Finite Group Databasebeta

← C139×#25396 #48019992

Subgroups — C139×#25396 #48019992

Order 35584.

1184 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C139C211yesmaximal, characteristic, complemented
2C2×#466×C139C211yesmaximal, characteristic, complemented
3C2×#459×C139C211yesmaximal, characteristic, complemented
4C2×#435×C139C211yesmaximal, characteristic, complemented
5#2541×C139C211yesmaximal, characteristic, complemented
6#2535×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#1999×C139C211yesmaximal, characteristic, complemented
10#1999×C139C211yesmaximal, characteristic, complemented
11#1961×C139C211yesmaximal, characteristic, complemented
12#1949×C139C211yesmaximal, characteristic, complemented
13#1895×C139C211yesmaximal, characteristic, complemented
14#1893×C139C211yesmaximal, characteristic, complemented
15#1762×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19C23×C8×C139C2211yescharacteristic
20C2×#127×C139—21no—
21C2×#127×C139C2211yescharacteristic
22C2×#121×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×#121×C139C2211yescharacteristic
28C2×C4×D4×C139C2211yescharacteristic
29C2×C4×D4×C139C2211yescharacteristic
30#469×C139—24no—
31#466×C139—24no—
32#459×C139—24no—
33#435×C139—24no—
34C2×#107×C139C2211yescharacteristic
35C2×#106×C139C2211yescharacteristic
36C2×C4⋊C8×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×C22⋊C8×C139C2211yescharacteristic
46C2×C22⋊C8×C139C2211yescharacteristic
47C2×#97×C139C2211yescharacteristic
48#397×C139—21no—
49#392×C139—21no—
50#392×C139—21no—
51#392×C139—21no—
52#390×C139—21no—
53#386×C139—21no—
54#386×C139—21no—
55#382×C139C2211yescharacteristic
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic
58C4×C4⋊C4×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62#340×C139C2211yescharacteristic
63C22×D4×C139—21no—
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—21no—
70C22×D4×C139—21no—
71C22×D4×C139D411yescharacteristic
72C22×D4×C139C2311yescharacteristic
73C22×D4×C139C2311yescharacteristic
74C22×D4×C139C2311yescharacteristic
75C23×C4×C139—21no—
76C23×C4×C139C2311yescharacteristic
77C23×C4×C139C2311yescharacteristic
78C2×D8×C139—22no—
79C2×D8×C139—22no—
80C2×D8×C139—22no—
81C2×D8×C139—22no—
82C2×D8×C139—41no—
83C2×D8×C139—41no—
84C2×M16×C139—22no—
85C2×M16×C139—22no—
86C2×M16×C139—41no—
87C22×C8×C139—22no—
88C22×C8×C139—22no—
89C22×C8×C139—41no—
90C22×C8×C139C2311yescharacteristic
91C22×C8×C139C2311yescharacteristic
92C22×C8×C139C2311yescharacteristic
93C22×C8×C139C2311yescharacteristic
94#127×C139—22no—
95#127×C139—22no—
96#127×C139—44no—
97#121×C139—22no—
98#121×C139—22no—
99#121×C139—22no—
100#121×C139—22no—
101#121×C139—22no—
102#121×C139—22no—
103#121×C139—41no—
104#121×C139—41no—
105#121×C139—41no—
106#121×C139—41no—
107#121×C139—41no—
108#121×C139—41no—
109C4×D4×C139—22no—
110C4×D4×C139—22no—
111C4×D4×C139—22no—
112C4×D4×C139—22no—
113C2×C4⋊C4×C139D411yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—21no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139D411yescharacteristic
129C2×C22⋊C4×C139D411yescharacteristic
130C2×C42×C139—21no—
131C2×C42×C139C2311yescharacteristic
132#107×C139—22no—
133#106×C139—22no—
134C4⋊C8×C139D414yescomplemented
135#102×C139—22no—
136#102×C139—22no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—41no—
141#102×C139—41no—
142#102×C139D414yescomplemented
143C22⋊C8×C139—22no—
144C22⋊C8×C139—22no—
145#97×C139—22no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139—21no—
149#95×C139—21no—
150#95×C139—21no—
151C24×C139—21no—
152C24×C139—21no—
153C24×C139—21no—
154C24×C139C2×D411yescharacteristic
155C24×C139C2×D411yescharacteristic
156C2×D4×C139—22no—
157C2×D4×C139—22no—
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—21no—
165C2×D4×C139—21no—
166C2×D4×C139—21no—
167C2×D4×C139—21no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139—41no—
176C2×D4×C139—42no—
177C2×D4×C139—42no—
178C2×D4×C139—42no—
179C2×D4×C139—42no—
180C2×D4×C139—42no—
181C2×D4×C139—42no—
182C2×D4×C139—42no—
183C2×D4×C139—42no—
184C2×D4×C139—42no—
185C2×D4×C139—42no—
186C2×D4×C139—42no—
187C2×D4×C139—42no—
188C2×D4×C139—42no—
189C2×D4×C139—42no—
190C2×D4×C139—42no—
191C2×D4×C139—42no—
192C2×D4×C139—81no—
193C2×D4×C139—81no—
194C2×D4×C139—81no—
195C2×D4×C139—81no—
196C2×D4×C139—81no—
197C2×D4×C139—81no—
198C2×D4×C139—81no—
199C2×D4×C139—81no—
200C2×D4×C139C2×D412yes—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—21no—
205C22×C4×C139—21no—
206C22×C4×C139—21no—
207C22×C4×C139—21no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—21no—
211C22×C4×C139—21no—
212C22×C4×C139—21no—
213C22×C4×C139—21no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139—42no—
219C22×C4×C139—81no—
220C22×C4×C139—81no—
221C22×C4×C139C2×D411yescharacteristic
222C22×C4×C139C2×D411yescharacteristic
223C22×C4×C139C2×D411yescharacteristic
224C22×C4×C139C2×D411yescharacteristic
225C22×C4×C139C2411yescharacteristic
226D8×C139—44no—
227D8×C139—44no—
228M16×C139—44no—
229C2×C8×C139—21no—
230C2×C8×C139—21no—
231C2×C8×C139—21no—
232C2×C8×C139—21no—
233C2×C8×C139—21no—
234C2×C8×C139—21no—
235C2×C8×C139—21no—
236C2×C8×C139—21no—
237C2×C8×C139—21no—
238C2×C8×C139—44no—
239C2×C8×C139C2×D412yes—
240C2×C8×C139C2×D412yes—
241C2×C8×C139C2×D412yes—
242C4⋊C4×C139—22no—
243C4⋊C4×C139—21no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139—21no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—21no—
251C4⋊C4×C139C2×D412yes—
252C4⋊C4×C139#4112yes—
253C22⋊C4×C139—22no—
254C22⋊C4×C139—22no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—42no—
257C22⋊C4×C139—42no—
258C22⋊C4×C139—42no—
259C22⋊C4×C139—42no—
260C22⋊C4×C139—42no—
261C22⋊C4×C139—42no—
262C22⋊C4×C139—81no—
263C22⋊C4×C139—81no—
264C42×C139—42no—
265C42×C139C2×D412yes—
266C42×C139#4112yes—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—22no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—21no—
279C23×C139—21no—
280C23×C139—21no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—41no—
285C23×C139—41no—
286C23×C139—41no—
287C23×C139—41no—
288C23×C139—41no—
289C23×C139—41no—
290C23×C139—41no—
291C23×C139—41no—
292C23×C139—41no—
293C23×C139—41no—
294C23×C139—41no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—41no—
298C23×C139—41no—
299C23×C139—41no—
300C23×C139—41no—
301C23×C139AGL(1,ℤ/8)12yes—
302C23×C139C22×D411yescharacteristic
303D4×C139—22no—
304D4×C139—22no—
305D4×C139—44no—
306D4×C139—41no—
307D4×C139—41no—
308D4×C139—41no—
309D4×C139—41no—
310D4×C139—41no—
311D4×C139—41no—
312D4×C139—41no—
313D4×C139—41no—
314D4×C139—41no—
315D4×C139—41no—
316D4×C139—84no—
317D4×C139—84no—
318D4×C139—84no—
319D4×C139—84no—
320D4×C139—84no—
321D4×C139—84no—
322D4×C139—84no—
323D4×C139—84no—
324C2×C4×C139—21no—
325C2×C4×C139—21no—
326C2×C4×C139—21no—
327C2×C4×C139—21no—
328C2×C4×C139—21no—
329C2×C4×C139—21no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—22no—
333C2×C4×C139—22no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—41no—
337C2×C4×C139—41no—
338C2×C4×C139—41no—
339C2×C4×C139—41no—
340C2×C4×C139—41no—
341C2×C4×C139—41no—
342C2×C4×C139—41no—
343C2×C4×C139—41no—
344C2×C4×C139—41no—
345C2×C4×C139—41no—
346C2×C4×C139—41no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—41no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
353C2×C4×C139—41no—
354C2×C4×C139—41no—
355C2×C4×C139—41no—
356C2×C4×C139—41no—
357C2×C4×C139—84no—
358C2×C4×C139#12112yes—
359C2×C4×C139#12112yes—
360C2×C4×C139C22×D411yescharacteristic
361C2×C4×C139C22×D411yescharacteristic
362C2×C4×C139C2×#4111yescharacteristic
363C2×C4×C139C2×#4111yescharacteristic
364C2×C4×C139H(5,𝔽2)11yescharacteristic
365C2×C4×C139H(5,𝔽2)11yescharacteristic
366C8×C139—22no—
367C8×C139—22no—
368C8×C139—22no—
369C8×C139—41no—
370C22×C139—22no—
371C22×C139—22no—
372C22×C139—22no—
373C22×C139—41no—
374C22×C139—41no—
375C22×C139—41no—
376C22×C139—41no—
377C22×C139—41no—
378C22×C139—42no—
379C22×C139—41no—
380C22×C139—42no—
381C22×C139—41no—
382C22×C139—42no—
383C22×C139—41no—
384C22×C139—41no—
385C22×C139—41no—
386C22×C139—41no—
387C22×C139—81no—
388C22×C139—81no—
389C22×C139—81no—
390C22×C139—81no—
391C22×C139—81no—
392C22×C139—81no—
393C22×C139—81no—
394C22×C139—81no—
395C22×C139—81no—
396C22×C139—81no—
397C22×C139—81no—
398C22×C139—81no—
399C22×C139—81no—
400C22×C139—81no—
401C22×C139—81no—
402C22×C139—81no—
403C22×C139—81no—
404C22×C139—81no—
405C22×C139C2×#12111yescharacteristic
406C22×C139D4211yescharacteristic
407C22×C139#54611yescharacteristic
408C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C139#57511yescharacteristic
410C22×C139#57611yescharacteristic
411C22×C139#57611yescharacteristic
412C4×C139—22no—
413C4×C139—22no—
414C4×C139—41no—
415C4×C139—41no—
416C4×C139—42no—
417C4×C139—42no—
418C4×C139—81no—
419C4×C139—81no—
420C4×C139—81no—
421C4×C139#53211yescharacteristic
422C4×C139#54011yescharacteristic
423C4×C139D4211yescharacteristic
424C4×C139#55011yescharacteristic
425C2×C139—42no—
426C2×C139—81no—
427C2×C139—82no—
428C2×C139—161no—
429C2×C139—161no—
430C2×C139#242811yescharacteristic
431C2×C139#305511yescharacteristic
432C2×C139#305811yescharacteristic
433C2×C139#326411yescharacteristic
434C2×C139#326811yescharacteristic
435C2×C139#330911yescharacteristic
436C2×C139#331811yescharacteristic
437#25396C13911yesmaximal, characteristic, direct product factor, Sylow
438C139#2539611yescharacteristic, direct product factor, Sylow
439C2×#469C2×C13911yescharacteristic, complemented
440C2×#466C2×C13911yescharacteristic, complemented
441C2×#459C2×C13911yescharacteristic, complemented
442C2×#435C2×C13911yescharacteristic, complemented
443#2541C2×C13911yescharacteristic, complemented
444#2535C2×C13911yescharacteristic, complemented
445#2034C2×C13911yescharacteristic, complemented
446#2033C2×C13911yescharacteristic, complemented
447#1999C2×C13911yescharacteristic, complemented
448#1999C2×C13911yescharacteristic, complemented
449#1961C2×C13911yescharacteristic, complemented
450#1949C2×C13911yescharacteristic, complemented
451#1895C2×C13911yescharacteristic, complemented
452#1893C2×C13911yescharacteristic, complemented
453#1762C2×C13911yescharacteristic, complemented
454C22×D8C22×C13911yescharacteristic
455C22×D8C22×C13911yescharacteristic
456C22×M16C22×C13911yescharacteristic
457C23×C8C22×C13911yescharacteristic
458C2×#127—21no—
459C2×#127C22×C13911yescharacteristic
460C2×#121C22×C13911yescharacteristic
461C2×#121C22×C13911yescharacteristic
462C2×#121C22×C13911yescharacteristic
463C2×#121C22×C13911yescharacteristic
464C2×#121C22×C13911yescharacteristic
465C2×#121C22×C13911yescharacteristic
466C2×C4×D4C22×C13911yescharacteristic
467C2×C4×D4C22×C13911yescharacteristic
468#469—24no—
469#466—24no—
470#459—24no—
471#435—24no—
472C2×#107C22×C13911yescharacteristic
473C2×#106C22×C13911yescharacteristic
474C2×C4⋊C8C22×C13911yescharacteristic
475C2×#102C22×C13911yescharacteristic
476C2×#102C22×C13911yescharacteristic
477C2×#102C22×C13911yescharacteristic
478C2×#102C22×C13911yescharacteristic
479C2×#102C22×C13911yescharacteristic
480C2×#102C22×C13911yescharacteristic
481C2×#102C22×C13911yescharacteristic
482C2×#102C22×C13911yescharacteristic
483C2×C22⋊C8C22×C13911yescharacteristic
484C2×C22⋊C8C22×C13911yescharacteristic
485C2×#97C22×C13911yescharacteristic
486#397—21no—
487#392—21no—
488#392—21no—
489#392—21no—
490#390—21no—
491#386—21no—
492#386—21no—
493#382C22×C13911yescharacteristic
494#380C22×C13911yescharacteristic
495#380C22×C13911yescharacteristic
496C4×C4⋊C4C22×C13911yescharacteristic
497#340C22×C13911yescharacteristic
498#340C22×C13911yescharacteristic
499#340C22×C13911yescharacteristic
500#340C22×C13911yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4D4×C13911yescharacteristic
510C22×D4C23×C13911yescharacteristic
511C22×D4C23×C13911yescharacteristic
512C22×D4C23×C13911yescharacteristic
513C23×C4—21no—
514C23×C4C23×C13911yescharacteristic
515C23×C4C23×C13911yescharacteristic
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—41no—
521C2×D8—41no—
522C2×M16—22no—
523C2×M16—22no—
524C2×M16—41no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—41no—
528C22×C8C23×C13911yescharacteristic
529C22×C8C23×C13911yescharacteristic
530C22×C8C23×C13911yescharacteristic
531C22×C8C23×C13911yescharacteristic
532#127—22no—
533#127—22no—
534#127—44no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—41no—
542#121—41no—
543#121—41no—
544#121—41no—
545#121—41no—
546#121—41no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—22no—
551C2×C4⋊C4D4×C13911yescharacteristic
552C2×C4⋊C4C23×C13911yescharacteristic
553C2×C4⋊C4C23×C13911yescharacteristic
554C2×C4⋊C4C23×C13911yescharacteristic
555C2×C4⋊C4C23×C13911yescharacteristic
556C2×C4⋊C4C23×C13911yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4D4×C13911yescharacteristic
567C2×C22⋊C4D4×C13911yescharacteristic
568C2×C42—21no—
569C2×C42C23×C13911yescharacteristic
570#107—22no—
571#106—22no—
572C4⋊C8D4×C13914yescomplemented
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—41no—
579#102—41no—
580#102D4×C13914yescomplemented
581C22⋊C8—22no—
582C22⋊C8—22no—
583#97—22no—
584#95—21no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24—21no—
591C24—21no—
592C24C2×D4×C13911yescharacteristic
593C24C2×D4×C13911yescharacteristic
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—42no—
620C2×D4—42no—
621C2×D4—42no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4—81no—
637C2×D4—81no—
638C2×D4C2×D4×C13912yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—42no—
657C22×C4—81no—
658C22×C4—81no—
659C22×C4C2×D4×C13911yescharacteristic
660C22×C4C2×D4×C13911yescharacteristic
661C22×C4C2×D4×C13911yescharacteristic
662C22×C4C2×D4×C13911yescharacteristic
663C22×C4C24×C13911yescharacteristic
664D8—44no—
665D8—44no—
666M16—44no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—44no—
677C2×C8C2×D4×C13912yes—
678C2×C8C2×D4×C13912yes—
679C2×C8C2×D4×C13912yes—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4C2×D4×C13912yes—
690C4⋊C4#41×C13912yes—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—81no—
701C22⋊C4—81no—
702C42—42no—
703C42C2×D4×C13912yes—
704C42#41×C13912yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23AGL(1,ℤ/8)×C13912yes—
740C23C22×D4×C13911yescharacteristic
741D4—22no—
742D4—22no—
743D4—44no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756D4—84no—
757D4—84no—
758D4—84no—
759D4—84no—
760D4—84no—
761D4—84no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4#121×C13912yes—
797C2×C4#121×C13912yes—
798C2×C4C22×D4×C13911yescharacteristic
799C2×C4C22×D4×C13911yescharacteristic
800C2×C4C2×#41×C13911yescharacteristic
801C2×C4C2×#41×C13911yescharacteristic
802C2×C4H(5,𝔽2)×C13911yescharacteristic
803C2×C4H(5,𝔽2)×C13911yescharacteristic
804C8—22no—
805C8—22no—
806C8—22no—
807C8—41no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—42no—
821C22—41no—
822C22—42no—
823C22—41no—
824C22—42no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22C2×#121×C13911yescharacteristic
844C22D42×C13911yescharacteristic
845C22#546×C13911yescharacteristic
846C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
847C22#575×C13911yescharacteristic
848C22#576×C13911yescharacteristic
849C22#576×C13911yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4#532×C13911yescharacteristic
860C4#540×C13911yescharacteristic
861C4D42×C13911yescharacteristic
862C4#550×C13911yescharacteristic
863C2—42no—
864C2—81no—
865C2—82no—
866C2—161no—
867C2—161no—
868C2#2428×C13911yescharacteristic
869C2#3055×C13911yescharacteristic
870C2#3058×C13911yescharacteristic
871C2#3264×C13911yescharacteristic
872C2#3268×C13911yescharacteristic
873C2#3309×C13911yescharacteristic
874C2#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×#469×C139C2semidirect
2. C2×#466×C139C2semidirect
3. C2×#459×C139C2semidirect
4. C2×#435×C139C2semidirect
5. #2541×C139C2semidirect
6. #2535×C139C2semidirect
7. #2034×C139C2semidirect
8. #2033×C139C2semidirect
9. #1999×C139C2semidirect
10. #1999×C139C2semidirect
11. #1961×C139C2semidirect
12. #1949×C139C2semidirect
13. #1895×C139C2semidirect
14. #1893×C139C2semidirect
15. #1762×C139C2semidirect
134. C4⋊C8×C139D4semidirect
142. #102×C139D4semidirect
437. #25396C139direct (N × H)
438. C139#25396direct (N × H)
439. C2×#469C2×C139semidirect
440. C2×#466C2×C139semidirect
441. C2×#459C2×C139semidirect
442. C2×#435C2×C139semidirect
443. #2541C2×C139semidirect
444. #2535C2×C139semidirect
445. #2034C2×C139semidirect
446. #2033C2×C139semidirect
447. #1999C2×C139semidirect
448. #1999C2×C139semidirect
449. #1961C2×C139semidirect
450. #1949C2×C139semidirect
451. #1895C2×C139semidirect
452. #1893C2×C139semidirect
453. #1762C2×C139semidirect
572. C4⋊C8D4×C139semidirect
580. #102D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1392
C2×#466×C1392
C2×#459×C1392
C2×#435×C1392
#2541×C1392
#2535×C1392
#2034×C1392
#2033×C1392
#1999×C1392
#1961×C1392
#1949×C1392
#1895×C1392
#1893×C1392
#1762×C1392
#25396139