Finite Group Databasebeta

← C139×#26588 #48021184

Subgroups — C139×#26588 #48021184

Order 35584.

950 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C139C211yesmaximal, characteristic
2C2×C4×SD16×C139C211yesmaximal, characteristic, complemented
3#2445×C139C211yesmaximal, characteristic
4#2365×C139C211yesmaximal, characteristic, complemented
5#2066×C139C211yesmaximal, characteristic, complemented
6#2014×C139C211yesmaximal, characteristic
7#2013×C139C211yesmaximal, characteristic, complemented
8#2013×C139C211yesmaximal, characteristic, complemented
9#1968×C139C211yesmaximal, characteristic, complemented
10#1926×C139C211yesmaximal, characteristic, complemented
11#1926×C139C211yesmaximal, characteristic, complemented
12#1916×C139C211yesmaximal, characteristic, complemented
13#1880×C139C211yesmaximal, characteristic, complemented
14#1877×C139C211yesmaximal, characteristic, complemented
15#1865×C139C211yesmaximal, characteristic, complemented
16C22×SD16×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×SD16×C139C2211yescharacteristic
20C2×C4⋊Q8×C139C2211yescharacteristic
21C2×#127×C139C2211yescharacteristic
22C2×#123×C139—21no—
23C2×C4×Q8×C139C2211yescharacteristic
24C2×C4×Q8×C139C2211yescharacteristic
25C2×C4×D4×C139C2211yescharacteristic
26#460×C139—24no—
27C4×SD16×C139—24no—
28C2×#106×C139C2211yescharacteristic
29C2×#106×C139C2211yescharacteristic
30C2×C4⋊C8×C139C2211yescharacteristic
31C2×#103×C139C2211yescharacteristic
32C2×#103×C139C2211yescharacteristic
33C2×#103×C139C2211yescharacteristic
34C2×#103×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×C4×C8×C139C2211yescharacteristic
40#394×C139—21no—
41#394×C139—21no—
42#391×C139C2211yescharacteristic
43#391×C139C2211yescharacteristic
44#390×C139C2211yescharacteristic
45#390×C139C2211yescharacteristic
46#390×C139C2211yescharacteristic
47#389×C139—21no—
48#389×C139C2211yescharacteristic
49#387×C139—21no—
50#387×C139—21no—
51#386×C139—21no—
52C4×C4⋊C4×C139—21no—
53C4×C4⋊C4×C139C2211yescharacteristic
54C4×C4⋊C4×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#336×C139C2211yescharacteristic
58#336×C139C2211yescharacteristic
59#336×C139C2211yescharacteristic
60#336×C139C2211yescharacteristic
61C22×Q8×C139C2311yescharacteristic
62C22×Q8×C139C2311yescharacteristic
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139C2311yescharacteristic
66C22×D4×C139C2311yescharacteristic
67C23×C4×C139—21no—
68C2×SD16×C139—22no—
69C2×SD16×C139—22no—
70C2×SD16×C139—22no—
71C2×SD16×C139—22no—
72C2×SD16×C139—22no—
73C2×SD16×C139—22no—
74C2×SD16×C139—22no—
75C2×SD16×C139—22no—
76C2×SD16×C139—41no—
77C2×SD16×C139—41no—
78C2×SD16×C139—41no—
79C2×SD16×C139—41no—
80C22×C8×C139C2311yescharacteristic
81C22×C8×C139C2311yescharacteristic
82C22×C8×C139C2311yescharacteristic
83C22×C8×C139C2311yescharacteristic
84C4⋊Q8×C139—22no—
85C4⋊Q8×C139—22no—
86#127×C139—22no—
87#127×C139—41no—
88#123×C139—44no—
89C4×Q8×C139—22no—
90C4×Q8×C139—22no—
91C4×Q8×C139—41no—
92C4×Q8×C139—41no—
93C4×D4×C139—22no—
94C4×D4×C139—41no—
95C2×C4⋊C4×C139—21no—
96C2×C4⋊C4×C139—21no—
97C2×C4⋊C4×C139—21no—
98C2×C4⋊C4×C139—21no—
99C2×C4⋊C4×C139—21no—
100C2×C4⋊C4×C139D411yescharacteristic
101C2×C4⋊C4×C139D411yescharacteristic
102C2×C4⋊C4×C139C2311yescharacteristic
103C2×C4⋊C4×C139C2311yescharacteristic
104C2×C4⋊C4×C139C2311yescharacteristic
105C2×C4⋊C4×C139C2311yescharacteristic
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×C42×C139—21no—
114C2×C42×C139—21no—
115C2×C42×C139—21no—
116C2×C42×C139C2311yescharacteristic
117C2×C42×C139C2311yescharacteristic
118C2×C42×C139C2311yescharacteristic
119#106×C139—22no—
120#106×C139—41no—
121C4⋊C8×C139—22no—
122#103×C139—22no—
123#103×C139—22no—
124#103×C139—41no—
125#103×C139—41no—
126#102×C139—22no—
127#102×C139—22no—
128#102×C139—41no—
129#102×C139D414yes—
130C4×C8×C139—22no—
131#95×C139—21no—
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—21no—
141C2×Q8×C139—21no—
142C2×Q8×C139—21no—
143C2×Q8×C139—21no—
144C2×Q8×C139—21no—
145C2×Q8×C139—21no—
146C2×Q8×C139—21no—
147C2×Q8×C139—21no—
148C2×Q8×C139—21no—
149C2×Q8×C139—21no—
150C2×Q8×C139—21no—
151C2×Q8×C139#4112yes—
152C2×Q8×C139#4112yes—
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—42no—
167C2×D4×C139—42no—
168C2×D4×C139—81no—
169C2×D4×C139—81no—
170C2×D4×C139C2×D412yes—
171C22×C4×C139—21no—
172C22×C4×C139—21no—
173C22×C4×C139—21no—
174C22×C4×C139—21no—
175C22×C4×C139—21no—
176C22×C4×C139—21no—
177C22×C4×C139—42no—
178C22×C4×C139—42no—
179C22×C4×C139—81no—
180C22×C4×C139C2×D411yescharacteristic
181C22×C4×C139C2×D411yescharacteristic
182C22×C4×C139C2×D411yescharacteristic
183C22×C4×C139C2×D411yescharacteristic
184C22×C4×C139C2×D411yescharacteristic
185C22×C4×C139C2×D411yescharacteristic
186C22×C4×C139C2411yescharacteristic
187SD16×C139—28no—
188SD16×C139—44no—
189SD16×C139—44no—
190SD16×C139—44no—
191C2×C8×C139—21no—
192C2×C8×C139—21no—
193C2×C8×C139—21no—
194C2×C8×C139—21no—
195C2×C8×C139—21no—
196C2×C8×C139—21no—
197C2×C8×C139—21no—
198C2×C8×C139—21no—
199C2×C8×C139—21no—
200C2×C8×C139—21no—
201C2×C8×C139C2×D412yes—
202C2×C8×C139#4112yes—
203C4⋊C4×C139—24no—
204C4⋊C4×C139—24no—
205C4⋊C4×C139—21no—
206C4⋊C4×C139—21no—
207C4⋊C4×C139—21no—
208C4⋊C4×C139—21no—
209C4⋊C4×C139—21no—
210C4⋊C4×C139—21no—
211C4⋊C4×C139—21no—
212C4⋊C4×C139—41no—
213C4⋊C4×C139—42no—
214C4⋊C4×C139—42no—
215C4⋊C4×C139—42no—
216C4⋊C4×C139SD1614yescomplemented
217C4⋊C4×C139C2×D412yes—
218C22⋊C4×C139—42no—
219C22⋊C4×C139—42no—
220C22⋊C4×C139—42no—
221C22⋊C4×C139—42no—
222C22⋊C4×C139—81no—
223C22⋊C4×C139—81no—
224C22⋊C4×C139—81no—
225C42×C139—21no—
226C42×C139—21no—
227C42×C139—21no—
228C42×C139—21no—
229C42×C139—21no—
230C42×C139—21no—
231C42×C139—42no—
232C42×C139—42no—
233C42×C139—42no—
234C23×C139—22no—
235C23×C139—41no—
236C23×C139—41no—
237C23×C139—41no—
238C23×C139—41no—
239C23×C139—41no—
240C23×C139—41no—
241C23×C139—41no—
242C23×C139—41no—
243C23×C139—41no—
244C23×C139—41no—
245C23×C139—41no—
246C23×C139—41no—
247C23×C139—41no—
248C23×C139C22×D411yescharacteristic
249Q8×C139—22no—
250Q8×C139—22no—
251Q8×C139—22no—
252Q8×C139—22no—
253Q8×C139—41no—
254Q8×C139—41no—
255Q8×C139—41no—
256Q8×C139—41no—
257D4×C139—22no—
258D4×C139—22no—
259D4×C139—41no—
260D4×C139—41no—
261D4×C139—41no—
262D4×C139—41no—
263D4×C139—41no—
264D4×C139—41no—
265D4×C139—84no—
266D4×C139—84no—
267C2×C4×C139—21no—
268C2×C4×C139—21no—
269C2×C4×C139—21no—
270C2×C4×C139—21no—
271C2×C4×C139—21no—
272C2×C4×C139—21no—
273C2×C4×C139—21no—
274C2×C4×C139—22no—
275C2×C4×C139—22no—
276C2×C4×C139—21no—
277C2×C4×C139—21no—
278C2×C4×C139—22no—
279C2×C4×C139—21no—
280C2×C4×C139—21no—
281C2×C4×C139—21no—
282C2×C4×C139—21no—
283C2×C4×C139—21no—
284C2×C4×C139—21no—
285C2×C4×C139—41no—
286C2×C4×C139—41no—
287C2×C4×C139—41no—
288C2×C4×C139—41no—
289C2×C4×C139—41no—
290C2×C4×C139—41no—
291C2×C4×C139—41no—
292C2×C4×C139—41no—
293C2×C4×C139—41no—
294C2×C4×C139—41no—
295C2×C4×C139—41no—
296C2×C4×C139—41no—
297C2×C4×C139—41no—
298C2×C4×C139—41no—
299C2×C4×C139—41no—
300C2×C4×C139—84no—
301C2×C4×C139C2×SD1612yes—
302C2×C4×C139C2×SD1612yes—
303C2×C4×C139C2×SD1612yes—
304C2×C4×C139C22×D411yescharacteristic
305C2×C4×C139C2×#4111yescharacteristic
306C2×C4×C139C2×#4111yescharacteristic
307C2×C4×C139C2×#4111yescharacteristic
308C2×C4×C139H(5,𝔽2)11yescharacteristic
309C2×C4×C139H(5,𝔽2)11yescharacteristic
310C8×C139—22no—
311C8×C139—22no—
312C8×C139—41no—
313C8×C139—41no—
314C22×C139—42no—
315C22×C139—42no—
316C22×C139—42no—
317C22×C139—81no—
318C22×C139—81no—
319C22×C139—81no—
320C22×C139—81no—
321C22×C139—81no—
322C22×C139—81no—
323C22×C139—81no—
324C22×C139—81no—
325C22×C139—81no—
326C22×C139—81no—
327C22×C139—81no—
328C22×C139#52511yescharacteristic
329C22×C139D4211yescharacteristic
330C22×C139#55011yescharacteristic
331C22×C139C22×SD1611yescharacteristic
332C22×C139#57511yescharacteristic
333C22×C139#57711yescharacteristic
334C22×C139#57711yescharacteristic
335C4×C139—22no—
336C4×C139—22no—
337C4×C139—22no—
338C4×C139—41no—
339C4×C139—42no—
340C4×C139—42no—
341C4×C139—41no—
342C4×C139—41no—
343C4×C139—42no—
344C4×C139—81no—
345C4×C139—81no—
346C4×C139—81no—
347C4×C139#52511yescharacteristic
348C4×C139#53811yescharacteristic
349C4×C139#54611yescharacteristic
350C4×C139#55311yescharacteristic
351C2×C139—82no—
352C2×C139—161no—
353C2×C139#245611yescharacteristic
354C2×C139#310311yescharacteristic
355C2×C139#312611yescharacteristic
356C2×C139#326711yescharacteristic
357C2×C139D4×SD1611yescharacteristic
358C2×C139#339211yescharacteristic
359C2×C139#340111yescharacteristic
360#26588C13911yesmaximal, characteristic, direct product factor, Sylow
361C139#2658811yescharacteristic, direct product factor, Sylow
362C2×#460C2×C13911yescharacteristic
363C2×C4×SD16C2×C13911yescharacteristic, complemented
364#2445C2×C13911yescharacteristic
365#2365C2×C13911yescharacteristic, complemented
366#2066C2×C13911yescharacteristic, complemented
367#2014C2×C13911yescharacteristic
368#2013C2×C13911yescharacteristic, complemented
369#2013C2×C13911yescharacteristic, complemented
370#1968C2×C13911yescharacteristic, complemented
371#1926C2×C13911yescharacteristic, complemented
372#1926C2×C13911yescharacteristic, complemented
373#1916C2×C13911yescharacteristic, complemented
374#1880C2×C13911yescharacteristic, complemented
375#1877C2×C13911yescharacteristic, complemented
376#1865C2×C13911yescharacteristic, complemented
377C22×SD16C22×C13911yescharacteristic
378C22×SD16C22×C13911yescharacteristic
379C22×SD16C22×C13911yescharacteristic
380C22×SD16C22×C13911yescharacteristic
381C2×C4⋊Q8C22×C13911yescharacteristic
382C2×#127C22×C13911yescharacteristic
383C2×#123—21no—
384C2×C4×Q8C22×C13911yescharacteristic
385C2×C4×Q8C22×C13911yescharacteristic
386C2×C4×D4C22×C13911yescharacteristic
387#460—24no—
388C4×SD16—24no—
389C2×#106C22×C13911yescharacteristic
390C2×#106C22×C13911yescharacteristic
391C2×C4⋊C8C22×C13911yescharacteristic
392C2×#103C22×C13911yescharacteristic
393C2×#103C22×C13911yescharacteristic
394C2×#103C22×C13911yescharacteristic
395C2×#103C22×C13911yescharacteristic
396C2×#102C22×C13911yescharacteristic
397C2×#102C22×C13911yescharacteristic
398C2×#102C22×C13911yescharacteristic
399C2×#102C22×C13911yescharacteristic
400C2×C4×C8C22×C13911yescharacteristic
401#394—21no—
402#394—21no—
403#391C22×C13911yescharacteristic
404#391C22×C13911yescharacteristic
405#390C22×C13911yescharacteristic
406#390C22×C13911yescharacteristic
407#390C22×C13911yescharacteristic
408#389—21no—
409#389C22×C13911yescharacteristic
410#387—21no—
411#387—21no—
412#386—21no—
413C4×C4⋊C4—21no—
414C4×C4⋊C4C22×C13911yescharacteristic
415C4×C4⋊C4C22×C13911yescharacteristic
416#340C22×C13911yescharacteristic
417#340C22×C13911yescharacteristic
418#336C22×C13911yescharacteristic
419#336C22×C13911yescharacteristic
420#336C22×C13911yescharacteristic
421#336C22×C13911yescharacteristic
422C22×Q8C23×C13911yescharacteristic
423C22×Q8C23×C13911yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4C23×C13911yescharacteristic
427C22×D4C23×C13911yescharacteristic
428C23×C4—21no—
429C2×SD16—22no—
430C2×SD16—22no—
431C2×SD16—22no—
432C2×SD16—22no—
433C2×SD16—22no—
434C2×SD16—22no—
435C2×SD16—22no—
436C2×SD16—22no—
437C2×SD16—41no—
438C2×SD16—41no—
439C2×SD16—41no—
440C2×SD16—41no—
441C22×C8C23×C13911yescharacteristic
442C22×C8C23×C13911yescharacteristic
443C22×C8C23×C13911yescharacteristic
444C22×C8C23×C13911yescharacteristic
445C4⋊Q8—22no—
446C4⋊Q8—22no—
447#127—22no—
448#127—41no—
449#123—44no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8—41no—
453C4×Q8—41no—
454C4×D4—22no—
455C4×D4—41no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4D4×C13911yescharacteristic
462C2×C4⋊C4D4×C13911yescharacteristic
463C2×C4⋊C4C23×C13911yescharacteristic
464C2×C4⋊C4C23×C13911yescharacteristic
465C2×C4⋊C4C23×C13911yescharacteristic
466C2×C4⋊C4C23×C13911yescharacteristic
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42C23×C13911yescharacteristic
478C2×C42C23×C13911yescharacteristic
479C2×C42C23×C13911yescharacteristic
480#106—22no—
481#106—41no—
482C4⋊C8—22no—
483#103—22no—
484#103—22no—
485#103—41no—
486#103—41no—
487#102—22no—
488#102—22no—
489#102—41no—
490#102D4×C13914yes—
491C4×C8—22no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95D4×C13911yescharacteristic
499#95D4×C13911yescharacteristic
500C24—21no—
501C24—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8#41×C13912yes—
513C2×Q8#41×C13912yes—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—42no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4C2×D4×C13912yes—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—81no—
541C22×C4C2×D4×C13911yescharacteristic
542C22×C4C2×D4×C13911yescharacteristic
543C22×C4C2×D4×C13911yescharacteristic
544C22×C4C2×D4×C13911yescharacteristic
545C22×C4C2×D4×C13911yescharacteristic
546C22×C4C2×D4×C13911yescharacteristic
547C22×C4C24×C13911yescharacteristic
548SD16—28no—
549SD16—44no—
550SD16—44no—
551SD16—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8C2×D4×C13912yes—
563C2×C8#41×C13912yes—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—41no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4SD16×C13914yescomplemented
578C4⋊C4C2×D4×C13912yes—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C22⋊C4—81no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—42no—
593C42—42no—
594C42—42no—
595C23—22no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23C22×D4×C13911yescharacteristic
610Q8—22no—
611Q8—22no—
612Q8—22no—
613Q8—22no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618D4—22no—
619D4—22no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—84no—
627D4—84no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4C2×SD16×C13912yes—
663C2×C4C2×SD16×C13912yes—
664C2×C4C2×SD16×C13912yes—
665C2×C4C22×D4×C13911yescharacteristic
666C2×C4C2×#41×C13911yescharacteristic
667C2×C4C2×#41×C13911yescharacteristic
668C2×C4C2×#41×C13911yescharacteristic
669C2×C4H(5,𝔽2)×C13911yescharacteristic
670C2×C4H(5,𝔽2)×C13911yescharacteristic
671C8—22no—
672C8—22no—
673C8—41no—
674C8—41no—
675C22—42no—
676C22—42no—
677C22—42no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22#525×C13911yescharacteristic
690C22D42×C13911yescharacteristic
691C22#550×C13911yescharacteristic
692C22C22×SD16×C13911yescharacteristic
693C22#575×C13911yescharacteristic
694C22#577×C13911yescharacteristic
695C22#577×C13911yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—41no—
700C4—42no—
701C4—42no—
702C4—41no—
703C4—41no—
704C4—42no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4#525×C13911yescharacteristic
709C4#538×C13911yescharacteristic
710C4#546×C13911yescharacteristic
711C4#553×C13911yescharacteristic
712C2—82no—
713C2—161no—
714C2#2456×C13911yescharacteristic
715C2#3103×C13911yescharacteristic
716C2#3126×C13911yescharacteristic
717C2#3267×C13911yescharacteristic
718C2D4×SD16×C13911yescharacteristic
719C2#3392×C13911yescharacteristic
720C2#3401×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#127×C139C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C4⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C139C2semidirect
4. #2365×C139C2semidirect
5. #2066×C139C2semidirect
7. #2013×C139C2semidirect
8. #2013×C139C2semidirect
9. #1968×C139C2semidirect
10. #1926×C139C2semidirect
11. #1926×C139C2semidirect
12. #1916×C139C2semidirect
13. #1880×C139C2semidirect
14. #1877×C139C2semidirect
15. #1865×C139C2semidirect
216. C4⋊C4×C139SD16semidirect
360. #26588C139direct (N × H)
361. C139#26588direct (N × H)
363. C2×C4×SD16C2×C139semidirect
365. #2365C2×C139semidirect
366. #2066C2×C139semidirect
368. #2013C2×C139semidirect
369. #2013C2×C139semidirect
370. #1968C2×C139semidirect
371. #1926C2×C139semidirect
372. #1926C2×C139semidirect
373. #1916C2×C139semidirect
374. #1880C2×C139semidirect
375. #1877C2×C139semidirect
376. #1865C2×C139semidirect
577. C4⋊C4SD16×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C1392
C2×C4×SD16×C1392
#2445×C1392
#2365×C1392
#2066×C1392
#2014×C1392
#2013×C1392
#1968×C1392
#1926×C1392
#1916×C1392
#1880×C1392
#1877×C1392
#1865×C1392
#26588139