Finite Group Databasebeta

← C139×#25159 #48019755

Subgroups — C139×#25159 #48019755

Order 35584.

1212 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C139C211yesmaximal, characteristic, complemented
2C2×#449×C139C211yesmaximal, characteristic, complemented
3C2×#449×C139C211yesmaximal, characteristic, complemented
4C2×C4×SD16×C139C211yesmaximal, characteristic, complemented
5#2428×C139C211yesmaximal, characteristic, complemented
6#2341×C139C211yesmaximal, characteristic, complemented
7#2065×C139C211yesmaximal, characteristic, complemented
8#2034×C139C211yesmaximal, characteristic, complemented
9#2033×C139C211yesmaximal, characteristic, complemented
10#2011×C139C211yesmaximal, characteristic, complemented
11#1970×C139C211yesmaximal, characteristic, complemented
12#1923×C139C211yesmaximal, characteristic, complemented
13#1880×C139C211yesmaximal, characteristic, complemented
14#1879×C139C211yesmaximal, characteristic, complemented
15#1863×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×SD16×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic
20C22×D8×C139C2211yescharacteristic
21C2×#127×C139C2211yescharacteristic
22C2×#121×C139—21no—
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×C4×Q8×C139C2211yescharacteristic
26C2×C4×Q8×C139C2211yescharacteristic
27C2×C4×D4×C139C2211yescharacteristic
28#460×C139—24no—
29#449×C139—24no—
30#449×C139—24no—
31C4×SD16×C139—24no—
32C2×#107×C139C2211yescharacteristic
33C2×#106×C139C2211yescharacteristic
34C2×C4⋊C8×C139C2211yescharacteristic
35C2×#103×C139C2211yescharacteristic
36C2×#103×C139C2211yescharacteristic
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
45C2×C4×C8×C139C2211yescharacteristic
46#394×C139—21no—
47#392×C139—21no—
48#390×C139—21no—
49#390×C139—21no—
50#390×C139C2211yescharacteristic
51#390×C139C2211yescharacteristic
52#390×C139C2211yescharacteristic
53#389×C139C2211yescharacteristic
54#386×C139—21no—
55#380×C139—21no—
56#380×C139C2211yescharacteristic
57C4×C22⋊C4×C139—21no—
58C4×C22⋊C4×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#336×C139C2211yescharacteristic
62#336×C139C2211yescharacteristic
63C2×#41×C139—22no—
64C2×#41×C139—22no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—41no—
68C2×#41×C139—41no—
69C22×Q8×C139C2311yescharacteristic
70C22×D4×C139—21no—
71C22×D4×C139—21no—
72C22×D4×C139—21no—
73C22×D4×C139—21no—
74C22×D4×C139—21no—
75C22×D4×C139C2311yescharacteristic
76C22×D4×C139C2311yescharacteristic
77C22×D4×C139C2311yescharacteristic
78C23×C4×C139—21no—
79C23×C4×C139—21no—
80C23×C4×C139C2311yescharacteristic
81C2×SD16×C139—22no—
82C2×SD16×C139—22no—
83C2×SD16×C139—22no—
84C2×SD16×C139—22no—
85C2×SD16×C139—22no—
86C2×SD16×C139D414yescomplemented
87C2×D8×C139—22no—
88C2×D8×C139—22no—
89C2×D8×C139—22no—
90C2×D8×C139—22no—
91C2×D8×C139—41no—
92C2×D8×C139—41no—
93C22×C8×C139C2311yescharacteristic
94C22×C8×C139C2311yescharacteristic
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97#127×C139—22no—
98#127×C139—41no—
99#121×C139—22no—
100#121×C139—22no—
101#121×C139—44no—
102#121×C139—41no—
103#121×C139—41no—
104C4×Q8×C139—22no—
105C4×Q8×C139—22no—
106C4×Q8×C139—41no—
107C4×Q8×C139—41no—
108C4×D4×C139—22no—
109C4×D4×C139—41no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139—21no—
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×C139D411yescharacteristic
128C2×C22⋊C4×C139D411yescharacteristic
129C2×C42×C139—21no—
130C2×C42×C139—21no—
131C2×C42×C139C2311yescharacteristic
132C2×C42×C139C2311yescharacteristic
133#107×C139—41no—
134#106×C139—22no—
135C4⋊C8×C139—22no—
136#103×C139—22no—
137#103×C139D414yescomplemented
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—22no—
143#102×C139—41no—
144C22⋊C8×C139—22no—
145C22⋊C8×C139—22no—
146C4×C8×C139—22no—
147#95×C139—21no—
148#95×C139—21no—
149#95×C139D411yescharacteristic
150#95×C139D411yescharacteristic
151C24×C139—21no—
152C24×C139—21no—
153C24×C139—21no—
154C24×C139C2×D411yescharacteristic
155#41×C139—44no—
156#41×C139—44no—
157#41×C139—44no—
158#41×C139—44no—
159C2×Q8×C139—21no—
160C2×Q8×C139—21no—
161C2×Q8×C139—21no—
162C2×Q8×C139C2×D412yes—
163C2×Q8×C139C2×D412yes—
164C2×Q8×C139#4112yes—
165C2×D4×C139—24no—
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—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—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×C139C2×D412yes—
197C2×D4×C139#4112yes—
198C22×C4×C139—21no—
199C22×C4×C139—24no—
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—42no—
211C22×C4×C139—42no—
212C22×C4×C139—42no—
213C22×C4×C139—42no—
214C22×C4×C139—81no—
215C22×C4×C139C2×D411yescharacteristic
216C22×C4×C139C2×D411yescharacteristic
217C22×C4×C139C2×D411yescharacteristic
218C22×C4×C139C2×D411yescharacteristic
219C22×C4×C139C2×D411yescharacteristic
220C22×C4×C139C2411yescharacteristic
221SD16×C139—28no—
222SD16×C139—44no—
223D8×C139—44no—
224D8×C139—44no—
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×C139—21no—
233C2×C8×C139—21no—
234C2×C8×C139—21no—
235C2×C8×C139C2×D412yes—
236C2×C8×C139C2×D412yes—
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—42no—
245C4⋊C4×C139—42no—
246C4⋊C4×C139—42no—
247C4⋊C4×C139C2×D412yes—
248C22⋊C4×C139—22no—
249C22⋊C4×C139—22no—
250C22⋊C4×C139—42no—
251C22⋊C4×C139—42no—
252C22⋊C4×C139—42no—
253C22⋊C4×C139—42no—
254C22⋊C4×C139—42no—
255C22⋊C4×C139—42no—
256C22⋊C4×C139—81no—
257C22⋊C4×C139—81no—
258C22⋊C4×C139—81no—
259C22⋊C4×C139—81no—
260C42×C139—21no—
261C42×C139—21no—
262C42×C139—21no—
263C42×C139—21no—
264C42×C139—42no—
265C42×C139—42no—
266C23×C139—21no—
267C23×C139—22no—
268C23×C139—22no—
269C23×C139—21no—
270C23×C139—21no—
271C23×C139—21no—
272C23×C139—21no—
273C23×C139—21no—
274C23×C139—21no—
275C23×C139—41no—
276C23×C139—41no—
277C23×C139—41no—
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×C139C22×D411yescharacteristic
295Q8×C139—22no—
296Q8×C139—22no—
297Q8×C139—22no—
298Q8×C139#12114yescomplemented
299D4×C139—22no—
300D4×C139—22no—
301D4×C139—22no—
302D4×C139—22no—
303D4×C139—48no—
304D4×C139—41no—
305D4×C139—41no—
306D4×C139—41no—
307D4×C139—41no—
308D4×C139—41no—
309D4×C139—41no—
310D4×C139—41no—
311D4×C139—41no—
312D4×C139—84no—
313D4×C139—84no—
314D4×C139—84no—
315D4×C139—84no—
316C2×C4×C139—22no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
319C2×C4×C139—22no—
320C2×C4×C139—22no—
321C2×C4×C139—21no—
322C2×C4×C139—21no—
323C2×C4×C139—21no—
324C2×C4×C139—21no—
325C2×C4×C139—21no—
326C2×C4×C139—22no—
327C2×C4×C139—21no—
328C2×C4×C139—21no—
329C2×C4×C139—21no—
330C2×C4×C139—21no—
331C2×C4×C139—21no—
332C2×C4×C139—21no—
333C2×C4×C139—48no—
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—84no—
350C2×C4×C139#13512yes—
351C2×C4×C139AGL(1,ℤ/8)12yes—
352C2×C4×C139C22×D411yescharacteristic
353C2×C4×C139C22×D411yescharacteristic
354C2×C4×C139C2×#4111yescharacteristic
355C2×C4×C139C2×#4111yescharacteristic
356C2×C4×C139H(5,𝔽2)11yescharacteristic
357C2×C4×C139H(5,𝔽2)11yescharacteristic
358C8×C139—22no—
359C8×C139—22no—
360C8×C139—41no—
361C8×C139—41no—
362C22×C139—41no—
363C22×C139—42no—
364C22×C139—41no—
365C22×C139—42no—
366C22×C139—42no—
367C22×C139—41no—
368C22×C139—42no—
369C22×C139—41no—
370C22×C139—41no—
371C22×C139—42no—
372C22×C139—42no—
373C22×C139—41no—
374C22×C139—41no—
375C22×C139—81no—
376C22×C139—81no—
377C22×C139—81no—
378C22×C139—81no—
379C22×C139—81no—
380C22×C139—81no—
381C22×C139—81no—
382C22×C139—81no—
383C22×C139—81no—
384C22×C139—81no—
385C22×C139—81no—
386C22×C139—81no—
387C22×C139—81no—
388C22×C139—81no—
389C22×C139—81no—
390C22×C139#52511yescharacteristic
391C22×C139D4211yescharacteristic
392C22×C139D4211yescharacteristic
393C22×C139C2×#13511yescharacteristic
394C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
395C22×C139#57611yescharacteristic
396C22×C139#57711yescharacteristic
397C4×C139—24no—
398C4×C139—22no—
399C4×C139—22no—
400C4×C139—41no—
401C4×C139—42no—
402C4×C139—41no—
403C4×C139—41no—
404C4×C139—81no—
405C4×C139—81no—
406C4×C139—81no—
407C4×C139C2×#12111yescharacteristic
408C4×C139#53811yescharacteristic
409C4×C139#54611yescharacteristic
410C4×C139#54611yescharacteristic
411C2×C139—81no—
412C2×C139—82no—
413C2×C139—82no—
414C2×C139—161no—
415C2×C139#242411yescharacteristic
416C2×C139#310611yescharacteristic
417C2×C139#311911yescharacteristic
418C2×C139#326511yescharacteristic
419C2×C139#327411yescharacteristic
420C2×C139#328211yescharacteristic
421C2×C139#328711yescharacteristic
422#25159C13911yesmaximal, characteristic, direct product factor, Sylow
423C139#2515911yescharacteristic, direct product factor, Sylow
424C2×#460C2×C13911yescharacteristic, complemented
425C2×#449C2×C13911yescharacteristic, complemented
426C2×#449C2×C13911yescharacteristic, complemented
427C2×C4×SD16C2×C13911yescharacteristic, complemented
428#2428C2×C13911yescharacteristic, complemented
429#2341C2×C13911yescharacteristic, complemented
430#2065C2×C13911yescharacteristic, complemented
431#2034C2×C13911yescharacteristic, complemented
432#2033C2×C13911yescharacteristic, complemented
433#2011C2×C13911yescharacteristic, complemented
434#1970C2×C13911yescharacteristic, complemented
435#1923C2×C13911yescharacteristic, complemented
436#1880C2×C13911yescharacteristic, complemented
437#1879C2×C13911yescharacteristic, complemented
438#1863C2×C13911yescharacteristic, complemented
439C22×#41C22×C13911yescharacteristic
440C22×SD16C22×C13911yescharacteristic
441C22×SD16C22×C13911yescharacteristic
442C22×D8C22×C13911yescharacteristic
443C22×D8C22×C13911yescharacteristic
444C2×#127C22×C13911yescharacteristic
445C2×#121—21no—
446C2×#121C22×C13911yescharacteristic
447C2×#121C22×C13911yescharacteristic
448C2×C4×Q8C22×C13911yescharacteristic
449C2×C4×Q8C22×C13911yescharacteristic
450C2×C4×D4C22×C13911yescharacteristic
451#460—24no—
452#449—24no—
453#449—24no—
454C4×SD16—24no—
455C2×#107C22×C13911yescharacteristic
456C2×#106C22×C13911yescharacteristic
457C2×C4⋊C8C22×C13911yescharacteristic
458C2×#103C22×C13911yescharacteristic
459C2×#103C22×C13911yescharacteristic
460C2×#102C22×C13911yescharacteristic
461C2×#102C22×C13911yescharacteristic
462C2×#102C22×C13911yescharacteristic
463C2×#102C22×C13911yescharacteristic
464C2×#102C22×C13911yescharacteristic
465C2×#102C22×C13911yescharacteristic
466C2×C22⋊C8C22×C13911yescharacteristic
467C2×C22⋊C8C22×C13911yescharacteristic
468C2×C4×C8C22×C13911yescharacteristic
469#394—21no—
470#392—21no—
471#390—21no—
472#390—21no—
473#390C22×C13911yescharacteristic
474#390C22×C13911yescharacteristic
475#390C22×C13911yescharacteristic
476#389C22×C13911yescharacteristic
477#386—21no—
478#380—21no—
479#380C22×C13911yescharacteristic
480C4×C22⋊C4—21no—
481C4×C22⋊C4C22×C13911yescharacteristic
482#340C22×C13911yescharacteristic
483#340C22×C13911yescharacteristic
484#336C22×C13911yescharacteristic
485#336C22×C13911yescharacteristic
486C2×#41—22no—
487C2×#41—22no—
488C2×#41—22no—
489C2×#41—22no—
490C2×#41—41no—
491C2×#41—41no—
492C22×Q8C23×C13911yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4C23×C13911yescharacteristic
499C22×D4C23×C13911yescharacteristic
500C22×D4C23×C13911yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C23×C13911yescharacteristic
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16D4×C13914yescomplemented
510C2×D8—22no—
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—22no—
514C2×D8—41no—
515C2×D8—41no—
516C22×C8C23×C13911yescharacteristic
517C22×C8C23×C13911yescharacteristic
518C22×C8C23×C13911yescharacteristic
519C22×C8C23×C13911yescharacteristic
520#127—22no—
521#127—41no—
522#121—22no—
523#121—22no—
524#121—44no—
525#121—41no—
526#121—41no—
527C4×Q8—22no—
528C4×Q8—22no—
529C4×Q8—41no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—41no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4C23×C13911yescharacteristic
537C2×C4⋊C4C23×C13911yescharacteristic
538C2×C4⋊C4C23×C13911yescharacteristic
539C2×C4⋊C4C23×C13911yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
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⋊C4D4×C13911yescharacteristic
551C2×C22⋊C4D4×C13911yescharacteristic
552C2×C42—21no—
553C2×C42—21no—
554C2×C42C23×C13911yescharacteristic
555C2×C42C23×C13911yescharacteristic
556#107—41no—
557#106—22no—
558C4⋊C8—22no—
559#103—22no—
560#103D4×C13914yescomplemented
561#102—22no—
562#102—22no—
563#102—22no—
564#102—22no—
565#102—22no—
566#102—41no—
567C22⋊C8—22no—
568C22⋊C8—22no—
569C4×C8—22no—
570#95—21no—
571#95—21no—
572#95D4×C13911yescharacteristic
573#95D4×C13911yescharacteristic
574C24—21no—
575C24—21no—
576C24—21no—
577C24C2×D4×C13911yescharacteristic
578#41—44no—
579#41—44no—
580#41—44no—
581#41—44no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8C2×D4×C13912yes—
586C2×Q8C2×D4×C13912yes—
587C2×Q8#41×C13912yes—
588C2×D4—24no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
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—42no—
606C2×D4—42no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—42no—
615C2×D4—81no—
616C2×D4—81no—
617C2×D4—81no—
618C2×D4—81no—
619C2×D4C2×D4×C13912yes—
620C2×D4#41×C13912yes—
621C22×C4—21no—
622C22×C4—24no—
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—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—81no—
638C22×C4C2×D4×C13911yescharacteristic
639C22×C4C2×D4×C13911yescharacteristic
640C22×C4C2×D4×C13911yescharacteristic
641C22×C4C2×D4×C13911yescharacteristic
642C22×C4C2×D4×C13911yescharacteristic
643C22×C4C24×C13911yescharacteristic
644SD16—28no—
645SD16—44no—
646D8—44no—
647D8—44no—
648C2×C8—21no—
649C2×C8—21no—
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×C8C2×D4×C13912yes—
659C2×C8C2×D4×C13912yes—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4C2×D4×C13912yes—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—42no—
674C22⋊C4—42no—
675C22⋊C4—42no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—81no—
680C22⋊C4—81no—
681C22⋊C4—81no—
682C22⋊C4—81no—
683C42—21no—
684C42—21no—
685C42—21no—
686C42—21no—
687C42—42no—
688C42—42no—
689C23—21no—
690C23—22no—
691C23—22no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23C22×D4×C13911yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8#121×C13914yescomplemented
722D4—22no—
723D4—22no—
724D4—22no—
725D4—22no—
726D4—48no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—41no—
732D4—41no—
733D4—41no—
734D4—41no—
735D4—84no—
736D4—84no—
737D4—84no—
738D4—84no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—48no—
757C2×C4—41no—
758C2×C4—41no—
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—84no—
773C2×C4#135×C13912yes—
774C2×C4AGL(1,ℤ/8)×C13912yes—
775C2×C4C22×D4×C13911yescharacteristic
776C2×C4C22×D4×C13911yescharacteristic
777C2×C4C2×#41×C13911yescharacteristic
778C2×C4C2×#41×C13911yescharacteristic
779C2×C4H(5,𝔽2)×C13911yescharacteristic
780C2×C4H(5,𝔽2)×C13911yescharacteristic
781C8—22no—
782C8—22no—
783C8—41no—
784C8—41no—
785C22—42no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—41no—
791C22—42no—
792C22—42no—
793C22—41no—
794C22—42no—
795C22—41no—
796C22—41no—
797C22—42no—
798C22—81no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22—81no—
810C22—81no—
811C22—81no—
812C22—81no—
813C22#525×C13911yescharacteristic
814C22D42×C13911yescharacteristic
815C22D42×C13911yescharacteristic
816C22C2×#135×C13911yescharacteristic
817C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
818C22#576×C13911yescharacteristic
819C22#577×C13911yescharacteristic
820C4—22no—
821C4—24no—
822C4—22no—
823C4—41no—
824C4—41no—
825C4—42no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4C2×#121×C13911yescharacteristic
831C4#538×C13911yescharacteristic
832C4#546×C13911yescharacteristic
833C4#546×C13911yescharacteristic
834C2—81no—
835C2—82no—
836C2—82no—
837C2—161no—
838C2#2424×C13911yescharacteristic
839C2#3106×C13911yescharacteristic
840C2#3119×C13911yescharacteristic
841C2#3265×C13911yescharacteristic
842C2#3274×C13911yescharacteristic
843C2#3282×C13911yescharacteristic
844C2#3287×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
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×#460×C139C2semidirect
2. C2×#449×C139C2semidirect
3. C2×#449×C139C2semidirect
4. C2×C4×SD16×C139C2semidirect
5. #2428×C139C2semidirect
6. #2341×C139C2semidirect
7. #2065×C139C2semidirect
8. #2034×C139C2semidirect
9. #2033×C139C2semidirect
10. #2011×C139C2semidirect
11. #1970×C139C2semidirect
12. #1923×C139C2semidirect
13. #1880×C139C2semidirect
14. #1879×C139C2semidirect
15. #1863×C139C2semidirect
86. C2×SD16×C139D4semidirect
137. #103×C139D4semidirect
298. Q8×C139#121semidirect
422. #25159C139direct (N × H)
423. C139#25159direct (N × H)
424. C2×#460C2×C139semidirect
425. C2×#449C2×C139semidirect
426. C2×#449C2×C139semidirect
427. C2×C4×SD16C2×C139semidirect
428. #2428C2×C139semidirect
429. #2341C2×C139semidirect
430. #2065C2×C139semidirect
431. #2034C2×C139semidirect
432. #2033C2×C139semidirect
433. #2011C2×C139semidirect
434. #1970C2×C139semidirect
435. #1923C2×C139semidirect
436. #1880C2×C139semidirect
437. #1879C2×C139semidirect
438. #1863C2×C139semidirect
509. C2×SD16D4×C139semidirect
560. #103D4×C139semidirect
721. Q8#121×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×#449×C1392
C2×C4×SD16×C1392
#2428×C1392
#2341×C1392
#2065×C1392
#2034×C1392
#2033×C1392
#2011×C1392
#1970×C1392
#1923×C1392
#1880×C1392
#1879×C1392
#1863×C1392
#25159139