Finite Group Databasebeta

← C139×#14095 #48008691

Subgroups — C139×#14095 #48008691

Order 35584.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C139C211yesmaximal, characteristic
2C2×#390×C139C211yesmaximal, characteristic
3C2×#387×C139C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊C4×C139C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C139C211yesmaximal, characteristic, complemented
6#1441×C139C211yesmaximal, characteristic, complemented
7#1439×C139C211yesmaximal, characteristic, complemented
8#1439×C139C211yesmaximal, characteristic, complemented
9#1438×C139C211yesmaximal, characteristic
10#1437×C139C211yesmaximal, characteristic, complemented
11#1437×C139C211yesmaximal, characteristic, complemented
12#1437×C139C211yesmaximal, characteristic, complemented
13#1437×C139C211yesmaximal, characteristic, complemented
14#1436×C139C211yesmaximal, characteristic, complemented
15C22⋊#95×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C24×C4×C139C2211yescharacteristic
18C2×#123×C139—24no—
19C2×#123×C139—24no—
20C2×#123×C139C418yescomplemented
21C22×C4⋊C4×C139C2211yescharacteristic
22C22×C4⋊C4×C139C2211yescharacteristic
23C22×C4⋊C4×C139C2211yescharacteristic
24C22×C4⋊C4×C139C2211yescharacteristic
25C22×C22⋊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×C42×C139C2211yescharacteristic
37C22×C42×C139C2211yescharacteristic
38C22×C42×C139C2211yescharacteristic
39C22×C42×C139C2211yescharacteristic
40#390×C139—24no—
41#387×C139—24no—
42C4×C4⋊C4×C139—24no—
43C4×C22⋊C4×C139—24no—
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
57C2×#95×C139C2211yescharacteristic
58C25×C139C2311yescharacteristic
59C25×C139C2311yescharacteristic
60C22×D4×C139—22no—
61C22×D4×C139—22no—
62C22×D4×C139—22no—
63C22×D4×C139—22no—
64C22×D4×C139—41no—
65C22×D4×C139—41no—
66C22×D4×C139C2×C414yes—
67C23×C4×C139—22no—
68C23×C4×C139—22no—
69C23×C4×C139—22no—
70C23×C4×C139—22no—
71C23×C4×C139—41no—
72C23×C4×C139—41no—
73C23×C4×C139C2×C414yes—
74C23×C4×C139C2311yescharacteristic
75C23×C4×C139C2311yescharacteristic
76C23×C4×C139C2311yescharacteristic
77C23×C4×C139C2311yescharacteristic
78C23×C4×C139C2311yescharacteristic
79C23×C4×C139C2311yescharacteristic
80C23×C4×C139C2311yescharacteristic
81C23×C4×C139C2311yescharacteristic
82C23×C4×C139C2311yescharacteristic
83C23×C4×C139C2311yescharacteristic
84C23×C4×C139C2311yescharacteristic
85C23×C4×C139C2311yescharacteristic
86C23×C4×C139C2311yescharacteristic
87#123×C139—232no—
88C2×C4⋊C4×C139—22no—
89C2×C4⋊C4×C139—22no—
90C2×C4⋊C4×C139—22no—
91C2×C4⋊C4×C139—22no—
92C2×C4⋊C4×C139—22no—
93C2×C4⋊C4×C139—22no—
94C2×C4⋊C4×C139—22no—
95C2×C4⋊C4×C139—41no—
96C2×C4⋊C4×C139C2×C414yes—
97C2×C4⋊C4×C139C2×C414yes—
98C2×C4⋊C4×C139D414yes—
99C2×C4⋊C4×C139D414yes—
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—22no—
122C2×C22⋊C4×C139—22no—
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×C139C2×C414yes—
130C2×C22⋊C4×C139C2×C414yes—
131C2×C22⋊C4×C139C2×C414yes—
132C2×C22⋊C4×C139D414yes—
133C2×C42×C139—22no—
134C2×C42×C139—22no—
135C2×C42×C139—22no—
136C2×C42×C139—22no—
137C2×C42×C139—22no—
138C2×C42×C139—22no—
139C2×C42×C139—22no—
140C2×C42×C139—22no—
141C2×C42×C139—22no—
142C2×C42×C139—41no—
143C2×C42×C139—41no—
144C2×C42×C139—41no—
145#95×C139—22no—
146#95×C139—22no—
147#95×C139—22no—
148#95×C139—22no—
149#95×C139—22no—
150#95×C139—22no—
151#95×C139—22no—
152#95×C139—22no—
153#95×C139—22no—
154#95×C139—22no—
155#95×C139—41no—
156#95×C139—41no—
157#95×C139—41no—
158#95×C139—41no—
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×C139—21no—
183C24×C139—21no—
184C24×C139—21no—
185C24×C139C22×C412yes—
186C24×C139C22×C412yes—
187C24×C139C2×D412yes—
188C24×C139#4112yes—
189C24×C139C2411yescharacteristic
190C2×D4×C139—28no—
191C2×D4×C139—28no—
192C2×D4×C139—44no—
193C2×D4×C139—44no—
194C2×D4×C139—44no—
195C2×D4×C139—44no—
196C2×D4×C139—44no—
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—28no—
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—28no—
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×C139—21no—
271C22×C4×C139—44no—
272C22×C4×C139—44no—
273C22×C4×C139—44no—
274C22×C4×C139—44no—
275C22×C4×C139—44no—
276C22×C4×C139C22×C412yes—
277C22×C4×C139C22×C412yes—
278C22×C4×C139C22×C412yes—
279C22×C4×C139C22×C412yes—
280C22×C4×C139C22×C412yes—
281C22×C4×C139C2×D412yes—
282C22×C4×C139C2×D412yes—
283C22×C4×C139C2×D412yes—
284C22×C4×C139C2×D412yes—
285C22×C4×C139C2×D412yes—
286C22×C4×C139C2×D412yes—
287C22×C4×C139C2×D412yes—
288C22×C4×C139C2×D412yes—
289C22×C4×C139#4112yes—
290C22×C4×C139#4112yes—
291C22×C4×C139#4112yes—
292C22×C4×C139#4112yes—
293C22×C4×C139#4112yes—
294C22×C4×C139#4112yes—
295C4⋊C4×C139—28no—
296C4⋊C4×C139—28no—
297C4⋊C4×C139—44no—
298C4⋊C4×C139C22⋊C4116yescomplemented
299C22⋊C4×C139—28no—
300C22⋊C4×C139—28no—
301C22⋊C4×C139—28no—
302C22⋊C4×C139—28no—
303C22⋊C4×C139—28no—
304C22⋊C4×C139—44no—
305C22⋊C4×C139—44no—
306C22⋊C4×C139—44no—
307C22⋊C4×C139—44no—
308C22⋊C4×C139—44no—
309C22⋊C4×C139—44no—
310C42×C139—28no—
311C42×C139—44no—
312C42×C139—44no—
313C42×C139—44no—
314C23×C139—22no—
315C23×C139—22no—
316C23×C139—22no—
317C23×C139—22no—
318C23×C139—22no—
319C23×C139—22no—
320C23×C139—22no—
321C23×C139—22no—
322C23×C139—22no—
323C23×C139—22no—
324C23×C139—22no—
325C23×C139—22no—
326C23×C139—22no—
327C23×C139—22no—
328C23×C139—22no—
329C23×C139—22no—
330C23×C139—22no—
331C23×C139—22no—
332C23×C139—22no—
333C23×C139—22no—
334C23×C139—22no—
335C23×C139—22no—
336C23×C139—22no—
337C23×C139—22no—
338C23×C139—22no—
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×C139—41no—
374C23×C139—41no—
375C23×C139—41no—
376C23×C139—41no—
377C23×C139—41no—
378C23×C139—41no—
379C23×C139—41no—
380C23×C139—41no—
381C23×C139—41no—
382C23×C139—41no—
383C23×C139C4×D414yes—
384C23×C139C23×C411yescharacteristic
385C23×C139C22×D411yescharacteristic
386C23×C139C22×D411yescharacteristic
387C23×C139C22×D411yescharacteristic
388C23×C139C2×#4111yescharacteristic
389C23×C139C2×#4111yescharacteristic
390C23×C139C2×#4111yescharacteristic
391C23×C139C2×#4111yescharacteristic
392C23×C139C2×#4111yescharacteristic
393C23×C139C2×#4111yescharacteristic
394C23×C139C2×#4111yescharacteristic
395C23×C139H(5,𝔽2)11yescharacteristic
396C23×C139H(5,𝔽2)11yescharacteristic
397C23×C139H(5,𝔽2)11yescharacteristic
398C23×C1392−1+411yescharacteristic
399D4×C139—416no—
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—22no—
423C2×C4×C139—22no—
424C2×C4×C139—22no—
425C2×C4×C139—22no—
426C2×C4×C139—22no—
427C2×C4×C139—22no—
428C2×C4×C139—22no—
429C2×C4×C139—22no—
430C2×C4×C139—22no—
431C2×C4×C139—22no—
432C2×C4×C139—22no—
433C2×C4×C139—22no—
434C2×C4×C139—22no—
435C2×C4×C139—22no—
436C2×C4×C139—22no—
437C2×C4×C139—22no—
438C2×C4×C139—22no—
439C2×C4×C139—22no—
440C2×C4×C139—22no—
441C2×C4×C139—22no—
442C2×C4×C139—22no—
443C2×C4×C139—22no—
444C2×C4×C139—22no—
445C2×C4×C139—416no—
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—41no—
479C2×C4×C139—41no—
480C2×C4×C139—41no—
481C2×C4×C139—41no—
482C2×C4×C139—41no—
483C2×C4×C139—41no—
484C2×C4×C139—41no—
485C2×C4×C139—41no—
486C2×C4×C139—41no—
487C2×C4×C139—41no—
488C2×C4×C139C2×C22⋊C414yes—
489C2×C4×C139C2×C22⋊C414yes—
490C2×C4×C139C2×C22⋊C414yes—
491C2×C4×C139#12314yescomplemented
492C22×C139—24no—
493C22×C139—24no—
494C22×C139—24no—
495C22×C139—42no—
496C22×C139—42no—
497C22×C139—42no—
498C22×C139—42no—
499C22×C139—42no—
500C22×C139—42no—
501C22×C139—42no—
502C22×C139—42no—
503C22×C139—42no—
504C22×C139—42no—
505C22×C139—42no—
506C22×C139—42no—
507C22×C139—42no—
508C22×C139—42no—
509C22×C139—42no—
510C22×C139—42no—
511C22×C139—42no—
512C22×C139—42no—
513C22×C139—42no—
514C22×C139—81no—
515C22×C139—81no—
516C22×C139—81no—
517C22×C139—81no—
518C22×C139—81no—
519C22×C139—81no—
520C22×C139—81no—
521C22×C139—81no—
522C22×C139C22×C22⋊C411yescharacteristic
523C22×C139C2×C4×D411yescharacteristic
524C22×C139C4×#4111yescharacteristic
525C22×C139C4×#4111yescharacteristic
526C22×C139C4×#4111yescharacteristic
527C22×C139#51811yescharacteristic
528C22×C139#52011yescharacteristic
529C22×C139C2×#12311yescharacteristic
530C22×C139#52511yescharacteristic
531C22×C139#52511yescharacteristic
532C22×C139#52511yescharacteristic
533C22×C139#52911yescharacteristic
534C22×C139#52911yescharacteristic
535C22×C139#53211yescharacteristic
536C22×C139#53211yescharacteristic
537C22×C139#53811yescharacteristic
538C22×C139#53911yescharacteristic
539C22×C139#54011yescharacteristic
540C22×C139#54211yescharacteristic
541C22×C139D4211yescharacteristic
542C22×C139D4211yescharacteristic
543C22×C139#54611yescharacteristic
544C22×C139#54611yescharacteristic
545C22×C139#54611yescharacteristic
546C22×C139#54711yescharacteristic
547C22×C139#54811yescharacteristic
548C22×C139#54811yescharacteristic
549C22×C139#55011yescharacteristic
550C22×C139#55011yescharacteristic
551C22×C139#55111yescharacteristic
552C22×C139#55111yescharacteristic
553C22×C139#55211yescharacteristic
554C22×C139#55311yescharacteristic
555C22×C139#55311yescharacteristic
556C22×C139#55911yescharacteristic
557C4×C139—24no—
558C4×C139—24no—
559C4×C139—24no—
560C4×C139—24no—
561C4×C139—42no—
562C4×C139—42no—
563C4×C139—42no—
564C4×C139—42no—
565C4×C139—42no—
566C4×C139—42no—
567C4×C139—42no—
568C4×C139—81no—
569C4×C139—81no—
570C2×C139—44no—
571C2×C139—82no—
572C2×C139#229711yescharacteristic
573C2×C139C4×#12311yescharacteristic
574C2×C139#233511yescharacteristic
575C2×C139D4×C22⋊C411yescharacteristic
576C2×C139#234111yescharacteristic
577C2×C139#235911yescharacteristic
578C2×C139#237411yescharacteristic
579C2×C139#244311yescharacteristic
580C2×C139#244511yescharacteristic
581C2×C139#245611yescharacteristic
582C2×C139#245811yescharacteristic
583C2×C139#246111yescharacteristic
584C2×C139#247111yescharacteristic
585C2×C139#255411yescharacteristic
586C2×C139#255811yescharacteristic
587#14095C13911yesmaximal, characteristic, direct product factor, Sylow
588C139#1409511yescharacteristic, direct product factor, Sylow
589C22×#123C2×C13911yescharacteristic
590C2×#390C2×C13911yescharacteristic
591C2×#387C2×C13911yescharacteristic, complemented
592C2×C4×C4⋊C4C2×C13911yescharacteristic, complemented
593C2×C4×C22⋊C4C2×C13911yescharacteristic, complemented
594#1441C2×C13911yescharacteristic, complemented
595#1439C2×C13911yescharacteristic, complemented
596#1439C2×C13911yescharacteristic, complemented
597#1438C2×C13911yescharacteristic
598#1437C2×C13911yescharacteristic, complemented
599#1437C2×C13911yescharacteristic, complemented
600#1437C2×C13911yescharacteristic, complemented
601#1437C2×C13911yescharacteristic, complemented
602#1436C2×C13911yescharacteristic, complemented
603C22⋊#95C2×C13911yescharacteristic, complemented
604C23×D4C22×C13911yescharacteristic
605C24×C4C22×C13911yescharacteristic
606C2×#123—24no—
607C2×#123—24no—
608C2×#123C4×C13918yescomplemented
609C22×C4⋊C4C22×C13911yescharacteristic
610C22×C4⋊C4C22×C13911yescharacteristic
611C22×C4⋊C4C22×C13911yescharacteristic
612C22×C4⋊C4C22×C13911yescharacteristic
613C22×C22⋊C4C22×C13911yescharacteristic
614C22×C22⋊C4C22×C13911yescharacteristic
615C22×C22⋊C4C22×C13911yescharacteristic
616C22×C22⋊C4C22×C13911yescharacteristic
617C22×C22⋊C4C22×C13911yescharacteristic
618C22×C22⋊C4C22×C13911yescharacteristic
619C22×C22⋊C4C22×C13911yescharacteristic
620C22×C22⋊C4C22×C13911yescharacteristic
621C22×C22⋊C4C22×C13911yescharacteristic
622C22×C22⋊C4C22×C13911yescharacteristic
623C22×C22⋊C4C22×C13911yescharacteristic
624C22×C42C22×C13911yescharacteristic
625C22×C42C22×C13911yescharacteristic
626C22×C42C22×C13911yescharacteristic
627C22×C42C22×C13911yescharacteristic
628#390—24no—
629#387—24no—
630C4×C4⋊C4—24no—
631C4×C22⋊C4—24no—
632C2×#95C22×C13911yescharacteristic
633C2×#95C22×C13911yescharacteristic
634C2×#95C22×C13911yescharacteristic
635C2×#95C22×C13911yescharacteristic
636C2×#95C22×C13911yescharacteristic
637C2×#95C22×C13911yescharacteristic
638C2×#95C22×C13911yescharacteristic
639C2×#95C22×C13911yescharacteristic
640C2×#95C22×C13911yescharacteristic
641C2×#95C22×C13911yescharacteristic
642C2×#95C22×C13911yescharacteristic
643C2×#95C22×C13911yescharacteristic
644C2×#95C22×C13911yescharacteristic
645C2×#95C22×C13911yescharacteristic
646C25C23×C13911yescharacteristic
647C25C23×C13911yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4C2×C4×C13914yes—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4C2×C4×C13914yes—
662C23×C4C23×C13911yescharacteristic
663C23×C4C23×C13911yescharacteristic
664C23×C4C23×C13911yescharacteristic
665C23×C4C23×C13911yescharacteristic
666C23×C4C23×C13911yescharacteristic
667C23×C4C23×C13911yescharacteristic
668C23×C4C23×C13911yescharacteristic
669C23×C4C23×C13911yescharacteristic
670C23×C4C23×C13911yescharacteristic
671C23×C4C23×C13911yescharacteristic
672C23×C4C23×C13911yescharacteristic
673C23×C4C23×C13911yescharacteristic
674C23×C4C23×C13911yescharacteristic
675#123—232no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4C2×C4×C13914yes—
685C2×C4⋊C4C2×C4×C13914yes—
686C2×C4⋊C4D4×C13914yes—
687C2×C4⋊C4D4×C13914yes—
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—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4C2×C4×C13914yes—
718C2×C22⋊C4C2×C4×C13914yes—
719C2×C22⋊C4C2×C4×C13914yes—
720C2×C22⋊C4D4×C13914yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—41no—
731C2×C42—41no—
732C2×C42—41no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95—41no—
746#95—41no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C22×C4×C13912yes—
774C24C22×C4×C13912yes—
775C24C2×D4×C13912yes—
776C24#41×C13912yes—
777C24C24×C13911yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
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—28no—
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—28no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4C22×C4×C13912yes—
865C22×C4C22×C4×C13912yes—
866C22×C4C22×C4×C13912yes—
867C22×C4C22×C4×C13912yes—
868C22×C4C22×C4×C13912yes—
869C22×C4C2×D4×C13912yes—
870C22×C4C2×D4×C13912yes—
871C22×C4C2×D4×C13912yes—
872C22×C4C2×D4×C13912yes—
873C22×C4C2×D4×C13912yes—
874C22×C4C2×D4×C13912yes—
875C22×C4C2×D4×C13912yes—
876C22×C4C2×D4×C13912yes—
877C22×C4#41×C13912yes—
878C22×C4#41×C13912yes—
879C22×C4#41×C13912yes—
880C22×C4#41×C13912yes—
881C22×C4#41×C13912yes—
882C22×C4#41×C13912yes—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—44no—
886C4⋊C4C22⋊C4×C139116yescomplemented
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C42—28no—
899C42—44no—
900C42—44no—
901C42—44no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
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—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23C4×D4×C13914yes—
972C23C23×C4×C13911yescharacteristic
973C23C22×D4×C13911yescharacteristic
974C23C22×D4×C13911yescharacteristic
975C23C22×D4×C13911yescharacteristic
976C23C2×#41×C13911yescharacteristic
977C23C2×#41×C13911yescharacteristic
978C23C2×#41×C13911yescharacteristic
979C23C2×#41×C13911yescharacteristic
980C23C2×#41×C13911yescharacteristic
981C23C2×#41×C13911yescharacteristic
982C23C2×#41×C13911yescharacteristic
983C23H(5,𝔽2)×C13911yescharacteristic
984C23H(5,𝔽2)×C13911yescharacteristic
985C23H(5,𝔽2)×C13911yescharacteristic
986C232−1+4×C13911yescharacteristic
987D4—416no—
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—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—416no—
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—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4C2×C22⋊C4×C13914yes—
1077C2×C4C2×C22⋊C4×C13914yes—
1078C2×C4C2×C22⋊C4×C13914yes—
1079C2×C4#123×C13914yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C22×C22⋊C4×C13911yescharacteristic
1111C22C2×C4×D4×C13911yescharacteristic
1112C22C4×#41×C13911yescharacteristic
1113C22C4×#41×C13911yescharacteristic
1114C22C4×#41×C13911yescharacteristic
1115C22#518×C13911yescharacteristic
1116C22#520×C13911yescharacteristic
1117C22C2×#123×C13911yescharacteristic
1118C22#525×C13911yescharacteristic
1119C22#525×C13911yescharacteristic
1120C22#525×C13911yescharacteristic
1121C22#529×C13911yescharacteristic
1122C22#529×C13911yescharacteristic
1123C22#532×C13911yescharacteristic
1124C22#532×C13911yescharacteristic
1125C22#538×C13911yescharacteristic
1126C22#539×C13911yescharacteristic
1127C22#540×C13911yescharacteristic
1128C22#542×C13911yescharacteristic
1129C22D42×C13911yescharacteristic
1130C22D42×C13911yescharacteristic
1131C22#546×C13911yescharacteristic
1132C22#546×C13911yescharacteristic
1133C22#546×C13911yescharacteristic
1134C22#547×C13911yescharacteristic
1135C22#548×C13911yescharacteristic
1136C22#548×C13911yescharacteristic
1137C22#550×C13911yescharacteristic
1138C22#550×C13911yescharacteristic
1139C22#551×C13911yescharacteristic
1140C22#551×C13911yescharacteristic
1141C22#552×C13911yescharacteristic
1142C22#553×C13911yescharacteristic
1143C22#553×C13911yescharacteristic
1144C22#559×C13911yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2#2297×C13911yescharacteristic
1161C2C4×#123×C13911yescharacteristic
1162C2#2335×C13911yescharacteristic
1163C2D4×C22⋊C4×C13911yescharacteristic
1164C2#2341×C13911yescharacteristic
1165C2#2359×C13911yescharacteristic
1166C2#2374×C13911yescharacteristic
1167C2#2443×C13911yescharacteristic
1168C2#2445×C13911yescharacteristic
1169C2#2456×C13911yescharacteristic
1170C2#2458×C13911yescharacteristic
1171C2#2461×C13911yescharacteristic
1172C2#2471×C13911yescharacteristic
1173C2#2554×C13911yescharacteristic
1174C2#2558×C13911yescharacteristic
subgroupG/H
center, socleC24×C139C24
commutatorC23C23×C4×C139
Frattini, cosocleC24C24×C139
prime radicalC23×D4×C139C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#387×C139C2semidirect
4. C2×C4×C4⋊C4×C139C2semidirect
5. C2×C4×C22⋊C4×C139C2semidirect
6. #1441×C139C2semidirect
7. #1439×C139C2semidirect
8. #1439×C139C2semidirect
10. #1437×C139C2semidirect
11. #1437×C139C2semidirect
12. #1437×C139C2semidirect
13. #1437×C139C2semidirect
14. #1436×C139C2semidirect
15. C22⋊#95×C139C2semidirect
20. C2×#123×C139C4semidirect
298. C4⋊C4×C139C22⋊C4semidirect
491. C2×C4×C139#123semidirect
587. #14095C139direct (N × H)
588. C139#14095direct (N × H)
591. C2×#387C2×C139semidirect
592. C2×C4×C4⋊C4C2×C139semidirect
593. C2×C4×C22⋊C4C2×C139semidirect
594. #1441C2×C139semidirect
595. #1439C2×C139semidirect
596. #1439C2×C139semidirect
598. #1437C2×C139semidirect
599. #1437C2×C139semidirect
600. #1437C2×C139semidirect
601. #1437C2×C139semidirect
602. #1436C2×C139semidirect
603. C22⋊#95C2×C139semidirect
608. C2×#123C4×C139semidirect
886. C4⋊C4C22⋊C4×C139semidirect
1079. C2×C4#123×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1392
C2×#390×C1392
C2×#387×C1392
C2×C4×C4⋊C4×C1392
C2×C4×C22⋊C4×C1392
#1441×C1392
#1439×C1392
#1438×C1392
#1437×C1392
#1436×C1392
C22⋊#95×C1392
#14095139