Finite Group Databasebeta

← C139×#22886 #48017482

Subgroups — C139×#22886 #48017482

Order 35584.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3002×C139C211yesmaximal, characteristic
2C2×#444×C139C211yesmaximal, characteristic, complemented
3#2933×C139C211yesmaximal, characteristic, complemented
4C22×#104×C139C211yesmaximal, characteristic, complemented
5#2880×C139C211yesmaximal, characteristic, complemented
6#1975×C139C211yesmaximal, characteristic, complemented
7#1938×C139C211yesmaximal, characteristic, complemented
8#1929×C139C211yesmaximal, characteristic, complemented
9#1896×C139C211yesmaximal, characteristic, complemented
10#1876×C139C211yesmaximal, characteristic, complemented
11#1876×C139C211yesmaximal, characteristic, complemented
12#1866×C139C211yesmaximal, characteristic, complemented
13#1855×C139C211yesmaximal, characteristic, complemented
14#1765×C139C211yesmaximal, characteristic, complemented
15#1749×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C2×#135×C139C2211yescharacteristic
18C2×#135×C139C2211yescharacteristic
19C2×#131×C139C2211yescharacteristic
20C2×#131×C139C2211yescharacteristic
21C2×#131×C139C2211yescharacteristic, complemented
22C22×M16×C139C2211yescharacteristic
23#525×C139C2211yescharacteristic
24C22×C42×C139C2211yescharacteristic
25#452×C139C411yescharacteristic, complemented
26#452×C139C411yescharacteristic, complemented
27#451×C139C411yescharacteristic, complemented
28#450×C139C411yescharacteristic, complemented
29#449×C139C411yescharacteristic, complemented
30#449×C139C411yescharacteristic, complemented
31#448×C139C411yescharacteristic, complemented
32#447×C139C411yescharacteristic, complemented
33#444×C139—24no—
34#436×C139—21no—
35#435×C139—21no—
36#435×C139—21no—
37C8×D4×C139—21no—
38C2×#108×C139C2211yescharacteristic, complemented
39C2×#108×C139C2211yescharacteristic, complemented
40#424×C139C2211yescharacteristic, complemented
41C2×#104×C139—24no—
42C2×#104×C139C2211yescharacteristic
43C2×#104×C139C2211yescharacteristic
44C2×#104×C139C2211yescharacteristic
45C2×#104×C139C2211yescharacteristic
46C2×#104×C139C2211yescharacteristic, complemented
47C2×#104×C139C2211yescharacteristic, complemented
48#416×C139C2211yescharacteristic
49#416×C139C2211yescharacteristic
50#408×C139—21no—
51#408×C139—21no—
52#408×C139C2211yescharacteristic
53#408×C139C2211yescharacteristic
54#408×C139C2211yescharacteristic, complemented
55#407×C139—21no—
56#407×C139C2211yescharacteristic
57C2×C22⋊C8×C139—21no—
58C2×C22⋊C8×C139C2211yescharacteristic
59C2×C22⋊C8×C139C2211yescharacteristic
60#405×C139C2211yescharacteristic, complemented
61C2×#97×C139C2211yescharacteristic, complemented
62C2×#97×C139C2211yescharacteristic, complemented
63#341×C139C2211yescharacteristic, complemented
64#341×C139C2211yescharacteristic, complemented
65#339×C139C2211yescharacteristic, complemented
66#339×C139C2211yescharacteristic, complemented
67#336×C139C2211yescharacteristic, complemented
68#336×C139C2211yescharacteristic, complemented
69C2×#41×C139—21no—
70C2×#41×C139—21no—
71C2×#41×C139—22no—
72C2×#41×C139—22no—
73C2×#41×C139—41no—
74C2×#41×C139—41no—
75C2×#41×C139C2×C411yescharacteristic
76C2×#41×C139C2×C411yescharacteristic
77C2×#41×C139C2311yescharacteristic
78C2×#41×C139C2311yescharacteristic
79C2×#41×C139C2311yescharacteristic
80C22×Q8×C139C2×C411yescharacteristic
81C22×D4×C139—21no—
82C22×D4×C139C2×C411yescharacteristic
83C23×C4×C139—21no—
84C23×C4×C139—21no—
85C23×C4×C139C2311yescharacteristic
86#135×C139—22no—
87#135×C139—22no—
88#135×C139—41no—
89#135×C139—41no—
90C2×Q16×C139C2×C411yescharacteristic, complemented
91C2×Q16×C139C2×C411yescharacteristic, complemented
92C2×SD16×C139C2×C411yescharacteristic, complemented
93C2×SD16×C139C2×C411yescharacteristic, complemented
94C2×SD16×C139C2×C411yescharacteristic, complemented
95C2×SD16×C139C2×C411yescharacteristic, complemented
96C2×D8×C139C2×C411yescharacteristic, complemented
97C2×D8×C139C2×C411yescharacteristic, complemented
98#131×C139—22no—
99#131×C139—22no—
100#131×C139—22no—
101#131×C139—41no—
102#131×C139—41no—
103#131×C139—41no—
104C2×M16×C139—21no—
105C2×M16×C139—21no—
106C2×M16×C139—21no—
107C2×M16×C139—21no—
108C2×M16×C139—22no—
109C2×M16×C139—41no—
110C2×M16×C139C2311yescharacteristic
111C2×M16×C139C2311yescharacteristic
112C2×M16×C139C2311yescharacteristic
113C2×M16×C139C2311yescharacteristic
114C22×C8×C139—21no—
115C22×C8×C139—21no—
116C22×C8×C139—21no—
117C22×C8×C139—21no—
118C22×C8×C139C2311yescharacteristic
119C22×C8×C139C2311yescharacteristic
120C22×C8×C139C2311yescharacteristic
121C22×C8×C139C2311yescharacteristic
122#123×C139—21no—
123C22⋊Q8×C139C2×C411yescharacteristic
124C22⋊Q8×C139C2×C411yescharacteristic
125#121×C139C2×C411yescharacteristic
126#121×C139C2×C411yescharacteristic
127#120×C139—21no—
128C4×D4×C139—21no—
129C4×D4×C139—21no—
130#117×C139C2311yescharacteristic
131C2×C42×C139—22no—
132C2×C42×C139—21no—
133C2×C42×C139—41no—
134C2×C42×C139C2311yescharacteristic
135C2×C42×C139C2311yescharacteristic
136#108×C139—22no—
137#108×C139—41no—
138C4⋊C8×C139—21no—
139C4⋊C8×C139—21no—
140#104×C139—22no—
141#104×C139—22no—
142#104×C139—22no—
143#104×C139—22no—
144#104×C139—41no—
145#104×C139D414yescomplemented
146#103×C139C2×C411yescharacteristic, complemented
147#103×C139C2×C411yescharacteristic, complemented
148#103×C139C2×C411yescharacteristic, complemented
149#103×C139C2×C411yescharacteristic, complemented
150#102×C139C2×C411yescharacteristic, complemented
151#102×C139C2×C411yescharacteristic, complemented
152#102×C139C2×C411yescharacteristic, complemented
153#102×C139C2×C411yescharacteristic, complemented
154C22⋊C8×C139—21no—
155C22⋊C8×C139—21no—
156C22⋊C8×C139—21no—
157C22⋊C8×C139—21no—
158C22⋊C8×C139—21no—
159C22⋊C8×C139—21no—
160C22⋊C8×C139—21no—
161C22⋊C8×C139—21no—
162C22⋊C8×C139C2×C411yescharacteristic
163C22⋊C8×C139C2×C411yescharacteristic
164C22⋊C8×C139C2×C411yescharacteristic
165C22⋊C8×C139C2×C411yescharacteristic
166C22⋊C8×C139D411yescharacteristic
167C22⋊C8×C139D411yescharacteristic
168C22⋊C8×C139D411yescharacteristic
169C22⋊C8×C139D411yescharacteristic
170#97×C139—21no—
171#97×C139—22no—
172#97×C139—41no—
173C4×C8×C139—21no—
174C24×C139—21no—
175C24×C139#4111yescharacteristic
176#41×C139—21no—
177#41×C139—21no—
178#41×C139—22no—
179#41×C139—22no—
180#41×C139—21no—
181#41×C139—21no—
182#41×C139—21no—
183#41×C139—21no—
184#41×C139—21no—
185#41×C139—21no—
186#41×C139—21no—
187#41×C139—21no—
188#41×C139—42no—
189#41×C139—42no—
190#41×C139—41no—
191#41×C139—41no—
192#41×C139—42no—
193#41×C139—42no—
194#41×C139C2×D412yes—
195#41×C139#4112yes—
196C2×Q8×C139—21no—
197C2×Q8×C139—22no—
198C2×Q8×C139—41no—
199C2×Q8×C139C22×C411yescharacteristic
200C2×Q8×C139C22×C411yescharacteristic
201C2×Q8×C139C22×C411yescharacteristic
202C2×D4×C139—21no—
203C2×D4×C139—22no—
204C2×D4×C139—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—21no—
208C2×D4×C139—21no—
209C2×D4×C139—21no—
210C2×D4×C139—21no—
211C2×D4×C139—41no—
212C2×D4×C139—42no—
213C2×D4×C139—42no—
214C2×D4×C139C22×C411yescharacteristic
215C2×D4×C139C22×C411yescharacteristic
216C2×D4×C139C22×C411yescharacteristic
217C22×C4×C139—21no—
218C22×C4×C139—21no—
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—21no—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
229C22×C4×C139—42no—
230C22×C4×C139—42no—
231C22×C4×C139—42no—
232C22×C4×C139—42no—
233C22×C4×C139—42no—
234C22×C4×C139C22×C411yescharacteristic
235C22×C4×C139C22×C411yescharacteristic
236C22×C4×C139C2×D411yescharacteristic
237C22×C4×C139C2×D411yescharacteristic
238C22×C4×C139#4111yescharacteristic
239C22×C4×C139C2411yescharacteristic
240Q16×C139—22no—
241Q16×C139—41no—
242SD16×C139—22no—
243SD16×C139—22no—
244SD16×C139—41no—
245SD16×C139—41no—
246D8×C139—22no—
247D8×C139—41no—
248M16×C139—21no—
249M16×C139—21no—
250M16×C139—21no—
251M16×C139—21no—
252M16×C139—21no—
253M16×C139—21no—
254M16×C139—21no—
255M16×C139—42no—
256M16×C139—42no—
257M16×C139—42no—
258M16×C139—42no—
259M16×C139C2×D412yes—
260C2×C8×C139—21no—
261C2×C8×C139—21no—
262C2×C8×C139—21no—
263C2×C8×C139—21no—
264C2×C8×C139—21no—
265C2×C8×C139—21no—
266C2×C8×C139—21no—
267C2×C8×C139—21no—
268C2×C8×C139—21no—
269C2×C8×C139—21no—
270C2×C8×C139—21no—
271C2×C8×C139—21no—
272C2×C8×C139—42no—
273C2×C8×C139—42no—
274C2×C8×C139—42no—
275C2×C8×C139—42no—
276C2×C8×C139C22×C411yescharacteristic
277C2×C8×C139C22×C411yescharacteristic
278C2×C8×C139C22×C411yescharacteristic
279C2×C8×C139C22×C411yescharacteristic
280C2×C8×C139C2×D411yescharacteristic
281C2×C8×C139C2×D411yescharacteristic
282C2×C8×C139C2×D411yescharacteristic
283C2×C8×C139C2×D411yescharacteristic
284C4⋊C4×C139—21no—
285C4⋊C4×C139—21no—
286C4⋊C4×C139C22×C411yescharacteristic
287C4⋊C4×C139C22×C411yescharacteristic
288C22⋊C4×C139—21no—
289C22⋊C4×C139—21no—
290C22⋊C4×C139—21no—
291C22⋊C4×C139—21no—
292C22⋊C4×C139—21no—
293C42×C139—21no—
294C42×C139—21no—
295C42×C139—21no—
296C42×C139—21no—
297C42×C139—42no—
298C42×C139C2×D412yes—
299C23×C139—21no—
300C23×C139—21no—
301C23×C139—21no—
302C23×C139—22no—
303C23×C139—21no—
304C23×C139—21no—
305C23×C139—41no—
306C23×C139—42no—
307C23×C139—42no—
308C23×C139—81no—
309C23×C139C4×D411yescharacteristic
310C23×C139C4×D411yescharacteristic
311C23×C139C2×#4111yescharacteristic
312Q8×C139—21no—
313Q8×C139—21no—
314Q8×C139—21no—
315Q8×C139—21no—
316Q8×C139—21no—
317Q8×C139—42no—
318Q8×C139C4×D412yes—
319D4×C139—22no—
320D4×C139—22no—
321D4×C139—21no—
322D4×C139—21no—
323D4×C139—21no—
324D4×C139—21no—
325D4×C139—21no—
326D4×C139—42no—
327D4×C139—42no—
328D4×C139—42no—
329D4×C139—41no—
330D4×C139—41no—
331D4×C139—41no—
332D4×C139—41no—
333D4×C139—42no—
334D4×C139—81no—
335D4×C139C4×D412yes—
336C2×C4×C139—21no—
337C2×C4×C139—21no—
338C2×C4×C139—21no—
339C2×C4×C139—21no—
340C2×C4×C139—21no—
341C2×C4×C139—21no—
342C2×C4×C139—21no—
343C2×C4×C139—21no—
344C2×C4×C139—22no—
345C2×C4×C139—21no—
346C2×C4×C139—22no—
347C2×C4×C139—21no—
348C2×C4×C139—21no—
349C2×C4×C139—22no—
350C2×C4×C139—21no—
351C2×C4×C139—21no—
352C2×C4×C139—21no—
353C2×C4×C139—21no—
354C2×C4×C139—22no—
355C2×C4×C139—42no—
356C2×C4×C139—42no—
357C2×C4×C139—42no—
358C2×C4×C139—41no—
359C2×C4×C139—41no—
360C2×C4×C139—41no—
361C2×C4×C139—48no—
362C2×C4×C139—41no—
363C2×C4×C139—41no—
364C2×C4×C139—41no—
365C2×C4×C139—41no—
366C2×C4×C139—41no—
367C2×C4×C139C4×D411yescharacteristic
368C2×C4×C139C4×D411yescharacteristic
369C2×C4×C139C23×C411yescharacteristic
370C2×C4×C139C22×D411yescharacteristic
371C2×C4×C139C22×D411yescharacteristic
372C2×C4×C139C2×#4111yescharacteristic
373C2×C4×C139H(5,𝔽2)11yescharacteristic
374C2×C4×C139H(5,𝔽2)11yescharacteristic
375C8×C139—21no—
376C8×C139—21no—
377C8×C139—21no—
378C8×C139—21no—
379C8×C139—21no—
380C8×C139—21no—
381C8×C139—22no—
382C8×C139—21no—
383C8×C139—21no—
384C8×C139—41no—
385C8×C139—41no—
386C8×C139—41no—
387C22×C139—21no—
388C22×C139—21no—
389C22×C139—21no—
390C22×C139—21no—
391C22×C139—21no—
392C22×C139—22no—
393C22×C139—21no—
394C22×C139—21no—
395C22×C139—42no—
396C22×C139—42no—
397C22×C139—41no—
398C22×C139—41no—
399C22×C139—41no—
400C22×C139—41no—
401C22×C139—41no—
402C22×C139—41no—
403C22×C139—41no—
404C22×C139—41no—
405C22×C139—84no—
406C22×C139#44412yescomplemented
407C22×C139C2×C4×D411yescharacteristic
408C22×C139#54611yescharacteristic
409C22×C139#55111yescharacteristic
410C4×C139—21no—
411C4×C139—21no—
412C4×C139—22no—
413C4×C139—42no—
414C4×C139—42no—
415C4×C139—41no—
416C4×C139—41no—
417C4×C139—41no—
418C4×C139—41no—
419C4×C139C2×C4×D411yescharacteristic
420C4×C139#51811yescharacteristic
421C4×C139D4211yescharacteristic
422C4×C139#54611yescharacteristic
423C2×C139—21no—
424C2×C139—22no—
425C2×C139—21no—
426C2×C139—41no—
427C2×C139—42no—
428C2×C139—81no—
429C2×C139—81no—
430C2×C139#235811yescharacteristic
431C2×C139C2×#44411yescharacteristic
432C2×C139#295611yescharacteristic
433#22886C13911yesmaximal, characteristic, direct product factor, Sylow
434C139#2288611yescharacteristic, direct product factor, Sylow
435#3002C2×C13911yescharacteristic
436C2×#444C2×C13911yescharacteristic, complemented
437#2933C2×C13911yescharacteristic, complemented
438C22×#104C2×C13911yescharacteristic, complemented
439#2880C2×C13911yescharacteristic, complemented
440#1975C2×C13911yescharacteristic, complemented
441#1938C2×C13911yescharacteristic, complemented
442#1929C2×C13911yescharacteristic, complemented
443#1896C2×C13911yescharacteristic, complemented
444#1876C2×C13911yescharacteristic, complemented
445#1876C2×C13911yescharacteristic, complemented
446#1866C2×C13911yescharacteristic, complemented
447#1855C2×C13911yescharacteristic, complemented
448#1765C2×C13911yescharacteristic, complemented
449#1749C2×C13911yescharacteristic, complemented
450C22×#41C22×C13911yescharacteristic
451C2×#135C22×C13911yescharacteristic
452C2×#135C22×C13911yescharacteristic
453C2×#131C22×C13911yescharacteristic
454C2×#131C22×C13911yescharacteristic
455C2×#131C22×C13911yescharacteristic, complemented
456C22×M16C22×C13911yescharacteristic
457#525C22×C13911yescharacteristic
458C22×C42C22×C13911yescharacteristic
459#452C4×C13911yescharacteristic, complemented
460#452C4×C13911yescharacteristic, complemented
461#451C4×C13911yescharacteristic, complemented
462#450C4×C13911yescharacteristic, complemented
463#449C4×C13911yescharacteristic, complemented
464#449C4×C13911yescharacteristic, complemented
465#448C4×C13911yescharacteristic, complemented
466#447C4×C13911yescharacteristic, complemented
467#444—24no—
468#436—21no—
469#435—21no—
470#435—21no—
471C8×D4—21no—
472C2×#108C22×C13911yescharacteristic, complemented
473C2×#108C22×C13911yescharacteristic, complemented
474#424C22×C13911yescharacteristic, complemented
475C2×#104—24no—
476C2×#104C22×C13911yescharacteristic
477C2×#104C22×C13911yescharacteristic
478C2×#104C22×C13911yescharacteristic
479C2×#104C22×C13911yescharacteristic
480C2×#104C22×C13911yescharacteristic, complemented
481C2×#104C22×C13911yescharacteristic, complemented
482#416C22×C13911yescharacteristic
483#416C22×C13911yescharacteristic
484#408—21no—
485#408—21no—
486#408C22×C13911yescharacteristic
487#408C22×C13911yescharacteristic
488#408C22×C13911yescharacteristic, complemented
489#407—21no—
490#407C22×C13911yescharacteristic
491C2×C22⋊C8—21no—
492C2×C22⋊C8C22×C13911yescharacteristic
493C2×C22⋊C8C22×C13911yescharacteristic
494#405C22×C13911yescharacteristic, complemented
495C2×#97C22×C13911yescharacteristic, complemented
496C2×#97C22×C13911yescharacteristic, complemented
497#341C22×C13911yescharacteristic, complemented
498#341C22×C13911yescharacteristic, complemented
499#339C22×C13911yescharacteristic, complemented
500#339C22×C13911yescharacteristic, complemented
501#336C22×C13911yescharacteristic, complemented
502#336C22×C13911yescharacteristic, complemented
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×C4×C13911yescharacteristic
510C2×#41C2×C4×C13911yescharacteristic
511C2×#41C23×C13911yescharacteristic
512C2×#41C23×C13911yescharacteristic
513C2×#41C23×C13911yescharacteristic
514C22×Q8C2×C4×C13911yescharacteristic
515C22×D4—21no—
516C22×D4C2×C4×C13911yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C13911yescharacteristic
520#135—22no—
521#135—22no—
522#135—41no—
523#135—41no—
524C2×Q16C2×C4×C13911yescharacteristic, complemented
525C2×Q16C2×C4×C13911yescharacteristic, complemented
526C2×SD16C2×C4×C13911yescharacteristic, complemented
527C2×SD16C2×C4×C13911yescharacteristic, complemented
528C2×SD16C2×C4×C13911yescharacteristic, complemented
529C2×SD16C2×C4×C13911yescharacteristic, complemented
530C2×D8C2×C4×C13911yescharacteristic, complemented
531C2×D8C2×C4×C13911yescharacteristic, complemented
532#131—22no—
533#131—22no—
534#131—22no—
535#131—41no—
536#131—41no—
537#131—41no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—21no—
541C2×M16—21no—
542C2×M16—22no—
543C2×M16—41no—
544C2×M16C23×C13911yescharacteristic
545C2×M16C23×C13911yescharacteristic
546C2×M16C23×C13911yescharacteristic
547C2×M16C23×C13911yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—21no—
551C22×C8—21no—
552C22×C8C23×C13911yescharacteristic
553C22×C8C23×C13911yescharacteristic
554C22×C8C23×C13911yescharacteristic
555C22×C8C23×C13911yescharacteristic
556#123—21no—
557C22⋊Q8C2×C4×C13911yescharacteristic
558C22⋊Q8C2×C4×C13911yescharacteristic
559#121C2×C4×C13911yescharacteristic
560#121C2×C4×C13911yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C23×C13911yescharacteristic
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C23×C13911yescharacteristic
569C2×C42C23×C13911yescharacteristic
570#108—22no—
571#108—41no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—22no—
575#104—22no—
576#104—22no—
577#104—22no—
578#104—41no—
579#104D4×C13914yescomplemented
580#103C2×C4×C13911yescharacteristic, complemented
581#103C2×C4×C13911yescharacteristic, complemented
582#103C2×C4×C13911yescharacteristic, complemented
583#103C2×C4×C13911yescharacteristic, complemented
584#102C2×C4×C13911yescharacteristic, complemented
585#102C2×C4×C13911yescharacteristic, complemented
586#102C2×C4×C13911yescharacteristic, complemented
587#102C2×C4×C13911yescharacteristic, complemented
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596C22⋊C8C2×C4×C13911yescharacteristic
597C22⋊C8C2×C4×C13911yescharacteristic
598C22⋊C8C2×C4×C13911yescharacteristic
599C22⋊C8C2×C4×C13911yescharacteristic
600C22⋊C8D4×C13911yescharacteristic
601C22⋊C8D4×C13911yescharacteristic
602C22⋊C8D4×C13911yescharacteristic
603C22⋊C8D4×C13911yescharacteristic
604#97—21no—
605#97—22no—
606#97—41no—
607C4×C8—21no—
608C24—21no—
609C24#41×C13911yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—21no—
619#41—21no—
620#41—21no—
621#41—21no—
622#41—42no—
623#41—42no—
624#41—41no—
625#41—41no—
626#41—42no—
627#41—42no—
628#41C2×D4×C13912yes—
629#41#41×C13912yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8C22×C4×C13911yescharacteristic
634C2×Q8C22×C4×C13911yescharacteristic
635C2×Q8C22×C4×C13911yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—41no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4C22×C4×C13911yescharacteristic
649C2×D4C22×C4×C13911yescharacteristic
650C2×D4C22×C4×C13911yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4C22×C4×C13911yescharacteristic
669C22×C4C22×C4×C13911yescharacteristic
670C22×C4C2×D4×C13911yescharacteristic
671C22×C4C2×D4×C13911yescharacteristic
672C22×C4#41×C13911yescharacteristic
673C22×C4C24×C13911yescharacteristic
674Q16—22no—
675Q16—41no—
676SD16—22no—
677SD16—22no—
678SD16—41no—
679SD16—41no—
680D8—22no—
681D8—41no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—21no—
687M16—21no—
688M16—21no—
689M16—42no—
690M16—42no—
691M16—42no—
692M16—42no—
693M16C2×D4×C13912yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—42no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—42no—
710C2×C8C22×C4×C13911yescharacteristic
711C2×C8C22×C4×C13911yescharacteristic
712C2×C8C22×C4×C13911yescharacteristic
713C2×C8C22×C4×C13911yescharacteristic
714C2×C8C2×D4×C13911yescharacteristic
715C2×C8C2×D4×C13911yescharacteristic
716C2×C8C2×D4×C13911yescharacteristic
717C2×C8C2×D4×C13911yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C22×C4×C13911yescharacteristic
721C4⋊C4C22×C4×C13911yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42C2×D4×C13912yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—41no—
740C23—42no—
741C23—42no—
742C23—81no—
743C23C4×D4×C13911yescharacteristic
744C23C4×D4×C13911yescharacteristic
745C23C2×#41×C13911yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—21no—
750Q8—21no—
751Q8—42no—
752Q8C4×D4×C13912yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—21no—
759D4—21no—
760D4—42no—
761D4—42no—
762D4—42no—
763D4—42no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—81no—
769D4C4×D4×C13912yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4C4×D4×C13911yescharacteristic
802C2×C4C4×D4×C13911yescharacteristic
803C2×C4C23×C4×C13911yescharacteristic
804C2×C4C22×D4×C13911yescharacteristic
805C2×C4C22×D4×C13911yescharacteristic
806C2×C4C2×#41×C13911yescharacteristic
807C2×C4H(5,𝔽2)×C13911yescharacteristic
808C2×C4H(5,𝔽2)×C13911yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—22no—
816C8—21no—
817C8—21no—
818C8—41no—
819C8—41no—
820C8—41no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—84no—
840C22#444×C13912yescomplemented
841C22C2×C4×D4×C13911yescharacteristic
842C22#546×C13911yescharacteristic
843C22#551×C13911yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—42no—
848C4—42no—
849C4—41no—
850C4—41no—
851C4—41no—
852C4—41no—
853C4C2×C4×D4×C13911yescharacteristic
854C4#518×C13911yescharacteristic
855C4D42×C13911yescharacteristic
856C4#546×C13911yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—81no—
864C2#2358×C13911yescharacteristic
865C2C2×#444×C13911yescharacteristic
866C2#2956×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
socleC22×C139C2×C4×D4
prime radical#3002×C139C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C2×C22⋊C8×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#444×C139C2semidirect
3. #2933×C139C2semidirect
4. C22×#104×C139C2semidirect
5. #2880×C139C2semidirect
6. #1975×C139C2semidirect
7. #1938×C139C2semidirect
8. #1929×C139C2semidirect
9. #1896×C139C2semidirect
10. #1876×C139C2semidirect
11. #1876×C139C2semidirect
12. #1866×C139C2semidirect
13. #1855×C139C2semidirect
14. #1765×C139C2semidirect
15. #1749×C139C2semidirect
21. C2×#131×C139C22semidirect
25. #452×C139C4semidirect
26. #452×C139C4semidirect
27. #451×C139C4semidirect
28. #450×C139C4semidirect
29. #449×C139C4semidirect
30. #449×C139C4semidirect
31. #448×C139C4semidirect
32. #447×C139C4semidirect
38. C2×#108×C139C22semidirect
39. C2×#108×C139C22semidirect
40. #424×C139C22semidirect
46. C2×#104×C139C22semidirect
47. C2×#104×C139C22semidirect
54. #408×C139C22semidirect
60. #405×C139C22semidirect
61. C2×#97×C139C22semidirect
62. C2×#97×C139C22semidirect
63. #341×C139C22semidirect
64. #341×C139C22semidirect
65. #339×C139C22semidirect
66. #339×C139C22semidirect
67. #336×C139C22semidirect
68. #336×C139C22semidirect
90. C2×Q16×C139C2×C4semidirect
91. C2×Q16×C139C2×C4semidirect
92. C2×SD16×C139C2×C4semidirect
93. C2×SD16×C139C2×C4semidirect
94. C2×SD16×C139C2×C4semidirect
95. C2×SD16×C139C2×C4semidirect
96. C2×D8×C139C2×C4semidirect
97. C2×D8×C139C2×C4semidirect
145. #104×C139D4semidirect
146. #103×C139C2×C4semidirect
147. #103×C139C2×C4semidirect
148. #103×C139C2×C4semidirect
149. #103×C139C2×C4semidirect
150. #102×C139C2×C4semidirect
151. #102×C139C2×C4semidirect
152. #102×C139C2×C4semidirect
153. #102×C139C2×C4semidirect
406. C22×C139#444semidirect
433. #22886C139direct (N × H)
434. C139#22886direct (N × H)
436. C2×#444C2×C139semidirect
437. #2933C2×C139semidirect
438. C22×#104C2×C139semidirect
439. #2880C2×C139semidirect
440. #1975C2×C139semidirect
441. #1938C2×C139semidirect
442. #1929C2×C139semidirect
443. #1896C2×C139semidirect
444. #1876C2×C139semidirect
445. #1876C2×C139semidirect
446. #1866C2×C139semidirect
447. #1855C2×C139semidirect
448. #1765C2×C139semidirect
449. #1749C2×C139semidirect
455. C2×#131C22×C139semidirect
459. #452C4×C139semidirect
460. #452C4×C139semidirect
461. #451C4×C139semidirect
462. #450C4×C139semidirect
463. #449C4×C139semidirect
464. #449C4×C139semidirect
465. #448C4×C139semidirect
466. #447C4×C139semidirect
472. C2×#108C22×C139semidirect
473. C2×#108C22×C139semidirect
474. #424C22×C139semidirect
480. C2×#104C22×C139semidirect
481. C2×#104C22×C139semidirect
488. #408C22×C139semidirect
494. #405C22×C139semidirect
495. C2×#97C22×C139semidirect
496. C2×#97C22×C139semidirect
497. #341C22×C139semidirect
498. #341C22×C139semidirect
499. #339C22×C139semidirect
500. #339C22×C139semidirect
501. #336C22×C139semidirect
502. #336C22×C139semidirect
524. C2×Q16C2×C4×C139semidirect
525. C2×Q16C2×C4×C139semidirect
526. C2×SD16C2×C4×C139semidirect
527. C2×SD16C2×C4×C139semidirect
528. C2×SD16C2×C4×C139semidirect
529. C2×SD16C2×C4×C139semidirect
530. C2×D8C2×C4×C139semidirect
531. C2×D8C2×C4×C139semidirect
579. #104D4×C139semidirect
580. #103C2×C4×C139semidirect
581. #103C2×C4×C139semidirect
582. #103C2×C4×C139semidirect
583. #103C2×C4×C139semidirect
584. #102C2×C4×C139semidirect
585. #102C2×C4×C139semidirect
586. #102C2×C4×C139semidirect
587. #102C2×C4×C139semidirect
840. C22#444×C139semidirect

Maximal subgroups

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

subgroupindex
#3002×C1392
C2×#444×C1392
#2933×C1392
C22×#104×C1392
#2880×C1392
#1975×C1392
#1938×C1392
#1929×C1392
#1896×C1392
#1876×C1392
#1866×C1392
#1855×C1392
#1765×C1392
#1749×C1392
#22886139