Finite Group Databasebeta

← C139×#18434 #48013030

Subgroups — C139×#18434 #48013030

Order 35584.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3560×C139C211yesmaximal, characteristic, complemented
2#3213×C139C211yesmaximal, characteristic, complemented
3#3211×C139C211yesmaximal, characteristic, complemented
4#2662×C139C211yesmaximal, characteristic, complemented
5#1606×C139C211yesmaximal, characteristic, complemented
6#1604×C139C211yesmaximal, characteristic, complemented
7#1603×C139C211yesmaximal, characteristic, complemented
8#1601×C139C211yesmaximal, characteristic, complemented
9#1600×C139C211yesmaximal, characteristic, complemented
10#1598×C139C211yesmaximal, characteristic, complemented
11#1597×C139C211yesmaximal, characteristic, complemented
12#1595×C139C211yesmaximal, characteristic, complemented
13#1509×C139C211yesmaximal, characteristic, complemented
14#1502×C139C211yesmaximal, characteristic, complemented
15#1473×C139C211yesmaximal, characteristic, complemented
16#563×C139—21no—
17#560×C139—21no—
18#553×C139—21no—
19#553×C139—21no—
20#551×C139—21no—
21#547×C139—21no—
22#546×C139—21no—
23#546×C139—21no—
24#542×C139—21no—
25#539×C139—21no—
26#539×C139C2211yescharacteristic
27#538×C139—21no—
28#538×C139—21no—
29#538×C139C2211yescharacteristic
30#537×C139C2211yescharacteristic
31#534×C139C2211yescharacteristic
32#532×C139C2211yescharacteristic
33#529×C139C2211yescharacteristic
34C2×#126×C139C2211yescharacteristic
35C2×#124×C139C2211yescharacteristic, complemented
36#496×C139—21no—
37#495×C139—21no—
38#489×C139—21no—
39#488×C139—21no—
40#464×C139—21no—
41#463×C139—21no—
42#463×C139—21no—
43#463×C139—21no—
44#451×C139C2211yescharacteristic, complemented
45#450×C139C2211yescharacteristic, complemented
46#448×C139C2211yescharacteristic
47#448×C139C2211yescharacteristic
48#448×C139C2211yescharacteristic, complemented
49#447×C139C2211yescharacteristic
50#447×C139C2211yescharacteristic
51#447×C139C2211yescharacteristic, complemented
52#432×C139C2211yescharacteristic, complemented
53#431×C139C2211yescharacteristic, complemented
54#396×C139—21no—
55#395×C139C2211yescharacteristic, complemented
56#394×C139—21no—
57#394×C139C2211yescharacteristic, complemented
58#393×C139C2211yescharacteristic
59#392×C139C2211yescharacteristic
60#390×C139—21no—
61#388×C139—21no—
62C4×C4⋊C4×C139C2211yescharacteristic, complemented
63#328×C139C2211yescharacteristic, complemented
64#328×C139C2211yescharacteristic, complemented
65#327×C139C2211yescharacteristic
66#327×C139C2211yescharacteristic
67#327×C139C2211yescharacteristic
68#327×C139C2211yescharacteristic
69#327×C139C2211yescharacteristic, complemented
70#327×C139C2211yescharacteristic, complemented
71#324×C139C2211yescharacteristic, complemented
72#324×C139C2211yescharacteristic, complemented
73#323×C139C2211yescharacteristic
74#323×C139C2211yescharacteristic
75C2×#41×C139—21no—
76C2×#41×C139—21no—
77C22×Q8×C139C2311yescharacteristic
78C22×D4×C139—21no—
79C22×D4×C139—21no—
80C22×D4×C139C2311yescharacteristic
81C2×Q16×C139—21no—
82C2×SD16×C139—21no—
83C2×SD16×C139—21no—
84C2×SD16×C139—21no—
85C2×SD16×C139—21no—
86C2×D8×C139—21no—
87C2×D8×C139—21no—
88C2×D8×C139—21no—
89C4⋊Q8×C139—21no—
90C4⋊Q8×C139D411yescharacteristic, complemented
91#127×C139D411yescharacteristic, complemented
92#126×C139—21no—
93#126×C139—21no—
94#126×C139—21no—
95#126×C139—21no—
96#126×C139—21no—
97#126×C139—21no—
98#126×C139—21no—
99#126×C139—21no—
100#126×C139—21no—
101#125×C139—21no—
102#125×C139—21no—
103#125×C139D411yescharacteristic, complemented
104#124×C139—21no—
105#124×C139—21no—
106#124×C139—21no—
107#124×C139—21no—
108#124×C139—21no—
109#124×C139—21no—
110#124×C139—21no—
111#124×C139—21no—
112#124×C139D411yescharacteristic, complemented
113#123×C139—21no—
114#123×C139—21no—
115#123×C139—21no—
116#123×C139—21no—
117#123×C139—21no—
118#123×C139—21no—
119#123×C139—21no—
120#123×C139—21no—
121#123×C139—21no—
122#123×C139—21no—
123#123×C139—21no—
124#123×C139—21no—
125C22⋊Q8×C139—21no—
126C22⋊Q8×C139—21no—
127C22⋊Q8×C139—21no—
128C22⋊Q8×C139—21no—
129C22⋊Q8×C139—21no—
130C22⋊Q8×C139—21no—
131C22⋊Q8×C139—21no—
132C22⋊Q8×C139C2311yescharacteristic
133#121×C139—21no—
134#121×C139—21no—
135#121×C139—21no—
136#121×C139—21no—
137#121×C139—21no—
138#121×C139—21no—
139#121×C139—21no—
140#121×C139—21no—
141#121×C139—21no—
142#121×C139—21no—
143#121×C139—21no—
144#121×C139—21no—
145#121×C139C2311yescharacteristic
146#121×C139C2311yescharacteristic
147#121×C139C2311yescharacteristic
148#120×C139—21no—
149#120×C139—21no—
150#120×C139—21no—
151#120×C139—21no—
152#120×C139—21no—
153C4×Q8×C139D411yescharacteristic, complemented
154C4×D4×C139—21no—
155C4×D4×C139—21no—
156C4×D4×C139—21no—
157C4×D4×C139—21no—
158C4×D4×C139—21no—
159C4×D4×C139—21no—
160C4×D4×C139—21no—
161C4×D4×C139—21no—
162C4×D4×C139D411yescharacteristic, complemented
163C4×D4×C139D411yescharacteristic, complemented
164C4×D4×C139D411yescharacteristic, complemented
165#117×C139—21no—
166#117×C139—21no—
167C2×C4⋊C4×C139—21no—
168C2×C4⋊C4×C139—21no—
169C2×C4⋊C4×C139—21no—
170C2×C4⋊C4×C139D411yescharacteristic
171C2×C4⋊C4×C139D411yescharacteristic
172C2×C4⋊C4×C139C2311yescharacteristic
173C2×C22⋊C4×C139—21no—
174C2×C22⋊C4×C139—21no—
175C2×C22⋊C4×C139—21no—
176C2×C22⋊C4×C139—21no—
177C2×C22⋊C4×C139—21no—
178C2×C22⋊C4×C139—21no—
179C2×C22⋊C4×C139—21no—
180C2×C22⋊C4×C139—21no—
181C2×C22⋊C4×C139D411yescharacteristic
182C2×C22⋊C4×C139D411yescharacteristic
183C2×C22⋊C4×C139C2311yescharacteristic
184C2×C42×C139—21no—
185C2×C42×C139C2311yescharacteristic
186C4⋊C8×C139—21no—
187C4⋊C8×C139—21no—
188#103×C139—21no—
189#103×C139—21no—
190#103×C139—21no—
191#103×C139—21no—
192#102×C139—21no—
193#102×C139—21no—
194#102×C139—21no—
195#102×C139—21no—
196C22⋊C8×C139C2311yescharacteristic
197C22⋊C8×C139C2311yescharacteristic
198C22⋊C8×C139C2311yescharacteristic
199C22⋊C8×C139C2311yescharacteristic
200#97×C139—21no—
201C4×C8×C139—21no—
202#95×C139—21no—
203#95×C139—21no—
204#95×C139C2311yescharacteristic
205#95×C139C2311yescharacteristic
206C24×C139—21no—
207C24×C139—21no—
208C24×C139C2×D411yescharacteristic
209#41×C139—81no—
210#41×C139—81no—
211#41×C139—81no—
212#41×C139—81no—
213C2×Q8×C139—21no—
214C2×Q8×C139—21no—
215C2×Q8×C139—21no—
216C2×Q8×C139—21no—
217C2×Q8×C139—81no—
218C2×Q8×C139C2×D411yescharacteristic
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—21no—
232C2×D4×C139—21no—
233C2×D4×C139—42no—
234C2×D4×C139—81no—
235C2×D4×C139—81no—
236C2×D4×C139—81no—
237C2×D4×C139—81no—
238C2×D4×C139—81no—
239C2×D4×C139C2×D411yescharacteristic
240C2×D4×C139C2×D411yescharacteristic
241C2×D4×C139C2×D411yescharacteristic
242C22×C4×C139—21no—
243C22×C4×C139—21no—
244C22×C4×C139—21no—
245C22×C4×C139—21no—
246C22×C4×C139—21no—
247C22×C4×C139—21no—
248C22×C4×C139—21no—
249C22×C4×C139—21no—
250C22×C4×C139—21no—
251C22×C4×C139—21no—
252C22×C4×C139—21no—
253C22×C4×C139C2×D411yescharacteristic
254C22×C4×C139C2×D411yescharacteristic
255C22×C4×C139C2×D411yescharacteristic
256C22×C4×C139C2×D411yescharacteristic
257C22×C4×C139C2×D411yescharacteristic
258C22×C4×C139C2411yescharacteristic
259Q16×C139—81no—
260SD16×C139—81no—
261SD16×C139—81no—
262SD16×C139—81no—
263SD16×C139—81no—
264D8×C139—81no—
265D8×C139—81no—
266D8×C139—81no—
267C2×C8×C139—21no—
268C2×C8×C139—21no—
269C2×C8×C139—21no—
270C2×C8×C139—21no—
271C4⋊C4×C139—21no—
272C4⋊C4×C139—21no—
273C4⋊C4×C139—21no—
274C4⋊C4×C139—21no—
275C4⋊C4×C139—21no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139—21no—
278C4⋊C4×C139—21no—
279C4⋊C4×C139—21no—
280C4⋊C4×C139—21no—
281C4⋊C4×C139—21no—
282C4⋊C4×C139—21no—
283C4⋊C4×C139—21no—
284C4⋊C4×C139—21no—
285C4⋊C4×C139—21no—
286C4⋊C4×C139—21no—
287C4⋊C4×C139—21no—
288C4⋊C4×C139—42no—
289C4⋊C4×C139—81no—
290C4⋊C4×C139C2×D411yescharacteristic
291C4⋊C4×C139C2×D411yescharacteristic
292C4⋊C4×C139C2×D411yescharacteristic
293C4⋊C4×C139C2×D411yescharacteristic
294C22⋊C4×C139—21no—
295C22⋊C4×C139—21no—
296C22⋊C4×C139—21no—
297C22⋊C4×C139—21no—
298C22⋊C4×C139—21no—
299C22⋊C4×C139—21no—
300C22⋊C4×C139—21no—
301C22⋊C4×C139—21no—
302C22⋊C4×C139—21no—
303C22⋊C4×C139—21no—
304C22⋊C4×C139—21no—
305C22⋊C4×C139—21no—
306C22⋊C4×C139—21no—
307C22⋊C4×C139—21no—
308C22⋊C4×C139—21no—
309C22⋊C4×C139—21no—
310C22⋊C4×C139—21no—
311C22⋊C4×C139—21no—
312C22⋊C4×C139—21no—
313C22⋊C4×C139—21no—
314C22⋊C4×C139—21no—
315C22⋊C4×C139—21no—
316C22⋊C4×C139—21no—
317C22⋊C4×C139—21no—
318C22⋊C4×C139—21no—
319C22⋊C4×C139—42no—
320C22⋊C4×C139—41no—
321C22⋊C4×C139—41no—
322C22⋊C4×C139—41no—
323C22⋊C4×C139—41no—
324C22⋊C4×C139—81no—
325C22⋊C4×C139—81no—
326C22⋊C4×C139—81no—
327C42×C139—21no—
328C42×C139—21no—
329C42×C139—21no—
330C42×C139—81no—
331C42×C139C2×D411yescharacteristic
332C42×C139C2×D411yescharacteristic
333C42×C139C2×D411yescharacteristic
334C42×C139C2×D411yescharacteristic
335C23×C139—21no—
336C23×C139—21no—
337C23×C139—21no—
338C23×C139—21no—
339C23×C139—21no—
340C23×C139—21no—
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—81no—
351C23×C139—81no—
352C23×C139—81no—
353C23×C139C22×D411yescharacteristic
354Q8×C139—41no—
355Q8×C139—41no—
356Q8×C139—41no—
357Q8×C139—41no—
358Q8×C139—41no—
359Q8×C139—81no—
360Q8×C139—81no—
361D4×C139—41no—
362D4×C139—41no—
363D4×C139—41no—
364D4×C139—41no—
365D4×C139—41no—
366D4×C139—41no—
367D4×C139—41no—
368D4×C139—41no—
369D4×C139—41no—
370D4×C139—41no—
371D4×C139—41no—
372D4×C139—41no—
373D4×C139—41no—
374D4×C139—81no—
375D4×C139—81no—
376D4×C139—81no—
377D4×C139—81no—
378D4×C139—81no—
379D4×C139—81no—
380D4×C139—81no—
381D4×C139—81no—
382D4×C139—81no—
383D4×C139—84no—
384C2×C4×C139—21no—
385C2×C4×C139—21no—
386C2×C4×C139—22no—
387C2×C4×C139—21no—
388C2×C4×C139—21no—
389C2×C4×C139—21no—
390C2×C4×C139—21no—
391C2×C4×C139—21no—
392C2×C4×C139—21no—
393C2×C4×C139—21no—
394C2×C4×C139—21no—
395C2×C4×C139—21no—
396C2×C4×C139—21no—
397C2×C4×C139—41no—
398C2×C4×C139—41no—
399C2×C4×C139—41no—
400C2×C4×C139—41no—
401C2×C4×C139—41no—
402C2×C4×C139—41no—
403C2×C4×C139—41no—
404C2×C4×C139—41no—
405C2×C4×C139—41no—
406C2×C4×C139—41no—
407C2×C4×C139—41no—
408C2×C4×C139—41no—
409C2×C4×C139—81no—
410C2×C4×C139—81no—
411C2×C4×C139—81no—
412C2×C4×C139—81no—
413C2×C4×C139—81no—
414C2×C4×C139—81no—
415C2×C4×C139—81no—
416C2×C4×C139—81no—
417C2×C4×C139#12011yescharacteristic
418C2×C4×C139#12011yescharacteristic
419C2×C4×C139#12011yescharacteristic
420C2×C4×C139#12011yescharacteristic
421C2×C4×C139C22×D411yescharacteristic
422C2×C4×C139C22×D411yescharacteristic
423C8×C139—41no—
424C8×C139—41no—
425C8×C139—41no—
426C8×C139—41no—
427C22×C139—21no—
428C22×C139—21no—
429C22×C139—41no—
430C22×C139—41no—
431C22×C139—41no—
432C22×C139—41no—
433C22×C139—41no—
434C22×C139—41no—
435C22×C139—41no—
436C22×C139—41no—
437C22×C139—41no—
438C22×C139—41no—
439C22×C139—41no—
440C22×C139—41no—
441C22×C139—81no—
442C22×C139—81no—
443C22×C139—81no—
444C22×C139—81no—
445C22×C139—81no—
446C22×C139—81no—
447C22×C139—81no—
448C22×C139—81no—
449C22×C139—81no—
450C22×C139—162no—
451C22×C139C2×#12011yescharacteristic
452C22×C139#57611yescharacteristic
453C22×C139#57711yescharacteristic
454C4×C139—21no—
455C4×C139—21no—
456C4×C139—21no—
457C4×C139—21no—
458C4×C139—21no—
459C4×C139—21no—
460C4×C139—42no—
461C4×C139—41no—
462C4×C139—41no—
463C4×C139—41no—
464C4×C139—41no—
465C4×C139—41no—
466C4×C139—41no—
467C4×C139—41no—
468C4×C139—41no—
469C4×C139—81no—
470C4×C139—81no—
471C2×C139—21no—
472C2×C139—21no—
473C2×C139—81no—
474C2×C139—81no—
475C2×C139—81no—
476C2×C139—81no—
477C2×C139—161no—
478C2×C139#301211yescharacteristic
479C2×C139#301811yescharacteristic
480C2×C139#302711yescharacteristic
481#18434C13911yesmaximal, characteristic, direct product factor, Sylow
482C139#1843411yescharacteristic, direct product factor, Sylow
483#3560C2×C13911yescharacteristic, complemented
484#3213C2×C13911yescharacteristic, complemented
485#3211C2×C13911yescharacteristic, complemented
486#2662C2×C13911yescharacteristic, complemented
487#1606C2×C13911yescharacteristic, complemented
488#1604C2×C13911yescharacteristic, complemented
489#1603C2×C13911yescharacteristic, complemented
490#1601C2×C13911yescharacteristic, complemented
491#1600C2×C13911yescharacteristic, complemented
492#1598C2×C13911yescharacteristic, complemented
493#1597C2×C13911yescharacteristic, complemented
494#1595C2×C13911yescharacteristic, complemented
495#1509C2×C13911yescharacteristic, complemented
496#1502C2×C13911yescharacteristic, complemented
497#1473C2×C13911yescharacteristic, complemented
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C13911yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C13911yescharacteristic
512#537C22×C13911yescharacteristic
513#534C22×C13911yescharacteristic
514#532C22×C13911yescharacteristic
515#529C22×C13911yescharacteristic
516C2×#126C22×C13911yescharacteristic
517C2×#124C22×C13911yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C13911yescharacteristic, complemented
527#450C22×C13911yescharacteristic, complemented
528#448C22×C13911yescharacteristic
529#448C22×C13911yescharacteristic
530#448C22×C13911yescharacteristic, complemented
531#447C22×C13911yescharacteristic
532#447C22×C13911yescharacteristic
533#447C22×C13911yescharacteristic, complemented
534#432C22×C13911yescharacteristic, complemented
535#431C22×C13911yescharacteristic, complemented
536#396—21no—
537#395C22×C13911yescharacteristic, complemented
538#394—21no—
539#394C22×C13911yescharacteristic, complemented
540#393C22×C13911yescharacteristic
541#392C22×C13911yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C13911yescharacteristic, complemented
545#328C22×C13911yescharacteristic, complemented
546#328C22×C13911yescharacteristic, complemented
547#327C22×C13911yescharacteristic
548#327C22×C13911yescharacteristic
549#327C22×C13911yescharacteristic
550#327C22×C13911yescharacteristic
551#327C22×C13911yescharacteristic, complemented
552#327C22×C13911yescharacteristic, complemented
553#324C22×C13911yescharacteristic, complemented
554#324C22×C13911yescharacteristic, complemented
555#323C22×C13911yescharacteristic
556#323C22×C13911yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C13911yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C13911yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C13911yescharacteristic, complemented
573#127D4×C13911yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C13911yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C13911yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C13911yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C13911yescharacteristic
628#121C23×C13911yescharacteristic
629#121C23×C13911yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C13911yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C13911yescharacteristic, complemented
645C4×D4D4×C13911yescharacteristic, complemented
646C4×D4D4×C13911yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C13911yescharacteristic
653C2×C4⋊C4D4×C13911yescharacteristic
654C2×C4⋊C4C23×C13911yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C13911yescharacteristic
664C2×C22⋊C4D4×C13911yescharacteristic
665C2×C22⋊C4C23×C13911yescharacteristic
666C2×C42—21no—
667C2×C42C23×C13911yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C13911yescharacteristic
679C22⋊C8C23×C13911yescharacteristic
680C22⋊C8C23×C13911yescharacteristic
681C22⋊C8C23×C13911yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C13911yescharacteristic
687#95C23×C13911yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C13911yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C13911yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C13911yescharacteristic
722C2×D4C2×D4×C13911yescharacteristic
723C2×D4C2×D4×C13911yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C13911yescharacteristic
736C22×C4C2×D4×C13911yescharacteristic
737C22×C4C2×D4×C13911yescharacteristic
738C22×C4C2×D4×C13911yescharacteristic
739C22×C4C2×D4×C13911yescharacteristic
740C22×C4C24×C13911yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C13911yescharacteristic
773C4⋊C4C2×D4×C13911yescharacteristic
774C4⋊C4C2×D4×C13911yescharacteristic
775C4⋊C4C2×D4×C13911yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C13911yescharacteristic
814C42C2×D4×C13911yescharacteristic
815C42C2×D4×C13911yescharacteristic
816C42C2×D4×C13911yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C13911yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C13911yescharacteristic
900C2×C4#120×C13911yescharacteristic
901C2×C4#120×C13911yescharacteristic
902C2×C4#120×C13911yescharacteristic
903C2×C4C22×D4×C13911yescharacteristic
904C2×C4C22×D4×C13911yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C13911yescharacteristic
934C22#576×C13911yescharacteristic
935C22#577×C13911yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2#3012×C13911yescharacteristic
961C2#3018×C13911yescharacteristic
962C2#3027×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3560×C139C2semidirect
2. #3213×C139C2semidirect
3. #3211×C139C2semidirect
4. #2662×C139C2semidirect
5. #1606×C139C2semidirect
6. #1604×C139C2semidirect
7. #1603×C139C2semidirect
8. #1601×C139C2semidirect
9. #1600×C139C2semidirect
10. #1598×C139C2semidirect
11. #1597×C139C2semidirect
12. #1595×C139C2semidirect
13. #1509×C139C2semidirect
14. #1502×C139C2semidirect
15. #1473×C139C2semidirect
35. C2×#124×C139C22semidirect
44. #451×C139C22semidirect
45. #450×C139C22semidirect
48. #448×C139C22semidirect
51. #447×C139C22semidirect
52. #432×C139C22semidirect
53. #431×C139C22semidirect
55. #395×C139C22semidirect
57. #394×C139C22semidirect
62. C4×C4⋊C4×C139C22semidirect
63. #328×C139C22semidirect
64. #328×C139C22semidirect
69. #327×C139C22semidirect
70. #327×C139C22semidirect
71. #324×C139C22semidirect
72. #324×C139C22semidirect
90. C4⋊Q8×C139D4semidirect
91. #127×C139D4semidirect
103. #125×C139D4semidirect
112. #124×C139D4semidirect
153. C4×Q8×C139D4semidirect
162. C4×D4×C139D4semidirect
163. C4×D4×C139D4semidirect
164. C4×D4×C139D4semidirect
481. #18434C139direct (N × H)
482. C139#18434direct (N × H)
483. #3560C2×C139semidirect
484. #3213C2×C139semidirect
485. #3211C2×C139semidirect
486. #2662C2×C139semidirect
487. #1606C2×C139semidirect
488. #1604C2×C139semidirect
489. #1603C2×C139semidirect
490. #1601C2×C139semidirect
491. #1600C2×C139semidirect
492. #1598C2×C139semidirect
493. #1597C2×C139semidirect
494. #1595C2×C139semidirect
495. #1509C2×C139semidirect
496. #1502C2×C139semidirect
497. #1473C2×C139semidirect
517. C2×#124C22×C139semidirect
526. #451C22×C139semidirect
527. #450C22×C139semidirect
530. #448C22×C139semidirect
533. #447C22×C139semidirect
534. #432C22×C139semidirect
535. #431C22×C139semidirect
537. #395C22×C139semidirect
539. #394C22×C139semidirect
544. C4×C4⋊C4C22×C139semidirect
545. #328C22×C139semidirect
546. #328C22×C139semidirect
551. #327C22×C139semidirect
552. #327C22×C139semidirect
553. #324C22×C139semidirect
554. #324C22×C139semidirect
572. C4⋊Q8D4×C139semidirect
573. #127D4×C139semidirect
585. #125D4×C139semidirect
594. #124D4×C139semidirect
635. C4×Q8D4×C139semidirect
644. C4×D4D4×C139semidirect
645. C4×D4D4×C139semidirect
646. C4×D4D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3560×C1392
#3213×C1392
#3211×C1392
#2662×C1392
#1606×C1392
#1604×C1392
#1603×C1392
#1601×C1392
#1600×C1392
#1598×C1392
#1597×C1392
#1595×C1392
#1509×C1392
#1502×C1392
#1473×C1392
#18434139