Finite Group Databasebeta

← C139×#25533 #48020129

Subgroups — C139×#25533 #48020129

Order 35584.

1444 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C139C211yesmaximal, characteristic, complemented
2C2×#480×C139C211yesmaximal, characteristic, complemented
3C2×#466×C139C211yesmaximal, characteristic, complemented
4#2416×C139C211yesmaximal, characteristic, complemented
5#2057×C139C211yesmaximal, characteristic, complemented
6#2033×C139C211yesmaximal, characteristic, complemented
7#2023×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1879×C139C211yesmaximal, characteristic, complemented
10#1874×C139C211yesmaximal, characteristic, complemented
11#1874×C139C211yesmaximal, characteristic, complemented
12#1869×C139C211yesmaximal, characteristic, complemented
13#1862×C139C211yesmaximal, characteristic, complemented
14#1852×C139C211yesmaximal, characteristic, complemented
15C2×#340×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139—21no—
17C22×D8×C139C2211yescharacteristic
18C23×C8×C139C2211yescharacteristic
19#547×C139—24no—
20#547×C139—24no—
21C2×C4⋊Q8×C139C2211yescharacteristic
22C2×#123×C139—21no—
23C2×#123×C139—21no—
24C2×C22⋊Q8×C139—21no—
25C2×#121×C139—21no—
26C2×#121×C139C2211yescharacteristic
27C2×#121×C139C2211yescharacteristic
28C2×#121×C139C2211yescharacteristic
29C2×#121×C139C2211yescharacteristic
30C2×C4×D4×C139C2211yescharacteristic
31C2×C4×D4×C139C2211yescharacteristic
32C22×C4⋊C4×C139C2211yescharacteristic
33C22×C4⋊C4×C139C2211yescharacteristic
34C22×C4⋊C4×C139C2211yescharacteristic
35#480×C139—24no—
36#466×C139—24no—
37C2×#107×C139C2211yescharacteristic
38C2×#107×C139C2211yescharacteristic
39C2×#107×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×C22⋊C8×C139C2211yescharacteristic
47C2×C22⋊C8×C139C2211yescharacteristic
48C2×C22⋊C8×C139C2211yescharacteristic
49#396×C139—21no—
50#394×C139—21no—
51#390×C139C2211yescharacteristic
52#389×C139C2211yescharacteristic
53#386×C139—21no—
54#380×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#336×C139C2211yescharacteristic
62#336×C139C2211yescharacteristic
63C2×#41×C139—28no—
64C2×#41×C139—44no—
65C2×#41×C139—44no—
66C22×Q8×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—21no—
70C22×D4×C139—21no—
71C22×D4×C139D411yescharacteristic
72C22×D4×C139C2311yescharacteristic
73C22×D4×C139C2311yescharacteristic
74C23×C4×C139—21no—
75C23×C4×C139—21no—
76C23×C4×C139—21no—
77C23×C4×C139—21no—
78C23×C4×C139C2311yescharacteristic
79C23×C4×C139C2311yescharacteristic
80C2×D8×C139—22no—
81C2×D8×C139—22no—
82C2×D8×C139—41no—
83C22×C8×C139—22no—
84C22×C8×C139—22no—
85C22×C8×C139—41no—
86C22×C8×C139C2311yescharacteristic
87C22×C8×C139C2311yescharacteristic
88C22×C8×C139C2311yescharacteristic
89C22×C8×C139C2311yescharacteristic
90C4⋊Q8×C139—22no—
91C4⋊Q8×C139—22no—
92#123×C139—28no—
93#123×C139—28no—
94C22⋊Q8×C139—28no—
95#121×C139—22no—
96#121×C139—22no—
97#121×C139—22no—
98#121×C139—22no—
99#121×C139—22no—
100#121×C139—22no—
101#121×C139—41no—
102#121×C139—44no—
103#121×C139D414yescomplemented
104C4×D4×C139—22no—
105C4×D4×C139—22no—
106C4×D4×C139—22no—
107C4×D4×C139—22no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139—22no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139—22no—
113C2×C4⋊C4×C139—22no—
114C2×C4⋊C4×C139—22no—
115C2×C4⋊C4×C139—21no—
116C2×C4⋊C4×C139—21no—
117C2×C4⋊C4×C139—41no—
118C2×C4⋊C4×C139D411yescharacteristic
119C2×C4⋊C4×C139D414yescomplemented
120C2×C4⋊C4×C139C2311yescharacteristic
121C2×C4⋊C4×C139C2311yescharacteristic
122C2×C4⋊C4×C139C2311yescharacteristic
123C2×C4⋊C4×C139C2311yescharacteristic
124C2×C4⋊C4×C139C2311yescharacteristic
125C2×C4⋊C4×C139C2311yescharacteristic
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—21no—
129C2×C22⋊C4×C139—21no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—21no—
134C2×C22⋊C4×C139D411yescharacteristic
135C2×C22⋊C4×C139D411yescharacteristic
136C2×C42×C139C2311yescharacteristic
137#107×C139—22no—
138#107×C139—22no—
139#107×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—22no—
144#102×C139—22no—
145#102×C139—41no—
146C22⋊C8×C139—22no—
147C22⋊C8×C139—22no—
148C22⋊C8×C139—41no—
149#95×C139—21no—
150#95×C139—21no—
151C24×C139—21no—
152C24×C139—21no—
153C24×C139C2×D411yescharacteristic
154C24×C139C2×D411yescharacteristic
155#41×C139—432no—
156C2×Q8×C139—24no—
157C2×Q8×C139—42no—
158C2×Q8×C139—42no—
159C2×D4×C139—22no—
160C2×D4×C139—22no—
161C2×D4×C139—24no—
162C2×D4×C139—24no—
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—42no—
175C2×D4×C139—42no—
176C2×D4×C139—42no—
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—81no—
184C2×D4×C139D814yescomplemented
185C2×D4×C139C2×D412yes—
186C22×C4×C139—21no—
187C22×C4×C139—21no—
188C22×C4×C139—21no—
189C22×C4×C139—21no—
190C22×C4×C139—24no—
191C22×C4×C139—24no—
192C22×C4×C139—24no—
193C22×C4×C139—21no—
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—42no—
210C22×C4×C139—42no—
211C22×C4×C139—42no—
212C22×C4×C139—42no—
213C22×C4×C139—81no—
214C22×C4×C139C2×D411yescharacteristic
215C22×C4×C139C2×D411yescharacteristic
216C22×C4×C139C2×D411yescharacteristic
217C22×C4×C139C2×D412yes—
218C22×C4×C139C2×D412yes—
219C22×C4×C139C2×D411yescharacteristic
220C22×C4×C139C2411yescharacteristic
221D8×C139—44no—
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—21no—
230C2×C8×C139—21no—
231C2×C8×C139—21no—
232C2×C8×C139—21no—
233C2×C8×C139—44no—
234C2×C8×C139#4112yescomplemented
235C4⋊C4×C139—24no—
236C4⋊C4×C139—24no—
237C4⋊C4×C139—24no—
238C4⋊C4×C139—22no—
239C4⋊C4×C139—21no—
240C4⋊C4×C139—21no—
241C4⋊C4×C139—21no—
242C4⋊C4×C139—21no—
243C4⋊C4×C139—21no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139—21no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—42no—
248C4⋊C4×C139—42no—
249C4⋊C4×C139C2×D412yes—
250C4⋊C4×C139C2×D412yes—
251C4⋊C4×C139C2×D412yes—
252C4⋊C4×C139#4112yescomplemented
253C22⋊C4×C139—24no—
254C22⋊C4×C139—24no—
255C22⋊C4×C139—22no—
256C22⋊C4×C139—24no—
257C22⋊C4×C139—22no—
258C22⋊C4×C139—42no—
259C22⋊C4×C139—42no—
260C22⋊C4×C139—42no—
261C22⋊C4×C139—42no—
262C22⋊C4×C139—81no—
263C42×C139—21no—
264C42×C139—21no—
265C23×C139—21no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—21no—
275C23×C139—22no—
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×C139—41no—
289C23×C139#12012yes—
290C23×C139C2×D812yes—
291C23×C139C2×D812yes—
292C23×C139AGL(1,ℤ/8)12yes—
293C23×C139C22×D411yescharacteristic
294Q8×C139—48no—
295D4×C139—28no—
296D4×C139—22no—
297D4×C139—22no—
298D4×C139—48no—
299D4×C139—48no—
300D4×C139—41no—
301D4×C139—41no—
302D4×C139—41no—
303D4×C139—41no—
304D4×C139—41no—
305D4×C139—41no—
306D4×C139—84no—
307D4×C139—84no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
311C2×C4×C139—21no—
312C2×C4×C139—22no—
313C2×C4×C139—22no—
314C2×C4×C139—22no—
315C2×C4×C139—22no—
316C2×C4×C139—21no—
317C2×C4×C139—21no—
318C2×C4×C139—22no—
319C2×C4×C139—22no—
320C2×C4×C139—22no—
321C2×C4×C139—21no—
322C2×C4×C139—22no—
323C2×C4×C139—21no—
324C2×C4×C139—21no—
325C2×C4×C139—21no—
326C2×C4×C139—48no—
327C2×C4×C139—48no—
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—48no—
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—41no—
346C2×C4×C139—41no—
347C2×C4×C139—84no—
348C2×C4×C139#12012yes—
349C2×C4×C139C2×D812yes—
350C2×C4×C139C22×D411yescharacteristic
351C2×C4×C139C22×D411yescharacteristic
352C2×C4×C139C2×#4111yescharacteristic
353C2×C4×C139C2×#4111yescharacteristic
354C2×C4×C139H(5,𝔽2)11yescharacteristic
355C2×C4×C1392−1+411yescharacteristic
356C8×C139—22no—
357C8×C139—41no—
358C8×C139—41no—
359C8×C139—41no—
360C22×C139—22no—
361C22×C139—22no—
362C22×C139—22no—
363C22×C139—22no—
364C22×C139—22no—
365C22×C139—22no—
366C22×C139—22no—
367C22×C139—22no—
368C22×C139—22no—
369C22×C139—41no—
370C22×C139—41no—
371C22×C139—41no—
372C22×C139—41no—
373C22×C139—42no—
374C22×C139—42no—
375C22×C139—42no—
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—81no—
386C22×C139—81no—
387C22×C139#44714yes—
388C22×C139C2×#12011yescharacteristic
389C22×C139#54611yescharacteristic
390C22×C139#54711yescharacteristic
391C22×C139C22×D811yescharacteristic
392C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
393C22×C139#57711yescharacteristic
394C22×C139#57811yescharacteristic
395C4×C139—22no—
396C4×C139—22no—
397C4×C139—41no—
398C4×C139—42no—
399C4×C139—42no—
400C4×C139—42no—
401C4×C139—41no—
402C4×C139—42no—
403C4×C139—81no—
404C4×C139—81no—
405C4×C139#53211yescharacteristic
406C4×C139#53711yescharacteristic
407C4×C139#54611yescharacteristic
408C4×C139#54711yescharacteristic
409C2×C139—24no—
410C2×C139—42no—
411C2×C139—82no—
412C2×C139—161no—
413C2×C139#243011yescharacteristic
414C2×C139C2×#44711yescharacteristic
415C2×C139#301311yescharacteristic
416C2×C139#329411yescharacteristic
417C2×C139#330811yescharacteristic
418C2×C139#333411yescharacteristic
419C2×C139#334511yescharacteristic
420#25533C13911yesmaximal, characteristic, direct product factor, Sylow
421C139#2553311yescharacteristic, direct product factor, Sylow
422C2×#547C2×C13911yescharacteristic, complemented
423C2×#480C2×C13911yescharacteristic, complemented
424C2×#466C2×C13911yescharacteristic, complemented
425#2416C2×C13911yescharacteristic, complemented
426#2057C2×C13911yescharacteristic, complemented
427#2033C2×C13911yescharacteristic, complemented
428#2023C2×C13911yescharacteristic, complemented
429#1999C2×C13911yescharacteristic, complemented
430#1879C2×C13911yescharacteristic, complemented
431#1874C2×C13911yescharacteristic, complemented
432#1874C2×C13911yescharacteristic, complemented
433#1869C2×C13911yescharacteristic, complemented
434#1862C2×C13911yescharacteristic, complemented
435#1852C2×C13911yescharacteristic, complemented
436C2×#340C2×C13911yescharacteristic, complemented
437C22×#41—21no—
438C22×D8C22×C13911yescharacteristic
439C23×C8C22×C13911yescharacteristic
440#547—24no—
441#547—24no—
442C2×C4⋊Q8C22×C13911yescharacteristic
443C2×#123—21no—
444C2×#123—21no—
445C2×C22⋊Q8—21no—
446C2×#121—21no—
447C2×#121C22×C13911yescharacteristic
448C2×#121C22×C13911yescharacteristic
449C2×#121C22×C13911yescharacteristic
450C2×#121C22×C13911yescharacteristic
451C2×C4×D4C22×C13911yescharacteristic
452C2×C4×D4C22×C13911yescharacteristic
453C22×C4⋊C4C22×C13911yescharacteristic
454C22×C4⋊C4C22×C13911yescharacteristic
455C22×C4⋊C4C22×C13911yescharacteristic
456#480—24no—
457#466—24no—
458C2×#107C22×C13911yescharacteristic
459C2×#107C22×C13911yescharacteristic
460C2×#107C22×C13911yescharacteristic
461C2×#102C22×C13911yescharacteristic
462C2×#102C22×C13911yescharacteristic
463C2×#102C22×C13911yescharacteristic
464C2×#102C22×C13911yescharacteristic
465C2×#102C22×C13911yescharacteristic
466C2×#102C22×C13911yescharacteristic
467C2×C22⋊C8C22×C13911yescharacteristic
468C2×C22⋊C8C22×C13911yescharacteristic
469C2×C22⋊C8C22×C13911yescharacteristic
470#396—21no—
471#394—21no—
472#390C22×C13911yescharacteristic
473#389C22×C13911yescharacteristic
474#386—21no—
475#380C22×C13911yescharacteristic
476#340C22×C13911yescharacteristic
477#340C22×C13911yescharacteristic
478#340C22×C13911yescharacteristic
479#340C22×C13911yescharacteristic
480#340C22×C13911yescharacteristic
481#340C22×C13911yescharacteristic
482#336C22×C13911yescharacteristic
483#336C22×C13911yescharacteristic
484C2×#41—28no—
485C2×#41—44no—
486C2×#41—44no—
487C22×Q8—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4D4×C13911yescharacteristic
493C22×D4C23×C13911yescharacteristic
494C22×D4C23×C13911yescharacteristic
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C23×C13911yescharacteristic
500C23×C4C23×C13911yescharacteristic
501C2×D8—22no—
502C2×D8—22no—
503C2×D8—41no—
504C22×C8—22no—
505C22×C8—22no—
506C22×C8—41no—
507C22×C8C23×C13911yescharacteristic
508C22×C8C23×C13911yescharacteristic
509C22×C8C23×C13911yescharacteristic
510C22×C8C23×C13911yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513#123—28no—
514#123—28no—
515C22⋊Q8—28no—
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—22no—
521#121—22no—
522#121—41no—
523#121—44no—
524#121D4×C13914yescomplemented
525C4×D4—22no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4D4×C13911yescharacteristic
540C2×C4⋊C4D4×C13914yescomplemented
541C2×C4⋊C4C23×C13911yescharacteristic
542C2×C4⋊C4C23×C13911yescharacteristic
543C2×C4⋊C4C23×C13911yescharacteristic
544C2×C4⋊C4C23×C13911yescharacteristic
545C2×C4⋊C4C23×C13911yescharacteristic
546C2×C4⋊C4C23×C13911yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C13911yescharacteristic
556C2×C22⋊C4D4×C13911yescharacteristic
557C2×C42C23×C13911yescharacteristic
558#107—22no—
559#107—22no—
560#107—22no—
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C22⋊C8—41no—
570#95—21no—
571#95—21no—
572C24—21no—
573C24—21no—
574C24C2×D4×C13911yescharacteristic
575C24C2×D4×C13911yescharacteristic
576#41—432no—
577C2×Q8—24no—
578C2×Q8—42no—
579C2×Q8—42no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—24no—
583C2×D4—24no—
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—81no—
605C2×D4D8×C13914yescomplemented
606C2×D4C2×D4×C13912yes—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
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—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—81no—
635C22×C4C2×D4×C13911yescharacteristic
636C22×C4C2×D4×C13911yescharacteristic
637C22×C4C2×D4×C13911yescharacteristic
638C22×C4C2×D4×C13912yes—
639C22×C4C2×D4×C13912yes—
640C22×C4C2×D4×C13911yescharacteristic
641C22×C4C24×C13911yescharacteristic
642D8—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—44no—
655C2×C8#41×C13912yescomplemented
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C13912yes—
671C4⋊C4C2×D4×C13912yes—
672C4⋊C4C2×D4×C13912yes—
673C4⋊C4#41×C13912yescomplemented
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—22no—
677C22⋊C4—24no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—81no—
684C42—21no—
685C42—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—22no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23#120×C13912yes—
711C23C2×D8×C13912yes—
712C23C2×D8×C13912yes—
713C23AGL(1,ℤ/8)×C13912yes—
714C23C22×D4×C13911yescharacteristic
715Q8—48no—
716D4—28no—
717D4—22no—
718D4—22no—
719D4—48no—
720D4—48no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—41no—
726D4—41no—
727D4—84no—
728D4—84no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—48no—
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—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—84no—
769C2×C4#120×C13912yes—
770C2×C4C2×D8×C13912yes—
771C2×C4C22×D4×C13911yescharacteristic
772C2×C4C22×D4×C13911yescharacteristic
773C2×C4C2×#41×C13911yescharacteristic
774C2×C4C2×#41×C13911yescharacteristic
775C2×C4H(5,𝔽2)×C13911yescharacteristic
776C2×C42−1+4×C13911yescharacteristic
777C8—22no—
778C8—41no—
779C8—41no—
780C8—41no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22#447×C13914yes—
809C22C2×#120×C13911yescharacteristic
810C22#546×C13911yescharacteristic
811C22#547×C13911yescharacteristic
812C22C22×D8×C13911yescharacteristic
813C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
814C22#577×C13911yescharacteristic
815C22#578×C13911yescharacteristic
816C4—22no—
817C4—22no—
818C4—42no—
819C4—41no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—41no—
824C4—81no—
825C4—81no—
826C4#532×C13911yescharacteristic
827C4#537×C13911yescharacteristic
828C4#546×C13911yescharacteristic
829C4#547×C13911yescharacteristic
830C2—24no—
831C2—42no—
832C2—82no—
833C2—161no—
834C2#2430×C13911yescharacteristic
835C2C2×#447×C13911yescharacteristic
836C2#3013×C13911yescharacteristic
837C2#3294×C13911yescharacteristic
838C2#3308×C13911yescharacteristic
839C2#3334×C13911yescharacteristic
840C2#3345×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#547×C139C2semidirect
2. C2×#480×C139C2semidirect
3. C2×#466×C139C2semidirect
4. #2416×C139C2semidirect
5. #2057×C139C2semidirect
6. #2033×C139C2semidirect
7. #2023×C139C2semidirect
8. #1999×C139C2semidirect
9. #1879×C139C2semidirect
10. #1874×C139C2semidirect
11. #1874×C139C2semidirect
12. #1869×C139C2semidirect
13. #1862×C139C2semidirect
14. #1852×C139C2semidirect
15. C2×#340×C139C2semidirect
103. #121×C139D4semidirect
119. C2×C4⋊C4×C139D4semidirect
184. C2×D4×C139D8semidirect
234. C2×C8×C139#41semidirect
252. C4⋊C4×C139#41semidirect
420. #25533C139direct (N × H)
421. C139#25533direct (N × H)
422. C2×#547C2×C139semidirect
423. C2×#480C2×C139semidirect
424. C2×#466C2×C139semidirect
425. #2416C2×C139semidirect
426. #2057C2×C139semidirect
427. #2033C2×C139semidirect
428. #2023C2×C139semidirect
429. #1999C2×C139semidirect
430. #1879C2×C139semidirect
431. #1874C2×C139semidirect
432. #1874C2×C139semidirect
433. #1869C2×C139semidirect
434. #1862C2×C139semidirect
435. #1852C2×C139semidirect
436. C2×#340C2×C139semidirect
524. #121D4×C139semidirect
540. C2×C4⋊C4D4×C139semidirect
605. C2×D4D8×C139semidirect
655. C2×C8#41×C139semidirect
673. C4⋊C4#41×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1392
C2×#480×C1392
C2×#466×C1392
#2416×C1392
#2057×C1392
#2033×C1392
#2023×C1392
#1999×C1392
#1879×C1392
#1874×C1392
#1869×C1392
#1862×C1392
#1852×C1392
C2×#340×C1392
#25533139