Finite Group Databasebeta

← C139×#25088 #48019684

Subgroups — C139×#25088 #48019684

Order 35584.

1310 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C139C211yesmaximal, characteristic, complemented
2C2×#463×C139C211yesmaximal, characteristic, complemented
3C2×#447×C139C211yesmaximal, characteristic
4C22×#102×C139C211yesmaximal, characteristic, complemented
5#2435×C139C211yesmaximal, characteristic, complemented
6#2361×C139C211yesmaximal, characteristic, complemented
7#2065×C139C211yesmaximal, characteristic, complemented
8#2054×C139C211yesmaximal, characteristic, complemented
9#2042×C139C211yesmaximal, characteristic, complemented
10#2012×C139C211yesmaximal, characteristic, complemented
11#1983×C139C211yesmaximal, characteristic, complemented
12#1926×C139C211yesmaximal, characteristic, complemented
13#1879×C139C211yesmaximal, characteristic, complemented
14#1872×C139C211yesmaximal, characteristic, complemented
15#1850×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic, complemented
18C22×D8×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic
20C23×C8×C139C2211yescharacteristic
21C2×#124×C139C2211yescharacteristic
22C2×#124×C139C2211yescharacteristic
23C2×C22⋊Q8×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×C4×D4×C139—21no—
26C2×C4×D4×C139C2211yescharacteristic, complemented
27C22×C4⋊C4×C139C2211yescharacteristic
28#465×C139—24no—
29#463×C139—24no—
30#447×C139—24no—
31C2×#106×C139C2211yescharacteristic, complemented
32C2×C4⋊C8×C139C2211yescharacteristic, complemented
33C2×C4⋊C8×C139C2211yescharacteristic, complemented
34C2×#103×C139C2211yescharacteristic, complemented
35C2×#103×C139C2211yescharacteristic, complemented
36C2×#103×C139C2211yescharacteristic, complemented
37C2×#102×C139—24no—
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic, complemented
45C2×C22⋊C8×C139C2211yescharacteristic
46#394×C139—21no—
47#394×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#385×C139—21no—
55#379×C139—21no—
56#379×C139—21no—
57C4×C4⋊C4×C139C2211yescharacteristic, complemented
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×C139—21no—
78C23×C4×C139C2311yescharacteristic
79C2×SD16×C139—22no—
80C2×SD16×C139—22no—
81C2×SD16×C139—41no—
82C2×D8×C139—22no—
83C2×D8×C139—22no—
84C2×D8×C139—22no—
85C2×D8×C139—22no—
86C2×D8×C139—41no—
87C2×D8×C139—41no—
88C22×C8×C139—22no—
89C22×C8×C139—22no—
90C22×C8×C139—41no—
91C22×C8×C139C2311yescharacteristic
92C22×C8×C139C2311yescharacteristic
93C22×C8×C139C2311yescharacteristic
94C22×C8×C139C2311yescharacteristic
95#124×C139—22no—
96#124×C139—22no—
97#124×C139—41no—
98#124×C139—41no—
99C22⋊Q8×C139—22no—
100C22⋊Q8×C139—22no—
101#121×C139—22no—
102#121×C139D414yes—
103C4×D4×C139—22no—
104C4×D4×C139—41no—
105C4×D4×C139—44no—
106C2×C4⋊C4×C139—22no—
107C2×C4⋊C4×C139—21no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139—41no—
111C2×C4⋊C4×C139C2311yescharacteristic
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
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×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139D411yescharacteristic
129C2×C22⋊C4×C139D411yescharacteristic
130C2×C42×C139—21no—
131C2×C42×C139C2311yescharacteristic
132C2×C42×C139C2311yescharacteristic
133#106×C139—22no—
134C4⋊C8×C139—22no—
135C4⋊C8×C139—41no—
136#103×C139—22no—
137#103×C139—22no—
138#103×C139—41no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—22no—
144#102×C139—22no—
145#102×C139D414yescomplemented
146C22⋊C8×C139—22no—
147#95×C139—21no—
148#95×C139—21no—
149#95×C139D411yescharacteristic
150#95×C139D411yescharacteristic
151C24×C139—21no—
152C24×C139—21no—
153C24×C139—21no—
154C24×C139—42no—
155C24×C139—42no—
156C24×C139—42no—
157C24×C139—42no—
158C24×C139—42no—
159C24×C139—81no—
160C24×C139—81no—
161C24×C139C2×D411yescharacteristic
162C2×Q8×C139—21no—
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×Q8×C139—21no—
166C2×Q8×C139—21no—
167C2×Q8×C139—21no—
168C2×D4×C139—28no—
169C2×D4×C139—24no—
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—21no—
185C2×D4×C139—44no—
186C2×D4×C139—44no—
187C2×D4×C139—42no—
188C2×D4×C139—42no—
189C2×D4×C139—44no—
190C2×D4×C139—42no—
191C2×D4×C139—42no—
192C2×D4×C139—42no—
193C2×D4×C139C2×D412yes—
194C2×D4×C139C2×D412yes—
195C2×D4×C139#4112yes—
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—42no—
206C22×C4×C139—42no—
207C22×C4×C139—42no—
208C22×C4×C139—42no—
209C22×C4×C139—81no—
210C22×C4×C139—81no—
211C22×C4×C139C2×D411yescharacteristic
212C22×C4×C139C2×D411yescharacteristic
213C22×C4×C139C2×D411yescharacteristic
214C22×C4×C139C2×D411yescharacteristic
215C22×C4×C139C2×D411yescharacteristic
216C22×C4×C139C2×D412yes—
217C22×C4×C139#4112yes—
218C22×C4×C139C2411yescharacteristic
219SD16×C139—44no—
220D8×C139—44no—
221D8×C139—44no—
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×C139—21no—
231C2×C8×C139—21no—
232C2×C8×C139—21no—
233C2×C8×C139—44no—
234C2×C8×C139C2×D412yes—
235C4⋊C4×C139—21no—
236C4⋊C4×C139—21no—
237C4⋊C4×C139—21no—
238C4⋊C4×C139—21no—
239C4⋊C4×C139—21no—
240C4⋊C4×C139—21no—
241C4⋊C4×C139—42no—
242C4⋊C4×C139—42no—
243C4⋊C4×C139—42no—
244C4⋊C4×C139C2×D412yes—
245C4⋊C4×C139C2×D412yes—
246C22⋊C4×C139—22no—
247C22⋊C4×C139—22no—
248C22⋊C4×C139—24no—
249C22⋊C4×C139—42no—
250C22⋊C4×C139—42no—
251C22⋊C4×C139—42no—
252C22⋊C4×C139—42no—
253C22⋊C4×C139—42no—
254C22⋊C4×C139—42no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—81no—
257C22⋊C4×C139—81no—
258C22⋊C4×C139—81no—
259C22⋊C4×C139—81no—
260C22⋊C4×C139—81no—
261C42×C139—21no—
262C42×C139—21no—
263C42×C139—21no—
264C42×C139—21no—
265C42×C139—42no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—21no—
270C23×C139—22no—
271C23×C139—22no—
272C23×C139—22no—
273C23×C139—48no—
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—41no—
292C23×C139—84no—
293C23×C139—84no—
294C23×C139—84no—
295C23×C139—84no—
296C23×C139—84no—
297C23×C139—84no—
298C23×C139#12112yes—
299C23×C139#13512yes—
300C23×C139AGL(1,ℤ/8)12yes—
301C23×C139C22×D411yescharacteristic
302Q8×C139—41no—
303Q8×C139—41no—
304Q8×C139—41no—
305Q8×C139—41no—
306D4×C139—22no—
307D4×C139—22no—
308D4×C139—22no—
309D4×C139—22no—
310D4×C139—22no—
311D4×C139—22no—
312D4×C139—48no—
313D4×C139—48no—
314D4×C139—41no—
315D4×C139—41no—
316D4×C139—41no—
317D4×C139—41no—
318D4×C139—41no—
319D4×C139—41no—
320C2×C4×C139—21no—
321C2×C4×C139—21no—
322C2×C4×C139—22no—
323C2×C4×C139—22no—
324C2×C4×C139—22no—
325C2×C4×C139—22no—
326C2×C4×C139—22no—
327C2×C4×C139—21no—
328C2×C4×C139—21no—
329C2×C4×C139—22no—
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—21no—
338C2×C4×C139—21no—
339C2×C4×C139—21no—
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—41no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
353C2×C4×C139—84no—
354C2×C4×C139—84no—
355C2×C4×C139#12112yes—
356C2×C4×C139C22×D411yescharacteristic
357C2×C4×C139C22×D411yescharacteristic
358C2×C4×C139C2×#4111yescharacteristic
359C2×C4×C139C2×#4111yescharacteristic
360C2×C4×C139H(5,𝔽2)11yescharacteristic
361C2×C4×C139H(5,𝔽2)11yescharacteristic
362C8×C139—22no—
363C8×C139—41no—
364C8×C139—41no—
365C8×C139—41no—
366C22×C139—22no—
367C22×C139—22no—
368C22×C139—22no—
369C22×C139—22no—
370C22×C139—22no—
371C22×C139—22no—
372C22×C139—42no—
373C22×C139—42no—
374C22×C139—42no—
375C22×C139—42no—
376C22×C139—42no—
377C22×C139—42no—
378C22×C139—42no—
379C22×C139—42no—
380C22×C139—42no—
381C22×C139—816no—
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×C139—81no—
392C22×C139—81no—
393C22×C139—81no—
394C22×C139#46314yescomplemented
395C22×C139C2×#12111yescharacteristic
396C22×C139D4211yescharacteristic
397C22×C139#54611yescharacteristic
398C22×C139C2×#13511yescharacteristic
399C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
400C22×C139#57611yescharacteristic
401C22×C139#57711yescharacteristic
402C4×C139—22no—
403C4×C139—41no—
404C4×C139—42no—
405C4×C139—41no—
406C4×C139—42no—
407C4×C139—41no—
408C4×C139—41no—
409C4×C139—81no—
410C4×C139—81no—
411C4×C139—81no—
412C4×C139#52511yescharacteristic
413C4×C139#53811yescharacteristic
414C4×C139D4211yescharacteristic
415C4×C139#54611yescharacteristic
416C2×C139—24no—
417C2×C139—82no—
418C2×C139—82no—
419C2×C139—82no—
420C2×C139#242411yescharacteristic
421C2×C139C2×#46311yescharacteristic
422C2×C139#304511yescharacteristic
423C2×C139#326411yescharacteristic
424C2×C139#328211yescharacteristic
425C2×C139#329711yescharacteristic
426C2×C139#330611yescharacteristic
427#25088C13911yesmaximal, characteristic, direct product factor, Sylow
428C139#2508811yescharacteristic, direct product factor, Sylow
429C2×#465C2×C13911yescharacteristic, complemented
430C2×#463C2×C13911yescharacteristic, complemented
431C2×#447C2×C13911yescharacteristic
432C22×#102C2×C13911yescharacteristic, complemented
433#2435C2×C13911yescharacteristic, complemented
434#2361C2×C13911yescharacteristic, complemented
435#2065C2×C13911yescharacteristic, complemented
436#2054C2×C13911yescharacteristic, complemented
437#2042C2×C13911yescharacteristic, complemented
438#2012C2×C13911yescharacteristic, complemented
439#1983C2×C13911yescharacteristic, complemented
440#1926C2×C13911yescharacteristic, complemented
441#1879C2×C13911yescharacteristic, complemented
442#1872C2×C13911yescharacteristic, complemented
443#1850C2×C13911yescharacteristic, complemented
444C23×D4C22×C13911yescharacteristic
445C22×SD16C22×C13911yescharacteristic, complemented
446C22×D8C22×C13911yescharacteristic
447C22×D8C22×C13911yescharacteristic
448C23×C8C22×C13911yescharacteristic
449C2×#124C22×C13911yescharacteristic
450C2×#124C22×C13911yescharacteristic
451C2×C22⋊Q8C22×C13911yescharacteristic
452C2×#121C22×C13911yescharacteristic
453C2×C4×D4—21no—
454C2×C4×D4C22×C13911yescharacteristic, complemented
455C22×C4⋊C4C22×C13911yescharacteristic
456#465—24no—
457#463—24no—
458#447—24no—
459C2×#106C22×C13911yescharacteristic, complemented
460C2×C4⋊C8C22×C13911yescharacteristic, complemented
461C2×C4⋊C8C22×C13911yescharacteristic, complemented
462C2×#103C22×C13911yescharacteristic, complemented
463C2×#103C22×C13911yescharacteristic, complemented
464C2×#103C22×C13911yescharacteristic, complemented
465C2×#102—24no—
466C2×#102C22×C13911yescharacteristic
467C2×#102C22×C13911yescharacteristic
468C2×#102C22×C13911yescharacteristic
469C2×#102C22×C13911yescharacteristic
470C2×#102C22×C13911yescharacteristic
471C2×#102C22×C13911yescharacteristic
472C2×#102C22×C13911yescharacteristic, complemented
473C2×C22⋊C8C22×C13911yescharacteristic
474#394—21no—
475#394—21no—
476#390C22×C13911yescharacteristic
477#390C22×C13911yescharacteristic
478#390C22×C13911yescharacteristic, complemented
479#389C22×C13911yescharacteristic, complemented
480#388—21no—
481#386—21no—
482#385—21no—
483#379—21no—
484#379—21no—
485C4×C4⋊C4C22×C13911yescharacteristic, complemented
486C4×C22⋊C4C22×C13911yescharacteristic
487#340C22×C13911yescharacteristic, complemented
488#340C22×C13911yescharacteristic, complemented
489#336C22×C13911yescharacteristic, complemented
490#336C22×C13911yescharacteristic, complemented
491C25—21no—
492C22×Q8C23×C13911yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C13911yescharacteristic
502C22×D4C23×C13911yescharacteristic
503C22×D4C23×C13911yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C13911yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—41no—
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8—22no—
517C22×C8—22no—
518C22×C8—41no—
519C22×C8C23×C13911yescharacteristic
520C22×C8C23×C13911yescharacteristic
521C22×C8C23×C13911yescharacteristic
522C22×C8C23×C13911yescharacteristic
523#124—22no—
524#124—22no—
525#124—41no—
526#124—41no—
527C22⋊Q8—22no—
528C22⋊Q8—22no—
529#121—22no—
530#121D4×C13914yes—
531C4×D4—22no—
532C4×D4—41no—
533C4×D4—44no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4C23×C13911yescharacteristic
540C2×C4⋊C4C23×C13911yescharacteristic
541C2×C4⋊C4C23×C13911yescharacteristic
542C2×C4⋊C4C23×C13911yescharacteristic
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⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4D4×C13911yescharacteristic
557C2×C22⋊C4D4×C13911yescharacteristic
558C2×C42—21no—
559C2×C42C23×C13911yescharacteristic
560C2×C42C23×C13911yescharacteristic
561#106—22no—
562C4⋊C8—22no—
563C4⋊C8—41no—
564#103—22no—
565#103—22no—
566#103—41no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102D4×C13914yescomplemented
574C22⋊C8—22no—
575#95—21no—
576#95—21no—
577#95D4×C13911yescharacteristic
578#95D4×C13911yescharacteristic
579C24—21no—
580C24—21no—
581C24—21no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C13911yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×D4—28no—
597C2×D4—24no—
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—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—44no—
614C2×D4—44no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4C2×D4×C13912yes—
622C2×D4C2×D4×C13912yes—
623C2×D4#41×C13912yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4C2×D4×C13911yescharacteristic
640C22×C4C2×D4×C13911yescharacteristic
641C22×C4C2×D4×C13911yescharacteristic
642C22×C4C2×D4×C13911yescharacteristic
643C22×C4C2×D4×C13911yescharacteristic
644C22×C4C2×D4×C13912yes—
645C22×C4#41×C13912yes—
646C22×C4C24×C13911yescharacteristic
647SD16—44no—
648D8—44no—
649D8—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—44no—
662C2×C8C2×D4×C13912yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4C2×D4×C13912yes—
673C4⋊C4C2×D4×C13912yes—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—24no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—81no—
685C22⋊C4—81no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—48no—
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—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C13912yes—
727C23#135×C13912yes—
728C23AGL(1,ℤ/8)×C13912yes—
729C23C22×D4×C13911yescharacteristic
730Q8—41no—
731Q8—41no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—48no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4#121×C13912yes—
784C2×C4C22×D4×C13911yescharacteristic
785C2×C4C22×D4×C13911yescharacteristic
786C2×C4C2×#41×C13911yescharacteristic
787C2×C4C2×#41×C13911yescharacteristic
788C2×C4H(5,𝔽2)×C13911yescharacteristic
789C2×C4H(5,𝔽2)×C13911yescharacteristic
790C8—22no—
791C8—41no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—816no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22#463×C13914yescomplemented
823C22C2×#121×C13911yescharacteristic
824C22D42×C13911yescharacteristic
825C22#546×C13911yescharacteristic
826C22C2×#135×C13911yescharacteristic
827C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
828C22#576×C13911yescharacteristic
829C22#577×C13911yescharacteristic
830C4—22no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—42no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4#525×C13911yescharacteristic
841C4#538×C13911yescharacteristic
842C4D42×C13911yescharacteristic
843C4#546×C13911yescharacteristic
844C2—24no—
845C2—82no—
846C2—82no—
847C2—82no—
848C2#2424×C13911yescharacteristic
849C2C2×#463×C13911yescharacteristic
850C2#3045×C13911yescharacteristic
851C2#3264×C13911yescharacteristic
852C2#3282×C13911yescharacteristic
853C2#3297×C13911yescharacteristic
854C2#3306×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×#465×C139C2semidirect
2. C2×#463×C139C2semidirect
4. C22×#102×C139C2semidirect
5. #2435×C139C2semidirect
6. #2361×C139C2semidirect
7. #2065×C139C2semidirect
8. #2054×C139C2semidirect
9. #2042×C139C2semidirect
10. #2012×C139C2semidirect
11. #1983×C139C2semidirect
12. #1926×C139C2semidirect
13. #1879×C139C2semidirect
14. #1872×C139C2semidirect
15. #1850×C139C2semidirect
17. C22×SD16×C139C22semidirect
26. C2×C4×D4×C139C22semidirect
31. C2×#106×C139C22semidirect
32. C2×C4⋊C8×C139C22semidirect
33. C2×C4⋊C8×C139C22semidirect
34. C2×#103×C139C22semidirect
35. C2×#103×C139C22semidirect
36. C2×#103×C139C22semidirect
44. C2×#102×C139C22semidirect
50. #390×C139C22semidirect
51. #389×C139C22semidirect
57. C4×C4⋊C4×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #336×C139C22semidirect
62. #336×C139C22semidirect
145. #102×C139D4semidirect
394. C22×C139#463semidirect
427. #25088C139direct (N × H)
428. C139#25088direct (N × H)
429. C2×#465C2×C139semidirect
430. C2×#463C2×C139semidirect
432. C22×#102C2×C139semidirect
433. #2435C2×C139semidirect
434. #2361C2×C139semidirect
435. #2065C2×C139semidirect
436. #2054C2×C139semidirect
437. #2042C2×C139semidirect
438. #2012C2×C139semidirect
439. #1983C2×C139semidirect
440. #1926C2×C139semidirect
441. #1879C2×C139semidirect
442. #1872C2×C139semidirect
443. #1850C2×C139semidirect
445. C22×SD16C22×C139semidirect
454. C2×C4×D4C22×C139semidirect
459. C2×#106C22×C139semidirect
460. C2×C4⋊C8C22×C139semidirect
461. C2×C4⋊C8C22×C139semidirect
462. C2×#103C22×C139semidirect
463. C2×#103C22×C139semidirect
464. C2×#103C22×C139semidirect
472. C2×#102C22×C139semidirect
478. #390C22×C139semidirect
479. #389C22×C139semidirect
485. C4×C4⋊C4C22×C139semidirect
487. #340C22×C139semidirect
488. #340C22×C139semidirect
489. #336C22×C139semidirect
490. #336C22×C139semidirect
573. #102D4×C139semidirect
822. C22#463×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#465×C1392
C2×#463×C1392
C2×#447×C1392
C22×#102×C1392
#2435×C1392
#2361×C1392
#2065×C1392
#2054×C1392
#2042×C1392
#2012×C1392
#1983×C1392
#1926×C1392
#1879×C1392
#1872×C1392
#1850×C1392
#25088139