Finite Group Databasebeta

← C139×#23975 #48018571

Subgroups — C139×#23975 #48018571

Order 35584.

1326 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#553×C139C211yesmaximal, characteristic, complemented
2C2×#449×C139C211yesmaximal, characteristic, complemented
3C2×#417×C139C211yesmaximal, characteristic, complemented
4#2407×C139C211yesmaximal, characteristic, complemented
5#2026×C139C211yesmaximal, characteristic, complemented
6#2025×C139C211yesmaximal, characteristic, complemented
7#2000×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1895×C139C211yesmaximal, characteristic, complemented
10#1879×C139C211yesmaximal, characteristic, complemented
11#1877×C139C211yesmaximal, characteristic, complemented
12#1875×C139C211yesmaximal, characteristic, complemented
13#1873×C139C211yesmaximal, characteristic, complemented
14#1870×C139C211yesmaximal, characteristic, complemented
15#1823×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C22×M16×C139C2211yescharacteristic
20#553×C139—24no—
21#553×C139—24no—
22C2×#126×C139—21no—
23C2×#125×C139C2211yescharacteristic
24C2×#123×C139—21no—
25C2×C22⋊Q8×C139C2211yescharacteristic
26C2×#121×C139—21no—
27C2×#121×C139C2211yescharacteristic
28C2×#121×C139C2211yescharacteristic
29C2×#121×C139C2211yescharacteristic
30C2×C4×D4×C139—21no—
31C2×C4×D4×C139C2211yescharacteristic
32C2×C4×D4×C139C2211yescharacteristic
33C2×#117×C139C2211yescharacteristic
34C22×C4⋊C4×C139C2211yescharacteristic
35#449×C139—24no—
36#417×C139—24no—
37C2×#103×C139C2211yescharacteristic
38C2×#103×C139C2211yescharacteristic
39C2×#103×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×C22⋊C8×C139C2211yescharacteristic
46C2×C22⋊C8×C139C2211yescharacteristic
47C2×C22⋊C8×C139C2211yescharacteristic
48#394×C139—21no—
49#392×C139—21no—
50#391×C139C2211yescharacteristic
51#390×C139C2211yescharacteristic
52#386×C139—21no—
53#385×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—22no—
64C2×#41×C139—22no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—41no—
68C2×#41×C139—41no—
69C22×Q8×C139C2311yescharacteristic
70C22×D4×C139—21no—
71C22×D4×C139—21no—
72C22×D4×C139—21no—
73C22×D4×C139—21no—
74C22×D4×C139D411yescharacteristic
75C22×D4×C139C2311yescharacteristic
76C22×D4×C139C2311yescharacteristic
77C23×C4×C139—21no—
78C23×C4×C139—21no—
79C23×C4×C139—21no—
80C23×C4×C139C2311yescharacteristic
81C23×C4×C139C2311yescharacteristic
82C2×SD16×C139—22no—
83C2×SD16×C139—22no—
84C2×SD16×C139—41no—
85C2×D8×C139—22no—
86C2×D8×C139—22no—
87C2×D8×C139—41no—
88C2×M16×C139—22no—
89C2×M16×C139—41no—
90C2×M16×C139—41no—
91C22×C8×C139C2311yescharacteristic
92C22×C8×C139C2311yescharacteristic
93C22×C8×C139C2311yescharacteristic
94C22×C8×C139C2311yescharacteristic
95#126×C139—28no—
96#125×C139—22no—
97#125×C139—22no—
98#123×C139—28no—
99C22⋊Q8×C139—22no—
100C22⋊Q8×C139—41no—
101#121×C139—28no—
102#121×C139—22no—
103#121×C139—22no—
104#121×C139—22no—
105#121×C139—22no—
106#121×C139—41no—
107#121×C139D414yescomplemented
108C4×D4×C139—28no—
109C4×D4×C139—22no—
110C4×D4×C139—22no—
111C4×D4×C139—22no—
112C4×D4×C139—22no—
113#117×C139—22no—
114#117×C139—22no—
115C2×C4⋊C4×C139—21no—
116C2×C4⋊C4×C139—22no—
117C2×C4⋊C4×C139—21no—
118C2×C4⋊C4×C139—21no—
119C2×C4⋊C4×C139—21no—
120C2×C4⋊C4×C139D411yescharacteristic
121C2×C4⋊C4×C139D414yescomplemented
122C2×C4⋊C4×C139C2311yescharacteristic
123C2×C4⋊C4×C139C2311yescharacteristic
124C2×C4⋊C4×C139C2311yescharacteristic
125C2×C4⋊C4×C139C2311yescharacteristic
126C2×C4⋊C4×C139C2311yescharacteristic
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×C139—21no—
135C2×C22⋊C4×C139—21no—
136C2×C22⋊C4×C139D411yescharacteristic
137C2×C22⋊C4×C139D411yescharacteristic
138C2×C42×C139—21no—
139C2×C42×C139C2311yescharacteristic
140#103×C139—22no—
141#103×C139—22no—
142#103×C139—22no—
143#102×C139—22no—
144#102×C139—22no—
145#102×C139—22no—
146#102×C139—41no—
147#102×C139—41no—
148C22⋊C8×C139—22no—
149C22⋊C8×C139—41no—
150C22⋊C8×C139—41no—
151#95×C139—21no—
152#95×C139—21no—
153#95×C139—21no—
154C24×C139—21no—
155C24×C139—21no—
156C24×C139C2×D411yescharacteristic
157C24×C139C2×D411yescharacteristic
158#41×C139—28no—
159#41×C139—44no—
160#41×C139—44no—
161#41×C139—44no—
162C2×Q8×C139—21no—
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×Q8×C139—21no—
166C2×Q8×C139—21no—
167C2×Q8×C139#4112yes—
168C2×D4×C139—22no—
169C2×D4×C139—24no—
170C2×D4×C139—24no—
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—21no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—41no—
182C2×D4×C139—41no—
183C2×D4×C139—42no—
184C2×D4×C139—42no—
185C2×D4×C139—42no—
186C2×D4×C139—42no—
187C2×D4×C139—42no—
188C2×D4×C139—42no—
189C2×D4×C139—42no—
190C2×D4×C139—81no—
191C2×D4×C139—81no—
192C2×D4×C139—81no—
193C2×D4×C139C2×D412yes—
194C2×D4×C139#4112yes—
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—24no—
204C22×C4×C139—24no—
205C22×C4×C139—21no—
206C22×C4×C139—21no—
207C22×C4×C139—21no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—21no—
211C22×C4×C139—21no—
212C22×C4×C139—21no—
213C22×C4×C139—42no—
214C22×C4×C139—42no—
215C22×C4×C139—42no—
216C22×C4×C139—81no—
217C22×C4×C139—81no—
218C22×C4×C139—81no—
219C22×C4×C139—81no—
220C22×C4×C139C2×D411yescharacteristic
221C22×C4×C139C2×D411yescharacteristic
222C22×C4×C139C2×D411yescharacteristic
223C22×C4×C139C2×D411yescharacteristic
224C22×C4×C139C2×D412yes—
225C22×C4×C139C2×D412yes—
226C22×C4×C139C2411yescharacteristic
227SD16×C139—44no—
228D8×C139—44no—
229M16×C139—44no—
230C2×C8×C139—21no—
231C2×C8×C139—21no—
232C2×C8×C139—21no—
233C2×C8×C139—21no—
234C2×C8×C139—21no—
235C2×C8×C139—21no—
236C2×C8×C139—21no—
237C2×C8×C139—21no—
238C2×C8×C139—21no—
239C2×C8×C139—21no—
240C2×C8×C139—21no—
241C2×C8×C139—21no—
242C4⋊C4×C139—24no—
243C4⋊C4×C139—24no—
244C4⋊C4×C139—24no—
245C4⋊C4×C139—22no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—21no—
251C4⋊C4×C139—21no—
252C4⋊C4×C139—21no—
253C4⋊C4×C139—42no—
254C4⋊C4×C139C2×D412yes—
255C4⋊C4×C139C2×D412yes—
256C4⋊C4×C139C2×D412yes—
257C22⋊C4×C139—24no—
258C22⋊C4×C139—24no—
259C22⋊C4×C139—24no—
260C22⋊C4×C139—22no—
261C22⋊C4×C139—24no—
262C22⋊C4×C139—22no—
263C22⋊C4×C139—42no—
264C22⋊C4×C139—42no—
265C22⋊C4×C139—42no—
266C22⋊C4×C139—81no—
267C22⋊C4×C139—81no—
268C42×C139—24no—
269C42×C139—21no—
270C42×C139—21no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—21no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—22no—
279C23×C139—21no—
280C23×C139—22no—
281C23×C139—21no—
282C23×C139—21no—
283C23×C139—21no—
284C23×C139—21no—
285C23×C139—21no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139—41no—
289C23×C139—41no—
290C23×C139—41no—
291C23×C139—41no—
292C23×C139—41no—
293C23×C139—41no—
294C23×C139—41no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—41no—
298C23×C139#12012yes—
299C23×C139C22×D411yescharacteristic
300Q8×C139—22no—
301Q8×C139—22no—
302Q8×C139—41no—
303Q8×C139—41no—
304D4×C139—22no—
305D4×C139—22no—
306D4×C139—22no—
307D4×C139—22no—
308D4×C139—44no—
309D4×C139—48no—
310D4×C139—48no—
311D4×C139—41no—
312D4×C139—41no—
313D4×C139—41no—
314D4×C139—41no—
315D4×C139—84no—
316D4×C139—84no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
319C2×C4×C139—22no—
320C2×C4×C139—22no—
321C2×C4×C139—22no—
322C2×C4×C139—22no—
323C2×C4×C139—21no—
324C2×C4×C139—21no—
325C2×C4×C139—22no—
326C2×C4×C139—21no—
327C2×C4×C139—22no—
328C2×C4×C139—22no—
329C2×C4×C139—21no—
330C2×C4×C139—22no—
331C2×C4×C139—21no—
332C2×C4×C139—21no—
333C2×C4×C139—21no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
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—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—41no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
353C2×C4×C139—41no—
354C2×C4×C139—41no—
355C2×C4×C139—84no—
356C2×C4×C139—84no—
357C2×C4×C139#12012yes—
358C2×C4×C139C22×D411yescharacteristic
359C2×C4×C139C22×D411yescharacteristic
360C2×C4×C139C2×#4111yescharacteristic
361C2×C4×C139C2×#4111yescharacteristic
362C2×C4×C139H(5,𝔽2)11yescharacteristic
363C2×C4×C139H(5,𝔽2)11yescharacteristic
364C8×C139—41no—
365C8×C139—41no—
366C8×C139—41no—
367C8×C139—41no—
368C22×C139—22no—
369C22×C139—22no—
370C22×C139—22no—
371C22×C139—41no—
372C22×C139—41no—
373C22×C139—41no—
374C22×C139—41no—
375C22×C139—42no—
376C22×C139—41no—
377C22×C139—42no—
378C22×C139—41no—
379C22×C139—42no—
380C22×C139—42no—
381C22×C139—41no—
382C22×C139—41no—
383C22×C139—42no—
384C22×C139—41no—
385C22×C139—41no—
386C22×C139—42no—
387C22×C139—41no—
388C22×C139—81no—
389C22×C139—81no—
390C22×C139—81no—
391C22×C139—81no—
392C22×C139—81no—
393C22×C139—81no—
394C22×C139—81no—
395C22×C139—81no—
396C22×C139C2×#12011yescharacteristic
397C22×C139#54611yescharacteristic
398C22×C139#54611yescharacteristic
399C22×C139#57511yescharacteristic
400C22×C139#57511yescharacteristic
401C22×C139#57611yescharacteristic
402C22×C139#57711yescharacteristic
403C4×C139—22no—
404C4×C139—41no—
405C4×C139—42no—
406C4×C139—41no—
407C4×C139—42no—
408C4×C139—41no—
409C4×C139—42no—
410C4×C139—42no—
411C4×C139—81no—
412C4×C139—81no—
413C4×C139#52511yescharacteristic
414C4×C139#53511yescharacteristic
415C4×C139#54611yescharacteristic
416C4×C139#54611yescharacteristic
417C2×C139—42no—
418C2×C139—81no—
419C2×C139—82no—
420C2×C139—82no—
421C2×C139#240411yescharacteristic
422C2×C139#300511yescharacteristic
423C2×C139#301211yescharacteristic
424C2×C139#330711yescharacteristic
425C2×C139#330911yescharacteristic
426C2×C139#332211yescharacteristic
427C2×C139#332611yescharacteristic
428#23975C13911yesmaximal, characteristic, direct product factor, Sylow
429C139#2397511yescharacteristic, direct product factor, Sylow
430C2×#553C2×C13911yescharacteristic, complemented
431C2×#449C2×C13911yescharacteristic, complemented
432C2×#417C2×C13911yescharacteristic, complemented
433#2407C2×C13911yescharacteristic, complemented
434#2026C2×C13911yescharacteristic, complemented
435#2025C2×C13911yescharacteristic, complemented
436#2000C2×C13911yescharacteristic, complemented
437#1999C2×C13911yescharacteristic, complemented
438#1895C2×C13911yescharacteristic, complemented
439#1879C2×C13911yescharacteristic, complemented
440#1877C2×C13911yescharacteristic, complemented
441#1875C2×C13911yescharacteristic, complemented
442#1873C2×C13911yescharacteristic, complemented
443#1870C2×C13911yescharacteristic, complemented
444#1823C2×C13911yescharacteristic, complemented
445C22×#41C22×C13911yescharacteristic
446C22×SD16C22×C13911yescharacteristic
447C22×D8C22×C13911yescharacteristic
448C22×M16C22×C13911yescharacteristic
449#553—24no—
450#553—24no—
451C2×#126—21no—
452C2×#125C22×C13911yescharacteristic
453C2×#123—21no—
454C2×C22⋊Q8C22×C13911yescharacteristic
455C2×#121—21no—
456C2×#121C22×C13911yescharacteristic
457C2×#121C22×C13911yescharacteristic
458C2×#121C22×C13911yescharacteristic
459C2×C4×D4—21no—
460C2×C4×D4C22×C13911yescharacteristic
461C2×C4×D4C22×C13911yescharacteristic
462C2×#117C22×C13911yescharacteristic
463C22×C4⋊C4C22×C13911yescharacteristic
464#449—24no—
465#417—24no—
466C2×#103C22×C13911yescharacteristic
467C2×#103C22×C13911yescharacteristic
468C2×#103C22×C13911yescharacteristic
469C2×#102C22×C13911yescharacteristic
470C2×#102C22×C13911yescharacteristic
471C2×#102C22×C13911yescharacteristic
472C2×#102C22×C13911yescharacteristic
473C2×#102C22×C13911yescharacteristic
474C2×C22⋊C8C22×C13911yescharacteristic
475C2×C22⋊C8C22×C13911yescharacteristic
476C2×C22⋊C8C22×C13911yescharacteristic
477#394—21no—
478#392—21no—
479#391C22×C13911yescharacteristic
480#390C22×C13911yescharacteristic
481#386—21no—
482#385—21no—
483#380C22×C13911yescharacteristic
484#340C22×C13911yescharacteristic
485#340C22×C13911yescharacteristic
486#340C22×C13911yescharacteristic
487#340C22×C13911yescharacteristic
488#340C22×C13911yescharacteristic
489#340C22×C13911yescharacteristic
490#336C22×C13911yescharacteristic
491#336C22×C13911yescharacteristic
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C22×Q8C23×C13911yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4D4×C13911yescharacteristic
504C22×D4C23×C13911yescharacteristic
505C22×D4C23×C13911yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C23×C13911yescharacteristic
510C23×C4C23×C13911yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—41no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C22×C8C23×C13911yescharacteristic
521C22×C8C23×C13911yescharacteristic
522C22×C8C23×C13911yescharacteristic
523C22×C8C23×C13911yescharacteristic
524#126—28no—
525#125—22no—
526#125—22no—
527#123—28no—
528C22⋊Q8—22no—
529C22⋊Q8—41no—
530#121—28no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—22no—
535#121—41no—
536#121D4×C13914yescomplemented
537C4×D4—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C13911yescharacteristic
550C2×C4⋊C4D4×C13914yescomplemented
551C2×C4⋊C4C23×C13911yescharacteristic
552C2×C4⋊C4C23×C13911yescharacteristic
553C2×C4⋊C4C23×C13911yescharacteristic
554C2×C4⋊C4C23×C13911yescharacteristic
555C2×C4⋊C4C23×C13911yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C13911yescharacteristic
566C2×C22⋊C4D4×C13911yescharacteristic
567C2×C42—21no—
568C2×C42C23×C13911yescharacteristic
569#103—22no—
570#103—22no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—41no—
576#102—41no—
577C22⋊C8—22no—
578C22⋊C8—41no—
579C22⋊C8—41no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—21no—
584C24—21no—
585C24C2×D4×C13911yescharacteristic
586C24C2×D4×C13911yescharacteristic
587#41—28no—
588#41—44no—
589#41—44no—
590#41—44no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8#41×C13912yes—
597C2×D4—22no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4—81no—
622C2×D4C2×D4×C13912yes—
623C2×D4#41×C13912yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—81no—
646C22×C4—81no—
647C22×C4—81no—
648C22×C4—81no—
649C22×C4C2×D4×C13911yescharacteristic
650C22×C4C2×D4×C13911yescharacteristic
651C22×C4C2×D4×C13911yescharacteristic
652C22×C4C2×D4×C13911yescharacteristic
653C22×C4C2×D4×C13912yes—
654C22×C4C2×D4×C13912yes—
655C22×C4C24×C13911yescharacteristic
656SD16—44no—
657D8—44no—
658M16—44no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4C2×D4×C13912yes—
684C4⋊C4C2×D4×C13912yes—
685C4⋊C4C2×D4×C13912yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—81no—
696C22⋊C4—81no—
697C42—24no—
698C42—21no—
699C42—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—22no—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23#120×C13912yes—
728C23C22×D4×C13911yescharacteristic
729Q8—22no—
730Q8—22no—
731Q8—41no—
732Q8—41no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—44no—
738D4—48no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—84no—
745D4—84no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—48no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—84no—
785C2×C4—84no—
786C2×C4#120×C13912yes—
787C2×C4C22×D4×C13911yescharacteristic
788C2×C4C22×D4×C13911yescharacteristic
789C2×C4C2×#41×C13911yescharacteristic
790C2×C4C2×#41×C13911yescharacteristic
791C2×C4H(5,𝔽2)×C13911yescharacteristic
792C2×C4H(5,𝔽2)×C13911yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—41no—
812C22—42no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22C2×#120×C13911yescharacteristic
826C22#546×C13911yescharacteristic
827C22#546×C13911yescharacteristic
828C22#575×C13911yescharacteristic
829C22#575×C13911yescharacteristic
830C22#576×C13911yescharacteristic
831C22#577×C13911yescharacteristic
832C4—22no—
833C4—41no—
834C4—42no—
835C4—41no—
836C4—42no—
837C4—41no—
838C4—42no—
839C4—42no—
840C4—81no—
841C4—81no—
842C4#525×C13911yescharacteristic
843C4#535×C13911yescharacteristic
844C4#546×C13911yescharacteristic
845C4#546×C13911yescharacteristic
846C2—42no—
847C2—81no—
848C2—82no—
849C2—82no—
850C2#2404×C13911yescharacteristic
851C2#3005×C13911yescharacteristic
852C2#3012×C13911yescharacteristic
853C2#3307×C13911yescharacteristic
854C2#3309×C13911yescharacteristic
855C2#3322×C13911yescharacteristic
856C2#3326×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×#553×C139C2semidirect
2. C2×#449×C139C2semidirect
3. C2×#417×C139C2semidirect
4. #2407×C139C2semidirect
5. #2026×C139C2semidirect
6. #2025×C139C2semidirect
7. #2000×C139C2semidirect
8. #1999×C139C2semidirect
9. #1895×C139C2semidirect
10. #1879×C139C2semidirect
11. #1877×C139C2semidirect
12. #1875×C139C2semidirect
13. #1873×C139C2semidirect
14. #1870×C139C2semidirect
15. #1823×C139C2semidirect
107. #121×C139D4semidirect
121. C2×C4⋊C4×C139D4semidirect
428. #23975C139direct (N × H)
429. C139#23975direct (N × H)
430. C2×#553C2×C139semidirect
431. C2×#449C2×C139semidirect
432. C2×#417C2×C139semidirect
433. #2407C2×C139semidirect
434. #2026C2×C139semidirect
435. #2025C2×C139semidirect
436. #2000C2×C139semidirect
437. #1999C2×C139semidirect
438. #1895C2×C139semidirect
439. #1879C2×C139semidirect
440. #1877C2×C139semidirect
441. #1875C2×C139semidirect
442. #1873C2×C139semidirect
443. #1870C2×C139semidirect
444. #1823C2×C139semidirect
536. #121D4×C139semidirect
550. C2×C4⋊C4D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#553×C1392
C2×#449×C1392
C2×#417×C1392
#2407×C1392
#2026×C1392
#2025×C1392
#2000×C1392
#1999×C1392
#1895×C1392
#1879×C1392
#1877×C1392
#1875×C1392
#1873×C1392
#1870×C1392
#1823×C1392
#23975139