Finite Group Databasebeta

← C139×#13995 #48008591

Subgroups — C139×#13995 #48008591

Order 35584.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C139C211yesmaximal, characteristic
2C23×C22⋊C4×C139C211yesmaximal, characteristic, complemented
3C2×#390×C139C212yesmaximal, complemented
4C2×#386×C139C211yesmaximal, characteristic, complemented
5C2×#386×C139C211yesmaximal, characteristic, complemented
6C2×#385×C139C211yesmaximal, characteristic, complemented
7C2×#379×C139C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C139C211yesmaximal, characteristic, complemented
9#1439×C139C212yesmaximal, complemented
10#1438×C139C212yesmaximal, complemented
11#1437×C139C212yesmaximal, complemented
12C26×C139C2211yescharacteristic
13C23×D4×C139C2211yescharacteristic
14C23×D4×C139C2212yes—
15C24×C4×C139C2211yescharacteristic
16C24×C4×C139C2211yescharacteristic
17C2×#120×C139—24no—
18C2×#120×C139—24no—
19C2×#120×C139C418yescomplemented
20C22×C4⋊C4×C139C2212yescomplemented
21C22×C22⋊C4×C139—24no—
22C22×C22⋊C4×C139—28no—
23C22×C22⋊C4×C139C2211yescharacteristic
24C22×C22⋊C4×C139C2212yes—
25C22×C22⋊C4×C139C2212yes—
26C22×C22⋊C4×C139C2212yes—
27C22×C22⋊C4×C139C2212yes—
28C22×C22⋊C4×C139C2211yescharacteristic
29C22×C22⋊C4×C139C2212yes—
30C22×C22⋊C4×C139C2211yescharacteristic
31C22×C22⋊C4×C139C2211yescharacteristic, complemented
32C22×C22⋊C4×C139C2212yescomplemented
33C22×C22⋊C4×C139C2211yescharacteristic, complemented
34C22×C42×C139C2212yescomplemented
35#390×C139—28no—
36#386×C139—24no—
37#386×C139—24no—
38#385×C139—24no—
39#379×C139—24no—
40C4×C22⋊C4×C139—24no—
41C2×#95×C139C2212yescomplemented
42C2×#95×C139C2212yescomplemented
43C2×#95×C139C2211yescharacteristic, complemented
44C2×#95×C139C2212yescomplemented
45C2×#95×C139C2211yescharacteristic, complemented
46C25×C139—24no—
47C25×C139—22no—
48C25×C139—24no—
49C25×C139—22no—
50C25×C139—22no—
51C25×C139—22no—
52C25×C139—22no—
53C25×C139—22no—
54C25×C139—42no—
55C25×C139—42no—
56C25×C139C2×C414yes—
57C25×C139C2311yescharacteristic
58C25×C139C2312yes—
59C25×C139C2311yescharacteristic
60C22×D4×C139—22no—
61C22×D4×C139—22no—
62C22×D4×C139—22no—
63C22×D4×C139—22no—
64C22×D4×C139—24no—
65C22×D4×C139—24no—
66C22×D4×C139—22no—
67C22×D4×C139—22no—
68C22×D4×C139—24no—
69C22×D4×C139—24no—
70C22×D4×C139—42no—
71C22×D4×C139—42no—
72C22×D4×C139C2×C414yes—
73C22×D4×C139C2×C418yescomplemented
74C23×C4×C139—22no—
75C23×C4×C139—22no—
76C23×C4×C139—22no—
77C23×C4×C139—24no—
78C23×C4×C139—24no—
79C23×C4×C139—22no—
80C23×C4×C139—22no—
81C23×C4×C139—42no—
82C23×C4×C139—42no—
83C23×C4×C139D414yescomplemented
84C23×C4×C139C2311yescharacteristic
85C23×C4×C139C2311yescharacteristic
86C23×C4×C139C2311yescharacteristic
87C23×C4×C139C2312yes—
88C23×C4×C139C2312yes—
89C23×C4×C139C2311yescharacteristic
90C23×C4×C139C2312yes—
91C23×C4×C139C2311yescharacteristic
92#120×C139—232no—
93C2×C4⋊C4×C139—24no—
94C2×C4⋊C4×C139—24no—
95C2×C4⋊C4×C139—42no—
96C2×C22⋊C4×C139—232no—
97C2×C22⋊C4×C139—24no—
98C2×C22⋊C4×C139—22no—
99C2×C22⋊C4×C139—22no—
100C2×C22⋊C4×C139—24no—
101C2×C22⋊C4×C139—24no—
102C2×C22⋊C4×C139—24no—
103C2×C22⋊C4×C139—24no—
104C2×C22⋊C4×C139—24no—
105C2×C22⋊C4×C139—24no—
106C2×C22⋊C4×C139—22no—
107C2×C22⋊C4×C139—22no—
108C2×C22⋊C4×C139—22no—
109C2×C22⋊C4×C139—24no—
110C2×C22⋊C4×C139—24no—
111C2×C22⋊C4×C139—24no—
112C2×C22⋊C4×C139—24no—
113C2×C22⋊C4×C139—24no—
114C2×C22⋊C4×C139—22no—
115C2×C22⋊C4×C139—22no—
116C2×C22⋊C4×C139—24no—
117C2×C22⋊C4×C139—24no—
118C2×C22⋊C4×C139—42no—
119C2×C22⋊C4×C139—42no—
120C2×C22⋊C4×C139—42no—
121C2×C22⋊C4×C139—42no—
122C2×C22⋊C4×C139C2×C414yes—
123C2×C22⋊C4×C139C2×C418yescomplemented
124C2×C22⋊C4×C139D414yes—
125C2×C22⋊C4×C139D414yes—
126C2×C22⋊C4×C139D418yescomplemented
127C2×C22⋊C4×C139D414yescomplemented
128C2×C42×C139—24no—
129C2×C42×C139—24no—
130C2×C42×C139—42no—
131#95×C139—24no—
132#95×C139—24no—
133#95×C139—24no—
134#95×C139—22no—
135#95×C139—22no—
136C24×C139—22no—
137C24×C139—22no—
138C24×C139—22no—
139C24×C139—22no—
140C24×C139—28no—
141C24×C139—28no—
142C24×C139—216no—
143C24×C139—216no—
144C24×C139—28no—
145C24×C139—22no—
146C24×C139—22no—
147C24×C139—22no—
148C24×C139—22no—
149C24×C139—22no—
150C24×C139—22no—
151C24×C139—22no—
152C24×C139—22no—
153C24×C139—22no—
154C24×C139—22no—
155C24×C139—22no—
156C24×C139—22no—
157C24×C139—28no—
158C24×C139—28no—
159C24×C139—21no—
160C24×C139—22no—
161C24×C139—21no—
162C24×C139—21no—
163C24×C139—21no—
164C24×C139—21no—
165C24×C139—21no—
166C24×C139—22no—
167C24×C139—22no—
168C24×C139—22no—
169C24×C139—48no—
170C24×C139—48no—
171C24×C139—48no—
172C24×C139—48no—
173C24×C139—48no—
174C24×C139—48no—
175C24×C139—48no—
176C24×C139—48no—
177C24×C139—48no—
178C24×C139—44no—
179C24×C139—44no—
180C24×C139—48no—
181C24×C139—44no—
182C24×C139—44no—
183C24×C139—44no—
184C24×C139—44no—
185C24×C139C22×C412yes—
186C24×C139C22×C414yes—
187C24×C139C22×C412yes—
188C24×C139C2×D414yes—
189C24×C139C2×D412yes—
190C24×C139C2×D412yes—
191C24×C139C2×D412yes—
192C24×C139C2×D412yes—
193C24×C139#4114yes—
194C24×C139#4112yes—
195C24×C139#4112yes—
196C24×C139C2411yescharacteristic
197C2×D4×C139—28no—
198C2×D4×C139—28no—
199C2×D4×C139—28no—
200C2×D4×C139—216no—
201C2×D4×C139—216no—
202C2×D4×C139—48no—
203C2×D4×C139—48no—
204C2×D4×C139—48no—
205C2×D4×C139—48no—
206C2×D4×C139—48no—
207C2×D4×C139—44no—
208C2×D4×C139—44no—
209C2×D4×C139—44no—
210C2×D4×C139—44no—
211C22×C4×C139—21no—
212C22×C4×C139—22no—
213C22×C4×C139—21no—
214C22×C4×C139—22no—
215C22×C4×C139—22no—
216C22×C4×C139—22no—
217C22×C4×C139—22no—
218C22×C4×C139—28no—
219C22×C4×C139—28no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—22no—
224C22×C4×C139—22no—
225C22×C4×C139—22no—
226C22×C4×C139—22no—
227C22×C4×C139—22no—
228C22×C4×C139—22no—
229C22×C4×C139—22no—
230C22×C4×C139—21no—
231C22×C4×C139—21no—
232C22×C4×C139—22no—
233C22×C4×C139—22no—
234C22×C4×C139—21no—
235C22×C4×C139—21no—
236C22×C4×C139—21no—
237C22×C4×C139—22no—
238C22×C4×C139—22no—
239C22×C4×C139—22no—
240C22×C4×C139—22no—
241C22×C4×C139—22no—
242C22×C4×C139—28no—
243C22×C4×C139—21no—
244C22×C4×C139—21no—
245C22×C4×C139—21no—
246C22×C4×C139—21no—
247C22×C4×C139—21no—
248C22×C4×C139—22no—
249C22×C4×C139—21no—
250C22×C4×C139—22no—
251C22×C4×C139—22no—
252C22×C4×C139—22no—
253C22×C4×C139—44no—
254C22×C4×C139—48no—
255C22×C4×C139—48no—
256C22×C4×C139—48no—
257C22×C4×C139—48no—
258C22×C4×C139—44no—
259C22×C4×C139—44no—
260C22×C4×C139C22×C412yes—
261C22×C4×C139C22×C414yes—
262C22×C4×C139C2×D414yes—
263C22×C4×C139C2×D412yes—
264C22×C4×C139C2×D414yes—
265C22×C4×C139C2×D414yes—
266C22×C4×C139C2×D414yes—
267C22×C4×C139C2×D412yes—
268C22×C4×C139C2×D414yes—
269C4⋊C4×C139—48no—
270C22⋊C4×C139—216no—
271C22⋊C4×C139—28no—
272C22⋊C4×C139—216no—
273C22⋊C4×C139—216no—
274C22⋊C4×C139—48no—
275C22⋊C4×C139—48no—
276C22⋊C4×C139—48no—
277C22⋊C4×C139—44no—
278C22⋊C4×C139—44no—
279C22⋊C4×C139—44no—
280C22⋊C4×C139C22⋊C4116yescomplemented
281C42×C139—48no—
282C23×C139—24no—
283C23×C139—24no—
284C23×C139—22no—
285C23×C139—22no—
286C23×C139—24no—
287C23×C139—22no—
288C23×C139—22no—
289C23×C139—24no—
290C23×C139—24no—
291C23×C139—24no—
292C23×C139—24no—
293C23×C139—24no—
294C23×C139—24no—
295C23×C139—24no—
296C23×C139—24no—
297C23×C139—24no—
298C23×C139—232no—
299C23×C139—24no—
300C23×C139—24no—
301C23×C139—24no—
302C23×C139—24no—
303C23×C139—24no—
304C23×C139—24no—
305C23×C139—24no—
306C23×C139—24no—
307C23×C139—24no—
308C23×C139—24no—
309C23×C139—24no—
310C23×C139—24no—
311C23×C139—24no—
312C23×C139—24no—
313C23×C139—24no—
314C23×C139—24no—
315C23×C139—24no—
316C23×C139—24no—
317C23×C139—22no—
318C23×C139—22no—
319C23×C139—24no—
320C23×C139—22no—
321C23×C139—24no—
322C23×C139—432no—
323C23×C139—432no—
324C23×C139—416no—
325C23×C139—416no—
326C23×C139—416no—
327C23×C139—432no—
328C23×C139—416no—
329C23×C139—432no—
330C23×C139—416no—
331C23×C139—42no—
332C23×C139—42no—
333C23×C139—42no—
334C23×C139—42no—
335C23×C139—42no—
336C23×C139—42no—
337C23×C139—42no—
338C23×C139—42no—
339C23×C139—42no—
340C23×C139—42no—
341C23×C139—42no—
342C23×C139—42no—
343C23×C139—42no—
344C23×C139—42no—
345C23×C139—42no—
346C23×C139—42no—
347C23×C139—416no—
348C23×C139—41no—
349C23×C139—41no—
350C23×C139—41no—
351C23×C139—41no—
352C23×C139—42no—
353C23×C139—41no—
354C23×C139—41no—
355C23×C139—41no—
356C23×C139—41no—
357C23×C139—42no—
358C23×C139—42no—
359C23×C139—42no—
360C23×C139—42no—
361C23×C139—42no—
362C23×C139—42no—
363C23×C139—42no—
364C23×C139—42no—
365C23×C139—42no—
366C23×C139C2×C22⋊C414yes—
367C23×C139C4×D418yes—
368C23×C139C4×D414yes—
369C23×C139C4×D414yes—
370C23×C139#12114yes—
371C23×C139#12114yes—
372C23×C139#12414yes—
373C23×C139#12714yes—
374C23×C139C23×C411yescharacteristic
375C23×C139C22×D411yescharacteristic
376C23×C139C22×D411yescharacteristic
377C23×C139C22×D411yescharacteristic
378C23×C139C22×D412yes—
379C23×C139C22×D411yescharacteristic
380C23×C139C2×#4111yescharacteristic
381C23×C139C2×#4111yescharacteristic
382C23×C139C2×#4112yes—
383C23×C139H(5,𝔽2)12yes—
384C23×C139H(5,𝔽2)12yes—
385D4×C139—432no—
386D4×C139—416no—
387C2×C4×C139—24no—
388C2×C4×C139—24no—
389C2×C4×C139—22no—
390C2×C4×C139—22no—
391C2×C4×C139—24no—
392C2×C4×C139—24no—
393C2×C4×C139—24no—
394C2×C4×C139—24no—
395C2×C4×C139—24no—
396C2×C4×C139—24no—
397C2×C4×C139—22no—
398C2×C4×C139—22no—
399C2×C4×C139—22no—
400C2×C4×C139—22no—
401C2×C4×C139—24no—
402C2×C4×C139—24no—
403C2×C4×C139—22no—
404C2×C4×C139—22no—
405C2×C4×C139—24no—
406C2×C4×C139—24no—
407C2×C4×C139—24no—
408C2×C4×C139—24no—
409C2×C4×C139—416no—
410C2×C4×C139—416no—
411C2×C4×C139—41no—
412C2×C4×C139—41no—
413C2×C4×C139—42no—
414C2×C4×C139—41no—
415C2×C4×C139—42no—
416C2×C4×C139—41no—
417C2×C4×C139—42no—
418C2×C4×C139—42no—
419C2×C4×C139—42no—
420C2×C4×C139—42no—
421C2×C4×C139—42no—
422C2×C4×C139—42no—
423C2×C4×C139—42no—
424C2×C4×C139—42no—
425C2×C4×C139—41no—
426C2×C4×C139—41no—
427C2×C4×C139—41no—
428C2×C4×C139—41no—
429C2×C4×C139—41no—
430C2×C4×C139—41no—
431C2×C4×C139—42no—
432C2×C4×C139—42no—
433C2×C4×C139—42no—
434C2×C4×C139—42no—
435C2×C4×C139C2×C22⋊C418yescomplemented
436C2×C4×C139#12014yescomplemented
437C22×C139—24no—
438C22×C139—28no—
439C22×C139—28no—
440C22×C139—24no—
441C22×C139—24no—
442C22×C139—28no—
443C22×C139—24no—
444C22×C139—28no—
445C22×C139—24no—
446C22×C139—24no—
447C22×C139—28no—
448C22×C139—28no—
449C22×C139—28no—
450C22×C139—464no—
451C22×C139—44no—
452C22×C139—44no—
453C22×C139—44no—
454C22×C139—44no—
455C22×C139—44no—
456C22×C139—44no—
457C22×C139—44no—
458C22×C139—44no—
459C22×C139—44no—
460C22×C139—44no—
461C22×C139—44no—
462C22×C139—44no—
463C22×C139—42no—
464C22×C139—44no—
465C22×C139—44no—
466C22×C139—42no—
467C22×C139—42no—
468C22×C139—81no—
469C22×C139—81no—
470C22×C139—82no—
471C22×C139—81no—
472C22×C139—82no—
473C22×C139—81no—
474C22×C139#39018yescomplemented
475C22×C139C22×C22⋊C411yescharacteristic
476C22×C139C2×C4×D411yescharacteristic
477C22×C139C2×C4×D412yes—
478C22×C139C2×C4×D411yescharacteristic
479C22×C139#51812yes—
480C22×C139C2×#12011yescharacteristic
481C22×C139C2×#12111yescharacteristic
482C22×C139C2×#12111yescharacteristic
483C22×C139#52511yescharacteristic
484C22×C139#52512yes—
485C22×C139C2×#12411yescharacteristic
486C22×C139C2×#12711yescharacteristic
487C22×C139#53411yescharacteristic
488C22×C139#53511yescharacteristic
489C22×C139#53812yes—
490C22×C139D4212yes—
491C22×C139D4212yes—
492C22×C139D4212yes—
493C22×C139#54612yes—
494C22×C139#54612yes—
495C22×C139#54612yes—
496C22×C139#54612yes—
497C22×C139#55112yes—
498C4×C139—28no—
499C4×C139—24no—
500C4×C139—42no—
501C4×C139—44no—
502C4×C139—44no—
503C4×C139—42no—
504C4×C139—81no—
505C4×C139—81no—
506C2×C139—28no—
507C2×C139—48no—
508C2×C139—82no—
509C2×C139C2×#39011yescharacteristic
510C2×C139C4×#12011yescharacteristic
511C2×C139#232111yescharacteristic
512C2×C139D4×C22⋊C412yes—
513C2×C139#235812yes—
514C2×C139#241011yescharacteristic
515C2×C139#241111yescharacteristic
516C2×C139#242412yes—
517C2×C139#243311yescharacteristic
518C2×C139#247212yes—
519C2×C139#253911yescharacteristic
520#13995C13911yesmaximal, characteristic, direct product factor, Sylow
521C139#1399511yescharacteristic, direct product factor, Sylow
522C22×#120C2×C13911yescharacteristic
523C23×C22⋊C4C2×C13911yescharacteristic, complemented
524C2×#390C2×C13912yescomplemented
525C2×#386C2×C13911yescharacteristic, complemented
526C2×#386C2×C13911yescharacteristic, complemented
527C2×#385C2×C13911yescharacteristic, complemented
528C2×#379C2×C13911yescharacteristic, complemented
529C2×C4×C22⋊C4C2×C13911yescharacteristic, complemented
530#1439C2×C13912yescomplemented
531#1438C2×C13912yescomplemented
532#1437C2×C13912yescomplemented
533C26C22×C13911yescharacteristic
534C23×D4C22×C13911yescharacteristic
535C23×D4C22×C13912yes—
536C24×C4C22×C13911yescharacteristic
537C24×C4C22×C13911yescharacteristic
538C2×#120—24no—
539C2×#120—24no—
540C2×#120C4×C13918yescomplemented
541C22×C4⋊C4C22×C13912yescomplemented
542C22×C22⋊C4—24no—
543C22×C22⋊C4—28no—
544C22×C22⋊C4C22×C13912yes—
545C22×C22⋊C4C22×C13911yescharacteristic
546C22×C22⋊C4C22×C13912yes—
547C22×C22⋊C4C22×C13912yes—
548C22×C22⋊C4C22×C13912yes—
549C22×C22⋊C4C22×C13912yes—
550C22×C22⋊C4C22×C13911yescharacteristic
551C22×C22⋊C4C22×C13911yescharacteristic
552C22×C22⋊C4C22×C13911yescharacteristic, complemented
553C22×C22⋊C4C22×C13912yescomplemented
554C22×C22⋊C4C22×C13911yescharacteristic, complemented
555C22×C42C22×C13912yescomplemented
556#390—28no—
557#386—24no—
558#386—24no—
559#385—24no—
560#379—24no—
561C4×C22⋊C4—24no—
562C2×#95C22×C13911yescharacteristic, complemented
563C2×#95C22×C13912yescomplemented
564C2×#95C22×C13912yescomplemented
565C2×#95C22×C13912yescomplemented
566C2×#95C22×C13911yescharacteristic, complemented
567C25—24no—
568C25—22no—
569C25—24no—
570C25—22no—
571C25—22no—
572C25—22no—
573C25—22no—
574C25—22no—
575C25—42no—
576C25—42no—
577C25C2×C4×C13914yes—
578C25C23×C13911yescharacteristic
579C25C23×C13912yes—
580C25C23×C13911yescharacteristic
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—42no—
593C22×D4C2×C4×C13914yes—
594C22×D4C2×C4×C13918yescomplemented
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—42no—
603C23×C4—42no—
604C23×C4D4×C13914yescomplemented
605C23×C4C23×C13911yescharacteristic
606C23×C4C23×C13911yescharacteristic
607C23×C4C23×C13911yescharacteristic
608C23×C4C23×C13912yes—
609C23×C4C23×C13912yes—
610C23×C4C23×C13911yescharacteristic
611C23×C4C23×C13912yes—
612C23×C4C23×C13911yescharacteristic
613#120—232no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—42no—
617C2×C22⋊C4—232no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—24no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—24no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4C2×C4×C13914yes—
644C2×C22⋊C4C2×C4×C13918yescomplemented
645C2×C22⋊C4D4×C13914yes—
646C2×C22⋊C4D4×C13914yes—
647C2×C22⋊C4D4×C13918yescomplemented
648C2×C22⋊C4D4×C13914yescomplemented
649C2×C42—24no—
650C2×C42—24no—
651C2×C42—42no—
652#95—24no—
653#95—24no—
654#95—24no—
655#95—22no—
656#95—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—28no—
663C24—216no—
664C24—216no—
665C24—28no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—28no—
679C24—28no—
680C24—21no—
681C24—22no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—44no—
700C24—44no—
701C24—48no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24C22×C4×C13912yes—
707C24C22×C4×C13914yes—
708C24C22×C4×C13912yes—
709C24C2×D4×C13914yes—
710C24C2×D4×C13912yes—
711C24C2×D4×C13912yes—
712C24C2×D4×C13912yes—
713C24C2×D4×C13912yes—
714C24#41×C13914yes—
715C24#41×C13912yes—
716C24#41×C13912yes—
717C24C24×C13911yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—216no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C22×C4×C13912yes—
782C22×C4C22×C4×C13914yes—
783C22×C4C2×D4×C13914yes—
784C22×C4C2×D4×C13912yes—
785C22×C4C2×D4×C13914yes—
786C22×C4C2×D4×C13914yes—
787C22×C4C2×D4×C13914yes—
788C22×C4C2×D4×C13912yes—
789C22×C4C2×D4×C13914yes—
790C4⋊C4—48no—
791C22⋊C4—216no—
792C22⋊C4—28no—
793C22⋊C4—216no—
794C22⋊C4—216no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4C22⋊C4×C139116yescomplemented
802C42—48no—
803C23—24no—
804C23—24no—
805C23—22no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—24no—
843C23—432no—
844C23—432no—
845C23—416no—
846C23—416no—
847C23—416no—
848C23—416no—
849C23—432no—
850C23—416no—
851C23—432no—
852C23—42no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—416no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23C2×C22⋊C4×C13914yes—
888C23C4×D4×C13918yes—
889C23C4×D4×C13914yes—
890C23C4×D4×C13914yes—
891C23#121×C13914yes—
892C23#121×C13914yes—
893C23#124×C13914yes—
894C23#127×C13914yes—
895C23C23×C4×C13911yescharacteristic
896C23C22×D4×C13911yescharacteristic
897C23C22×D4×C13911yescharacteristic
898C23C22×D4×C13911yescharacteristic
899C23C22×D4×C13912yes—
900C23C22×D4×C13911yescharacteristic
901C23C2×#41×C13911yescharacteristic
902C23C2×#41×C13911yescharacteristic
903C23C2×#41×C13912yes—
904C23H(5,𝔽2)×C13912yes—
905C23H(5,𝔽2)×C13912yes—
906D4—432no—
907D4—416no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—42no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4C2×C22⋊C4×C13918yescomplemented
957C2×C4#120×C13914yescomplemented
958C22—24no—
959C22—24no—
960C22—24no—
961C22—28no—
962C22—28no—
963C22—24no—
964C22—24no—
965C22—28no—
966C22—24no—
967C22—28no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—44no—
988C22—44no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—82no—
993C22—81no—
994C22—82no—
995C22#390×C13918yescomplemented
996C22C22×C22⋊C4×C13911yescharacteristic
997C22C2×C4×D4×C13911yescharacteristic
998C22C2×C4×D4×C13911yescharacteristic
999C22C2×C4×D4×C13912yes—
1000C22#518×C13912yes—
1001C22C2×#120×C13911yescharacteristic
1002C22C2×#121×C13911yescharacteristic
1003C22C2×#121×C13911yescharacteristic
1004C22#525×C13911yescharacteristic
1005C22#525×C13912yes—
1006C22C2×#124×C13911yescharacteristic
1007C22C2×#127×C13911yescharacteristic
1008C22#534×C13911yescharacteristic
1009C22#535×C13911yescharacteristic
1010C22#538×C13912yes—
1011C22D42×C13912yes—
1012C22D42×C13912yes—
1013C22D42×C13912yes—
1014C22#546×C13912yes—
1015C22#546×C13912yes—
1016C22#546×C13912yes—
1017C22#546×C13912yes—
1018C22#551×C13912yes—
1019C4—28no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—44no—
1024C4—44no—
1025C4—81no—
1026C4—81no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×#390×C13911yescharacteristic
1031C2C4×#120×C13911yescharacteristic
1032C2#2321×C13911yescharacteristic
1033C2D4×C22⋊C4×C13912yes—
1034C2#2358×C13912yes—
1035C2#2410×C13911yescharacteristic
1036C2#2411×C13911yescharacteristic
1037C2#2424×C13912yes—
1038C2#2433×C13911yescharacteristic
1039C2#2472×C13912yes—
1040C2#2539×C13911yescharacteristic
subgroupG/H
center, socleC24×C139C24
commutatorC23C23×C4×C139
Frattini, cosocleC24C24×C139
prime radicalC22×#120×C139C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C139C2semidirect
3. C2×#390×C139C2semidirect
4. C2×#386×C139C2semidirect
5. C2×#386×C139C2semidirect
6. C2×#385×C139C2semidirect
7. C2×#379×C139C2semidirect
8. C2×C4×C22⋊C4×C139C2semidirect
9. #1439×C139C2semidirect
10. #1438×C139C2semidirect
11. #1437×C139C2semidirect
19. C2×#120×C139C4semidirect
20. C22×C4⋊C4×C139C22semidirect
31. C22×C22⋊C4×C139C22semidirect
32. C22×C22⋊C4×C139C22semidirect
33. C22×C22⋊C4×C139C22semidirect
34. C22×C42×C139C22semidirect
41. C2×#95×C139C22semidirect
42. C2×#95×C139C22semidirect
43. C2×#95×C139C22semidirect
44. C2×#95×C139C22semidirect
45. C2×#95×C139C22semidirect
73. C22×D4×C139C2×C4semidirect
83. C23×C4×C139D4semidirect
123. C2×C22⋊C4×C139C2×C4semidirect
126. C2×C22⋊C4×C139D4semidirect
127. C2×C22⋊C4×C139D4semidirect
280. C22⋊C4×C139C22⋊C4semidirect
435. C2×C4×C139C2×C22⋊C4semidirect
436. C2×C4×C139#120semidirect
474. C22×C139#390semidirect
520. #13995C139direct (N × H)
521. C139#13995direct (N × H)
523. C23×C22⋊C4C2×C139semidirect
524. C2×#390C2×C139semidirect
525. C2×#386C2×C139semidirect
526. C2×#386C2×C139semidirect
527. C2×#385C2×C139semidirect
528. C2×#379C2×C139semidirect
529. C2×C4×C22⋊C4C2×C139semidirect
530. #1439C2×C139semidirect
531. #1438C2×C139semidirect
532. #1437C2×C139semidirect
540. C2×#120C4×C139semidirect
541. C22×C4⋊C4C22×C139semidirect
552. C22×C22⋊C4C22×C139semidirect
553. C22×C22⋊C4C22×C139semidirect
554. C22×C22⋊C4C22×C139semidirect
555. C22×C42C22×C139semidirect
562. C2×#95C22×C139semidirect
563. C2×#95C22×C139semidirect
564. C2×#95C22×C139semidirect
565. C2×#95C22×C139semidirect
566. C2×#95C22×C139semidirect
594. C22×D4C2×C4×C139semidirect
604. C23×C4D4×C139semidirect
644. C2×C22⋊C4C2×C4×C139semidirect
647. C2×C22⋊C4D4×C139semidirect
648. C2×C22⋊C4D4×C139semidirect
801. C22⋊C4C22⋊C4×C139semidirect
956. C2×C4C2×C22⋊C4×C139semidirect
957. C2×C4#120×C139semidirect
995. C22#390×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1392
C23×C22⋊C4×C1392
C2×#390×C1392
C2×#386×C1392
C2×#385×C1392
C2×#379×C1392
C2×C4×C22⋊C4×C1392
#1439×C1392
#1438×C1392
#1437×C1392
#13995139