Finite Group Databasebeta

← C139×#23857 #48018453

Subgroups — C139×#23857 #48018453

Order 35584.

1852 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C139C211yesmaximal, characteristic, complemented
2C2×#550×C139C211yesmaximal, characteristic, complemented
3C2×#452×C139C211yesmaximal, characteristic, complemented
4C2×#449×C139C211yesmaximal, characteristic, complemented
5C2×#449×C139C211yesmaximal, characteristic, complemented
6#2407×C139C211yesmaximal, characteristic, complemented
7#2014×C139C211yesmaximal, characteristic, complemented
8#2011×C139C211yesmaximal, characteristic, complemented
9#2000×C139C211yesmaximal, characteristic, complemented
10#1999×C139C211yesmaximal, characteristic, complemented
11#1893×C139C211yesmaximal, characteristic, complemented
12#1880×C139C211yesmaximal, characteristic, complemented
13#1878×C139C211yesmaximal, characteristic, complemented
14#1869×C139C211yesmaximal, characteristic, complemented
15#1788×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C22×#41×C139C2211yescharacteristic
19C2×#135×C139—24no—
20C2×#135×C139—24no—
21C2×#135×C139—24no—
22C22×Q16×C139C2211yescharacteristic
23C22×SD16×C139C2211yescharacteristic
24C22×SD16×C139C2211yescharacteristic
25C22×SD16×C139C2211yescharacteristic
26C22×D8×C139C2211yescharacteristic
27C22×D8×C139C2211yescharacteristic
28C23×C8×C139C2211yescharacteristic
29#550×C139—24no—
30#550×C139—24no—
31C2×#127×C139—21no—
32C2×#127×C139C2211yescharacteristic
33C2×C22⋊Q8×C139C2211yescharacteristic
34C2×#121×C139—21no—
35C2×#121×C139—21no—
36C2×#121×C139C2211yescharacteristic
37C2×#121×C139C2211yescharacteristic
38C2×#121×C139C2211yescharacteristic
39C2×C4×Q8×C139C2211yescharacteristic
40C2×C4×D4×C139—21no—
41C2×C4×D4×C139C2211yescharacteristic
42#452×C139—24no—
43#449×C139—24no—
44#449×C139—24no—
45C2×#103×C139C2211yescharacteristic
46C2×#103×C139C2211yescharacteristic
47C2×#103×C139C2211yescharacteristic
48C2×#102×C139C2211yescharacteristic
49C2×#102×C139C2211yescharacteristic
50C2×#102×C139C2211yescharacteristic
51C2×#102×C139C2211yescharacteristic
52C2×#102×C139C2211yescharacteristic
53C2×C22⋊C8×C139C2211yescharacteristic
54C2×C22⋊C8×C139C2211yescharacteristic
55C2×C22⋊C8×C139C2211yescharacteristic
56#394×C139—21no—
57#392×C139—21no—
58#391×C139C2211yescharacteristic
59#390×C139C2211yescharacteristic
60#386×C139—21no—
61#385×C139—21no—
62#380×C139C2211yescharacteristic
63#340×C139C2211yescharacteristic
64#340×C139C2211yescharacteristic
65#336×C139C2211yescharacteristic
66#336×C139C2211yescharacteristic
67C2×#41×C139—22no—
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—22no—
76C2×#41×C139—22no—
77C2×#41×C139—22no—
78C2×#41×C139—41no—
79C2×#41×C139—41no—
80C2×#41×C139—41no—
81C2×#41×C139—41no—
82C2×#41×C139—41no—
83C2×#41×C139—41no—
84C2×#41×C139D414yescomplemented
85C22×Q8×C139C2311yescharacteristic
86C22×Q8×C139C2311yescharacteristic
87C22×D4×C139—21no—
88C22×D4×C139—21no—
89C22×D4×C139—21no—
90C22×D4×C139—21no—
91C22×D4×C139—21no—
92C22×D4×C139—21no—
93C22×D4×C139—21no—
94C22×D4×C139—21no—
95C22×D4×C139D411yescharacteristic
96C22×D4×C139C2311yescharacteristic
97C22×D4×C139C2311yescharacteristic
98C22×D4×C139C2311yescharacteristic
99C23×C4×C139—21no—
100C23×C4×C139—21no—
101C23×C4×C139—21no—
102C23×C4×C139C2311yescharacteristic
103C23×C4×C139C2311yescharacteristic
104#135×C139—232no—
105C2×Q16×C139—22no—
106C2×Q16×C139—22no—
107C2×Q16×C139D414yescomplemented
108C2×SD16×C139—22no—
109C2×SD16×C139—22no—
110C2×SD16×C139—22no—
111C2×SD16×C139—22no—
112C2×SD16×C139—22no—
113C2×SD16×C139—22no—
114C2×SD16×C139—22no—
115C2×SD16×C139—41no—
116C2×SD16×C139D414yescomplemented
117C2×D8×C139—22no—
118C2×D8×C139—22no—
119C2×D8×C139—22no—
120C2×D8×C139—22no—
121C2×D8×C139—22no—
122C2×D8×C139—41no—
123C22×C8×C139—22no—
124C22×C8×C139—22no—
125C22×C8×C139—22no—
126C22×C8×C139C2311yescharacteristic
127C22×C8×C139C2311yescharacteristic
128C22×C8×C139C2311yescharacteristic
129C22×C8×C139C2311yescharacteristic
130#127×C139—28no—
131#127×C139—22no—
132#127×C139—22no—
133C22⋊Q8×C139—22no—
134C22⋊Q8×C139—41no—
135#121×C139—28no—
136#121×C139—28no—
137#121×C139—22no—
138#121×C139—22no—
139#121×C139—22no—
140#121×C139—22no—
141#121×C139—41no—
142#121×C139D414yescomplemented
143C4×Q8×C139—22no—
144C4×Q8×C139—22no—
145C4×D4×C139—28no—
146C4×D4×C139—22no—
147C4×D4×C139—22no—
148C2×C4⋊C4×C139—21no—
149C2×C4⋊C4×C139—21no—
150C2×C4⋊C4×C139D411yescharacteristic
151C2×C4⋊C4×C139C2311yescharacteristic
152C2×C4⋊C4×C139C2311yescharacteristic
153C2×C4⋊C4×C139C2311yescharacteristic
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×C139D411yescharacteristic
162C2×C22⋊C4×C139D411yescharacteristic
163C2×C42×C139—21no—
164C2×C42×C139C2311yescharacteristic
165#103×C139—22no—
166#103×C139—22no—
167#103×C139—22no—
168#102×C139—22no—
169#102×C139—22no—
170#102×C139—22no—
171#102×C139—41no—
172#102×C139—41no—
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—21no—
181C24×C139—21no—
182C24×C139C2×D411yescharacteristic
183C24×C139C2×D411yescharacteristic
184#41×C139—28no—
185#41×C139—28no—
186#41×C139—44no—
187#41×C139—44no—
188#41×C139—44no—
189#41×C139—44no—
190#41×C139—44no—
191#41×C139—44no—
192#41×C139—44no—
193#41×C139—44no—
194#41×C139—44no—
195#41×C139—44no—
196C2×Q8×C139—21no—
197C2×Q8×C139—21no—
198C2×Q8×C139—21no—
199C2×Q8×C139—21no—
200C2×Q8×C139—21no—
201C2×Q8×C139—21no—
202C2×Q8×C139—21no—
203C2×Q8×C139—21no—
204C2×Q8×C139C2×D412yes—
205C2×Q8×C139C2×D412yes—
206C2×Q8×C139C2×D412yes—
207C2×Q8×C139C2×D412yes—
208C2×D4×C139—24no—
209C2×D4×C139—24no—
210C2×D4×C139—22no—
211C2×D4×C139—24no—
212C2×D4×C139—24no—
213C2×D4×C139—24no—
214C2×D4×C139—24no—
215C2×D4×C139—22no—
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—21no—
230C2×D4×C139—21no—
231C2×D4×C139—41no—
232C2×D4×C139—42no—
233C2×D4×C139—42no—
234C2×D4×C139—42no—
235C2×D4×C139—42no—
236C2×D4×C139—42no—
237C2×D4×C139—42no—
238C2×D4×C139—42no—
239C2×D4×C139—42no—
240C2×D4×C139—42no—
241C2×D4×C139—42no—
242C2×D4×C139—42no—
243C2×D4×C139—81no—
244C2×D4×C139—81no—
245C2×D4×C139—81no—
246C2×D4×C139—81no—
247C2×D4×C139—81no—
248C2×D4×C139—81no—
249C2×D4×C139—81no—
250C2×D4×C139C2×D412yes—
251C2×D4×C139C2×D412yes—
252C2×D4×C139C2×D412yes—
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—21no—
260C22×C4×C139—21no—
261C22×C4×C139—24no—
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—21no—
269C22×C4×C139—21no—
270C22×C4×C139—42no—
271C22×C4×C139—42no—
272C22×C4×C139—42no—
273C22×C4×C139—42no—
274C22×C4×C139—42no—
275C22×C4×C139—42no—
276C22×C4×C139—42no—
277C22×C4×C139C2×D411yescharacteristic
278C22×C4×C139C2×D411yescharacteristic
279C22×C4×C139C2×D411yescharacteristic
280C22×C4×C139C2×D412yes—
281C22×C4×C139C2×D412yes—
282C22×C4×C139C2×D411yescharacteristic
283C22×C4×C139C2411yescharacteristic
284Q16×C139—28no—
285SD16×C139—28no—
286SD16×C139—28no—
287SD16×C139—44no—
288D8×C139—28no—
289D8×C139—44no—
290C2×C8×C139—28no—
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×C139—21no—
300C2×C8×C139—21no—
301C2×C8×C139C2×D412yes—
302C2×C8×C139C2×D412yes—
303C4⋊C4×C139—24no—
304C4⋊C4×C139—22no—
305C4⋊C4×C139—21no—
306C4⋊C4×C139—21no—
307C4⋊C4×C139—21no—
308C4⋊C4×C139—21no—
309C4⋊C4×C139—21no—
310C4⋊C4×C139—42no—
311C4⋊C4×C139C2×D412yes—
312C22⋊C4×C139—24no—
313C22⋊C4×C139—22no—
314C22⋊C4×C139—24no—
315C22⋊C4×C139—22no—
316C22⋊C4×C139—42no—
317C22⋊C4×C139—42no—
318C22⋊C4×C139—42no—
319C22⋊C4×C139—81no—
320C22⋊C4×C139—81no—
321C42×C139—24no—
322C42×C139—21no—
323C42×C139—21no—
324C23×C139—21no—
325C23×C139—21no—
326C23×C139—21no—
327C23×C139—21no—
328C23×C139—21no—
329C23×C139—21no—
330C23×C139—21no—
331C23×C139—22no—
332C23×C139—22no—
333C23×C139—21no—
334C23×C139—22no—
335C23×C139—21no—
336C23×C139—21no—
337C23×C139—21no—
338C23×C139—21no—
339C23×C139—21no—
340C23×C139—41no—
341C23×C139—41no—
342C23×C139—41no—
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#12012yes—
359C23×C139C22×D411yescharacteristic
360Q8×C139—22no—
361Q8×C139—22no—
362Q8×C139—22no—
363Q8×C139—22no—
364Q8×C139—22no—
365Q8×C139—41no—
366Q8×C139—41no—
367Q8×C139#12014yes—
368D4×C139—22no—
369D4×C139—22no—
370D4×C139—22no—
371D4×C139—22no—
372D4×C139—22no—
373D4×C139—22no—
374D4×C139—44no—
375D4×C139—48no—
376D4×C139—48no—
377D4×C139—48no—
378D4×C139—48no—
379D4×C139—41no—
380D4×C139—41no—
381D4×C139—41no—
382D4×C139—41no—
383D4×C139—41no—
384D4×C139—41no—
385D4×C139—84no—
386D4×C139—84no—
387D4×C139—84no—
388D4×C139—84no—
389C2×C4×C139—21no—
390C2×C4×C139—22no—
391C2×C4×C139—21no—
392C2×C4×C139—21no—
393C2×C4×C139—22no—
394C2×C4×C139—22no—
395C2×C4×C139—21no—
396C2×C4×C139—22no—
397C2×C4×C139—22no—
398C2×C4×C139—22no—
399C2×C4×C139—22no—
400C2×C4×C139—21no—
401C2×C4×C139—22no—
402C2×C4×C139—21no—
403C2×C4×C139—21no—
404C2×C4×C139—22no—
405C2×C4×C139—21no—
406C2×C4×C139—21no—
407C2×C4×C139—21no—
408C2×C4×C139—48no—
409C2×C4×C139—48no—
410C2×C4×C139—48no—
411C2×C4×C139—41no—
412C2×C4×C139—41no—
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#12012yes—
426C2×C4×C139#13512yescomplemented
427C2×C4×C139C22×D411yescharacteristic
428C2×C4×C139C22×D411yescharacteristic
429C2×C4×C139C22×D411yescharacteristic
430C2×C4×C139C22×D411yescharacteristic
431C2×C4×C139H(5,𝔽2)11yescharacteristic
432C2×C4×C139H(5,𝔽2)11yescharacteristic
433C8×C139—22no—
434C8×C139—22no—
435C8×C139—41no—
436C8×C139—41no—
437C22×C139—22no—
438C22×C139—22no—
439C22×C139—22no—
440C22×C139—41no—
441C22×C139—41no—
442C22×C139—41no—
443C22×C139—41no—
444C22×C139—42no—
445C22×C139—42no—
446C22×C139—42no—
447C22×C139—41no—
448C22×C139—41no—
449C22×C139—42no—
450C22×C139—42no—
451C22×C139—41no—
452C22×C139—42no—
453C22×C139—42no—
454C22×C139—41no—
455C22×C139—42no—
456C22×C139—41no—
457C22×C139—41no—
458C22×C139—42no—
459C22×C139—41no—
460C22×C139—81no—
461C22×C139—81no—
462C22×C139—81no—
463C22×C139—81no—
464C22×C139—81no—
465C22×C139—81no—
466C22×C139—81no—
467C22×C139—81no—
468C22×C139—81no—
469C22×C139—81no—
470C22×C139—81no—
471C22×C139—81no—
472C22×C139C2×#12011yescharacteristic
473C22×C139D4211yescharacteristic
474C22×C139D4211yescharacteristic
475C22×C139C2×#13511yescharacteristic
476C22×C139#57511yescharacteristic
477C22×C139#57611yescharacteristic
478C22×C139#57711yescharacteristic
479C4×C139—22no—
480C4×C139—24no—
481C4×C139—22no—
482C4×C139—41no—
483C4×C139—42no—
484C4×C139—41no—
485C4×C139—42no—
486C4×C139—81no—
487C4×C139—81no—
488C4×C139C2×#12011yescharacteristic
489C4×C139#53411yescharacteristic
490C4×C139D4211yescharacteristic
491C4×C139D4211yescharacteristic
492C2×C139—42no—
493C2×C139—81no—
494C2×C139—82no—
495C2×C139—82no—
496C2×C139—82no—
497C2×C139#240311yescharacteristic
498C2×C139#300211yescharacteristic
499C2×C139#301211yescharacteristic
500C2×C139#326811yescharacteristic
501C2×C139#327111yescharacteristic
502C2×C139#328411yescharacteristic
503C2×C139#328711yescharacteristic
504#23857C13911yesmaximal, characteristic, direct product factor, Sylow
505C139#2385711yescharacteristic, direct product factor, Sylow
506C22×#135C2×C13911yescharacteristic, complemented
507C2×#550C2×C13911yescharacteristic, complemented
508C2×#452C2×C13911yescharacteristic, complemented
509C2×#449C2×C13911yescharacteristic, complemented
510C2×#449C2×C13911yescharacteristic, complemented
511#2407C2×C13911yescharacteristic, complemented
512#2014C2×C13911yescharacteristic, complemented
513#2011C2×C13911yescharacteristic, complemented
514#2000C2×C13911yescharacteristic, complemented
515#1999C2×C13911yescharacteristic, complemented
516#1893C2×C13911yescharacteristic, complemented
517#1880C2×C13911yescharacteristic, complemented
518#1878C2×C13911yescharacteristic, complemented
519#1869C2×C13911yescharacteristic, complemented
520#1788C2×C13911yescharacteristic, complemented
521C22×#41C22×C13911yescharacteristic
522C22×#41C22×C13911yescharacteristic
523C22×#41C22×C13911yescharacteristic
524C2×#135—24no—
525C2×#135—24no—
526C2×#135—24no—
527C22×Q16C22×C13911yescharacteristic
528C22×SD16C22×C13911yescharacteristic
529C22×SD16C22×C13911yescharacteristic
530C22×SD16C22×C13911yescharacteristic
531C22×D8C22×C13911yescharacteristic
532C22×D8C22×C13911yescharacteristic
533C23×C8C22×C13911yescharacteristic
534#550—24no—
535#550—24no—
536C2×#127—21no—
537C2×#127C22×C13911yescharacteristic
538C2×C22⋊Q8C22×C13911yescharacteristic
539C2×#121—21no—
540C2×#121—21no—
541C2×#121C22×C13911yescharacteristic
542C2×#121C22×C13911yescharacteristic
543C2×#121C22×C13911yescharacteristic
544C2×C4×Q8C22×C13911yescharacteristic
545C2×C4×D4—21no—
546C2×C4×D4C22×C13911yescharacteristic
547#452—24no—
548#449—24no—
549#449—24no—
550C2×#103C22×C13911yescharacteristic
551C2×#103C22×C13911yescharacteristic
552C2×#103C22×C13911yescharacteristic
553C2×#102C22×C13911yescharacteristic
554C2×#102C22×C13911yescharacteristic
555C2×#102C22×C13911yescharacteristic
556C2×#102C22×C13911yescharacteristic
557C2×#102C22×C13911yescharacteristic
558C2×C22⋊C8C22×C13911yescharacteristic
559C2×C22⋊C8C22×C13911yescharacteristic
560C2×C22⋊C8C22×C13911yescharacteristic
561#394—21no—
562#392—21no—
563#391C22×C13911yescharacteristic
564#390C22×C13911yescharacteristic
565#386—21no—
566#385—21no—
567#380C22×C13911yescharacteristic
568#340C22×C13911yescharacteristic
569#340C22×C13911yescharacteristic
570#336C22×C13911yescharacteristic
571#336C22×C13911yescharacteristic
572C2×#41—22no—
573C2×#41—22no—
574C2×#41—22no—
575C2×#41—22no—
576C2×#41—22no—
577C2×#41—22no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—41no—
584C2×#41—41no—
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—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—21no—
600C22×D4D4×C13911yescharacteristic
601C22×D4C23×C13911yescharacteristic
602C22×D4C23×C13911yescharacteristic
603C22×D4C23×C13911yescharacteristic
604C23×C4—21no—
605C23×C4—21no—
606C23×C4—21no—
607C23×C4C23×C13911yescharacteristic
608C23×C4C23×C13911yescharacteristic
609#135—232no—
610C2×Q16—22no—
611C2×Q16—22no—
612C2×Q16D4×C13914yescomplemented
613C2×SD16—22no—
614C2×SD16—22no—
615C2×SD16—22no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—41no—
621C2×SD16D4×C13914yescomplemented
622C2×D8—22no—
623C2×D8—22no—
624C2×D8—22no—
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—41no—
628C22×C8—22no—
629C22×C8—22no—
630C22×C8—22no—
631C22×C8C23×C13911yescharacteristic
632C22×C8C23×C13911yescharacteristic
633C22×C8C23×C13911yescharacteristic
634C22×C8C23×C13911yescharacteristic
635#127—28no—
636#127—22no—
637#127—22no—
638C22⋊Q8—22no—
639C22⋊Q8—41no—
640#121—28no—
641#121—28no—
642#121—22no—
643#121—22no—
644#121—22no—
645#121—22no—
646#121—41no—
647#121D4×C13914yescomplemented
648C4×Q8—22no—
649C4×Q8—22no—
650C4×D4—28no—
651C4×D4—22no—
652C4×D4—22no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4D4×C13911yescharacteristic
656C2×C4⋊C4C23×C13911yescharacteristic
657C2×C4⋊C4C23×C13911yescharacteristic
658C2×C4⋊C4C23×C13911yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4D4×C13911yescharacteristic
667C2×C22⋊C4D4×C13911yescharacteristic
668C2×C42—21no—
669C2×C42C23×C13911yescharacteristic
670#103—22no—
671#103—22no—
672#103—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—41no—
677#102—41no—
678C22⋊C8—22no—
679C22⋊C8—22no—
680C22⋊C8—22no—
681#95—21no—
682#95—21no—
683#95—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×D4×C13911yescharacteristic
688C24C2×D4×C13911yescharacteristic
689#41—28no—
690#41—28no—
691#41—44no—
692#41—44no—
693#41—44no—
694#41—44no—
695#41—44no—
696#41—44no—
697#41—44no—
698#41—44no—
699#41—44no—
700#41—44no—
701C2×Q8—21no—
702C2×Q8—21no—
703C2×Q8—21no—
704C2×Q8—21no—
705C2×Q8—21no—
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—21no—
709C2×Q8C2×D4×C13912yes—
710C2×Q8C2×D4×C13912yes—
711C2×Q8C2×D4×C13912yes—
712C2×Q8C2×D4×C13912yes—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—24no—
718C2×D4—24no—
719C2×D4—24no—
720C2×D4—22no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
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—41no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4C2×D4×C13912yes—
756C2×D4C2×D4×C13912yes—
757C2×D4C2×D4×C13912yes—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—24no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—42no—
776C22×C4—42no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4C2×D4×C13911yescharacteristic
783C22×C4C2×D4×C13911yescharacteristic
784C22×C4C2×D4×C13911yescharacteristic
785C22×C4C2×D4×C13912yes—
786C22×C4C2×D4×C13912yes—
787C22×C4C2×D4×C13911yescharacteristic
788C22×C4C24×C13911yescharacteristic
789Q16—28no—
790SD16—28no—
791SD16—28no—
792SD16—44no—
793D8—28no—
794D8—44no—
795C2×C8—28no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8C2×D4×C13912yes—
807C2×C8C2×D4×C13912yes—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—42no—
816C4⋊C4C2×D4×C13912yes—
817C22⋊C4—24no—
818C22⋊C4—22no—
819C22⋊C4—24no—
820C22⋊C4—22no—
821C22⋊C4—42no—
822C22⋊C4—42no—
823C22⋊C4—42no—
824C22⋊C4—81no—
825C22⋊C4—81no—
826C42—24no—
827C42—21no—
828C42—21no—
829C23—21no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—22no—
838C23—21no—
839C23—22no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23#120×C13912yes—
864C23C22×D4×C13911yescharacteristic
865Q8—22no—
866Q8—22no—
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—41no—
871Q8—41no—
872Q8#120×C13914yes—
873D4—22no—
874D4—22no—
875D4—22no—
876D4—22no—
877D4—22no—
878D4—22no—
879D4—44no—
880D4—48no—
881D4—48no—
882D4—48no—
883D4—48no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—84no—
891D4—84no—
892D4—84no—
893D4—84no—
894C2×C4—21no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—22no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—22no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—48no—
914C2×C4—48no—
915C2×C4—48no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4#120×C13912yes—
931C2×C4#135×C13912yescomplemented
932C2×C4C22×D4×C13911yescharacteristic
933C2×C4C22×D4×C13911yescharacteristic
934C2×C4C22×D4×C13911yescharacteristic
935C2×C4C22×D4×C13911yescharacteristic
936C2×C4H(5,𝔽2)×C13911yescharacteristic
937C2×C4H(5,𝔽2)×C13911yescharacteristic
938C8—22no—
939C8—22no—
940C8—41no—
941C8—41no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—42no—
951C22—41no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—41no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—42no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22C2×#120×C13911yescharacteristic
978C22D42×C13911yescharacteristic
979C22D42×C13911yescharacteristic
980C22C2×#135×C13911yescharacteristic
981C22#575×C13911yescharacteristic
982C22#576×C13911yescharacteristic
983C22#577×C13911yescharacteristic
984C4—22no—
985C4—24no—
986C4—22no—
987C4—41no—
988C4—42no—
989C4—41no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4C2×#120×C13911yescharacteristic
994C4#534×C13911yescharacteristic
995C4D42×C13911yescharacteristic
996C4D42×C13911yescharacteristic
997C2—42no—
998C2—81no—
999C2—82no—
1000C2—82no—
1001C2—82no—
1002C2#2403×C13911yescharacteristic
1003C2#3002×C13911yescharacteristic
1004C2#3012×C13911yescharacteristic
1005C2#3268×C13911yescharacteristic
1006C2#3271×C13911yescharacteristic
1007C2#3284×C13911yescharacteristic
1008C2#3287×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×#550×C139C2semidirect
3. C2×#452×C139C2semidirect
4. C2×#449×C139C2semidirect
5. C2×#449×C139C2semidirect
6. #2407×C139C2semidirect
7. #2014×C139C2semidirect
8. #2011×C139C2semidirect
9. #2000×C139C2semidirect
10. #1999×C139C2semidirect
11. #1893×C139C2semidirect
12. #1880×C139C2semidirect
13. #1878×C139C2semidirect
14. #1869×C139C2semidirect
15. #1788×C139C2semidirect
84. C2×#41×C139D4semidirect
107. C2×Q16×C139D4semidirect
116. C2×SD16×C139D4semidirect
142. #121×C139D4semidirect
426. C2×C4×C139#135semidirect
504. #23857C139direct (N × H)
505. C139#23857direct (N × H)
506. C22×#135C2×C139semidirect
507. C2×#550C2×C139semidirect
508. C2×#452C2×C139semidirect
509. C2×#449C2×C139semidirect
510. C2×#449C2×C139semidirect
511. #2407C2×C139semidirect
512. #2014C2×C139semidirect
513. #2011C2×C139semidirect
514. #2000C2×C139semidirect
515. #1999C2×C139semidirect
516. #1893C2×C139semidirect
517. #1880C2×C139semidirect
518. #1878C2×C139semidirect
519. #1869C2×C139semidirect
520. #1788C2×C139semidirect
589. C2×#41D4×C139semidirect
612. C2×Q16D4×C139semidirect
621. C2×SD16D4×C139semidirect
647. #121D4×C139semidirect
931. C2×C4#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×#550×C1392
C2×#452×C1392
C2×#449×C1392
#2407×C1392
#2014×C1392
#2011×C1392
#2000×C1392
#1999×C1392
#1893×C1392
#1880×C1392
#1878×C1392
#1869×C1392
#1788×C1392
#23857139