Finite Group Databasebeta

← C139×#13967 #48008563

Subgroups — C139×#13967 #48008563

Order 35584.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C139C211yesmaximal, characteristic
2C22×C4×D4×C139C211yesmaximal, characteristic, complemented
3C23×C22⋊C4×C139C211yesmaximal, characteristic, complemented
4C2×#386×C139C212yesmaximal, complemented
5C2×#386×C139C211yesmaximal, characteristic, complemented
6C2×#379×C139C211yesmaximal, characteristic, complemented
7#1439×C139C212yesmaximal, complemented
8#1438×C139C212yesmaximal, complemented
9#1437×C139C212yesmaximal, complemented
10C22⋊#95×C139C211yesmaximal, characteristic, complemented
11C22⋊#95×C139C211yesmaximal, characteristic, complemented
12C26×C139C2211yescharacteristic
13C23×D4×C139C2212yes—
14C23×D4×C139C2211yescharacteristic
15C24×C4×C139C2211yescharacteristic
16C24×C4×C139C2211yescharacteristic
17C24×C4×C139C2211yescharacteristic, complemented
18C2×#120×C139—24no—
19C2×#120×C139—24no—
20C2×#120×C139C418yescomplemented
21C2×C4×D4×C139—24no—
22C2×C4×D4×C139—24no—
23C2×C4×D4×C139—24no—
24C22×C4⋊C4×C139C2211yescharacteristic, complemented
25C22×C22⋊C4×C139—24no—
26C22×C22⋊C4×C139—28no—
27C22×C22⋊C4×C139C2211yescharacteristic
28C22×C22⋊C4×C139C2212yes—
29C22×C22⋊C4×C139C2212yes—
30C22×C22⋊C4×C139C2212yes—
31C22×C22⋊C4×C139C2211yescharacteristic
32C22×C22⋊C4×C139C2212yes—
33C22×C22⋊C4×C139C2211yescharacteristic
34C22×C22⋊C4×C139C2212yes—
35C22×C22⋊C4×C139C2211yescharacteristic, complemented
36C22×C22⋊C4×C139C2212yescomplemented
37C22×C42×C139C2211yescharacteristic, complemented
38#386×C139—24no—
39#386×C139—28no—
40#379×C139—24no—
41C2×#95×C139C2212yescomplemented
42C2×#95×C139C2212yescomplemented
43C2×#95×C139C2212yescomplemented
44C2×#95×C139C2212yescomplemented
45C2×#95×C139C2212yescomplemented
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×C414yescomplemented
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—24no—
67C22×D4×C139—24no—
68C22×D4×C139—42no—
69C22×D4×C139—42no—
70C22×D4×C139C2×C414yes—
71C22×D4×C139C2×C418yescomplemented
72C22×D4×C139D414yes—
73C22×D4×C139D414yes—
74C23×C4×C139—22no—
75C23×C4×C139—22no—
76C23×C4×C139—22no—
77C23×C4×C139—22no—
78C23×C4×C139—24no—
79C23×C4×C139—24no—
80C23×C4×C139—22no—
81C23×C4×C139—22no—
82C23×C4×C139—22no—
83C23×C4×C139—22no—
84C23×C4×C139—24no—
85C23×C4×C139—42no—
86C23×C4×C139—42no—
87C23×C4×C139—42no—
88C23×C4×C139D414yescomplemented
89C23×C4×C139C2312yes—
90C23×C4×C139C2312yes—
91C23×C4×C139C2311yescharacteristic
92C23×C4×C139C2311yescharacteristic
93C23×C4×C139C2311yescharacteristic
94C23×C4×C139C2312yes—
95C23×C4×C139C2311yescharacteristic
96C23×C4×C139C2311yescharacteristic
97#120×C139—232no—
98C4×D4×C139—232no—
99C2×C4⋊C4×C139—22no—
100C2×C4⋊C4×C139—22no—
101C2×C4⋊C4×C139—22no—
102C2×C22⋊C4×C139—232no—
103C2×C22⋊C4×C139—24no—
104C2×C22⋊C4×C139—22no—
105C2×C22⋊C4×C139—22no—
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—24no—
115C2×C22⋊C4×C139—22no—
116C2×C22⋊C4×C139—22no—
117C2×C22⋊C4×C139—22no—
118C2×C22⋊C4×C139—24no—
119C2×C22⋊C4×C139—22no—
120C2×C22⋊C4×C139—24no—
121C2×C22⋊C4×C139—24no—
122C2×C22⋊C4×C139—22no—
123C2×C22⋊C4×C139—24no—
124C2×C22⋊C4×C139—24no—
125C2×C22⋊C4×C139—24no—
126C2×C22⋊C4×C139—42no—
127C2×C22⋊C4×C139—42no—
128C2×C22⋊C4×C139—42no—
129C2×C22⋊C4×C139C2×C414yescomplemented
130C2×C22⋊C4×C139C2×C418yescomplemented
131C2×C22⋊C4×C139D418yescomplemented
132C2×C22⋊C4×C139D414yescomplemented
133C2×C42×C139—22no—
134C2×C42×C139—22no—
135C2×C42×C139—22no—
136#95×C139—24no—
137#95×C139—24no—
138#95×C139—24no—
139#95×C139—42no—
140#95×C139—42no—
141C24×C139—22no—
142C24×C139—22no—
143C24×C139—22no—
144C24×C139—22no—
145C24×C139—28no—
146C24×C139—28no—
147C24×C139—216no—
148C24×C139—28no—
149C24×C139—216no—
150C24×C139—22no—
151C24×C139—22no—
152C24×C139—22no—
153C24×C139—21no—
154C24×C139—21no—
155C24×C139—22no—
156C24×C139—22no—
157C24×C139—22no—
158C24×C139—21no—
159C24×C139—21no—
160C24×C139—22no—
161C24×C139—22no—
162C24×C139—22no—
163C24×C139—22no—
164C24×C139—22no—
165C24×C139—22no—
166C24×C139—22no—
167C24×C139—22no—
168C24×C139—22no—
169C24×C139—22no—
170C24×C139—28no—
171C24×C139—28no—
172C24×C139—48no—
173C24×C139—48no—
174C24×C139—48no—
175C24×C139—48no—
176C24×C139—48no—
177C24×C139—48no—
178C24×C139—48no—
179C24×C139—48no—
180C24×C139—48no—
181C24×C139—44no—
182C24×C139—44no—
183C24×C139—48no—
184C24×C139—44no—
185C24×C139—44no—
186C24×C139—44no—
187C24×C139—44no—
188C24×C139C22×C412yes—
189C24×C139C22×C414yes—
190C24×C139C22×C412yes—
191C24×C139C2×D412yes—
192C24×C139C2×D412yes—
193C24×C139C2×D414yes—
194C24×C139C2×D412yes—
195C24×C139C2×D412yes—
196C24×C139C2×D412yes—
197C24×C139C2×D412yes—
198C24×C139#4114yes—
199C24×C139#4112yes—
200C24×C139#4112yes—
201C24×C139C2411yescharacteristic
202C2×D4×C139—28no—
203C2×D4×C139—28no—
204C2×D4×C139—28no—
205C2×D4×C139—28no—
206C2×D4×C139—28no—
207C2×D4×C139—28no—
208C2×D4×C139—216no—
209C2×D4×C139—216no—
210C2×D4×C139—48no—
211C2×D4×C139—48no—
212C2×D4×C139—48no—
213C2×D4×C139—48no—
214C2×D4×C139—48no—
215C2×D4×C139C22⋊C4116yescomplemented
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139—21no—
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—22no—
223C22×C4×C139—28no—
224C22×C4×C139—28no—
225C22×C4×C139—28no—
226C22×C4×C139—22no—
227C22×C4×C139—22no—
228C22×C4×C139—22no—
229C22×C4×C139—21no—
230C22×C4×C139—21no—
231C22×C4×C139—22no—
232C22×C4×C139—22no—
233C22×C4×C139—22no—
234C22×C4×C139—22no—
235C22×C4×C139—22no—
236C22×C4×C139—21no—
237C22×C4×C139—21no—
238C22×C4×C139—21no—
239C22×C4×C139—21no—
240C22×C4×C139—22no—
241C22×C4×C139—22no—
242C22×C4×C139—22no—
243C22×C4×C139—22no—
244C22×C4×C139—22no—
245C22×C4×C139—22no—
246C22×C4×C139—22no—
247C22×C4×C139—22no—
248C22×C4×C139—22no—
249C22×C4×C139—22no—
250C22×C4×C139—28no—
251C22×C4×C139—22no—
252C22×C4×C139—22no—
253C22×C4×C139—22no—
254C22×C4×C139—22no—
255C22×C4×C139—22no—
256C22×C4×C139—22no—
257C22×C4×C139—22no—
258C22×C4×C139—44no—
259C22×C4×C139—48no—
260C22×C4×C139—48no—
261C22×C4×C139—48no—
262C22×C4×C139—48no—
263C22×C4×C139—48no—
264C22×C4×C139—48no—
265C22×C4×C139—44no—
266C22×C4×C139—44no—
267C22×C4×C139—44no—
268C22×C4×C139—44no—
269C22×C4×C139C22×C414yes—
270C22×C4×C139C22×C412yes—
271C22×C4×C139C2×D414yes—
272C22×C4×C139C2×D412yes—
273C22×C4×C139C2×D412yes—
274C22×C4×C139C2×D412yes—
275C22×C4×C139C2×D412yes—
276C22×C4×C139C2×D412yes—
277C22×C4×C139C2×D414yes—
278C22×C4×C139C2×D412yes—
279C4⋊C4×C139—28no—
280C22⋊C4×C139—216no—
281C22⋊C4×C139—28no—
282C22⋊C4×C139—28no—
283C22⋊C4×C139—28no—
284C22⋊C4×C139—216no—
285C22⋊C4×C139—216no—
286C22⋊C4×C139—48no—
287C22⋊C4×C139—48no—
288C22⋊C4×C139—48no—
289C22⋊C4×C139—44no—
290C42×C139—28no—
291C23×C139—24no—
292C23×C139—24no—
293C23×C139—22no—
294C23×C139—22no—
295C23×C139—24no—
296C23×C139—22no—
297C23×C139—22no—
298C23×C139—24no—
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—232no—
308C23×C139—24no—
309C23×C139—24no—
310C23×C139—22no—
311C23×C139—22no—
312C23×C139—24no—
313C23×C139—24no—
314C23×C139—24no—
315C23×C139—24no—
316C23×C139—24no—
317C23×C139—24no—
318C23×C139—24no—
319C23×C139—22no—
320C23×C139—22no—
321C23×C139—22no—
322C23×C139—22no—
323C23×C139—24no—
324C23×C139—24no—
325C23×C139—24no—
326C23×C139—24no—
327C23×C139—24no—
328C23×C139—24no—
329C23×C139—24no—
330C23×C139—24no—
331C23×C139—24no—
332C23×C139—24no—
333C23×C139—24no—
334C23×C139—24no—
335C23×C139—24no—
336C23×C139—24no—
337C23×C139—24no—
338C23×C139—432no—
339C23×C139—432no—
340C23×C139—416no—
341C23×C139—416no—
342C23×C139—416no—
343C23×C139—416no—
344C23×C139—432no—
345C23×C139—432no—
346C23×C139—416no—
347C23×C139—41no—
348C23×C139—42no—
349C23×C139—42no—
350C23×C139—42no—
351C23×C139—42no—
352C23×C139—41no—
353C23×C139—42no—
354C23×C139—41no—
355C23×C139—42no—
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×C139—42no—
367C23×C139—42no—
368C23×C139—42no—
369C23×C139—42no—
370C23×C139—42no—
371C23×C139—42no—
372C23×C139—42no—
373C23×C139—416no—
374C23×C139C2×C22⋊C414yes—
375C23×C139C2×C22⋊C414yescomplemented
376C23×C139C4×D414yes—
377C23×C139C4×D414yes—
378C23×C139C4×D418yescomplemented
379C23×C139#12014yes—
380C23×C139#12114yes—
381C23×C139#12114yes—
382C23×C139#12314yes—
383C23×C139C23×C411yescharacteristic
384C23×C139C22×D411yescharacteristic
385C23×C139C22×D411yescharacteristic
386C23×C139C22×D411yescharacteristic
387C23×C139C22×D411yescharacteristic
388C23×C139C22×D412yes—
389C23×C139C2×#4111yescharacteristic
390C23×C139C2×#4111yescharacteristic
391C23×C139C2×#4112yes—
392C23×C139H(5,𝔽2)12yes—
393C23×C139H(5,𝔽2)12yes—
394D4×C139—232no—
395D4×C139—432no—
396C2×C4×C139—22no—
397C2×C4×C139—22no—
398C2×C4×C139—22no—
399C2×C4×C139—22no—
400C2×C4×C139—22no—
401C2×C4×C139—22no—
402C2×C4×C139—22no—
403C2×C4×C139—22no—
404C2×C4×C139—24no—
405C2×C4×C139—24no—
406C2×C4×C139—24no—
407C2×C4×C139—24no—
408C2×C4×C139—24no—
409C2×C4×C139—22no—
410C2×C4×C139—22no—
411C2×C4×C139—24no—
412C2×C4×C139—22no—
413C2×C4×C139—22no—
414C2×C4×C139—22no—
415C2×C4×C139—24no—
416C2×C4×C139—24no—
417C2×C4×C139—24no—
418C2×C4×C139—24no—
419C2×C4×C139—416no—
420C2×C4×C139—416no—
421C2×C4×C139—416no—
422C2×C4×C139—41no—
423C2×C4×C139—42no—
424C2×C4×C139—41no—
425C2×C4×C139—41no—
426C2×C4×C139—41no—
427C2×C4×C139—42no—
428C2×C4×C139—42no—
429C2×C4×C139—42no—
430C2×C4×C139—42no—
431C2×C4×C139—42no—
432C2×C4×C139—42no—
433C2×C4×C139—42no—
434C2×C4×C139—42no—
435C2×C4×C139—42no—
436C2×C4×C139—42no—
437C2×C4×C139—42no—
438C2×C4×C139—42no—
439C2×C4×C139—42no—
440C2×C4×C139—42no—
441C2×C4×C139—42no—
442C2×C4×C139—42no—
443C2×C4×C139—42no—
444C2×C4×C139—42no—
445C2×C4×C139C2×C22⋊C414yescomplemented
446C2×C4×C139#12014yescomplemented
447C22×C139—24no—
448C22×C139—28no—
449C22×C139—28no—
450C22×C139—24no—
451C22×C139—24no—
452C22×C139—24no—
453C22×C139—28no—
454C22×C139—28no—
455C22×C139—24no—
456C22×C139—24no—
457C22×C139—28no—
458C22×C139—28no—
459C22×C139—28no—
460C22×C139—24no—
461C22×C139—28no—
462C22×C139—464no—
463C22×C139—42no—
464C22×C139—44no—
465C22×C139—44no—
466C22×C139—44no—
467C22×C139—44no—
468C22×C139—42no—
469C22×C139—44no—
470C22×C139—42no—
471C22×C139—44no—
472C22×C139—42no—
473C22×C139—44no—
474C22×C139—44no—
475C22×C139—44no—
476C22×C139—44no—
477C22×C139—44no—
478C22×C139—44no—
479C22×C139—44no—
480C22×C139—42no—
481C22×C139—44no—
482C22×C139—44no—
483C22×C139—42no—
484C22×C139#38618yescomplemented
485C22×C139C22×C22⋊C411yescharacteristic
486C22×C139C2×C4×D411yescharacteristic
487C22×C139C2×C4×D412yes—
488C22×C139C2×C4×D411yescharacteristic
489C22×C139#51812yes—
490C22×C139C2×#12011yescharacteristic
491C22×C139C2×#12011yescharacteristic
492C22×C139C2×#12111yescharacteristic
493C22×C139C2×#12111yescharacteristic
494C22×C139C2×#12311yescharacteristic
495C22×C139#52511yescharacteristic
496C22×C139#52512yes—
497C22×C139#53411yescharacteristic
498C22×C139#53511yescharacteristic
499C22×C139#53812yes—
500C22×C139D4212yes—
501C22×C139D4212yes—
502C22×C139D4212yes—
503C22×C139#54612yes—
504C22×C139#54612yes—
505C22×C139#54612yes—
506C22×C139#54612yes—
507C22×C139#55112yes—
508C4×C139—24no—
509C4×C139—24no—
510C4×C139—44no—
511C4×C139—42no—
512C4×C139—42no—
513C4×C139—42no—
514C4×C139—44no—
515C4×C139—82no—
516C2×C139—28no—
517C2×C139—44no—
518C2×C139—48no—
519C2×C139C2×#38611yescharacteristic
520C2×C139C4×#12011yescharacteristic
521C2×C139#232111yescharacteristic
522C2×C139D4×C22⋊C412yes—
523C2×C139#235812yes—
524C2×C139#240311yescharacteristic
525C2×C139#240411yescharacteristic
526C2×C139#240811yescharacteristic
527C2×C139#241812yes—
528C2×C139#242412yes—
529C2×C139#253411yescharacteristic
530#13967C13911yesmaximal, characteristic, direct product factor, Sylow
531C139#1396711yescharacteristic, direct product factor, Sylow
532C22×#120C2×C13911yescharacteristic
533C22×C4×D4C2×C13911yescharacteristic, complemented
534C23×C22⋊C4C2×C13911yescharacteristic, complemented
535C2×#386C2×C13912yescomplemented
536C2×#386C2×C13911yescharacteristic, complemented
537C2×#379C2×C13911yescharacteristic, complemented
538#1439C2×C13912yescomplemented
539#1438C2×C13912yescomplemented
540#1437C2×C13912yescomplemented
541C22⋊#95C2×C13911yescharacteristic, complemented
542C22⋊#95C2×C13911yescharacteristic, complemented
543C26C22×C13911yescharacteristic
544C23×D4C22×C13912yes—
545C23×D4C22×C13911yescharacteristic
546C24×C4C22×C13911yescharacteristic
547C24×C4C22×C13911yescharacteristic
548C24×C4C22×C13911yescharacteristic, complemented
549C2×#120—24no—
550C2×#120—24no—
551C2×#120C4×C13918yescomplemented
552C2×C4×D4—24no—
553C2×C4×D4—24no—
554C2×C4×D4—24no—
555C22×C4⋊C4C22×C13911yescharacteristic, complemented
556C22×C22⋊C4—24no—
557C22×C22⋊C4—28no—
558C22×C22⋊C4C22×C13912yes—
559C22×C22⋊C4C22×C13911yescharacteristic
560C22×C22⋊C4C22×C13912yes—
561C22×C22⋊C4C22×C13912yes—
562C22×C22⋊C4C22×C13911yescharacteristic
563C22×C22⋊C4C22×C13912yes—
564C22×C22⋊C4C22×C13912yes—
565C22×C22⋊C4C22×C13911yescharacteristic
566C22×C22⋊C4C22×C13911yescharacteristic, complemented
567C22×C22⋊C4C22×C13912yescomplemented
568C22×C42C22×C13911yescharacteristic, complemented
569#386—24no—
570#386—28no—
571#379—24no—
572C2×#95C22×C13912yescomplemented
573C2×#95C22×C13912yescomplemented
574C2×#95C22×C13912yescomplemented
575C2×#95C22×C13912yescomplemented
576C2×#95C22×C13912yescomplemented
577C25—24no—
578C25—22no—
579C25—24no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—22no—
585C25—42no—
586C25—42no—
587C25C2×C4×C13914yescomplemented
588C25C23×C13911yescharacteristic
589C25C23×C13912yes—
590C25C23×C13911yescharacteristic
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4C2×C4×C13914yes—
602C22×D4C2×C4×C13918yescomplemented
603C22×D4D4×C13914yes—
604C22×D4D4×C13914yes—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—24no—
616C23×C4—42no—
617C23×C4—42no—
618C23×C4—42no—
619C23×C4D4×C13914yescomplemented
620C23×C4C23×C13912yes—
621C23×C4C23×C13912yes—
622C23×C4C23×C13911yescharacteristic
623C23×C4C23×C13911yescharacteristic
624C23×C4C23×C13911yescharacteristic
625C23×C4C23×C13912yes—
626C23×C4C23×C13911yescharacteristic
627C23×C4C23×C13911yescharacteristic
628#120—232no—
629C4×D4—232no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C22⋊C4—232no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—42no—
658C2×C22⋊C4—42no—
659C2×C22⋊C4—42no—
660C2×C22⋊C4C2×C4×C13914yescomplemented
661C2×C22⋊C4C2×C4×C13918yescomplemented
662C2×C22⋊C4D4×C13918yescomplemented
663C2×C22⋊C4D4×C13914yescomplemented
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667#95—24no—
668#95—24no—
669#95—24no—
670#95—42no—
671#95—42no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—28no—
678C24—216no—
679C24—28no—
680C24—216no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—48no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24C22×C4×C13912yes—
720C24C22×C4×C13914yes—
721C24C22×C4×C13912yes—
722C24C2×D4×C13912yes—
723C24C2×D4×C13912yes—
724C24C2×D4×C13914yes—
725C24C2×D4×C13912yes—
726C24C2×D4×C13912yes—
727C24C2×D4×C13912yes—
728C24C2×D4×C13912yes—
729C24#41×C13914yes—
730C24#41×C13912yes—
731C24#41×C13912yes—
732C24C24×C13911yescharacteristic
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4C22⋊C4×C139116yescomplemented
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4C22×C4×C13914yes—
801C22×C4C22×C4×C13912yes—
802C22×C4C2×D4×C13914yes—
803C22×C4C2×D4×C13912yes—
804C22×C4C2×D4×C13912yes—
805C22×C4C2×D4×C13912yes—
806C22×C4C2×D4×C13912yes—
807C22×C4C2×D4×C13912yes—
808C22×C4C2×D4×C13914yes—
809C22×C4C2×D4×C13912yes—
810C4⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C42—28no—
822C23—24no—
823C23—24no—
824C23—22no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—22no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—232no—
839C23—24no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—432no—
870C23—432no—
871C23—416no—
872C23—416no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—432no—
877C23—432no—
878C23—41no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—41no—
884C23—42no—
885C23—41no—
886C23—42no—
887C23—42no—
888C23—41no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—416no—
905C23C2×C22⋊C4×C13914yes—
906C23C2×C22⋊C4×C13914yescomplemented
907C23C4×D4×C13914yes—
908C23C4×D4×C13914yes—
909C23C4×D4×C13918yescomplemented
910C23#120×C13914yes—
911C23#121×C13914yes—
912C23#121×C13914yes—
913C23#123×C13914yes—
914C23C23×C4×C13911yescharacteristic
915C23C22×D4×C13911yescharacteristic
916C23C22×D4×C13911yescharacteristic
917C23C22×D4×C13911yescharacteristic
918C23C22×D4×C13911yescharacteristic
919C23C22×D4×C13912yes—
920C23C2×#41×C13911yescharacteristic
921C23C2×#41×C13911yescharacteristic
922C23C2×#41×C13912yes—
923C23H(5,𝔽2)×C13912yes—
924C23H(5,𝔽2)×C13912yes—
925D4—232no—
926D4—432no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—41no—
954C2×C4—42no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—41no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4C2×C22⋊C4×C13914yescomplemented
977C2×C4#120×C13914yescomplemented
978C22—24no—
979C22—24no—
980C22—24no—
981C22—28no—
982C22—28no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—28no—
987C22—28no—
988C22—24no—
989C22—28no—
990C22—28no—
991C22—28no—
992C22—28no—
993C22—464no—
994C22—44no—
995C22—42no—
996C22—44no—
997C22—42no—
998C22—44no—
999C22—42no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—42no—
1004C22—44no—
1005C22—44no—
1006C22—42no—
1007C22—44no—
1008C22—42no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22#386×C13918yescomplemented
1016C22C22×C22⋊C4×C13911yescharacteristic
1017C22C2×C4×D4×C13911yescharacteristic
1018C22C2×C4×D4×C13911yescharacteristic
1019C22C2×C4×D4×C13912yes—
1020C22#518×C13912yes—
1021C22C2×#120×C13911yescharacteristic
1022C22C2×#120×C13911yescharacteristic
1023C22C2×#121×C13911yescharacteristic
1024C22C2×#121×C13911yescharacteristic
1025C22C2×#123×C13911yescharacteristic
1026C22#525×C13911yescharacteristic
1027C22#525×C13912yes—
1028C22#534×C13911yescharacteristic
1029C22#535×C13911yescharacteristic
1030C22#538×C13912yes—
1031C22D42×C13912yes—
1032C22D42×C13912yes—
1033C22D42×C13912yes—
1034C22#546×C13912yes—
1035C22#546×C13912yes—
1036C22#546×C13912yes—
1037C22#546×C13912yes—
1038C22#551×C13912yes—
1039C4—24no—
1040C4—24no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×#386×C13911yescharacteristic
1051C2C4×#120×C13911yescharacteristic
1052C2#2321×C13911yescharacteristic
1053C2D4×C22⋊C4×C13912yes—
1054C2#2358×C13912yes—
1055C2#2403×C13911yescharacteristic
1056C2#2404×C13911yescharacteristic
1057C2#2408×C13911yescharacteristic
1058C2#2418×C13912yes—
1059C2#2424×C13912yes—
1060C2#2534×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. C22×C4×D4×C139C2semidirect
3. C23×C22⋊C4×C139C2semidirect
4. C2×#386×C139C2semidirect
5. C2×#386×C139C2semidirect
6. C2×#379×C139C2semidirect
7. #1439×C139C2semidirect
8. #1438×C139C2semidirect
9. #1437×C139C2semidirect
10. C22⋊#95×C139C2semidirect
11. C22⋊#95×C139C2semidirect
17. C24×C4×C139C22semidirect
20. C2×#120×C139C4semidirect
24. C22×C4⋊C4×C139C22semidirect
35. C22×C22⋊C4×C139C22semidirect
36. C22×C22⋊C4×C139C22semidirect
37. C22×C42×C139C22semidirect
41. C2×#95×C139C22semidirect
42. C2×#95×C139C22semidirect
43. C2×#95×C139C22semidirect
44. C2×#95×C139C22semidirect
45. C2×#95×C139C22semidirect
56. C25×C139C2×C4semidirect
71. C22×D4×C139C2×C4semidirect
88. C23×C4×C139D4semidirect
129. C2×C22⋊C4×C139C2×C4semidirect
130. C2×C22⋊C4×C139C2×C4semidirect
131. C2×C22⋊C4×C139D4semidirect
132. C2×C22⋊C4×C139D4semidirect
215. C2×D4×C139C22⋊C4semidirect
375. C23×C139C2×C22⋊C4semidirect
378. C23×C139C4×D4semidirect
445. C2×C4×C139C2×C22⋊C4semidirect
446. C2×C4×C139#120semidirect
484. C22×C139#386semidirect
530. #13967C139direct (N × H)
531. C139#13967direct (N × H)
533. C22×C4×D4C2×C139semidirect
534. C23×C22⋊C4C2×C139semidirect
535. C2×#386C2×C139semidirect
536. C2×#386C2×C139semidirect
537. C2×#379C2×C139semidirect
538. #1439C2×C139semidirect
539. #1438C2×C139semidirect
540. #1437C2×C139semidirect
541. C22⋊#95C2×C139semidirect
542. C22⋊#95C2×C139semidirect
548. C24×C4C22×C139semidirect
551. C2×#120C4×C139semidirect
555. C22×C4⋊C4C22×C139semidirect
566. C22×C22⋊C4C22×C139semidirect
567. C22×C22⋊C4C22×C139semidirect
568. C22×C42C22×C139semidirect
572. C2×#95C22×C139semidirect
573. C2×#95C22×C139semidirect
574. C2×#95C22×C139semidirect
575. C2×#95C22×C139semidirect
576. C2×#95C22×C139semidirect
587. C25C2×C4×C139semidirect
602. C22×D4C2×C4×C139semidirect
619. C23×C4D4×C139semidirect
660. C2×C22⋊C4C2×C4×C139semidirect
661. C2×C22⋊C4C2×C4×C139semidirect
662. C2×C22⋊C4D4×C139semidirect
663. C2×C22⋊C4D4×C139semidirect
746. C2×D4C22⋊C4×C139semidirect
906. C23C2×C22⋊C4×C139semidirect
909. C23C4×D4×C139semidirect
976. C2×C4C2×C22⋊C4×C139semidirect
977. C2×C4#120×C139semidirect
1015. C22#386×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1392
C22×C4×D4×C1392
C23×C22⋊C4×C1392
C2×#386×C1392
C2×#379×C1392
#1439×C1392
#1438×C1392
#1437×C1392
C22⋊#95×C1392
#13967139