Finite Group Databasebeta

← C139×#26246 #48020842

Subgroups — C139×#26246 #48020842

Order 35584.

1006 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C139C211yesmaximal, characteristic, complemented
2C2×#482×C139C211yesmaximal, characteristic, complemented
3#2541×C139C211yesmaximal, characteristic
4#2352×C139C211yesmaximal, characteristic, complemented
5#2034×C139C211yesmaximal, characteristic, complemented
6#2033×C139C211yesmaximal, characteristic, complemented
7#2033×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#1982×C139C211yesmaximal, characteristic, complemented
10#1961×C139C211yesmaximal, characteristic, complemented
11#1955×C139C211yesmaximal, characteristic, complemented
12#1949×C139C211yesmaximal, characteristic, complemented
13#1875×C139C211yesmaximal, characteristic, complemented
14#1874×C139C211yesmaximal, characteristic, complemented
15#1776×C139C211yesmaximal, characteristic, complemented
16C2×#127×C139—21no—
17C2×#127×C139C2211yescharacteristic
18C2×#121×C139C2211yescharacteristic
19C2×#121×C139C2211yescharacteristic
20C2×#121×C139C2211yescharacteristic
21C2×#121×C139C2211yescharacteristic
22C2×C4×D4×C139C2211yescharacteristic
23C2×#117×C139C2211yescharacteristic
24C22×C4⋊C4×C139C2211yescharacteristic
25#482×C139—24no—
26#481×C139—24no—
27C2×#107×C139C2211yescharacteristic
28C2×#107×C139C2211yescharacteristic
29C2×#106×C139C2211yescharacteristic
30C2×#106×C139C2211yescharacteristic
31C2×C4⋊C8×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×C22⋊C8×C139C2211yescharacteristic
41C2×C22⋊C8×C139C2211yescharacteristic
42C2×C22⋊C8×C139C2211yescharacteristic
43C2×C22⋊C8×C139C2211yescharacteristic
44C2×#97×C139C2211yescharacteristic
45#392×C139—21no—
46#392×C139—21no—
47#390×C139—21no—
48#388×C139—21no—
49#387×C139—21no—
50#386×C139—21no—
51#382×C139C2211yescharacteristic
52#380×C139C2211yescharacteristic
53#380×C139C2211yescharacteristic
54C4×C4⋊C4×C139C2211yescharacteristic
55C4×C4⋊C4×C139C2211yescharacteristic
56C4×C22⋊C4×C139—21no—
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61C22×D4×C139—21no—
62C22×D4×C139—21no—
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139—21no—
67C22×D4×C139D411yescharacteristic
68C22×D4×C139C2311yescharacteristic
69C22×D4×C139C2311yescharacteristic
70C23×C4×C139—21no—
71C23×C4×C139C2311yescharacteristic
72C23×C4×C139C2311yescharacteristic
73C22×C8×C139C2311yescharacteristic
74C22×C8×C139C2311yescharacteristic
75C22×C8×C139C2311yescharacteristic
76C22×C8×C139C2311yescharacteristic
77#127×C139—22no—
78#127×C139—22no—
79#127×C139—44no—
80#121×C139—22no—
81#121×C139—22no—
82#121×C139—22no—
83#121×C139—22no—
84#121×C139—41no—
85#121×C139—41no—
86#121×C139—41no—
87#121×C139—41no—
88C4×D4×C139—22no—
89C4×D4×C139—22no—
90#117×C139—22no—
91#117×C139—41no—
92C2×C4⋊C4×C139—22no—
93C2×C4⋊C4×C139—21no—
94C2×C4⋊C4×C139—41no—
95C2×C4⋊C4×C139D411yescharacteristic
96C2×C4⋊C4×C139C2311yescharacteristic
97C2×C4⋊C4×C139C2311yescharacteristic
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C4⋊C4×C139C2311yescharacteristic
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C4⋊C4×C139C2311yescharacteristic
102C2×C22⋊C4×C139—21no—
103C2×C22⋊C4×C139—21no—
104C2×C22⋊C4×C139—21no—
105C2×C22⋊C4×C139—21no—
106C2×C22⋊C4×C139—21no—
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
109C2×C22⋊C4×C139D411yescharacteristic
110C2×C22⋊C4×C139D411yescharacteristic
111C2×C42×C139—21no—
112C2×C42×C139—21no—
113C2×C42×C139—21no—
114C2×C42×C139C2311yescharacteristic
115#107×C139—22no—
116#107×C139—22no—
117#106×C139—22no—
118#106×C139D414yescomplemented
119C4⋊C8×C139—22no—
120#102×C139—22no—
121#102×C139—22no—
122#102×C139—22no—
123#102×C139—22no—
124#102×C139—41no—
125#102×C139—41no—
126#102×C139—41no—
127#102×C139—41no—
128C22⋊C8×C139—22no—
129C22⋊C8×C139—22no—
130C22⋊C8×C139—41no—
131C22⋊C8×C139—41no—
132#97×C139—22no—
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—21no—
140C24×C139—21no—
141C24×C139C2×D411yescharacteristic
142C24×C139C2×D411yescharacteristic
143C2×D4×C139—22no—
144C2×D4×C139—22no—
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—41no—
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—
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×C139—81no—
176C22×C4×C139—21no—
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—21no—
189C22×C4×C139—21no—
190C22×C4×C139—21no—
191C22×C4×C139—21no—
192C22×C4×C139—21no—
193C22×C4×C139—21no—
194C22×C4×C139—42no—
195C22×C4×C139—42no—
196C22×C4×C139—81no—
197C22×C4×C139C2×D411yescharacteristic
198C22×C4×C139C2×D411yescharacteristic
199C22×C4×C139C2×D411yescharacteristic
200C22×C4×C139C2×D411yescharacteristic
201C22×C4×C139C2411yescharacteristic
202C2×C8×C139—21no—
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×C139—21no—
213C2×C8×C139C2×D412yes—
214C4⋊C4×C139—22no—
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×C139C2×D412yes—
226C4⋊C4×C139C2×D412yes—
227C4⋊C4×C139#4112yes—
228C22⋊C4×C139—22no—
229C22⋊C4×C139—22no—
230C22⋊C4×C139—42no—
231C22⋊C4×C139—42no—
232C22⋊C4×C139—42no—
233C22⋊C4×C139—42no—
234C22⋊C4×C139—42no—
235C22⋊C4×C139—42no—
236C22⋊C4×C139—81no—
237C42×C139—42no—
238C42×C139—42no—
239C42×C139—81no—
240C42×C139#4112yes—
241C42×C139#4112yes—
242C23×C139—21no—
243C23×C139—21no—
244C23×C139—21no—
245C23×C139—21no—
246C23×C139—21no—
247C23×C139—21no—
248C23×C139—21no—
249C23×C139—21no—
250C23×C139—21no—
251C23×C139—21no—
252C23×C139—21no—
253C23×C139—21no—
254C23×C139—21no—
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×C139AGL(1,ℤ/8)12yes—
270C23×C139C22×D411yescharacteristic
271D4×C139—44no—
272D4×C139—41no—
273D4×C139—41no—
274D4×C139—41no—
275D4×C139—41no—
276D4×C139—41no—
277D4×C139—41no—
278D4×C139—41no—
279D4×C139—41no—
280D4×C139—84no—
281D4×C139—84no—
282D4×C139—84no—
283D4×C139—84no—
284D4×C139—84no—
285D4×C139—84no—
286C2×C4×C139—21no—
287C2×C4×C139—21no—
288C2×C4×C139—21no—
289C2×C4×C139—21no—
290C2×C4×C139—21no—
291C2×C4×C139—21no—
292C2×C4×C139—21no—
293C2×C4×C139—22no—
294C2×C4×C139—22no—
295C2×C4×C139—21no—
296C2×C4×C139—22no—
297C2×C4×C139—21no—
298C2×C4×C139—21no—
299C2×C4×C139—41no—
300C2×C4×C139—41no—
301C2×C4×C139—41no—
302C2×C4×C139—41no—
303C2×C4×C139—41no—
304C2×C4×C139—41no—
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—84no—
323C2×C4×C139#12312yes—
324C2×C4×C139#12312yes—
325C2×C4×C139C22×D411yescharacteristic
326C2×C4×C139C2×#4111yescharacteristic
327C2×C4×C139C2×#4111yescharacteristic
328C2×C4×C139C2×#4111yescharacteristic
329C2×C4×C139H(5,𝔽2)11yescharacteristic
330C2×C4×C139H(5,𝔽2)11yescharacteristic
331C8×C139—22no—
332C8×C139—41no—
333C8×C139—41no—
334C8×C139—41no—
335C22×C139—22no—
336C22×C139—22no—
337C22×C139—22no—
338C22×C139—41no—
339C22×C139—41no—
340C22×C139—41no—
341C22×C139—41no—
342C22×C139—41no—
343C22×C139—41no—
344C22×C139—41no—
345C22×C139—41no—
346C22×C139—41no—
347C22×C139—41no—
348C22×C139—41no—
349C22×C139—81no—
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×C139C2×#12311yescharacteristic
364C22×C139D4211yescharacteristic
365C22×C139#54611yescharacteristic
366C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C139#57511yescharacteristic
368C22×C139#57611yescharacteristic
369C22×C139#57711yescharacteristic
370C4×C139—22no—
371C4×C139—22no—
372C4×C139—41no—
373C4×C139—41no—
374C4×C139—42no—
375C4×C139—42no—
376C4×C139—42no—
377C4×C139—81no—
378C4×C139—81no—
379C4×C139—81no—
380C4×C139#53211yescharacteristic
381C4×C139#54011yescharacteristic
382C4×C139#55011yescharacteristic
383C4×C139#55911yescharacteristic
384C2×C139—42no—
385C2×C139—81no—
386C2×C139—161no—
387C2×C139—161no—
388C2×C139#244511yescharacteristic
389C2×C139#309411yescharacteristic
390C2×C139#309611yescharacteristic
391C2×C139#326511yescharacteristic
392C2×C139#326811yescharacteristic
393C2×C139#331711yescharacteristic
394C2×C139#331811yescharacteristic
395#26246C13911yesmaximal, characteristic, direct product factor, Sylow
396C139#2624611yescharacteristic, direct product factor, Sylow
397C2×#481C2×C13911yescharacteristic, complemented
398C2×#482C2×C13911yescharacteristic, complemented
399#2541C2×C13911yescharacteristic
400#2352C2×C13911yescharacteristic, complemented
401#2034C2×C13911yescharacteristic, complemented
402#2033C2×C13911yescharacteristic, complemented
403#2033C2×C13911yescharacteristic, complemented
404#2033C2×C13911yescharacteristic, complemented
405#1982C2×C13911yescharacteristic, complemented
406#1961C2×C13911yescharacteristic, complemented
407#1955C2×C13911yescharacteristic, complemented
408#1949C2×C13911yescharacteristic, complemented
409#1875C2×C13911yescharacteristic, complemented
410#1874C2×C13911yescharacteristic, complemented
411#1776C2×C13911yescharacteristic, complemented
412C2×#127—21no—
413C2×#127C22×C13911yescharacteristic
414C2×#121C22×C13911yescharacteristic
415C2×#121C22×C13911yescharacteristic
416C2×#121C22×C13911yescharacteristic
417C2×#121C22×C13911yescharacteristic
418C2×C4×D4C22×C13911yescharacteristic
419C2×#117C22×C13911yescharacteristic
420C22×C4⋊C4C22×C13911yescharacteristic
421#482—24no—
422#481—24no—
423C2×#107C22×C13911yescharacteristic
424C2×#107C22×C13911yescharacteristic
425C2×#106C22×C13911yescharacteristic
426C2×#106C22×C13911yescharacteristic
427C2×C4⋊C8C22×C13911yescharacteristic
428C2×#102C22×C13911yescharacteristic
429C2×#102C22×C13911yescharacteristic
430C2×#102C22×C13911yescharacteristic
431C2×#102C22×C13911yescharacteristic
432C2×#102C22×C13911yescharacteristic
433C2×#102C22×C13911yescharacteristic
434C2×#102C22×C13911yescharacteristic
435C2×#102C22×C13911yescharacteristic
436C2×C22⋊C8C22×C13911yescharacteristic
437C2×C22⋊C8C22×C13911yescharacteristic
438C2×C22⋊C8C22×C13911yescharacteristic
439C2×C22⋊C8C22×C13911yescharacteristic
440C2×#97C22×C13911yescharacteristic
441#392—21no—
442#392—21no—
443#390—21no—
444#388—21no—
445#387—21no—
446#386—21no—
447#382C22×C13911yescharacteristic
448#380C22×C13911yescharacteristic
449#380C22×C13911yescharacteristic
450C4×C4⋊C4C22×C13911yescharacteristic
451C4×C4⋊C4C22×C13911yescharacteristic
452C4×C22⋊C4—21no—
453#340C22×C13911yescharacteristic
454#340C22×C13911yescharacteristic
455#340C22×C13911yescharacteristic
456#340C22×C13911yescharacteristic
457C22×D4—21no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4D4×C13911yescharacteristic
464C22×D4C23×C13911yescharacteristic
465C22×D4C23×C13911yescharacteristic
466C23×C4—21no—
467C23×C4C23×C13911yescharacteristic
468C23×C4C23×C13911yescharacteristic
469C22×C8C23×C13911yescharacteristic
470C22×C8C23×C13911yescharacteristic
471C22×C8C23×C13911yescharacteristic
472C22×C8C23×C13911yescharacteristic
473#127—22no—
474#127—22no—
475#127—44no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—41no—
481#121—41no—
482#121—41no—
483#121—41no—
484C4×D4—22no—
485C4×D4—22no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4D4×C13911yescharacteristic
492C2×C4⋊C4C23×C13911yescharacteristic
493C2×C4⋊C4C23×C13911yescharacteristic
494C2×C4⋊C4C23×C13911yescharacteristic
495C2×C4⋊C4C23×C13911yescharacteristic
496C2×C4⋊C4C23×C13911yescharacteristic
497C2×C4⋊C4C23×C13911yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4D4×C13911yescharacteristic
506C2×C22⋊C4D4×C13911yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42—21no—
510C2×C42C23×C13911yescharacteristic
511#107—22no—
512#107—22no—
513#106—22no—
514#106D4×C13914yescomplemented
515C4⋊C8—22no—
516#102—22no—
517#102—22no—
518#102—22no—
519#102—22no—
520#102—41no—
521#102—41no—
522#102—41no—
523#102—41no—
524C22⋊C8—22no—
525C22⋊C8—22no—
526C22⋊C8—41no—
527C22⋊C8—41no—
528#97—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C13911yescharacteristic
538C24C2×D4×C13911yescharacteristic
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
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—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
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—81no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C22×C4—21no—
573C22×C4—21no—
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—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—81no—
593C22×C4C2×D4×C13911yescharacteristic
594C22×C4C2×D4×C13911yescharacteristic
595C22×C4C2×D4×C13911yescharacteristic
596C22×C4C2×D4×C13911yescharacteristic
597C22×C4C24×C13911yescharacteristic
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
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×C8C2×D4×C13912yes—
610C4⋊C4—22no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—42no—
621C4⋊C4C2×D4×C13912yes—
622C4⋊C4C2×D4×C13912yes—
623C4⋊C4#41×C13912yes—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—81no—
633C42—42no—
634C42—42no—
635C42—81no—
636C42#41×C13912yes—
637C42#41×C13912yes—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—41no—
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—
665C23AGL(1,ℤ/8)×C13912yes—
666C23C22×D4×C13911yescharacteristic
667D4—44no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—84no—
677D4—84no—
678D4—84no—
679D4—84no—
680D4—84no—
681D4—84no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
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—84no—
719C2×C4#123×C13912yes—
720C2×C4#123×C13912yes—
721C2×C4C22×D4×C13911yescharacteristic
722C2×C4C2×#41×C13911yescharacteristic
723C2×C4C2×#41×C13911yescharacteristic
724C2×C4C2×#41×C13911yescharacteristic
725C2×C4H(5,𝔽2)×C13911yescharacteristic
726C2×C4H(5,𝔽2)×C13911yescharacteristic
727C8—22no—
728C8—41no—
729C8—41no—
730C8—41no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22C2×#123×C13911yescharacteristic
760C22D42×C13911yescharacteristic
761C22#546×C13911yescharacteristic
762C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
763C22#575×C13911yescharacteristic
764C22#576×C13911yescharacteristic
765C22#577×C13911yescharacteristic
766C4—22no—
767C4—22no—
768C4—42no—
769C4—41no—
770C4—41no—
771C4—42no—
772C4—42no—
773C4—81no—
774C4—81no—
775C4—81no—
776C4#532×C13911yescharacteristic
777C4#540×C13911yescharacteristic
778C4#550×C13911yescharacteristic
779C4#559×C13911yescharacteristic
780C2—42no—
781C2—81no—
782C2—161no—
783C2—161no—
784C2#2445×C13911yescharacteristic
785C2#3094×C13911yescharacteristic
786C2#3096×C13911yescharacteristic
787C2#3265×C13911yescharacteristic
788C2#3268×C13911yescharacteristic
789C2#3317×C13911yescharacteristic
790C2#3318×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#2541×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#481×C139C2semidirect
2. C2×#482×C139C2semidirect
4. #2352×C139C2semidirect
5. #2034×C139C2semidirect
6. #2033×C139C2semidirect
7. #2033×C139C2semidirect
8. #2033×C139C2semidirect
9. #1982×C139C2semidirect
10. #1961×C139C2semidirect
11. #1955×C139C2semidirect
12. #1949×C139C2semidirect
13. #1875×C139C2semidirect
14. #1874×C139C2semidirect
15. #1776×C139C2semidirect
118. #106×C139D4semidirect
395. #26246C139direct (N × H)
396. C139#26246direct (N × H)
397. C2×#481C2×C139semidirect
398. C2×#482C2×C139semidirect
400. #2352C2×C139semidirect
401. #2034C2×C139semidirect
402. #2033C2×C139semidirect
403. #2033C2×C139semidirect
404. #2033C2×C139semidirect
405. #1982C2×C139semidirect
406. #1961C2×C139semidirect
407. #1955C2×C139semidirect
408. #1949C2×C139semidirect
409. #1875C2×C139semidirect
410. #1874C2×C139semidirect
411. #1776C2×C139semidirect
514. #106D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1392
C2×#482×C1392
#2541×C1392
#2352×C1392
#2034×C1392
#2033×C1392
#1982×C1392
#1961×C1392
#1955×C1392
#1949×C1392
#1875×C1392
#1874×C1392
#1776×C1392
#26246139