Finite Group Databasebeta

← C139×#26984 #48021580

Subgroups — C139×#26984 #48021580

Order 35584.

1050 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C139C211yesmaximal, characteristic, complemented
2C2×#442×C139C211yesmaximal, characteristic, complemented
3#2428×C139C211yesmaximal, characteristic, complemented
4#2422×C139C211yesmaximal, characteristic, complemented
5#2084×C139C211yesmaximal, characteristic, complemented
6#2034×C139C211yesmaximal, characteristic, complemented
7#2011×C139C211yesmaximal, characteristic, complemented
8#1999×C139C211yesmaximal, characteristic, complemented
9#1957×C139C211yesmaximal, characteristic, complemented
10#1936×C139C211yesmaximal, characteristic, complemented
11#1934×C139C211yesmaximal, characteristic, complemented
12#1895×C139C211yesmaximal, characteristic, complemented
13#1879×C139C211yesmaximal, characteristic, complemented
14#1864×C139C211yesmaximal, characteristic, complemented
15#1753×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19C2×#127×C139C2211yescharacteristic
20C2×#123×C139—21no—
21C2×#121×C139—21no—
22C2×#121×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×C4×D4×C139C2211yescharacteristic
26C2×C4×D4×C139C2211yescharacteristic
27#469×C139—24no—
28#442×C139—24no—
29C2×#106×C139C2211yescharacteristic
30C2×#106×C139C2211yescharacteristic
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×C22⋊C8×C139C2211yescharacteristic
40C2×#97×C139C2211yescharacteristic
41C2×C4×C8×C139C2211yescharacteristic
42#397×C139—21no—
43#394×C139—21no—
44#394×C139—21no—
45#392×C139—21no—
46#390×C139C2211yescharacteristic
47#390×C139C2211yescharacteristic
48#389×C139C2211yescharacteristic
49#389×C139C2211yescharacteristic
50#386×C139—21no—
51#385×C139—21no—
52#384×C139C2211yescharacteristic
53#380×C139C2211yescharacteristic
54C4×C22⋊C4×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#336×C139C2211yescharacteristic
60#336×C139C2211yescharacteristic
61C22×D4×C139—21no—
62C22×D4×C139—21no—
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139C2311yescharacteristic
67C22×D4×C139C2311yescharacteristic
68C22×D4×C139C2311yescharacteristic
69C23×C4×C139—21no—
70C23×C4×C139—21no—
71C23×C4×C139C2311yescharacteristic
72C2×D8×C139—22no—
73C2×D8×C139—22no—
74C2×D8×C139—22no—
75C2×D8×C139—22no—
76C2×D8×C139—22no—
77C2×D8×C139—41no—
78C2×M16×C139—22no—
79C2×M16×C139—22no—
80C2×M16×C139—41no—
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83C22×C8×C139C2311yescharacteristic
84C22×C8×C139C2311yescharacteristic
85#127×C139—22no—
86#127×C139—41no—
87#123×C139—44no—
88#121×C139—22no—
89#121×C139—22no—
90#121×C139—22no—
91#121×C139—44no—
92#121×C139—41no—
93#121×C139—41no—
94#121×C139—41no—
95C4×D4×C139—22no—
96C4×D4×C139—22no—
97C4×D4×C139—41no—
98C4×D4×C139—41no—
99C2×C4⋊C4×C139—21no—
100C2×C4⋊C4×C139—21no—
101C2×C4⋊C4×C139—21no—
102C2×C4⋊C4×C139—21no—
103C2×C4⋊C4×C139C2311yescharacteristic
104C2×C4⋊C4×C139C2311yescharacteristic
105C2×C4⋊C4×C139C2311yescharacteristic
106C2×C4⋊C4×C139C2311yescharacteristic
107C2×C4⋊C4×C139C2311yescharacteristic
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×C22⋊C4×C139D411yescharacteristic
119C2×C22⋊C4×C139D411yescharacteristic
120C2×C42×C139C2311yescharacteristic
121C2×C42×C139C2311yescharacteristic
122#106×C139—22no—
123#106×C139—22no—
124#102×C139—22no—
125#102×C139—22no—
126#102×C139—22no—
127#102×C139—22no—
128#102×C139—41no—
129#102×C139—41no—
130#102×C139—41no—
131#102×C139D414yescomplemented
132C22⋊C8×C139—22no—
133#97×C139—22no—
134C4×C8×C139—41no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139—21no—
138#95×C139D411yescharacteristic
139#95×C139D411yescharacteristic
140C24×C139—21no—
141C24×C139—21no—
142C24×C139—21no—
143C24×C139C2×D411yescharacteristic
144C2×D4×C139—21no—
145C2×D4×C139—21no—
146C2×D4×C139—21no—
147C2×D4×C139—21no—
148C2×D4×C139—21no—
149C2×D4×C139—21no—
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—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—42no—
161C2×D4×C139—42no—
162C2×D4×C139—42no—
163C2×D4×C139—42no—
164C2×D4×C139—42no—
165C2×D4×C139—42no—
166C2×D4×C139—42no—
167C2×D4×C139—42no—
168C2×D4×C139—42no—
169C2×D4×C139—42no—
170C2×D4×C139—81no—
171C2×D4×C139—81no—
172C2×D4×C139—81no—
173C2×D4×C139—81no—
174C2×D4×C139—81no—
175C2×D4×C139C2×D412yes—
176C2×D4×C139#4112yes—
177C22×C4×C139—21no—
178C22×C4×C139—21no—
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—42no—
189C22×C4×C139—42no—
190C22×C4×C139—42no—
191C22×C4×C139—42no—
192C22×C4×C139—81no—
193C22×C4×C139—81no—
194C22×C4×C139C2×D411yescharacteristic
195C22×C4×C139C2×D411yescharacteristic
196C22×C4×C139C2×D411yescharacteristic
197C22×C4×C139C2×D411yescharacteristic
198C22×C4×C139C2×D411yescharacteristic
199C22×C4×C139C2411yescharacteristic
200D8×C139—28no—
201D8×C139—44no—
202M16×C139—44no—
203C2×C8×C139—21no—
204C2×C8×C139—21no—
205C2×C8×C139—21no—
206C2×C8×C139—21no—
207C2×C8×C139—21no—
208C2×C8×C139—21no—
209C2×C8×C139—21no—
210C2×C8×C139—21no—
211C2×C8×C139—21no—
212C2×C8×C139C2×D412yes—
213C2×C8×C139#4112yes—
214C2×C8×C139#4112yes—
215C4⋊C4×C139—21no—
216C4⋊C4×C139—21no—
217C4⋊C4×C139—21no—
218C4⋊C4×C139—21no—
219C4⋊C4×C139—21no—
220C4⋊C4×C139—21no—
221C4⋊C4×C139—21no—
222C4⋊C4×C139—21no—
223C4⋊C4×C139—21no—
224C4⋊C4×C139—42no—
225C4⋊C4×C139—42no—
226C4⋊C4×C139—42no—
227C4⋊C4×C139—81no—
228C4⋊C4×C139C2×D412yes—
229C22⋊C4×C139—22no—
230C22⋊C4×C139—22no—
231C22⋊C4×C139—42no—
232C22⋊C4×C139—42no—
233C22⋊C4×C139—42no—
234C22⋊C4×C139—42no—
235C22⋊C4×C139—42no—
236C22⋊C4×C139—42no—
237C22⋊C4×C139—42no—
238C22⋊C4×C139—42no—
239C22⋊C4×C139—42no—
240C22⋊C4×C139—81no—
241C42×C139—21no—
242C42×C139—21no—
243C42×C139—21no—
244C42×C139—21no—
245C23×C139—21no—
246C23×C139—22no—
247C23×C139—21no—
248C23×C139—22no—
249C23×C139—21no—
250C23×C139—21no—
251C23×C139—21no—
252C23×C139—21no—
253C23×C139—21no—
254C23×C139—41no—
255C23×C139—41no—
256C23×C139—41no—
257C23×C139—41no—
258C23×C139—41no—
259C23×C139—41no—
260C23×C139—41no—
261C23×C139—41no—
262C23×C139—41no—
263C23×C139—41no—
264C23×C139—41no—
265C23×C139—41no—
266C23×C139—41no—
267C23×C139—41no—
268C23×C139—41no—
269C23×C139—41no—
270C23×C139—41no—
271C23×C139—41no—
272C23×C139—41no—
273C23×C139C22×D411yescharacteristic
274D4×C139—22no—
275D4×C139—22no—
276D4×C139—22no—
277D4×C139—22no—
278D4×C139—41no—
279D4×C139—41no—
280D4×C139—41no—
281D4×C139—41no—
282D4×C139—41no—
283D4×C139—41no—
284D4×C139—41no—
285D4×C139—41no—
286D4×C139—84no—
287D4×C139—84no—
288D4×C139—84no—
289D4×C139—84no—
290D4×C139—84no—
291C2×C4×C139—21no—
292C2×C4×C139—21no—
293C2×C4×C139—21no—
294C2×C4×C139—21no—
295C2×C4×C139—21no—
296C2×C4×C139—21no—
297C2×C4×C139—21no—
298C2×C4×C139—21no—
299C2×C4×C139—22no—
300C2×C4×C139—21no—
301C2×C4×C139—21no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—21no—
305C2×C4×C139—41no—
306C2×C4×C139—41no—
307C2×C4×C139—41no—
308C2×C4×C139—41no—
309C2×C4×C139—41no—
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—84no—
324C2×C4×C139—84no—
325C2×C4×C139AGL(1,ℤ/8)12yes—
326C2×C4×C139AGL(1,ℤ/8)12yes—
327C2×C4×C139C22×D411yescharacteristic
328C2×C4×C139C2×#4111yescharacteristic
329C2×C4×C139C2×#4111yescharacteristic
330C2×C4×C139C2×#4111yescharacteristic
331C2×C4×C139H(5,𝔽2)11yescharacteristic
332C2×C4×C139H(5,𝔽2)11yescharacteristic
333C8×C139—22no—
334C8×C139—22no—
335C8×C139—22no—
336C8×C139—41no—
337C22×C139—41no—
338C22×C139—41no—
339C22×C139—41no—
340C22×C139—42no—
341C22×C139—42no—
342C22×C139—41no—
343C22×C139—42no—
344C22×C139—42no—
345C22×C139—41no—
346C22×C139—42no—
347C22×C139—41no—
348C22×C139—41no—
349C22×C139—42no—
350C22×C139—81no—
351C22×C139—81no—
352C22×C139—81no—
353C22×C139—81no—
354C22×C139—81no—
355C22×C139—81no—
356C22×C139—81no—
357C22×C139—81no—
358C22×C139—81no—
359C22×C139—81no—
360C22×C139—81no—
361C22×C139—81no—
362C22×C139—81no—
363C22×C139—81no—
364C22×C139—81no—
365C22×C139#53211yescharacteristic
366C22×C139D4211yescharacteristic
367C22×C139#54611yescharacteristic
368C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C139#57611yescharacteristic
371C22×C139#57711yescharacteristic
372C4×C139—22no—
373C4×C139—22no—
374C4×C139—41no—
375C4×C139—41no—
376C4×C139—42no—
377C4×C139—41no—
378C4×C139—81no—
379C4×C139—81no—
380C4×C139—81no—
381C4×C139—81no—
382C4×C139#52511yescharacteristic
383C4×C139#54011yescharacteristic
384C4×C139#54611yescharacteristic
385C4×C139#55311yescharacteristic
386C2×C139—81no—
387C2×C139—82no—
388C2×C139—82no—
389C2×C139—161no—
390C2×C139#246411yescharacteristic
391C2×C139#317911yescharacteristic
392C2×C139#318411yescharacteristic
393C2×C139#327211yescharacteristic
394C2×C139#327411yescharacteristic
395C2×C139#330611yescharacteristic
396C2×C139#331811yescharacteristic
397#26984C13911yesmaximal, characteristic, direct product factor, Sylow
398C139#2698411yescharacteristic, direct product factor, Sylow
399C2×#469C2×C13911yescharacteristic, complemented
400C2×#442C2×C13911yescharacteristic, complemented
401#2428C2×C13911yescharacteristic, complemented
402#2422C2×C13911yescharacteristic, complemented
403#2084C2×C13911yescharacteristic, complemented
404#2034C2×C13911yescharacteristic, complemented
405#2011C2×C13911yescharacteristic, complemented
406#1999C2×C13911yescharacteristic, complemented
407#1957C2×C13911yescharacteristic, complemented
408#1936C2×C13911yescharacteristic, complemented
409#1934C2×C13911yescharacteristic, complemented
410#1895C2×C13911yescharacteristic, complemented
411#1879C2×C13911yescharacteristic, complemented
412#1864C2×C13911yescharacteristic, complemented
413#1753C2×C13911yescharacteristic, complemented
414C22×D8C22×C13911yescharacteristic
415C22×D8C22×C13911yescharacteristic
416C22×M16C22×C13911yescharacteristic
417C2×#127C22×C13911yescharacteristic
418C2×#123—21no—
419C2×#121—21no—
420C2×#121C22×C13911yescharacteristic
421C2×#121C22×C13911yescharacteristic
422C2×#121C22×C13911yescharacteristic
423C2×C4×D4C22×C13911yescharacteristic
424C2×C4×D4C22×C13911yescharacteristic
425#469—24no—
426#442—24no—
427C2×#106C22×C13911yescharacteristic
428C2×#106C22×C13911yescharacteristic
429C2×#102C22×C13911yescharacteristic
430C2×#102C22×C13911yescharacteristic
431C2×#102C22×C13911yescharacteristic
432C2×#102C22×C13911yescharacteristic
433C2×#102C22×C13911yescharacteristic
434C2×#102C22×C13911yescharacteristic
435C2×#102C22×C13911yescharacteristic
436C2×#102C22×C13911yescharacteristic
437C2×C22⋊C8C22×C13911yescharacteristic
438C2×#97C22×C13911yescharacteristic
439C2×C4×C8C22×C13911yescharacteristic
440#397—21no—
441#394—21no—
442#394—21no—
443#392—21no—
444#390C22×C13911yescharacteristic
445#390C22×C13911yescharacteristic
446#389C22×C13911yescharacteristic
447#389C22×C13911yescharacteristic
448#386—21no—
449#385—21no—
450#384C22×C13911yescharacteristic
451#380C22×C13911yescharacteristic
452C4×C22⋊C4C22×C13911yescharacteristic
453#340C22×C13911yescharacteristic
454#340C22×C13911yescharacteristic
455#340C22×C13911yescharacteristic
456#340C22×C13911yescharacteristic
457#336C22×C13911yescharacteristic
458#336C22×C13911yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C23×C13911yescharacteristic
465C22×D4C23×C13911yescharacteristic
466C22×D4C23×C13911yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C13911yescharacteristic
470C2×D8—22no—
471C2×D8—22no—
472C2×D8—22no—
473C2×D8—22no—
474C2×D8—22no—
475C2×D8—41no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—41no—
479C22×C8C23×C13911yescharacteristic
480C22×C8C23×C13911yescharacteristic
481C22×C8C23×C13911yescharacteristic
482C22×C8C23×C13911yescharacteristic
483#127—22no—
484#127—41no—
485#123—44no—
486#121—22no—
487#121—22no—
488#121—22no—
489#121—44no—
490#121—41no—
491#121—41no—
492#121—41no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—41no—
496C4×D4—41no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4C23×C13911yescharacteristic
502C2×C4⋊C4C23×C13911yescharacteristic
503C2×C4⋊C4C23×C13911yescharacteristic
504C2×C4⋊C4C23×C13911yescharacteristic
505C2×C4⋊C4C23×C13911yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C13911yescharacteristic
517C2×C22⋊C4D4×C13911yescharacteristic
518C2×C42C23×C13911yescharacteristic
519C2×C42C23×C13911yescharacteristic
520#106—22no—
521#106—22no—
522#102—22no—
523#102—22no—
524#102—22no—
525#102—22no—
526#102—41no—
527#102—41no—
528#102—41no—
529#102D4×C13914yescomplemented
530C22⋊C8—22no—
531#97—22no—
532C4×C8—41no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95D4×C13911yescharacteristic
537#95D4×C13911yescharacteristic
538C24—21no—
539C24—21no—
540C24—21no—
541C24C2×D4×C13911yescharacteristic
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C2×D4C2×D4×C13912yes—
574C2×D4#41×C13912yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—81no—
591C22×C4—81no—
592C22×C4C2×D4×C13911yescharacteristic
593C22×C4C2×D4×C13911yescharacteristic
594C22×C4C2×D4×C13911yescharacteristic
595C22×C4C2×D4×C13911yescharacteristic
596C22×C4C2×D4×C13911yescharacteristic
597C22×C4C24×C13911yescharacteristic
598D8—28no—
599D8—44no—
600M16—44no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8C2×D4×C13912yes—
611C2×C8#41×C13912yes—
612C2×C8#41×C13912yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C13912yes—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C23—21no—
644C23—22no—
645C23—21no—
646C23—22no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23C22×D4×C13911yescharacteristic
672D4—22no—
673D4—22no—
674D4—22no—
675D4—22no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686D4—84no—
687D4—84no—
688D4—84no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4AGL(1,ℤ/8)×C13912yes—
724C2×C4AGL(1,ℤ/8)×C13912yes—
725C2×C4C22×D4×C13911yescharacteristic
726C2×C4C2×#41×C13911yescharacteristic
727C2×C4C2×#41×C13911yescharacteristic
728C2×C4C2×#41×C13911yescharacteristic
729C2×C4H(5,𝔽2)×C13911yescharacteristic
730C2×C4H(5,𝔽2)×C13911yescharacteristic
731C8—22no—
732C8—22no—
733C8—22no—
734C8—41no—
735C22—42no—
736C22—41no—
737C22—41no—
738C22—42no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—42no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22#532×C13911yescharacteristic
764C22D42×C13911yescharacteristic
765C22#546×C13911yescharacteristic
766C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
767C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
768C22#576×C13911yescharacteristic
769C22#577×C13911yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—81no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4#525×C13911yescharacteristic
781C4#540×C13911yescharacteristic
782C4#546×C13911yescharacteristic
783C4#553×C13911yescharacteristic
784C2—81no—
785C2—82no—
786C2—82no—
787C2—161no—
788C2#2464×C13911yescharacteristic
789C2#3179×C13911yescharacteristic
790C2#3184×C13911yescharacteristic
791C2#3272×C13911yescharacteristic
792C2#3274×C13911yescharacteristic
793C2#3306×C13911yescharacteristic
794C2#3318×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×#442×C139C2semidirect
3. #2428×C139C2semidirect
4. #2422×C139C2semidirect
5. #2084×C139C2semidirect
6. #2034×C139C2semidirect
7. #2011×C139C2semidirect
8. #1999×C139C2semidirect
9. #1957×C139C2semidirect
10. #1936×C139C2semidirect
11. #1934×C139C2semidirect
12. #1895×C139C2semidirect
13. #1879×C139C2semidirect
14. #1864×C139C2semidirect
15. #1753×C139C2semidirect
131. #102×C139D4semidirect
397. #26984C139direct (N × H)
398. C139#26984direct (N × H)
399. C2×#469C2×C139semidirect
400. C2×#442C2×C139semidirect
401. #2428C2×C139semidirect
402. #2422C2×C139semidirect
403. #2084C2×C139semidirect
404. #2034C2×C139semidirect
405. #2011C2×C139semidirect
406. #1999C2×C139semidirect
407. #1957C2×C139semidirect
408. #1936C2×C139semidirect
409. #1934C2×C139semidirect
410. #1895C2×C139semidirect
411. #1879C2×C139semidirect
412. #1864C2×C139semidirect
413. #1753C2×C139semidirect
529. #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×#442×C1392
#2428×C1392
#2422×C1392
#2084×C1392
#2034×C1392
#2011×C1392
#1999×C1392
#1957×C1392
#1936×C1392
#1934×C1392
#1895×C1392
#1879×C1392
#1864×C1392
#1753×C1392
#26984139