Finite Group Databasebeta

← C139×#21458 #48016054

Subgroups — C139×#21458 #48016054

Order 35584.

1616 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#518×C139C211yesmaximal, characteristic, complemented
2C2×#447×C139C211yesmaximal, characteristic
3C2×#442×C139C211yesmaximal, characteristic, complemented
4C2×C4×D8×C139C211yesmaximal, characteristic, complemented
5#2324×C139C211yesmaximal, characteristic, complemented
6#1879×C139C211yesmaximal, characteristic, complemented
7#1879×C139C211yesmaximal, characteristic, complemented
8#1875×C139C211yesmaximal, characteristic, complemented
9#1864×C139C211yesmaximal, characteristic, complemented
10#1862×C139C211yesmaximal, characteristic, complemented
11#1854×C139C211yesmaximal, characteristic, complemented
12#1786×C139C211yesmaximal, characteristic, complemented
13#1762×C139C211yesmaximal, characteristic, complemented
14C4×#102×C139C211yesmaximal, characteristic, complemented
15#1750×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C2×#121×C139C2211yescharacteristic
20#518×C139—24no—
21#518×C139—24no—
22C2×C4×D4×C139—21no—
23C2×C4×D4×C139—21no—
24C2×C4×D4×C139C2211yescharacteristic
25C2×C4×D4×C139C2211yescharacteristic
26C2×C4×D4×C139C2211yescharacteristic
27C2×C4×D4×C139C2211yescharacteristic
28C2×C4×D4×C139C2211yescharacteristic, complemented
29C2×#117×C139C2211yescharacteristic
30C2×#117×C139C2211yescharacteristic
31C22×C22⋊C4×C139—21no—
32C22×C22⋊C4×C139—21no—
33#447×C139C418yescomplemented
34#442×C139—24no—
35C4×D8×C139—24no—
36C2×#107×C139C2211yescharacteristic, complemented
37C2×#106×C139C2211yescharacteristic, complemented
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic, complemented
45C2×#102×C139C2211yescharacteristic, complemented
46C2×C22⋊C8×C139C2211yescharacteristic
47C2×C22⋊C8×C139C2211yescharacteristic
48C2×#97×C139C2211yescharacteristic, complemented
49C2×C4×C8×C139C2211yescharacteristic, complemented
50#390×C139—21no—
51#390×C139C2211yescharacteristic, complemented
52#389×C139C2211yescharacteristic, complemented
53#388×C139—21no—
54#386×C139—21no—
55#385×C139—21no—
56#380×C139C2211yescharacteristic
57C4×C4⋊C4×C139C2211yescharacteristic, complemented
58#340×C139C2211yescharacteristic, complemented
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#336×C139C2211yescharacteristic, complemented
63#336×C139C2211yescharacteristic, complemented
64C25×C139—21no—
65C22×D4×C139—22no—
66C22×D4×C139—22no—
67C22×D4×C139—22no—
68C22×D4×C139—22no—
69C22×D4×C139—21no—
70C22×D4×C139—21no—
71C22×D4×C139—22no—
72C22×D4×C139C2×C414yescomplemented
73C22×D4×C139C2311yescharacteristic
74C22×D4×C139C2311yescharacteristic
75C22×D4×C139C2311yescharacteristic
76C23×C4×C139—21no—
77C23×C4×C139—21no—
78C23×C4×C139—21no—
79C23×C4×C139—21no—
80C23×C4×C139—21no—
81C23×C4×C139C2311yescharacteristic
82C2×D8×C139—22no—
83C2×D8×C139—22no—
84C2×D8×C139—22no—
85C2×D8×C139—22no—
86C2×D8×C139C2×C414yescomplemented
87C2×D8×C139C2×C414yescomplemented
88C22×C8×C139C2311yescharacteristic
89C22×C8×C139C2311yescharacteristic
90C22×C8×C139C2311yescharacteristic
91C22×C8×C139C2311yescharacteristic
92#121×C139—22no—
93#121×C139C2×C414yescomplemented
94C4×D4×C139—28no—
95C4×D4×C139—28no—
96C4×D4×C139—22no—
97C4×D4×C139—22no—
98C4×D4×C139—22no—
99C4×D4×C139—22no—
100C4×D4×C139—22no—
101C4×D4×C139—22no—
102C4×D4×C139—22no—
103C4×D4×C139—22no—
104C4×D4×C139D414yescomplemented
105C4×D4×C139D414yescomplemented
106#117×C139—22no—
107#117×C139—22no—
108#117×C139—22no—
109#117×C139—22no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139D411yescharacteristic
112C2×C4⋊C4×C139D411yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C22⋊C4×C139—28no—
119C2×C22⋊C4×C139—28no—
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
135C2×C42×C139C2311yescharacteristic
136#107×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—22no—
144#102×C139C2×C414yescomplemented
145#102×C139C2×C414yescomplemented
146C22⋊C8×C139—22no—
147C22⋊C8×C139C2×C414yescomplemented
148#97×C139—22no—
149C4×C8×C139—22no—
150#95×C139—21no—
151#95×C139—21no—
152#95×C139—21no—
153C24×C139—24no—
154C24×C139—24no—
155C24×C139—21no—
156C24×C139—21no—
157C24×C139—24no—
158C24×C139—21no—
159C24×C139—81no—
160C24×C139—81no—
161C24×C139—81no—
162C24×C139—81no—
163C24×C139C2×D411yescharacteristic
164C2×D4×C139—24no—
165C2×D4×C139—24no—
166C2×D4×C139—28no—
167C2×D4×C139—28no—
168C2×D4×C139—28no—
169C2×D4×C139—28no—
170C2×D4×C139—24no—
171C2×D4×C139—24no—
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—81no—
184C2×D4×C139—81no—
185C2×D4×C139C22×C412yes—
186C2×D4×C139C22×C412yes—
187C2×D4×C139C22×C412yes—
188C2×D4×C139C2×D412yes—
189C2×D4×C139C2×D412yes—
190C2×D4×C139#4112yes—
191C2×D4×C139#4112yes—
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—24no—
200C22×C4×C139—24no—
201C22×C4×C139—24no—
202C22×C4×C139—24no—
203C22×C4×C139—21no—
204C22×C4×C139—21no—
205C22×C4×C139—42no—
206C22×C4×C139—81no—
207C22×C4×C139—81no—
208C22×C4×C139—81no—
209C22×C4×C139—81no—
210C22×C4×C139—81no—
211C22×C4×C139—81no—
212C22×C4×C139—81no—
213C22×C4×C139—81no—
214C22×C4×C139—81no—
215C22×C4×C139—81no—
216C22×C4×C139C22×C412yes—
217C22×C4×C139C2×D411yescharacteristic
218C22×C4×C139C2×D411yescharacteristic
219C22×C4×C139C2×D411yescharacteristic
220C22×C4×C139C2×D411yescharacteristic
221C22×C4×C139C2×D411yescharacteristic
222C22×C4×C139#4112yes—
223C22×C4×C139C2411yescharacteristic
224D8×C139—28no—
225D8×C139—28no—
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—21no—
234C2×C8×C139—21no—
235C2×C8×C139—21no—
236C2×C8×C139C22×C412yes—
237C2×C8×C139C22×C412yes—
238C4⋊C4×C139—22no—
239C4⋊C4×C139—22no—
240C4⋊C4×C139—21no—
241C4⋊C4×C139—21no—
242C4⋊C4×C139—21no—
243C4⋊C4×C139—21no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139—21no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—81no—
248C4⋊C4×C139C22×C412yes—
249C4⋊C4×C139C2×D412yes—
250C4⋊C4×C139C2×D412yes—
251C22⋊C4×C139—24no—
252C22⋊C4×C139—24no—
253C22⋊C4×C139—24no—
254C22⋊C4×C139—24no—
255C22⋊C4×C139—22no—
256C22⋊C4×C139—22no—
257C22⋊C4×C139—24no—
258C22⋊C4×C139—24no—
259C22⋊C4×C139—42no—
260C22⋊C4×C139—81no—
261C22⋊C4×C139—81no—
262C22⋊C4×C139—81no—
263C42×C139—24no—
264C42×C139—21no—
265C42×C139—21no—
266C42×C139—81no—
267C42×C139C2×D412yes—
268C42×C139C2×D412yes—
269C23×C139—216no—
270C23×C139—22no—
271C23×C139—22no—
272C23×C139—21no—
273C23×C139—22no—
274C23×C139—22no—
275C23×C139—21no—
276C23×C139—22no—
277C23×C139—22no—
278C23×C139—21no—
279C23×C139—21no—
280C23×C139—21no—
281C23×C139—21no—
282C23×C139—22no—
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—41no—
293C23×C139—41no—
294C23×C139—41no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—84no—
298C23×C139—84no—
299C23×C139—84no—
300C23×C139—84no—
301C23×C139—84no—
302C23×C139—84no—
303C23×C139C4×D412yes—
304C23×C139C22×D411yescharacteristic
305D4×C139—216no—
306D4×C139—22no—
307D4×C139—22no—
308D4×C139—22no—
309D4×C139—22no—
310D4×C139—22no—
311D4×C139—22no—
312D4×C139—22no—
313D4×C139—22no—
314D4×C139—41no—
315D4×C139—41no—
316D4×C139—84no—
317D4×C139C4×D414yes—
318D4×C139C4×D414yes—
319C2×C4×C139—21no—
320C2×C4×C139—21no—
321C2×C4×C139—21no—
322C2×C4×C139—21no—
323C2×C4×C139—21no—
324C2×C4×C139—21no—
325C2×C4×C139—22no—
326C2×C4×C139—22no—
327C2×C4×C139—22no—
328C2×C4×C139—22no—
329C2×C4×C139—22no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—22no—
333C2×C4×C139—22no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—21no—
337C2×C4×C139—21no—
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—84no—
352C2×C4×C139—84no—
353C2×C4×C139—84no—
354C2×C4×C139—84no—
355C2×C4×C139C4×D412yes—
356C2×C4×C139#12012yes—
357C2×C4×C139#12012yes—
358C2×C4×C139C23×C411yescharacteristic
359C2×C4×C139C22×D411yescharacteristic
360C2×C4×C139C22×D411yescharacteristic
361C2×C4×C139C2×#4111yescharacteristic
362C2×C4×C139C2×#4111yescharacteristic
363C2×C4×C139C2×#4111yescharacteristic
364C8×C139—22no—
365C8×C139—22no—
366C8×C139—41no—
367C8×C139—41no—
368C22×C139—22no—
369C22×C139—22no—
370C22×C139—22no—
371C22×C139—24no—
372C22×C139—24no—
373C22×C139—41no—
374C22×C139—42no—
375C22×C139—42no—
376C22×C139—41no—
377C22×C139—42no—
378C22×C139—42no—
379C22×C139—42no—
380C22×C139—42no—
381C22×C139—42no—
382C22×C139—42no—
383C22×C139—42no—
384C22×C139—42no—
385C22×C139—41no—
386C22×C139—42no—
387C22×C139—42no—
388C22×C139—41no—
389C22×C139—42no—
390C22×C139—42no—
391C22×C139—42no—
392C22×C139—816no—
393C22×C139—81no—
394C22×C139—81no—
395C22×C139—81no—
396C22×C139—81no—
397C22×C139C2×C4×D411yescharacteristic
398C22×C139C2×#12011yescharacteristic
399C22×C139#52511yescharacteristic
400C22×C139#57611yescharacteristic
401C22×C139#57611yescharacteristic
402C22×C139#57611yescharacteristic
403C22×C139#57711yescharacteristic
404C4×C139—22no—
405C4×C139—22no—
406C4×C139—22no—
407C4×C139—42no—
408C4×C139—41no—
409C4×C139—42no—
410C4×C139—41no—
411C4×C139—42no—
412C4×C139—81no—
413C4×C139—81no—
414C4×C139C2×C4×D411yescharacteristic
415C4×C139C2×C4×D411yescharacteristic
416C4×C139#52511yescharacteristic
417C4×C139#52511yescharacteristic
418C2×C139—42no—
419C2×C139—44no—
420C2×C139—44no—
421C2×C139—82no—
422C2×C139C4×#12011yescharacteristic
423C2×C139#294611yescharacteristic
424C2×C139#294811yescharacteristic
425C2×C139#300811yescharacteristic
426C2×C139#301211yescharacteristic
427C2×C139#311811yescharacteristic
428C2×C139#312211yescharacteristic
429#21458C13911yesmaximal, characteristic, direct product factor, Sylow
430C139#2145811yescharacteristic, direct product factor, Sylow
431C2×#518C2×C13911yescharacteristic, complemented
432C2×#447C2×C13911yescharacteristic
433C2×#442C2×C13911yescharacteristic, complemented
434C2×C4×D8C2×C13911yescharacteristic, complemented
435#2324C2×C13911yescharacteristic, complemented
436#1879C2×C13911yescharacteristic, complemented
437#1879C2×C13911yescharacteristic, complemented
438#1875C2×C13911yescharacteristic, complemented
439#1864C2×C13911yescharacteristic, complemented
440#1862C2×C13911yescharacteristic, complemented
441#1854C2×C13911yescharacteristic, complemented
442#1786C2×C13911yescharacteristic, complemented
443#1762C2×C13911yescharacteristic, complemented
444C4×#102C2×C13911yescharacteristic, complemented
445#1750C2×C13911yescharacteristic, complemented
446C23×D4C22×C13911yescharacteristic
447C22×D8C22×C13911yescharacteristic
448C22×D8C22×C13911yescharacteristic
449C2×#121C22×C13911yescharacteristic
450#518—24no—
451#518—24no—
452C2×C4×D4—21no—
453C2×C4×D4—21no—
454C2×C4×D4C22×C13911yescharacteristic
455C2×C4×D4C22×C13911yescharacteristic
456C2×C4×D4C22×C13911yescharacteristic
457C2×C4×D4C22×C13911yescharacteristic
458C2×C4×D4C22×C13911yescharacteristic, complemented
459C2×#117C22×C13911yescharacteristic
460C2×#117C22×C13911yescharacteristic
461C22×C22⋊C4—21no—
462C22×C22⋊C4—21no—
463#447C4×C13918yescomplemented
464#442—24no—
465C4×D8—24no—
466C2×#107C22×C13911yescharacteristic, complemented
467C2×#106C22×C13911yescharacteristic, complemented
468C2×#102C22×C13911yescharacteristic
469C2×#102C22×C13911yescharacteristic
470C2×#102C22×C13911yescharacteristic
471C2×#102C22×C13911yescharacteristic
472C2×#102C22×C13911yescharacteristic
473C2×#102C22×C13911yescharacteristic
474C2×#102C22×C13911yescharacteristic, complemented
475C2×#102C22×C13911yescharacteristic, complemented
476C2×C22⋊C8C22×C13911yescharacteristic
477C2×C22⋊C8C22×C13911yescharacteristic
478C2×#97C22×C13911yescharacteristic, complemented
479C2×C4×C8C22×C13911yescharacteristic, complemented
480#390—21no—
481#390C22×C13911yescharacteristic, complemented
482#389C22×C13911yescharacteristic, complemented
483#388—21no—
484#386—21no—
485#385—21no—
486#380C22×C13911yescharacteristic
487C4×C4⋊C4C22×C13911yescharacteristic, complemented
488#340C22×C13911yescharacteristic, complemented
489#340C22×C13911yescharacteristic, complemented
490#340C22×C13911yescharacteristic, complemented
491#340C22×C13911yescharacteristic, complemented
492#336C22×C13911yescharacteristic, complemented
493#336C22×C13911yescharacteristic, complemented
494C25—21no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4C2×C4×C13914yescomplemented
503C22×D4C23×C13911yescharacteristic
504C22×D4C23×C13911yescharacteristic
505C22×D4C23×C13911yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C23×C13911yescharacteristic
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8C2×C4×C13914yescomplemented
517C2×D8C2×C4×C13914yescomplemented
518C22×C8C23×C13911yescharacteristic
519C22×C8C23×C13911yescharacteristic
520C22×C8C23×C13911yescharacteristic
521C22×C8C23×C13911yescharacteristic
522#121—22no—
523#121C2×C4×C13914yescomplemented
524C4×D4—28no—
525C4×D4—28no—
526C4×D4—22no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4D4×C13914yescomplemented
535C4×D4D4×C13914yescomplemented
536#117—22no—
537#117—22no—
538#117—22no—
539#117—22no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C13911yescharacteristic
542C2×C4⋊C4D4×C13911yescharacteristic
543C2×C4⋊C4C23×C13911yescharacteristic
544C2×C4⋊C4C23×C13911yescharacteristic
545C2×C4⋊C4C23×C13911yescharacteristic
546C2×C4⋊C4C23×C13911yescharacteristic
547C2×C4⋊C4C23×C13911yescharacteristic
548C2×C22⋊C4—28no—
549C2×C22⋊C4—28no—
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⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4D4×C13911yescharacteristic
561C2×C22⋊C4D4×C13911yescharacteristic
562C2×C42—21no—
563C2×C42—21no—
564C2×C42C23×C13911yescharacteristic
565C2×C42C23×C13911yescharacteristic
566#107—22no—
567#106—22no—
568#102—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102C2×C4×C13914yescomplemented
575#102C2×C4×C13914yescomplemented
576C22⋊C8—22no—
577C22⋊C8C2×C4×C13914yescomplemented
578#97—22no—
579C4×C8—22no—
580#95—21no—
581#95—21no—
582#95—21no—
583C24—24no—
584C24—24no—
585C24—21no—
586C24—21no—
587C24—24no—
588C24—21no—
589C24—81no—
590C24—81no—
591C24—81no—
592C24—81no—
593C24C2×D4×C13911yescharacteristic
594C2×D4—24no—
595C2×D4—24no—
596C2×D4—28no—
597C2×D4—28no—
598C2×D4—28no—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—24no—
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—81no—
614C2×D4—81no—
615C2×D4C22×C4×C13912yes—
616C2×D4C22×C4×C13912yes—
617C2×D4C22×C4×C13912yes—
618C2×D4C2×D4×C13912yes—
619C2×D4C2×D4×C13912yes—
620C2×D4#41×C13912yes—
621C2×D4#41×C13912yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—81no—
637C22×C4—81no—
638C22×C4—81no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4—81no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4C22×C4×C13912yes—
647C22×C4C2×D4×C13911yescharacteristic
648C22×C4C2×D4×C13911yescharacteristic
649C22×C4C2×D4×C13911yescharacteristic
650C22×C4C2×D4×C13911yescharacteristic
651C22×C4C2×D4×C13911yescharacteristic
652C22×C4#41×C13912yes—
653C22×C4C24×C13911yescharacteristic
654D8—28no—
655D8—28no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8C22×C4×C13912yes—
667C2×C8C22×C4×C13912yes—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—81no—
678C4⋊C4C22×C4×C13912yes—
679C4⋊C4C2×D4×C13912yes—
680C4⋊C4C2×D4×C13912yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—42no—
690C22⋊C4—81no—
691C22⋊C4—81no—
692C22⋊C4—81no—
693C42—24no—
694C42—21no—
695C42—21no—
696C42—81no—
697C42C2×D4×C13912yes—
698C42C2×D4×C13912yes—
699C23—216no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—22no—
704C23—22no—
705C23—21no—
706C23—22no—
707C23—22no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—84no—
728C23—84no—
729C23—84no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23C4×D4×C13912yes—
734C23C22×D4×C13911yescharacteristic
735D4—216no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—22no—
743D4—22no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4C4×D4×C13914yes—
748D4C4×D4×C13914yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
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—84no—
781C2×C4—84no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4—84no—
785C2×C4C4×D4×C13912yes—
786C2×C4#120×C13912yes—
787C2×C4#120×C13912yes—
788C2×C4C23×C4×C13911yescharacteristic
789C2×C4C22×D4×C13911yescharacteristic
790C2×C4C22×D4×C13911yescharacteristic
791C2×C4C2×#41×C13911yescharacteristic
792C2×C4C2×#41×C13911yescharacteristic
793C2×C4C2×#41×C13911yescharacteristic
794C8—22no—
795C8—22no—
796C8—41no—
797C8—41no—
798C22—22no—
799C22—24no—
800C22—24no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22C2×C4×D4×C13911yescharacteristic
828C22C2×#120×C13911yescharacteristic
829C22#525×C13911yescharacteristic
830C22#576×C13911yescharacteristic
831C22#576×C13911yescharacteristic
832C22#576×C13911yescharacteristic
833C22#577×C13911yescharacteristic
834C4—22no—
835C4—22no—
836C4—22no—
837C4—42no—
838C4—41no—
839C4—42no—
840C4—41no—
841C4—42no—
842C4—81no—
843C4—81no—
844C4C2×C4×D4×C13911yescharacteristic
845C4C2×C4×D4×C13911yescharacteristic
846C4#525×C13911yescharacteristic
847C4#525×C13911yescharacteristic
848C2—42no—
849C2—44no—
850C2—44no—
851C2—82no—
852C2C4×#120×C13911yescharacteristic
853C2#2946×C13911yescharacteristic
854C2#2948×C13911yescharacteristic
855C2#3008×C13911yescharacteristic
856C2#3012×C13911yescharacteristic
857C2#3118×C13911yescharacteristic
858C2#3122×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC2×#447×C139C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×#117×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#518×C139C2semidirect
3. C2×#442×C139C2semidirect
4. C2×C4×D8×C139C2semidirect
5. #2324×C139C2semidirect
6. #1879×C139C2semidirect
7. #1879×C139C2semidirect
8. #1875×C139C2semidirect
9. #1864×C139C2semidirect
10. #1862×C139C2semidirect
11. #1854×C139C2semidirect
12. #1786×C139C2semidirect
13. #1762×C139C2semidirect
14. C4×#102×C139C2semidirect
15. #1750×C139C2semidirect
28. C2×C4×D4×C139C22semidirect
33. #447×C139C4semidirect
36. C2×#107×C139C22semidirect
37. C2×#106×C139C22semidirect
44. C2×#102×C139C22semidirect
45. C2×#102×C139C22semidirect
48. C2×#97×C139C22semidirect
49. C2×C4×C8×C139C22semidirect
51. #390×C139C22semidirect
52. #389×C139C22semidirect
57. C4×C4⋊C4×C139C22semidirect
58. #340×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #336×C139C22semidirect
63. #336×C139C22semidirect
72. C22×D4×C139C2×C4semidirect
86. C2×D8×C139C2×C4semidirect
87. C2×D8×C139C2×C4semidirect
93. #121×C139C2×C4semidirect
104. C4×D4×C139D4semidirect
105. C4×D4×C139D4semidirect
144. #102×C139C2×C4semidirect
145. #102×C139C2×C4semidirect
147. C22⋊C8×C139C2×C4semidirect
429. #21458C139direct (N × H)
430. C139#21458direct (N × H)
431. C2×#518C2×C139semidirect
433. C2×#442C2×C139semidirect
434. C2×C4×D8C2×C139semidirect
435. #2324C2×C139semidirect
436. #1879C2×C139semidirect
437. #1879C2×C139semidirect
438. #1875C2×C139semidirect
439. #1864C2×C139semidirect
440. #1862C2×C139semidirect
441. #1854C2×C139semidirect
442. #1786C2×C139semidirect
443. #1762C2×C139semidirect
444. C4×#102C2×C139semidirect
445. #1750C2×C139semidirect
458. C2×C4×D4C22×C139semidirect
463. #447C4×C139semidirect
466. C2×#107C22×C139semidirect
467. C2×#106C22×C139semidirect
474. C2×#102C22×C139semidirect
475. C2×#102C22×C139semidirect
478. C2×#97C22×C139semidirect
479. C2×C4×C8C22×C139semidirect
481. #390C22×C139semidirect
482. #389C22×C139semidirect
487. C4×C4⋊C4C22×C139semidirect
488. #340C22×C139semidirect
489. #340C22×C139semidirect
490. #340C22×C139semidirect
491. #340C22×C139semidirect
492. #336C22×C139semidirect
493. #336C22×C139semidirect
502. C22×D4C2×C4×C139semidirect
516. C2×D8C2×C4×C139semidirect
517. C2×D8C2×C4×C139semidirect
523. #121C2×C4×C139semidirect
534. C4×D4D4×C139semidirect
535. C4×D4D4×C139semidirect
574. #102C2×C4×C139semidirect
575. #102C2×C4×C139semidirect
577. C22⋊C8C2×C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#518×C1392
C2×#447×C1392
C2×#442×C1392
C2×C4×D8×C1392
#2324×C1392
#1879×C1392
#1875×C1392
#1864×C1392
#1862×C1392
#1854×C1392
#1786×C1392
#1762×C1392
C4×#102×C1392
#1750×C1392
#21458139