharacteristic
633C22×C4C2×D4×C13911yescharacteristic
634C22×C4C24×C13911yescharacteristic
635SD16—44no—
636SD16—44no—
637D8—28no—
638D8—44no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—44no—
648C2×C8C2×D4×C13912yes—
649C2×C8C2×D4×C13912yes—
650C2×C8#41×C13912yes—
651C2×C8#41×C13912yes—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—81no—
661C4⋊C4C2×D4×C13912yes—
662C4⋊C4C2×D4×C13912yes—
663C22⋊C4—22no—
664C22⋊C4—41no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—81no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—22no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23AGL(1,ℤ/8)×C13912yes—
707C23C22×D4×C13911yescharacteristic
708Q8—41no—
709Q8—41no—
710Q8—41no—
711Q8—41no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—41no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—84no—
725D4—84no—
726D4—84no—
727D4—84no—
728D4—84no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—84no—
764C2×C4—84no—
765C2×C4C22×D4×C13911yescharacteristic
766C2×C4C22×D4×C13911yescharacteristic
767C2×C4C2×#41×C13911yescharacteristic
768C2×C4C2×#41×C13911yescharacteristic
769C2×C4H(5,𝔽2)×C13911yescharacteristic
770C2×C4H(5,𝔽2)×C13911yescharacteristic
771C8—22no—
772C8—41no—
773C8—41no—
774C8#121×C13914yescomplemented
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—81no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22#532×C13911yescharacteristic
804C22D42×C13911yescharacteristic
805C22D42×C13911yescharacteristic
806C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
807C22#575×C13911yescharacteristic
808C22#576×C13911yescharacteristic
809C22#577×C13911yescharacteristic
810C4—41no—
811C4—41no—
812C4—41no—
813C4—42no—
814C4—41no—
815C4—41no—
816C4—42no—
817C4—81no—
818C4—81no—
819C4—81no—
820C4C2×#121×C13911yescharacteristic
821C4#540×C13911yescharacteristic
822C4#546×C13911yescharacteristic
823C4#550×C13911yescharacteristic
824C2—42no—
825C2—82no—
826C2—82no—
827C2—161no—
828C2#2428×C13911yescharacteristic
829C2#3179×C13911yescharacteristic
830C2#3180×C13911yescharacteristic
831C2#3264×C13911yescharacteristic
832C2#3265×C13911yescharacteristic
833C2#3267×C13911yescharacteristic
834C2#3268×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×#496×C139C2semidirect
2. C2×#466×C139C2semidirect
3. C2×#465×C139C2semidirect
4. C2×#442×C139C2semidirect
5. #2428×C139C2semidirect
6. #2427×C139C2semidirect
7. #2042×C139C2semidirect
8. #2041×C139C2semidirect
9. #2000×C139C2semidirect
10. #1999×C139C2semidirect
11. #1973×C139C2semidirect
12. #1944×C139C2semidirect
13. #1879×C139C2semidirect
14. #1877×C139C2semidirect
15. #1752×C139C2semidirect
86. C2×D8×C139D4semidirect
133. #106×C139D4semidirect
356. C8×C139#121semidirect
417. #25421C139direct (N × H)
418. C139#25421direct (N × H)
419. C2×#496C2×C139semidirect
420. C2×#466C2×C139semidirect
421. C2×#465C2×C139semidirect
422. C2×#442C2×C139semidirect
423. #2428C2×C139semidirect
424. #2427C2×C139semidirect
425. #2042C2×C139semidirect
426. #2041C2×C139semidirect
427. #2000C2×C139semidirect
428. #1999C2×C139semidirect
429. #1973C2×C139semidirect
430. #1944C2×C139semidirect
431. #1879C2×C139semidirect
432. #1877C2×C139semidirect
433. #1752C2×C139semidirect
504. C2×D8D4×C139semidirect
551. #106D4×C139semidirect
774. C8#121×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#496×C1392
C2×#466×C1392
C2×#465×C1392
C2×#442×C1392
#2428×C1392
#2427×C1392
#2042×C1392
#2041×C1392
#2000×C1392
#1999×C1392
#1973×C1392
#1944×C1392
#1879×C1392
#1877×C1392
#1752×C1392
#25421139