Finite Group Databasebeta

← C139×#25554 #48020150

Subgroups — C139×#25554 #48020150

Order 35584.

1236 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#555×C139C211yesmaximal, characteristic, complemented
2C2×#482×C139C211yesmaximal, characteristic, complemented
3C2×#469×C139C211yesmaximal, characteristic, complemented
4#2416×C139C211yesmaximal, characteristic, complemented
5#2058×C139C211yesmaximal, characteristic, complemented
6#2034×C139C211yesmaximal, characteristic, complemented
7#2023×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1879×C139C211yesmaximal, characteristic, complemented
10#1875×C139C211yesmaximal, characteristic, complemented
11#1874×C139C211yesmaximal, characteristic, complemented
12#1870×C139C211yesmaximal, characteristic, complemented
13#1862×C139C211yesmaximal, characteristic, complemented
14#1854×C139C211yesmaximal, characteristic, complemented
15#1736×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17C22×M16×C139C2211yescharacteristic
18#555×C139—24no—
19#555×C139—24no—
20C2×C4⋊Q8×C139C2211yescharacteristic
21C2×#124×C139—21no—
22C2×#124×C139—21no—
23C2×#121×C139—21no—
24C2×#121×C139—21no—
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×#121×C139C2211yescharacteristic
28C2×#121×C139C2211yescharacteristic
29C2×C4×D4×C139C2211yescharacteristic
30C2×C4×D4×C139C2211yescharacteristic
31C2×#117×C139—21no—
32C2×#117×C139C2211yescharacteristic
33C2×#117×C139C2211yescharacteristic
34C22×C4⋊C4×C139C2211yescharacteristic
35#482×C139—24no—
36#469×C139—24no—
37C2×#107×C139C2211yescharacteristic
38C2×#106×C139C2211yescharacteristic
39C2×#106×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×C22⋊C8×C139C2211yescharacteristic
47C2×C22⋊C8×C139C2211yescharacteristic
48C2×C22⋊C8×C139C2211yescharacteristic
49#396×C139—21no—
50#394×C139—21no—
51#390×C139C2211yescharacteristic
52#389×C139C2211yescharacteristic
53#386×C139—21no—
54#380×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#336×C139C2211yescharacteristic
62#336×C139C2211yescharacteristic
63C22×Q8×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139D411yescharacteristic
69C22×D4×C139C2311yescharacteristic
70C22×D4×C139C2311yescharacteristic
71C23×C4×C139—21no—
72C23×C4×C139—21no—
73C23×C4×C139C2311yescharacteristic
74C23×C4×C139C2311yescharacteristic
75C2×D8×C139—22no—
76C2×D8×C139—22no—
77C2×D8×C139—41no—
78C2×M16×C139—22no—
79C2×M16×C139—22no—
80C2×M16×C139—41no—
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83C22×C8×C139C2311yescharacteristic
84C22×C8×C139C2311yescharacteristic
85C4⋊Q8×C139—22no—
86C4⋊Q8×C139—22no—
87#124×C139—28no—
88#124×C139—28no—
89#121×C139—28no—
90#121×C139—22no—
91#121×C139—22no—
92#121×C139—22no—
93#121×C139—22no—
94#121×C139—22no—
95#121×C139—22no—
96#121×C139—41no—
97#121×C139—44no—
98#121×C139D414yescomplemented
99C4×D4×C139—22no—
100C4×D4×C139—22no—
101C4×D4×C139—22no—
102C4×D4×C139—22no—
103#117×C139—28no—
104#117×C139—22no—
105#117×C139—22no—
106#117×C139—22no—
107#117×C139D414yescomplemented
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—22no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139—41no—
113C2×C4⋊C4×C139D411yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C4⋊C4×C139C2311yescharacteristic
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—21no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—21no—
129C2×C22⋊C4×C139—21no—
130C2×C22⋊C4×C139D411yescharacteristic
131C2×C22⋊C4×C139D411yescharacteristic
132C2×C42×C139—21no—
133C2×C42×C139—21no—
134C2×C42×C139C2311yescharacteristic
135#107×C139—22no—
136#106×C139—22no—
137#106×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—41no—
144C22⋊C8×C139—22no—
145C22⋊C8×C139—22no—
146C22⋊C8×C139—41no—
147#95×C139—21no—
148#95×C139—21no—
149C24×C139—21no—
150C24×C139—21no—
151C24×C139C2×D411yescharacteristic
152C24×C139C2×D411yescharacteristic
153C2×Q8×C139—24no—
154C2×Q8×C139—81no—
155C2×Q8×C139—81no—
156C2×D4×C139—22no—
157C2×D4×C139—24no—
158C2×D4×C139—24no—
159C2×D4×C139—22no—
160C2×D4×C139—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—21no—
165C2×D4×C139—21no—
166C2×D4×C139—21no—
167C2×D4×C139—21no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—41no—
172C2×D4×C139—42no—
173C2×D4×C139—42no—
174C2×D4×C139—42no—
175C2×D4×C139—42no—
176C2×D4×C139—42no—
177C2×D4×C139—81no—
178C2×D4×C139—81no—
179C2×D4×C139—81no—
180C2×D4×C139—81no—
181C2×D4×C139—81no—
182C2×D4×C139C2×D412yes—
183C22×C4×C139—21no—
184C22×C4×C139—21no—
185C22×C4×C139—21no—
186C22×C4×C139—21no—
187C22×C4×C139—24no—
188C22×C4×C139—21no—
189C22×C4×C139—21no—
190C22×C4×C139—21no—
191C22×C4×C139—21no—
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—42no—
201C22×C4×C139—42no—
202C22×C4×C139—42no—
203C22×C4×C139—42no—
204C22×C4×C139—81no—
205C22×C4×C139C2×D411yescharacteristic
206C22×C4×C139C2×D411yescharacteristic
207C22×C4×C139C2×D411yescharacteristic
208C22×C4×C139C2×D412yes—
209C22×C4×C139C2×D412yes—
210C22×C4×C139C2×D411yescharacteristic
211C22×C4×C139C2411yescharacteristic
212D8×C139—44no—
213M16×C139—44no—
214C2×C8×C139—21no—
215C2×C8×C139—21no—
216C2×C8×C139—21no—
217C2×C8×C139—21no—
218C2×C8×C139—21no—
219C2×C8×C139—21no—
220C2×C8×C139—21no—
221C2×C8×C139—21no—
222C2×C8×C139—21no—
223C2×C8×C139—21no—
224C2×C8×C139—21no—
225C2×C8×C139#4112yes—
226C4⋊C4×C139—24no—
227C4⋊C4×C139—22no—
228C4⋊C4×C139—21no—
229C4⋊C4×C139—21no—
230C4⋊C4×C139—21no—
231C4⋊C4×C139—21no—
232C4⋊C4×C139—21no—
233C4⋊C4×C139—21no—
234C4⋊C4×C139—21no—
235C4⋊C4×C139—21no—
236C4⋊C4×C139—42no—
237C4⋊C4×C139—42no—
238C4⋊C4×C139C2×D412yes—
239C4⋊C4×C139C2×D412yes—
240C4⋊C4×C139C2×D412yes—
241C4⋊C4×C139#4112yes—
242C22⋊C4×C139—24no—
243C22⋊C4×C139—24no—
244C22⋊C4×C139—24no—
245C22⋊C4×C139—24no—
246C22⋊C4×C139—22no—
247C22⋊C4×C139—24no—
248C22⋊C4×C139—22no—
249C22⋊C4×C139—42no—
250C22⋊C4×C139—42no—
251C22⋊C4×C139—42no—
252C22⋊C4×C139—42no—
253C22⋊C4×C139—81no—
254C42×C139—24no—
255C42×C139—24no—
256C42×C139—21no—
257C42×C139—21no—
258C23×C139—21no—
259C23×C139—21no—
260C23×C139—21no—
261C23×C139—21no—
262C23×C139—21no—
263C23×C139—21no—
264C23×C139—21no—
265C23×C139—22no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—41no—
273C23×C139—41no—
274C23×C139—41no—
275C23×C139—41no—
276C23×C139—41no—
277C23×C139—41no—
278C23×C139—41no—
279C23×C139—41no—
280C23×C139—41no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—41no—
285C23×C139#12012yes—
286C23×C139C22×D411yescharacteristic
287Q8×C139—84no—
288D4×C139—22no—
289D4×C139—22no—
290D4×C139—44no—
291D4×C139—41no—
292D4×C139—41no—
293D4×C139—41no—
294D4×C139—41no—
295D4×C139—41no—
296D4×C139—41no—
297D4×C139—84no—
298D4×C139—84no—
299D4×C139—84no—
300D4×C139—84no—
301C2×C4×C139—21no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—21no—
305C2×C4×C139—22no—
306C2×C4×C139—22no—
307C2×C4×C139—22no—
308C2×C4×C139—22no—
309C2×C4×C139—21no—
310C2×C4×C139—22no—
311C2×C4×C139—21no—
312C2×C4×C139—22no—
313C2×C4×C139—22no—
314C2×C4×C139—21no—
315C2×C4×C139—22no—
316C2×C4×C139—21no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
319C2×C4×C139—48no—
320C2×C4×C139—41no—
321C2×C4×C139—41no—
322C2×C4×C139—41no—
323C2×C4×C139—41no—
324C2×C4×C139—41no—
325C2×C4×C139—41no—
326C2×C4×C139—41no—
327C2×C4×C139—41no—
328C2×C4×C139—41no—
329C2×C4×C139—41no—
330C2×C4×C139—41no—
331C2×C4×C139—41no—
332C2×C4×C139—41no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139—41no—
336C2×C4×C139—41no—
337C2×C4×C139—41no—
338C2×C4×C139—84no—
339C2×C4×C139#12012yes—
340C2×C4×C139AGL(1,ℤ/8)12yes—
341C2×C4×C139C22×D411yescharacteristic
342C2×C4×C139C22×D411yescharacteristic
343C2×C4×C139C2×#4111yescharacteristic
344C2×C4×C139C2×#4111yescharacteristic
345C2×C4×C139H(5,𝔽2)11yescharacteristic
346C2×C4×C1392−1+411yescharacteristic
347C8×C139—22no—
348C8×C139—41no—
349C8×C139—41no—
350C8×C139—41no—
351C22×C139—22no—
352C22×C139—22no—
353C22×C139—22no—
354C22×C139—41no—
355C22×C139—41no—
356C22×C139—41no—
357C22×C139—41no—
358C22×C139—41no—
359C22×C139—41no—
360C22×C139—41no—
361C22×C139—42no—
362C22×C139—42no—
363C22×C139—41no—
364C22×C139—41no—
365C22×C139—42no—
366C22×C139—41no—
367C22×C139—41no—
368C22×C139—81no—
369C22×C139—81no—
370C22×C139—81no—
371C22×C139—81no—
372C22×C139—81no—
373C22×C139—81no—
374C22×C139—81no—
375C22×C139—81no—
376C22×C139—81no—
377C22×C139—81no—
378C22×C139—81no—
379C22×C139C2×#12011yescharacteristic
380C22×C139#54611yescharacteristic
381C22×C139#54711yescharacteristic
382C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
383C22×C139#57511yescharacteristic
384C22×C139#57611yescharacteristic
385C22×C139#57711yescharacteristic
386C4×C139—22no—
387C4×C139—22no—
388C4×C139—41no—
389C4×C139—42no—
390C4×C139—41no—
391C4×C139—42no—
392C4×C139—42no—
393C4×C139—42no—
394C4×C139—81no—
395C4×C139—81no—
396C4×C139#53211yescharacteristic
397C4×C139#53711yescharacteristic
398C4×C139#54611yescharacteristic
399C4×C139#54711yescharacteristic
400C2×C139—42no—
401C2×C139—81no—
402C2×C139—82no—
403C2×C139—161no—
404C2×C139#243011yescharacteristic
405C2×C139#300611yescharacteristic
406C2×C139#301211yescharacteristic
407C2×C139#332111yescharacteristic
408C2×C139#332511yescharacteristic
409C2×C139#334711yescharacteristic
410C2×C139#335411yescharacteristic
411#25554C13911yesmaximal, characteristic, direct product factor, Sylow
412C139#2555411yescharacteristic, direct product factor, Sylow
413C2×#555C2×C13911yescharacteristic, complemented
414C2×#482C2×C13911yescharacteristic, complemented
415C2×#469C2×C13911yescharacteristic, complemented
416#2416C2×C13911yescharacteristic, complemented
417#2058C2×C13911yescharacteristic, complemented
418#2034C2×C13911yescharacteristic, complemented
419#2023C2×C13911yescharacteristic, complemented
420#1999C2×C13911yescharacteristic, complemented
421#1879C2×C13911yescharacteristic, complemented
422#1875C2×C13911yescharacteristic, complemented
423#1874C2×C13911yescharacteristic, complemented
424#1870C2×C13911yescharacteristic, complemented
425#1862C2×C13911yescharacteristic, complemented
426#1854C2×C13911yescharacteristic, complemented
427#1736C2×C13911yescharacteristic, complemented
428C22×D8C22×C13911yescharacteristic
429C22×M16C22×C13911yescharacteristic
430#555—24no—
431#555—24no—
432C2×C4⋊Q8C22×C13911yescharacteristic
433C2×#124—21no—
434C2×#124—21no—
435C2×#121—21no—
436C2×#121—21no—
437C2×#121C22×C13911yescharacteristic
438C2×#121C22×C13911yescharacteristic
439C2×#121C22×C13911yescharacteristic
440C2×#121C22×C13911yescharacteristic
441C2×C4×D4C22×C13911yescharacteristic
442C2×C4×D4C22×C13911yescharacteristic
443C2×#117—21no—
444C2×#117C22×C13911yescharacteristic
445C2×#117C22×C13911yescharacteristic
446C22×C4⋊C4C22×C13911yescharacteristic
447#482—24no—
448#469—24no—
449C2×#107C22×C13911yescharacteristic
450C2×#106C22×C13911yescharacteristic
451C2×#106C22×C13911yescharacteristic
452C2×#102C22×C13911yescharacteristic
453C2×#102C22×C13911yescharacteristic
454C2×#102C22×C13911yescharacteristic
455C2×#102C22×C13911yescharacteristic
456C2×#102C22×C13911yescharacteristic
457C2×#102C22×C13911yescharacteristic
458C2×C22⋊C8C22×C13911yescharacteristic
459C2×C22⋊C8C22×C13911yescharacteristic
460C2×C22⋊C8C22×C13911yescharacteristic
461#396—21no—
462#394—21no—
463#390C22×C13911yescharacteristic
464#389C22×C13911yescharacteristic
465#386—21no—
466#380C22×C13911yescharacteristic
467#340C22×C13911yescharacteristic
468#340C22×C13911yescharacteristic
469#340C22×C13911yescharacteristic
470#340C22×C13911yescharacteristic
471#340C22×C13911yescharacteristic
472#340C22×C13911yescharacteristic
473#336C22×C13911yescharacteristic
474#336C22×C13911yescharacteristic
475C22×Q8—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4D4×C13911yescharacteristic
481C22×D4C23×C13911yescharacteristic
482C22×D4C23×C13911yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C13911yescharacteristic
486C23×C4C23×C13911yescharacteristic
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—41no—
490C2×M16—22no—
491C2×M16—22no—
492C2×M16—41no—
493C22×C8C23×C13911yescharacteristic
494C22×C8C23×C13911yescharacteristic
495C22×C8C23×C13911yescharacteristic
496C22×C8C23×C13911yescharacteristic
497C4⋊Q8—22no—
498C4⋊Q8—22no—
499#124—28no—
500#124—28no—
501#121—28no—
502#121—22no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—41no—
509#121—44no—
510#121D4×C13914yescomplemented
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—22no—
515#117—28no—
516#117—22no—
517#117—22no—
518#117—22no—
519#117D4×C13914yescomplemented
520C2×C4⋊C4—21no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—41no—
525C2×C4⋊C4D4×C13911yescharacteristic
526C2×C4⋊C4C23×C13911yescharacteristic
527C2×C4⋊C4C23×C13911yescharacteristic
528C2×C4⋊C4C23×C13911yescharacteristic
529C2×C4⋊C4C23×C13911yescharacteristic
530C2×C4⋊C4C23×C13911yescharacteristic
531C2×C4⋊C4C23×C13911yescharacteristic
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4D4×C13911yescharacteristic
543C2×C22⋊C4D4×C13911yescharacteristic
544C2×C42—21no—
545C2×C42—21no—
546C2×C42C23×C13911yescharacteristic
547#107—22no—
548#106—22no—
549#106—22no—
550#102—22no—
551#102—22no—
552#102—22no—
553#102—22no—
554#102—22no—
555#102—41no—
556C22⋊C8—22no—
557C22⋊C8—22no—
558C22⋊C8—41no—
559#95—21no—
560#95—21no—
561C24—21no—
562C24—21no—
563C24C2×D4×C13911yescharacteristic
564C24C2×D4×C13911yescharacteristic
565C2×Q8—24no—
566C2×Q8—81no—
567C2×Q8—81no—
568C2×D4—22no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—22no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4C2×D4×C13912yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4C2×D4×C13911yescharacteristic
618C22×C4C2×D4×C13911yescharacteristic
619C22×C4C2×D4×C13911yescharacteristic
620C22×C4C2×D4×C13912yes—
621C22×C4C2×D4×C13912yes—
622C22×C4C2×D4×C13911yescharacteristic
623C22×C4C24×C13911yescharacteristic
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8#41×C13912yes—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—42no—
649C4⋊C4—42no—
650C4⋊C4C2×D4×C13912yes—
651C4⋊C4C2×D4×C13912yes—
652C4⋊C4C2×D4×C13912yes—
653C4⋊C4#41×C13912yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—24no—
660C22⋊C4—22no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—81no—
666C42—24no—
667C42—24no—
668C42—21no—
669C42—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23#120×C13912yes—
698C23C22×D4×C13911yescharacteristic
699Q8—84no—
700D4—22no—
701D4—22no—
702D4—44no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—84no—
710D4—84no—
711D4—84no—
712D4—84no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—48no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4#120×C13912yes—
752C2×C4AGL(1,ℤ/8)×C13912yes—
753C2×C4C22×D4×C13911yescharacteristic
754C2×C4C22×D4×C13911yescharacteristic
755C2×C4C2×#41×C13911yescharacteristic
756C2×C4C2×#41×C13911yescharacteristic
757C2×C4H(5,𝔽2)×C13911yescharacteristic
758C2×C42−1+4×C13911yescharacteristic
759C8—22no—
760C8—41no—
761C8—41no—
762C8—41no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×#120×C13911yescharacteristic
792C22#546×C13911yescharacteristic
793C22#547×C13911yescharacteristic
794C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
795C22#575×C13911yescharacteristic
796C22#576×C13911yescharacteristic
797C22#577×C13911yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—42no—
806C4—81no—
807C4—81no—
808C4#532×C13911yescharacteristic
809C4#537×C13911yescharacteristic
810C4#546×C13911yescharacteristic
811C4#547×C13911yescharacteristic
812C2—42no—
813C2—81no—
814C2—82no—
815C2—161no—
816C2#2430×C13911yescharacteristic
817C2#3006×C13911yescharacteristic
818C2#3012×C13911yescharacteristic
819C2#3321×C13911yescharacteristic
820C2#3325×C13911yescharacteristic
821C2#3347×C13911yescharacteristic
822C2#3354×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#555×C139C2semidirect
2. C2×#482×C139C2semidirect
3. C2×#469×C139C2semidirect
4. #2416×C139C2semidirect
5. #2058×C139C2semidirect
6. #2034×C139C2semidirect
7. #2023×C139C2semidirect
8. #1999×C139C2semidirect
9. #1879×C139C2semidirect
10. #1875×C139C2semidirect
11. #1874×C139C2semidirect
12. #1870×C139C2semidirect
13. #1862×C139C2semidirect
14. #1854×C139C2semidirect
15. #1736×C139C2semidirect
98. #121×C139D4semidirect
107. #117×C139D4semidirect
411. #25554C139direct (N × H)
412. C139#25554direct (N × H)
413. C2×#555C2×C139semidirect
414. C2×#482C2×C139semidirect
415. C2×#469C2×C139semidirect
416. #2416C2×C139semidirect
417. #2058C2×C139semidirect
418. #2034C2×C139semidirect
419. #2023C2×C139semidirect
420. #1999C2×C139semidirect
421. #1879C2×C139semidirect
422. #1875C2×C139semidirect
423. #1874C2×C139semidirect
424. #1870C2×C139semidirect
425. #1862C2×C139semidirect
426. #1854C2×C139semidirect
427. #1736C2×C139semidirect
510. #121D4×C139semidirect
519. #117D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#555×C1392
C2×#482×C1392
C2×#469×C1392
#2416×C1392
#2058×C1392
#2034×C1392
#2023×C1392
#1999×C1392
#1879×C1392
#1875×C1392
#1874×C1392
#1870×C1392
#1862×C1392
#1854×C1392
#1736×C1392
#25554139