Finite Group Databasebeta

← C139×#26936 #48021532

Subgroups — C139×#26936 #48021532

Order 35584.

876 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C139C211yesmaximal, characteristic, complemented
2C2×#464×C139C211yesmaximal, characteristic, complemented
3#2426×C139C211yesmaximal, characteristic
4#2362×C139C211yesmaximal, characteristic, complemented
5#2088×C139C211yesmaximal, characteristic, complemented
6#2042×C139C211yesmaximal, characteristic, complemented
7#2001×C139C211yesmaximal, characteristic, complemented
8#2000×C139C211yesmaximal, characteristic
9#1968×C139C211yesmaximal, characteristic, complemented
10#1925×C139C211yesmaximal, characteristic, complemented
11#1923×C139C211yesmaximal, characteristic, complemented
12#1878×C139C211yesmaximal, characteristic, complemented
13#1875×C139C211yesmaximal, characteristic
14#1863×C139C211yesmaximal, characteristic, complemented
15C4×#103×C139C211yesmaximal, characteristic, complemented
16C22×Q16×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C2×#124×C139C2211yescharacteristic
19C2×C22⋊Q8×C139C2211yescharacteristic
20C2×C22⋊Q8×C139C2211yescharacteristic
21C2×#121×C139C2211yescharacteristic
22C2×C4×Q8×C139C2211yescharacteristic
23C2×C4×Q8×C139C2211yescharacteristic
24C2×#117×C139C2211yescharacteristic
25#485×C139—24no—
26#464×C139—24no—
27C2×#107×C139C2211yescharacteristic
28C2×#106×C139C2211yescharacteristic
29C2×C4⋊C8×C139C2211yescharacteristic
30C2×#103×C139C2211yescharacteristic
31C2×#103×C139C2211yescharacteristic
32C2×#103×C139C2211yescharacteristic
33C2×#103×C139C2211yescharacteristic
34C2×#103×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×C22⋊C8×C139C2211yescharacteristic
39C2×C22⋊C8×C139C2211yescharacteristic
40C2×C4×C8×C139C2211yescharacteristic
41#396×C139—21no—
42#394×C139—21no—
43#391×C139C2211yescharacteristic
44#390×C139—21no—
45#390×C139C2211yescharacteristic
46#389×C139C2211yescharacteristic
47#389×C139C2211yescharacteristic
48#388×C139—21no—
49#388×C139—21no—
50#388×C139—21no—
51#387×C139—21no—
52C4×C4⋊C4×C139—21no—
53C4×C4⋊C4×C139C2211yescharacteristic
54C4×C22⋊C4×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#336×C139C2211yescharacteristic
60#336×C139C2211yescharacteristic
61C22×Q8×C139C2311yescharacteristic
62C22×Q8×C139C2311yescharacteristic
63C22×D4×C139—21no—
64C22×D4×C139C2311yescharacteristic
65C23×C4×C139C2311yescharacteristic
66C2×Q16×C139—22no—
67C2×Q16×C139—22no—
68C2×Q16×C139—41no—
69C2×SD16×C139—22no—
70C2×SD16×C139—22no—
71C2×SD16×C139—41no—
72C22×C8×C139C2311yescharacteristic
73C22×C8×C139C2311yescharacteristic
74C22×C8×C139C2311yescharacteristic
75C22×C8×C139C2311yescharacteristic
76#124×C139—22no—
77#124×C139—41no—
78C22⋊Q8×C139—22no—
79C22⋊Q8×C139—22no—
80C22⋊Q8×C139—22no—
81C22⋊Q8×C139—41no—
82#121×C139—22no—
83#121×C139—41no—
84C4×Q8×C139—22no—
85C4×Q8×C139—22no—
86C4×Q8×C139—41no—
87C4×Q8×C139—41no—
88#117×C139—22no—
89#117×C139—41no—
90C2×C4⋊C4×C139—21no—
91C2×C4⋊C4×C139—21no—
92C2×C4⋊C4×C139—21no—
93C2×C4⋊C4×C139—21no—
94C2×C4⋊C4×C139—21no—
95C2×C4⋊C4×C139—21no—
96C2×C4⋊C4×C139C2311yescharacteristic
97C2×C4⋊C4×C139C2311yescharacteristic
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C4⋊C4×C139C2311yescharacteristic
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C22⋊C4×C139—21no—
102C2×C22⋊C4×C139—21no—
103C2×C22⋊C4×C139—21no—
104C2×C22⋊C4×C139—21no—
105C2×C22⋊C4×C139—21no—
106C2×C22⋊C4×C139—21no—
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
109C2×C22⋊C4×C139D411yescharacteristic
110C2×C22⋊C4×C139D411yescharacteristic
111C2×C42×C139—21no—
112C2×C42×C139—21no—
113C2×C42×C139—21no—
114C2×C42×C139—21no—
115C2×C42×C139C2311yescharacteristic
116C2×C42×C139C2311yescharacteristic
117#107×C139—22no—
118#106×C139—22no—
119C4⋊C8×C139—22no—
120#103×C139—22no—
121#103×C139—22no—
122#103×C139—22no—
123#103×C139—41no—
124#103×C139D414yescomplemented
125#102×C139—22no—
126#102×C139—22no—
127#102×C139—41no—
128C22⋊C8×C139—22no—
129C22⋊C8×C139—41no—
130C4×C8×C139—41no—
131#95×C139—21no—
132#95×C139—21no—
133#95×C139—21no—
134#95×C139—21no—
135#95×C139—21no—
136#95×C139D411yescharacteristic
137#95×C139D411yescharacteristic
138C24×C139—21no—
139C24×C139C2×D411yescharacteristic
140C2×Q8×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×C139C2×D412yes—
151C2×Q8×C139#4112yes—
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—42no—
159C2×D4×C139—42no—
160C2×D4×C139—81no—
161C22×C4×C139—21no—
162C22×C4×C139—21no—
163C22×C4×C139—21no—
164C22×C4×C139—21no—
165C22×C4×C139—21no—
166C22×C4×C139—21no—
167C22×C4×C139—21no—
168C22×C4×C139—21no—
169C22×C4×C139—21no—
170C22×C4×C139—21no—
171C22×C4×C139—21no—
172C22×C4×C139—21no—
173C22×C4×C139—21no—
174C22×C4×C139C2×D411yescharacteristic
175C22×C4×C139C2×D411yescharacteristic
176C22×C4×C139C2×D411yescharacteristic
177C22×C4×C139C2×D411yescharacteristic
178C22×C4×C139C2×D411yescharacteristic
179C22×C4×C139C2411yescharacteristic
180Q16×C139—44no—
181SD16×C139—44no—
182C2×C8×C139—21no—
183C2×C8×C139—21no—
184C2×C8×C139—21no—
185C2×C8×C139—21no—
186C2×C8×C139—21no—
187C2×C8×C139—21no—
188C2×C8×C139—21no—
189C2×C8×C139—21no—
190C2×C8×C139—21no—
191C2×C8×C139—21no—
192C2×C8×C139—21no—
193C2×C8×C139C2×D412yes—
194C4⋊C4×C139—24no—
195C4⋊C4×C139—21no—
196C4⋊C4×C139—21no—
197C4⋊C4×C139—21no—
198C4⋊C4×C139—21no—
199C4⋊C4×C139—21no—
200C4⋊C4×C139—21no—
201C4⋊C4×C139—21no—
202C4⋊C4×C139—42no—
203C4⋊C4×C139—42no—
204C4⋊C4×C139—42no—
205C4⋊C4×C139—42no—
206C4⋊C4×C139—81no—
207C4⋊C4×C139C2×D412yes—
208C4⋊C4×C139#4112yes—
209C4⋊C4×C139#4112yes—
210C22⋊C4×C139—24no—
211C22⋊C4×C139—22no—
212C22⋊C4×C139—41no—
213C22⋊C4×C139—42no—
214C22⋊C4×C139—42no—
215C22⋊C4×C139—42no—
216C22⋊C4×C139—42no—
217C22⋊C4×C139—42no—
218C22⋊C4×C139—42no—
219C22⋊C4×C139—81no—
220C42×C139—21no—
221C42×C139—21no—
222C42×C139—21no—
223C42×C139—21no—
224C42×C139—42no—
225C42×C139—42no—
226C42×C139—42no—
227C42×C139—42no—
228C23×C139—21no—
229C23×C139—21no—
230C23×C139—21no—
231C23×C139—21no—
232C23×C139—21no—
233C23×C139—21no—
234C23×C139—21no—
235C23×C139—41no—
236C23×C139—41no—
237C23×C139—41no—
238C23×C139—41no—
239C23×C139—41no—
240C23×C139—41no—
241C23×C139—41no—
242C23×C139C22×D411yescharacteristic
243Q8×C139—22no—
244Q8×C139—22no—
245Q8×C139—22no—
246Q8×C139—22no—
247Q8×C139—41no—
248Q8×C139—41no—
249Q8×C139—41no—
250Q8×C139—41no—
251D4×C139—41no—
252D4×C139—41no—
253D4×C139—41no—
254D4×C139—41no—
255D4×C139—84no—
256C2×C4×C139—21no—
257C2×C4×C139—21no—
258C2×C4×C139—22no—
259C2×C4×C139—22no—
260C2×C4×C139—21no—
261C2×C4×C139—21no—
262C2×C4×C139—21no—
263C2×C4×C139—22no—
264C2×C4×C139—21no—
265C2×C4×C139—22no—
266C2×C4×C139—21no—
267C2×C4×C139—22no—
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—21no—
275C2×C4×C139—41no—
276C2×C4×C139—41no—
277C2×C4×C139—41no—
278C2×C4×C139—41no—
279C2×C4×C139—41no—
280C2×C4×C139—41no—
281C2×C4×C139—41no—
282C2×C4×C139—41no—
283C2×C4×C139—41no—
284C2×C4×C139—41no—
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#13512yes—
296C2×C4×C139C22×D411yescharacteristic
297C2×C4×C139C2×#4111yescharacteristic
298C2×C4×C139C2×#4111yescharacteristic
299C2×C4×C139C2×#4111yescharacteristic
300C2×C4×C139H(5,𝔽2)11yescharacteristic
301C2×C4×C139H(5,𝔽2)11yescharacteristic
302C8×C139—22no—
303C8×C139—41no—
304C8×C139—41no—
305C8×C139—41no—
306C22×C139—41no—
307C22×C139—41no—
308C22×C139—41no—
309C22×C139—41no—
310C22×C139—41no—
311C22×C139—41no—
312C22×C139—41no—
313C22×C139—81no—
314C22×C139—81no—
315C22×C139—81no—
316C22×C139—81no—
317C22×C139—81no—
318C22×C139—81no—
319C22×C139—81no—
320C22×C139#52511yescharacteristic
321C22×C139D4211yescharacteristic
322C22×C139#54611yescharacteristic
323C22×C139C2×#13511yescharacteristic
324C22×C139#57511yescharacteristic
325C22×C139#57711yescharacteristic
326C22×C139#57811yescharacteristic
327C4×C139—22no—
328C4×C139—42no—
329C4×C139—41no—
330C4×C139—42no—
331C4×C139—42no—
332C4×C139—41no—
333C4×C139—41no—
334C4×C139—42no—
335C4×C139—41no—
336C4×C139—42no—
337C4×C139—81no—
338C4×C139—81no—
339C4×C139#53211yescharacteristic
340C4×C139#54011yescharacteristic
341C4×C139#54611yescharacteristic
342C4×C139#55311yescharacteristic
343C2×C139—81no—
344C2×C139—161no—
345C2×C139#246411yescharacteristic
346C2×C139#310211yescharacteristic
347C2×C139#312111yescharacteristic
348C2×C139#327711yescharacteristic
349C2×C139#328411yescharacteristic
350C2×C139#330011yescharacteristic
351C2×C139#331111yescharacteristic
352#26936C13911yesmaximal, characteristic, direct product factor, Sylow
353C139#2693611yescharacteristic, direct product factor, Sylow
354C2×#485C2×C13911yescharacteristic, complemented
355C2×#464C2×C13911yescharacteristic, complemented
356#2426C2×C13911yescharacteristic
357#2362C2×C13911yescharacteristic, complemented
358#2088C2×C13911yescharacteristic, complemented
359#2042C2×C13911yescharacteristic, complemented
360#2001C2×C13911yescharacteristic, complemented
361#2000C2×C13911yescharacteristic
362#1968C2×C13911yescharacteristic, complemented
363#1925C2×C13911yescharacteristic, complemented
364#1923C2×C13911yescharacteristic, complemented
365#1878C2×C13911yescharacteristic, complemented
366#1875C2×C13911yescharacteristic
367#1863C2×C13911yescharacteristic, complemented
368C4×#103C2×C13911yescharacteristic, complemented
369C22×Q16C22×C13911yescharacteristic
370C22×SD16C22×C13911yescharacteristic
371C2×#124C22×C13911yescharacteristic
372C2×C22⋊Q8C22×C13911yescharacteristic
373C2×C22⋊Q8C22×C13911yescharacteristic
374C2×#121C22×C13911yescharacteristic
375C2×C4×Q8C22×C13911yescharacteristic
376C2×C4×Q8C22×C13911yescharacteristic
377C2×#117C22×C13911yescharacteristic
378#485—24no—
379#464—24no—
380C2×#107C22×C13911yescharacteristic
381C2×#106C22×C13911yescharacteristic
382C2×C4⋊C8C22×C13911yescharacteristic
383C2×#103C22×C13911yescharacteristic
384C2×#103C22×C13911yescharacteristic
385C2×#103C22×C13911yescharacteristic
386C2×#103C22×C13911yescharacteristic
387C2×#103C22×C13911yescharacteristic
388C2×#102C22×C13911yescharacteristic
389C2×#102C22×C13911yescharacteristic
390C2×#102C22×C13911yescharacteristic
391C2×C22⋊C8C22×C13911yescharacteristic
392C2×C22⋊C8C22×C13911yescharacteristic
393C2×C4×C8C22×C13911yescharacteristic
394#396—21no—
395#394—21no—
396#391C22×C13911yescharacteristic
397#390—21no—
398#390C22×C13911yescharacteristic
399#389C22×C13911yescharacteristic
400#389C22×C13911yescharacteristic
401#388—21no—
402#388—21no—
403#388—21no—
404#387—21no—
405C4×C4⋊C4—21no—
406C4×C4⋊C4C22×C13911yescharacteristic
407C4×C22⋊C4C22×C13911yescharacteristic
408#340C22×C13911yescharacteristic
409#340C22×C13911yescharacteristic
410#340C22×C13911yescharacteristic
411#340C22×C13911yescharacteristic
412#336C22×C13911yescharacteristic
413#336C22×C13911yescharacteristic
414C22×Q8C23×C13911yescharacteristic
415C22×Q8C23×C13911yescharacteristic
416C22×D4—21no—
417C22×D4C23×C13911yescharacteristic
418C23×C4C23×C13911yescharacteristic
419C2×Q16—22no—
420C2×Q16—22no—
421C2×Q16—41no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16—41no—
425C22×C8C23×C13911yescharacteristic
426C22×C8C23×C13911yescharacteristic
427C22×C8C23×C13911yescharacteristic
428C22×C8C23×C13911yescharacteristic
429#124—22no—
430#124—41no—
431C22⋊Q8—22no—
432C22⋊Q8—22no—
433C22⋊Q8—22no—
434C22⋊Q8—41no—
435#121—22no—
436#121—41no—
437C4×Q8—22no—
438C4×Q8—22no—
439C4×Q8—41no—
440C4×Q8—41no—
441#117—22no—
442#117—41no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4C23×C13911yescharacteristic
450C2×C4⋊C4C23×C13911yescharacteristic
451C2×C4⋊C4C23×C13911yescharacteristic
452C2×C4⋊C4C23×C13911yescharacteristic
453C2×C4⋊C4C23×C13911yescharacteristic
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4D4×C13911yescharacteristic
463C2×C22⋊C4D4×C13911yescharacteristic
464C2×C42—21no—
465C2×C42—21no—
466C2×C42—21no—
467C2×C42—21no—
468C2×C42C23×C13911yescharacteristic
469C2×C42C23×C13911yescharacteristic
470#107—22no—
471#106—22no—
472C4⋊C8—22no—
473#103—22no—
474#103—22no—
475#103—22no—
476#103—41no—
477#103D4×C13914yescomplemented
478#102—22no—
479#102—22no—
480#102—41no—
481C22⋊C8—22no—
482C22⋊C8—41no—
483C4×C8—41no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95D4×C13911yescharacteristic
490#95D4×C13911yescharacteristic
491C24—21no—
492C24C2×D4×C13911yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8C2×D4×C13912yes—
504C2×Q8#41×C13912yes—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—42no—
512C2×D4—42no—
513C2×D4—81no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4C2×D4×C13911yescharacteristic
528C22×C4C2×D4×C13911yescharacteristic
529C22×C4C2×D4×C13911yescharacteristic
530C22×C4C2×D4×C13911yescharacteristic
531C22×C4C2×D4×C13911yescharacteristic
532C22×C4C24×C13911yescharacteristic
533Q16—44no—
534SD16—44no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8C2×D4×C13912yes—
547C4⋊C4—24no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—81no—
560C4⋊C4C2×D4×C13912yes—
561C4⋊C4#41×C13912yes—
562C4⋊C4#41×C13912yes—
563C22⋊C4—24no—
564C22⋊C4—22no—
565C22⋊C4—41no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—81no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—42no—
578C42—42no—
579C42—42no—
580C42—42no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23C22×D4×C13911yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—22no—
599Q8—22no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4#135×C13912yes—
649C2×C4C22×D4×C13911yescharacteristic
650C2×C4C2×#41×C13911yescharacteristic
651C2×C4C2×#41×C13911yescharacteristic
652C2×C4C2×#41×C13911yescharacteristic
653C2×C4H(5,𝔽2)×C13911yescharacteristic
654C2×C4H(5,𝔽2)×C13911yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22#525×C13911yescharacteristic
674C22D42×C13911yescharacteristic
675C22#546×C13911yescharacteristic
676C22C2×#135×C13911yescharacteristic
677C22#575×C13911yescharacteristic
678C22#577×C13911yescharacteristic
679C22#578×C13911yescharacteristic
680C4—22no—
681C4—41no—
682C4—42no—
683C4—41no—
684C4—42no—
685C4—42no—
686C4—41no—
687C4—42no—
688C4—42no—
689C4—41no—
690C4—81no—
691C4—81no—
692C4#532×C13911yescharacteristic
693C4#540×C13911yescharacteristic
694C4#546×C13911yescharacteristic
695C4#553×C13911yescharacteristic
696C2—81no—
697C2—161no—
698C2#2464×C13911yescharacteristic
699C2#3102×C13911yescharacteristic
700C2#3121×C13911yescharacteristic
701C2#3277×C13911yescharacteristic
702C2#3284×C13911yescharacteristic
703C2#3300×C13911yescharacteristic
704C2#3311×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#121×C139C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C139C2semidirect
2. C2×#464×C139C2semidirect
4. #2362×C139C2semidirect
5. #2088×C139C2semidirect
6. #2042×C139C2semidirect
7. #2001×C139C2semidirect
9. #1968×C139C2semidirect
10. #1925×C139C2semidirect
11. #1923×C139C2semidirect
12. #1878×C139C2semidirect
14. #1863×C139C2semidirect
15. C4×#103×C139C2semidirect
124. #103×C139D4semidirect
352. #26936C139direct (N × H)
353. C139#26936direct (N × H)
354. C2×#485C2×C139semidirect
355. C2×#464C2×C139semidirect
357. #2362C2×C139semidirect
358. #2088C2×C139semidirect
359. #2042C2×C139semidirect
360. #2001C2×C139semidirect
362. #1968C2×C139semidirect
363. #1925C2×C139semidirect
364. #1923C2×C139semidirect
365. #1878C2×C139semidirect
367. #1863C2×C139semidirect
368. C4×#103C2×C139semidirect
477. #103D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1392
C2×#464×C1392
#2426×C1392
#2362×C1392
#2088×C1392
#2042×C1392
#2001×C1392
#2000×C1392
#1968×C1392
#1925×C1392
#1923×C1392
#1878×C1392
#1875×C1392
#1863×C1392
C4×#103×C1392
#26936139