Finite Group Databasebeta

← C139×#23850 #48018446

Subgroups — C139×#23850 #48018446

Order 35584.

1934 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C139C211yesmaximal, characteristic, complemented
2C2×#546×C139C211yesmaximal, characteristic, complemented
3C2×#449×C139C211yesmaximal, characteristic, complemented
4C2×#450×C139C211yesmaximal, characteristic, complemented
5C2×#447×C139C211yesmaximal, characteristic, complemented
6#2407×C139C211yesmaximal, characteristic, complemented
7#2015×C139C211yesmaximal, characteristic, complemented
8#2012×C139C211yesmaximal, characteristic, complemented
9#2001×C139C211yesmaximal, characteristic, complemented
10#2000×C139C211yesmaximal, characteristic, complemented
11#1893×C139C211yesmaximal, characteristic, complemented
12#1879×C139C211yesmaximal, characteristic, complemented
13#1877×C139C211yesmaximal, characteristic, complemented
14#1869×C139C211yesmaximal, characteristic, complemented
15#1788×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic, complemented
18C23×D4×C139C2211yescharacteristic
19C2×#135×C139—24no—
20C2×#135×C139—24no—
21C2×#135×C139—24no—
22C22×Q16×C139C2211yescharacteristic, complemented
23C22×SD16×C139C2211yescharacteristic
24C22×SD16×C139C2211yescharacteristic
25C22×SD16×C139C2211yescharacteristic, complemented
26C22×D8×C139C2211yescharacteristic
27C22×D8×C139C2211yescharacteristic
28C23×C8×C139C2211yescharacteristic, complemented
29#546×C139—24no—
30#546×C139—24no—
31C2×#124×C139C2211yescharacteristic
32C2×#123×C139—21no—
33C2×C22⋊Q8×C139C2211yescharacteristic
34C2×C22⋊Q8×C139C2211yescharacteristic
35C2×#121×C139—21no—
36C2×#121×C139C2211yescharacteristic
37C2×#121×C139C2211yescharacteristic
38C2×#120×C139—21no—
39C2×C4×D4×C139C2211yescharacteristic
40C2×C4×D4×C139C2211yescharacteristic
41C22×C22⋊C4×C139—21no—
42#450×C139—24no—
43#449×C139—24no—
44#447×C139—24no—
45C2×#103×C139C2211yescharacteristic, complemented
46C2×#103×C139C2211yescharacteristic, complemented
47C2×#103×C139C2211yescharacteristic, complemented
48C2×#102×C139C2211yescharacteristic
49C2×#102×C139C2211yescharacteristic
50C2×#102×C139C2211yescharacteristic
51C2×#102×C139C2211yescharacteristic
52C2×#102×C139C2211yescharacteristic, complemented
53C2×C22⋊C8×C139C2211yescharacteristic
54C2×C22⋊C8×C139C2211yescharacteristic
55C2×C22⋊C8×C139C2211yescharacteristic, complemented
56#394×C139—21no—
57#392×C139—21no—
58#391×C139C2211yescharacteristic, complemented
59#390×C139C2211yescharacteristic, complemented
60#386×C139—21no—
61#385×C139—21no—
62#380×C139C2211yescharacteristic, complemented
63#340×C139C2211yescharacteristic, complemented
64#340×C139C2211yescharacteristic, complemented
65#336×C139C2211yescharacteristic, complemented
66#336×C139C2211yescharacteristic, complemented
67C25×C139—21no—
68C2×#41×C139—22no—
69C2×#41×C139—22no—
70C2×#41×C139—22no—
71C2×#41×C139—22no—
72C2×#41×C139—22no—
73C2×#41×C139—22no—
74C2×#41×C139—22no—
75C2×#41×C139—41no—
76C2×#41×C139—41no—
77C2×#41×C139—41no—
78C2×#41×C139—41no—
79C2×#41×C139D414yescomplemented
80C22×Q8×C139C2311yescharacteristic
81C22×Q8×C139C2311yescharacteristic
82C22×D4×C139—21no—
83C22×D4×C139—21no—
84C22×D4×C139—22no—
85C22×D4×C139—22no—
86C22×D4×C139—22no—
87C22×D4×C139—22no—
88C22×D4×C139—21no—
89C22×D4×C139—21no—
90C22×D4×C139—21no—
91C22×D4×C139—41no—
92C22×D4×C139—41no—
93C22×D4×C139D411yescharacteristic
94C22×D4×C139C2311yescharacteristic
95C22×D4×C139C2311yescharacteristic
96C22×D4×C139C2311yescharacteristic
97C23×C4×C139—21no—
98C23×C4×C139—21no—
99C23×C4×C139—21no—
100C23×C4×C139C2311yescharacteristic
101C23×C4×C139C2311yescharacteristic
102#135×C139—232no—
103C2×Q16×C139—22no—
104C2×Q16×C139—22no—
105C2×Q16×C139—22no—
106C2×SD16×C139—22no—
107C2×SD16×C139—22no—
108C2×SD16×C139—22no—
109C2×SD16×C139—22no—
110C2×SD16×C139—22no—
111C2×SD16×C139—22no—
112C2×SD16×C139—22no—
113C2×SD16×C139—41no—
114C2×SD16×C139D414yescomplemented
115C2×D8×C139—22no—
116C2×D8×C139—22no—
117C2×D8×C139—22no—
118C2×D8×C139—22no—
119C2×D8×C139—41no—
120C2×D8×C139D414yescomplemented
121C22×C8×C139—22no—
122C22×C8×C139—22no—
123C22×C8×C139—22no—
124C22×C8×C139C2311yescharacteristic
125C22×C8×C139C2311yescharacteristic
126C22×C8×C139C2311yescharacteristic
127C22×C8×C139C2311yescharacteristic
128#124×C139—22no—
129#124×C139—22no—
130#123×C139—28no—
131C22⋊Q8×C139—22no—
132C22⋊Q8×C139—22no—
133C22⋊Q8×C139—22no—
134C22⋊Q8×C139—41no—
135#121×C139—28no—
136#121×C139—22no—
137#121×C139—22no—
138#121×C139—41no—
139#121×C139D414yescomplemented
140#120×C139—28no—
141C4×D4×C139—22no—
142C4×D4×C139—22no—
143C4×D4×C139—22no—
144C4×D4×C139—22no—
145C2×C4⋊C4×C139—21no—
146C2×C4⋊C4×C139—21no—
147C2×C4⋊C4×C139D411yescharacteristic
148C2×C4⋊C4×C139C2311yescharacteristic
149C2×C4⋊C4×C139C2311yescharacteristic
150C2×C4⋊C4×C139C2311yescharacteristic
151C2×C22⋊C4×C139—28no—
152C2×C22⋊C4×C139—21no—
153C2×C22⋊C4×C139—21no—
154C2×C22⋊C4×C139—21no—
155C2×C22⋊C4×C139—21no—
156C2×C22⋊C4×C139—21no—
157C2×C22⋊C4×C139—21no—
158C2×C22⋊C4×C139—21no—
159C2×C22⋊C4×C139—21no—
160C2×C22⋊C4×C139—21no—
161C2×C22⋊C4×C139—21no—
162C2×C22⋊C4×C139D411yescharacteristic
163C2×C22⋊C4×C139D411yescharacteristic
164C2×C42×C139C2311yescharacteristic
165#103×C139—22no—
166#103×C139—41no—
167#103×C139—41no—
168#102×C139—22no—
169#102×C139—22no—
170#102×C139—22no—
171#102×C139—22no—
172#102×C139—22no—
173C22⋊C8×C139—22no—
174C22⋊C8×C139—22no—
175C22⋊C8×C139—22no—
176#95×C139—21no—
177#95×C139—21no—
178#95×C139—21no—
179C24×C139—21no—
180C24×C139—24no—
181C24×C139—21no—
182C24×C139—21no—
183C24×C139—42no—
184C24×C139—42no—
185C24×C139—42no—
186C24×C139—42no—
187C24×C139—81no—
188C24×C139—81no—
189C24×C139C2×D411yescharacteristic
190C24×C139C2×D411yescharacteristic
191#41×C139—28no—
192#41×C139—28no—
193#41×C139—44no—
194#41×C139—44no—
195#41×C139—44no—
196#41×C139—44no—
197#41×C139—44no—
198#41×C139—44no—
199C2×Q8×C139—21no—
200C2×Q8×C139—21no—
201C2×Q8×C139—21no—
202C2×Q8×C139—21no—
203C2×Q8×C139—21no—
204C2×Q8×C139—21no—
205C2×Q8×C139—21no—
206C2×Q8×C139—21no—
207C2×Q8×C139—21no—
208C2×Q8×C139—21no—
209C2×Q8×C139C2×D412yes—
210C2×Q8×C139C2×D412yes—
211C2×D4×C139—24no—
212C2×D4×C139—22no—
213C2×D4×C139—24no—
214C2×D4×C139—22no—
215C2×D4×C139—24no—
216C2×D4×C139—21no—
217C2×D4×C139—21no—
218C2×D4×C139—21no—
219C2×D4×C139—21no—
220C2×D4×C139—21no—
221C2×D4×C139—21no—
222C2×D4×C139—21no—
223C2×D4×C139—21no—
224C2×D4×C139—21no—
225C2×D4×C139—21no—
226C2×D4×C139—21no—
227C2×D4×C139—21no—
228C2×D4×C139—21no—
229C2×D4×C139—41no—
230C2×D4×C139—42no—
231C2×D4×C139—42no—
232C2×D4×C139—42no—
233C2×D4×C139—44no—
234C2×D4×C139—44no—
235C2×D4×C139—44no—
236C2×D4×C139—42no—
237C2×D4×C139—42no—
238C2×D4×C139—42no—
239C2×D4×C139—42no—
240C2×D4×C139—44no—
241C2×D4×C139—42no—
242C2×D4×C139—42no—
243C2×D4×C139—81no—
244C2×D4×C139—81no—
245C2×D4×C139—81no—
246C2×D4×C139C2×D412yes—
247C2×D4×C139C2×D412yes—
248C2×D4×C139C2×D412yes—
249C2×D4×C139C2×D412yes—
250C2×D4×C139C2×D412yes—
251C22×C4×C139—21no—
252C22×C4×C139—21no—
253C22×C4×C139—21no—
254C22×C4×C139—21no—
255C22×C4×C139—21no—
256C22×C4×C139—21no—
257C22×C4×C139—21no—
258C22×C4×C139—24no—
259C22×C4×C139—24no—
260C22×C4×C139—21no—
261C22×C4×C139—21no—
262C22×C4×C139—21no—
263C22×C4×C139—21no—
264C22×C4×C139—21no—
265C22×C4×C139—21no—
266C22×C4×C139—21no—
267C22×C4×C139—21no—
268C22×C4×C139—42no—
269C22×C4×C139—42no—
270C22×C4×C139—42no—
271C22×C4×C139—42no—
272C22×C4×C139—42no—
273C22×C4×C139—81no—
274C22×C4×C139—81no—
275C22×C4×C139C2×D411yescharacteristic
276C22×C4×C139C2×D411yescharacteristic
277C22×C4×C139C2×D411yescharacteristic
278C22×C4×C139C2×D411yescharacteristic
279C22×C4×C139C2×D412yes—
280C22×C4×C139C2×D412yes—
281C22×C4×C139C2411yescharacteristic
282Q16×C139—28no—
283SD16×C139—28no—
284SD16×C139—28no—
285SD16×C139—44no—
286D8×C139—28no—
287D8×C139—44no—
288C2×C8×C139—28no—
289C2×C8×C139—21no—
290C2×C8×C139—21no—
291C2×C8×C139—21no—
292C2×C8×C139—21no—
293C2×C8×C139—21no—
294C2×C8×C139—21no—
295C2×C8×C139—21no—
296C2×C8×C139—21no—
297C2×C8×C139—21no—
298C2×C8×C139—21no—
299C2×C8×C139C2×D412yes—
300C2×C8×C139C2×D412yes—
301C4⋊C4×C139—24no—
302C4⋊C4×C139—22no—
303C4⋊C4×C139—21no—
304C4⋊C4×C139—21no—
305C4⋊C4×C139—21no—
306C4⋊C4×C139—21no—
307C4⋊C4×C139—21no—
308C4⋊C4×C139—42no—
309C4⋊C4×C139C2×D412yes—
310C22⋊C4×C139—24no—
311C22⋊C4×C139—24no—
312C22⋊C4×C139—24no—
313C22⋊C4×C139—24no—
314C22⋊C4×C139—22no—
315C22⋊C4×C139—22no—
316C22⋊C4×C139—24no—
317C22⋊C4×C139—42no—
318C22⋊C4×C139—42no—
319C22⋊C4×C139—42no—
320C22⋊C4×C139—81no—
321C22⋊C4×C139—81no—
322C42×C139—21no—
323C42×C139—21no—
324C23×C139—21no—
325C23×C139—22no—
326C23×C139—21no—
327C23×C139—21no—
328C23×C139—21no—
329C23×C139—21no—
330C23×C139—22no—
331C23×C139—22no—
332C23×C139—21no—
333C23×C139—21no—
334C23×C139—21no—
335C23×C139—21no—
336C23×C139—21no—
337C23×C139—21no—
338C23×C139—21no—
339C23×C139—22no—
340C23×C139—22no—
341C23×C139—48no—
342C23×C139—48no—
343C23×C139—41no—
344C23×C139—41no—
345C23×C139—41no—
346C23×C139—41no—
347C23×C139—41no—
348C23×C139—41no—
349C23×C139—41no—
350C23×C139—41no—
351C23×C139—41no—
352C23×C139—41no—
353C23×C139—41no—
354C23×C139—41no—
355C23×C139—41no—
356C23×C139—41no—
357C23×C139—41no—
358C23×C139—41no—
359C23×C139—84no—
360C23×C139—84no—
361C23×C139—84no—
362C23×C139—84no—
363C23×C139—84no—
364C23×C139#12012yes—
365C23×C139#13512yescomplemented
366C23×C139C22×D411yescharacteristic
367Q8×C139—22no—
368Q8×C139—22no—
369Q8×C139—22no—
370Q8×C139—22no—
371Q8×C139—41no—
372Q8×C139—41no—
373Q8×C139—41no—
374Q8×C139—41no—
375D4×C139—22no—
376D4×C139—22no—
377D4×C139—22no—
378D4×C139—22no—
379D4×C139—22no—
380D4×C139—22no—
381D4×C139—22no—
382D4×C139—44no—
383D4×C139—48no—
384D4×C139—48no—
385D4×C139—48no—
386D4×C139—41no—
387D4×C139—41no—
388D4×C139—41no—
389D4×C139—41no—
390D4×C139—84no—
391D4×C139—84no—
392D4×C139#12014yes—
393C2×C4×C139—21no—
394C2×C4×C139—21no—
395C2×C4×C139—22no—
396C2×C4×C139—22no—
397C2×C4×C139—22no—
398C2×C4×C139—22no—
399C2×C4×C139—21no—
400C2×C4×C139—21no—
401C2×C4×C139—22no—
402C2×C4×C139—22no—
403C2×C4×C139—21no—
404C2×C4×C139—21no—
405C2×C4×C139—22no—
406C2×C4×C139—21no—
407C2×C4×C139—21no—
408C2×C4×C139—21no—
409C2×C4×C139—21no—
410C2×C4×C139—21no—
411C2×C4×C139—48no—
412C2×C4×C139—48no—
413C2×C4×C139—41no—
414C2×C4×C139—41no—
415C2×C4×C139—41no—
416C2×C4×C139—41no—
417C2×C4×C139—41no—
418C2×C4×C139—41no—
419C2×C4×C139—41no—
420C2×C4×C139—41no—
421C2×C4×C139—41no—
422C2×C4×C139—41no—
423C2×C4×C139—41no—
424C2×C4×C139—41no—
425C2×C4×C139—41no—
426C2×C4×C139—41no—
427C2×C4×C139—41no—
428C2×C4×C139—41no—
429C2×C4×C139—84no—
430C2×C4×C139#12012yes—
431C2×C4×C139C22×D411yescharacteristic
432C2×C4×C139C22×D411yescharacteristic
433C2×C4×C139C22×D411yescharacteristic
434C2×C4×C139C22×D411yescharacteristic
435C2×C4×C139H(5,𝔽2)11yescharacteristic
436C2×C4×C139H(5,𝔽2)11yescharacteristic
437C8×C139—22no—
438C8×C139—22no—
439C8×C139—41no—
440C8×C139—41no—
441C22×C139—22no—
442C22×C139—24no—
443C22×C139—22no—
444C22×C139—22no—
445C22×C139—22no—
446C22×C139—22no—
447C22×C139—22no—
448C22×C139—41no—
449C22×C139—42no—
450C22×C139—41no—
451C22×C139—41no—
452C22×C139—42no—
453C22×C139—42no—
454C22×C139—41no—
455C22×C139—41no—
456C22×C139—41no—
457C22×C139—42no—
458C22×C139—41no—
459C22×C139—42no—
460C22×C139—41no—
461C22×C139—42no—
462C22×C139—42no—
463C22×C139—42no—
464C22×C139—42no—
465C22×C139—42no—
466C22×C139—42no—
467C22×C139—42no—
468C22×C139—816no—
469C22×C139—81no—
470C22×C139—81no—
471C22×C139—81no—
472C22×C139—81no—
473C22×C139—81no—
474C22×C139—81no—
475C22×C139—81no—
476C22×C139—81no—
477C22×C139C2×#12011yescharacteristic
478C22×C139D4211yescharacteristic
479C22×C139D4211yescharacteristic
480C22×C139C2×#13511yescharacteristic
481C22×C139#57511yescharacteristic
482C22×C139#57611yescharacteristic
483C22×C139#57711yescharacteristic
484C4×C139—22no—
485C4×C139—41no—
486C4×C139—42no—
487C4×C139—42no—
488C4×C139—41no—
489C4×C139—41no—
490C4×C139—42no—
491C4×C139—81no—
492C4×C139—81no—
493C4×C139C2×#12011yescharacteristic
494C4×C139#53411yescharacteristic
495C4×C139D4211yescharacteristic
496C4×C139D4211yescharacteristic
497C2×C139—42no—
498C2×C139—42no—
499C2×C139—44no—
500C2×C139—82no—
501C2×C139—82no—
502C2×C139#240311yescharacteristic
503C2×C139#300211yescharacteristic
504C2×C139#301211yescharacteristic
505C2×C139#326711yescharacteristic
506C2×C139#326811yescharacteristic
507C2×C139#328011yescharacteristic
508C2×C139#328211yescharacteristic
509#23850C13911yesmaximal, characteristic, direct product factor, Sylow
510C139#2385011yescharacteristic, direct product factor, Sylow
511C22×#135C2×C13911yescharacteristic, complemented
512C2×#546C2×C13911yescharacteristic, complemented
513C2×#449C2×C13911yescharacteristic, complemented
514C2×#450C2×C13911yescharacteristic, complemented
515C2×#447C2×C13911yescharacteristic, complemented
516#2407C2×C13911yescharacteristic, complemented
517#2015C2×C13911yescharacteristic, complemented
518#2012C2×C13911yescharacteristic, complemented
519#2001C2×C13911yescharacteristic, complemented
520#2000C2×C13911yescharacteristic, complemented
521#1893C2×C13911yescharacteristic, complemented
522#1879C2×C13911yescharacteristic, complemented
523#1877C2×C13911yescharacteristic, complemented
524#1869C2×C13911yescharacteristic, complemented
525#1788C2×C13911yescharacteristic, complemented
526C22×#41C22×C13911yescharacteristic
527C22×#41C22×C13911yescharacteristic, complemented
528C23×D4C22×C13911yescharacteristic
529C2×#135—24no—
530C2×#135—24no—
531C2×#135—24no—
532C22×Q16C22×C13911yescharacteristic, complemented
533C22×SD16C22×C13911yescharacteristic
534C22×SD16C22×C13911yescharacteristic
535C22×SD16C22×C13911yescharacteristic, complemented
536C22×D8C22×C13911yescharacteristic
537C22×D8C22×C13911yescharacteristic
538C23×C8C22×C13911yescharacteristic, complemented
539#546—24no—
540#546—24no—
541C2×#124C22×C13911yescharacteristic
542C2×#123—21no—
543C2×C22⋊Q8C22×C13911yescharacteristic
544C2×C22⋊Q8C22×C13911yescharacteristic
545C2×#121—21no—
546C2×#121C22×C13911yescharacteristic
547C2×#121C22×C13911yescharacteristic
548C2×#120—21no—
549C2×C4×D4C22×C13911yescharacteristic
550C2×C4×D4C22×C13911yescharacteristic
551C22×C22⋊C4—21no—
552#450—24no—
553#449—24no—
554#447—24no—
555C2×#103C22×C13911yescharacteristic, complemented
556C2×#103C22×C13911yescharacteristic, complemented
557C2×#103C22×C13911yescharacteristic, complemented
558C2×#102C22×C13911yescharacteristic
559C2×#102C22×C13911yescharacteristic
560C2×#102C22×C13911yescharacteristic
561C2×#102C22×C13911yescharacteristic
562C2×#102C22×C13911yescharacteristic, complemented
563C2×C22⋊C8C22×C13911yescharacteristic
564C2×C22⋊C8C22×C13911yescharacteristic
565C2×C22⋊C8C22×C13911yescharacteristic, complemented
566#394—21no—
567#392—21no—
568#391C22×C13911yescharacteristic, complemented
569#390C22×C13911yescharacteristic, complemented
570#386—21no—
571#385—21no—
572#380C22×C13911yescharacteristic, complemented
573#340C22×C13911yescharacteristic, complemented
574#340C22×C13911yescharacteristic, complemented
575#336C22×C13911yescharacteristic, complemented
576#336C22×C13911yescharacteristic, complemented
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41D4×C13914yescomplemented
590C22×Q8C23×C13911yescharacteristic
591C22×Q8C23×C13911yescharacteristic
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—22no—
597C22×D4—22no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4D4×C13911yescharacteristic
604C22×D4C23×C13911yescharacteristic
605C22×D4C23×C13911yescharacteristic
606C22×D4C23×C13911yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C13911yescharacteristic
611C23×C4C23×C13911yescharacteristic
612#135—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C13914yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—41no—
630C2×D8D4×C13914yescomplemented
631C22×C8—22no—
632C22×C8—22no—
633C22×C8—22no—
634C22×C8C23×C13911yescharacteristic
635C22×C8C23×C13911yescharacteristic
636C22×C8C23×C13911yescharacteristic
637C22×C8C23×C13911yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—41no—
645#121—28no—
646#121—22no—
647#121—22no—
648#121—41no—
649#121D4×C13914yescomplemented
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C13911yescharacteristic
658C2×C4⋊C4C23×C13911yescharacteristic
659C2×C4⋊C4C23×C13911yescharacteristic
660C2×C4⋊C4C23×C13911yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C13911yescharacteristic
673C2×C22⋊C4D4×C13911yescharacteristic
674C2×C42C23×C13911yescharacteristic
675#103—22no—
676#103—41no—
677#103—41no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—24no—
691C24—21no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C13911yescharacteristic
700C24C2×D4×C13911yescharacteristic
701#41—28no—
702#41—28no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C13912yes—
720C2×Q8C2×D4×C13912yes—
721C2×D4—24no—
722C2×D4—22no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—44no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C13912yes—
757C2×D4C2×D4×C13912yes—
758C2×D4C2×D4×C13912yes—
759C2×D4C2×D4×C13912yes—
760C2×D4C2×D4×C13912yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C13911yescharacteristic
786C22×C4C2×D4×C13911yescharacteristic
787C22×C4C2×D4×C13911yescharacteristic
788C22×C4C2×D4×C13911yescharacteristic
789C22×C4C2×D4×C13912yes—
790C22×C4C2×D4×C13912yes—
791C22×C4C24×C13911yescharacteristic
792Q16—28no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—44no—
798C2×C8—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C13912yes—
810C2×C8C2×D4×C13912yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C13912yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—22no—
826C22⋊C4—24no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—21no—
835C23—22no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—22no—
850C23—22no—
851C23—48no—
852C23—48no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—84no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23#120×C13912yes—
875C23#135×C13912yescomplemented
876C23C22×D4×C13911yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—44no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C13914yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C13912yes—
941C2×C4C22×D4×C13911yescharacteristic
942C2×C4C22×D4×C13911yescharacteristic
943C2×C4C22×D4×C13911yescharacteristic
944C2×C4C22×D4×C13911yescharacteristic
945C2×C4H(5,𝔽2)×C13911yescharacteristic
946C2×C4H(5,𝔽2)×C13911yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—24no—
955C22—22no—
956C22—22no—
957C22—22no—
958C22—41no—
959C22—42no—
960C22—41no—
961C22—42no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—41no—
966C22—42no—
967C22—42no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C13911yescharacteristic
988C22D42×C13911yescharacteristic
989C22D42×C13911yescharacteristic
990C22C2×#135×C13911yescharacteristic
991C22#575×C13911yescharacteristic
992C22#576×C13911yescharacteristic
993C22#577×C13911yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C13911yescharacteristic
1004C4#534×C13911yescharacteristic
1005C4D42×C13911yescharacteristic
1006C4D42×C13911yescharacteristic
1007C2—42no—
1008C2—42no—
1009C2—44no—
1010C2—82no—
1011C2—82no—
1012C2#2403×C13911yescharacteristic
1013C2#3002×C13911yescharacteristic
1014C2#3012×C13911yescharacteristic
1015C2#3267×C13911yescharacteristic
1016C2#3268×C13911yescharacteristic
1017C2#3280×C13911yescharacteristic
1018C2#3282×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. C22×#135×C139C2semidirect
2. C2×#546×C139C2semidirect
3. C2×#449×C139C2semidirect
4. C2×#450×C139C2semidirect
5. C2×#447×C139C2semidirect
6. #2407×C139C2semidirect
7. #2015×C139C2semidirect
8. #2012×C139C2semidirect
9. #2001×C139C2semidirect
10. #2000×C139C2semidirect
11. #1893×C139C2semidirect
12. #1879×C139C2semidirect
13. #1877×C139C2semidirect
14. #1869×C139C2semidirect
15. #1788×C139C2semidirect
17. C22×#41×C139C22semidirect
22. C22×Q16×C139C22semidirect
25. C22×SD16×C139C22semidirect
28. C23×C8×C139C22semidirect
45. C2×#103×C139C22semidirect
46. C2×#103×C139C22semidirect
47. C2×#103×C139C22semidirect
52. C2×#102×C139C22semidirect
55. C2×C22⋊C8×C139C22semidirect
58. #391×C139C22semidirect
59. #390×C139C22semidirect
62. #380×C139C22semidirect
63. #340×C139C22semidirect
64. #340×C139C22semidirect
65. #336×C139C22semidirect
66. #336×C139C22semidirect
79. C2×#41×C139D4semidirect
114. C2×SD16×C139D4semidirect
120. C2×D8×C139D4semidirect
139. #121×C139D4semidirect
365. C23×C139#135semidirect
509. #23850C139direct (N × H)
510. C139#23850direct (N × H)
511. C22×#135C2×C139semidirect
512. C2×#546C2×C139semidirect
513. C2×#449C2×C139semidirect
514. C2×#450C2×C139semidirect
515. C2×#447C2×C139semidirect
516. #2407C2×C139semidirect
517. #2015C2×C139semidirect
518. #2012C2×C139semidirect
519. #2001C2×C139semidirect
520. #2000C2×C139semidirect
521. #1893C2×C139semidirect
522. #1879C2×C139semidirect
523. #1877C2×C139semidirect
524. #1869C2×C139semidirect
525. #1788C2×C139semidirect
527. C22×#41C22×C139semidirect
532. C22×Q16C22×C139semidirect
535. C22×SD16C22×C139semidirect
538. C23×C8C22×C139semidirect
555. C2×#103C22×C139semidirect
556. C2×#103C22×C139semidirect
557. C2×#103C22×C139semidirect
562. C2×#102C22×C139semidirect
565. C2×C22⋊C8C22×C139semidirect
568. #391C22×C139semidirect
569. #390C22×C139semidirect
572. #380C22×C139semidirect
573. #340C22×C139semidirect
574. #340C22×C139semidirect
575. #336C22×C139semidirect
576. #336C22×C139semidirect
589. C2×#41D4×C139semidirect
624. C2×SD16D4×C139semidirect
630. C2×D8D4×C139semidirect
649. #121D4×C139semidirect
875. C23#135×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1392
C2×#546×C1392
C2×#449×C1392
C2×#450×C1392
C2×#447×C1392
#2407×C1392
#2015×C1392
#2012×C1392
#2001×C1392
#2000×C1392
#1893×C1392
#1879×C1392
#1877×C1392
#1869×C1392
#1788×C1392
#23850139