Finite Group Databasebeta

← C139×#15913 #48010509

Subgroups — C139×#15913 #48010509

Order 35584.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1152 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#126×C139C211yesmaximal, characteristic, complemented
2C2×#397×C139C211yesmaximal, characteristic, complemented
3C2×#396×C139C211yesmaximal, characteristic, complemented
4C2×#390×C139C211yesmaximal, characteristic
5#1444×C139C211yesmaximal, characteristic, complemented
6#1440×C139C211yesmaximal, characteristic, complemented
7#1439×C139C211yesmaximal, characteristic, complemented
8#1439×C139C211yesmaximal, characteristic, complemented
9#1439×C139C211yesmaximal, characteristic, complemented
10#1438×C139C211yesmaximal, characteristic
11#1438×C139C211yesmaximal, characteristic
12#1437×C139C211yesmaximal, characteristic, complemented
13#1436×C139C211yesmaximal, characteristic, complemented
14#1436×C139C211yesmaximal, characteristic, complemented
15C4⋊#95×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C2×#126×C139—24no—
18C2×#126×C139—24no—
19C2×#126×C139—24no—
20C22×C4⋊C4×C139C2211yescharacteristic
21C22×C4⋊C4×C139C2211yescharacteristic
22C22×C4⋊C4×C139C2211yescharacteristic
23C22×C4⋊C4×C139C2211yescharacteristic
24C22×C4⋊C4×C139C2211yescharacteristic
25C22×C4⋊C4×C139C2211yescharacteristic
26C22×C22⋊C4×C139C2211yescharacteristic
27C22×C22⋊C4×C139C2211yescharacteristic
28C22×C22⋊C4×C139C2211yescharacteristic
29C22×C22⋊C4×C139C2211yescharacteristic
30C22×C22⋊C4×C139C2211yescharacteristic
31C22×C22⋊C4×C139C2211yescharacteristic
32C22×C22⋊C4×C139C2211yescharacteristic
33C22×C22⋊C4×C139C2211yescharacteristic
34C22×C22⋊C4×C139C2211yescharacteristic
35C22×C22⋊C4×C139C2211yescharacteristic
36C22×C22⋊C4×C139C2211yescharacteristic
37C22×C22⋊C4×C139C2211yescharacteristic
38C22×C42×C139C2211yescharacteristic
39C22×C42×C139C2211yescharacteristic
40#397×C139—24no—
41#396×C139—24no—
42#390×C139—24no—
43C2×#95×C139C2211yescharacteristic
44C2×#95×C139C2211yescharacteristic
45C2×#95×C139C2211yescharacteristic
46C2×#95×C139C2211yescharacteristic
47C2×#95×C139C2211yescharacteristic
48C2×#95×C139C2211yescharacteristic
49C2×#95×C139C2211yescharacteristic
50C2×#95×C139C2211yescharacteristic
51C2×#95×C139C2211yescharacteristic
52C2×#95×C139C2211yescharacteristic
53C2×#95×C139C2211yescharacteristic
54C2×#95×C139C2211yescharacteristic
55C2×#95×C139C2211yescharacteristic
56C2×#95×C139C2211yescharacteristic
57C25×C139C2311yescharacteristic
58C25×C139C2311yescharacteristic
59C22×D4×C139—22no—
60C22×D4×C139—22no—
61C22×D4×C139—22no—
62C22×D4×C139—22no—
63C22×D4×C139—22no—
64C22×D4×C139—41no—
65C22×D4×C139—41no—
66C23×C4×C139C2311yescharacteristic
67C23×C4×C139C2311yescharacteristic
68C23×C4×C139C2311yescharacteristic
69C23×C4×C139C2311yescharacteristic
70C23×C4×C139C2311yescharacteristic
71C23×C4×C139C2311yescharacteristic
72C23×C4×C139C2311yescharacteristic
73C23×C4×C139C2311yescharacteristic
74C23×C4×C139C2311yescharacteristic
75C23×C4×C139C2311yescharacteristic
76C23×C4×C139C2311yescharacteristic
77C23×C4×C139C2311yescharacteristic
78C23×C4×C139C2311yescharacteristic
79#126×C139—232no—
80C2×C4⋊C4×C139—22no—
81C2×C4⋊C4×C139—22no—
82C2×C4⋊C4×C139—22no—
83C2×C4⋊C4×C139—22no—
84C2×C4⋊C4×C139—22no—
85C2×C4⋊C4×C139—22no—
86C2×C4⋊C4×C139—22no—
87C2×C4⋊C4×C139—22no—
88C2×C4⋊C4×C139—22no—
89C2×C4⋊C4×C139—22no—
90C2×C4⋊C4×C139—22no—
91C2×C4⋊C4×C139—22no—
92C2×C4⋊C4×C139—41no—
93C2×C4⋊C4×C139—41no—
94C2×C4⋊C4×C139—41no—
95C2×C4⋊C4×C139—41no—
96C2×C4⋊C4×C139D414yescomplemented
97C2×C4⋊C4×C139D414yescomplemented
98C2×C22⋊C4×C139—22no—
99C2×C22⋊C4×C139—22no—
100C2×C22⋊C4×C139—22no—
101C2×C22⋊C4×C139—22no—
102C2×C22⋊C4×C139—22no—
103C2×C22⋊C4×C139—22no—
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—22no—
110C2×C22⋊C4×C139—22no—
111C2×C22⋊C4×C139—22no—
112C2×C22⋊C4×C139—22no—
113C2×C22⋊C4×C139—22no—
114C2×C22⋊C4×C139—22no—
115C2×C22⋊C4×C139—22no—
116C2×C22⋊C4×C139—22no—
117C2×C22⋊C4×C139—22no—
118C2×C22⋊C4×C139—22no—
119C2×C22⋊C4×C139—22no—
120C2×C22⋊C4×C139—22no—
121C2×C22⋊C4×C139—41no—
122C2×C22⋊C4×C139—41no—
123C2×C22⋊C4×C139—41no—
124C2×C22⋊C4×C139—41no—
125C2×C22⋊C4×C139—41no—
126C2×C22⋊C4×C139—41no—
127C2×C22⋊C4×C139—41no—
128C2×C22⋊C4×C139—41no—
129C2×C22⋊C4×C139—41no—
130C2×C22⋊C4×C139—41no—
131C2×C22⋊C4×C139—41no—
132C2×C22⋊C4×C139—41no—
133C2×C22⋊C4×C139D414yes—
134C2×C42×C139—22no—
135C2×C42×C139—22no—
136C2×C42×C139—22no—
137C2×C42×C139—22no—
138C2×C42×C139—22no—
139C2×C42×C139—41no—
140#95×C139—22no—
141#95×C139—22no—
142#95×C139—22no—
143#95×C139—22no—
144#95×C139—22no—
145#95×C139—22no—
146#95×C139—22no—
147#95×C139—22no—
148#95×C139—22no—
149#95×C139—41no—
150#95×C139—41no—
151#95×C139—41no—
152#95×C139—41no—
153#95×C139—41no—
154C24×C139—21no—
155C24×C139—21no—
156C24×C139—21no—
157C24×C139—21no—
158C24×C139—21no—
159C24×C139—21no—
160C24×C139—21no—
161C24×C139—21no—
162C24×C139—21no—
163C24×C139—21no—
164C24×C139—21no—
165C24×C139—21no—
166C24×C139—21no—
167C24×C139—21no—
168C24×C139—21no—
169C24×C139—21no—
170C24×C139—21no—
171C24×C139—21no—
172C24×C139—21no—
173C24×C139—21no—
174C24×C139—21no—
175C24×C139—21no—
176C24×C139—21no—
177C24×C139—21no—
178C24×C139—21no—
179C24×C139—21no—
180C24×C139—21no—
181C24×C139—21no—
182C24×C139C2×D412yes—
183C24×C139#4112yes—
184C24×C139C2411yescharacteristic
185C2×D4×C139—28no—
186C2×D4×C139—44no—
187C2×D4×C139—44no—
188C2×D4×C139—44no—
189C2×D4×C139—44no—
190C2×D4×C139—44no—
191C2×D4×C139—44no—
192C22×C4×C139—21no—
193C22×C4×C139—21no—
194C22×C4×C139—21no—
195C22×C4×C139—21no—
196C22×C4×C139—21no—
197C22×C4×C139—21no—
198C22×C4×C139—21no—
199C22×C4×C139—21no—
200C22×C4×C139—21no—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
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—21no—
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—21no—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
229C22×C4×C139—21no—
230C22×C4×C139—21no—
231C22×C4×C139—21no—
232C22×C4×C139—21no—
233C22×C4×C139—21no—
234C22×C4×C139—21no—
235C22×C4×C139—21no—
236C22×C4×C139—21no—
237C22×C4×C139—21no—
238C22×C4×C139—21no—
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—21no—
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×C139—21no—
254C22×C4×C139—21no—
255C22×C4×C139—21no—
256C22×C4×C139—21no—
257C22×C4×C139—21no—
258C22×C4×C139—21no—
259C22×C4×C139—21no—
260C22×C4×C139—21no—
261C22×C4×C139—21no—
262C22×C4×C139—21no—
263C22×C4×C139—21no—
264C22×C4×C139—21no—
265C22×C4×C139—21no—
266C22×C4×C139—21no—
267C22×C4×C139—21no—
268C22×C4×C139—21no—
269C22×C4×C139—21no—
270C22×C4×C139C2×D412yes—
271C22×C4×C139C2×D412yes—
272C22×C4×C139C2×D412yes—
273C22×C4×C139C2×D412yes—
274C22×C4×C139C2×D412yes—
275C22×C4×C139C2×D412yes—
276C22×C4×C139C2×D412yes—
277C22×C4×C139C2×D412yes—
278C22×C4×C139#4112yes—
279C22×C4×C139#4112yes—
280C22×C4×C139#4112yes—
281C22×C4×C139#4112yes—
282C22×C4×C139#4112yes—
283C4⋊C4×C139—28no—
284C4⋊C4×C139—28no—
285C4⋊C4×C139—28no—
286C4⋊C4×C139—44no—
287C4⋊C4×C139—44no—
288C4⋊C4×C139—44no—
289C22⋊C4×C139—28no—
290C22⋊C4×C139—28no—
291C22⋊C4×C139—28no—
292C22⋊C4×C139—44no—
293C22⋊C4×C139—44no—
294C22⋊C4×C139—44no—
295C22⋊C4×C139—44no—
296C22⋊C4×C139—44no—
297C22⋊C4×C139—44no—
298C22⋊C4×C139—44no—
299C22⋊C4×C139—44no—
300C22⋊C4×C139—44no—
301C42×C139—28no—
302C42×C139—44no—
303C23×C139—22no—
304C23×C139—22no—
305C23×C139—22no—
306C23×C139—22no—
307C23×C139—22no—
308C23×C139—22no—
309C23×C139—22no—
310C23×C139—22no—
311C23×C139—22no—
312C23×C139—22no—
313C23×C139—22no—
314C23×C139—22no—
315C23×C139—22no—
316C23×C139—22no—
317C23×C139—41no—
318C23×C139—41no—
319C23×C139—41no—
320C23×C139—41no—
321C23×C139—41no—
322C23×C139—41no—
323C23×C139—41no—
324C23×C139—41no—
325C23×C139—41no—
326C23×C139—41no—
327C23×C139—41no—
328C23×C139—41no—
329C23×C139—41no—
330C23×C139—41no—
331C23×C139—41no—
332C23×C139—41no—
333C23×C139—41no—
334C23×C139—41no—
335C23×C139—41no—
336C23×C139—41no—
337C23×C139—41no—
338C23×C139—41no—
339C23×C139—41no—
340C23×C139—41no—
341C23×C139—41no—
342C23×C139—41no—
343C23×C139—41no—
344C23×C139—41no—
345C23×C139—41no—
346C23×C139—41no—
347C23×C139—41no—
348C23×C139—41no—
349C23×C139—41no—
350C23×C139—41no—
351C23×C139—41no—
352C23×C139—41no—
353C23×C139—41no—
354C23×C139—41no—
355C23×C139—41no—
356C23×C139—41no—
357C23×C139—41no—
358C23×C139—41no—
359C23×C139—41no—
360C23×C139—41no—
361C23×C139—41no—
362C23×C139—41no—
363C23×C139—41no—
364C23×C139—41no—
365C23×C139—41no—
366C23×C139—41no—
367C23×C139—41no—
368C23×C139—41no—
369C23×C139—41no—
370C23×C139—41no—
371C23×C139—41no—
372C23×C139—41no—
373C23×C139C22×D411yescharacteristic
374C23×C139C22×D411yescharacteristic
375C23×C139C22×D411yescharacteristic
376C23×C139C2×#4111yescharacteristic
377C23×C139C2×#4111yescharacteristic
378C23×C139C2×#4111yescharacteristic
379C23×C139C2×#4111yescharacteristic
380C23×C139C2×#4111yescharacteristic
381C23×C139C2×#4111yescharacteristic
382C23×C139H(5,𝔽2)11yescharacteristic
383C23×C139H(5,𝔽2)11yescharacteristic
384C23×C139H(5,𝔽2)11yescharacteristic
385C23×C139H(5,𝔽2)11yescharacteristic
386C23×C1392−1+411yescharacteristic
387C23×C1392−1+411yescharacteristic
388D4×C139—416no—
389C2×C4×C139—22no—
390C2×C4×C139—22no—
391C2×C4×C139—22no—
392C2×C4×C139—22no—
393C2×C4×C139—22no—
394C2×C4×C139—22no—
395C2×C4×C139—22no—
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—22no—
405C2×C4×C139—22no—
406C2×C4×C139—22no—
407C2×C4×C139—22no—
408C2×C4×C139—22no—
409C2×C4×C139—22no—
410C2×C4×C139—22no—
411C2×C4×C139—22no—
412C2×C4×C139—22no—
413C2×C4×C139—22no—
414C2×C4×C139—22no—
415C2×C4×C139—22no—
416C2×C4×C139—22no—
417C2×C4×C139—22no—
418C2×C4×C139—22no—
419C2×C4×C139—22no—
420C2×C4×C139—22no—
421C2×C4×C139—22no—
422C2×C4×C139—41no—
423C2×C4×C139—41no—
424C2×C4×C139—41no—
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—41no—
432C2×C4×C139—41no—
433C2×C4×C139—41no—
434C2×C4×C139—41no—
435C2×C4×C139—41no—
436C2×C4×C139—41no—
437C2×C4×C139—41no—
438C2×C4×C139—41no—
439C2×C4×C139—41no—
440C2×C4×C139—41no—
441C2×C4×C139—41no—
442C2×C4×C139—41no—
443C2×C4×C139—41no—
444C2×C4×C139—41no—
445C2×C4×C139—41no—
446C2×C4×C139—41no—
447C2×C4×C139—41no—
448C2×C4×C139—41no—
449C2×C4×C139—41no—
450C2×C4×C139—41no—
451C2×C4×C139—41no—
452C2×C4×C139—41no—
453C2×C4×C139—41no—
454C2×C4×C139—41no—
455C2×C4×C139—41no—
456C2×C4×C139—41no—
457C2×C4×C139—41no—
458C2×C4×C139—41no—
459C2×C4×C139—41no—
460C2×C4×C139—41no—
461C2×C4×C139—41no—
462C2×C4×C139—41no—
463C2×C4×C139—41no—
464C2×C4×C139—41no—
465C2×C4×C139—41no—
466C2×C4×C139—41no—
467C2×C4×C139—41no—
468C2×C4×C139—41no—
469C2×C4×C139—41no—
470C2×C4×C139—41no—
471C2×C4×C139—41no—
472C2×C4×C139—41no—
473C2×C4×C139—41no—
474C2×C4×C139—41no—
475C2×C4×C139—41no—
476C2×C4×C139—41no—
477C2×C4×C139—41no—
478C2×C4×C139#12014yes—
479C2×C4×C139#12614yescomplemented
480C22×C139—42no—
481C22×C139—42no—
482C22×C139—42no—
483C22×C139—42no—
484C22×C139—42no—
485C22×C139—42no—
486C22×C139—42no—
487C22×C139—42no—
488C22×C139—42no—
489C22×C139—42no—
490C22×C139—42no—
491C22×C139—42no—
492C22×C139—42no—
493C22×C139—42no—
494C22×C139—81no—
495C22×C139—81no—
496C22×C139—81no—
497C22×C139—81no—
498C22×C139—81no—
499C22×C139—81no—
500C22×C139—81no—
501C22×C139—81no—
502C22×C139—81no—
503C22×C139—81no—
504C22×C139—81no—
505C22×C139—81no—
506C22×C139—81no—
507C22×C139—81no—
508C22×C139—81no—
509C22×C139—81no—
510C22×C139C2×#12011yescharacteristic
511C22×C139#52511yescharacteristic
512C22×C139C2×#12611yescharacteristic
513C22×C139#52911yescharacteristic
514C22×C139#53211yescharacteristic
515C22×C139#53211yescharacteristic
516C22×C139#53511yescharacteristic
517C22×C139#53711yescharacteristic
518C22×C139#53711yescharacteristic
519C22×C139#53811yescharacteristic
520C22×C139#53811yescharacteristic
521C22×C139#53911yescharacteristic
522C22×C139#53911yescharacteristic
523C22×C139#54211yescharacteristic
524C22×C139#54211yescharacteristic
525C22×C139#54611yescharacteristic
526C22×C139#54611yescharacteristic
527C22×C139#54611yescharacteristic
528C22×C139#54611yescharacteristic
529C22×C139#54611yescharacteristic
530C22×C139#54711yescharacteristic
531C22×C139#54711yescharacteristic
532C22×C139#54711yescharacteristic
533C22×C139#54811yescharacteristic
534C22×C139#55011yescharacteristic
535C22×C139#55011yescharacteristic
536C22×C139#55011yescharacteristic
537C22×C139#55111yescharacteristic
538C22×C139#55111yescharacteristic
539C22×C139#55311yescharacteristic
540C22×C139#55311yescharacteristic
541C22×C139#55611yescharacteristic
542C22×C139#55611yescharacteristic
543C22×C139#56011yescharacteristic
544C22×C139#56311yescharacteristic
545C4×C139—24no—
546C4×C139—24no—
547C4×C139—42no—
548C4×C139—42no—
549C4×C139—42no—
550C4×C139—42no—
551C4×C139—42no—
552C4×C139—42no—
553C4×C139—42no—
554C4×C139—81no—
555C4×C139—81no—
556C4×C139—81no—
557C4×C139—81no—
558C2×C139—82no—
559C2×C139—82no—
560C2×C139#240711yescharacteristic
561C2×C139#243011yescharacteristic
562C2×C139#243111yescharacteristic
563C2×C139#246611yescharacteristic
564C2×C139#248011yescharacteristic
565C2×C139#251211yescharacteristic
566C2×C139#251211yescharacteristic
567C2×C139#255411yescharacteristic
568C2×C139#256011yescharacteristic
569C2×C139#269111yescharacteristic
570C2×C139#270511yescharacteristic
571C2×C139#271411yescharacteristic
572C2×C139#271511yescharacteristic
573C2×C139#272311yescharacteristic
574C2×C139#272711yescharacteristic
575#15913C13911yesmaximal, characteristic, direct product factor, Sylow
576C139#1591311yescharacteristic, direct product factor, Sylow
577C22×#126C2×C13911yescharacteristic, complemented
578C2×#397C2×C13911yescharacteristic, complemented
579C2×#396C2×C13911yescharacteristic, complemented
580C2×#390C2×C13911yescharacteristic
581#1444C2×C13911yescharacteristic, complemented
582#1440C2×C13911yescharacteristic, complemented
583#1439C2×C13911yescharacteristic, complemented
584#1439C2×C13911yescharacteristic, complemented
585#1439C2×C13911yescharacteristic, complemented
586#1438C2×C13911yescharacteristic
587#1438C2×C13911yescharacteristic
588#1437C2×C13911yescharacteristic, complemented
589#1436C2×C13911yescharacteristic, complemented
590#1436C2×C13911yescharacteristic, complemented
591C4⋊#95C2×C13911yescharacteristic, complemented
592C23×D4C22×C13911yescharacteristic
593C2×#126—24no—
594C2×#126—24no—
595C2×#126—24no—
596C22×C4⋊C4C22×C13911yescharacteristic
597C22×C4⋊C4C22×C13911yescharacteristic
598C22×C4⋊C4C22×C13911yescharacteristic
599C22×C4⋊C4C22×C13911yescharacteristic
600C22×C4⋊C4C22×C13911yescharacteristic
601C22×C4⋊C4C22×C13911yescharacteristic
602C22×C22⋊C4C22×C13911yescharacteristic
603C22×C22⋊C4C22×C13911yescharacteristic
604C22×C22⋊C4C22×C13911yescharacteristic
605C22×C22⋊C4C22×C13911yescharacteristic
606C22×C22⋊C4C22×C13911yescharacteristic
607C22×C22⋊C4C22×C13911yescharacteristic
608C22×C22⋊C4C22×C13911yescharacteristic
609C22×C22⋊C4C22×C13911yescharacteristic
610C22×C22⋊C4C22×C13911yescharacteristic
611C22×C22⋊C4C22×C13911yescharacteristic
612C22×C22⋊C4C22×C13911yescharacteristic
613C22×C22⋊C4C22×C13911yescharacteristic
614C22×C42C22×C13911yescharacteristic
615C22×C42C22×C13911yescharacteristic
616#397—24no—
617#396—24no—
618#390—24no—
619C2×#95C22×C13911yescharacteristic
620C2×#95C22×C13911yescharacteristic
621C2×#95C22×C13911yescharacteristic
622C2×#95C22×C13911yescharacteristic
623C2×#95C22×C13911yescharacteristic
624C2×#95C22×C13911yescharacteristic
625C2×#95C22×C13911yescharacteristic
626C2×#95C22×C13911yescharacteristic
627C2×#95C22×C13911yescharacteristic
628C2×#95C22×C13911yescharacteristic
629C2×#95C22×C13911yescharacteristic
630C2×#95C22×C13911yescharacteristic
631C2×#95C22×C13911yescharacteristic
632C2×#95C22×C13911yescharacteristic
633C25C23×C13911yescharacteristic
634C25C23×C13911yescharacteristic
635C22×D4—22no—
636C22×D4—22no—
637C22×D4—22no—
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—41no—
641C22×D4—41no—
642C23×C4C23×C13911yescharacteristic
643C23×C4C23×C13911yescharacteristic
644C23×C4C23×C13911yescharacteristic
645C23×C4C23×C13911yescharacteristic
646C23×C4C23×C13911yescharacteristic
647C23×C4C23×C13911yescharacteristic
648C23×C4C23×C13911yescharacteristic
649C23×C4C23×C13911yescharacteristic
650C23×C4C23×C13911yescharacteristic
651C23×C4C23×C13911yescharacteristic
652C23×C4C23×C13911yescharacteristic
653C23×C4C23×C13911yescharacteristic
654C23×C4C23×C13911yescharacteristic
655#126—232no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4D4×C13914yescomplemented
673C2×C4⋊C4D4×C13914yescomplemented
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4—41no—
702C2×C22⋊C4—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4D4×C13914yes—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—22no—
714C2×C42—22no—
715C2×C42—41no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—41no—
726#95—41no—
727#95—41no—
728#95—41no—
729#95—41no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24C2×D4×C13912yes—
759C24#41×C13912yes—
760C24C24×C13911yescharacteristic
761C2×D4—28no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—44no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
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—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4C2×D4×C13912yes—
847C22×C4C2×D4×C13912yes—
848C22×C4C2×D4×C13912yes—
849C22×C4C2×D4×C13912yes—
850C22×C4C2×D4×C13912yes—
851C22×C4C2×D4×C13912yes—
852C22×C4C2×D4×C13912yes—
853C22×C4C2×D4×C13912yes—
854C22×C4#41×C13912yes—
855C22×C4#41×C13912yes—
856C22×C4#41×C13912yes—
857C22×C4#41×C13912yes—
858C22×C4#41×C13912yes—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—44no—
863C4⋊C4—44no—
864C4⋊C4—44no—
865C22⋊C4—28no—
866C22⋊C4—28no—
867C22⋊C4—28no—
868C22⋊C4—44no—
869C22⋊C4—44no—
870C22⋊C4—44no—
871C22⋊C4—44no—
872C22⋊C4—44no—
873C22⋊C4—44no—
874C22⋊C4—44no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C42—28no—
878C42—44no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23C22×D4×C13911yescharacteristic
950C23C22×D4×C13911yescharacteristic
951C23C22×D4×C13911yescharacteristic
952C23C2×#41×C13911yescharacteristic
953C23C2×#41×C13911yescharacteristic
954C23C2×#41×C13911yescharacteristic
955C23C2×#41×C13911yescharacteristic
956C23C2×#41×C13911yescharacteristic
957C23C2×#41×C13911yescharacteristic
958C23H(5,𝔽2)×C13911yescharacteristic
959C23H(5,𝔽2)×C13911yescharacteristic
960C23H(5,𝔽2)×C13911yescharacteristic
961C23H(5,𝔽2)×C13911yescharacteristic
962C232−1+4×C13911yescharacteristic
963C232−1+4×C13911yescharacteristic
964D4—416no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4#120×C13914yes—
1055C2×C4#126×C13914yescomplemented
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22—81no—
1082C22—81no—
1083C22—81no—
1084C22—81no—
1085C22—81no—
1086C22C2×#120×C13911yescharacteristic
1087C22#525×C13911yescharacteristic
1088C22C2×#126×C13911yescharacteristic
1089C22#529×C13911yescharacteristic
1090C22#532×C13911yescharacteristic
1091C22#532×C13911yescharacteristic
1092C22#535×C13911yescharacteristic
1093C22#537×C13911yescharacteristic
1094C22#537×C13911yescharacteristic
1095C22#538×C13911yescharacteristic
1096C22#538×C13911yescharacteristic
1097C22#539×C13911yescharacteristic
1098C22#539×C13911yescharacteristic
1099C22#542×C13911yescharacteristic
1100C22#542×C13911yescharacteristic
1101C22#546×C13911yescharacteristic
1102C22#546×C13911yescharacteristic
1103C22#546×C13911yescharacteristic
1104C22#546×C13911yescharacteristic
1105C22#546×C13911yescharacteristic
1106C22#547×C13911yescharacteristic
1107C22#547×C13911yescharacteristic
1108C22#547×C13911yescharacteristic
1109C22#548×C13911yescharacteristic
1110C22#550×C13911yescharacteristic
1111C22#550×C13911yescharacteristic
1112C22#550×C13911yescharacteristic
1113C22#551×C13911yescharacteristic
1114C22#551×C13911yescharacteristic
1115C22#553×C13911yescharacteristic
1116C22#553×C13911yescharacteristic
1117C22#556×C13911yescharacteristic
1118C22#556×C13911yescharacteristic
1119C22#560×C13911yescharacteristic
1120C22#563×C13911yescharacteristic
1121C4—24no—
1122C4—24no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—81no—
1131C4—81no—
1132C4—81no—
1133C4—81no—
1134C2—82no—
1135C2—82no—
1136C2#2407×C13911yescharacteristic
1137C2#2430×C13911yescharacteristic
1138C2#2431×C13911yescharacteristic
1139C2#2466×C13911yescharacteristic
1140C2#2480×C13911yescharacteristic
1141C2#2512×C13911yescharacteristic
1142C2#2512×C13911yescharacteristic
1143C2#2554×C13911yescharacteristic
1144C2#2560×C13911yescharacteristic
1145C2#2691×C13911yescharacteristic
1146C2#2705×C13911yescharacteristic
1147C2#2714×C13911yescharacteristic
1148C2#2715×C13911yescharacteristic
1149C2#2723×C13911yescharacteristic
1150C2#2727×C13911yescharacteristic
subgroupG/H
center, socleC24×C139C24
commutator, Frattini, cosocleC24C24×C139
prime radicalC23×D4×C139C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#126×C139C2semidirect
2. C2×#397×C139C2semidirect
3. C2×#396×C139C2semidirect
5. #1444×C139C2semidirect
6. #1440×C139C2semidirect
7. #1439×C139C2semidirect
8. #1439×C139C2semidirect
9. #1439×C139C2semidirect
12. #1437×C139C2semidirect
13. #1436×C139C2semidirect
14. #1436×C139C2semidirect
15. C4⋊#95×C139C2semidirect
96. C2×C4⋊C4×C139D4semidirect
97. C2×C4⋊C4×C139D4semidirect
479. C2×C4×C139#126semidirect
575. #15913C139direct (N × H)
576. C139#15913direct (N × H)
577. C22×#126C2×C139semidirect
578. C2×#397C2×C139semidirect
579. C2×#396C2×C139semidirect
581. #1444C2×C139semidirect
582. #1440C2×C139semidirect
583. #1439C2×C139semidirect
584. #1439C2×C139semidirect
585. #1439C2×C139semidirect
588. #1437C2×C139semidirect
589. #1436C2×C139semidirect
590. #1436C2×C139semidirect
591. C4⋊#95C2×C139semidirect
672. C2×C4⋊C4D4×C139semidirect
673. C2×C4⋊C4D4×C139semidirect
1055. C2×C4#126×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#126×C1392
C2×#397×C1392
C2×#396×C1392
C2×#390×C1392
#1444×C1392
#1440×C1392
#1439×C1392
#1438×C1392
#1437×C1392
#1436×C1392
C4⋊#95×C1392
#15913139