Finite Group Databasebeta

← C139×#24469 #48019065

Subgroups — C139×#24469 #48019065

Order 35584.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3489×C139C211yesmaximal, characteristic, complemented
2#3055×C139C211yesmaximal, characteristic, complemented
3C2×#454×C139C211yesmaximal, characteristic, complemented
4#3006×C139C211yesmaximal, characteristic, complemented
5C2×#421×C139C211yesmaximal, characteristic, complemented
6#2620×C139C211yesmaximal, characteristic, complemented
7#2039×C139C211yesmaximal, characteristic, complemented
8#2038×C139C211yesmaximal, characteristic, complemented
9#2006×C139C211yesmaximal, characteristic, complemented
10#2003×C139C211yesmaximal, characteristic, complemented
11#1901×C139C211yesmaximal, characteristic, complemented
12#1897×C139C211yesmaximal, characteristic, complemented
13#1883×C139C211yesmaximal, characteristic, complemented
14#1859×C139C211yesmaximal, characteristic, complemented
15#1793×C139C211yesmaximal, characteristic, complemented
16C2×2−1+4×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C139C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C139C2211yescharacteristic, complemented
21C22×M16×C139C2211yescharacteristic
22D4×Q8×C139—21no—
23#548×C139—21no—
24#547×C139—21no—
25#547×C139—22no—
26#546×C139—21no—
27#546×C139—22no—
28#537×C139—21no—
29#537×C139C2211yescharacteristic
30#536×C139—21no—
31#536×C139C2211yescharacteristic
32C2×#124×C139C2211yescharacteristic, complemented
33#525×C139—21no—
34#525×C139C2211yescharacteristic
35C2×C22⋊Q8×C139—21no—
36C2×C22⋊Q8×C139C2211yescharacteristic
37C2×#121×C139C2211yescharacteristic
38#520×C139C2211yescharacteristic
39C2×#117×C139C2211yescharacteristic
40#469×C139—21no—
41#468×C139—21no—
42#466×C139—21no—
43#465×C139—21no—
44#454×C139—24no—
45#449×C139—21no—
46#449×C139—21no—
47#448×C139—21no—
48#447×C139—21no—
49#428×C139C2211yescharacteristic, complemented
50#421×C139—24no—
51C2×#104×C139C2211yescharacteristic
52C2×#104×C139C2211yescharacteristic
53C2×#104×C139C2211yescharacteristic
54C2×#104×C139C2211yescharacteristic
55C2×#104×C139C2211yescharacteristic, complemented
56C2×#104×C139C2211yescharacteristic, complemented
57#418×C139C2211yescharacteristic, complemented
58#417×C139C2211yescharacteristic
59#417×C139C2211yescharacteristic
60#417×C139C2211yescharacteristic, complemented
61C2×#101×C139C2211yescharacteristic, complemented
62C2×#101×C139C2211yescharacteristic, complemented
63#407×C139C2211yescharacteristic
64#396×C139—22no—
65#394×C139—22no—
66#391×C139C2211yescharacteristic, complemented
67#390×C139C2211yescharacteristic, complemented
68#384×C139C2211yescharacteristic, complemented
69#343×C139C2211yescharacteristic, complemented
70#343×C139C2211yescharacteristic, complemented
71#339×C139C2211yescharacteristic, complemented
72#339×C139C2211yescharacteristic, complemented
732−1+4×C139—22no—
742−1+4×C139—22no—
752−1+4×C139—41no—
762−1+4×C139—41no—
77C2×#41×C139—21no—
78C2×#41×C139—21no—
79C2×#41×C139—21no—
80C2×#41×C139—22no—
81C2×#41×C139—21no—
82C2×#41×C139—22no—
83C2×#41×C139—22no—
84C2×#41×C139—41no—
85C2×#41×C139—41no—
86C2×#41×C139D411yescharacteristic
87C2×#41×C139D411yescharacteristic
88C2×#41×C139C2311yescharacteristic
89C2×#41×C139C2311yescharacteristic
90C2×#41×C139C2311yescharacteristic
91C22×Q8×C139—21no—
92C22×Q8×C139—21no—
93C22×Q8×C139D411yescharacteristic
94C22×Q8×C139C2311yescharacteristic
95C22×D4×C139—21no—
96C22×D4×C139—21no—
97C22×D4×C139D411yescharacteristic
98C22×D4×C139C2311yescharacteristic
99C23×C4×C139—21no—
100C23×C4×C139C2311yescharacteristic
101AGL(1,ℤ/8)×C139—22no—
102AGL(1,ℤ/8)×C139—22no—
103AGL(1,ℤ/8)×C139—22no—
104AGL(1,ℤ/8)×C139—41no—
105AGL(1,ℤ/8)×C139—41no—
106AGL(1,ℤ/8)×C139—41no—
107C2×SD16×C139—21no—
108C2×SD16×C139—21no—
109C2×SD16×C139—21no—
110C2×D8×C139—21no—
111C2×D8×C139—21no—
112C2×D8×C139—21no—
113C2×M16×C139—21no—
114C2×M16×C139—22no—
115C2×M16×C139—41no—
116C2×M16×C139C2311yescharacteristic
117C2×M16×C139C2311yescharacteristic
118C2×M16×C139C2311yescharacteristic
119C2×M16×C139C2311yescharacteristic
120C22×C8×C139—21no—
121C4⋊Q8×C139—22no—
122C4⋊Q8×C139—21no—
123#124×C139—22no—
124#124×C139—21no—
125#124×C139—22no—
126#124×C139—41no—
127#123×C139—22no—
128#123×C139—22no—
129#123×C139—22no—
130#123×C139—21no—
131#123×C139—22no—
132C22⋊Q8×C139—22no—
133C22⋊Q8×C139—22no—
134C22⋊Q8×C139—22no—
135C22⋊Q8×C139—21no—
136C22⋊Q8×C139—21no—
137C22⋊Q8×C139—21no—
138C22⋊Q8×C139—21no—
139C22⋊Q8×C139—21no—
140C22⋊Q8×C139—21no—
141C22⋊Q8×C139—21no—
142C22⋊Q8×C139—21no—
143C22⋊Q8×C139D411yescharacteristic
144C22⋊Q8×C139D411yescharacteristic
145#121×C139—22no—
146#121×C139—22no—
147#121×C139—22no—
148#121×C139—21no—
149#121×C139—21no—
150#121×C139—22no—
151#121×C139—21no—
152#121×C139—21no—
153#121×C139—21no—
154#121×C139—21no—
155#121×C139D411yescharacteristic
156#121×C139D411yescharacteristic
157#120×C139—22no—
158#120×C139—21no—
159C4×Q8×C139—21no—
160C4×D4×C139—22no—
161C4×D4×C139—22no—
162C4×D4×C139—21no—
163C4×D4×C139—22no—
164C4×D4×C139—21no—
165C4×D4×C139—21no—
166#117×C139—21no—
167#117×C139—22no—
168#117×C139—41no—
169#117×C139C2311yescharacteristic
170C2×C4⋊C4×C139—22no—
171C2×C4⋊C4×C139—21no—
172C2×C4⋊C4×C139—21no—
173C2×C4⋊C4×C139—22no—
174C2×C4⋊C4×C139D412yes—
175C2×C4⋊C4×C139C2311yescharacteristic
176C2×C4⋊C4×C139C2311yescharacteristic
177C2×C22⋊C4×C139—22no—
178C2×C22⋊C4×C139—21no—
179C2×C22⋊C4×C139—21no—
180C2×C22⋊C4×C139—22no—
181C2×C22⋊C4×C139—22no—
182C2×C22⋊C4×C139D412yes—
183C2×C42×C139C2311yescharacteristic
184C2×C42×C139C2311yescharacteristic
185#107×C139—21no—
186#106×C139—21no—
187#104×C139—22no—
188#104×C139—22no—
189#104×C139—22no—
190#104×C139—22no—
191#104×C139—41no—
192#104×C139D414yescomplemented
193#103×C139—21no—
194#103×C139—21no—
195#103×C139—21no—
196#102×C139—21no—
197#102×C139—21no—
198#102×C139—21no—
199#102×C139—21no—
200#102×C139—21no—
201#101×C139—22no—
202#101×C139—41no—
203C22⋊C8×C139—21no—
204C22⋊C8×C139—21no—
205#95×C139—22no—
206C24×C139—21no—
207C24×C139—21no—
208C24×C139C2×D411yescharacteristic
209#41×C139—21no—
210#41×C139—21no—
211#41×C139—22no—
212#41×C139—22no—
213#41×C139—21no—
214#41×C139—21no—
215#41×C139—21no—
216#41×C139—21no—
217#41×C139—21no—
218#41×C139—21no—
219#41×C139—21no—
220#41×C139—21no—
221#41×C139—42no—
222#41×C139—42no—
223#41×C139—41no—
224#41×C139—41no—
225#41×C139—42no—
226#41×C139—42no—
227#41×C139—42no—
228#41×C139—42no—
229#41×C139—44no—
230#41×C139—44no—
231#41×C139—42no—
232#41×C139—42no—
233#41×C139C2×D412yes—
234#41×C139#4112yes—
235C2×Q8×C139—22no—
236C2×Q8×C139—21no—
237C2×Q8×C139—21no—
238C2×Q8×C139—21no—
239C2×Q8×C139—21no—
240C2×Q8×C139—21no—
241C2×Q8×C139—21no—
242C2×Q8×C139—21no—
243C2×Q8×C139—22no—
244C2×Q8×C139—41no—
245C2×Q8×C139—42no—
246C2×Q8×C139—42no—
247C2×Q8×C139—42no—
248C2×Q8×C139—42no—
249C2×Q8×C139C2×D411yescharacteristic
250C2×Q8×C139C2×D411yescharacteristic
251C2×Q8×C139C2×D411yescharacteristic
252C2×D4×C139—21no—
253C2×D4×C139—22no—
254C2×D4×C139—22no—
255C2×D4×C139—21no—
256C2×D4×C139—21no—
257C2×D4×C139—21no—
258C2×D4×C139—21no—
259C2×D4×C139—21no—
260C2×D4×C139—22no—
261C2×D4×C139—21no—
262C2×D4×C139—21no—
263C2×D4×C139—21no—
264C2×D4×C139—21no—
265C2×D4×C139—21no—
266C2×D4×C139—21no—
267C2×D4×C139—21no—
268C2×D4×C139—21no—
269C2×D4×C139—41no—
270C2×D4×C139—42no—
271C2×D4×C139—42no—
272C2×D4×C139—41no—
273C2×D4×C139—41no—
274C2×D4×C139—82no—
275C2×D4×C139C2×D411yescharacteristic
276C2×D4×C139C2×D411yescharacteristic
277C2×D4×C139C2×D411yescharacteristic
278C22×C4×C139—21no—
279C22×C4×C139—21no—
280C22×C4×C139—21no—
281C22×C4×C139—21no—
282C22×C4×C139—21no—
283C22×C4×C139—22no—
284C22×C4×C139—22no—
285C22×C4×C139—21no—
286C22×C4×C139—21no—
287C22×C4×C139—22no—
288C22×C4×C139—21no—
289C22×C4×C139—21no—
290C22×C4×C139—21no—
291C22×C4×C139—21no—
292C22×C4×C139—21no—
293C22×C4×C139—21no—
294C22×C4×C139—42no—
295C22×C4×C139—42no—
296C22×C4×C139C2×D412yes—
297C22×C4×C139C2×D411yescharacteristic
298C22×C4×C139C2×D411yescharacteristic
299C22×C4×C139C2×D411yescharacteristic
300C22×C4×C139C2×D411yescharacteristic
301C22×C4×C139C2×D411yescharacteristic
302C22×C4×C139C2×D412yes—
303C22×C4×C139C2411yescharacteristic
304SD16×C139—42no—
305SD16×C139—42no—
306SD16×C139—42no—
307D8×C139—42no—
308D8×C139—42no—
309D8×C139—42no—
310M16×C139—21no—
311M16×C139—21no—
312M16×C139—21no—
313M16×C139—21no—
314M16×C139—21no—
315M16×C139—21no—
316M16×C139—21no—
317M16×C139—42no—
318M16×C139C2×D412yes—
319C2×C8×C139—21no—
320C2×C8×C139—21no—
321C2×C8×C139—21no—
322C2×C8×C139—21no—
323C2×C8×C139—42no—
324C4⋊C4×C139—22no—
325C4⋊C4×C139—22no—
326C4⋊C4×C139—22no—
327C4⋊C4×C139—22no—
328C4⋊C4×C139—21no—
329C4⋊C4×C139—22no—
330C4⋊C4×C139—22no—
331C4⋊C4×C139—21no—
332C4⋊C4×C139—21no—
333C4⋊C4×C139—21no—
334C4⋊C4×C139—21no—
335C4⋊C4×C139—21no—
336C4⋊C4×C139—42no—
337C4⋊C4×C139—82no—
338C4⋊C4×C139C2×D411yescharacteristic
339C4⋊C4×C139C2×D411yescharacteristic
340C22⋊C4×C139—22no—
341C22⋊C4×C139—22no—
342C22⋊C4×C139—22no—
343C22⋊C4×C139—22no—
344C22⋊C4×C139—22no—
345C22⋊C4×C139—21no—
346C22⋊C4×C139—22no—
347C22⋊C4×C139—22no—
348C22⋊C4×C139—21no—
349C22⋊C4×C139—21no—
350C22⋊C4×C139—21no—
351C22⋊C4×C139—21no—
352C22⋊C4×C139—44no—
353C22⋊C4×C139—42no—
354C22⋊C4×C139—41no—
355C22⋊C4×C139—41no—
356C22⋊C4×C139—82no—
357C42×C139—22no—
358C42×C139—21no—
359C42×C139—21no—
360C42×C139—21no—
361C42×C139—21no—
362C42×C139C2×D412yes—
363C23×C139—21no—
364C23×C139—21no—
365C23×C139—21no—
366C23×C139—21no—
367C23×C139—21no—
368C23×C139—41no—
369C23×C139—41no—
370C23×C139—42no—
371C23×C139—42no—
372C23×C139—42no—
373C23×C139—42no—
374C23×C139—41no—
375C23×C139—41no—
376C23×C139—41no—
377C23×C139—81no—
378C23×C139#12011yescharacteristic
379C23×C139#12011yescharacteristic
380C23×C139C22×D411yescharacteristic
381Q8×C139—21no—
382Q8×C139—21no—
383Q8×C139—21no—
384Q8×C139—21no—
385Q8×C139—21no—
386Q8×C139—42no—
387Q8×C139—44no—
388Q8×C139—41no—
389Q8×C139—41no—
390Q8×C139—41no—
391Q8×C139—41no—
392Q8×C139#12112yes—
393D4×C139—22no—
394D4×C139—22no—
395D4×C139—21no—
396D4×C139—21no—
397D4×C139—21no—
398D4×C139—21no—
399D4×C139—21no—
400D4×C139—42no—
401D4×C139—42no—
402D4×C139—42no—
403D4×C139—42no—
404D4×C139—44no—
405D4×C139—41no—
406D4×C139—41no—
407D4×C139—41no—
408D4×C139—41no—
409D4×C139—41no—
410D4×C139—41no—
411D4×C139—41no—
412D4×C139—41no—
413D4×C139—81no—
414D4×C139—82no—
415D4×C139—82no—
416D4×C139—82no—
417D4×C139#12112yes—
418C2×C4×C139—21no—
419C2×C4×C139—21no—
420C2×C4×C139—21no—
421C2×C4×C139—21no—
422C2×C4×C139—21no—
423C2×C4×C139—21no—
424C2×C4×C139—21no—
425C2×C4×C139—21no—
426C2×C4×C139—21no—
427C2×C4×C139—22no—
428C2×C4×C139—21no—
429C2×C4×C139—21no—
430C2×C4×C139—22no—
431C2×C4×C139—21no—
432C2×C4×C139—22no—
433C2×C4×C139—21no—
434C2×C4×C139—21no—
435C2×C4×C139—22no—
436C2×C4×C139—21no—
437C2×C4×C139—22no—
438C2×C4×C139—22no—
439C2×C4×C139—22no—
440C2×C4×C139—42no—
441C2×C4×C139—42no—
442C2×C4×C139—42no—
443C2×C4×C139—44no—
444C2×C4×C139—41no—
445C2×C4×C139—41no—
446C2×C4×C139—44no—
447C2×C4×C139—41no—
448C2×C4×C139—41no—
449C2×C4×C139—41no—
450C2×C4×C139—41no—
451C2×C4×C139—42no—
452C2×C4×C139—41no—
453C2×C4×C139—42no—
454C2×C4×C139—41no—
455C2×C4×C139—41no—
456C2×C4×C139—41no—
457C2×C4×C139—82no—
458C2×C4×C139#12011yescharacteristic
459C2×C4×C139#12011yescharacteristic
460C2×C4×C139C22×D411yescharacteristic
461C2×C4×C139C22×D411yescharacteristic
462C2×C4×C139C22×D411yescharacteristic
463C2×C4×C139C2×#4111yescharacteristic
464C2×C4×C139H(5,𝔽2)11yescharacteristic
465C2×C4×C139H(5,𝔽2)11yescharacteristic
466C8×C139—22no—
467C8×C139—41no—
468C8×C139—41no—
469C8×C139—41no—
470C22×C139—21no—
471C22×C139—21no—
472C22×C139—21no—
473C22×C139—21no—
474C22×C139—22no—
475C22×C139—21no—
476C22×C139—21no—
477C22×C139—21no—
478C22×C139—21no—
479C22×C139—41no—
480C22×C139—41no—
481C22×C139—41no—
482C22×C139—41no—
483C22×C139—41no—
484C22×C139—41no—
485C22×C139—41no—
486C22×C139—41no—
487C22×C139—81no—
488C22×C139—81no—
489C22×C139—82no—
490C22×C139—82no—
491C22×C139—84no—
492C22×C139—81no—
493C22×C139—81no—
494C22×C139—81no—
495C22×C139C2×#12011yescharacteristic
496C22×C139D4211yescharacteristic
497C22×C139#54611yescharacteristic
498C4×C139—21no—
499C4×C139—21no—
500C4×C139—22no—
501C4×C139—42no—
502C4×C139—42no—
503C4×C139—41no—
504C4×C139—41no—
505C4×C139—41no—
506C4×C139—42no—
507C4×C139—41no—
508C4×C139—81no—
509C4×C139—81no—
510C4×C139C2×#12111yescharacteristic
511C4×C139#53411yescharacteristic
512C4×C139D4211yescharacteristic
513C4×C139#54611yescharacteristic
514C2×C139—21no—
515C2×C139—21no—
516C2×C139—41no—
517C2×C139—41no—
518C2×C139—42no—
519C2×C139—81no—
520C2×C139—81no—
521C2×C139—161no—
522C2×C139#241011yescharacteristic
523C2×C139#302011yescharacteristic
524C2×C139#302111yescharacteristic
525#24469C13911yesmaximal, characteristic, direct product factor, Sylow
526C139#2446911yescharacteristic, direct product factor, Sylow
527#3489C2×C13911yescharacteristic, complemented
528#3055C2×C13911yescharacteristic, complemented
529C2×#454C2×C13911yescharacteristic, complemented
530#3006C2×C13911yescharacteristic, complemented
531C2×#421C2×C13911yescharacteristic, complemented
532#2620C2×C13911yescharacteristic, complemented
533#2039C2×C13911yescharacteristic, complemented
534#2038C2×C13911yescharacteristic, complemented
535#2006C2×C13911yescharacteristic, complemented
536#2003C2×C13911yescharacteristic, complemented
537#1901C2×C13911yescharacteristic, complemented
538#1897C2×C13911yescharacteristic, complemented
539#1883C2×C13911yescharacteristic, complemented
540#1859C2×C13911yescharacteristic, complemented
541#1793C2×C13911yescharacteristic, complemented
542C2×2−1+4C22×C13911yescharacteristic
543C22×#41C22×C13911yescharacteristic
544C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
545C2×AGL(1,ℤ/8)C22×C13911yescharacteristic
546C2×AGL(1,ℤ/8)C22×C13911yescharacteristic, complemented
547C22×M16C22×C13911yescharacteristic
548D4×Q8—21no—
549#548—21no—
550#547—21no—
551#547—22no—
552#546—21no—
553#546—22no—
554#537—21no—
555#537C22×C13911yescharacteristic
556#536—21no—
557#536C22×C13911yescharacteristic
558C2×#124C22×C13911yescharacteristic, complemented
559#525—21no—
560#525C22×C13911yescharacteristic
561C2×C22⋊Q8—21no—
562C2×C22⋊Q8C22×C13911yescharacteristic
563C2×#121C22×C13911yescharacteristic
564#520C22×C13911yescharacteristic
565C2×#117C22×C13911yescharacteristic
566#469—21no—
567#468—21no—
568#466—21no—
569#465—21no—
570#454—24no—
571#449—21no—
572#449—21no—
573#448—21no—
574#447—21no—
575#428C22×C13911yescharacteristic, complemented
576#421—24no—
577C2×#104C22×C13911yescharacteristic
578C2×#104C22×C13911yescharacteristic
579C2×#104C22×C13911yescharacteristic
580C2×#104C22×C13911yescharacteristic
581C2×#104C22×C13911yescharacteristic, complemented
582C2×#104C22×C13911yescharacteristic, complemented
583#418C22×C13911yescharacteristic, complemented
584#417C22×C13911yescharacteristic
585#417C22×C13911yescharacteristic
586#417C22×C13911yescharacteristic, complemented
587C2×#101C22×C13911yescharacteristic, complemented
588C2×#101C22×C13911yescharacteristic, complemented
589#407C22×C13911yescharacteristic
590#396—22no—
591#394—22no—
592#391C22×C13911yescharacteristic, complemented
593#390C22×C13911yescharacteristic, complemented
594#384C22×C13911yescharacteristic, complemented
595#343C22×C13911yescharacteristic, complemented
596#343C22×C13911yescharacteristic, complemented
597#339C22×C13911yescharacteristic, complemented
598#339C22×C13911yescharacteristic, complemented
5992−1+4—22no—
6002−1+4—22no—
6012−1+4—41no—
6022−1+4—41no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—22no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—22no—
610C2×#41—41no—
611C2×#41—41no—
612C2×#41D4×C13911yescharacteristic
613C2×#41D4×C13911yescharacteristic
614C2×#41C23×C13911yescharacteristic
615C2×#41C23×C13911yescharacteristic
616C2×#41C23×C13911yescharacteristic
617C22×Q8—21no—
618C22×Q8—21no—
619C22×Q8D4×C13911yescharacteristic
620C22×Q8C23×C13911yescharacteristic
621C22×D4—21no—
622C22×D4—21no—
623C22×D4D4×C13911yescharacteristic
624C22×D4C23×C13911yescharacteristic
625C23×C4—21no—
626C23×C4C23×C13911yescharacteristic
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632AGL(1,ℤ/8)—41no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×SD16—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×D8—21no—
639C2×M16—21no—
640C2×M16—22no—
641C2×M16—41no—
642C2×M16C23×C13911yescharacteristic
643C2×M16C23×C13911yescharacteristic
644C2×M16C23×C13911yescharacteristic
645C2×M16C23×C13911yescharacteristic
646C22×C8—21no—
647C4⋊Q8—22no—
648C4⋊Q8—21no—
649#124—22no—
650#124—21no—
651#124—22no—
652#124—41no—
653#123—22no—
654#123—22no—
655#123—22no—
656#123—21no—
657#123—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8D4×C13911yescharacteristic
670C22⋊Q8D4×C13911yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—21no—
675#121—21no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121D4×C13911yescharacteristic
682#121D4×C13911yescharacteristic
683#120—22no—
684#120—21no—
685C4×Q8—21no—
686C4×D4—22no—
687C4×D4—22no—
688C4×D4—21no—
689C4×D4—22no—
690C4×D4—21no—
691C4×D4—21no—
692#117—21no—
693#117—22no—
694#117—41no—
695#117C23×C13911yescharacteristic
696C2×C4⋊C4—22no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4D4×C13912yes—
701C2×C4⋊C4C23×C13911yescharacteristic
702C2×C4⋊C4C23×C13911yescharacteristic
703C2×C22⋊C4—22no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4D4×C13912yes—
709C2×C42C23×C13911yescharacteristic
710C2×C42C23×C13911yescharacteristic
711#107—21no—
712#106—21no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—22no—
717#104—41no—
718#104D4×C13914yescomplemented
719#103—21no—
720#103—21no—
721#103—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#102—21no—
727#101—22no—
728#101—41no—
729C22⋊C8—21no—
730C22⋊C8—21no—
731#95—22no—
732C24—21no—
733C24—21no—
734C24C2×D4×C13911yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C13912yes—
760#41#41×C13912yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C13911yescharacteristic
776C2×Q8C2×D4×C13911yescharacteristic
777C2×Q8C2×D4×C13911yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C13911yescharacteristic
802C2×D4C2×D4×C13911yescharacteristic
803C2×D4C2×D4×C13911yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C13912yes—
823C22×C4C2×D4×C13911yescharacteristic
824C22×C4C2×D4×C13911yescharacteristic
825C22×C4C2×D4×C13911yescharacteristic
826C22×C4C2×D4×C13911yescharacteristic
827C22×C4C2×D4×C13911yescharacteristic
828C22×C4C2×D4×C13912yes—
829C22×C4C24×C13911yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C13912yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C13911yescharacteristic
865C4⋊C4C2×D4×C13911yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C13912yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23#120×C13911yescharacteristic
905C23#120×C13911yescharacteristic
906C23C22×D4×C13911yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8#121×C13912yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—44no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4#121×C13912yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—44no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4#120×C13911yescharacteristic
985C2×C4#120×C13911yescharacteristic
986C2×C4C22×D4×C13911yescharacteristic
987C2×C4C22×D4×C13911yescharacteristic
988C2×C4C22×D4×C13911yescharacteristic
989C2×C4C2×#41×C13911yescharacteristic
990C2×C4H(5,𝔽2)×C13911yescharacteristic
991C2×C4H(5,𝔽2)×C13911yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×#120×C13911yescharacteristic
1022C22D42×C13911yescharacteristic
1023C22#546×C13911yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—42no—
1029C4—41no—
1030C4—41no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×#121×C13911yescharacteristic
1037C4#534×C13911yescharacteristic
1038C4D42×C13911yescharacteristic
1039C4#546×C13911yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2#2410×C13911yescharacteristic
1049C2#3020×C13911yescharacteristic
1050C2#3021×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3489×C139C2semidirect
2. #3055×C139C2semidirect
3. C2×#454×C139C2semidirect
4. #3006×C139C2semidirect
5. C2×#421×C139C2semidirect
6. #2620×C139C2semidirect
7. #2039×C139C2semidirect
8. #2038×C139C2semidirect
9. #2006×C139C2semidirect
10. #2003×C139C2semidirect
11. #1901×C139C2semidirect
12. #1897×C139C2semidirect
13. #1883×C139C2semidirect
14. #1859×C139C2semidirect
15. #1793×C139C2semidirect
20. C2×AGL(1,ℤ/8)×C139C22semidirect
32. C2×#124×C139C22semidirect
49. #428×C139C22semidirect
55. C2×#104×C139C22semidirect
56. C2×#104×C139C22semidirect
57. #418×C139C22semidirect
60. #417×C139C22semidirect
61. C2×#101×C139C22semidirect
62. C2×#101×C139C22semidirect
66. #391×C139C22semidirect
67. #390×C139C22semidirect
68. #384×C139C22semidirect
69. #343×C139C22semidirect
70. #343×C139C22semidirect
71. #339×C139C22semidirect
72. #339×C139C22semidirect
192. #104×C139D4semidirect
525. #24469C139direct (N × H)
526. C139#24469direct (N × H)
527. #3489C2×C139semidirect
528. #3055C2×C139semidirect
529. C2×#454C2×C139semidirect
530. #3006C2×C139semidirect
531. C2×#421C2×C139semidirect
532. #2620C2×C139semidirect
533. #2039C2×C139semidirect
534. #2038C2×C139semidirect
535. #2006C2×C139semidirect
536. #2003C2×C139semidirect
537. #1901C2×C139semidirect
538. #1897C2×C139semidirect
539. #1883C2×C139semidirect
540. #1859C2×C139semidirect
541. #1793C2×C139semidirect
546. C2×AGL(1,ℤ/8)C22×C139semidirect
558. C2×#124C22×C139semidirect
575. #428C22×C139semidirect
581. C2×#104C22×C139semidirect
582. C2×#104C22×C139semidirect
583. #418C22×C139semidirect
586. #417C22×C139semidirect
587. C2×#101C22×C139semidirect
588. C2×#101C22×C139semidirect
592. #391C22×C139semidirect
593. #390C22×C139semidirect
594. #384C22×C139semidirect
595. #343C22×C139semidirect
596. #343C22×C139semidirect
597. #339C22×C139semidirect
598. #339C22×C139semidirect
718. #104D4×C139semidirect

Maximal subgroups

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

subgroupindex
#3489×C1392
#3055×C1392
C2×#454×C1392
#3006×C1392
C2×#421×C1392
#2620×C1392
#2039×C1392
#2038×C1392
#2006×C1392
#2003×C1392
#1901×C1392
#1897×C1392
#1883×C1392
#1859×C1392
#1793×C1392
#24469139