Finite Group Databasebeta

← C139×#25101 #48019697

Subgroups — C139×#25101 #48019697

Order 35584.

1248 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C139C211yesmaximal, characteristic, complemented
2C2×#463×C139C211yesmaximal, characteristic, complemented
3C2×#447×C139C211yesmaximal, characteristic
4C2×#418×C139C211yesmaximal, characteristic, complemented
5#2435×C139C211yesmaximal, characteristic, complemented
6#2363×C139C211yesmaximal, characteristic, complemented
7#2067×C139C211yesmaximal, characteristic, complemented
8#2054×C139C211yesmaximal, characteristic, complemented
9#2042×C139C211yesmaximal, characteristic, complemented
10#2012×C139C211yesmaximal, characteristic, complemented
11#1983×C139C211yesmaximal, characteristic, complemented
12#1925×C139C211yesmaximal, characteristic, complemented
13#1879×C139C211yesmaximal, characteristic, complemented
14#1873×C139C211yesmaximal, characteristic, complemented
15#1851×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic, complemented
18C22×D8×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic
20C22×M16×C139C2211yescharacteristic
21C2×#124×C139C2211yescharacteristic
22C2×#124×C139C2211yescharacteristic
23C2×C22⋊Q8×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×C4×D4×C139C2211yescharacteristic, complemented
26C2×#117×C139C2211yescharacteristic
27#468×C139—24no—
28#463×C139—24no—
29#447×C139—24no—
30C2×#107×C139C2211yescharacteristic, complemented
31C2×C4⋊C8×C139C2211yescharacteristic, complemented
32C2×C4⋊C8×C139C2211yescharacteristic, complemented
33#418×C139—24no—
34C2×#103×C139C2211yescharacteristic, complemented
35C2×#103×C139C2211yescharacteristic, complemented
36C2×#103×C139C2211yescharacteristic, complemented
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic, complemented
44C2×C22⋊C8×C139C2211yescharacteristic
45#394×C139—21no—
46#394×C139—21no—
47#390×C139—21no—
48#390×C139C2211yescharacteristic
49#390×C139C2211yescharacteristic
50#390×C139C2211yescharacteristic, complemented
51#389×C139C2211yescharacteristic, complemented
52#388×C139—21no—
53#386×C139—21no—
54#379×C139—21no—
55#379×C139—21no—
56C4×C4⋊C4×C139C2211yescharacteristic, complemented
57C4×C22⋊C4×C139—21no—
58C4×C22⋊C4×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#336×C139C2211yescharacteristic, complemented
62#336×C139C2211yescharacteristic, complemented
63C25×C139—21no—
64C22×Q8×C139C2311yescharacteristic
65C22×D4×C139—22no—
66C22×D4×C139—22no—
67C22×D4×C139—21no—
68C22×D4×C139—22no—
69C22×D4×C139—21no—
70C22×D4×C139—22no—
71C22×D4×C139—41no—
72C22×D4×C139—41no—
73C22×D4×C139C2311yescharacteristic
74C22×D4×C139C2311yescharacteristic
75C22×D4×C139C2311yescharacteristic
76C23×C4×C139—21no—
77C23×C4×C139C2311yescharacteristic
78C2×SD16×C139—22no—
79C2×SD16×C139—22no—
80C2×SD16×C139—41no—
81C2×D8×C139—22no—
82C2×D8×C139—22no—
83C2×D8×C139—22no—
84C2×D8×C139—22no—
85C2×D8×C139—41no—
86C2×D8×C139—41no—
87C2×M16×C139—22no—
88C2×M16×C139—22no—
89C2×M16×C139—41no—
90C22×C8×C139C2311yescharacteristic
91C22×C8×C139C2311yescharacteristic
92C22×C8×C139C2311yescharacteristic
93C22×C8×C139C2311yescharacteristic
94#124×C139—22no—
95#124×C139—22no—
96#124×C139—41no—
97#124×C139—41no—
98C22⋊Q8×C139—22no—
99C22⋊Q8×C139—22no—
100#121×C139—22no—
101#121×C139D414yes—
102C4×D4×C139—22no—
103C4×D4×C139—41no—
104#117×C139—22no—
105#117×C139—41no—
106C2×C4⋊C4×C139—21no—
107C2×C4⋊C4×C139—21no—
108C2×C4⋊C4×C139C2311yescharacteristic
109C2×C4⋊C4×C139C2311yescharacteristic
110C2×C4⋊C4×C139C2311yescharacteristic
111C2×C4⋊C4×C139C2311yescharacteristic
112C2×C22⋊C4×C139—21no—
113C2×C22⋊C4×C139—21no—
114C2×C22⋊C4×C139—21no—
115C2×C22⋊C4×C139—21no—
116C2×C22⋊C4×C139—21no—
117C2×C22⋊C4×C139—21no—
118C2×C22⋊C4×C139—21no—
119C2×C22⋊C4×C139—21no—
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×C139D411yescharacteristic
127C2×C22⋊C4×C139D411yescharacteristic
128C2×C42×C139—21no—
129C2×C42×C139—21no—
130C2×C42×C139C2311yescharacteristic
131C2×C42×C139C2311yescharacteristic
132#107×C139—22no—
133C4⋊C8×C139—22no—
134C4⋊C8×C139—41no—
135#103×C139—22no—
136#103×C139—22no—
137#103×C139—41no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—22no—
144#102×C139D414yescomplemented
145C22⋊C8×C139—22no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139D411yescharacteristic
149#95×C139D411yescharacteristic
150C24×C139—21no—
151C24×C139—21no—
152C24×C139—21no—
153C24×C139—42no—
154C24×C139—42no—
155C24×C139—42no—
156C24×C139—42no—
157C24×C139—42no—
158C24×C139—81no—
159C24×C139—81no—
160C24×C139C2×D411yescharacteristic
161C2×Q8×C139—21no—
162C2×Q8×C139—21no—
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×Q8×C139—21no—
166C2×Q8×C139—21no—
167C2×D4×C139—28no—
168C2×D4×C139—24no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139—21no—
176C2×D4×C139—21no—
177C2×D4×C139—21no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—21no—
183C2×D4×C139—21no—
184C2×D4×C139—44no—
185C2×D4×C139—44no—
186C2×D4×C139—42no—
187C2×D4×C139—42no—
188C2×D4×C139—44no—
189C2×D4×C139—42no—
190C2×D4×C139—81no—
191C2×D4×C139—81no—
192C2×D4×C139C2×D412yes—
193C2×D4×C139C2×D412yes—
194C2×D4×C139#4112yes—
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—42no—
205C22×C4×C139—42no—
206C22×C4×C139—81no—
207C22×C4×C139C2×D411yescharacteristic
208C22×C4×C139C2×D411yescharacteristic
209C22×C4×C139C2×D411yescharacteristic
210C22×C4×C139C2×D411yescharacteristic
211C22×C4×C139C2×D411yescharacteristic
212C22×C4×C139C2×D412yes—
213C22×C4×C139#4112yes—
214C22×C4×C139C2411yescharacteristic
215SD16×C139—44no—
216D8×C139—44no—
217D8×C139—44no—
218M16×C139—44no—
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—21no—
226C2×C8×C139—21no—
227C2×C8×C139—21no—
228C2×C8×C139—21no—
229C2×C8×C139—21no—
230C2×C8×C139C2×D412yes—
231C4⋊C4×C139—21no—
232C4⋊C4×C139—21no—
233C4⋊C4×C139—21no—
234C4⋊C4×C139—21no—
235C4⋊C4×C139—21no—
236C4⋊C4×C139—21no—
237C4⋊C4×C139—42no—
238C4⋊C4×C139—81no—
239C4⋊C4×C139C2×D412yes—
240C4⋊C4×C139C2×D412yes—
241C22⋊C4×C139—24no—
242C22⋊C4×C139—41no—
243C22⋊C4×C139—41no—
244C22⋊C4×C139—42no—
245C22⋊C4×C139—42no—
246C22⋊C4×C139—42no—
247C22⋊C4×C139—42no—
248C22⋊C4×C139—42no—
249C22⋊C4×C139—42no—
250C22⋊C4×C139—42no—
251C22⋊C4×C139—42no—
252C22⋊C4×C139—81no—
253C22⋊C4×C139—81no—
254C22⋊C4×C139—81no—
255C22⋊C4×C139—81no—
256C22⋊C4×C139—81no—
257C42×C139—21no—
258C42×C139—21no—
259C42×C139—21no—
260C42×C139—21no—
261C42×C139—42no—
262C42×C139—81no—
263C23×C139—21no—
264C23×C139—21no—
265C23×C139—21no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—22no—
270C23×C139—22no—
271C23×C139—22no—
272C23×C139—48no—
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—41no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139—41no—
289C23×C139—41no—
290C23×C139—41no—
291C23×C139—84no—
292C23×C139—84no—
293C23×C139—84no—
294C23×C139—84no—
295C23×C139—84no—
296C23×C139—84no—
297C23×C139#12112yes—
298C23×C139C22×D411yescharacteristic
299Q8×C139—41no—
300Q8×C139—41no—
301Q8×C139—41no—
302Q8×C139—41no—
303D4×C139—22no—
304D4×C139—22no—
305D4×C139—22no—
306D4×C139—22no—
307D4×C139—22no—
308D4×C139—22no—
309D4×C139—48no—
310D4×C139—41no—
311D4×C139—41no—
312D4×C139—41no—
313D4×C139—41no—
314D4×C139—41no—
315D4×C139—41no—
316D4×C139—84no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
319C2×C4×C139—22no—
320C2×C4×C139—22no—
321C2×C4×C139—22no—
322C2×C4×C139—22no—
323C2×C4×C139—22no—
324C2×C4×C139—21no—
325C2×C4×C139—21no—
326C2×C4×C139—22no—
327C2×C4×C139—21no—
328C2×C4×C139—21no—
329C2×C4×C139—21no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—21no—
333C2×C4×C139—21no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—21no—
337C2×C4×C139—41no—
338C2×C4×C139—41no—
339C2×C4×C139—41no—
340C2×C4×C139—41no—
341C2×C4×C139—41no—
342C2×C4×C139—41no—
343C2×C4×C139—41no—
344C2×C4×C139—41no—
345C2×C4×C139—41no—
346C2×C4×C139—41no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—84no—
351C2×C4×C139#12112yes—
352C2×C4×C139C22×D411yescharacteristic
353C2×C4×C139C22×D411yescharacteristic
354C2×C4×C139C2×#4111yescharacteristic
355C2×C4×C139C2×#4111yescharacteristic
356C2×C4×C139H(5,𝔽2)11yescharacteristic
357C2×C4×C139H(5,𝔽2)11yescharacteristic
358C8×C139—22no—
359C8×C139—41no—
360C8×C139—41no—
361C8×C139—41no—
362C22×C139—22no—
363C22×C139—22no—
364C22×C139—22no—
365C22×C139—41no—
366C22×C139—41no—
367C22×C139—41no—
368C22×C139—41no—
369C22×C139—42no—
370C22×C139—42no—
371C22×C139—42no—
372C22×C139—42no—
373C22×C139—42no—
374C22×C139—42no—
375C22×C139—42no—
376C22×C139—42no—
377C22×C139—42no—
378C22×C139—816no—
379C22×C139—81no—
380C22×C139—81no—
381C22×C139—81no—
382C22×C139—81no—
383C22×C139—81no—
384C22×C139—81no—
385C22×C139—81no—
386C22×C139—81no—
387C22×C139—81no—
388C22×C139—81no—
389C22×C139—81no—
390C22×C139—81no—
391C22×C139C2×#12111yescharacteristic
392C22×C139D4211yescharacteristic
393C22×C139#54611yescharacteristic
394C22×C139#57511yescharacteristic
395C22×C139#57511yescharacteristic
396C22×C139#57611yescharacteristic
397C22×C139#57611yescharacteristic
398C4×C139—22no—
399C4×C139—41no—
400C4×C139—41no—
401C4×C139—42no—
402C4×C139—42no—
403C4×C139—41no—
404C4×C139—41no—
405C4×C139—81no—
406C4×C139—81no—
407C4×C139—81no—
408C4×C139#52511yescharacteristic
409C4×C139#53811yescharacteristic
410C4×C139D4211yescharacteristic
411C4×C139#54611yescharacteristic
412C2×C139—42no—
413C2×C139—82no—
414C2×C139—82no—
415C2×C139—82no—
416C2×C139#242411yescharacteristic
417C2×C139#304011yescharacteristic
418C2×C139#304111yescharacteristic
419C2×C139#326811yescharacteristic
420C2×C139#327311yescharacteristic
421C2×C139#331911yescharacteristic
422C2×C139#332211yescharacteristic
423#25101C13911yesmaximal, characteristic, direct product factor, Sylow
424C139#2510111yescharacteristic, direct product factor, Sylow
425C2×#468C2×C13911yescharacteristic, complemented
426C2×#463C2×C13911yescharacteristic, complemented
427C2×#447C2×C13911yescharacteristic
428C2×#418C2×C13911yescharacteristic, complemented
429#2435C2×C13911yescharacteristic, complemented
430#2363C2×C13911yescharacteristic, complemented
431#2067C2×C13911yescharacteristic, complemented
432#2054C2×C13911yescharacteristic, complemented
433#2042C2×C13911yescharacteristic, complemented
434#2012C2×C13911yescharacteristic, complemented
435#1983C2×C13911yescharacteristic, complemented
436#1925C2×C13911yescharacteristic, complemented
437#1879C2×C13911yescharacteristic, complemented
438#1873C2×C13911yescharacteristic, complemented
439#1851C2×C13911yescharacteristic, complemented
440C23×D4C22×C13911yescharacteristic
441C22×SD16C22×C13911yescharacteristic, complemented
442C22×D8C22×C13911yescharacteristic
443C22×D8C22×C13911yescharacteristic
444C22×M16C22×C13911yescharacteristic
445C2×#124C22×C13911yescharacteristic
446C2×#124C22×C13911yescharacteristic
447C2×C22⋊Q8C22×C13911yescharacteristic
448C2×#121C22×C13911yescharacteristic
449C2×C4×D4C22×C13911yescharacteristic, complemented
450C2×#117C22×C13911yescharacteristic
451#468—24no—
452#463—24no—
453#447—24no—
454C2×#107C22×C13911yescharacteristic, complemented
455C2×C4⋊C8C22×C13911yescharacteristic, complemented
456C2×C4⋊C8C22×C13911yescharacteristic, complemented
457#418—24no—
458C2×#103C22×C13911yescharacteristic, complemented
459C2×#103C22×C13911yescharacteristic, complemented
460C2×#103C22×C13911yescharacteristic, complemented
461C2×#102C22×C13911yescharacteristic
462C2×#102C22×C13911yescharacteristic
463C2×#102C22×C13911yescharacteristic
464C2×#102C22×C13911yescharacteristic
465C2×#102C22×C13911yescharacteristic
466C2×#102C22×C13911yescharacteristic
467C2×#102C22×C13911yescharacteristic, complemented
468C2×C22⋊C8C22×C13911yescharacteristic
469#394—21no—
470#394—21no—
471#390—21no—
472#390C22×C13911yescharacteristic
473#390C22×C13911yescharacteristic
474#390C22×C13911yescharacteristic, complemented
475#389C22×C13911yescharacteristic, complemented
476#388—21no—
477#386—21no—
478#379—21no—
479#379—21no—
480C4×C4⋊C4C22×C13911yescharacteristic, complemented
481C4×C22⋊C4—21no—
482C4×C22⋊C4C22×C13911yescharacteristic
483#340C22×C13911yescharacteristic, complemented
484#340C22×C13911yescharacteristic, complemented
485#336C22×C13911yescharacteristic, complemented
486#336C22×C13911yescharacteristic, complemented
487C25—21no—
488C22×Q8C23×C13911yescharacteristic
489C22×D4—22no—
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4C23×C13911yescharacteristic
498C22×D4C23×C13911yescharacteristic
499C22×D4C23×C13911yescharacteristic
500C23×C4—21no—
501C23×C4C23×C13911yescharacteristic
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—41no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—22no—
508C2×D8—22no—
509C2×D8—41no—
510C2×D8—41no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C22×C8C23×C13911yescharacteristic
515C22×C8C23×C13911yescharacteristic
516C22×C8C23×C13911yescharacteristic
517C22×C8C23×C13911yescharacteristic
518#124—22no—
519#124—22no—
520#124—41no—
521#124—41no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524#121—22no—
525#121D4×C13914yes—
526C4×D4—22no—
527C4×D4—41no—
528#117—22no—
529#117—41no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4C23×C13911yescharacteristic
533C2×C4⋊C4C23×C13911yescharacteristic
534C2×C4⋊C4C23×C13911yescharacteristic
535C2×C4⋊C4C23×C13911yescharacteristic
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⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4D4×C13911yescharacteristic
551C2×C22⋊C4D4×C13911yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C13911yescharacteristic
555C2×C42C23×C13911yescharacteristic
556#107—22no—
557C4⋊C8—22no—
558C4⋊C8—41no—
559#103—22no—
560#103—22no—
561#103—41no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102D4×C13914yescomplemented
569C22⋊C8—22no—
570#95—21no—
571#95—21no—
572#95D4×C13911yescharacteristic
573#95D4×C13911yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24—42no—
578C24—42no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—81no—
583C24—81no—
584C24C2×D4×C13911yescharacteristic
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×D4—28no—
592C2×D4—24no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—81no—
616C2×D4C2×D4×C13912yes—
617C2×D4C2×D4×C13912yes—
618C2×D4#41×C13912yes—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—81no—
631C22×C4C2×D4×C13911yescharacteristic
632C22×C4C2×D4×C13911yescharacteristic
633C22×C4C2×D4×C13911yescharacteristic
634C22×C4C2×D4×C13911yescharacteristic
635C22×C4C2×D4×C13911yescharacteristic
636C22×C4C2×D4×C13912yes—
637C22×C4#41×C13912yes—
638C22×C4C24×C13911yescharacteristic
639SD16—44no—
640D8—44no—
641D8—44no—
642M16—44no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8C2×D4×C13912yes—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—42no—
662C4⋊C4—81no—
663C4⋊C4C2×D4×C13912yes—
664C4⋊C4C2×D4×C13912yes—
665C22⋊C4—24no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—42no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—81no—
677C22⋊C4—81no—
678C22⋊C4—81no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C42—21no—
682C42—21no—
683C42—21no—
684C42—21no—
685C42—42no—
686C42—81no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—48no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—84no—
716C23—84no—
717C23—84no—
718C23—84no—
719C23—84no—
720C23—84no—
721C23#121×C13912yes—
722C23C22×D4×C13911yescharacteristic
723Q8—41no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727D4—22no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—22no—
732D4—22no—
733D4—48no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—84no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4#121×C13912yes—
776C2×C4C22×D4×C13911yescharacteristic
777C2×C4C22×D4×C13911yescharacteristic
778C2×C4C2×#41×C13911yescharacteristic
779C2×C4C2×#41×C13911yescharacteristic
780C2×C4H(5,𝔽2)×C13911yescharacteristic
781C2×C4H(5,𝔽2)×C13911yescharacteristic
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—816no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22C2×#121×C13911yescharacteristic
816C22D42×C13911yescharacteristic
817C22#546×C13911yescharacteristic
818C22#575×C13911yescharacteristic
819C22#575×C13911yescharacteristic
820C22#576×C13911yescharacteristic
821C22#576×C13911yescharacteristic
822C4—22no—
823C4—42no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—42no—
829C4—81no—
830C4—81no—
831C4—81no—
832C4#525×C13911yescharacteristic
833C4#538×C13911yescharacteristic
834C4D42×C13911yescharacteristic
835C4#546×C13911yescharacteristic
836C2—42no—
837C2—82no—
838C2—82no—
839C2—82no—
840C2#2424×C13911yescharacteristic
841C2#3040×C13911yescharacteristic
842C2#3041×C13911yescharacteristic
843C2#3268×C13911yescharacteristic
844C2#3273×C13911yescharacteristic
845C2#3319×C13911yescharacteristic
846C2#3322×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#447×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C139C2semidirect
2. C2×#463×C139C2semidirect
4. C2×#418×C139C2semidirect
5. #2435×C139C2semidirect
6. #2363×C139C2semidirect
7. #2067×C139C2semidirect
8. #2054×C139C2semidirect
9. #2042×C139C2semidirect
10. #2012×C139C2semidirect
11. #1983×C139C2semidirect
12. #1925×C139C2semidirect
13. #1879×C139C2semidirect
14. #1873×C139C2semidirect
15. #1851×C139C2semidirect
17. C22×SD16×C139C22semidirect
25. C2×C4×D4×C139C22semidirect
30. C2×#107×C139C22semidirect
31. C2×C4⋊C8×C139C22semidirect
32. C2×C4⋊C8×C139C22semidirect
34. C2×#103×C139C22semidirect
35. C2×#103×C139C22semidirect
36. C2×#103×C139C22semidirect
43. C2×#102×C139C22semidirect
50. #390×C139C22semidirect
51. #389×C139C22semidirect
56. C4×C4⋊C4×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #336×C139C22semidirect
62. #336×C139C22semidirect
144. #102×C139D4semidirect
423. #25101C139direct (N × H)
424. C139#25101direct (N × H)
425. C2×#468C2×C139semidirect
426. C2×#463C2×C139semidirect
428. C2×#418C2×C139semidirect
429. #2435C2×C139semidirect
430. #2363C2×C139semidirect
431. #2067C2×C139semidirect
432. #2054C2×C139semidirect
433. #2042C2×C139semidirect
434. #2012C2×C139semidirect
435. #1983C2×C139semidirect
436. #1925C2×C139semidirect
437. #1879C2×C139semidirect
438. #1873C2×C139semidirect
439. #1851C2×C139semidirect
441. C22×SD16C22×C139semidirect
449. C2×C4×D4C22×C139semidirect
454. C2×#107C22×C139semidirect
455. C2×C4⋊C8C22×C139semidirect
456. C2×C4⋊C8C22×C139semidirect
458. C2×#103C22×C139semidirect
459. C2×#103C22×C139semidirect
460. C2×#103C22×C139semidirect
467. C2×#102C22×C139semidirect
474. #390C22×C139semidirect
475. #389C22×C139semidirect
480. C4×C4⋊C4C22×C139semidirect
483. #340C22×C139semidirect
484. #340C22×C139semidirect
485. #336C22×C139semidirect
486. #336C22×C139semidirect
568. #102D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1392
C2×#463×C1392
C2×#447×C1392
C2×#418×C1392
#2435×C1392
#2363×C1392
#2067×C1392
#2054×C1392
#2042×C1392
#2012×C1392
#1983×C1392
#1925×C1392
#1879×C1392
#1873×C1392
#1851×C1392
#25101139