Finite Group Databasebeta

← C139×#25890 #48020486

Subgroups — C139×#25890 #48020486

Order 35584.

1432 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C139C211yesmaximal, characteristic
2C2×#488×C139C211yesmaximal, characteristic, complemented
3C2×#478×C139C211yesmaximal, characteristic, complemented
4#2562×C139C211yesmaximal, characteristic, complemented
5#2036×C139C211yesmaximal, characteristic, complemented
6#2035×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#1983×C139C211yesmaximal, characteristic, complemented
10#1954×C139C211yesmaximal, characteristic, complemented
11#1788×C139C211yesmaximal, characteristic, complemented
12#1788×C139C211yesmaximal, characteristic, complemented
13#1786×C139C211yesmaximal, characteristic, complemented
14#1786×C139C211yesmaximal, characteristic, complemented
15C4×#102×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×D4×C139C2211yescharacteristic
18#546×C139—24no—
19#546×C139—24no—
20C2×#125×C139C2211yescharacteristic, complemented
21C2×#124×C139C2211yescharacteristic
22C2×#123×C139—21no—
23C2×C22⋊Q8×C139C2211yescharacteristic
24C2×#121×C139—21no—
25C2×#121×C139C2211yescharacteristic
26C2×#120×C139—21no—
27C2×C4×D4×C139C2211yescharacteristic
28C2×C4×D4×C139C2211yescharacteristic
29C22×C22⋊C4×C139—21no—
30#488×C139—24no—
31#478×C139—24no—
32C2×#107×C139C2211yescharacteristic, complemented
33C2×#106×C139C2211yescharacteristic, complemented
34C2×C4⋊C8×C139C2211yescharacteristic, complemented
35C2×#103×C139C2211yescharacteristic, complemented
36C2×#103×C139C2211yescharacteristic, complemented
37C2×#103×C139C2211yescharacteristic, complemented
38C2×#103×C139C2211yescharacteristic, complemented
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×#102×C139C2211yescharacteristic
47C2×C22⋊C8×C139C2211yescharacteristic
48C2×C22⋊C8×C139C2211yescharacteristic
49C2×C22⋊C8×C139C2211yescharacteristic, complemented
50C2×C22⋊C8×C139C2211yescharacteristic, complemented
51C2×C4×C8×C139C2211yescharacteristic, complemented
52#400×C139—21no—
53#394×C139—21no—
54#388×C139—21no—
55#388×C139—21no—
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic
58#380×C139C2211yescharacteristic, complemented
59#380×C139C2211yescharacteristic, complemented
60C4×C4⋊C4×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63C25×C139—21no—
64C2×#41×C139—22no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—41no—
69C2×#41×C139—41no—
70C22×Q8×C139C2311yescharacteristic
71C22×D4×C139—21no—
72C22×D4×C139—21no—
73C22×D4×C139—22no—
74C22×D4×C139—22no—
75C22×D4×C139—22no—
76C22×D4×C139—22no—
77C22×D4×C139—21no—
78C22×D4×C139—41no—
79C22×D4×C139—41no—
80C22×D4×C139D411yescharacteristic
81C22×D4×C139C2311yescharacteristic
82C22×D4×C139C2311yescharacteristic
83C23×C4×C139—21no—
84C23×C4×C139—21no—
85C23×C4×C139C2311yescharacteristic
86C23×C4×C139C2311yescharacteristic
87C22×C8×C139C2311yescharacteristic
88C22×C8×C139C2311yescharacteristic
89C22×C8×C139C2311yescharacteristic
90C22×C8×C139C2311yescharacteristic
91#125×C139—22no—
92#125×C139—22no—
93#124×C139—22no—
94#124×C139D414yes—
95#123×C139—28no—
96C22⋊Q8×C139—22no—
97C22⋊Q8×C139—22no—
98#121×C139—28no—
99#121×C139—22no—
100#121×C139—22no—
101#120×C139—28no—
102C4×D4×C139—22no—
103C4×D4×C139—22no—
104C4×D4×C139—22no—
105C4×D4×C139D414yes—
106C2×C4⋊C4×C139—21no—
107C2×C4⋊C4×C139—21no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139D411yescharacteristic
110C2×C4⋊C4×C139C2311yescharacteristic
111C2×C4⋊C4×C139C2311yescharacteristic
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C22⋊C4×C139—28no—
116C2×C22⋊C4×C139—21no—
117C2×C22⋊C4×C139—21no—
118C2×C22⋊C4×C139—21no—
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—21no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139D411yescharacteristic
126C2×C22⋊C4×C139D411yescharacteristic
127C2×C42×C139—21no—
128C2×C42×C139C2311yescharacteristic
129#107×C139—22no—
130#106×C139—22no—
131C4⋊C8×C139—22no—
132#103×C139—22no—
133#103×C139—22no—
134#103×C139—41no—
135#103×C139—41no—
136#102×C139—22no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—41no—
143#102×C139—41no—
144C22⋊C8×C139—41no—
145C22⋊C8×C139—41no—
146C22⋊C8×C139—41no—
147C22⋊C8×C139—41no—
148C4×C8×C139—22no—
149#95×C139—21no—
150#95×C139—21no—
151#95×C139—21no—
152#95×C139—21no—
153#95×C139—21no—
154C24×C139—21no—
155C24×C139—24no—
156C24×C139—21no—
157C24×C139—42no—
158C24×C139—42no—
159C24×C139—42no—
160C24×C139—42no—
161C24×C139—81no—
162C24×C139—81no—
163C24×C139C2×D411yescharacteristic
164C24×C139C2×D411yescharacteristic
165#41×C139—44no—
166#41×C139—44no—
167#41×C139—44no—
168#41×C139—44no—
169C2×Q8×C139—21no—
170C2×Q8×C139—21no—
171C2×Q8×C139—21no—
172C2×Q8×C139—21no—
173C2×Q8×C139—21no—
174C2×Q8×C139C2×D412yes—
175C2×D4×C139—24no—
176C2×D4×C139—24no—
177C2×D4×C139—22no—
178C2×D4×C139—24no—
179C2×D4×C139—22no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—21no—
183C2×D4×C139—21no—
184C2×D4×C139—21no—
185C2×D4×C139—21no—
186C2×D4×C139—21no—
187C2×D4×C139—21no—
188C2×D4×C139—41no—
189C2×D4×C139—42no—
190C2×D4×C139—42no—
191C2×D4×C139—44no—
192C2×D4×C139—44no—
193C2×D4×C139—44no—
194C2×D4×C139—42no—
195C2×D4×C139—42no—
196C2×D4×C139—44no—
197C2×D4×C139—81no—
198C2×D4×C139—81no—
199C2×D4×C139C2×D412yes—
200C2×D4×C139C2×D412yes—
201C2×D4×C139#4112yes—
202C2×D4×C139#4112yes—
203C22×C4×C139—24no—
204C22×C4×C139—21no—
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—21no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139—24no—
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—42no—
224C22×C4×C139—42no—
225C22×C4×C139—81no—
226C22×C4×C139—81no—
227C22×C4×C139C2×D411yescharacteristic
228C22×C4×C139C2×D411yescharacteristic
229C22×C4×C139C2×D411yescharacteristic
230C22×C4×C139C2×D411yescharacteristic
231C22×C4×C139C2411yescharacteristic
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—
242C2×C8×C139—21no—
243C2×C8×C139—21no—
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—21no—
254C4⋊C4×C139—21no—
255C4⋊C4×C139—42no—
256C4⋊C4×C139—42no—
257C4⋊C4×C139C2×D412yes—
258C22⋊C4×C139—24no—
259C22⋊C4×C139—24no—
260C22⋊C4×C139—22no—
261C22⋊C4×C139—24no—
262C22⋊C4×C139—24no—
263C22⋊C4×C139—24no—
264C22⋊C4×C139—22no—
265C22⋊C4×C139—42no—
266C22⋊C4×C139—42no—
267C22⋊C4×C139—81no—
268C22⋊C4×C139—81no—
269C42×C139—81no—
270C42×C139C2×D412yes—
271C42×C139C2×D412yes—
272C23×C139—21no—
273C23×C139—22no—
274C23×C139—21no—
275C23×C139—21no—
276C23×C139—22no—
277C23×C139—22no—
278C23×C139—21no—
279C23×C139—21no—
280C23×C139—21no—
281C23×C139—22no—
282C23×C139—21no—
283C23×C139—21no—
284C23×C139—21no—
285C23×C139—21no—
286C23×C139—21no—
287C23×C139—21no—
288C23×C139—21no—
289C23×C139—48no—
290C23×C139—48no—
291C23×C139—41no—
292C23×C139—41no—
293C23×C139—41no—
294C23×C139—41no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—41no—
298C23×C139—41no—
299C23×C139—41no—
300C23×C139—41no—
301C23×C139—84no—
302C23×C139—84no—
303C23×C139—84no—
304C23×C139—84no—
305C23×C139—84no—
306C23×C139#13512yes—
307C23×C139C22×D411yescharacteristic
308Q8×C139—22no—
309Q8×C139—22no—
310Q8×C139—41no—
311Q8×C139—41no—
312D4×C139—22no—
313D4×C139—22no—
314D4×C139—22no—
315D4×C139—22no—
316D4×C139—22no—
317D4×C139—44no—
318D4×C139—48no—
319D4×C139—48no—
320D4×C139—41no—
321D4×C139—41no—
322D4×C139—84no—
323D4×C139#12414yes—
324C2×C4×C139—21no—
325C2×C4×C139—21no—
326C2×C4×C139—21no—
327C2×C4×C139—21no—
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—41no—
356C2×C4×C139—41no—
357C2×C4×C139—41no—
358C2×C4×C139—41no—
359C2×C4×C139—41no—
360C2×C4×C139—41no—
361C2×C4×C139—84no—
362C2×C4×C139#12012yes—
363C2×C4×C139#12012yes—
364C2×C4×C139C22×D411yescharacteristic
365C2×C4×C139C22×D411yescharacteristic
366C2×C4×C139C2×#4111yescharacteristic
367C2×C4×C139C2×#4111yescharacteristic
368C2×C4×C139H(5,𝔽2)11yescharacteristic
369C2×C4×C139H(5,𝔽2)11yescharacteristic
370C8×C139—41no—
371C8×C139—41no—
372C8×C139—41no—
373C8×C139—41no—
374C22×C139—24no—
375C22×C139—22no—
376C22×C139—22no—
377C22×C139—22no—
378C22×C139—41no—
379C22×C139—42no—
380C22×C139—42no—
381C22×C139—41no—
382C22×C139—42no—
383C22×C139—42no—
384C22×C139—41no—
385C22×C139—42no—
386C22×C139—41no—
387C22×C139—42no—
388C22×C139—41no—
389C22×C139—42no—
390C22×C139—41no—
391C22×C139—42no—
392C22×C139—41no—
393C22×C139—42no—
394C22×C139—41no—
395C22×C139—41no—
396C22×C139—41no—
397C22×C139—41no—
398C22×C139—816no—
399C22×C139—81no—
400C22×C139—81no—
401C22×C139—81no—
402C22×C139—81no—
403C22×C139C2×#12011yescharacteristic
404C22×C139#54611yescharacteristic
405C22×C139#54611yescharacteristic
406C22×C139C2×#13511yescharacteristic
407C22×C139#57511yescharacteristic
408C22×C139#57611yescharacteristic
409C22×C139#57711yescharacteristic
410C4×C139—22no—
411C4×C139—22no—
412C4×C139—41no—
413C4×C139—41no—
414C4×C139—42no—
415C4×C139—42no—
416C4×C139—81no—
417C4×C139—81no—
418C4×C139—81no—
419C4×C139—81no—
420C4×C139C2×#12411yescharacteristic
421C4×C139#53511yescharacteristic
422C4×C139#54611yescharacteristic
423C4×C139#54611yescharacteristic
424C2×C139—42no—
425C2×C139—44no—
426C2×C139—81no—
427C2×C139—82no—
428C2×C139#243511yescharacteristic
429C2×C139#300211yescharacteristic
430C2×C139#301211yescharacteristic
431C2×C139#329611yescharacteristic
432C2×C139#329711yescharacteristic
433C2×C139#332211yescharacteristic
434C2×C139#332311yescharacteristic
435#25890C13911yesmaximal, characteristic, direct product factor, Sylow
436C139#2589011yescharacteristic, direct product factor, Sylow
437C2×#546C2×C13911yescharacteristic
438C2×#488C2×C13911yescharacteristic, complemented
439C2×#478C2×C13911yescharacteristic, complemented
440#2562C2×C13911yescharacteristic, complemented
441#2036C2×C13911yescharacteristic, complemented
442#2035C2×C13911yescharacteristic, complemented
443#2034C2×C13911yescharacteristic, complemented
444#2033C2×C13911yescharacteristic, complemented
445#1983C2×C13911yescharacteristic, complemented
446#1954C2×C13911yescharacteristic, complemented
447#1788C2×C13911yescharacteristic, complemented
448#1788C2×C13911yescharacteristic, complemented
449#1786C2×C13911yescharacteristic, complemented
450#1786C2×C13911yescharacteristic, complemented
451C4×#102C2×C13911yescharacteristic, complemented
452C22×#41C22×C13911yescharacteristic
453C23×D4C22×C13911yescharacteristic
454#546—24no—
455#546—24no—
456C2×#125C22×C13911yescharacteristic, complemented
457C2×#124C22×C13911yescharacteristic
458C2×#123—21no—
459C2×C22⋊Q8C22×C13911yescharacteristic
460C2×#121—21no—
461C2×#121C22×C13911yescharacteristic
462C2×#120—21no—
463C2×C4×D4C22×C13911yescharacteristic
464C2×C4×D4C22×C13911yescharacteristic
465C22×C22⋊C4—21no—
466#488—24no—
467#478—24no—
468C2×#107C22×C13911yescharacteristic, complemented
469C2×#106C22×C13911yescharacteristic, complemented
470C2×C4⋊C8C22×C13911yescharacteristic, complemented
471C2×#103C22×C13911yescharacteristic, complemented
472C2×#103C22×C13911yescharacteristic, complemented
473C2×#103C22×C13911yescharacteristic, complemented
474C2×#103C22×C13911yescharacteristic, complemented
475C2×#102C22×C13911yescharacteristic
476C2×#102C22×C13911yescharacteristic
477C2×#102C22×C13911yescharacteristic
478C2×#102C22×C13911yescharacteristic
479C2×#102C22×C13911yescharacteristic
480C2×#102C22×C13911yescharacteristic
481C2×#102C22×C13911yescharacteristic
482C2×#102C22×C13911yescharacteristic
483C2×C22⋊C8C22×C13911yescharacteristic
484C2×C22⋊C8C22×C13911yescharacteristic
485C2×C22⋊C8C22×C13911yescharacteristic, complemented
486C2×C22⋊C8C22×C13911yescharacteristic, complemented
487C2×C4×C8C22×C13911yescharacteristic, complemented
488#400—21no—
489#394—21no—
490#388—21no—
491#388—21no—
492#380C22×C13911yescharacteristic
493#380C22×C13911yescharacteristic
494#380C22×C13911yescharacteristic, complemented
495#380C22×C13911yescharacteristic, complemented
496C4×C4⋊C4C22×C13911yescharacteristic, complemented
497#340C22×C13911yescharacteristic, complemented
498#340C22×C13911yescharacteristic, complemented
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C23×C13911yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C13911yescharacteristic
517C22×D4C23×C13911yescharacteristic
518C22×D4C23×C13911yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4C23×C13911yescharacteristic
522C23×C4C23×C13911yescharacteristic
523C22×C8C23×C13911yescharacteristic
524C22×C8C23×C13911yescharacteristic
525C22×C8C23×C13911yescharacteristic
526C22×C8C23×C13911yescharacteristic
527#125—22no—
528#125—22no—
529#124—22no—
530#124D4×C13914yes—
531#123—28no—
532C22⋊Q8—22no—
533C22⋊Q8—22no—
534#121—28no—
535#121—22no—
536#121—22no—
537#120—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4D4×C13914yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4D4×C13911yescharacteristic
546C2×C4⋊C4C23×C13911yescharacteristic
547C2×C4⋊C4C23×C13911yescharacteristic
548C2×C4⋊C4C23×C13911yescharacteristic
549C2×C4⋊C4C23×C13911yescharacteristic
550C2×C4⋊C4C23×C13911yescharacteristic
551C2×C22⋊C4—28no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4D4×C13911yescharacteristic
562C2×C22⋊C4D4×C13911yescharacteristic
563C2×C42—21no—
564C2×C42C23×C13911yescharacteristic
565#107—22no—
566#106—22no—
567C4⋊C8—22no—
568#103—22no—
569#103—22no—
570#103—41no—
571#103—41no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580C22⋊C8—41no—
581C22⋊C8—41no—
582C22⋊C8—41no—
583C22⋊C8—41no—
584C4×C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590C24—21no—
591C24—24no—
592C24—21no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—81no—
598C24—81no—
599C24C2×D4×C13911yescharacteristic
600C24C2×D4×C13911yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×D4×C13912yes—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—22no—
614C2×D4—24no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—44no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—44no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C13912yes—
636C2×D4C2×D4×C13912yes—
637C2×D4#41×C13912yes—
638C2×D4#41×C13912yes—
639C22×C4—24no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—24no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4C2×D4×C13911yescharacteristic
664C22×C4C2×D4×C13911yescharacteristic
665C22×C4C2×D4×C13911yescharacteristic
666C22×C4C2×D4×C13911yescharacteristic
667C22×C4C24×C13911yescharacteristic
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C4⋊C4—24no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4C2×D4×C13912yes—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C42—81no—
706C42C2×D4×C13912yes—
707C42C2×D4×C13912yes—
708C23—21no—
709C23—22no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—48no—
726C23—48no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—84no—
738C23—84no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23#135×C13912yes—
743C23C22×D4×C13911yescharacteristic
744Q8—22no—
745Q8—22no—
746Q8—41no—
747Q8—41no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—44no—
754D4—48no—
755D4—48no—
756D4—41no—
757D4—41no—
758D4—84no—
759D4#124×C13914yes—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
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—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4#120×C13912yes—
799C2×C4#120×C13912yes—
800C2×C4C22×D4×C13911yescharacteristic
801C2×C4C22×D4×C13911yescharacteristic
802C2×C4C2×#41×C13911yescharacteristic
803C2×C4C2×#41×C13911yescharacteristic
804C2×C4H(5,𝔽2)×C13911yescharacteristic
805C2×C4H(5,𝔽2)×C13911yescharacteristic
806C8—41no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—24no—
813C22—22no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—42no—
832C22—41no—
833C22—42no—
834C22—816no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C2×#120×C13911yescharacteristic
840C22#546×C13911yescharacteristic
841C22#546×C13911yescharacteristic
842C22C2×#135×C13911yescharacteristic
843C22#575×C13911yescharacteristic
844C22#576×C13911yescharacteristic
845C22#577×C13911yescharacteristic
846C4—22no—
847C4—22no—
848C4—41no—
849C4—41no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4C2×#124×C13911yescharacteristic
857C4#535×C13911yescharacteristic
858C4#546×C13911yescharacteristic
859C4#546×C13911yescharacteristic
860C2—42no—
861C2—44no—
862C2—81no—
863C2—82no—
864C2#2435×C13911yescharacteristic
865C2#3002×C13911yescharacteristic
866C2#3012×C13911yescharacteristic
867C2#3296×C13911yescharacteristic
868C2#3297×C13911yescharacteristic
869C2#3322×C13911yescharacteristic
870C2#3323×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#546×C139C2
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
2. C2×#488×C139C2semidirect
3. C2×#478×C139C2semidirect
4. #2562×C139C2semidirect
5. #2036×C139C2semidirect
6. #2035×C139C2semidirect
7. #2034×C139C2semidirect
8. #2033×C139C2semidirect
9. #1983×C139C2semidirect
10. #1954×C139C2semidirect
11. #1788×C139C2semidirect
12. #1788×C139C2semidirect
13. #1786×C139C2semidirect
14. #1786×C139C2semidirect
15. C4×#102×C139C2semidirect
20. C2×#125×C139C22semidirect
32. C2×#107×C139C22semidirect
33. C2×#106×C139C22semidirect
34. C2×C4⋊C8×C139C22semidirect
35. C2×#103×C139C22semidirect
36. C2×#103×C139C22semidirect
37. C2×#103×C139C22semidirect
38. C2×#103×C139C22semidirect
49. C2×C22⋊C8×C139C22semidirect
50. C2×C22⋊C8×C139C22semidirect
51. C2×C4×C8×C139C22semidirect
58. #380×C139C22semidirect
59. #380×C139C22semidirect
60. C4×C4⋊C4×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
435. #25890C139direct (N × H)
436. C139#25890direct (N × H)
438. C2×#488C2×C139semidirect
439. C2×#478C2×C139semidirect
440. #2562C2×C139semidirect
441. #2036C2×C139semidirect
442. #2035C2×C139semidirect
443. #2034C2×C139semidirect
444. #2033C2×C139semidirect
445. #1983C2×C139semidirect
446. #1954C2×C139semidirect
447. #1788C2×C139semidirect
448. #1788C2×C139semidirect
449. #1786C2×C139semidirect
450. #1786C2×C139semidirect
451. C4×#102C2×C139semidirect
456. C2×#125C22×C139semidirect
468. C2×#107C22×C139semidirect
469. C2×#106C22×C139semidirect
470. C2×C4⋊C8C22×C139semidirect
471. C2×#103C22×C139semidirect
472. C2×#103C22×C139semidirect
473. C2×#103C22×C139semidirect
474. C2×#103C22×C139semidirect
485. C2×C22⋊C8C22×C139semidirect
486. C2×C22⋊C8C22×C139semidirect
487. C2×C4×C8C22×C139semidirect
494. #380C22×C139semidirect
495. #380C22×C139semidirect
496. C4×C4⋊C4C22×C139semidirect
497. #340C22×C139semidirect
498. #340C22×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1392
C2×#488×C1392
C2×#478×C1392
#2562×C1392
#2036×C1392
#2035×C1392
#2034×C1392
#2033×C1392
#1983×C1392
#1954×C1392
#1788×C1392
#1786×C1392
C4×#102×C1392
#25890139