Finite Group Databasebeta

← C139×#25136 #48019732

Subgroups — C139×#25136 #48019732

Order 35584.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C139C211yesmaximal, characteristic, complemented
2C2×#450×C139C211yesmaximal, characteristic, complemented
3C2×#436×C139C211yesmaximal, characteristic, complemented
4C2×#418×C139C211yesmaximal, characteristic, complemented
5#2415×C139C211yesmaximal, characteristic, complemented
6#2408×C139C211yesmaximal, characteristic
7#2067×C139C211yesmaximal, characteristic, complemented
8#2055×C139C211yesmaximal, characteristic, complemented
9#2034×C139C211yesmaximal, characteristic, complemented
10#2000×C139C211yesmaximal, characteristic, complemented
11#1968×C139C211yesmaximal, characteristic, complemented
12#1934×C139C211yesmaximal, characteristic, complemented
13#1895×C139C211yesmaximal, characteristic, complemented
14#1894×C139C211yesmaximal, characteristic, complemented
15#1854×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×M16×C139C2211yescharacteristic
20C22×M16×C139C2211yescharacteristic, complemented
21C2×C22⋊Q8×C139C2211yescharacteristic
22C2×C22⋊Q8×C139C2211yescharacteristic, complemented
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#120×C139—21no—
26C2×C4×D4×C139C2211yescharacteristic
27C2×#117×C139C2211yescharacteristic
28#468×C139—24no—
29#450×C139—24no—
30#436×C139—24no—
31C2×#107×C139C2211yescharacteristic, complemented
32C2×#106×C139C2211yescharacteristic, complemented
33C2×C4⋊C8×C139C2211yescharacteristic, complemented
34#418×C139—24no—
35C2×#103×C139C2211yescharacteristic, complemented
36C2×#103×C139C2211yescharacteristic, complemented
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×C22⋊C8×C139C2211yescharacteristic
44C2×C22⋊C8×C139C2211yescharacteristic, complemented
45C2×C4×C8×C139C2211yescharacteristic, complemented
46#397×C139—21no—
47#394×C139—21no—
48#394×C139—21no—
49#392×C139—21no—
50#391×C139C2211yescharacteristic, complemented
51#390×C139C2211yescharacteristic
52#390×C139C2211yescharacteristic
53#389×C139—21no—
54#389×C139C2211yescharacteristic, complemented
55#388×C139—21no—
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic, complemented
58#379×C139—21no—
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63C25×C139—21no—
64C22×Q8×C139C2311yescharacteristic
65C22×D4×C139—22no—
66C22×D4×C139—22no—
67C22×D4×C139—21no—
68C22×D4×C139—21no—
69C22×D4×C139—22no—
70C22×D4×C139—21no—
71C22×D4×C139—22no—
72C22×D4×C139—41no—
73C22×D4×C139—41no—
74C22×D4×C139D411yescharacteristic
75C22×D4×C139C2311yescharacteristic
76C22×D4×C139C2311yescharacteristic
77C23×C4×C139C2311yescharacteristic
78C23×C4×C139C2311yescharacteristic
79C2×SD16×C139—22no—
80C2×SD16×C139—22no—
81C2×SD16×C139—22no—
82C2×SD16×C139—22no—
83C2×SD16×C139—41no—
84C2×SD16×C139—41no—
85C2×M16×C139—22no—
86C2×M16×C139—22no—
87C2×M16×C139—22no—
88C2×M16×C139—22no—
89C2×M16×C139—41no—
90C2×M16×C139—41no—
91C22×C8×C139C2311yescharacteristic
92C22×C8×C139C2311yescharacteristic
93C22×C8×C139C2311yescharacteristic
94C22×C8×C139C2311yescharacteristic
95C22⋊Q8×C139—22no—
96C22⋊Q8×C139—22no—
97C22⋊Q8×C139—22no—
98C22⋊Q8×C139—41no—
99#121×C139—22no—
100#121×C139—22no—
101#121×C139—41no—
102#121×C139—41no—
103#120×C139—44no—
104C4×D4×C139—22no—
105C4×D4×C139—22no—
106#117×C139—22no—
107#117×C139—41no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139D411yescharacteristic
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C22⋊C4×C139—21no—
118C2×C22⋊C4×C139—21no—
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—41no—
134C4⋊C8×C139—22no—
135#103×C139—22no—
136#103×C139—41no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139D414yescomplemented
143C22⋊C8×C139—22no—
144C22⋊C8×C139D414yescomplemented
145C4×C8×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—42no—
154C24×C139—42no—
155C24×C139—42no—
156C24×C139—42no—
157C24×C139—42no—
158C24×C139—81no—
159C24×C139—81no—
160C24×C139C2×D411yescharacteristic
161C24×C139C2×D411yescharacteristic
162C2×Q8×C139—21no—
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×Q8×C139—21no—
166C2×Q8×C139—21no—
167C2×Q8×C139—21no—
168C2×D4×C139—28no—
169C2×D4×C139—22no—
170C2×D4×C139—22no—
171C2×D4×C139—21no—
172C2×D4×C139—21no—
173C2×D4×C139—21no—
174C2×D4×C139—21no—
175C2×D4×C139—21no—
176C2×D4×C139—21no—
177C2×D4×C139—21no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—44no—
182C2×D4×C139—44no—
183C2×D4×C139—41no—
184C2×D4×C139—42no—
185C2×D4×C139—42no—
186C2×D4×C139—44no—
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×C139C2×D412yes—
195C2×D4×C139#4112yes—
196C22×C4×C139—21no—
197C22×C4×C139—21no—
198C22×C4×C139—21no—
199C22×C4×C139—21no—
200C22×C4×C139—21no—
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×C139C2×D411yescharacteristic
213C22×C4×C139C2×D411yescharacteristic
214C22×C4×C139C2×D411yescharacteristic
215C22×C4×C139C2×D412yes—
216C22×C4×C139C2×D411yescharacteristic
217C22×C4×C139#4112yes—
218C22×C4×C139C2411yescharacteristic
219SD16×C139—44no—
220SD16×C139—44no—
221M16×C139—44no—
222M16×C139—44no—
223C2×C8×C139—21no—
224C2×C8×C139—21no—
225C2×C8×C139—21no—
226C2×C8×C139—21no—
227C2×C8×C139—21no—
228C2×C8×C139—21no—
229C2×C8×C139—21no—
230C2×C8×C139—21no—
231C2×C8×C139—21no—
232C2×C8×C139C2×D412yes—
233C2×C8×C139C2×D412yes—
234C2×C8×C139C2×D412yes—
235C4⋊C4×C139—22no—
236C4⋊C4×C139—21no—
237C4⋊C4×C139—21no—
238C4⋊C4×C139—21no—
239C4⋊C4×C139—21no—
240C4⋊C4×C139—21no—
241C4⋊C4×C139—21no—
242C4⋊C4×C139—21no—
243C4⋊C4×C139—21no—
244C4⋊C4×C139—21no—
245C4⋊C4×C139—42no—
246C4⋊C4×C139—42no—
247C4⋊C4×C139—42no—
248C4⋊C4×C139C2×D412yes—
249C22⋊C4×C139—22no—
250C22⋊C4×C139—22no—
251C22⋊C4×C139—42no—
252C22⋊C4×C139—42no—
253C22⋊C4×C139—42no—
254C22⋊C4×C139—42no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—42no—
257C22⋊C4×C139—42no—
258C22⋊C4×C139—42no—
259C22⋊C4×C139—42no—
260C22⋊C4×C139—81no—
261C22⋊C4×C139—81no—
262C42×C139—21no—
263C42×C139—21no—
264C42×C139—42no—
265C23×C139—21no—
266C23×C139—21no—
267C23×C139—21no—
268C23×C139—21no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—22no—
274C23×C139—22no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—21no—
279C23×C139—21no—
280C23×C139—48no—
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—84no—
294C23×C139—84no—
295C23×C139—84no—
296C23×C139—84no—
297C23×C139—84no—
298C23×C139—84no—
299C23×C139#12112yes—
300C23×C139C22×D411yescharacteristic
301Q8×C139—41no—
302Q8×C139—41no—
303Q8×C139—41no—
304Q8×C139—41no—
305D4×C139—22no—
306D4×C139—22no—
307D4×C139—22no—
308D4×C139—22no—
309D4×C139—44no—
310D4×C139—48no—
311D4×C139—41no—
312D4×C139—41no—
313D4×C139—41no—
314D4×C139—41no—
315D4×C139—84no—
316D4×C139—84no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
319C2×C4×C139—21no—
320C2×C4×C139—21no—
321C2×C4×C139—22no—
322C2×C4×C139—22no—
323C2×C4×C139—22no—
324C2×C4×C139—22no—
325C2×C4×C139—21no—
326C2×C4×C139—21no—
327C2×C4×C139—22no—
328C2×C4×C139—21no—
329C2×C4×C139—21no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—41no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139—41no—
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#12112yes—
354C2×C4×C139AGL(1,ℤ/8)12yes—
355C2×C4×C139C22×D411yescharacteristic
356C2×C4×C139C22×D411yescharacteristic
357C2×C4×C139C2×#4111yescharacteristic
358C2×C4×C139C2×#4111yescharacteristic
359C2×C4×C139H(5,𝔽2)11yescharacteristic
360C2×C4×C139H(5,𝔽2)11yescharacteristic
361C8×C139—22no—
362C8×C139—22no—
363C8×C139—22no—
364C8×C139—41no—
365C22×C139—22no—
366C22×C139—22no—
367C22×C139—22no—
368C22×C139—41no—
369C22×C139—41no—
370C22×C139—41no—
371C22×C139—41no—
372C22×C139—41no—
373C22×C139—42no—
374C22×C139—42no—
375C22×C139—41no—
376C22×C139—42no—
377C22×C139—41no—
378C22×C139—42no—
379C22×C139—41no—
380C22×C139—41no—
381C22×C139—41no—
382C22×C139—42no—
383C22×C139—41no—
384C22×C139—42no—
385C22×C139—816no—
386C22×C139—81no—
387C22×C139—81no—
388C22×C139—81no—
389C22×C139—81no—
390C22×C139—81no—
391C22×C139—81no—
392C22×C139—81no—
393C22×C139—81no—
394C22×C139C2×#12111yescharacteristic
395C22×C139D4211yescharacteristic
396C22×C139#54611yescharacteristic
397C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C139#57511yescharacteristic
399C22×C139#57711yescharacteristic
400C22×C139#57711yescharacteristic
401C4×C139—22no—
402C4×C139—22no—
403C4×C139—41no—
404C4×C139—42no—
405C4×C139—41no—
406C4×C139—81no—
407C4×C139—81no—
408C4×C139—81no—
409C4×C139—81no—
410C4×C139—81no—
411C4×C139#52511yescharacteristic
412C4×C139#53811yescharacteristic
413C4×C139D4211yescharacteristic
414C4×C139#54611yescharacteristic
415C2×C139—42no—
416C2×C139—81no—
417C2×C139—82no—
418C2×C139—82no—
419C2×C139#242411yescharacteristic
420C2×C139#305511yescharacteristic
421C2×C139#305711yescharacteristic
422C2×C139#327211yescharacteristic
423C2×C139#327511yescharacteristic
424C2×C139#332311yescharacteristic
425C2×C139#332411yescharacteristic
426#25136C13911yesmaximal, characteristic, direct product factor, Sylow
427C139#2513611yescharacteristic, direct product factor, Sylow
428C2×#468C2×C13911yescharacteristic, complemented
429C2×#450C2×C13911yescharacteristic, complemented
430C2×#436C2×C13911yescharacteristic, complemented
431C2×#418C2×C13911yescharacteristic, complemented
432#2415C2×C13911yescharacteristic, complemented
433#2408C2×C13911yescharacteristic
434#2067C2×C13911yescharacteristic, complemented
435#2055C2×C13911yescharacteristic, complemented
436#2034C2×C13911yescharacteristic, complemented
437#2000C2×C13911yescharacteristic, complemented
438#1968C2×C13911yescharacteristic, complemented
439#1934C2×C13911yescharacteristic, complemented
440#1895C2×C13911yescharacteristic, complemented
441#1894C2×C13911yescharacteristic, complemented
442#1854C2×C13911yescharacteristic, complemented
443C23×D4C22×C13911yescharacteristic
444C22×SD16C22×C13911yescharacteristic
445C22×SD16C22×C13911yescharacteristic
446C22×M16C22×C13911yescharacteristic
447C22×M16C22×C13911yescharacteristic, complemented
448C2×C22⋊Q8C22×C13911yescharacteristic
449C2×C22⋊Q8C22×C13911yescharacteristic, complemented
450C2×#121C22×C13911yescharacteristic
451C2×#121C22×C13911yescharacteristic
452C2×#120—21no—
453C2×C4×D4C22×C13911yescharacteristic
454C2×#117C22×C13911yescharacteristic
455#468—24no—
456#450—24no—
457#436—24no—
458C2×#107C22×C13911yescharacteristic, complemented
459C2×#106C22×C13911yescharacteristic, complemented
460C2×C4⋊C8C22×C13911yescharacteristic, complemented
461#418—24no—
462C2×#103C22×C13911yescharacteristic, complemented
463C2×#103C22×C13911yescharacteristic, complemented
464C2×#102C22×C13911yescharacteristic
465C2×#102C22×C13911yescharacteristic
466C2×#102C22×C13911yescharacteristic
467C2×#102C22×C13911yescharacteristic
468C2×#102C22×C13911yescharacteristic
469C2×#102C22×C13911yescharacteristic
470C2×C22⋊C8C22×C13911yescharacteristic
471C2×C22⋊C8C22×C13911yescharacteristic, complemented
472C2×C4×C8C22×C13911yescharacteristic, complemented
473#397—21no—
474#394—21no—
475#394—21no—
476#392—21no—
477#391C22×C13911yescharacteristic, complemented
478#390C22×C13911yescharacteristic
479#390C22×C13911yescharacteristic
480#389—21no—
481#389C22×C13911yescharacteristic, complemented
482#388—21no—
483#380C22×C13911yescharacteristic
484#380C22×C13911yescharacteristic, complemented
485#379—21no—
486#340C22×C13911yescharacteristic, complemented
487#340C22×C13911yescharacteristic, complemented
488#340C22×C13911yescharacteristic, complemented
489#340C22×C13911yescharacteristic, complemented
490C25—21no—
491C22×Q8C23×C13911yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4D4×C13911yescharacteristic
502C22×D4C23×C13911yescharacteristic
503C22×D4C23×C13911yescharacteristic
504C23×C4C23×C13911yescharacteristic
505C23×C4C23×C13911yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8C23×C13911yescharacteristic
519C22×C8C23×C13911yescharacteristic
520C22×C8C23×C13911yescharacteristic
521C22×C8C23×C13911yescharacteristic
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528#121—41no—
529#121—41no—
530#120—44no—
531C4×D4—22no—
532C4×D4—22no—
533#117—22no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4D4×C13911yescharacteristic
539C2×C4⋊C4C23×C13911yescharacteristic
540C2×C4⋊C4C23×C13911yescharacteristic
541C2×C4⋊C4C23×C13911yescharacteristic
542C2×C4⋊C4C23×C13911yescharacteristic
543C2×C4⋊C4C23×C13911yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C13911yescharacteristic
556C2×C22⋊C4D4×C13911yescharacteristic
557C2×C42—21no—
558C2×C42C23×C13911yescharacteristic
559#107—22no—
560#106—41no—
561C4⋊C8—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102D4×C13914yescomplemented
570C22⋊C8—22no—
571C22⋊C8D4×C13914yescomplemented
572C4×C8—22no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C24—21no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×D4×C13911yescharacteristic
588C24C2×D4×C13911yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—22no—
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—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×D4×C13912yes—
622C2×D4#41×C13912yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4C2×D4×C13911yescharacteristic
640C22×C4C2×D4×C13911yescharacteristic
641C22×C4C2×D4×C13911yescharacteristic
642C22×C4C2×D4×C13912yes—
643C22×C4C2×D4×C13911yescharacteristic
644C22×C4#41×C13912yes—
645C22×C4C24×C13911yescharacteristic
646SD16—44no—
647SD16—44no—
648M16—44no—
649M16—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8C2×D4×C13912yes—
660C2×C8C2×D4×C13912yes—
661C2×C8C2×D4×C13912yes—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4C2×D4×C13912yes—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C13912yes—
727C23C22×D4×C13911yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4#121×C13912yes—
781C2×C4AGL(1,ℤ/8)×C13912yes—
782C2×C4C22×D4×C13911yescharacteristic
783C2×C4C22×D4×C13911yescharacteristic
784C2×C4C2×#41×C13911yescharacteristic
785C2×C4C2×#41×C13911yescharacteristic
786C2×C4H(5,𝔽2)×C13911yescharacteristic
787C2×C4H(5,𝔽2)×C13911yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—41no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×#121×C13911yescharacteristic
822C22D42×C13911yescharacteristic
823C22#546×C13911yescharacteristic
824C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
825C22#575×C13911yescharacteristic
826C22#577×C13911yescharacteristic
827C22#577×C13911yescharacteristic
828C4—22no—
829C4—22no—
830C4—41no—
831C4—41no—
832C4—42no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4#525×C13911yescharacteristic
839C4#538×C13911yescharacteristic
840C4D42×C13911yescharacteristic
841C4#546×C13911yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2#2424×C13911yescharacteristic
847C2#3055×C13911yescharacteristic
848C2#3057×C13911yescharacteristic
849C2#3272×C13911yescharacteristic
850C2#3275×C13911yescharacteristic
851C2#3323×C13911yescharacteristic
852C2#3324×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#2408×C139C2
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×#468×C139C2semidirect
2. C2×#450×C139C2semidirect
3. C2×#436×C139C2semidirect
4. C2×#418×C139C2semidirect
5. #2415×C139C2semidirect
7. #2067×C139C2semidirect
8. #2055×C139C2semidirect
9. #2034×C139C2semidirect
10. #2000×C139C2semidirect
11. #1968×C139C2semidirect
12. #1934×C139C2semidirect
13. #1895×C139C2semidirect
14. #1894×C139C2semidirect
15. #1854×C139C2semidirect
20. C22×M16×C139C22semidirect
22. C2×C22⋊Q8×C139C22semidirect
31. C2×#107×C139C22semidirect
32. C2×#106×C139C22semidirect
33. C2×C4⋊C8×C139C22semidirect
35. C2×#103×C139C22semidirect
36. C2×#103×C139C22semidirect
44. C2×C22⋊C8×C139C22semidirect
45. C2×C4×C8×C139C22semidirect
50. #391×C139C22semidirect
54. #389×C139C22semidirect
57. #380×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
142. #102×C139D4semidirect
144. C22⋊C8×C139D4semidirect
426. #25136C139direct (N × H)
427. C139#25136direct (N × H)
428. C2×#468C2×C139semidirect
429. C2×#450C2×C139semidirect
430. C2×#436C2×C139semidirect
431. C2×#418C2×C139semidirect
432. #2415C2×C139semidirect
434. #2067C2×C139semidirect
435. #2055C2×C139semidirect
436. #2034C2×C139semidirect
437. #2000C2×C139semidirect
438. #1968C2×C139semidirect
439. #1934C2×C139semidirect
440. #1895C2×C139semidirect
441. #1894C2×C139semidirect
442. #1854C2×C139semidirect
447. C22×M16C22×C139semidirect
449. C2×C22⋊Q8C22×C139semidirect
458. C2×#107C22×C139semidirect
459. C2×#106C22×C139semidirect
460. C2×C4⋊C8C22×C139semidirect
462. C2×#103C22×C139semidirect
463. C2×#103C22×C139semidirect
471. C2×C22⋊C8C22×C139semidirect
472. C2×C4×C8C22×C139semidirect
477. #391C22×C139semidirect
481. #389C22×C139semidirect
484. #380C22×C139semidirect
486. #340C22×C139semidirect
487. #340C22×C139semidirect
488. #340C22×C139semidirect
489. #340C22×C139semidirect
569. #102D4×C139semidirect
571. C22⋊C8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1392
C2×#450×C1392
C2×#436×C1392
C2×#418×C1392
#2415×C1392
#2408×C1392
#2067×C1392
#2055×C1392
#2034×C1392
#2000×C1392
#1968×C1392
#1934×C1392
#1895×C1392
#1894×C1392
#1854×C1392
#25136139