Finite Group Databasebeta

← C139×#13876 #48008472

Subgroups — C139×#13876 #48008472

Order 35584.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C139C212yesmaximal
2C2×#384×C139C211yesmaximal, characteristic, complemented
3C2×#380×C139C211yesmaximal, characteristic
4C2×#380×C139C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C139C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C139C211yesmaximal, characteristic
7#1442×C139C212yesmaximal, complemented
8#1439×C139C212yesmaximal
9#1436×C139C212yesmaximal, complemented
10C4⋊#95×C139C211yesmaximal, characteristic, complemented
11C4⋊#95×C139C211yesmaximal, characteristic, complemented
12C24×C4×C139C2211yescharacteristic
13C22×C4⋊C4×C139C2211yescharacteristic
14C22×C4⋊C4×C139C2211yescharacteristic
15C22×C4⋊C4×C139C2212yes—
16C22×C4⋊C4×C139C2212yes—
17C22×C4⋊C4×C139C2211yescharacteristic
18C22×C4⋊C4×C139C2211yescharacteristic
19C22×C22⋊C4×C139C2212yes—
20C22×C22⋊C4×C139C2212yes—
21C22×C22⋊C4×C139C2211yescharacteristic
22C22×C22⋊C4×C139C2211yescharacteristic
23C22×C42×C139C2212yes—
24C22×C42×C139C2211yescharacteristic
25C22×C42×C139C2211yescharacteristic
26#388×C139—28no—
27#384×C139—24no—
28#380×C139—24no—
29#380×C139—24no—
30C4×C4⋊C4×C139—24no—
31C4×C22⋊C4×C139C418yescomplemented
32C2×#95×C139C2212yes—
33C2×#95×C139C2212yes—
34C2×#95×C139C2212yes—
35C2×#95×C139C2212yes—
36C2×#95×C139C2212yes—
37C2×#95×C139C2212yes—
38C2×#95×C139C2212yes—
39C2×#95×C139C2211yescharacteristic
40C2×#95×C139C2211yescharacteristic
41C25×C139C2311yescharacteristic
42C23×C4×C139—22no—
43C23×C4×C139—22no—
44C23×C4×C139—22no—
45C23×C4×C139—22no—
46C23×C4×C139—22no—
47C23×C4×C139—22no—
48C23×C4×C139C2×C414yes—
49C23×C4×C139C2312yes—
50C23×C4×C139C2312yes—
51C23×C4×C139C2311yescharacteristic
52C23×C4×C139C2311yescharacteristic
53C23×C4×C139C2312yes—
54C23×C4×C139C2312yes—
55C23×C4×C139C2311yescharacteristic
56C23×C4×C139C2311yescharacteristic
57C23×C4×C139C2311yescharacteristic
58C23×C4×C139C2311yescharacteristic
59C2×C4⋊C4×C139—22no—
60C2×C4⋊C4×C139—22no—
61C2×C4⋊C4×C139—22no—
62C2×C4⋊C4×C139—22no—
63C2×C4⋊C4×C139—22no—
64C2×C4⋊C4×C139—22no—
65C2×C4⋊C4×C139—24no—
66C2×C4⋊C4×C139—24no—
67C2×C4⋊C4×C139—22no—
68C2×C4⋊C4×C139—24no—
69C2×C4⋊C4×C139—24no—
70C2×C4⋊C4×C139—22no—
71C2×C4⋊C4×C139—22no—
72C2×C4⋊C4×C139—22no—
73C2×C4⋊C4×C139—42no—
74C2×C4⋊C4×C139—42no—
75C2×C4⋊C4×C139D414yes—
76C2×C4⋊C4×C139D414yes—
77C2×C22⋊C4×C139—22no—
78C2×C22⋊C4×C139—22no—
79C2×C22⋊C4×C139—24no—
80C2×C22⋊C4×C139—24no—
81C2×C22⋊C4×C139—24no—
82C2×C22⋊C4×C139—24no—
83C2×C22⋊C4×C139—42no—
84C2×C22⋊C4×C139—42no—
85C2×C22⋊C4×C139C2×C414yes—
86C2×C22⋊C4×C139C2×C414yes—
87C2×C22⋊C4×C139D414yes—
88C2×C22⋊C4×C139Q814yes—
89C2×C42×C139—22no—
90C2×C42×C139—22no—
91C2×C42×C139—22no—
92C2×C42×C139—22no—
93C2×C42×C139—24no—
94C2×C42×C139—24no—
95C2×C42×C139—42no—
96C2×C42×C139C2×C414yes—
97C2×C42×C139C2×C414yes—
98#95×C139—24no—
99#95×C139—24no—
100#95×C139—24no—
101#95×C139—24no—
102#95×C139—24no—
103#95×C139—24no—
104#95×C139—42no—
105#95×C139C2×C414yes—
106#95×C139C2×C414yes—
107C24×C139—21no—
108C24×C139—21no—
109C24×C139—21no—
110C24×C139—21no—
111C24×C139—21no—
112C24×C139—21no—
113C24×C139—21no—
114C24×C139—21no—
115C24×C139—21no—
116C24×C139—21no—
117C24×C139—21no—
118C24×C139—21no—
119C24×C139C22×C412yes—
120C24×C139C2×D412yes—
121C24×C139C2×Q812yes—
122C24×C139C2411yescharacteristic
123C22×C4×C139—21no—
124C22×C4×C139—21no—
125C22×C4×C139—21no—
126C22×C4×C139—21no—
127C22×C4×C139—21no—
128C22×C4×C139—21no—
129C22×C4×C139—21no—
130C22×C4×C139—21no—
131C22×C4×C139—21no—
132C22×C4×C139—21no—
133C22×C4×C139—21no—
134C22×C4×C139—21no—
135C22×C4×C139—21no—
136C22×C4×C139—21no—
137C22×C4×C139—21no—
138C22×C4×C139—22no—
139C22×C4×C139—22no—
140C22×C4×C139—22no—
141C22×C4×C139—22no—
142C22×C4×C139—21no—
143C22×C4×C139—21no—
144C22×C4×C139—21no—
145C22×C4×C139—22no—
146C22×C4×C139—22no—
147C22×C4×C139—22no—
148C22×C4×C139—22no—
149C22×C4×C139—21no—
150C22×C4×C139—21no—
151C22×C4×C139—21no—
152C22×C4×C139—21no—
153C22×C4×C139—21no—
154C22×C4×C139—22no—
155C22×C4×C139—22no—
156C22×C4×C139—22no—
157C22×C4×C139—21no—
158C22×C4×C139—22no—
159C22×C4×C139—28no—
160C22×C4×C139—28no—
161C22×C4×C139—28no—
162C22×C4×C139—22no—
163C22×C4×C139—22no—
164C22×C4×C139—22no—
165C22×C4×C139—22no—
166C22×C4×C139—22no—
167C22×C4×C139—22no—
168C22×C4×C139—22no—
169C22×C4×C139—22no—
170C22×C4×C139—22no—
171C22×C4×C139—22no—
172C22×C4×C139—22no—
173C22×C4×C139—22no—
174C22×C4×C139—22no—
175C22×C4×C139—22no—
176C22×C4×C139—44no—
177C22×C4×C139—44no—
178C22×C4×C139—44no—
179C22×C4×C139—44no—
180C22×C4×C139C22×C412yes—
181C22×C4×C139C22×C412yes—
182C22×C4×C139C22×C412yes—
183C22×C4×C139C22×C412yes—
184C22×C4×C139C22×C412yes—
185C22×C4×C139C22×C412yes—
186C22×C4×C139C2×D414yes—
187C22×C4×C139C2×D414yes—
188C22×C4×C139C2×D412yes—
189C22×C4×C139C2×D412yes—
190C22×C4×C139C2×D412yes—
191C22×C4×C139C2×D412yes—
192C22×C4×C139C2×Q812yes—
193C22×C4×C139C2×Q812yes—
194C22×C4×C139#4112yes—
195C22×C4×C139#4112yes—
196C22×C4×C139#4112yes—
197C22×C4×C139#4112yes—
198C22×C4×C139#4112yes—
199C22×C4×C139#4112yes—
200C4⋊C4×C139—28no—
201C4⋊C4×C139—28no—
202C4⋊C4×C139—48no—
203C4⋊C4×C139—48no—
204C4⋊C4×C139—44no—
205C4⋊C4×C139—44no—
206C22⋊C4×C139—28no—
207C22⋊C4×C139—48no—
208C22⋊C4×C139—48no—
209C22⋊C4×C139C4⋊C4116yescomplemented
210C42×C139—28no—
211C42×C139—28no—
212C42×C139—48no—
213C23×C139—22no—
214C23×C139—22no—
215C23×C139—22no—
216C23×C139—22no—
217C23×C139—22no—
218C23×C139—22no—
219C23×C139—22no—
220C23×C139—22no—
221C23×C139—22no—
222C23×C139—22no—
223C23×C139—22no—
224C23×C139—22no—
225C23×C139—22no—
226C23×C139—22no—
227C23×C139—22no—
228C23×C139—22no—
229C23×C139—22no—
230C23×C139—22no—
231C23×C139—41no—
232C23×C139—41no—
233C23×C139—41no—
234C23×C139—41no—
235C23×C139—41no—
236C23×C139—41no—
237C23×C139—41no—
238C23×C139—41no—
239C23×C139—41no—
240C23×C139—41no—
241C23×C139—41no—
242C23×C139—41no—
243C23×C139—41no—
244C23×C139—41no—
245C23×C139—41no—
246C23×C139—41no—
247C23×C139C2×C4⋊C414yes—
248C23×C139C23×C411yescharacteristic
249C23×C139C22×D411yescharacteristic
250C23×C139C22×D411yescharacteristic
251C23×C139C22×D411yescharacteristic
252C23×C139C22×Q811yescharacteristic
253C23×C139C2×#4111yescharacteristic
254C23×C139C2×#4111yescharacteristic
255C23×C139C2×#4111yescharacteristic
256C23×C139C2×#4111yescharacteristic
257C23×C139C2×#4111yescharacteristic
258C23×C139C2×#4111yescharacteristic
259C23×C139H(5,𝔽2)11yescharacteristic
260C23×C139H(5,𝔽2)11yescharacteristic
261C23×C1392−1+411yescharacteristic
262C23×C1392−1+411yescharacteristic
263C2×C4×C139—22no—
264C2×C4×C139—22no—
265C2×C4×C139—22no—
266C2×C4×C139—22no—
267C2×C4×C139—22no—
268C2×C4×C139—22no—
269C2×C4×C139—22no—
270C2×C4×C139—22no—
271C2×C4×C139—22no—
272C2×C4×C139—22no—
273C2×C4×C139—22no—
274C2×C4×C139—22no—
275C2×C4×C139—22no—
276C2×C4×C139—22no—
277C2×C4×C139—22no—
278C2×C4×C139—22no—
279C2×C4×C139—22no—
280C2×C4×C139—22no—
281C2×C4×C139—22no—
282C2×C4×C139—22no—
283C2×C4×C139—22no—
284C2×C4×C139—22no—
285C2×C4×C139—22no—
286C2×C4×C139—22no—
287C2×C4×C139—24no—
288C2×C4×C139—24no—
289C2×C4×C139—24no—
290C2×C4×C139—24no—
291C2×C4×C139—24no—
292C2×C4×C139—24no—
293C2×C4×C139—41no—
294C2×C4×C139—41no—
295C2×C4×C139—41no—
296C2×C4×C139—41no—
297C2×C4×C139—42no—
298C2×C4×C139—42no—
299C2×C4×C139—42no—
300C2×C4×C139—42no—
301C2×C4×C139—42no—
302C2×C4×C139—41no—
303C2×C4×C139—42no—
304C2×C4×C139—41no—
305C2×C4×C139—42no—
306C2×C4×C139—42no—
307C2×C4×C139—41no—
308C2×C4×C139—41no—
309C2×C4×C139—416no—
310C2×C4×C139—42no—
311C2×C4×C139—42no—
312C2×C4×C139—42no—
313C2×C4×C139—42no—
314C2×C4×C139—42no—
315C2×C4×C139—42no—
316C2×C4×C139—42no—
317C2×C4×C139—42no—
318C2×C4×C139—42no—
319C2×C4×C139—42no—
320C2×C4×C139—42no—
321C2×C4×C139—42no—
322C2×C4×C139—42no—
323C2×C4×C139—42no—
324C2×C4×C139C2×C4⋊C414yes—
325C2×C4×C139C2×C4⋊C414yes—
326C2×C4×C139#11714yes—
327C2×C4×C139#11714yes—
328C2×C4×C139C4×D414yes—
329C2×C4×C139C4×D414yes—
330C2×C4×C139#12114yes—
331C2×C4×C139#12314yes—
332C2×C4×C139#12414yes—
333C2×C4×C139#12614yes—
334C22×C139—24no—
335C22×C139—24no—
336C22×C139—24no—
337C22×C139—42no—
338C22×C139—42no—
339C22×C139—42no—
340C22×C139—42no—
341C22×C139—42no—
342C22×C139—42no—
343C22×C139—42no—
344C22×C139—42no—
345C22×C139—42no—
346C22×C139—42no—
347C22×C139—42no—
348C22×C139—42no—
349C22×C139C22×C4⋊C411yescharacteristic
350C22×C139C2×#11711yescharacteristic
351C22×C139C2×#11711yescharacteristic
352C22×C139C2×C4×D411yescharacteristic
353C22×C139C2×C4×D411yescharacteristic
354C22×C139#52011yescharacteristic
355C22×C139#52011yescharacteristic
356C22×C139C2×#12111yescharacteristic
357C22×C139C2×#12311yescharacteristic
358C22×C139C2×#12411yescharacteristic
359C22×C139C2×#12611yescharacteristic
360C22×C139#53211yescharacteristic
361C22×C139#53211yescharacteristic
362C22×C139#53311yescharacteristic
363C22×C139#53311yescharacteristic
364C22×C139#54011yescharacteristic
365C22×C139#54111yescharacteristic
366C22×C139#54211yescharacteristic
367C22×C139#54211yescharacteristic
368C22×C139D4211yescharacteristic
369C22×C139D4211yescharacteristic
370C22×C139#54611yescharacteristic
371C22×C139#54711yescharacteristic
372C22×C139#54711yescharacteristic
373C22×C139#54711yescharacteristic
374C22×C139#54811yescharacteristic
375C22×C139D4×Q811yescharacteristic
376C22×C139D4×Q811yescharacteristic
377C22×C139#55011yescharacteristic
378C22×C139#55211yescharacteristic
379C22×C139#55311yescharacteristic
380C22×C139#55411yescharacteristic
381C22×C139#55411yescharacteristic
382C22×C139#55511yescharacteristic
383C22×C139#55611yescharacteristic
384C4×C139—24no—
385C4×C139—24no—
386C4×C139—24no—
387C4×C139—42no—
388C4×C139—44no—
389C4×C139—44no—
390C4×C139—42no—
391C4×C139—82no—
392C4×C139—82no—
393C4×C139#38818yescomplemented
394C2×C139—44no—
395C2×C139#228511yescharacteristic
396C2×C139C2×#38811yescharacteristic
397C2×C139#231411yescharacteristic
398C2×C139D4×C4⋊C411yescharacteristic
399C2×C139D4×C4⋊C411yescharacteristic
400C2×C139#235211yescharacteristic
401C2×C139#235411yescharacteristic
402C2×C139#242211yescharacteristic
403C2×C139#242311yescharacteristic
404C2×C139#242811yescharacteristic
405C2×C139#242911yescharacteristic
406C2×C139#249111yescharacteristic
407C2×C139#249211yescharacteristic
408C2×C139#249611yescharacteristic
409C2×C139#249711yescharacteristic
410#13876C13911yesmaximal, characteristic, direct product factor, Sylow
411C139#1387611yescharacteristic, direct product factor, Sylow
412C2×#388C2×C13912yes—
413C2×#384C2×C13911yescharacteristic, complemented
414C2×#380C2×C13911yescharacteristic
415C2×#380C2×C13911yescharacteristic
416C2×C4×C4⋊C4C2×C13911yescharacteristic, complemented
417C2×C4×C22⋊C4C2×C13911yescharacteristic
418#1442C2×C13912yescomplemented
419#1439C2×C13912yes—
420#1436C2×C13912yescomplemented
421C4⋊#95C2×C13911yescharacteristic, complemented
422C4⋊#95C2×C13911yescharacteristic, complemented
423C24×C4C22×C13911yescharacteristic
424C22×C4⋊C4C22×C13911yescharacteristic
425C22×C4⋊C4C22×C13911yescharacteristic
426C22×C4⋊C4C22×C13912yes—
427C22×C4⋊C4C22×C13912yes—
428C22×C4⋊C4C22×C13911yescharacteristic
429C22×C4⋊C4C22×C13911yescharacteristic
430C22×C22⋊C4C22×C13912yes—
431C22×C22⋊C4C22×C13912yes—
432C22×C22⋊C4C22×C13911yescharacteristic
433C22×C22⋊C4C22×C13911yescharacteristic
434C22×C42C22×C13912yes—
435C22×C42C22×C13911yescharacteristic
436C22×C42C22×C13911yescharacteristic
437#388—28no—
438#384—24no—
439#380—24no—
440#380—24no—
441C4×C4⋊C4—24no—
442C4×C22⋊C4C4×C13918yescomplemented
443C2×#95C22×C13912yes—
444C2×#95C22×C13912yes—
445C2×#95C22×C13912yes—
446C2×#95C22×C13912yes—
447C2×#95C22×C13912yes—
448C2×#95C22×C13912yes—
449C2×#95C22×C13912yes—
450C2×#95C22×C13911yescharacteristic
451C2×#95C22×C13911yescharacteristic
452C25C23×C13911yescharacteristic
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—22no—
459C23×C4C2×C4×C13914yes—
460C23×C4C23×C13912yes—
461C23×C4C23×C13912yes—
462C23×C4C23×C13911yescharacteristic
463C23×C4C23×C13911yescharacteristic
464C23×C4C23×C13912yes—
465C23×C4C23×C13912yes—
466C23×C4C23×C13911yescharacteristic
467C23×C4C23×C13911yescharacteristic
468C23×C4C23×C13911yescharacteristic
469C23×C4C23×C13911yescharacteristic
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4D4×C13914yes—
487C2×C4⋊C4D4×C13914yes—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4C2×C4×C13914yes—
497C2×C22⋊C4C2×C4×C13914yes—
498C2×C22⋊C4D4×C13914yes—
499C2×C22⋊C4Q8×C13914yes—
500C2×C42—22no—
501C2×C42—22no—
502C2×C42—22no—
503C2×C42—22no—
504C2×C42—24no—
505C2×C42—24no—
506C2×C42—42no—
507C2×C42C2×C4×C13914yes—
508C2×C42C2×C4×C13914yes—
509#95—24no—
510#95—24no—
511#95—24no—
512#95—24no—
513#95—24no—
514#95—24no—
515#95—42no—
516#95C2×C4×C13914yes—
517#95C2×C4×C13914yes—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24—21no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24C22×C4×C13912yes—
531C24C2×D4×C13912yes—
532C24C2×Q8×C13912yes—
533C24C24×C13911yescharacteristic
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4C22×C4×C13912yes—
592C22×C4C22×C4×C13912yes—
593C22×C4C22×C4×C13912yes—
594C22×C4C22×C4×C13912yes—
595C22×C4C22×C4×C13912yes—
596C22×C4C22×C4×C13912yes—
597C22×C4C2×D4×C13914yes—
598C22×C4C2×D4×C13914yes—
599C22×C4C2×D4×C13912yes—
600C22×C4C2×D4×C13912yes—
601C22×C4C2×D4×C13912yes—
602C22×C4C2×D4×C13912yes—
603C22×C4C2×Q8×C13912yes—
604C22×C4C2×Q8×C13912yes—
605C22×C4#41×C13912yes—
606C22×C4#41×C13912yes—
607C22×C4#41×C13912yes—
608C22×C4#41×C13912yes—
609C22×C4#41×C13912yes—
610C22×C4#41×C13912yes—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C22⋊C4—28no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4C4⋊C4×C139116yescomplemented
621C42—28no—
622C42—28no—
623C42—48no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23C2×C4⋊C4×C13914yes—
659C23C23×C4×C13911yescharacteristic
660C23C22×D4×C13911yescharacteristic
661C23C22×D4×C13911yescharacteristic
662C23C22×D4×C13911yescharacteristic
663C23C22×Q8×C13911yescharacteristic
664C23C2×#41×C13911yescharacteristic
665C23C2×#41×C13911yescharacteristic
666C23C2×#41×C13911yescharacteristic
667C23C2×#41×C13911yescharacteristic
668C23C2×#41×C13911yescharacteristic
669C23C2×#41×C13911yescharacteristic
670C23H(5,𝔽2)×C13911yescharacteristic
671C23H(5,𝔽2)×C13911yescharacteristic
672C232−1+4×C13911yescharacteristic
673C232−1+4×C13911yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4C2×C4⋊C4×C13914yes—
736C2×C4C2×C4⋊C4×C13914yes—
737C2×C4#117×C13914yes—
738C2×C4#117×C13914yes—
739C2×C4C4×D4×C13914yes—
740C2×C4C4×D4×C13914yes—
741C2×C4#121×C13914yes—
742C2×C4#123×C13914yes—
743C2×C4#124×C13914yes—
744C2×C4#126×C13914yes—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22C22×C4⋊C4×C13911yescharacteristic
761C22C2×#117×C13911yescharacteristic
762C22C2×#117×C13911yescharacteristic
763C22C2×C4×D4×C13911yescharacteristic
764C22C2×C4×D4×C13911yescharacteristic
765C22#520×C13911yescharacteristic
766C22#520×C13911yescharacteristic
767C22C2×#121×C13911yescharacteristic
768C22C2×#123×C13911yescharacteristic
769C22C2×#124×C13911yescharacteristic
770C22C2×#126×C13911yescharacteristic
771C22#532×C13911yescharacteristic
772C22#532×C13911yescharacteristic
773C22#533×C13911yescharacteristic
774C22#533×C13911yescharacteristic
775C22#540×C13911yescharacteristic
776C22#541×C13911yescharacteristic
777C22#542×C13911yescharacteristic
778C22#542×C13911yescharacteristic
779C22D42×C13911yescharacteristic
780C22D42×C13911yescharacteristic
781C22#546×C13911yescharacteristic
782C22#547×C13911yescharacteristic
783C22#547×C13911yescharacteristic
784C22#547×C13911yescharacteristic
785C22#548×C13911yescharacteristic
786C22D4×Q8×C13911yescharacteristic
787C22D4×Q8×C13911yescharacteristic
788C22#550×C13911yescharacteristic
789C22#552×C13911yescharacteristic
790C22#553×C13911yescharacteristic
791C22#554×C13911yescharacteristic
792C22#554×C13911yescharacteristic
793C22#555×C13911yescharacteristic
794C22#556×C13911yescharacteristic
795C4—24no—
796C4—24no—
797C4—24no—
798C4—42no—
799C4—42no—
800C4—44no—
801C4—44no—
802C4—82no—
803C4—82no—
804C4#388×C13918yescomplemented
805C2—44no—
806C2#2285×C13911yescharacteristic
807C2C2×#388×C13911yescharacteristic
808C2#2314×C13911yescharacteristic
809C2D4×C4⋊C4×C13911yescharacteristic
810C2D4×C4⋊C4×C13911yescharacteristic
811C2#2352×C13911yescharacteristic
812C2#2354×C13911yescharacteristic
813C2#2422×C13911yescharacteristic
814C2#2423×C13911yescharacteristic
815C2#2428×C13911yescharacteristic
816C2#2429×C13911yescharacteristic
817C2#2491×C13911yescharacteristic
818C2#2492×C13911yescharacteristic
819C2#2496×C13911yescharacteristic
820C2#2497×C13911yescharacteristic
subgroupG/H
center, socleC24×C139C24
commutatorC23C23×C4×C139
Frattini, cosocleC24C24×C139
prime radicalC25×C139C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#384×C139C2semidirect
5. C2×C4×C4⋊C4×C139C2semidirect
7. #1442×C139C2semidirect
9. #1436×C139C2semidirect
10. C4⋊#95×C139C2semidirect
11. C4⋊#95×C139C2semidirect
31. C4×C22⋊C4×C139C4semidirect
209. C22⋊C4×C139C4⋊C4semidirect
393. C4×C139#388semidirect
410. #13876C139direct (N × H)
411. C139#13876direct (N × H)
413. C2×#384C2×C139semidirect
416. C2×C4×C4⋊C4C2×C139semidirect
418. #1442C2×C139semidirect
420. #1436C2×C139semidirect
421. C4⋊#95C2×C139semidirect
422. C4⋊#95C2×C139semidirect
442. C4×C22⋊C4C4×C139semidirect
620. C22⋊C4C4⋊C4×C139semidirect
804. C4#388×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1392
C2×#384×C1392
C2×#380×C1392
C2×C4×C4⋊C4×C1392
C2×C4×C22⋊C4×C1392
#1442×C1392
#1439×C1392
#1436×C1392
C4⋊#95×C1392
#13876139