Finite Group Databasebeta

← C139×#25097 #48019693

Subgroups — C139×#25097 #48019693

Order 35584.

1378 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C139C211yesmaximal, characteristic, complemented
2C2×#459×C139C211yesmaximal, characteristic, complemented
3C2×#447×C139C211yesmaximal, characteristic, complemented
4C2×#418×C139C211yesmaximal, characteristic, complemented
5#2433×C139C211yesmaximal, characteristic, complemented
6#2363×C139C211yesmaximal, characteristic, complemented
7#2065×C139C211yesmaximal, characteristic, complemented
8#2054×C139C211yesmaximal, characteristic, complemented
9#2041×C139C211yesmaximal, characteristic, complemented
10#2011×C139C211yesmaximal, characteristic, complemented
11#1982×C139C211yesmaximal, characteristic, complemented
12#1926×C139C211yesmaximal, characteristic, complemented
13#1879×C139C211yesmaximal, characteristic, complemented
14#1875×C139C211yesmaximal, characteristic, complemented
15#1851×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic, complemented
20C22×M16×C139C2211yescharacteristic
21C2×#127×C139C2211yescharacteristic
22C2×#127×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#120×C139—21no—
26C2×#120×C139—21no—
27C2×C4×D4×C139C2211yescharacteristic, complemented
28C2×#117×C139C2211yescharacteristic
29#469×C139—24no—
30#459×C139—24no—
31#447×C139—24no—
32C2×#106×C139C2211yescharacteristic, complemented
33C2×C4⋊C8×C139C2211yescharacteristic, complemented
34C2×C4⋊C8×C139C2211yescharacteristic, complemented
35#418×C139—24no—
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic, complemented
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#390×C139—21no—
50#390×C139C2211yescharacteristic
51#390×C139C2211yescharacteristic
52#390×C139C2211yescharacteristic, complemented
53#389×C139C2211yescharacteristic, complemented
54#388×C139—21no—
55#386×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×D4×C139—22no—
65C22×D4×C139—22no—
66C22×D4×C139—21no—
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
80C22×D4×C139C2311yescharacteristic
81C23×C4×C139—21no—
82C23×C4×C139C2311yescharacteristic
83C2×D8×C139—22no—
84C2×D8×C139—22no—
85C2×D8×C139—22no—
86C2×D8×C139—22no—
87C2×D8×C139—22no—
88C2×D8×C139—22no—
89C2×D8×C139—41no—
90C2×D8×C139—41no—
91C2×D8×C139—41no—
92C2×M16×C139—22no—
93C2×M16×C139—22no—
94C2×M16×C139—41no—
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97C22×C8×C139C2311yescharacteristic
98C22×C8×C139C2311yescharacteristic
99#127×C139—22no—
100#127×C139—22no—
101#127×C139—41no—
102#127×C139—41no—
103#121×C139—22no—
104#121×C139—22no—
105#121×C139—22no—
106#121×C139D414yescomplemented
107#120×C139—44no—
108#120×C139—44no—
109C4×D4×C139—22no—
110C4×D4×C139—41no—
111#117×C139—22no—
112#117×C139—41no—
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×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×C139—21no—
132C2×C42×C139C2311yescharacteristic
133C2×C42×C139C2311yescharacteristic
134#106×C139—22no—
135C4⋊C8×C139—22no—
136C4⋊C8×C139—41no—
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—22no—
144#102×C139—22no—
145#102×C139—41no—
146#102×C139D414yescomplemented
147C22⋊C8×C139—22no—
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—21no—
156C24×C139—42no—
157C24×C139—42no—
158C24×C139—42no—
159C24×C139—42no—
160C24×C139—42no—
161C24×C139—81no—
162C24×C139—81no—
163C24×C139C2×D411yescharacteristic
164C2×D4×C139—28no—
165C2×D4×C139—24no—
166C2×D4×C139—21no—
167C2×D4×C139—21no—
168C2×D4×C139—21no—
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—21no—
185C2×D4×C139—21no—
186C2×D4×C139—21no—
187C2×D4×C139—44no—
188C2×D4×C139—44no—
189C2×D4×C139—42no—
190C2×D4×C139—42no—
191C2×D4×C139—44no—
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—42no—
204C2×D4×C139—81no—
205C2×D4×C139—81no—
206C2×D4×C139—81no—
207C2×D4×C139—81no—
208C2×D4×C139—81no—
209C2×D4×C139—81no—
210C2×D4×C139C2×D412yes—
211C2×D4×C139C2×D412yes—
212C2×D4×C139#4112yes—
213C22×C4×C139—21no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139—21no—
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—42no—
222C22×C4×C139—42no—
223C22×C4×C139—81no—
224C22×C4×C139C2×D411yescharacteristic
225C22×C4×C139C2×D411yescharacteristic
226C22×C4×C139C2×D411yescharacteristic
227C22×C4×C139C2×D412yes—
228C22×C4×C139C2×D411yescharacteristic
229C22×C4×C139C2×D411yescharacteristic
230C22×C4×C139#4112yes—
231C22×C4×C139C2411yescharacteristic
232D8×C139—44no—
233D8×C139—44no—
234D8×C139—44no—
235M16×C139—44no—
236C2×C8×C139—21no—
237C2×C8×C139—21no—
238C2×C8×C139—21no—
239C2×C8×C139—21no—
240C2×C8×C139—21no—
241C2×C8×C139—21no—
242C2×C8×C139—21no—
243C2×C8×C139—21no—
244C2×C8×C139—21no—
245C2×C8×C139—21no—
246C2×C8×C139—21no—
247C2×C8×C139C2×D412yes—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—21no—
251C4⋊C4×C139—21no—
252C4⋊C4×C139—21no—
253C4⋊C4×C139—21no—
254C4⋊C4×C139—81no—
255C4⋊C4×C139C2×D412yes—
256C4⋊C4×C139C2×D412yes—
257C22⋊C4×C139—24no—
258C22⋊C4×C139—22no—
259C22⋊C4×C139—22no—
260C22⋊C4×C139—42no—
261C22⋊C4×C139—42no—
262C22⋊C4×C139—42no—
263C22⋊C4×C139—42no—
264C22⋊C4×C139—42no—
265C22⋊C4×C139—42no—
266C22⋊C4×C139—42no—
267C22⋊C4×C139—42no—
268C22⋊C4×C139—81no—
269C42×C139—21no—
270C42×C139—21no—
271C42×C139—21no—
272C42×C139—21no—
273C42×C139—42no—
274C42×C139—81no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—21no—
279C23×C139—21no—
280C23×C139—21no—
281C23×C139—22no—
282C23×C139—22no—
283C23×C139—22no—
284C23×C139—48no—
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—41no—
298C23×C139—41no—
299C23×C139—41no—
300C23×C139—41no—
301C23×C139—41no—
302C23×C139—41no—
303C23×C139—41no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—41no—
307C23×C139—41no—
308C23×C139—41no—
309C23×C139—41no—
310C23×C139—84no—
311C23×C139—84no—
312C23×C139—84no—
313C23×C139—84no—
314C23×C139—84no—
315C23×C139—84no—
316C23×C139#12112yes—
317C23×C139C22×D411yescharacteristic
318D4×C139—22no—
319D4×C139—22no—
320D4×C139—22no—
321D4×C139—22no—
322D4×C139—22no—
323D4×C139—22no—
324D4×C139—48no—
325D4×C139—41no—
326D4×C139—41no—
327D4×C139—41no—
328D4×C139—41no—
329D4×C139—41no—
330D4×C139—41no—
331D4×C139—41no—
332D4×C139—41no—
333D4×C139—41no—
334D4×C139—41no—
335D4×C139—84no—
336D4×C139—84no—
337D4×C139—84no—
338D4×C139—84no—
339D4×C139—84no—
340D4×C139—84no—
341C2×C4×C139—21no—
342C2×C4×C139—21no—
343C2×C4×C139—21no—
344C2×C4×C139—21no—
345C2×C4×C139—21no—
346C2×C4×C139—21no—
347C2×C4×C139—22no—
348C2×C4×C139—22no—
349C2×C4×C139—22no—
350C2×C4×C139—22no—
351C2×C4×C139—22no—
352C2×C4×C139—21no—
353C2×C4×C139—22no—
354C2×C4×C139—21no—
355C2×C4×C139—21no—
356C2×C4×C139—21no—
357C2×C4×C139—21no—
358C2×C4×C139—21no—
359C2×C4×C139—41no—
360C2×C4×C139—41no—
361C2×C4×C139—41no—
362C2×C4×C139—41no—
363C2×C4×C139—41no—
364C2×C4×C139—41no—
365C2×C4×C139—41no—
366C2×C4×C139—41no—
367C2×C4×C139—41no—
368C2×C4×C139—41no—
369C2×C4×C139—84no—
370C2×C4×C139#12112yes—
371C2×C4×C139AGL(1,ℤ/8)12yes—
372C2×C4×C139AGL(1,ℤ/8)12yes—
373C2×C4×C139C22×D411yescharacteristic
374C2×C4×C139C22×D411yescharacteristic
375C2×C4×C139C2×#4111yescharacteristic
376C2×C4×C139C2×#4111yescharacteristic
377C2×C4×C139H(5,𝔽2)11yescharacteristic
378C2×C4×C139H(5,𝔽2)11yescharacteristic
379C8×C139—22no—
380C8×C139—41no—
381C8×C139—41no—
382C8×C139—41no—
383C22×C139—22no—
384C22×C139—22no—
385C22×C139—22no—
386C22×C139—41no—
387C22×C139—41no—
388C22×C139—41no—
389C22×C139—41no—
390C22×C139—42no—
391C22×C139—42no—
392C22×C139—42no—
393C22×C139—42no—
394C22×C139—42no—
395C22×C139—42no—
396C22×C139—42no—
397C22×C139—42no—
398C22×C139—42no—
399C22×C139—816no—
400C22×C139—81no—
401C22×C139—81no—
402C22×C139—81no—
403C22×C139—81no—
404C22×C139—81no—
405C22×C139—81no—
406C22×C139—81no—
407C22×C139—81no—
408C22×C139—81no—
409C22×C139—81no—
410C22×C139—81no—
411C22×C139—81no—
412C22×C139—81no—
413C22×C139—81no—
414C22×C139—81no—
415C22×C139—81no—
416C22×C139—81no—
417C22×C139—81no—
418C22×C139—81no—
419C22×C139C2×#12111yescharacteristic
420C22×C139D4211yescharacteristic
421C22×C139#54611yescharacteristic
422C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
423C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
424C22×C139#57611yescharacteristic
425C22×C139#57611yescharacteristic
426C4×C139—22no—
427C4×C139—22no—
428C4×C139—22no—
429C4×C139—42no—
430C4×C139—41no—
431C4×C139—42no—
432C4×C139—41no—
433C4×C139—81no—
434C4×C139—81no—
435C4×C139#52511yescharacteristic
436C4×C139#53811yescharacteristic
437C4×C139D4211yescharacteristic
438C4×C139#54611yescharacteristic
439C2×C139—42no—
440C2×C139—82no—
441C2×C139—82no—
442C2×C139—82no—
443C2×C139—161no—
444C2×C139#242411yescharacteristic
445C2×C139#303811yescharacteristic
446C2×C139#304111yescharacteristic
447C2×C139#326411yescharacteristic
448C2×C139#327411yescharacteristic
449C2×C139#331811yescharacteristic
450C2×C139#332511yescharacteristic
451#25097C13911yesmaximal, characteristic, direct product factor, Sylow
452C139#2509711yescharacteristic, direct product factor, Sylow
453C2×#469C2×C13911yescharacteristic, complemented
454C2×#459C2×C13911yescharacteristic, complemented
455C2×#447C2×C13911yescharacteristic, complemented
456C2×#418C2×C13911yescharacteristic, complemented
457#2433C2×C13911yescharacteristic, complemented
458#2363C2×C13911yescharacteristic, complemented
459#2065C2×C13911yescharacteristic, complemented
460#2054C2×C13911yescharacteristic, complemented
461#2041C2×C13911yescharacteristic, complemented
462#2011C2×C13911yescharacteristic, complemented
463#1982C2×C13911yescharacteristic, complemented
464#1926C2×C13911yescharacteristic, complemented
465#1879C2×C13911yescharacteristic, complemented
466#1875C2×C13911yescharacteristic, complemented
467#1851C2×C13911yescharacteristic, complemented
468C23×D4C22×C13911yescharacteristic
469C22×D8C22×C13911yescharacteristic
470C22×D8C22×C13911yescharacteristic
471C22×D8C22×C13911yescharacteristic, complemented
472C22×M16C22×C13911yescharacteristic
473C2×#127C22×C13911yescharacteristic
474C2×#127C22×C13911yescharacteristic
475C2×#121C22×C13911yescharacteristic
476C2×#121C22×C13911yescharacteristic
477C2×#120—21no—
478C2×#120—21no—
479C2×C4×D4C22×C13911yescharacteristic, complemented
480C2×#117C22×C13911yescharacteristic
481#469—24no—
482#459—24no—
483#447—24no—
484C2×#106C22×C13911yescharacteristic, complemented
485C2×C4⋊C8C22×C13911yescharacteristic, complemented
486C2×C4⋊C8C22×C13911yescharacteristic, complemented
487#418—24no—
488C2×#102C22×C13911yescharacteristic
489C2×#102C22×C13911yescharacteristic
490C2×#102C22×C13911yescharacteristic
491C2×#102C22×C13911yescharacteristic
492C2×#102C22×C13911yescharacteristic
493C2×#102C22×C13911yescharacteristic
494C2×#102C22×C13911yescharacteristic, complemented
495C2×#102C22×C13911yescharacteristic, complemented
496C2×#102C22×C13911yescharacteristic, complemented
497C2×#102C22×C13911yescharacteristic, complemented
498C2×C22⋊C8C22×C13911yescharacteristic
499#392—21no—
500#392—21no—
501#390—21no—
502#390C22×C13911yescharacteristic
503#390C22×C13911yescharacteristic
504#390C22×C13911yescharacteristic, complemented
505#389C22×C13911yescharacteristic, complemented
506#388—21no—
507#386—21no—
508C4×C4⋊C4C22×C13911yescharacteristic, complemented
509C4×C22⋊C4—21no—
510C4×C22⋊C4C22×C13911yescharacteristic
511#340C22×C13911yescharacteristic, complemented
512#340C22×C13911yescharacteristic, complemented
513#336C22×C13911yescharacteristic, complemented
514#336C22×C13911yescharacteristic, complemented
515C25—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4C23×C13911yescharacteristic
530C22×D4C23×C13911yescharacteristic
531C22×D4C23×C13911yescharacteristic
532C22×D4C23×C13911yescharacteristic
533C23×C4—21no—
534C23×C4C23×C13911yescharacteristic
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×M16—22no—
545C2×M16—22no—
546C2×M16—41no—
547C22×C8C23×C13911yescharacteristic
548C22×C8C23×C13911yescharacteristic
549C22×C8C23×C13911yescharacteristic
550C22×C8C23×C13911yescharacteristic
551#127—22no—
552#127—22no—
553#127—41no—
554#127—41no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121D4×C13914yescomplemented
559#120—44no—
560#120—44no—
561C4×D4—22no—
562C4×D4—41no—
563#117—22no—
564#117—41no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4C23×C13911yescharacteristic
567C2×C4⋊C4C23×C13911yescharacteristic
568C2×C4⋊C4C23×C13911yescharacteristic
569C2×C4⋊C4C23×C13911yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4D4×C13911yescharacteristic
581C2×C22⋊C4D4×C13911yescharacteristic
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C13911yescharacteristic
585C2×C42C23×C13911yescharacteristic
586#106—22no—
587C4⋊C8—22no—
588C4⋊C8—41no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—41no—
598#102D4×C13914yescomplemented
599C22⋊C8—22no—
600#95—21no—
601#95—21no—
602#95D4×C13911yescharacteristic
603#95D4×C13911yescharacteristic
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—42no—
613C24—81no—
614C24—81no—
615C24C2×D4×C13911yescharacteristic
616C2×D4—28no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—44no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—81no—
657C2×D4—81no—
658C2×D4—81no—
659C2×D4—81no—
660C2×D4—81no—
661C2×D4—81no—
662C2×D4C2×D4×C13912yes—
663C2×D4C2×D4×C13912yes—
664C2×D4#41×C13912yes—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—81no—
676C22×C4C2×D4×C13911yescharacteristic
677C22×C4C2×D4×C13911yescharacteristic
678C22×C4C2×D4×C13911yescharacteristic
679C22×C4C2×D4×C13912yes—
680C22×C4C2×D4×C13911yescharacteristic
681C22×C4C2×D4×C13911yescharacteristic
682C22×C4#41×C13912yes—
683C22×C4C24×C13911yescharacteristic
684D8—44no—
685D8—44no—
686D8—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C13912yes—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—81no—
707C4⋊C4C2×D4×C13912yes—
708C4⋊C4C2×D4×C13912yes—
709C22⋊C4—24no—
710C22⋊C4—22no—
711C22⋊C4—22no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—42no—
726C42—81no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—48no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—84no—
763C23—84no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23#121×C13912yes—
769C23C22×D4×C13911yescharacteristic
770D4—22no—
771D4—22no—
772D4—22no—
773D4—22no—
774D4—22no—
775D4—22no—
776D4—48no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4—84no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—84no—
822C2×C4#121×C13912yes—
823C2×C4AGL(1,ℤ/8)×C13912yes—
824C2×C4AGL(1,ℤ/8)×C13912yes—
825C2×C4C22×D4×C13911yescharacteristic
826C2×C4C22×D4×C13911yescharacteristic
827C2×C4C2×#41×C13911yescharacteristic
828C2×C4C2×#41×C13911yescharacteristic
829C2×C4H(5,𝔽2)×C13911yescharacteristic
830C2×C4H(5,𝔽2)×C13911yescharacteristic
831C8—22no—
832C8—41no—
833C8—41no—
834C8—41no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—816no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22C2×#121×C13911yescharacteristic
872C22D42×C13911yescharacteristic
873C22#546×C13911yescharacteristic
874C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
875C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
876C22#576×C13911yescharacteristic
877C22#576×C13911yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—42no—
882C4—41no—
883C4—42no—
884C4—41no—
885C4—81no—
886C4—81no—
887C4#525×C13911yescharacteristic
888C4#538×C13911yescharacteristic
889C4D42×C13911yescharacteristic
890C4#546×C13911yescharacteristic
891C2—42no—
892C2—82no—
893C2—82no—
894C2—82no—
895C2—161no—
896C2#2424×C13911yescharacteristic
897C2#3038×C13911yescharacteristic
898C2#3041×C13911yescharacteristic
899C2#3264×C13911yescharacteristic
900C2#3274×C13911yescharacteristic
901C2#3318×C13911yescharacteristic
902C2#3325×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
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×#469×C139C2semidirect
2. C2×#459×C139C2semidirect
3. C2×#447×C139C2semidirect
4. C2×#418×C139C2semidirect
5. #2433×C139C2semidirect
6. #2363×C139C2semidirect
7. #2065×C139C2semidirect
8. #2054×C139C2semidirect
9. #2041×C139C2semidirect
10. #2011×C139C2semidirect
11. #1982×C139C2semidirect
12. #1926×C139C2semidirect
13. #1879×C139C2semidirect
14. #1875×C139C2semidirect
15. #1851×C139C2semidirect
19. C22×D8×C139C22semidirect
27. C2×C4×D4×C139C22semidirect
32. C2×#106×C139C22semidirect
33. C2×C4⋊C8×C139C22semidirect
34. C2×C4⋊C8×C139C22semidirect
42. C2×#102×C139C22semidirect
43. C2×#102×C139C22semidirect
44. C2×#102×C139C22semidirect
45. C2×#102×C139C22semidirect
52. #390×C139C22semidirect
53. #389×C139C22semidirect
56. C4×C4⋊C4×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #336×C139C22semidirect
62. #336×C139C22semidirect
106. #121×C139D4semidirect
146. #102×C139D4semidirect
451. #25097C139direct (N × H)
452. C139#25097direct (N × H)
453. C2×#469C2×C139semidirect
454. C2×#459C2×C139semidirect
455. C2×#447C2×C139semidirect
456. C2×#418C2×C139semidirect
457. #2433C2×C139semidirect
458. #2363C2×C139semidirect
459. #2065C2×C139semidirect
460. #2054C2×C139semidirect
461. #2041C2×C139semidirect
462. #2011C2×C139semidirect
463. #1982C2×C139semidirect
464. #1926C2×C139semidirect
465. #1879C2×C139semidirect
466. #1875C2×C139semidirect
467. #1851C2×C139semidirect
471. C22×D8C22×C139semidirect
479. C2×C4×D4C22×C139semidirect
484. C2×#106C22×C139semidirect
485. C2×C4⋊C8C22×C139semidirect
486. C2×C4⋊C8C22×C139semidirect
494. C2×#102C22×C139semidirect
495. C2×#102C22×C139semidirect
496. C2×#102C22×C139semidirect
497. C2×#102C22×C139semidirect
504. #390C22×C139semidirect
505. #389C22×C139semidirect
508. C4×C4⋊C4C22×C139semidirect
511. #340C22×C139semidirect
512. #340C22×C139semidirect
513. #336C22×C139semidirect
514. #336C22×C139semidirect
558. #121D4×C139semidirect
598. #102D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1392
C2×#459×C1392
C2×#447×C1392
C2×#418×C1392
#2433×C1392
#2363×C1392
#2065×C1392
#2054×C1392
#2041×C1392
#2011×C1392
#1982×C1392
#1926×C1392
#1879×C1392
#1875×C1392
#1851×C1392
#25097139