Finite Group Databasebeta

← C139×#25080 #48019676

Subgroups — C139×#25080 #48019676

Order 35584.

1356 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C139C211yesmaximal, characteristic, complemented
2C2×#460×C139C211yesmaximal, characteristic, complemented
3C2×#450×C139C211yesmaximal, characteristic, complemented
4C22×#102×C139C211yesmaximal, characteristic, complemented
5#2433×C139C211yesmaximal, characteristic
6#2360×C139C211yesmaximal, characteristic, complemented
7#2065×C139C211yesmaximal, characteristic, complemented
8#2055×C139C211yesmaximal, characteristic, complemented
9#2041×C139C211yesmaximal, characteristic, complemented
10#2014×C139C211yesmaximal, characteristic, complemented
11#1982×C139C211yesmaximal, characteristic, complemented
12#1926×C139C211yesmaximal, characteristic, complemented
13#1880×C139C211yesmaximal, characteristic, complemented
14#1874×C139C211yesmaximal, characteristic, complemented
15#1850×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×SD16×C139C2211yescharacteristic, complemented
20C23×C8×C139C2211yescharacteristic
21C2×#127×C139C2211yescharacteristic
22C2×#127×C139C2211yescharacteristic
23C2×C22⋊Q8×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#120×C139—21no—
26C2×#120×C139—21no—
27C2×C4×Q8×C139C2211yescharacteristic, complemented
28C22×C4⋊C4×C139C2211yescharacteristic
29#465×C139—24no—
30#460×C139—24no—
31#450×C139—24no—
32C2×#106×C139C2211yescharacteristic, complemented
33C2×C4⋊C8×C139C2211yescharacteristic, complemented
34C2×C4⋊C8×C139C2211yescharacteristic, complemented
35C2×#103×C139C2211yescharacteristic, complemented
36C2×#102×C139—24no—
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic, complemented
44C2×#102×C139C2211yescharacteristic, complemented
45C2×#102×C139C2211yescharacteristic, complemented
46C2×C22⋊C8×C139C2211yescharacteristic
47#392×C139—21no—
48#392×C139—21no—
49#391×C139C2211yescharacteristic, complemented
50#390×C139C2211yescharacteristic
51#390×C139C2211yescharacteristic
52#389×C139—21no—
53#389×C139C2211yescharacteristic, complemented
54#387×C139—21no—
55#385×C139—21no—
56C4×C4⋊C4×C139C2211yescharacteristic, complemented
57C4×C22⋊C4×C139—21no—
58C4×C22⋊C4×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#336×C139C2211yescharacteristic, complemented
62#336×C139C2211yescharacteristic, complemented
63C25×C139—21no—
64C22×Q8×C139C2311yescharacteristic
65C22×D4×C139—22no—
66C22×D4×C139—22no—
67C22×D4×C139—21no—
68C22×D4×C139—22no—
69C22×D4×C139—21no—
70C22×D4×C139—21no—
71C22×D4×C139—21no—
72C22×D4×C139—21no—
73C22×D4×C139—21no—
74C22×D4×C139—22no—
75C22×D4×C139—41no—
76C22×D4×C139—41no—
77C22×D4×C139C2311yescharacteristic
78C22×D4×C139C2311yescharacteristic
79C22×D4×C139C2311yescharacteristic
80C23×C4×C139—21no—
81C23×C4×C139C2311yescharacteristic
82C2×SD16×C139—22no—
83C2×SD16×C139—22no—
84C2×SD16×C139—22no—
85C2×SD16×C139—22no—
86C2×SD16×C139—22no—
87C2×SD16×C139—22no—
88C2×SD16×C139—41no—
89C2×SD16×C139—41no—
90C2×SD16×C139—41no—
91C22×C8×C139—22no—
92C22×C8×C139—22no—
93C22×C8×C139—41no—
94C22×C8×C139C2311yescharacteristic
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97C22×C8×C139C2311yescharacteristic
98#127×C139—22no—
99#127×C139—22no—
100#127×C139—41no—
101#127×C139—41no—
102C22⋊Q8×C139—22no—
103C22⋊Q8×C139D414yescomplemented
104#121×C139—22no—
105#121×C139—22no—
106#120×C139—44no—
107#120×C139—44no—
108C4×Q8×C139—22no—
109C4×Q8×C139—41no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139—22no—
112C2×C4⋊C4×C139—21no—
113C2×C4⋊C4×C139—21no—
114C2×C4⋊C4×C139—21no—
115C2×C4⋊C4×C139—41no—
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C4⋊C4×C139C2311yescharacteristic
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×C139D411yescharacteristic
127C2×C22⋊C4×C139D411yescharacteristic
128C2×C42×C139—21no—
129C2×C42×C139—21no—
130C2×C42×C139C2311yescharacteristic
131C2×C42×C139C2311yescharacteristic
132#106×C139—22no—
133C4⋊C8×C139—22no—
134C4⋊C8×C139—41no—
135#103×C139—22no—
136#102×C139—22no—
137#102×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—41no—
144#102×C139D414yescomplemented
145C22⋊C8×C139—22no—
146#95×C139—21no—
147#95×C139—21no—
148#95×C139—21no—
149#95×C139—21no—
150#95×C139D411yescharacteristic
151#95×C139D411yescharacteristic
152C24×C139—21no—
153C24×C139—21no—
154C24×C139—21no—
155C24×C139—42no—
156C24×C139—42no—
157C24×C139—42no—
158C24×C139—42no—
159C24×C139—42no—
160C24×C139—81no—
161C24×C139—81no—
162C24×C139C2×D411yescharacteristic
163C2×Q8×C139—21no—
164C2×Q8×C139—21no—
165C2×Q8×C139—21no—
166C2×Q8×C139—21no—
167C2×Q8×C139—21no—
168C2×Q8×C139C2×D412yes—
169C2×D4×C139—28no—
170C2×D4×C139—21no—
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—21no—
182C2×D4×C139—21no—
183C2×D4×C139—21no—
184C2×D4×C139—21no—
185C2×D4×C139—21no—
186C2×D4×C139—44no—
187C2×D4×C139—44no—
188C2×D4×C139—42no—
189C2×D4×C139—42no—
190C2×D4×C139—44no—
191C2×D4×C139—42no—
192C2×D4×C139—42no—
193C2×D4×C139—42no—
194C2×D4×C139—42no—
195C2×D4×C139—42no—
196C2×D4×C139—42no—
197C2×D4×C139—42no—
198C2×D4×C139—42no—
199C2×D4×C139—42no—
200C2×D4×C139—42no—
201C2×D4×C139—42no—
202C2×D4×C139—42no—
203C2×D4×C139—81no—
204C2×D4×C139—81no—
205C2×D4×C139—81no—
206C2×D4×C139—81no—
207C2×D4×C139C2×D412yes—
208C2×D4×C139#4112yes—
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—42no—
220C22×C4×C139—81no—
221C22×C4×C139C2×D411yescharacteristic
222C22×C4×C139C2×D411yescharacteristic
223C22×C4×C139C2×D411yescharacteristic
224C22×C4×C139C2×D412yes—
225C22×C4×C139C2×D411yescharacteristic
226C22×C4×C139C2×D411yescharacteristic
227C22×C4×C139#4112yes—
228C22×C4×C139C2411yescharacteristic
229SD16×C139—44no—
230SD16×C139—44no—
231SD16×C139—44no—
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—21no—
239C2×C8×C139—21no—
240C2×C8×C139—21no—
241C2×C8×C139—21no—
242C2×C8×C139—21no—
243C2×C8×C139—44no—
244C2×C8×C139C2×D412yes—
245C4⋊C4×C139—24no—
246C4⋊C4×C139—21no—
247C4⋊C4×C139—21no—
248C4⋊C4×C139—21no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—21no—
251C4⋊C4×C139—21no—
252C4⋊C4×C139—42no—
253C4⋊C4×C139—42no—
254C4⋊C4×C139—81no—
255C4⋊C4×C139C2×D412yes—
256C4⋊C4×C139C2×D412yes—
257C22⋊C4×C139—24no—
258C22⋊C4×C139—22no—
259C22⋊C4×C139—42no—
260C22⋊C4×C139—42no—
261C22⋊C4×C139—42no—
262C22⋊C4×C139—42no—
263C22⋊C4×C139—42no—
264C22⋊C4×C139SD1614yescomplemented
265C42×C139—21no—
266C42×C139—21no—
267C42×C139—21no—
268C42×C139—21no—
269C42×C139—42no—
270C42×C139—81no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—21no—
275C23×C139—22no—
276C23×C139—22no—
277C23×C139—48no—
278C23×C139—41no—
279C23×C139—41no—
280C23×C139—41no—
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—84no—
298C23×C139—84no—
299C23×C139—84no—
300C23×C139—84no—
301C23×C139—84no—
302C23×C139—84no—
303C23×C139#12112yes—
304C23×C139C2×SD1612yes—
305C23×C139AGL(1,ℤ/8)12yes—
306C23×C139C22×D411yescharacteristic
307Q8×C139—22no—
308Q8×C139—22no—
309Q8×C139—41no—
310Q8×C139—41no—
311D4×C139—22no—
312D4×C139—22no—
313D4×C139—22no—
314D4×C139—22no—
315D4×C139—48no—
316D4×C139—41no—
317D4×C139—41no—
318D4×C139—41no—
319D4×C139—41no—
320D4×C139—41no—
321D4×C139—41no—
322D4×C139—41no—
323D4×C139—41no—
324D4×C139—84no—
325D4×C139—84no—
326D4×C139—84no—
327D4×C139—84no—
328D4×C139—84no—
329C2×C4×C139—21no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—21no—
333C2×C4×C139—21no—
334C2×C4×C139—21no—
335C2×C4×C139—22no—
336C2×C4×C139—22no—
337C2×C4×C139—22no—
338C2×C4×C139—22no—
339C2×C4×C139—22no—
340C2×C4×C139—22no—
341C2×C4×C139—21no—
342C2×C4×C139—22no—
343C2×C4×C139—21no—
344C2×C4×C139—21no—
345C2×C4×C139—21no—
346C2×C4×C139—21no—
347C2×C4×C139—21no—
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—41no—
358C2×C4×C139—41no—
359C2×C4×C139—41no—
360C2×C4×C139—84no—
361C2×C4×C139#12112yes—
362C2×C4×C139C2×SD1612yes—
363C2×C4×C139C2×SD1612yes—
364C2×C4×C139C22×D411yescharacteristic
365C2×C4×C139C22×D411yescharacteristic
366C2×C4×C139C2×#4111yescharacteristic
367C2×C4×C139C2×#4111yescharacteristic
368C2×C4×C139H(5,𝔽2)11yescharacteristic
369C2×C4×C139H(5,𝔽2)11yescharacteristic
370C8×C139—22no—
371C8×C139—41no—
372C8×C139—41no—
373C8×C139—41no—
374C22×C139—22no—
375C22×C139—22no—
376C22×C139—22no—
377C22×C139—22no—
378C22×C139—22no—
379C22×C139—22no—
380C22×C139—42no—
381C22×C139—42no—
382C22×C139—42no—
383C22×C139—42no—
384C22×C139—42no—
385C22×C139—42no—
386C22×C139—816no—
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#46014yescomplemented
403C22×C139C2×#12111yescharacteristic
404C22×C139D4211yescharacteristic
405C22×C139#54611yescharacteristic
406C22×C139C22×SD1611yescharacteristic
407C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
408C22×C139#57611yescharacteristic
409C22×C139#57711yescharacteristic
410C4×C139—22no—
411C4×C139—22no—
412C4×C139—22no—
413C4×C139—42no—
414C4×C139—41no—
415C4×C139—42no—
416C4×C139—42no—
417C4×C139—41no—
418C4×C139—81no—
419C4×C139—81no—
420C4×C139#52511yescharacteristic
421C4×C139#53811yescharacteristic
422C4×C139D4211yescharacteristic
423C4×C139#54611yescharacteristic
424C2×C139—24no—
425C2×C139—82no—
426C2×C139—82no—
427C2×C139—161no—
428C2×C139#242411yescharacteristic
429C2×C139C2×#46011yescharacteristic
430C2×C139#304511yescharacteristic
431C2×C139#326411yescharacteristic
432C2×C139D4×SD1611yescharacteristic
433C2×C139#329511yescharacteristic
434C2×C139#331011yescharacteristic
435#25080C13911yesmaximal, characteristic, direct product factor, Sylow
436C139#2508011yescharacteristic, direct product factor, Sylow
437C2×#465C2×C13911yescharacteristic, complemented
438C2×#460C2×C13911yescharacteristic, complemented
439C2×#450C2×C13911yescharacteristic, complemented
440C22×#102C2×C13911yescharacteristic, complemented
441#2433C2×C13911yescharacteristic
442#2360C2×C13911yescharacteristic, complemented
443#2065C2×C13911yescharacteristic, complemented
444#2055C2×C13911yescharacteristic, complemented
445#2041C2×C13911yescharacteristic, complemented
446#2014C2×C13911yescharacteristic, complemented
447#1982C2×C13911yescharacteristic, complemented
448#1926C2×C13911yescharacteristic, complemented
449#1880C2×C13911yescharacteristic, complemented
450#1874C2×C13911yescharacteristic, complemented
451#1850C2×C13911yescharacteristic, complemented
452C23×D4C22×C13911yescharacteristic
453C22×SD16C22×C13911yescharacteristic
454C22×SD16C22×C13911yescharacteristic
455C22×SD16C22×C13911yescharacteristic, complemented
456C23×C8C22×C13911yescharacteristic
457C2×#127C22×C13911yescharacteristic
458C2×#127C22×C13911yescharacteristic
459C2×C22⋊Q8C22×C13911yescharacteristic
460C2×#121C22×C13911yescharacteristic
461C2×#120—21no—
462C2×#120—21no—
463C2×C4×Q8C22×C13911yescharacteristic, complemented
464C22×C4⋊C4C22×C13911yescharacteristic
465#465—24no—
466#460—24no—
467#450—24no—
468C2×#106C22×C13911yescharacteristic, complemented
469C2×C4⋊C8C22×C13911yescharacteristic, complemented
470C2×C4⋊C8C22×C13911yescharacteristic, complemented
471C2×#103C22×C13911yescharacteristic, complemented
472C2×#102—24no—
473C2×#102C22×C13911yescharacteristic
474C2×#102C22×C13911yescharacteristic
475C2×#102C22×C13911yescharacteristic
476C2×#102C22×C13911yescharacteristic
477C2×#102C22×C13911yescharacteristic
478C2×#102C22×C13911yescharacteristic
479C2×#102C22×C13911yescharacteristic, complemented
480C2×#102C22×C13911yescharacteristic, complemented
481C2×#102C22×C13911yescharacteristic, complemented
482C2×C22⋊C8C22×C13911yescharacteristic
483#392—21no—
484#392—21no—
485#391C22×C13911yescharacteristic, complemented
486#390C22×C13911yescharacteristic
487#390C22×C13911yescharacteristic
488#389—21no—
489#389C22×C13911yescharacteristic, complemented
490#387—21no—
491#385—21no—
492C4×C4⋊C4C22×C13911yescharacteristic, complemented
493C4×C22⋊C4—21no—
494C4×C22⋊C4C22×C13911yescharacteristic
495#340C22×C13911yescharacteristic, complemented
496#340C22×C13911yescharacteristic, complemented
497#336C22×C13911yescharacteristic, complemented
498#336C22×C13911yescharacteristic, complemented
499C25—21no—
500C22×Q8C23×C13911yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C23×C13911yescharacteristic
514C22×D4C23×C13911yescharacteristic
515C22×D4C23×C13911yescharacteristic
516C23×C4—21no—
517C23×C4C23×C13911yescharacteristic
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8C23×C13911yescharacteristic
531C22×C8C23×C13911yescharacteristic
532C22×C8C23×C13911yescharacteristic
533C22×C8C23×C13911yescharacteristic
534#127—22no—
535#127—22no—
536#127—41no—
537#127—41no—
538C22⋊Q8—22no—
539C22⋊Q8D4×C13914yescomplemented
540#121—22no—
541#121—22no—
542#120—44no—
543#120—44no—
544C4×Q8—22no—
545C4×Q8—41no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4C23×C13911yescharacteristic
553C2×C4⋊C4C23×C13911yescharacteristic
554C2×C4⋊C4C23×C13911yescharacteristic
555C2×C4⋊C4C23×C13911yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4D4×C13911yescharacteristic
563C2×C22⋊C4D4×C13911yescharacteristic
564C2×C42—21no—
565C2×C42—21no—
566C2×C42C23×C13911yescharacteristic
567C2×C42C23×C13911yescharacteristic
568#106—22no—
569C4⋊C8—22no—
570C4⋊C8—41no—
571#103—22no—
572#102—22no—
573#102—22no—
574#102—22no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—41no—
580#102D4×C13914yescomplemented
581C22⋊C8—22no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586#95D4×C13911yescharacteristic
587#95D4×C13911yescharacteristic
588C24—21no—
589C24—21no—
590C24—21no—
591C24—42no—
592C24—42no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—81no—
597C24—81no—
598C24C2×D4×C13911yescharacteristic
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8C2×D4×C13912yes—
605C2×D4—28no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—44no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—81no—
642C2×D4—81no—
643C2×D4C2×D4×C13912yes—
644C2×D4#41×C13912yes—
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—42no—
655C22×C4—42no—
656C22×C4—81no—
657C22×C4C2×D4×C13911yescharacteristic
658C22×C4C2×D4×C13911yescharacteristic
659C22×C4C2×D4×C13911yescharacteristic
660C22×C4C2×D4×C13912yes—
661C22×C4C2×D4×C13911yescharacteristic
662C22×C4C2×D4×C13911yescharacteristic
663C22×C4#41×C13912yes—
664C22×C4C24×C13911yescharacteristic
665SD16—44no—
666SD16—44no—
667SD16—44no—
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—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—44no—
680C2×C8C2×D4×C13912yes—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—81no—
691C4⋊C4C2×D4×C13912yes—
692C4⋊C4C2×D4×C13912yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4SD16×C13914yescomplemented
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—42no—
706C42—81no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—22no—
712C23—22no—
713C23—48no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
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—84no—
734C23—84no—
735C23—84no—
736C23—84no—
737C23—84no—
738C23—84no—
739C23#121×C13912yes—
740C23C2×SD16×C13912yes—
741C23AGL(1,ℤ/8)×C13912yes—
742C23C22×D4×C13911yescharacteristic
743Q8—22no—
744Q8—22no—
745Q8—41no—
746Q8—41no—
747D4—22no—
748D4—22no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4—84no—
762D4—84no—
763D4—84no—
764D4—84no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
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—41no—
796C2×C4—84no—
797C2×C4#121×C13912yes—
798C2×C4C2×SD16×C13912yes—
799C2×C4C2×SD16×C13912yes—
800C2×C4C22×D4×C13911yescharacteristic
801C2×C4C22×D4×C13911yescharacteristic
802C2×C4C2×#41×C13911yescharacteristic
803C2×C4C2×#41×C13911yescharacteristic
804C2×C4H(5,𝔽2)×C13911yescharacteristic
805C2×C4H(5,𝔽2)×C13911yescharacteristic
806C8—22no—
807C8—41no—
808C8—41no—
809C8—41no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—816no—
823C22—81no—
824C22—81no—
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#460×C13914yescomplemented
839C22C2×#121×C13911yescharacteristic
840C22D42×C13911yescharacteristic
841C22#546×C13911yescharacteristic
842C22C22×SD16×C13911yescharacteristic
843C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
844C22#576×C13911yescharacteristic
845C22#577×C13911yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4#525×C13911yescharacteristic
857C4#538×C13911yescharacteristic
858C4D42×C13911yescharacteristic
859C4#546×C13911yescharacteristic
860C2—24no—
861C2—82no—
862C2—82no—
863C2—161no—
864C2#2424×C13911yescharacteristic
865C2C2×#460×C13911yescharacteristic
866C2#3045×C13911yescharacteristic
867C2#3264×C13911yescharacteristic
868C2D4×SD16×C13911yescharacteristic
869C2#3295×C13911yescharacteristic
870C2#3310×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radical#2433×C139C2
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×#465×C139C2semidirect
2. C2×#460×C139C2semidirect
3. C2×#450×C139C2semidirect
4. C22×#102×C139C2semidirect
6. #2360×C139C2semidirect
7. #2065×C139C2semidirect
8. #2055×C139C2semidirect
9. #2041×C139C2semidirect
10. #2014×C139C2semidirect
11. #1982×C139C2semidirect
12. #1926×C139C2semidirect
13. #1880×C139C2semidirect
14. #1874×C139C2semidirect
15. #1850×C139C2semidirect
19. C22×SD16×C139C22semidirect
27. C2×C4×Q8×C139C22semidirect
32. C2×#106×C139C22semidirect
33. C2×C4⋊C8×C139C22semidirect
34. C2×C4⋊C8×C139C22semidirect
35. C2×#103×C139C22semidirect
43. C2×#102×C139C22semidirect
44. C2×#102×C139C22semidirect
45. C2×#102×C139C22semidirect
49. #391×C139C22semidirect
53. #389×C139C22semidirect
56. C4×C4⋊C4×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #336×C139C22semidirect
62. #336×C139C22semidirect
103. C22⋊Q8×C139D4semidirect
144. #102×C139D4semidirect
264. C22⋊C4×C139SD16semidirect
402. C22×C139#460semidirect
435. #25080C139direct (N × H)
436. C139#25080direct (N × H)
437. C2×#465C2×C139semidirect
438. C2×#460C2×C139semidirect
439. C2×#450C2×C139semidirect
440. C22×#102C2×C139semidirect
442. #2360C2×C139semidirect
443. #2065C2×C139semidirect
444. #2055C2×C139semidirect
445. #2041C2×C139semidirect
446. #2014C2×C139semidirect
447. #1982C2×C139semidirect
448. #1926C2×C139semidirect
449. #1880C2×C139semidirect
450. #1874C2×C139semidirect
451. #1850C2×C139semidirect
455. C22×SD16C22×C139semidirect
463. C2×C4×Q8C22×C139semidirect
468. C2×#106C22×C139semidirect
469. C2×C4⋊C8C22×C139semidirect
470. C2×C4⋊C8C22×C139semidirect
471. C2×#103C22×C139semidirect
479. C2×#102C22×C139semidirect
480. C2×#102C22×C139semidirect
481. C2×#102C22×C139semidirect
485. #391C22×C139semidirect
489. #389C22×C139semidirect
492. C4×C4⋊C4C22×C139semidirect
495. #340C22×C139semidirect
496. #340C22×C139semidirect
497. #336C22×C139semidirect
498. #336C22×C139semidirect
539. C22⋊Q8D4×C139semidirect
580. #102D4×C139semidirect
700. C22⋊C4SD16×C139semidirect
838. C22#460×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#465×C1392
C2×#460×C1392
C2×#450×C1392
C22×#102×C1392
#2433×C1392
#2360×C1392
#2065×C1392
#2055×C1392
#2041×C1392
#2014×C1392
#1982×C1392
#1926×C1392
#1880×C1392
#1874×C1392
#1850×C1392
#25080139