Finite Group Databasebeta

← C139×#24424 #48019020

Subgroups — C139×#24424 #48019020

Order 35584.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C139C211yesmaximal, characteristic, complemented
2C2×#466×C139C211yesmaximal, characteristic, complemented
3C2×#447×C139C211yesmaximal, characteristic, complemented
4C2×#447×C139C211yesmaximal, characteristic, complemented
5C22×#102×C139C211yesmaximal, characteristic, complemented
6#2416×C139C211yesmaximal, characteristic, complemented
7#2041×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#2011×C139C211yesmaximal, characteristic, complemented
10#1999×C139C211yesmaximal, characteristic, complemented
11#1879×C139C211yesmaximal, characteristic, complemented
12#1874×C139C211yesmaximal, characteristic, complemented
13#1869×C139C211yesmaximal, characteristic, complemented
14#1862×C139C211yesmaximal, characteristic, complemented
15#1786×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139—21no—
17C23×D4×C139C2211yescharacteristic
18C23×D4×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic
20C22×D8×C139C2211yescharacteristic, complemented
21C22×D8×C139C2211yescharacteristic, complemented
22C23×C8×C139C2211yescharacteristic, complemented
23D42×C139—24no—
24D42×C139—24no—
25C2×#127×C139C2211yescharacteristic
26C2×#121×C139—21no—
27C2×#121×C139—21no—
28C2×#121×C139C2211yescharacteristic
29C2×#121×C139C2211yescharacteristic
30C2×#121×C139C2211yescharacteristic, complemented
31C2×#121×C139C2211yescharacteristic, complemented
32C2×#120×C139—21no—
33C2×#120×C139—21no—
34C2×C4×D4×C139C2211yescharacteristic
35C2×C4×D4×C139C2211yescharacteristic
36C22×C4⋊C4×C139C2211yescharacteristic, complemented
37#466×C139—24no—
38#447×C139—24no—
39#447×C139—24no—
40C2×#107×C139C2211yescharacteristic, complemented
41C2×#102×C139—24no—
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic, complemented
46C2×#102×C139C2211yescharacteristic, complemented
47C2×#102×C139C2211yescharacteristic, complemented
48C2×#102×C139C2211yescharacteristic, complemented
49C2×#102×C139C2211yescharacteristic, complemented
50C2×#102×C139C2211yescharacteristic, complemented
51C2×#102×C139C2211yescharacteristic, complemented
52C2×C22⋊C8×C139C2211yescharacteristic, complemented
53C2×C22⋊C8×C139C2211yescharacteristic, complemented
54C2×C22⋊C8×C139C2211yescharacteristic, complemented
55#396×C139—21no—
56#394×C139—21no—
57#390×C139C2211yescharacteristic, complemented
58#389×C139C2211yescharacteristic, complemented
59#386×C139—21no—
60#380×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63#336×C139C2211yescharacteristic, complemented
64#336×C139C2211yescharacteristic, complemented
65C25×C139—21no—
66C25×C139—21no—
67C22×D4×C139—22no—
68C22×D4×C139—22no—
69C22×D4×C139—28no—
70C22×D4×C139—21no—
71C22×D4×C139—21no—
72C22×D4×C139—22no—
73C22×D4×C139—22no—
74C22×D4×C139—22no—
75C22×D4×C139—22no—
76C22×D4×C139—21no—
77C22×D4×C139—21no—
78C22×D4×C139—21no—
79C22×D4×C139—21no—
80C22×D4×C139—21no—
81C22×D4×C139—22no—
82C22×D4×C139—21no—
83C22×D4×C139—41no—
84C22×D4×C139—41no—
85C22×D4×C139—41no—
86C22×D4×C139—41no—
87C22×D4×C139—44no—
88C22×D4×C139—44no—
89C22×D4×C139D411yescharacteristic
90C22×D4×C139D414yescomplemented
91C22×D4×C139C2311yescharacteristic
92C22×D4×C139C2311yescharacteristic
93C22×D4×C139C2311yescharacteristic
94C22×D4×C139C2311yescharacteristic
95C23×C4×C139—21no—
96C23×C4×C139—21no—
97C23×C4×C139C2311yescharacteristic
98C23×C4×C139C2311yescharacteristic
99C2×D8×C139—22no—
100C2×D8×C139—22no—
101C2×D8×C139—22no—
102C2×D8×C139—22no—
103C2×D8×C139—22no—
104C2×D8×C139—22no—
105C2×D8×C139—41no—
106C2×D8×C139—41no—
107C2×D8×C139—41no—
108C22×C8×C139—22no—
109C22×C8×C139—22no—
110C22×C8×C139—41no—
111C22×C8×C139C2311yescharacteristic
112C22×C8×C139C2311yescharacteristic
113C22×C8×C139C2311yescharacteristic
114C22×C8×C139C2311yescharacteristic
115#127×C139—22no—
116#127×C139—22no—
117#121×C139—28no—
118#121×C139—22no—
119#121×C139—22no—
120#121×C139—22no—
121#121×C139—22no—
122#121×C139—22no—
123#121×C139—22no—
124#121×C139—41no—
125#121×C139—44no—
126#121×C139D414yescomplemented
127#120×C139—28no—
128#120×C139—28no—
129C4×D4×C139—22no—
130C4×D4×C139—22no—
131C4×D4×C139—22no—
132C4×D4×C139—22no—
133C2×C4⋊C4×C139—22no—
134C2×C4⋊C4×C139—21no—
135C2×C4⋊C4×C139—21no—
136C2×C4⋊C4×C139—41no—
137C2×C4⋊C4×C139D411yescharacteristic
138C2×C4⋊C4×C139C2311yescharacteristic
139C2×C4⋊C4×C139C2311yescharacteristic
140C2×C4⋊C4×C139C2311yescharacteristic
141C2×C4⋊C4×C139C2311yescharacteristic
142C2×C22⋊C4×C139—21no—
143C2×C22⋊C4×C139—21no—
144C2×C22⋊C4×C139—21no—
145C2×C22⋊C4×C139—21no—
146C2×C22⋊C4×C139—21no—
147C2×C22⋊C4×C139—21no—
148C2×C22⋊C4×C139—21no—
149C2×C22⋊C4×C139—21no—
150C2×C22⋊C4×C139D411yescharacteristic
151C2×C22⋊C4×C139D411yescharacteristic
152C2×C42×C139C2311yescharacteristic
153#107×C139—22no—
154#102×C139—22no—
155#102×C139—22no—
156#102×C139—22no—
157#102×C139—22no—
158#102×C139—22no—
159#102×C139—22no—
160#102×C139—22no—
161#102×C139—22no—
162#102×C139—41no—
163#102×C139D414yescomplemented
164C22⋊C8×C139—22no—
165C22⋊C8×C139—22no—
166C22⋊C8×C139—41no—
167#95×C139—21no—
168#95×C139—21no—
169C24×C139—21no—
170C24×C139—24no—
171C24×C139—21no—
172C24×C139—21no—
173C24×C139—24no—
174C24×C139—21no—
175C24×C139—42no—
176C24×C139—42no—
177C24×C139—42no—
178C24×C139—42no—
179C24×C139—42no—
180C24×C139—42no—
181C24×C139—42no—
182C24×C139—42no—
183C24×C139—81no—
184C24×C139—81no—
185C24×C139—81no—
186C24×C139—81no—
187C24×C139C2×D411yescharacteristic
188C24×C139C2×D411yescharacteristic
189C2×D4×C139—22no—
190C2×D4×C139—22no—
191C2×D4×C139—28no—
192C2×D4×C139—24no—
193C2×D4×C139—24no—
194C2×D4×C139—24no—
195C2×D4×C139—24no—
196C2×D4×C139—24no—
197C2×D4×C139—24no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—21no—
208C2×D4×C139—21no—
209C2×D4×C139—21no—
210C2×D4×C139—21no—
211C2×D4×C139—21no—
212C2×D4×C139—21no—
213C2×D4×C139—21no—
214C2×D4×C139—21no—
215C2×D4×C139—21no—
216C2×D4×C139—21no—
217C2×D4×C139—44no—
218C2×D4×C139—44no—
219C2×D4×C139—44no—
220C2×D4×C139—42no—
221C2×D4×C139—42no—
222C2×D4×C139—42no—
223C2×D4×C139—42no—
224C2×D4×C139—42no—
225C2×D4×C139—42no—
226C2×D4×C139—44no—
227C2×D4×C139—44no—
228C2×D4×C139—432no—
229C2×D4×C139—44no—
230C2×D4×C139—42no—
231C2×D4×C139—42no—
232C2×D4×C139—42no—
233C2×D4×C139—42no—
234C2×D4×C139—44no—
235C2×D4×C139—42no—
236C2×D4×C139—42no—
237C2×D4×C139—42no—
238C2×D4×C139—42no—
239C2×D4×C139—42no—
240C2×D4×C139—81no—
241C2×D4×C139—81no—
242C2×D4×C139—81no—
243C2×D4×C139D814yescomplemented
244C2×D4×C139C2×D412yes—
245C2×D4×C139C2×D412yes—
246C2×D4×C139C2×D412yes—
247C2×D4×C139C2×D412yes—
248C2×D4×C139#4112yes—
249C22×C4×C139—21no—
250C22×C4×C139—21no—
251C22×C4×C139—21no—
252C22×C4×C139—21no—
253C22×C4×C139—24no—
254C22×C4×C139—21no—
255C22×C4×C139—21no—
256C22×C4×C139—21no—
257C22×C4×C139—21no—
258C22×C4×C139—21no—
259C22×C4×C139—21no—
260C22×C4×C139—21no—
261C22×C4×C139—21no—
262C22×C4×C139—21no—
263C22×C4×C139—21no—
264C22×C4×C139—42no—
265C22×C4×C139—42no—
266C22×C4×C139—42no—
267C22×C4×C139—42no—
268C22×C4×C139—81no—
269C22×C4×C139C2×D411yescharacteristic
270C22×C4×C139C2×D411yescharacteristic
271C22×C4×C139C2×D411yescharacteristic
272C22×C4×C139C2×D412yes—
273C22×C4×C139C2×D412yes—
274C22×C4×C139C2×D411yescharacteristic
275C22×C4×C139C2411yescharacteristic
276D8×C139—44no—
277D8×C139—44no—
278D8×C139—44no—
279C2×C8×C139—21no—
280C2×C8×C139—21no—
281C2×C8×C139—21no—
282C2×C8×C139—21no—
283C2×C8×C139—21no—
284C2×C8×C139—21no—
285C2×C8×C139—21no—
286C2×C8×C139—21no—
287C2×C8×C139—21no—
288C2×C8×C139—21no—
289C2×C8×C139—21no—
290C2×C8×C139—44no—
291C2×C8×C139C2×D412yescomplemented
292C4⋊C4×C139—22no—
293C4⋊C4×C139—21no—
294C4⋊C4×C139—21no—
295C4⋊C4×C139—21no—
296C4⋊C4×C139—21no—
297C4⋊C4×C139—21no—
298C4⋊C4×C139—21no—
299C4⋊C4×C139—42no—
300C4⋊C4×C139—42no—
301C4⋊C4×C139C2×D412yes—
302C4⋊C4×C139C2×D412yescomplemented
303C22⋊C4×C139—24no—
304C22⋊C4×C139—24no—
305C22⋊C4×C139—22no—
306C22⋊C4×C139—24no—
307C22⋊C4×C139—22no—
308C22⋊C4×C139—42no—
309C22⋊C4×C139—42no—
310C22⋊C4×C139—42no—
311C22⋊C4×C139—42no—
312C22⋊C4×C139—81no—
313C42×C139—21no—
314C42×C139—21no—
315C23×C139—21no—
316C23×C139—21no—
317C23×C139—21no—
318C23×C139—21no—
319C23×C139—21no—
320C23×C139—22no—
321C23×C139—21no—
322C23×C139—22no—
323C23×C139—21no—
324C23×C139—22no—
325C23×C139—21no—
326C23×C139—21no—
327C23×C139—21no—
328C23×C139—22no—
329C23×C139—22no—
330C23×C139—48no—
331C23×C139—48no—
332C23×C139—48no—
333C23×C139—41no—
334C23×C139—41no—
335C23×C139—41no—
336C23×C139—41no—
337C23×C139—41no—
338C23×C139—41no—
339C23×C139—41no—
340C23×C139—41no—
341C23×C139—41no—
342C23×C139—41no—
343C23×C139—41no—
344C23×C139—41no—
345C23×C139—41no—
346C23×C139—41no—
347C23×C139—41no—
348C23×C139—41no—
349C23×C139—48no—
350C23×C139—41no—
351C23×C139—41no—
352C23×C139—41no—
353C23×C139—41no—
354C23×C139—41no—
355C23×C139—41no—
356C23×C139—41no—
357C23×C139—84no—
358C23×C139—84no—
359C23×C139—84no—
360C23×C139—84no—
361C23×C139—84no—
362C23×C139—84no—
363C23×C139—84no—
364C23×C139—84no—
365C23×C139—84no—
366C23×C139—84no—
367C23×C139#12012yes—
368C23×C139C2×D812yes—
369C23×C139C2×D812yes—
370C23×C139AGL(1,ℤ/8)12yes—
371C23×C139C22×D411yescharacteristic
372D4×C139—28no—
373D4×C139—22no—
374D4×C139—22no—
375D4×C139—22no—
376D4×C139—22no—
377D4×C139—22no—
378D4×C139—22no—
379D4×C139—22no—
380D4×C139—48no—
381D4×C139—48no—
382D4×C139—48no—
383D4×C139—48no—
384D4×C139—48no—
385D4×C139—41no—
386D4×C139—41no—
387D4×C139—41no—
388D4×C139—41no—
389D4×C139—41no—
390D4×C139—41no—
391D4×C139—41no—
392D4×C139—41no—
393D4×C139—84no—
394D4×C139—84no—
395D4×C139—84no—
396D4×C139#12114yescomplemented
397C2×C4×C139—21no—
398C2×C4×C139—21no—
399C2×C4×C139—21no—
400C2×C4×C139—21no—
401C2×C4×C139—22no—
402C2×C4×C139—22no—
403C2×C4×C139—22no—
404C2×C4×C139—22no—
405C2×C4×C139—21no—
406C2×C4×C139—21no—
407C2×C4×C139—22no—
408C2×C4×C139—21no—
409C2×C4×C139—22no—
410C2×C4×C139—21no—
411C2×C4×C139—21no—
412C2×C4×C139—21no—
413C2×C4×C139—48no—
414C2×C4×C139—41no—
415C2×C4×C139—41no—
416C2×C4×C139—41no—
417C2×C4×C139—41no—
418C2×C4×C139—41no—
419C2×C4×C139—41no—
420C2×C4×C139—41no—
421C2×C4×C139—41no—
422C2×C4×C139—41no—
423C2×C4×C139—41no—
424C2×C4×C139—41no—
425C2×C4×C139—41no—
426C2×C4×C139—41no—
427C2×C4×C139—41no—
428C2×C4×C139—84no—
429C2×C4×C139#12012yes—
430C2×C4×C139C2×D812yes—
431C2×C4×C139C22×D411yescharacteristic
432C2×C4×C139C22×D411yescharacteristic
433C2×C4×C139C22×D411yescharacteristic
434C2×C4×C139C2×#4111yescharacteristic
435C2×C4×C139H(5,𝔽2)11yescharacteristic
436C2×C4×C139H(5,𝔽2)11yescharacteristic
437C8×C139—22no—
438C8×C139—41no—
439C8×C139—41no—
440C8×C139—41no—
441C22×C139—22no—
442C22×C139—22no—
443C22×C139—22no—
444C22×C139—22no—
445C22×C139—22no—
446C22×C139—22no—
447C22×C139—24no—
448C22×C139—22no—
449C22×C139—22no—
450C22×C139—22no—
451C22×C139—41no—
452C22×C139—42no—
453C22×C139—41no—
454C22×C139—42no—
455C22×C139—41no—
456C22×C139—42no—
457C22×C139—42no—
458C22×C139—42no—
459C22×C139—41no—
460C22×C139—42no—
461C22×C139—42no—
462C22×C139—42no—
463C22×C139—42no—
464C22×C139—42no—
465C22×C139—42no—
466C22×C139—42no—
467C22×C139—816no—
468C22×C139—816no—
469C22×C139—81no—
470C22×C139—81no—
471C22×C139—81no—
472C22×C139—81no—
473C22×C139—81no—
474C22×C139—81no—
475C22×C139—81no—
476C22×C139—81no—
477C22×C139—81no—
478C22×C139—81no—
479C22×C139—81no—
480C22×C139—81no—
481C22×C139—81no—
482C22×C139—81no—
483C22×C139—81no—
484C22×C139#44714yescomplemented
485C22×C139C2×#12011yescharacteristic
486C22×C139D4211yescharacteristic
487C22×C139#54611yescharacteristic
488C22×C139C22×D811yescharacteristic
489C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
490C22×C139#57611yescharacteristic
491C22×C139#57711yescharacteristic
492C4×C139—22no—
493C4×C139—22no—
494C4×C139—41no—
495C4×C139—42no—
496C4×C139—41no—
497C4×C139—42no—
498C4×C139—81no—
499C4×C139—81no—
500C4×C139C2×#12111yescharacteristic
501C4×C139#53411yescharacteristic
502C4×C139D4211yescharacteristic
503C4×C139#54611yescharacteristic
504C2×C139—24no—
505C2×C139—42no—
506C2×C139—44no—
507C2×C139—82no—
508C2×C139—82no—
509C2×C139—161no—
510C2×C139#241011yescharacteristic
511C2×C139C2×#44711yescharacteristic
512C2×C139#301211yescharacteristic
513C2×C139#326511yescharacteristic
514C2×C139D4×D811yescharacteristic
515C2×C139#329411yescharacteristic
516C2×C139#331811yescharacteristic
517#24424C13911yesmaximal, characteristic, direct product factor, Sylow
518C139#2442411yescharacteristic, direct product factor, Sylow
519C2×D42C2×C13911yescharacteristic, complemented
520C2×#466C2×C13911yescharacteristic, complemented
521C2×#447C2×C13911yescharacteristic, complemented
522C2×#447C2×C13911yescharacteristic, complemented
523C22×#102C2×C13911yescharacteristic, complemented
524#2416C2×C13911yescharacteristic, complemented
525#2041C2×C13911yescharacteristic, complemented
526#2033C2×C13911yescharacteristic, complemented
527#2011C2×C13911yescharacteristic, complemented
528#1999C2×C13911yescharacteristic, complemented
529#1879C2×C13911yescharacteristic, complemented
530#1874C2×C13911yescharacteristic, complemented
531#1869C2×C13911yescharacteristic, complemented
532#1862C2×C13911yescharacteristic, complemented
533#1786C2×C13911yescharacteristic, complemented
534C23×D4—21no—
535C23×D4C22×C13911yescharacteristic
536C23×D4C22×C13911yescharacteristic
537C22×D8C22×C13911yescharacteristic
538C22×D8C22×C13911yescharacteristic, complemented
539C22×D8C22×C13911yescharacteristic, complemented
540C23×C8C22×C13911yescharacteristic, complemented
541D42—24no—
542D42—24no—
543C2×#127C22×C13911yescharacteristic
544C2×#121—21no—
545C2×#121—21no—
546C2×#121C22×C13911yescharacteristic
547C2×#121C22×C13911yescharacteristic
548C2×#121C22×C13911yescharacteristic, complemented
549C2×#121C22×C13911yescharacteristic, complemented
550C2×#120—21no—
551C2×#120—21no—
552C2×C4×D4C22×C13911yescharacteristic
553C2×C4×D4C22×C13911yescharacteristic
554C22×C4⋊C4C22×C13911yescharacteristic, complemented
555#466—24no—
556#447—24no—
557#447—24no—
558C2×#107C22×C13911yescharacteristic, complemented
559C2×#102—24no—
560C2×#102C22×C13911yescharacteristic
561C2×#102C22×C13911yescharacteristic
562C2×#102C22×C13911yescharacteristic
563C2×#102C22×C13911yescharacteristic, complemented
564C2×#102C22×C13911yescharacteristic, complemented
565C2×#102C22×C13911yescharacteristic, complemented
566C2×#102C22×C13911yescharacteristic, complemented
567C2×#102C22×C13911yescharacteristic, complemented
568C2×#102C22×C13911yescharacteristic, complemented
569C2×#102C22×C13911yescharacteristic, complemented
570C2×C22⋊C8C22×C13911yescharacteristic, complemented
571C2×C22⋊C8C22×C13911yescharacteristic, complemented
572C2×C22⋊C8C22×C13911yescharacteristic, complemented
573#396—21no—
574#394—21no—
575#390C22×C13911yescharacteristic, complemented
576#389C22×C13911yescharacteristic, complemented
577#386—21no—
578#380C22×C13911yescharacteristic, complemented
579#340C22×C13911yescharacteristic, complemented
580#340C22×C13911yescharacteristic, complemented
581#336C22×C13911yescharacteristic, complemented
582#336C22×C13911yescharacteristic, complemented
583C25—21no—
584C25—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—28no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4—41no—
604C22×D4—41no—
605C22×D4—44no—
606C22×D4—44no—
607C22×D4D4×C13911yescharacteristic
608C22×D4D4×C13914yescomplemented
609C22×D4C23×C13911yescharacteristic
610C22×D4C23×C13911yescharacteristic
611C22×D4C23×C13911yescharacteristic
612C22×D4C23×C13911yescharacteristic
613C23×C4—21no—
614C23×C4—21no—
615C23×C4C23×C13911yescharacteristic
616C23×C4C23×C13911yescharacteristic
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×D8—22no—
621C2×D8—22no—
622C2×D8—22no—
623C2×D8—41no—
624C2×D8—41no—
625C2×D8—41no—
626C22×C8—22no—
627C22×C8—22no—
628C22×C8—41no—
629C22×C8C23×C13911yescharacteristic
630C22×C8C23×C13911yescharacteristic
631C22×C8C23×C13911yescharacteristic
632C22×C8C23×C13911yescharacteristic
633#127—22no—
634#127—22no—
635#121—28no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—22no—
640#121—22no—
641#121—22no—
642#121—41no—
643#121—44no—
644#121D4×C13914yescomplemented
645#120—28no—
646#120—28no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4D4×C13911yescharacteristic
656C2×C4⋊C4C23×C13911yescharacteristic
657C2×C4⋊C4C23×C13911yescharacteristic
658C2×C4⋊C4C23×C13911yescharacteristic
659C2×C4⋊C4C23×C13911yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4D4×C13911yescharacteristic
669C2×C22⋊C4D4×C13911yescharacteristic
670C2×C42C23×C13911yescharacteristic
671#107—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—41no—
681#102D4×C13914yescomplemented
682C22⋊C8—22no—
683C22⋊C8—22no—
684C22⋊C8—41no—
685#95—21no—
686#95—21no—
687C24—21no—
688C24—24no—
689C24—21no—
690C24—21no—
691C24—24no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24—42no—
701C24—81no—
702C24—81no—
703C24—81no—
704C24—81no—
705C24C2×D4×C13911yescharacteristic
706C24C2×D4×C13911yescharacteristic
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—432no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D4D8×C13914yescomplemented
762C2×D4C2×D4×C13912yes—
763C2×D4C2×D4×C13912yes—
764C2×D4C2×D4×C13912yes—
765C2×D4C2×D4×C13912yes—
766C2×D4#41×C13912yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—81no—
787C22×C4C2×D4×C13911yescharacteristic
788C22×C4C2×D4×C13911yescharacteristic
789C22×C4C2×D4×C13911yescharacteristic
790C22×C4C2×D4×C13912yes—
791C22×C4C2×D4×C13912yes—
792C22×C4C2×D4×C13911yescharacteristic
793C22×C4C24×C13911yescharacteristic
794D8—44no—
795D8—44no—
796D8—44no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—44no—
809C2×C8C2×D4×C13912yescomplemented
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C13912yes—
820C4⋊C4C2×D4×C13912yescomplemented
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C42—21no—
832C42—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—22no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—48no—
849C23—48no—
850C23—48no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—48no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23—84no—
881C23—84no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23#120×C13912yes—
886C23C2×D8×C13912yes—
887C23C2×D8×C13912yes—
888C23AGL(1,ℤ/8)×C13912yes—
889C23C22×D4×C13911yescharacteristic
890D4—28no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—22no—
898D4—48no—
899D4—48no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—84no—
912D4—84no—
913D4—84no—
914D4#121×C13914yescomplemented
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—48no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—84no—
947C2×C4#120×C13912yes—
948C2×C4C2×D8×C13912yes—
949C2×C4C22×D4×C13911yescharacteristic
950C2×C4C22×D4×C13911yescharacteristic
951C2×C4C22×D4×C13911yescharacteristic
952C2×C4C2×#41×C13911yescharacteristic
953C2×C4H(5,𝔽2)×C13911yescharacteristic
954C2×C4H(5,𝔽2)×C13911yescharacteristic
955C8—22no—
956C8—41no—
957C8—41no—
958C8—41no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—24no—
968C22—22no—
969C22—42no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—41no—
974C22—42no—
975C22—41no—
976C22—42no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—816no—
986C22—816no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—81no—
997C22—81no—
998C22—81no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22#447×C13914yescomplemented
1003C22C2×#120×C13911yescharacteristic
1004C22D42×C13911yescharacteristic
1005C22#546×C13911yescharacteristic
1006C22C22×D8×C13911yescharacteristic
1007C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
1008C22#576×C13911yescharacteristic
1009C22#577×C13911yescharacteristic
1010C4—22no—
1011C4—22no—
1012C4—42no—
1013C4—41no—
1014C4—42no—
1015C4—41no—
1016C4—81no—
1017C4—81no—
1018C4C2×#121×C13911yescharacteristic
1019C4#534×C13911yescharacteristic
1020C4D42×C13911yescharacteristic
1021C4#546×C13911yescharacteristic
1022C2—24no—
1023C2—42no—
1024C2—44no—
1025C2—82no—
1026C2—82no—
1027C2—161no—
1028C2#2410×C13911yescharacteristic
1029C2C2×#447×C13911yescharacteristic
1030C2#3012×C13911yescharacteristic
1031C2#3265×C13911yescharacteristic
1032C2D4×D8×C13911yescharacteristic
1033C2#3294×C13911yescharacteristic
1034C2#3318×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
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×D42×C139C2semidirect
2. C2×#466×C139C2semidirect
3. C2×#447×C139C2semidirect
4. C2×#447×C139C2semidirect
5. C22×#102×C139C2semidirect
6. #2416×C139C2semidirect
7. #2041×C139C2semidirect
8. #2033×C139C2semidirect
9. #2011×C139C2semidirect
10. #1999×C139C2semidirect
11. #1879×C139C2semidirect
12. #1874×C139C2semidirect
13. #1869×C139C2semidirect
14. #1862×C139C2semidirect
15. #1786×C139C2semidirect
20. C22×D8×C139C22semidirect
21. C22×D8×C139C22semidirect
22. C23×C8×C139C22semidirect
30. C2×#121×C139C22semidirect
31. C2×#121×C139C22semidirect
36. C22×C4⋊C4×C139C22semidirect
40. C2×#107×C139C22semidirect
45. C2×#102×C139C22semidirect
46. C2×#102×C139C22semidirect
47. C2×#102×C139C22semidirect
48. C2×#102×C139C22semidirect
49. C2×#102×C139C22semidirect
50. C2×#102×C139C22semidirect
51. C2×#102×C139C22semidirect
52. C2×C22⋊C8×C139C22semidirect
53. C2×C22⋊C8×C139C22semidirect
54. C2×C22⋊C8×C139C22semidirect
57. #390×C139C22semidirect
58. #389×C139C22semidirect
60. #380×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
63. #336×C139C22semidirect
64. #336×C139C22semidirect
90. C22×D4×C139D4semidirect
126. #121×C139D4semidirect
163. #102×C139D4semidirect
243. C2×D4×C139D8semidirect
291. C2×C8×C139C2×D4semidirect
302. C4⋊C4×C139C2×D4semidirect
396. D4×C139#121semidirect
484. C22×C139#447semidirect
517. #24424C139direct (N × H)
518. C139#24424direct (N × H)
519. C2×D42C2×C139semidirect
520. C2×#466C2×C139semidirect
521. C2×#447C2×C139semidirect
522. C2×#447C2×C139semidirect
523. C22×#102C2×C139semidirect
524. #2416C2×C139semidirect
525. #2041C2×C139semidirect
526. #2033C2×C139semidirect
527. #2011C2×C139semidirect
528. #1999C2×C139semidirect
529. #1879C2×C139semidirect
530. #1874C2×C139semidirect
531. #1869C2×C139semidirect
532. #1862C2×C139semidirect
533. #1786C2×C139semidirect
538. C22×D8C22×C139semidirect
539. C22×D8C22×C139semidirect
540. C23×C8C22×C139semidirect
548. C2×#121C22×C139semidirect
549. C2×#121C22×C139semidirect
554. C22×C4⋊C4C22×C139semidirect
558. C2×#107C22×C139semidirect
563. C2×#102C22×C139semidirect
564. C2×#102C22×C139semidirect
565. C2×#102C22×C139semidirect
566. C2×#102C22×C139semidirect
567. C2×#102C22×C139semidirect
568. C2×#102C22×C139semidirect
569. C2×#102C22×C139semidirect
570. C2×C22⋊C8C22×C139semidirect
571. C2×C22⋊C8C22×C139semidirect
572. C2×C22⋊C8C22×C139semidirect
575. #390C22×C139semidirect
576. #389C22×C139semidirect
578. #380C22×C139semidirect
579. #340C22×C139semidirect
580. #340C22×C139semidirect
581. #336C22×C139semidirect
582. #336C22×C139semidirect
608. C22×D4D4×C139semidirect
644. #121D4×C139semidirect
681. #102D4×C139semidirect
761. C2×D4D8×C139semidirect
809. C2×C8C2×D4×C139semidirect
820. C4⋊C4C2×D4×C139semidirect
914. D4#121×C139semidirect
1002. C22#447×C139semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1392
C2×#466×C1392
C2×#447×C1392
C22×#102×C1392
#2416×C1392
#2041×C1392
#2033×C1392
#2011×C1392
#1999×C1392
#1879×C1392
#1874×C1392
#1869×C1392
#1862×C1392
#1786×C1392
#24424139