Finite Group Databasebeta

← C139×#24890 #48019486

Subgroups — C139×#24890 #48019486

Order 35584.

1154 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C139C211yesmaximal, characteristic, complemented
2C2×#418×C139C211yesmaximal, characteristic, complemented
3#2408×C139C211yesmaximal, characteristic
4#2354×C139C211yesmaximal, characteristic, complemented
5#2093×C139C211yesmaximal, characteristic, complemented
6#2071×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#1926×C139C211yesmaximal, characteristic, complemented
10#1926×C139C211yesmaximal, characteristic, complemented
11#1875×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
23C2×#117×C139C2211yescharacteristic, complemented
24#482×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×C139—21no—
44#390×C139C2211yescharacteristic
45#390×C139C2211yescharacteristic
46#388×C139—21no—
47#388×C139—21no—
48#384×C139C2211yescharacteristic, complemented
49#380×C139C2211yescharacteristic
50#380×C139C2211yescharacteristic
51#380×C139C2211yescharacteristic, complemented
52#379×C139—21no—
53C4×C4⋊C4×C139—21no—
54C4×C4⋊C4×C139C2211yescharacteristic, complemented
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×C139C2311yescharacteristic
75C23×C4×C139C2311yescharacteristic
76C2×M16×C139—22no—
77C2×M16×C139—22no—
78C2×M16×C139—41no—
79C22×C8×C139C2311yescharacteristic
80C22×C8×C139C2311yescharacteristic
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83#121×C139—22no—
84#121×C139—22no—
85#121×C139—41no—
86#121×C139—41no—
87#120×C139—44no—
88C4×D4×C139—22no—
89C4×D4×C139—22no—
90#117×C139—22no—
91#117×C139—22no—
92#117×C139—41no—
93#117×C139—41no—
94C2×C4⋊C4×C139—21no—
95C2×C4⋊C4×C139—21no—
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×C139—21no—
114C2×C22⋊C4×C139D411yescharacteristic
115C2×C22⋊C4×C139D411yescharacteristic
116C2×C42×C139—21no—
117C2×C42×C139—21no—
118C2×C42×C139—21no—
119C2×C42×C139C2311yescharacteristic
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—22no—
127#102×C139—22no—
128#102×C139—22no—
129#102×C139—41no—
130#102×C139—41no—
131#102×C139D414yescomplemented
132C22⋊C8×C139—22no—
133C22⋊C8×C139—22no—
134C22⋊C8×C139—41no—
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×C139C2×D411yescharacteristic
195C22×C4×C139C2×D411yescharacteristic
196C22×C4×C139C2×D411yescharacteristic
197C22×C4×C139C2×D411yescharacteristic
198C22×C4×C139#4112yes—
199C22×C4×C139#4112yes—
200C22×C4×C139C2411yescharacteristic
201M16×C139—44no—
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—21no—
225C4⋊C4×C139—21no—
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—81no—
239C22⋊C4×C139—81no—
240C22⋊C4×C139—81no—
241C22⋊C4×C139—81no—
242C42×C139—21no—
243C42×C139—21no—
244C42×C139—42no—
245C42×C139—42no—
246C42×C139—42no—
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—22no—
256C23×C139—22no—
257C23×C139—21no—
258C23×C139—21no—
259C23×C139—21no—
260C23×C139—21no—
261C23×C139—21no—
262C23×C139—48no—
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—84no—
276C23×C139—84no—
277C23×C139—84no—
278C23×C139—84no—
279C23×C139—84no—
280C23×C139—84no—
281C23×C139#12312yes—
282C23×C139C22×D411yescharacteristic
283D4×C139—22no—
284D4×C139—22no—
285D4×C139—22no—
286D4×C139—22no—
287D4×C139—44no—
288D4×C139—48no—
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—21no—
298C2×C4×C139—21no—
299C2×C4×C139—22no—
300C2×C4×C139—22no—
301C2×C4×C139—22no—
302C2×C4×C139—22no—
303C2×C4×C139—21no—
304C2×C4×C139—21no—
305C2×C4×C139—22no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
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#12312yes—
332C2×C4×C139AGL(1,ℤ/8)12yes—
333C2×C4×C139C22×D411yescharacteristic
334C2×C4×C139C2×#4111yescharacteristic
335C2×C4×C139C2×#4111yescharacteristic
336C2×C4×C139C2×#4111yescharacteristic
337C2×C4×C139H(5,𝔽2)11yescharacteristic
338C2×C4×C139H(5,𝔽2)11yescharacteristic
339C8×C139—22no—
340C8×C139—41no—
341C8×C139—41no—
342C8×C139—41no—
343C22×C139—22no—
344C22×C139—22no—
345C22×C139—22no—
346C22×C139—41no—
347C22×C139—41no—
348C22×C139—41no—
349C22×C139—41no—
350C22×C139—41no—
351C22×C139—41no—
352C22×C139—41no—
353C22×C139—42no—
354C22×C139—42no—
355C22×C139—41no—
356C22×C139—42no—
357C22×C139—41no—
358C22×C139—42no—
359C22×C139—41no—
360C22×C139—42no—
361C22×C139—41no—
362C22×C139—42no—
363C22×C139—816no—
364C22×C139—81no—
365C22×C139—81no—
366C22×C139—81no—
367C22×C139—81no—
368C22×C139—81no—
369C22×C139—81no—
370C22×C139—81no—
371C22×C139—81no—
372C22×C139C2×#12311yescharacteristic
373C22×C139D4211yescharacteristic
374C22×C139#54611yescharacteristic
375C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C139#57511yescharacteristic
377C22×C139#57611yescharacteristic
378C22×C139#57711yescharacteristic
379C4×C139—22no—
380C4×C139—22no—
381C4×C139—41no—
382C4×C139—41no—
383C4×C139—42no—
384C4×C139—81no—
385C4×C139—81no—
386C4×C139—81no—
387C4×C139—81no—
388C4×C139—81no—
389C4×C139#52511yescharacteristic
390C4×C139#53811yescharacteristic
391C4×C139#54611yescharacteristic
392C4×C139#55111yescharacteristic
393C2×C139—42no—
394C2×C139—81no—
395C2×C139—82no—
396C2×C139—82no—
397C2×C139#241811yescharacteristic
398C2×C139#309411yescharacteristic
399C2×C139#309611yescharacteristic
400C2×C139#326711yescharacteristic
401C2×C139#327411yescharacteristic
402C2×C139#331911yescharacteristic
403C2×C139#332411yescharacteristic
404#24890C13911yesmaximal, characteristic, direct product factor, Sylow
405C139#2489011yescharacteristic, direct product factor, Sylow
406C2×#482C2×C13911yescharacteristic, complemented
407C2×#418C2×C13911yescharacteristic, complemented
408#2408C2×C13911yescharacteristic
409#2354C2×C13911yescharacteristic, complemented
410#2093C2×C13911yescharacteristic, complemented
411#2071C2×C13911yescharacteristic, complemented
412#2034C2×C13911yescharacteristic, complemented
413#2033C2×C13911yescharacteristic, complemented
414#1926C2×C13911yescharacteristic, complemented
415#1926C2×C13911yescharacteristic, complemented
416#1875C2×C13911yescharacteristic, complemented
417#1870C2×C13911yescharacteristic, complemented
418#1854C2×C13911yescharacteristic, complemented
419#1809C2×C13911yescharacteristic, complemented
420#1786C2×C13911yescharacteristic, complemented
421C23×D4C22×C13911yescharacteristic
422C22×M16C22×C13911yescharacteristic
423C2×#121C22×C13911yescharacteristic
424C2×#121C22×C13911yescharacteristic
425C2×#120—21no—
426C2×C4×D4C22×C13911yescharacteristic
427C2×#117C22×C13911yescharacteristic
428C2×#117C22×C13911yescharacteristic, complemented
429#482—24no—
430C2×#107C22×C13911yescharacteristic, complemented
431C2×#107C22×C13911yescharacteristic, complemented
432C2×#106C22×C13911yescharacteristic, complemented
433C2×#106C22×C13911yescharacteristic, complemented
434#418—24no—
435C2×#102C22×C13911yescharacteristic
436C2×#102C22×C13911yescharacteristic
437C2×#102C22×C13911yescharacteristic
438C2×#102C22×C13911yescharacteristic
439C2×#102C22×C13911yescharacteristic
440C2×#102C22×C13911yescharacteristic
441C2×#102C22×C13911yescharacteristic
442C2×#102C22×C13911yescharacteristic
443C2×C22⋊C8C22×C13911yescharacteristic
444C2×C22⋊C8C22×C13911yescharacteristic, complemented
445C2×C22⋊C8C22×C13911yescharacteristic, complemented
446#394—21no—
447#392—21no—
448#390—21no—
449#390C22×C13911yescharacteristic
450#390C22×C13911yescharacteristic
451#388—21no—
452#388—21no—
453#384C22×C13911yescharacteristic, complemented
454#380C22×C13911yescharacteristic
455#380C22×C13911yescharacteristic
456#380C22×C13911yescharacteristic, complemented
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C22×C13911yescharacteristic, complemented
460#340C22×C13911yescharacteristic, complemented
461#340C22×C13911yescharacteristic, complemented
462#340C22×C13911yescharacteristic, complemented
463#340C22×C13911yescharacteristic, complemented
464#336C22×C13911yescharacteristic, complemented
465#336C22×C13911yescharacteristic, complemented
466C25—21no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—41no—
475C22×D4—41no—
476C22×D4D4×C13911yescharacteristic
477C22×D4C23×C13911yescharacteristic
478C22×D4C23×C13911yescharacteristic
479C23×C4C23×C13911yescharacteristic
480C23×C4C23×C13911yescharacteristic
481C2×M16—22no—
482C2×M16—22no—
483C2×M16—41no—
484C22×C8C23×C13911yescharacteristic
485C22×C8C23×C13911yescharacteristic
486C22×C8C23×C13911yescharacteristic
487C22×C8C23×C13911yescharacteristic
488#121—22no—
489#121—22no—
490#121—41no—
491#121—41no—
492#120—44no—
493C4×D4—22no—
494C4×D4—22no—
495#117—22no—
496#117—22no—
497#117—41no—
498#117—41no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4D4×C13911yescharacteristic
502C2×C4⋊C4C23×C13911yescharacteristic
503C2×C4⋊C4C23×C13911yescharacteristic
504C2×C4⋊C4C23×C13911yescharacteristic
505C2×C4⋊C4C23×C13911yescharacteristic
506C2×C4⋊C4C23×C13911yescharacteristic
507C2×C4⋊C4C23×C13911yescharacteristic
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⋊C4D4×C13911yescharacteristic
520C2×C22⋊C4D4×C13911yescharacteristic
521C2×C42—21no—
522C2×C42—21no—
523C2×C42—21no—
524C2×C42C23×C13911yescharacteristic
525#107—22no—
526#107—41no—
527#106—22no—
528#106—41no—
529#102—22no—
530#102—22no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—41no—
535#102—41no—
536#102D4×C13914yescomplemented
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—41no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24—21no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—42no—
550C24—42no—
551C24—81no—
552C24—81no—
553C24C2×D4×C13911yescharacteristic
554C24C2×D4×C13911yescharacteristic
555C2×D4—28no—
556C2×D4—22no—
557C2×D4—22no—
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—44no—
569C2×D4—44no—
570C2×D4—41no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—81no—
580C2×D4—81no—
581C2×D4C2×D4×C13912yes—
582C2×D4#41×C13912yes—
583C22×C4—21no—
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×C4C2×D4×C13911yescharacteristic
600C22×C4C2×D4×C13911yescharacteristic
601C22×C4C2×D4×C13911yescharacteristic
602C22×C4C2×D4×C13911yescharacteristic
603C22×C4#41×C13912yes—
604C22×C4#41×C13912yes—
605C22×C4C24×C13911yescharacteristic
606M16—44no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8C2×D4×C13912yes—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—42no—
632C4⋊C4—81no—
633C4⋊C4C2×D4×C13912yes—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C22⋊C4—81no—
646C22⋊C4—81no—
647C42—21no—
648C42—21no—
649C42—42no—
650C42—42no—
651C42—42no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
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—
687C23C22×D4×C13911yescharacteristic
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—44no—
693D4—48no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—41no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
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#123×C13912yes—
737C2×C4AGL(1,ℤ/8)×C13912yes—
738C2×C4C22×D4×C13911yescharacteristic
739C2×C4C2×#41×C13911yescharacteristic
740C2×C4C2×#41×C13911yescharacteristic
741C2×C4C2×#41×C13911yescharacteristic
742C2×C4H(5,𝔽2)×C13911yescharacteristic
743C2×C4H(5,𝔽2)×C13911yescharacteristic
744C8—22no—
745C8—41no—
746C8—41no—
747C8—41no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—42no—
757C22—41no—
758C22—42no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—816no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22C2×#123×C13911yescharacteristic
778C22D42×C13911yescharacteristic
779C22#546×C13911yescharacteristic
780C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
781C22#575×C13911yescharacteristic
782C22#576×C13911yescharacteristic
783C22#577×C13911yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—42no—
789C4—81no—
790C4—81no—
791C4—81no—
792C4—81no—
793C4—81no—
794C4#525×C13911yescharacteristic
795C4#538×C13911yescharacteristic
796C4#546×C13911yescharacteristic
797C4#551×C13911yescharacteristic
798C2—42no—
799C2—81no—
800C2—82no—
801C2—82no—
802C2#2418×C13911yescharacteristic
803C2#3094×C13911yescharacteristic
804C2#3096×C13911yescharacteristic
805C2#3267×C13911yescharacteristic
806C2#3274×C13911yescharacteristic
807C2#3319×C13911yescharacteristic
808C2#3324×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×#482×C139C2semidirect
2. C2×#418×C139C2semidirect
4. #2354×C139C2semidirect
5. #2093×C139C2semidirect
6. #2071×C139C2semidirect
7. #2034×C139C2semidirect
8. #2033×C139C2semidirect
9. #1926×C139C2semidirect
10. #1926×C139C2semidirect
11. #1875×C139C2semidirect
12. #1870×C139C2semidirect
13. #1854×C139C2semidirect
14. #1809×C139C2semidirect
15. #1786×C139C2semidirect
23. C2×#117×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. #384×C139C22semidirect
51. #380×C139C22semidirect
54. C4×C4⋊C4×C139C22semidirect
55. #340×C139C22semidirect
56. #340×C139C22semidirect
57. #340×C139C22semidirect
58. #340×C139C22semidirect
59. #336×C139C22semidirect
60. #336×C139C22semidirect
131. #102×C139D4semidirect
404. #24890C139direct (N × H)
405. C139#24890direct (N × H)
406. C2×#482C2×C139semidirect
407. C2×#418C2×C139semidirect
409. #2354C2×C139semidirect
410. #2093C2×C139semidirect
411. #2071C2×C139semidirect
412. #2034C2×C139semidirect
413. #2033C2×C139semidirect
414. #1926C2×C139semidirect
415. #1926C2×C139semidirect
416. #1875C2×C139semidirect
417. #1870C2×C139semidirect
418. #1854C2×C139semidirect
419. #1809C2×C139semidirect
420. #1786C2×C139semidirect
428. C2×#117C22×C139semidirect
430. C2×#107C22×C139semidirect
431. C2×#107C22×C139semidirect
432. C2×#106C22×C139semidirect
433. C2×#106C22×C139semidirect
444. C2×C22⋊C8C22×C139semidirect
445. C2×C22⋊C8C22×C139semidirect
453. #384C22×C139semidirect
456. #380C22×C139semidirect
459. C4×C4⋊C4C22×C139semidirect
460. #340C22×C139semidirect
461. #340C22×C139semidirect
462. #340C22×C139semidirect
463. #340C22×C139semidirect
464. #336C22×C139semidirect
465. #336C22×C139semidirect
536. #102D4×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×#418×C1392
#2408×C1392
#2354×C1392
#2093×C1392
#2071×C1392
#2034×C1392
#2033×C1392
#1926×C1392
#1875×C1392
#1870×C1392
#1854×C1392
#1809×C1392
#1786×C1392
#24890139