Finite Group Databasebeta

← C139×#24560 #48019156

Subgroups — C139×#24560 #48019156

Order 35584.

1162 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C139C211yesmaximal, characteristic, complemented
2C2×#407×C139C211yesmaximal, characteristic, complemented
3#2847×C139C211yesmaximal, characteristic
4#2280×C139C211yesmaximal, characteristic, complemented
5#2077×C139C211yesmaximal, characteristic, complemented
6#2075×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#1895×C139C211yesmaximal, characteristic, complemented
10#1895×C139C211yesmaximal, characteristic, complemented
11#1875×C139C211yesmaximal, characteristic, complemented
12#1854×C139C211yesmaximal, characteristic, complemented
13#1825×C139C211yesmaximal, characteristic, complemented
14#1809×C139C211yesmaximal, characteristic, complemented
15#1809×C139C211yesmaximal, characteristic, complemented
16C24×C4×C139C2211yescharacteristic
17C22×M16×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19C2×#121×C139C2211yescharacteristic
20C2×#121×C139C2211yescharacteristic
21C2×#121×C139C2211yescharacteristic
22C2×#120×C139—21no—
23C2×#117×C139C2211yescharacteristic
24C2×#117×C139C2211yescharacteristic
25#482×C139—24no—
26C2×#107×C139C2211yescharacteristic, complemented
27C2×#107×C139C2211yescharacteristic, complemented
28C2×#106×C139C2211yescharacteristic, complemented
29C2×#106×C139C2211yescharacteristic, complemented
30C2×#102×C139C2211yescharacteristic, complemented
31C2×#102×C139C2211yescharacteristic, complemented
32C2×#102×C139C2211yescharacteristic, complemented
33C2×#102×C139C2211yescharacteristic, complemented
34#407×C139—24no—
35C2×C22⋊C8×C139C2211yescharacteristic
36C2×C22⋊C8×C139C2211yescharacteristic
37C2×C22⋊C8×C139C2211yescharacteristic
38C2×C22⋊C8×C139C2211yescharacteristic
39#386×C139—21no—
40#386×C139—21no—
41#386×C139—21no—
42#381×C139—21no—
43#380×C139C2211yescharacteristic
44#380×C139C2211yescharacteristic
45#380×C139C2211yescharacteristic
46#380×C139C2211yescharacteristic
47#380×C139C2211yescharacteristic
48#380×C139C2211yescharacteristic
49#380×C139C2211yescharacteristic
50#379×C139—21no—
51C4×C22⋊C4×C139—21no—
52C4×C22⋊C4×C139—21no—
53#340×C139C2211yescharacteristic, complemented
54#340×C139C2211yescharacteristic, complemented
55#340×C139C2211yescharacteristic, complemented
56#340×C139C2211yescharacteristic, complemented
57#340×C139C2211yescharacteristic, complemented
58#340×C139C2211yescharacteristic, complemented
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61C25×C139D411yescharacteristic
62C22×D4×C139—21no—
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139C2311yescharacteristic
66C23×C4×C139—22no—
67C23×C4×C139—22no—
68C23×C4×C139—22no—
69C23×C4×C139—22no—
70C23×C4×C139—41no—
71C23×C4×C139—41no—
72C23×C4×C139D411yescharacteristic
73C23×C4×C139D411yescharacteristic
74C23×C4×C139D411yescharacteristic
75C23×C4×C139C2311yescharacteristic
76C23×C4×C139C2311yescharacteristic
77C23×C4×C139C2311yescharacteristic
78C2×M16×C139—22no—
79C2×M16×C139—22no—
80C2×M16×C139—22no—
81C2×M16×C139—22no—
82C2×M16×C139—41no—
83C2×M16×C139—41no—
84C22×C8×C139C2311yescharacteristic
85C22×C8×C139C2311yescharacteristic
86C22×C8×C139C2311yescharacteristic
87C22×C8×C139C2311yescharacteristic
88#121×C139—22no—
89#121×C139—22no—
90#121×C139—22no—
91#121×C139—22no—
92#121×C139—41no—
93#121×C139—41no—
94#120×C139—44no—
95#117×C139—22no—
96#117×C139—22no—
97#117×C139—41no—
98#117×C139—41no—
99C2×C4⋊C4×C139C2311yescharacteristic
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C4⋊C4×C139C2311yescharacteristic
102C2×C4⋊C4×C139C2311yescharacteristic
103C2×C4⋊C4×C139C2311yescharacteristic
104C2×C4⋊C4×C139C2311yescharacteristic
105C2×C4⋊C4×C139C2311yescharacteristic
106C2×C22⋊C4×C139—21no—
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
109C2×C22⋊C4×C139—21no—
110C2×C22⋊C4×C139—21no—
111C2×C22⋊C4×C139—21no—
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×C42×C139—21no—
119C2×C42×C139—21no—
120#107×C139—22no—
121#107×C139—41no—
122#106×C139—22no—
123#106×C139—41no—
124#102×C139—22no—
125#102×C139—22no—
126#102×C139—41no—
127#102×C139—41no—
128C22⋊C8×C139—22no—
129C22⋊C8×C139—22no—
130C22⋊C8×C139—22no—
131C22⋊C8×C139D414yescomplemented
132#95×C139—21no—
133#95×C139—21no—
134#95×C139—21no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139—21no—
138#95×C139—21no—
139C24×C139—22no—
140C24×C139—22no—
141C24×C139—22no—
142C24×C139—21no—
143C24×C139—41no—
144C24×C139—41no—
145C24×C139—41no—
146C24×C139—41no—
147C24×C139C2×D411yescharacteristic
148C24×C139C2×D411yescharacteristic
149C24×C139C2×D411yescharacteristic
150C2×D4×C139—21no—
151C2×D4×C139—21no—
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—42no—
157C2×D4×C139—42no—
158C2×D4×C139—42no—
159C2×D4×C139—42no—
160C2×D4×C139—42no—
161C2×D4×C139—42no—
162C2×D4×C139—42no—
163C2×D4×C139—42no—
164C2×D4×C139—42no—
165C22×C4×C139—21no—
166C22×C4×C139—21no—
167C22×C4×C139—21no—
168C22×C4×C139—21no—
169C22×C4×C139—21no—
170C22×C4×C139—21no—
171C22×C4×C139—21no—
172C22×C4×C139—21no—
173C22×C4×C139—22no—
174C22×C4×C139—22no—
175C22×C4×C139—22no—
176C22×C4×C139—22no—
177C22×C4×C139—22no—
178C22×C4×C139—22no—
179C22×C4×C139—21no—
180C22×C4×C139—21no—
181C22×C4×C139—21no—
182C22×C4×C139—21no—
183C22×C4×C139—21no—
184C22×C4×C139—21no—
185C22×C4×C139—21no—
186C22×C4×C139—21no—
187C22×C4×C139—21no—
188C22×C4×C139—21no—
189C22×C4×C139—21no—
190C22×C4×C139—21no—
191C22×C4×C139—21no—
192C22×C4×C139—41no—
193C22×C4×C139—41no—
194C22×C4×C139—41no—
195C22×C4×C139—44no—
196C22×C4×C139—44no—
197C22×C4×C139—44no—
198C22×C4×C139—44no—
199C22×C4×C139C2×D411yescharacteristic
200C22×C4×C139C2×D411yescharacteristic
201C22×C4×C139C2×D412yes—
202C22×C4×C139C2×D411yescharacteristic
203C22×C4×C139#4112yes—
204C22×C4×C139#4112yes—
205C22×C4×C139#4112yes—
206C22×C4×C139C2411yescharacteristic
207M16×C139—44no—
208M16×C139—44no—
209C2×C8×C139—21no—
210C2×C8×C139—21no—
211C2×C8×C139—21no—
212C2×C8×C139—21no—
213C2×C8×C139—21no—
214C2×C8×C139—21no—
215C2×C8×C139—21no—
216C2×C8×C139—21no—
217C2×C8×C139—21no—
218C2×C8×C139—21no—
219C2×C8×C139C2×D412yes—
220C2×C8×C139C2×D412yes—
221C4⋊C4×C139—21no—
222C4⋊C4×C139—21no—
223C4⋊C4×C139—21no—
224C4⋊C4×C139—21no—
225C4⋊C4×C139—21no—
226C4⋊C4×C139—21no—
227C4⋊C4×C139—21no—
228C4⋊C4×C139—21no—
229C4⋊C4×C139—21no—
230C4⋊C4×C139—21no—
231C4⋊C4×C139—21no—
232C4⋊C4×C139—21no—
233C4⋊C4×C139—21no—
234C4⋊C4×C139—21no—
235C22⋊C4×C139—42no—
236C22⋊C4×C139—42no—
237C22⋊C4×C139—42no—
238C22⋊C4×C139—42no—
239C22⋊C4×C139—42no—
240C22⋊C4×C139—42no—
241C22⋊C4×C139—42no—
242C22⋊C4×C139—42no—
243C22⋊C4×C139—42no—
244C22⋊C4×C139—42no—
245C22⋊C4×C139—42no—
246C22⋊C4×C139—42no—
247C42×C139—42no—
248C42×C139—42no—
249C23×C139—21no—
250C23×C139—21no—
251C23×C139—21no—
252C23×C139—21no—
253C23×C139—21no—
254C23×C139—21no—
255C23×C139—21no—
256C23×C139—21no—
257C23×C139—21no—
258C23×C139—21no—
259C23×C139—21no—
260C23×C139—21no—
261C23×C139—21no—
262C23×C139—21no—
263C23×C139—21no—
264C23×C139—21no—
265C23×C139—21no—
266C23×C139—21no—
267C23×C139—44no—
268C23×C139—44no—
269C23×C139—44no—
270C23×C139—44no—
271C23×C139—44no—
272C23×C139—44no—
273C23×C139—44no—
274C23×C139—41no—
275C23×C139—41no—
276C23×C139—41no—
277C23×C139—41no—
278C23×C139—41no—
279C23×C139—41no—
280C23×C139—41no—
281C23×C139#12112yes—
282C23×C139#12312yes—
283C23×C139AGL(1,ℤ/8)12yes—
284C23×C139C22×D411yescharacteristic
285D4×C139—41no—
286D4×C139—41no—
287D4×C139—41no—
288D4×C139—41no—
289D4×C139—84no—
290D4×C139—84no—
291D4×C139—84no—
292C2×C4×C139—21no—
293C2×C4×C139—21no—
294C2×C4×C139—21no—
295C2×C4×C139—21no—
296C2×C4×C139—22no—
297C2×C4×C139—22no—
298C2×C4×C139—22no—
299C2×C4×C139—22no—
300C2×C4×C139—22no—
301C2×C4×C139—22no—
302C2×C4×C139—22no—
303C2×C4×C139—22no—
304C2×C4×C139—21no—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—44no—
308C2×C4×C139—44no—
309C2×C4×C139—44no—
310C2×C4×C139—41no—
311C2×C4×C139—41no—
312C2×C4×C139—41no—
313C2×C4×C139—41no—
314C2×C4×C139—41no—
315C2×C4×C139—41no—
316C2×C4×C139—41no—
317C2×C4×C139—41no—
318C2×C4×C139—41no—
319C2×C4×C139—41no—
320C2×C4×C139—41no—
321C2×C4×C139—41no—
322C2×C4×C139—41no—
323C2×C4×C139—41no—
324C2×C4×C139—41no—
325C2×C4×C139—41no—
326C2×C4×C139—41no—
327C2×C4×C139—41no—
328C2×C4×C139—41no—
329C2×C4×C139—41no—
330C2×C4×C139—41no—
331C2×C4×C139—41no—
332C2×C4×C139—41no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139#12112yes—
336C2×C4×C139#12312yes—
337C2×C4×C139C22×D411yescharacteristic
338C2×C4×C139C2×#4111yescharacteristic
339C2×C4×C139C2×#4111yescharacteristic
340C2×C4×C139C2×#4111yescharacteristic
341C2×C4×C139H(5,𝔽2)11yescharacteristic
342C2×C4×C139H(5,𝔽2)11yescharacteristic
343C8×C139—22no—
344C8×C139—22no—
345C8×C139—41no—
346C8×C139—41no—
347C22×C139—22no—
348C22×C139—22no—
349C22×C139—22no—
350C22×C139—22no—
351C22×C139—22no—
352C22×C139—22no—
353C22×C139—22no—
354C22×C139—22no—
355C22×C139—22no—
356C22×C139—416no—
357C22×C139—41no—
358C22×C139—41no—
359C22×C139—41no—
360C22×C139—41no—
361C22×C139—41no—
362C22×C139—41no—
363C22×C139—41no—
364C22×C139—41no—
365C22×C139—41no—
366C22×C139—41no—
367C22×C139—41no—
368C22×C139—41no—
369C22×C139—81no—
370C22×C139—81no—
371C22×C139—81no—
372C22×C139—81no—
373C22×C139—81no—
374C22×C139—81no—
375C22×C139—81no—
376C22×C139C2×#12111yescharacteristic
377C22×C139C2×#12311yescharacteristic
378C22×C139#53411yescharacteristic
379C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C139#57511yescharacteristic
381C22×C139#57511yescharacteristic
382C22×C139#57511yescharacteristic
383C4×C139—22no—
384C4×C139—22no—
385C4×C139—41no—
386C4×C139—81no—
387C4×C139—81no—
388C4×C139—81no—
389C4×C139—81no—
390C4×C139—81no—
391C4×C139—81no—
392C4×C139—81no—
393C4×C139#54611yescharacteristic
394C4×C139#54611yescharacteristic
395C4×C139#55111yescharacteristic
396C4×C139#55111yescharacteristic
397C2×C139—42no—
398C2×C139—42no—
399C2×C139—42no—
400C2×C139—161no—
401C2×C139#241211yescharacteristic
402C2×C139#305411yescharacteristic
403C2×C139#305511yescharacteristic
404C2×C139#309311yescharacteristic
405C2×C139#309411yescharacteristic
406C2×C139#319411yescharacteristic
407C2×C139#319711yescharacteristic
408#24560C13911yesmaximal, characteristic, direct product factor, Sylow
409C139#2456011yescharacteristic, direct product factor, Sylow
410C2×#482C2×C13911yescharacteristic, complemented
411C2×#407C2×C13911yescharacteristic, complemented
412#2847C2×C13911yescharacteristic
413#2280C2×C13911yescharacteristic, complemented
414#2077C2×C13911yescharacteristic, complemented
415#2075C2×C13911yescharacteristic, complemented
416#2034C2×C13911yescharacteristic, complemented
417#2033C2×C13911yescharacteristic, complemented
418#1895C2×C13911yescharacteristic, complemented
419#1895C2×C13911yescharacteristic, complemented
420#1875C2×C13911yescharacteristic, complemented
421#1854C2×C13911yescharacteristic, complemented
422#1825C2×C13911yescharacteristic, complemented
423#1809C2×C13911yescharacteristic, complemented
424#1809C2×C13911yescharacteristic, complemented
425C24×C4C22×C13911yescharacteristic
426C22×M16C22×C13911yescharacteristic
427C22×M16C22×C13911yescharacteristic
428C2×#121C22×C13911yescharacteristic
429C2×#121C22×C13911yescharacteristic
430C2×#121C22×C13911yescharacteristic
431C2×#120—21no—
432C2×#117C22×C13911yescharacteristic
433C2×#117C22×C13911yescharacteristic
434#482—24no—
435C2×#107C22×C13911yescharacteristic, complemented
436C2×#107C22×C13911yescharacteristic, complemented
437C2×#106C22×C13911yescharacteristic, complemented
438C2×#106C22×C13911yescharacteristic, complemented
439C2×#102C22×C13911yescharacteristic, complemented
440C2×#102C22×C13911yescharacteristic, complemented
441C2×#102C22×C13911yescharacteristic, complemented
442C2×#102C22×C13911yescharacteristic, complemented
443#407—24no—
444C2×C22⋊C8C22×C13911yescharacteristic
445C2×C22⋊C8C22×C13911yescharacteristic
446C2×C22⋊C8C22×C13911yescharacteristic
447C2×C22⋊C8C22×C13911yescharacteristic
448#386—21no—
449#386—21no—
450#386—21no—
451#381—21no—
452#380C22×C13911yescharacteristic
453#380C22×C13911yescharacteristic
454#380C22×C13911yescharacteristic
455#380C22×C13911yescharacteristic
456#380C22×C13911yescharacteristic
457#380C22×C13911yescharacteristic
458#380C22×C13911yescharacteristic
459#379—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462#340C22×C13911yescharacteristic, complemented
463#340C22×C13911yescharacteristic, complemented
464#340C22×C13911yescharacteristic, complemented
465#340C22×C13911yescharacteristic, complemented
466#340C22×C13911yescharacteristic, complemented
467#340C22×C13911yescharacteristic, complemented
468#340C22×C13911yescharacteristic, complemented
469#340C22×C13911yescharacteristic, complemented
470C25D4×C13911yescharacteristic
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4C23×C13911yescharacteristic
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—41no—
480C23×C4—41no—
481C23×C4D4×C13911yescharacteristic
482C23×C4D4×C13911yescharacteristic
483C23×C4D4×C13911yescharacteristic
484C23×C4C23×C13911yescharacteristic
485C23×C4C23×C13911yescharacteristic
486C23×C4C23×C13911yescharacteristic
487C2×M16—22no—
488C2×M16—22no—
489C2×M16—22no—
490C2×M16—22no—
491C2×M16—41no—
492C2×M16—41no—
493C22×C8C23×C13911yescharacteristic
494C22×C8C23×C13911yescharacteristic
495C22×C8C23×C13911yescharacteristic
496C22×C8C23×C13911yescharacteristic
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—41no—
502#121—41no—
503#120—44no—
504#117—22no—
505#117—22no—
506#117—41no—
507#117—41no—
508C2×C4⋊C4C23×C13911yescharacteristic
509C2×C4⋊C4C23×C13911yescharacteristic
510C2×C4⋊C4C23×C13911yescharacteristic
511C2×C4⋊C4C23×C13911yescharacteristic
512C2×C4⋊C4C23×C13911yescharacteristic
513C2×C4⋊C4C23×C13911yescharacteristic
514C2×C4⋊C4C23×C13911yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C42—21no—
528C2×C42—21no—
529#107—22no—
530#107—41no—
531#106—22no—
532#106—41no—
533#102—22no—
534#102—22no—
535#102—41no—
536#102—41no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—22no—
540C22⋊C8D4×C13914yescomplemented
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—21no—
552C24—41no—
553C24—41no—
554C24—41no—
555C24—41no—
556C24C2×D4×C13911yescharacteristic
557C24C2×D4×C13911yescharacteristic
558C24C2×D4×C13911yescharacteristic
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—41no—
602C22×C4—41no—
603C22×C4—41no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4C2×D4×C13911yescharacteristic
609C22×C4C2×D4×C13911yescharacteristic
610C22×C4C2×D4×C13912yes—
611C22×C4C2×D4×C13911yescharacteristic
612C22×C4#41×C13912yes—
613C22×C4#41×C13912yes—
614C22×C4#41×C13912yes—
615C22×C4C24×C13911yescharacteristic
616M16—44no—
617M16—44no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8C2×D4×C13912yes—
629C2×C8C2×D4×C13912yes—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C42—42no—
657C42—42no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23#121×C13912yes—
691C23#123×C13912yes—
692C23AGL(1,ℤ/8)×C13912yes—
693C23C22×D4×C13911yescharacteristic
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4#121×C13912yes—
745C2×C4#123×C13912yes—
746C2×C4C22×D4×C13911yescharacteristic
747C2×C4C2×#41×C13911yescharacteristic
748C2×C4C2×#41×C13911yescharacteristic
749C2×C4C2×#41×C13911yescharacteristic
750C2×C4H(5,𝔽2)×C13911yescharacteristic
751C2×C4H(5,𝔽2)×C13911yescharacteristic
752C8—22no—
753C8—22no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—416no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22C2×#121×C13911yescharacteristic
786C22C2×#123×C13911yescharacteristic
787C22#534×C13911yescharacteristic
788C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
789C22#575×C13911yescharacteristic
790C22#575×C13911yescharacteristic
791C22#575×C13911yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—81no—
796C4—81no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4#546×C13911yescharacteristic
803C4#546×C13911yescharacteristic
804C4#551×C13911yescharacteristic
805C4#551×C13911yescharacteristic
806C2—42no—
807C2—42no—
808C2—42no—
809C2—161no—
810C2#2412×C13911yescharacteristic
811C2#3054×C13911yescharacteristic
812C2#3055×C13911yescharacteristic
813C2#3093×C13911yescharacteristic
814C2#3094×C13911yescharacteristic
815C2#3194×C13911yescharacteristic
816C2#3197×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#2847×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C24×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#482×C139C2semidirect
2. C2×#407×C139C2semidirect
4. #2280×C139C2semidirect
5. #2077×C139C2semidirect
6. #2075×C139C2semidirect
7. #2034×C139C2semidirect
8. #2033×C139C2semidirect
9. #1895×C139C2semidirect
10. #1895×C139C2semidirect
11. #1875×C139C2semidirect
12. #1854×C139C2semidirect
13. #1825×C139C2semidirect
14. #1809×C139C2semidirect
15. #1809×C139C2semidirect
26. C2×#107×C139C22semidirect
27. C2×#107×C139C22semidirect
28. C2×#106×C139C22semidirect
29. C2×#106×C139C22semidirect
30. C2×#102×C139C22semidirect
31. C2×#102×C139C22semidirect
32. C2×#102×C139C22semidirect
33. C2×#102×C139C22semidirect
53. #340×C139C22semidirect
54. #340×C139C22semidirect
55. #340×C139C22semidirect
56. #340×C139C22semidirect
57. #340×C139C22semidirect
58. #340×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
131. C22⋊C8×C139D4semidirect
408. #24560C139direct (N × H)
409. C139#24560direct (N × H)
410. C2×#482C2×C139semidirect
411. C2×#407C2×C139semidirect
413. #2280C2×C139semidirect
414. #2077C2×C139semidirect
415. #2075C2×C139semidirect
416. #2034C2×C139semidirect
417. #2033C2×C139semidirect
418. #1895C2×C139semidirect
419. #1895C2×C139semidirect
420. #1875C2×C139semidirect
421. #1854C2×C139semidirect
422. #1825C2×C139semidirect
423. #1809C2×C139semidirect
424. #1809C2×C139semidirect
435. C2×#107C22×C139semidirect
436. C2×#107C22×C139semidirect
437. C2×#106C22×C139semidirect
438. C2×#106C22×C139semidirect
439. C2×#102C22×C139semidirect
440. C2×#102C22×C139semidirect
441. C2×#102C22×C139semidirect
442. C2×#102C22×C139semidirect
462. #340C22×C139semidirect
463. #340C22×C139semidirect
464. #340C22×C139semidirect
465. #340C22×C139semidirect
466. #340C22×C139semidirect
467. #340C22×C139semidirect
468. #340C22×C139semidirect
469. #340C22×C139semidirect
540. C22⋊C8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1392
C2×#407×C1392
#2847×C1392
#2280×C1392
#2077×C1392
#2075×C1392
#2034×C1392
#2033×C1392
#1895×C1392
#1875×C1392
#1854×C1392
#1825×C1392
#1809×C1392
#24560139