Finite Group Databasebeta

← C139×#25093 #48019689

Subgroups — C139×#25093 #48019689

Order 35584.

1322 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C139C211yesmaximal, characteristic, complemented
2C2×#460×C139C211yesmaximal, characteristic, complemented
3C2×#450×C139C211yesmaximal, characteristic, complemented
4C2×#418×C139C211yesmaximal, characteristic, complemented
5#2433×C139C211yesmaximal, characteristic
6#2362×C139C211yesmaximal, characteristic, complemented
7#2067×C139C211yesmaximal, characteristic, complemented
8#2055×C139C211yesmaximal, characteristic, complemented
9#2041×C139C211yesmaximal, characteristic, complemented
10#2014×C139C211yesmaximal, characteristic, complemented
11#1982×C139C211yesmaximal, characteristic, complemented
12#1925×C139C211yesmaximal, characteristic, complemented
13#1880×C139C211yesmaximal, characteristic, complemented
14#1875×C139C211yesmaximal, characteristic, complemented
15#1851×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×SD16×C139C2211yescharacteristic, complemented
20C22×M16×C139C2211yescharacteristic
21C2×#127×C139C2211yescharacteristic
22C2×#127×C139C2211yescharacteristic
23C2×C22⋊Q8×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#120×C139—21no—
26C2×#120×C139—21no—
27C2×C4×Q8×C139C2211yescharacteristic, complemented
28C2×#117×C139C2211yescharacteristic
29#468×C139—24no—
30#460×C139—24no—
31#450×C139—24no—
32C2×#107×C139C2211yescharacteristic, complemented
33C2×C4⋊C8×C139C2211yescharacteristic, complemented
34C2×C4⋊C8×C139C2211yescharacteristic, complemented
35#418×C139—24no—
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×#102×C139C2211yescharacteristic, complemented
45C2×#102×C139C2211yescharacteristic, complemented
46C2×C22⋊C8×C139C2211yescharacteristic
47#392×C139—21no—
48#392×C139—21no—
49#391×C139C2211yescharacteristic, complemented
50#390×C139C2211yescharacteristic
51#390×C139C2211yescharacteristic
52#389×C139C2211yescharacteristic, complemented
53#388×C139—21no—
54#388×C139—21no—
55#387×C139—21no—
56C4×C4⋊C4×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—21no—
71C22×D4×C139—21no—
72C22×D4×C139—21no—
73C22×D4×C139—21no—
74C22×D4×C139—22no—
75C22×D4×C139—41no—
76C22×D4×C139—41no—
77C22×D4×C139C2311yescharacteristic
78C22×D4×C139C2311yescharacteristic
79C22×D4×C139C2311yescharacteristic
80C23×C4×C139C2311yescharacteristic
81C2×SD16×C139—22no—
82C2×SD16×C139—22no—
83C2×SD16×C139—22no—
84C2×SD16×C139—22no—
85C2×SD16×C139—22no—
86C2×SD16×C139—22no—
87C2×SD16×C139—41no—
88C2×SD16×C139—41no—
89C2×SD16×C139—41no—
90C2×M16×C139—22no—
91C2×M16×C139—22no—
92C2×M16×C139—41no—
93C22×C8×C139C2311yescharacteristic
94C22×C8×C139C2311yescharacteristic
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97#127×C139—22no—
98#127×C139—22no—
99#127×C139—41no—
100#127×C139—41no—
101C22⋊Q8×C139—22no—
102C22⋊Q8×C139D414yescomplemented
103#121×C139—22no—
104#121×C139—22no—
105#120×C139—44no—
106#120×C139—44no—
107C4×Q8×C139—22no—
108C4×Q8×C139—41no—
109#117×C139—22no—
110#117×C139—41no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139—21no—
113C2×C4⋊C4×C139—21no—
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
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×C139D411yescharacteristic
126C2×C22⋊C4×C139D411yescharacteristic
127C2×C42×C139—21no—
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#102×C139—22no—
137#102×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—
144#102×C139D414yescomplemented
145C22⋊C8×C139—22no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139—21no—
149#95×C139—21no—
150#95×C139D411yescharacteristic
151#95×C139D411yescharacteristic
152C24×C139—21no—
153C24×C139—21no—
154C24×C139—21no—
155C24×C139—42no—
156C24×C139—42no—
157C24×C139—42no—
158C24×C139—42no—
159C24×C139—42no—
160C24×C139—81no—
161C24×C139—81no—
162C24×C139C2×D411yescharacteristic
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×Q8×C139—21no—
166C2×Q8×C139—21no—
167C2×Q8×C139—21no—
168C2×Q8×C139C2×D412yes—
169C2×D4×C139—28no—
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—21no—
186C2×D4×C139—44no—
187C2×D4×C139—44no—
188C2×D4×C139—42no—
189C2×D4×C139—42no—
190C2×D4×C139—44no—
191C2×D4×C139—42no—
192C2×D4×C139—42no—
193C2×D4×C139—42no—
194C2×D4×C139—42no—
195C2×D4×C139—42no—
196C2×D4×C139—42no—
197C2×D4×C139—42no—
198C2×D4×C139—42no—
199C2×D4×C139—42no—
200C2×D4×C139—42no—
201C2×D4×C139—42no—
202C2×D4×C139—42no—
203C2×D4×C139—81no—
204C2×D4×C139—81no—
205C2×D4×C139—81no—
206C2×D4×C139—81no—
207C2×D4×C139C2×D412yes—
208C2×D4×C139#4112yes—
209C22×C4×C139—21no—
210C22×C4×C139—21no—
211C22×C4×C139—21no—
212C22×C4×C139—21no—
213C22×C4×C139—21no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139C2×D411yescharacteristic
219C22×C4×C139C2×D411yescharacteristic
220C22×C4×C139C2×D411yescharacteristic
221C22×C4×C139C2×D412yes—
222C22×C4×C139C2×D411yescharacteristic
223C22×C4×C139C2×D411yescharacteristic
224C22×C4×C139#4112yes—
225C22×C4×C139C2411yescharacteristic
226SD16×C139—44no—
227SD16×C139—44no—
228SD16×C139—44no—
229M16×C139—44no—
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×C139—21no—
237C2×C8×C139—21no—
238C2×C8×C139—21no—
239C2×C8×C139—21no—
240C2×C8×C139—21no—
241C2×C8×C139C2×D412yes—
242C4⋊C4×C139—24no—
243C4⋊C4×C139—21no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139—21no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—42no—
250C4⋊C4×C139—42no—
251C4⋊C4×C139C2×D412yes—
252C4⋊C4×C139C2×D412yes—
253C22⋊C4×C139—24no—
254C22⋊C4×C139—22no—
255C22⋊C4×C139—22no—
256C22⋊C4×C139—42no—
257C22⋊C4×C139—42no—
258C22⋊C4×C139—42no—
259C22⋊C4×C139—42no—
260C22⋊C4×C139—42no—
261C22⋊C4×C139—42no—
262C42×C139—21no—
263C42×C139—21no—
264C42×C139—21no—
265C42×C139—21no—
266C42×C139—42no—
267C42×C139—42no—
268C42×C139—42no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—21no—
275C23×C139—22no—
276C23×C139—22no—
277C23×C139—48no—
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—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×C139#12112yes—
304C23×C139C22×D411yescharacteristic
305Q8×C139—22no—
306Q8×C139—22no—
307Q8×C139—41no—
308Q8×C139—41no—
309D4×C139—22no—
310D4×C139—22no—
311D4×C139—22no—
312D4×C139—22no—
313D4×C139—48no—
314D4×C139—41no—
315D4×C139—41no—
316D4×C139—41no—
317D4×C139—41no—
318D4×C139—41no—
319D4×C139—41no—
320D4×C139—41no—
321D4×C139—41no—
322D4×C139—84no—
323D4×C139—84no—
324D4×C139—84no—
325D4×C139—84no—
326D4×C139—84no—
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—22no—
334C2×C4×C139—22no—
335C2×C4×C139—22no—
336C2×C4×C139—22no—
337C2×C4×C139—22no—
338C2×C4×C139—22no—
339C2×C4×C139—21no—
340C2×C4×C139—22no—
341C2×C4×C139—21no—
342C2×C4×C139—21no—
343C2×C4×C139—21no—
344C2×C4×C139—21no—
345C2×C4×C139—21no—
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—41no—
354C2×C4×C139—41no—
355C2×C4×C139—41no—
356C2×C4×C139—41no—
357C2×C4×C139—41no—
358C2×C4×C139#12112yes—
359C2×C4×C139AGL(1,ℤ/8)12yes—
360C2×C4×C139AGL(1,ℤ/8)12yes—
361C2×C4×C139C22×D411yescharacteristic
362C2×C4×C139C22×D411yescharacteristic
363C2×C4×C139C2×#4111yescharacteristic
364C2×C4×C139C2×#4111yescharacteristic
365C2×C4×C139H(5,𝔽2)11yescharacteristic
366C2×C4×C139H(5,𝔽2)11yescharacteristic
367C8×C139—22no—
368C8×C139—41no—
369C8×C139—41no—
370C8×C139—41no—
371C22×C139—22no—
372C22×C139—22no—
373C22×C139—22no—
374C22×C139—41no—
375C22×C139—41no—
376C22×C139—41no—
377C22×C139—41no—
378C22×C139—42no—
379C22×C139—42no—
380C22×C139—42no—
381C22×C139—42no—
382C22×C139—42no—
383C22×C139—42no—
384C22×C139—816no—
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—81no—
395C22×C139—81no—
396C22×C139—81no—
397C22×C139—81no—
398C22×C139—81no—
399C22×C139—81no—
400C22×C139C2×#12111yescharacteristic
401C22×C139D4211yescharacteristic
402C22×C139#54611yescharacteristic
403C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
404C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
405C22×C139#57711yescharacteristic
406C22×C139#57711yescharacteristic
407C4×C139—22no—
408C4×C139—22no—
409C4×C139—22no—
410C4×C139—42no—
411C4×C139—41no—
412C4×C139—42no—
413C4×C139—42no—
414C4×C139—41no—
415C4×C139—81no—
416C4×C139—81no—
417C4×C139#52511yescharacteristic
418C4×C139#53811yescharacteristic
419C4×C139D4211yescharacteristic
420C4×C139#54611yescharacteristic
421C2×C139—42no—
422C2×C139—82no—
423C2×C139—82no—
424C2×C139—161no—
425C2×C139#242411yescharacteristic
426C2×C139#303811yescharacteristic
427C2×C139#304311yescharacteristic
428C2×C139#326511yescharacteristic
429C2×C139#327211yescharacteristic
430C2×C139#331011yescharacteristic
431C2×C139#332411yescharacteristic
432#25093C13911yesmaximal, characteristic, direct product factor, Sylow
433C139#2509311yescharacteristic, direct product factor, Sylow
434C2×#468C2×C13911yescharacteristic, complemented
435C2×#460C2×C13911yescharacteristic, complemented
436C2×#450C2×C13911yescharacteristic, complemented
437C2×#418C2×C13911yescharacteristic, complemented
438#2433C2×C13911yescharacteristic
439#2362C2×C13911yescharacteristic, complemented
440#2067C2×C13911yescharacteristic, complemented
441#2055C2×C13911yescharacteristic, complemented
442#2041C2×C13911yescharacteristic, complemented
443#2014C2×C13911yescharacteristic, complemented
444#1982C2×C13911yescharacteristic, complemented
445#1925C2×C13911yescharacteristic, complemented
446#1880C2×C13911yescharacteristic, complemented
447#1875C2×C13911yescharacteristic, complemented
448#1851C2×C13911yescharacteristic, complemented
449C23×D4C22×C13911yescharacteristic
450C22×SD16C22×C13911yescharacteristic
451C22×SD16C22×C13911yescharacteristic
452C22×SD16C22×C13911yescharacteristic, complemented
453C22×M16C22×C13911yescharacteristic
454C2×#127C22×C13911yescharacteristic
455C2×#127C22×C13911yescharacteristic
456C2×C22⋊Q8C22×C13911yescharacteristic
457C2×#121C22×C13911yescharacteristic
458C2×#120—21no—
459C2×#120—21no—
460C2×C4×Q8C22×C13911yescharacteristic, complemented
461C2×#117C22×C13911yescharacteristic
462#468—24no—
463#460—24no—
464#450—24no—
465C2×#107C22×C13911yescharacteristic, complemented
466C2×C4⋊C8C22×C13911yescharacteristic, complemented
467C2×C4⋊C8C22×C13911yescharacteristic, complemented
468#418—24no—
469C2×#103C22×C13911yescharacteristic, complemented
470C2×#102C22×C13911yescharacteristic
471C2×#102C22×C13911yescharacteristic
472C2×#102C22×C13911yescharacteristic
473C2×#102C22×C13911yescharacteristic
474C2×#102C22×C13911yescharacteristic
475C2×#102C22×C13911yescharacteristic
476C2×#102C22×C13911yescharacteristic, complemented
477C2×#102C22×C13911yescharacteristic, complemented
478C2×#102C22×C13911yescharacteristic, complemented
479C2×C22⋊C8C22×C13911yescharacteristic
480#392—21no—
481#392—21no—
482#391C22×C13911yescharacteristic, complemented
483#390C22×C13911yescharacteristic
484#390C22×C13911yescharacteristic
485#389C22×C13911yescharacteristic, complemented
486#388—21no—
487#388—21no—
488#387—21no—
489C4×C4⋊C4—21no—
490C4×C4⋊C4C22×C13911yescharacteristic, complemented
491C4×C22⋊C4C22×C13911yescharacteristic
492#340C22×C13911yescharacteristic, complemented
493#340C22×C13911yescharacteristic, complemented
494#336C22×C13911yescharacteristic, complemented
495#336C22×C13911yescharacteristic, complemented
496C25—21no—
497C22×Q8C23×C13911yescharacteristic
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—22no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C23×C13911yescharacteristic
511C22×D4C23×C13911yescharacteristic
512C22×D4C23×C13911yescharacteristic
513C23×C4C23×C13911yescharacteristic
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C22×C8C23×C13911yescharacteristic
527C22×C8C23×C13911yescharacteristic
528C22×C8C23×C13911yescharacteristic
529C22×C8C23×C13911yescharacteristic
530#127—22no—
531#127—22no—
532#127—41no—
533#127—41no—
534C22⋊Q8—22no—
535C22⋊Q8D4×C13914yescomplemented
536#121—22no—
537#121—22no—
538#120—44no—
539#120—44no—
540C4×Q8—22no—
541C4×Q8—41no—
542#117—22no—
543#117—41no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4C23×C13911yescharacteristic
548C2×C4⋊C4C23×C13911yescharacteristic
549C2×C4⋊C4C23×C13911yescharacteristic
550C2×C4⋊C4C23×C13911yescharacteristic
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⋊C4D4×C13911yescharacteristic
559C2×C22⋊C4D4×C13911yescharacteristic
560C2×C42—21no—
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C13911yescharacteristic
564C2×C42C23×C13911yescharacteristic
565#107—22no—
566C4⋊C8—22no—
567C4⋊C8—41no—
568#103—22no—
569#102—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—41no—
577#102D4×C13914yescomplemented
578C22⋊C8—22no—
579#95—21no—
580#95—21no—
581#95—21no—
582#95—21no—
583#95D4×C13911yescharacteristic
584#95D4×C13911yescharacteristic
585C24—21no—
586C24—21no—
587C24—21no—
588C24—42no—
589C24—42no—
590C24—42no—
591C24—42no—
592C24—42no—
593C24—81no—
594C24—81no—
595C24C2×D4×C13911yescharacteristic
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C13912yes—
602C2×D4—28no—
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—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4—81no—
639C2×D4—81no—
640C2×D4C2×D4×C13912yes—
641C2×D4#41×C13912yes—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4C2×D4×C13911yescharacteristic
652C22×C4C2×D4×C13911yescharacteristic
653C22×C4C2×D4×C13911yescharacteristic
654C22×C4C2×D4×C13912yes—
655C22×C4C2×D4×C13911yescharacteristic
656C22×C4C2×D4×C13911yescharacteristic
657C22×C4#41×C13912yes—
658C22×C4C24×C13911yescharacteristic
659SD16—44no—
660SD16—44no—
661SD16—44no—
662M16—44no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8C2×D4×C13912yes—
675C4⋊C4—24no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4C2×D4×C13912yes—
685C4⋊C4C2×D4×C13912yes—
686C22⋊C4—24no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C42—21no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—42no—
700C42—42no—
701C42—42no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—22no—
710C23—48no—
711C23—41no—
712C23—41no—
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—41no—
728C23—41no—
729C23—41no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23#121×C13912yes—
737C23C22×D4×C13911yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—41no—
741Q8—41no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—22no—
746D4—48no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—84no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4#121×C13912yes—
792C2×C4AGL(1,ℤ/8)×C13912yes—
793C2×C4AGL(1,ℤ/8)×C13912yes—
794C2×C4C22×D4×C13911yescharacteristic
795C2×C4C22×D4×C13911yescharacteristic
796C2×C4C2×#41×C13911yescharacteristic
797C2×C4C2×#41×C13911yescharacteristic
798C2×C4H(5,𝔽2)×C13911yescharacteristic
799C2×C4H(5,𝔽2)×C13911yescharacteristic
800C8—22no—
801C8—41no—
802C8—41no—
803C8—41no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—816no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22C2×#121×C13911yescharacteristic
834C22D42×C13911yescharacteristic
835C22#546×C13911yescharacteristic
836C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
837C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
838C22#577×C13911yescharacteristic
839C22#577×C13911yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—42no—
844C4—41no—
845C4—42no—
846C4—41no—
847C4—42no—
848C4—81no—
849C4—81no—
850C4#525×C13911yescharacteristic
851C4#538×C13911yescharacteristic
852C4D42×C13911yescharacteristic
853C4#546×C13911yescharacteristic
854C2—42no—
855C2—82no—
856C2—82no—
857C2—161no—
858C2#2424×C13911yescharacteristic
859C2#3038×C13911yescharacteristic
860C2#3043×C13911yescharacteristic
861C2#3265×C13911yescharacteristic
862C2#3272×C13911yescharacteristic
863C2#3310×C13911yescharacteristic
864C2#3324×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#2433×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×#460×C139C2semidirect
3. C2×#450×C139C2semidirect
4. C2×#418×C139C2semidirect
6. #2362×C139C2semidirect
7. #2067×C139C2semidirect
8. #2055×C139C2semidirect
9. #2041×C139C2semidirect
10. #2014×C139C2semidirect
11. #1982×C139C2semidirect
12. #1925×C139C2semidirect
13. #1880×C139C2semidirect
14. #1875×C139C2semidirect
15. #1851×C139C2semidirect
19. C22×SD16×C139C22semidirect
27. C2×C4×Q8×C139C22semidirect
32. C2×#107×C139C22semidirect
33. C2×C4⋊C8×C139C22semidirect
34. C2×C4⋊C8×C139C22semidirect
36. C2×#103×C139C22semidirect
43. C2×#102×C139C22semidirect
44. C2×#102×C139C22semidirect
45. C2×#102×C139C22semidirect
49. #391×C139C22semidirect
52. #389×C139C22semidirect
57. C4×C4⋊C4×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #336×C139C22semidirect
62. #336×C139C22semidirect
102. C22⋊Q8×C139D4semidirect
144. #102×C139D4semidirect
432. #25093C139direct (N × H)
433. C139#25093direct (N × H)
434. C2×#468C2×C139semidirect
435. C2×#460C2×C139semidirect
436. C2×#450C2×C139semidirect
437. C2×#418C2×C139semidirect
439. #2362C2×C139semidirect
440. #2067C2×C139semidirect
441. #2055C2×C139semidirect
442. #2041C2×C139semidirect
443. #2014C2×C139semidirect
444. #1982C2×C139semidirect
445. #1925C2×C139semidirect
446. #1880C2×C139semidirect
447. #1875C2×C139semidirect
448. #1851C2×C139semidirect
452. C22×SD16C22×C139semidirect
460. C2×C4×Q8C22×C139semidirect
465. C2×#107C22×C139semidirect
466. C2×C4⋊C8C22×C139semidirect
467. C2×C4⋊C8C22×C139semidirect
469. C2×#103C22×C139semidirect
476. C2×#102C22×C139semidirect
477. C2×#102C22×C139semidirect
478. C2×#102C22×C139semidirect
482. #391C22×C139semidirect
485. #389C22×C139semidirect
490. C4×C4⋊C4C22×C139semidirect
492. #340C22×C139semidirect
493. #340C22×C139semidirect
494. #336C22×C139semidirect
495. #336C22×C139semidirect
535. C22⋊Q8D4×C139semidirect
577. #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×#460×C1392
C2×#450×C1392
C2×#418×C1392
#2433×C1392
#2362×C1392
#2067×C1392
#2055×C1392
#2041×C1392
#2014×C1392
#1982×C1392
#1925×C1392
#1880×C1392
#1875×C1392
#1851×C1392
#25093139