Finite Group Databasebeta

← C139×#24878 #48019474

Subgroups — C139×#24878 #48019474

Order 35584.

1168 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C139C211yesmaximal, characteristic, complemented
2C2×#418×C139C211yesmaximal, characteristic, complemented
3#2408×C139C211yesmaximal, characteristic
4#2352×C139C211yesmaximal, characteristic, complemented
5#2092×C139C211yesmaximal, characteristic, complemented
6#2073×C139C211yesmaximal, characteristic, complemented
7#2033×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#1926×C139C211yesmaximal, characteristic, complemented
10#1925×C139C211yesmaximal, characteristic, complemented
11#1874×C139C211yesmaximal, characteristic, complemented
12#1870×C139C211yesmaximal, characteristic, complemented
13#1854×C139C211yesmaximal, characteristic, complemented
14#1809×C139C211yesmaximal, characteristic, complemented
15#1786×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×M16×C139C2211yescharacteristic
18C2×#121×C139C2211yescharacteristic
19C2×#121×C139C2211yescharacteristic
20C2×#120×C139—21no—
21C2×C4×D4×C139C2211yescharacteristic
22C2×#117×C139C2211yescharacteristic
23C22×C4⋊C4×C139C2211yescharacteristic, complemented
24#481×C139—24no—
25C2×#107×C139C2211yescharacteristic, complemented
26C2×#107×C139C2211yescharacteristic, complemented
27C2×#106×C139C2211yescharacteristic, complemented
28C2×#106×C139C2211yescharacteristic, complemented
29#418×C139—24no—
30C2×#102×C139C2211yescharacteristic
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×C22⋊C8×C139C2211yescharacteristic
39C2×C22⋊C8×C139C2211yescharacteristic, complemented
40C2×C22⋊C8×C139C2211yescharacteristic, complemented
41#394×C139—21no—
42#392×C139—21no—
43#390×C139C2211yescharacteristic
44#390×C139C2211yescharacteristic
45#388×C139—21no—
46#387×C139—21no—
47#386×C139—21no—
48#382×C139C2211yescharacteristic, complemented
49#380×C139C2211yescharacteristic
50#380×C139C2211yescharacteristic
51#380×C139C2211yescharacteristic, complemented
52#379×C139—21no—
53C4×C4⋊C4×C139C2211yescharacteristic, complemented
54C4×C22⋊C4×C139—21no—
55#340×C139C2211yescharacteristic, complemented
56#340×C139C2211yescharacteristic, complemented
57#340×C139C2211yescharacteristic, complemented
58#340×C139C2211yescharacteristic, complemented
59#336×C139C2211yescharacteristic, complemented
60#336×C139C2211yescharacteristic, complemented
61C25×C139—21no—
62C22×D4×C139—22no—
63C22×D4×C139—22no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139—21no—
67C22×D4×C139—22no—
68C22×D4×C139—22no—
69C22×D4×C139—41no—
70C22×D4×C139—41no—
71C22×D4×C139D411yescharacteristic
72C22×D4×C139C2311yescharacteristic
73C22×D4×C139C2311yescharacteristic
74C23×C4×C139—21no—
75C23×C4×C139C2311yescharacteristic
76C23×C4×C139C2311yescharacteristic
77C2×M16×C139—22no—
78C2×M16×C139—22no—
79C2×M16×C139—41no—
80C22×C8×C139C2311yescharacteristic
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83C22×C8×C139C2311yescharacteristic
84#121×C139—22no—
85#121×C139—22no—
86#121×C139—41no—
87#121×C139—41no—
88#120×C139—44no—
89C4×D4×C139—22no—
90C4×D4×C139—22no—
91#117×C139—22no—
92#117×C139—41no—
93C2×C4⋊C4×C139—22no—
94C2×C4⋊C4×C139—21no—
95C2×C4⋊C4×C139—41no—
96C2×C4⋊C4×C139D411yescharacteristic
97C2×C4⋊C4×C139C2311yescharacteristic
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C4⋊C4×C139C2311yescharacteristic
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C4⋊C4×C139C2311yescharacteristic
102C2×C4⋊C4×C139C2311yescharacteristic
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×C139—21no—
110C2×C22⋊C4×C139—21no—
111C2×C22⋊C4×C139—21no—
112C2×C22⋊C4×C139—21no—
113C2×C22⋊C4×C139D411yescharacteristic
114C2×C22⋊C4×C139D411yescharacteristic
115C2×C42×C139—21no—
116C2×C42×C139—21no—
117C2×C42×C139C2311yescharacteristic
118#107×C139—41no—
119#107×C139—41no—
120#106×C139—22no—
121#106×C139—22no—
122#102×C139—22no—
123#102×C139—22no—
124#102×C139—22no—
125#102×C139—22no—
126#102×C139—22no—
127#102×C139—41no—
128#102×C139—41no—
129#102×C139D414yescomplemented
130C22⋊C8×C139—22no—
131C22⋊C8×C139—22no—
132C22⋊C8×C139—41no—
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×C139—42no—
142C24×C139—42no—
143C24×C139—42no—
144C24×C139—42no—
145C24×C139—42no—
146C24×C139—81no—
147C24×C139—81no—
148C24×C139C2×D411yescharacteristic
149C24×C139C2×D411yescharacteristic
150C2×D4×C139—28no—
151C2×D4×C139—22no—
152C2×D4×C139—22no—
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—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—44no—
164C2×D4×C139—44no—
165C2×D4×C139—41no—
166C2×D4×C139—42no—
167C2×D4×C139—42no—
168C2×D4×C139—44no—
169C2×D4×C139—42no—
170C2×D4×C139—42no—
171C2×D4×C139—42no—
172C2×D4×C139—42no—
173C2×D4×C139—42no—
174C2×D4×C139—81no—
175C2×D4×C139—81no—
176C2×D4×C139C2×D412yes—
177C2×D4×C139#4112yes—
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×C139#4112yes—
202C22×C4×C139#4112yes—
203C22×C4×C139C2411yescharacteristic
204M16×C139—44no—
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×C139—21no—
214C2×C8×C139—21no—
215C2×C8×C139—21no—
216C2×C8×C139C2×D412yes—
217C4⋊C4×C139—22no—
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—21no—
225C4⋊C4×C139—21no—
226C4⋊C4×C139—21no—
227C4⋊C4×C139—21no—
228C4⋊C4×C139—21no—
229C4⋊C4×C139—42no—
230C4⋊C4×C139C2×D412yes—
231C22⋊C4×C139—22no—
232C22⋊C4×C139—22no—
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—
241C22⋊C4×C139—81no—
242C22⋊C4×C139—81no—
243C42×C139—21no—
244C42×C139—21no—
245C42×C139—42no—
246C42×C139—81no—
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—21no—
256C23×C139—21no—
257C23×C139—21no—
258C23×C139—21no—
259C23×C139—22no—
260C23×C139—22no—
261C23×C139—48no—
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×C139—41no—
274C23×C139—84no—
275C23×C139—84no—
276C23×C139—84no—
277C23×C139—84no—
278C23×C139—84no—
279C23×C139—84no—
280C23×C139#12312yes—
281C23×C139AGL(1,ℤ/8)12yes—
282C23×C139C22×D411yescharacteristic
283D4×C139—22no—
284D4×C139—22no—
285D4×C139—22no—
286D4×C139—22no—
287D4×C139—48no—
288D4×C139—44no—
289D4×C139—41no—
290D4×C139—41no—
291D4×C139—41no—
292D4×C139—41no—
293D4×C139—84no—
294D4×C139—84no—
295C2×C4×C139—21no—
296C2×C4×C139—21no—
297C2×C4×C139—22no—
298C2×C4×C139—22no—
299C2×C4×C139—22no—
300C2×C4×C139—22no—
301C2×C4×C139—21no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—22no—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
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—84no—
333C2×C4×C139#12312yes—
334C2×C4×C139C22×D411yescharacteristic
335C2×C4×C139C2×#4111yescharacteristic
336C2×C4×C139C2×#4111yescharacteristic
337C2×C4×C139C2×#4111yescharacteristic
338C2×C4×C139H(5,𝔽2)11yescharacteristic
339C2×C4×C139H(5,𝔽2)11yescharacteristic
340C8×C139—22no—
341C8×C139—41no—
342C8×C139—41no—
343C8×C139—41no—
344C22×C139—22no—
345C22×C139—22no—
346C22×C139—22no—
347C22×C139—22no—
348C22×C139—22no—
349C22×C139—22no—
350C22×C139—41no—
351C22×C139—41no—
352C22×C139—41no—
353C22×C139—41no—
354C22×C139—41no—
355C22×C139—41no—
356C22×C139—41no—
357C22×C139—41no—
358C22×C139—42no—
359C22×C139—42no—
360C22×C139—42no—
361C22×C139—42no—
362C22×C139—42no—
363C22×C139—42no—
364C22×C139—816no—
365C22×C139—81no—
366C22×C139—81no—
367C22×C139—81no—
368C22×C139—81no—
369C22×C139—81no—
370C22×C139—81no—
371C22×C139—81no—
372C22×C139—81no—
373C22×C139C2×#12311yescharacteristic
374C22×C139D4211yescharacteristic
375C22×C139#54611yescharacteristic
376C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C139#57511yescharacteristic
378C22×C139#57611yescharacteristic
379C22×C139#57711yescharacteristic
380C4×C139—22no—
381C4×C139—41no—
382C4×C139—41no—
383C4×C139—41no—
384C4×C139—42no—
385C4×C139—81no—
386C4×C139—81no—
387C4×C139—81no—
388C4×C139—81no—
389C4×C139—81no—
390C4×C139#52511yescharacteristic
391C4×C139#53811yescharacteristic
392C4×C139#54611yescharacteristic
393C4×C139#55111yescharacteristic
394C2×C139—42no—
395C2×C139—42no—
396C2×C139—82no—
397C2×C139—82no—
398C2×C139#241811yescharacteristic
399C2×C139#309411yescharacteristic
400C2×C139#309611yescharacteristic
401C2×C139#326511yescharacteristic
402C2×C139#327311yescharacteristic
403C2×C139#331811yescharacteristic
404C2×C139#332311yescharacteristic
405#24878C13911yesmaximal, characteristic, direct product factor, Sylow
406C139#2487811yescharacteristic, direct product factor, Sylow
407C2×#481C2×C13911yescharacteristic, complemented
408C2×#418C2×C13911yescharacteristic, complemented
409#2408C2×C13911yescharacteristic
410#2352C2×C13911yescharacteristic, complemented
411#2092C2×C13911yescharacteristic, complemented
412#2073C2×C13911yescharacteristic, complemented
413#2033C2×C13911yescharacteristic, complemented
414#2033C2×C13911yescharacteristic, complemented
415#1926C2×C13911yescharacteristic, complemented
416#1925C2×C13911yescharacteristic, complemented
417#1874C2×C13911yescharacteristic, complemented
418#1870C2×C13911yescharacteristic, complemented
419#1854C2×C13911yescharacteristic, complemented
420#1809C2×C13911yescharacteristic, complemented
421#1786C2×C13911yescharacteristic, complemented
422C23×D4C22×C13911yescharacteristic
423C22×M16C22×C13911yescharacteristic
424C2×#121C22×C13911yescharacteristic
425C2×#121C22×C13911yescharacteristic
426C2×#120—21no—
427C2×C4×D4C22×C13911yescharacteristic
428C2×#117C22×C13911yescharacteristic
429C22×C4⋊C4C22×C13911yescharacteristic, complemented
430#481—24no—
431C2×#107C22×C13911yescharacteristic, complemented
432C2×#107C22×C13911yescharacteristic, complemented
433C2×#106C22×C13911yescharacteristic, complemented
434C2×#106C22×C13911yescharacteristic, complemented
435#418—24no—
436C2×#102C22×C13911yescharacteristic
437C2×#102C22×C13911yescharacteristic
438C2×#102C22×C13911yescharacteristic
439C2×#102C22×C13911yescharacteristic
440C2×#102C22×C13911yescharacteristic
441C2×#102C22×C13911yescharacteristic
442C2×#102C22×C13911yescharacteristic
443C2×#102C22×C13911yescharacteristic
444C2×C22⋊C8C22×C13911yescharacteristic
445C2×C22⋊C8C22×C13911yescharacteristic, complemented
446C2×C22⋊C8C22×C13911yescharacteristic, complemented
447#394—21no—
448#392—21no—
449#390C22×C13911yescharacteristic
450#390C22×C13911yescharacteristic
451#388—21no—
452#387—21no—
453#386—21no—
454#382C22×C13911yescharacteristic, complemented
455#380C22×C13911yescharacteristic
456#380C22×C13911yescharacteristic
457#380C22×C13911yescharacteristic, complemented
458#379—21no—
459C4×C4⋊C4C22×C13911yescharacteristic, complemented
460C4×C22⋊C4—21no—
461#340C22×C13911yescharacteristic, complemented
462#340C22×C13911yescharacteristic, complemented
463#340C22×C13911yescharacteristic, complemented
464#340C22×C13911yescharacteristic, complemented
465#336C22×C13911yescharacteristic, complemented
466#336C22×C13911yescharacteristic, complemented
467C25—21no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—41no—
476C22×D4—41no—
477C22×D4D4×C13911yescharacteristic
478C22×D4C23×C13911yescharacteristic
479C22×D4C23×C13911yescharacteristic
480C23×C4—21no—
481C23×C4C23×C13911yescharacteristic
482C23×C4C23×C13911yescharacteristic
483C2×M16—22no—
484C2×M16—22no—
485C2×M16—41no—
486C22×C8C23×C13911yescharacteristic
487C22×C8C23×C13911yescharacteristic
488C22×C8C23×C13911yescharacteristic
489C22×C8C23×C13911yescharacteristic
490#121—22no—
491#121—22no—
492#121—41no—
493#121—41no—
494#120—44no—
495C4×D4—22no—
496C4×D4—22no—
497#117—22no—
498#117—41no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4D4×C13911yescharacteristic
503C2×C4⋊C4C23×C13911yescharacteristic
504C2×C4⋊C4C23×C13911yescharacteristic
505C2×C4⋊C4C23×C13911yescharacteristic
506C2×C4⋊C4C23×C13911yescharacteristic
507C2×C4⋊C4C23×C13911yescharacteristic
508C2×C4⋊C4C23×C13911yescharacteristic
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⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4D4×C13911yescharacteristic
520C2×C22⋊C4D4×C13911yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42C23×C13911yescharacteristic
524#107—41no—
525#107—41no—
526#106—22no—
527#106—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535#102D4×C13914yescomplemented
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—41no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545C24—21no—
546C24—21no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—81no—
553C24—81no—
554C24C2×D4×C13911yescharacteristic
555C24C2×D4×C13911yescharacteristic
556C2×D4—28no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—41no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—81no—
581C2×D4—81no—
582C2×D4C2×D4×C13912yes—
583C2×D4#41×C13912yes—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
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—42no—
601C22×C4—42no—
602C22×C4—81no—
603C22×C4C2×D4×C13911yescharacteristic
604C22×C4C2×D4×C13911yescharacteristic
605C22×C4C2×D4×C13911yescharacteristic
606C22×C4C2×D4×C13911yescharacteristic
607C22×C4#41×C13912yes—
608C22×C4#41×C13912yes—
609C22×C4C24×C13911yescharacteristic
610M16—44no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8C2×D4×C13912yes—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—42no—
636C4⋊C4C2×D4×C13912yes—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—42no—
652C42—81no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—22no—
666C23—22no—
667C23—48no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23#123×C13912yes—
687C23AGL(1,ℤ/8)×C13912yes—
688C23C22×D4×C13911yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—44no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—41no—
699D4—84no—
700D4—84no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—41no—
718C2×C4—41no—
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—84no—
739C2×C4#123×C13912yes—
740C2×C4C22×D4×C13911yescharacteristic
741C2×C4C2×#41×C13911yescharacteristic
742C2×C4C2×#41×C13911yescharacteristic
743C2×C4C2×#41×C13911yescharacteristic
744C2×C4H(5,𝔽2)×C13911yescharacteristic
745C2×C4H(5,𝔽2)×C13911yescharacteristic
746C8—22no—
747C8—41no—
748C8—41no—
749C8—41no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—816no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22C2×#123×C13911yescharacteristic
780C22D42×C13911yescharacteristic
781C22#546×C13911yescharacteristic
782C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
783C22#575×C13911yescharacteristic
784C22#576×C13911yescharacteristic
785C22#577×C13911yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—42no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4#525×C13911yescharacteristic
797C4#538×C13911yescharacteristic
798C4#546×C13911yescharacteristic
799C4#551×C13911yescharacteristic
800C2—42no—
801C2—42no—
802C2—82no—
803C2—82no—
804C2#2418×C13911yescharacteristic
805C2#3094×C13911yescharacteristic
806C2#3096×C13911yescharacteristic
807C2#3265×C13911yescharacteristic
808C2#3273×C13911yescharacteristic
809C2#3318×C13911yescharacteristic
810C2#3323×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#2408×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×#418×C139C2semidirect
4. #2352×C139C2semidirect
5. #2092×C139C2semidirect
6. #2073×C139C2semidirect
7. #2033×C139C2semidirect
8. #2033×C139C2semidirect
9. #1926×C139C2semidirect
10. #1925×C139C2semidirect
11. #1874×C139C2semidirect
12. #1870×C139C2semidirect
13. #1854×C139C2semidirect
14. #1809×C139C2semidirect
15. #1786×C139C2semidirect
23. C22×C4⋊C4×C139C22semidirect
25. C2×#107×C139C22semidirect
26. C2×#107×C139C22semidirect
27. C2×#106×C139C22semidirect
28. C2×#106×C139C22semidirect
39. C2×C22⋊C8×C139C22semidirect
40. C2×C22⋊C8×C139C22semidirect
48. #382×C139C22semidirect
51. #380×C139C22semidirect
53. C4×C4⋊C4×C139C22semidirect
55. #340×C139C22semidirect
56. #340×C139C22semidirect
57. #340×C139C22semidirect
58. #340×C139C22semidirect
59. #336×C139C22semidirect
60. #336×C139C22semidirect
129. #102×C139D4semidirect
405. #24878C139direct (N × H)
406. C139#24878direct (N × H)
407. C2×#481C2×C139semidirect
408. C2×#418C2×C139semidirect
410. #2352C2×C139semidirect
411. #2092C2×C139semidirect
412. #2073C2×C139semidirect
413. #2033C2×C139semidirect
414. #2033C2×C139semidirect
415. #1926C2×C139semidirect
416. #1925C2×C139semidirect
417. #1874C2×C139semidirect
418. #1870C2×C139semidirect
419. #1854C2×C139semidirect
420. #1809C2×C139semidirect
421. #1786C2×C139semidirect
429. C22×C4⋊C4C22×C139semidirect
431. C2×#107C22×C139semidirect
432. C2×#107C22×C139semidirect
433. C2×#106C22×C139semidirect
434. C2×#106C22×C139semidirect
445. C2×C22⋊C8C22×C139semidirect
446. C2×C22⋊C8C22×C139semidirect
454. #382C22×C139semidirect
457. #380C22×C139semidirect
459. C4×C4⋊C4C22×C139semidirect
461. #340C22×C139semidirect
462. #340C22×C139semidirect
463. #340C22×C139semidirect
464. #340C22×C139semidirect
465. #336C22×C139semidirect
466. #336C22×C139semidirect
535. #102D4×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×#418×C1392
#2408×C1392
#2352×C1392
#2092×C1392
#2073×C1392
#2033×C1392
#1926×C1392
#1925×C1392
#1874×C1392
#1870×C1392
#1854×C1392
#1809×C1392
#1786×C1392
#24878139