Finite Group Databasebeta

← C139×#24897 #48019493

Subgroups — C139×#24897 #48019493

Order 35584.

1204 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×#447×C139C211yesmaximal, characteristic
2C2×C4×D8×C139C211yesmaximal, characteristic, complemented
3#2420×C139C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C139C211yesmaximal, characteristic, complemented
5#2092×C139C211yesmaximal, characteristic, complemented
6#2076×C139C211yesmaximal, characteristic, complemented
7#2054×C139C211yesmaximal, characteristic, complemented
8#2034×C139C211yesmaximal, characteristic, complemented
9#1934×C139C211yesmaximal, characteristic, complemented
10#1923×C139C211yesmaximal, characteristic, complemented
11#1879×C139C211yesmaximal, characteristic, complemented
12#1879×C139C211yesmaximal, characteristic, complemented
13#1864×C139C211yesmaximal, characteristic, complemented
14#1804×C139C211yesmaximal, characteristic, complemented
15#1786×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C2×#121×C139C2211yescharacteristic
20C2×C4×D4×C139C2211yescharacteristic
21C2×C4×D4×C139C2211yescharacteristic
22C2×C4×D4×C139C2211yescharacteristic, complemented
23C22×C22⋊C4×C139—21no—
24#447×C139—24no—
25C4×D8×C139—24no—
26C2×#107×C139C2211yescharacteristic, complemented
27C2×#106×C139C2211yescharacteristic, complemented
28C2×C4⋊C8×C139C2211yescharacteristic, complemented
29C2×#102×C139C2211yescharacteristic
30C2×#102×C139C2211yescharacteristic
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic, complemented
36C2×#102×C139C2211yescharacteristic, complemented
37C2×C22⋊C8×C139C2211yescharacteristic
38C2×C22⋊C8×C139C2211yescharacteristic
39C2×C4×C8×C139C2211yescharacteristic, complemented
40#397×C139—21no—
41#394×C139—21no—
42#390×C139C2211yescharacteristic
43#390×C139C2211yescharacteristic
44#390×C139C2211yescharacteristic, complemented
45#389×C139C2211yescharacteristic, complemented
46#386×C139—21no—
47#386×C139—21no—
48#386×C139—21no—
49#382×C139C2211yescharacteristic, complemented
50#381×C139—21no—
51#380×C139C2211yescharacteristic
52#380×C139C2211yescharacteristic
53#379×C139—21no—
54C4×C22⋊C4×C139C2211yescharacteristic
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—22no—
65C22×D4×C139—22no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139—41no—
69C22×D4×C139—41no—
70C22×D4×C139C2311yescharacteristic
71C22×D4×C139C2311yescharacteristic
72C22×D4×C139C2311yescharacteristic
73C23×C4×C139—21no—
74C23×C4×C139—21no—
75C23×C4×C139—21no—
76C23×C4×C139C2311yescharacteristic
77C2×D8×C139—22no—
78C2×D8×C139—22no—
79C2×D8×C139—22no—
80C2×D8×C139—22no—
81C2×D8×C139—41no—
82C2×D8×C139D414yes—
83C22×C8×C139C2311yescharacteristic
84C22×C8×C139C2311yescharacteristic
85C22×C8×C139C2311yescharacteristic
86C22×C8×C139C2311yescharacteristic
87#121×C139—22no—
88#121×C139—41no—
89C4×D4×C139—22no—
90C4×D4×C139—22no—
91C4×D4×C139—22no—
92C4×D4×C139—41no—
93C4×D4×C139—41no—
94C4×D4×C139—41no—
95C2×C4⋊C4×C139—21no—
96C2×C4⋊C4×C139C2311yescharacteristic
97C2×C4⋊C4×C139C2311yescharacteristic
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C4⋊C4×C139C2311yescharacteristic
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C22⋊C4×C139—21no—
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×C139—21no—
110C2×C22⋊C4×C139—21no—
111C2×C22⋊C4×C139—21no—
112C2×C22⋊C4×C139—21no—
113C2×C22⋊C4×C139—44no—
114C2×C22⋊C4×C139D411yescharacteristic
115C2×C22⋊C4×C139D411yescharacteristic
116C2×C42×C139C2311yescharacteristic
117C2×C42×C139C2311yescharacteristic
118#107×C139—22no—
119#106×C139—41no—
120C4⋊C8×C139—41no—
121#102×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—
129C22⋊C8×C139—22no—
130C22⋊C8×C139—41no—
131C4×C8×C139—22no—
132#95×C139—21no—
133#95×C139—21no—
134#95×C139—21no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139D411yescharacteristic
138#95×C139D411yescharacteristic
139C24×C139—21no—
140C24×C139—24no—
141C24×C139—21no—
142C24×C139—21no—
143C24×C139—42no—
144C24×C139—42no—
145C24×C139—42no—
146C24×C139—42no—
147C24×C139—81no—
148C24×C139—81no—
149C24×C139C2×D411yescharacteristic
150C2×D4×C139—24no—
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—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—42no—
165C2×D4×C139—42no—
166C2×D4×C139—44no—
167C2×D4×C139—44no—
168C2×D4×C139—44no—
169C2×D4×C139—44no—
170C2×D4×C139—42no—
171C2×D4×C139—42no—
172C2×D4×C139—81no—
173C2×D4×C139C2×D412yes—
174C2×D4×C139C2×D412yes—
175C2×D4×C139#4112yes—
176C2×D4×C139#4112yes—
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—42no—
190C22×C4×C139—42no—
191C22×C4×C139—42no—
192C22×C4×C139—42no—
193C22×C4×C139—42no—
194C22×C4×C139—42no—
195C22×C4×C139—81no—
196C22×C4×C139—81no—
197C22×C4×C139—81no—
198C22×C4×C139C2×D411yescharacteristic
199C22×C4×C139C2×D411yescharacteristic
200C22×C4×C139C2×D411yescharacteristic
201C22×C4×C139C2×D411yescharacteristic
202C22×C4×C139C2×D411yescharacteristic
203C22×C4×C139C2411yescharacteristic
204D8×C139—28no—
205D8×C139—44no—
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×C139—21no—
217C2×C8×C139C2×D412yes—
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—81no—
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—81no—
239C22⋊C4×C139—81no—
240C22⋊C4×C139—81no—
241C22⋊C4×C139—81no—
242C22⋊C4×C139—81no—
243C42×C139—21no—
244C42×C139—21no—
245C42×C139—21no—
246C42×C139—21no—
247C23×C139—21no—
248C23×C139—22no—
249C23×C139—22no—
250C23×C139—21no—
251C23×C139—22no—
252C23×C139—21no—
253C23×C139—21no—
254C23×C139—21no—
255C23×C139—21no—
256C23×C139—22no—
257C23×C139—22no—
258C23×C139—48no—
259C23×C139—48no—
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×C139—41no—
274C23×C139—41no—
275C23×C139—41no—
276C23×C139—84no—
277C23×C139—84no—
278C23×C139—84no—
279C23×C139—84no—
280C23×C139—84no—
281C23×C139#13512yes—
282C23×C139C22×D411yescharacteristic
283D4×C139—22no—
284D4×C139—22no—
285D4×C139—22no—
286D4×C139—22no—
287D4×C139—22no—
288D4×C139—22no—
289D4×C139—22no—
290D4×C139—48no—
291D4×C139—41no—
292D4×C139—41no—
293D4×C139—41no—
294D4×C139—41no—
295D4×C139—84no—
296D4×C139#12314yes—
297C2×C4×C139—21no—
298C2×C4×C139—21no—
299C2×C4×C139—21no—
300C2×C4×C139—21no—
301C2×C4×C139—21no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—21no—
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—84no—
331C2×C4×C139—84no—
332C2×C4×C139—84no—
333C2×C4×C139AGL(1,ℤ/8)12yes—
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—24no—
346C22×C139—22no—
347C22×C139—22no—
348C22×C139—42no—
349C22×C139—41no—
350C22×C139—42no—
351C22×C139—41no—
352C22×C139—42no—
353C22×C139—41no—
354C22×C139—42no—
355C22×C139—42no—
356C22×C139—42no—
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×C139#52511yescharacteristic
374C22×C139D4211yescharacteristic
375C22×C139#54611yescharacteristic
376C22×C139C2×#13511yescharacteristic
377C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C139#57611yescharacteristic
379C22×C139#57611yescharacteristic
380C4×C139—22no—
381C4×C139—41no—
382C4×C139—41no—
383C4×C139—41no—
384C4×C139—41no—
385C4×C139—81no—
386C4×C139—81no—
387C4×C139—81no—
388C4×C139—81no—
389C4×C139—81no—
390C4×C139C2×#12311yescharacteristic
391C4×C139#53811yescharacteristic
392C4×C139#54611yescharacteristic
393C4×C139#55111yescharacteristic
394C2×C139—42no—
395C2×C139—44no—
396C2×C139—82no—
397C2×C139—82no—
398C2×C139#241811yescharacteristic
399C2×C139#310511yescharacteristic
400C2×C139#312211yescharacteristic
401C2×C139#326411yescharacteristic
402C2×C139#328011yescharacteristic
403C2×C139#329711yescharacteristic
404C2×C139#332511yescharacteristic
405#24897C13911yesmaximal, characteristic, direct product factor, Sylow
406C139#2489711yescharacteristic, direct product factor, Sylow
407C2×#447C2×C13911yescharacteristic
408C2×C4×D8C2×C13911yescharacteristic, complemented
409#2420C2×C13911yescharacteristic, complemented
410D4×C22⋊C4C2×C13911yescharacteristic, complemented
411#2092C2×C13911yescharacteristic, complemented
412#2076C2×C13911yescharacteristic, complemented
413#2054C2×C13911yescharacteristic, complemented
414#2034C2×C13911yescharacteristic, complemented
415#1934C2×C13911yescharacteristic, complemented
416#1923C2×C13911yescharacteristic, complemented
417#1879C2×C13911yescharacteristic, complemented
418#1879C2×C13911yescharacteristic, complemented
419#1864C2×C13911yescharacteristic, complemented
420#1804C2×C13911yescharacteristic, complemented
421#1786C2×C13911yescharacteristic, complemented
422C23×D4C22×C13911yescharacteristic
423C22×D8C22×C13911yescharacteristic
424C22×D8C22×C13911yescharacteristic
425C2×#121C22×C13911yescharacteristic
426C2×C4×D4C22×C13911yescharacteristic
427C2×C4×D4C22×C13911yescharacteristic
428C2×C4×D4C22×C13911yescharacteristic, complemented
429C22×C22⋊C4—21no—
430#447—24no—
431C4×D8—24no—
432C2×#107C22×C13911yescharacteristic, complemented
433C2×#106C22×C13911yescharacteristic, complemented
434C2×C4⋊C8C22×C13911yescharacteristic, complemented
435C2×#102C22×C13911yescharacteristic
436C2×#102C22×C13911yescharacteristic
437C2×#102C22×C13911yescharacteristic
438C2×#102C22×C13911yescharacteristic
439C2×#102C22×C13911yescharacteristic
440C2×#102C22×C13911yescharacteristic
441C2×#102C22×C13911yescharacteristic, complemented
442C2×#102C22×C13911yescharacteristic, complemented
443C2×C22⋊C8C22×C13911yescharacteristic
444C2×C22⋊C8C22×C13911yescharacteristic
445C2×C4×C8C22×C13911yescharacteristic, complemented
446#397—21no—
447#394—21no—
448#390C22×C13911yescharacteristic
449#390C22×C13911yescharacteristic
450#390C22×C13911yescharacteristic, complemented
451#389C22×C13911yescharacteristic, complemented
452#386—21no—
453#386—21no—
454#386—21no—
455#382C22×C13911yescharacteristic, complemented
456#381—21no—
457#380C22×C13911yescharacteristic
458#380C22×C13911yescharacteristic
459#379—21no—
460C4×C22⋊C4C22×C13911yescharacteristic
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—22no—
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4C23×C13911yescharacteristic
477C22×D4C23×C13911yescharacteristic
478C22×D4C23×C13911yescharacteristic
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4C23×C13911yescharacteristic
483C2×D8—22no—
484C2×D8—22no—
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—41no—
488C2×D8D4×C13914yes—
489C22×C8C23×C13911yescharacteristic
490C22×C8C23×C13911yescharacteristic
491C22×C8C23×C13911yescharacteristic
492C22×C8C23×C13911yescharacteristic
493#121—22no—
494#121—41no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—41no—
499C4×D4—41no—
500C4×D4—41no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4C23×C13911yescharacteristic
503C2×C4⋊C4C23×C13911yescharacteristic
504C2×C4⋊C4C23×C13911yescharacteristic
505C2×C4⋊C4C23×C13911yescharacteristic
506C2×C4⋊C4C23×C13911yescharacteristic
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⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—44no—
520C2×C22⋊C4D4×C13911yescharacteristic
521C2×C22⋊C4D4×C13911yescharacteristic
522C2×C42C23×C13911yescharacteristic
523C2×C42C23×C13911yescharacteristic
524#107—22no—
525#106—41no—
526C4⋊C8—41no—
527#102—22no—
528#102—22no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—41no—
534#102—41no—
535C22⋊C8—22no—
536C22⋊C8—41no—
537C4×C8—22no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95D4×C13911yescharacteristic
544#95D4×C13911yescharacteristic
545C24—21no—
546C24—24no—
547C24—21no—
548C24—21no—
549C24—42no—
550C24—42no—
551C24—42no—
552C24—42no—
553C24—81no—
554C24—81no—
555C24C2×D4×C13911yescharacteristic
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
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—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—81no—
579C2×D4C2×D4×C13912yes—
580C2×D4C2×D4×C13912yes—
581C2×D4#41×C13912yes—
582C2×D4#41×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—42no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4C2×D4×C13911yescharacteristic
605C22×C4C2×D4×C13911yescharacteristic
606C22×C4C2×D4×C13911yescharacteristic
607C22×C4C2×D4×C13911yescharacteristic
608C22×C4C2×D4×C13911yescharacteristic
609C22×C4C24×C13911yescharacteristic
610D8—28no—
611D8—44no—
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×C8—21no—
623C2×C8C2×D4×C13912yes—
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—81no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C23—21no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—22no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—22no—
664C23—48no—
665C23—48no—
666C23—41no—
667C23—41no—
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—41no—
681C23—41no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—84no—
687C23#135×C13912yes—
688C23C22×D4×C13911yescharacteristic
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—48no—
697D4—41no—
698D4—41no—
699D4—41no—
700D4—41no—
701D4—84no—
702D4#123×C13914yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
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—84no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4AGL(1,ℤ/8)×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—24no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
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—
779C22#525×C13911yescharacteristic
780C22D42×C13911yescharacteristic
781C22#546×C13911yescharacteristic
782C22C2×#135×C13911yescharacteristic
783C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
784C22#576×C13911yescharacteristic
785C22#576×C13911yescharacteristic
786C4—22no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4C2×#123×C13911yescharacteristic
797C4#538×C13911yescharacteristic
798C4#546×C13911yescharacteristic
799C4#551×C13911yescharacteristic
800C2—42no—
801C2—44no—
802C2—82no—
803C2—82no—
804C2#2418×C13911yescharacteristic
805C2#3105×C13911yescharacteristic
806C2#3122×C13911yescharacteristic
807C2#3264×C13911yescharacteristic
808C2#3280×C13911yescharacteristic
809C2#3297×C13911yescharacteristic
810C2#3325×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#447×C139C2
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
2. C2×C4×D8×C139C2semidirect
3. #2420×C139C2semidirect
4. D4×C22⋊C4×C139C2semidirect
5. #2092×C139C2semidirect
6. #2076×C139C2semidirect
7. #2054×C139C2semidirect
8. #2034×C139C2semidirect
9. #1934×C139C2semidirect
10. #1923×C139C2semidirect
11. #1879×C139C2semidirect
12. #1879×C139C2semidirect
13. #1864×C139C2semidirect
14. #1804×C139C2semidirect
15. #1786×C139C2semidirect
22. C2×C4×D4×C139C22semidirect
26. C2×#107×C139C22semidirect
27. C2×#106×C139C22semidirect
28. C2×C4⋊C8×C139C22semidirect
35. C2×#102×C139C22semidirect
36. C2×#102×C139C22semidirect
39. C2×C4×C8×C139C22semidirect
44. #390×C139C22semidirect
45. #389×C139C22semidirect
49. #382×C139C22semidirect
55. #340×C139C22semidirect
56. #340×C139C22semidirect
57. #340×C139C22semidirect
58. #340×C139C22semidirect
59. #336×C139C22semidirect
60. #336×C139C22semidirect
405. #24897C139direct (N × H)
406. C139#24897direct (N × H)
408. C2×C4×D8C2×C139semidirect
409. #2420C2×C139semidirect
410. D4×C22⋊C4C2×C139semidirect
411. #2092C2×C139semidirect
412. #2076C2×C139semidirect
413. #2054C2×C139semidirect
414. #2034C2×C139semidirect
415. #1934C2×C139semidirect
416. #1923C2×C139semidirect
417. #1879C2×C139semidirect
418. #1879C2×C139semidirect
419. #1864C2×C139semidirect
420. #1804C2×C139semidirect
421. #1786C2×C139semidirect
428. C2×C4×D4C22×C139semidirect
432. C2×#107C22×C139semidirect
433. C2×#106C22×C139semidirect
434. C2×C4⋊C8C22×C139semidirect
441. C2×#102C22×C139semidirect
442. C2×#102C22×C139semidirect
445. C2×C4×C8C22×C139semidirect
450. #390C22×C139semidirect
451. #389C22×C139semidirect
455. #382C22×C139semidirect
461. #340C22×C139semidirect
462. #340C22×C139semidirect
463. #340C22×C139semidirect
464. #340C22×C139semidirect
465. #336C22×C139semidirect
466. #336C22×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1392
C2×C4×D8×C1392
#2420×C1392
D4×C22⋊C4×C1392
#2092×C1392
#2076×C1392
#2054×C1392
#2034×C1392
#1934×C1392
#1923×C1392
#1879×C1392
#1864×C1392
#1804×C1392
#1786×C1392
#24897139