Finite Group Databasebeta

← C139×#22062 #48016658

Subgroups — C139×#22062 #48016658

Order 35584.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3002×C139C211yesmaximal, characteristic
2#2930×C139C211yesmaximal, characteristic, complemented
3#2879×C139C211yesmaximal, characteristic, complemented
4#1975×C139C211yesmaximal, characteristic, complemented
5#1974×C139C211yesmaximal, characteristic, complemented
6#1938×C139C211yesmaximal, characteristic, complemented
7#1937×C139C211yesmaximal, characteristic, complemented
8#1929×C139C211yesmaximal, characteristic, complemented
9#1929×C139C211yesmaximal, characteristic, complemented
10#1876×C139C211yesmaximal, characteristic, complemented
11#1876×C139C211yesmaximal, characteristic, complemented
12#1871×C139C211yesmaximal, characteristic, complemented
13#1855×C139C211yesmaximal, characteristic, complemented
14#1789×C139C211yesmaximal, characteristic, complemented
15#1753×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C2×#135×C139C2211yescharacteristic
18C2×#135×C139C2211yescharacteristic
19C2×#131×C139C2211yescharacteristic, complemented
20C22×M16×C139C2211yescharacteristic
21C22×M16×C139C2211yescharacteristic
22#525×C139C2211yescharacteristic
23#452×C139C411yescharacteristic, complemented
24#452×C139C411yescharacteristic, complemented
25#451×C139C411yescharacteristic, complemented
26#450×C139C411yescharacteristic, complemented
27#449×C139C411yescharacteristic, complemented
28#449×C139C411yescharacteristic, complemented
29#448×C139C411yescharacteristic, complemented
30#447×C139C411yescharacteristic, complemented
31#436×C139—21no—
32#436×C139—21no—
33#435×C139—21no—
34#435×C139—21no—
35C2×#108×C139C2211yescharacteristic, complemented
36C2×#108×C139C2211yescharacteristic, complemented
37#424×C139C2211yescharacteristic, complemented
38C2×#104×C139C2211yescharacteristic
39C2×#104×C139C2211yescharacteristic
40C2×#104×C139C2211yescharacteristic
41C2×#104×C139C2211yescharacteristic
42C2×#104×C139C2211yescharacteristic, complemented
43C2×#104×C139C2211yescharacteristic, complemented
44#416×C139C2211yescharacteristic
45#416×C139C2211yescharacteristic
46#408×C139—21no—
47#408×C139—21no—
48#408×C139C2211yescharacteristic
49#408×C139C2211yescharacteristic
50#408×C139C2211yescharacteristic
51#408×C139C2211yescharacteristic
52#408×C139C2211yescharacteristic, complemented
53#407×C139—21no—
54#407×C139—21no—
55#407×C139C2211yescharacteristic
56C2×C22⋊C8×C139C2211yescharacteristic
57#405×C139C2211yescharacteristic, complemented
58C2×#97×C139C2211yescharacteristic, complemented
59C2×C4×C8×C139C2211yescharacteristic, complemented
60C4×C22⋊C4×C139C2211yescharacteristic
61#341×C139C2211yescharacteristic, complemented
62#341×C139C2211yescharacteristic, complemented
63#339×C139C2211yescharacteristic, complemented
64#339×C139C2211yescharacteristic, complemented
65#336×C139C2211yescharacteristic, complemented
66#336×C139C2211yescharacteristic, complemented
67C2×#41×C139—21no—
68C2×#41×C139—21no—
69C2×#41×C139—41no—
70C2×#41×C139—41no—
71C2×#41×C139—41no—
72C2×#41×C139—41no—
73C2×#41×C139C2×C411yescharacteristic
74C2×#41×C139C2×C411yescharacteristic
75C2×#41×C139C2311yescharacteristic
76C2×#41×C139C2311yescharacteristic
77C2×#41×C139C2311yescharacteristic
78C22×Q8×C139C2×C411yescharacteristic
79C22×D4×C139—21no—
80C22×D4×C139C2×C411yescharacteristic
81C23×C4×C139—21no—
82C23×C4×C139C2311yescharacteristic
83#135×C139—41no—
84#135×C139—41no—
85#135×C139—41no—
86#135×C139—41no—
87C2×Q16×C139C2×C411yescharacteristic
88C2×Q16×C139C2×C411yescharacteristic
89C2×SD16×C139C2×C411yescharacteristic
90C2×SD16×C139C2×C411yescharacteristic
91C2×SD16×C139C2×C411yescharacteristic
92C2×SD16×C139C2×C411yescharacteristic
93C2×D8×C139C2×C411yescharacteristic
94C2×D8×C139C2×C411yescharacteristic
95#131×C139—41no—
96#131×C139—41no—
97C2×M16×C139—21no—
98C2×M16×C139—21no—
99C2×M16×C139—41no—
100C2×M16×C139—41no—
101C2×M16×C139—41no—
102C2×M16×C139—41no—
103C2×M16×C139D411yescharacteristic
104C2×M16×C139D411yescharacteristic
105C2×M16×C139D411yescharacteristic
106C2×M16×C139D411yescharacteristic
107C2×M16×C139C2311yescharacteristic
108C2×M16×C139C2311yescharacteristic
109C2×M16×C139C2311yescharacteristic
110C2×M16×C139C2311yescharacteristic
111C22×C8×C139—21no—
112C22×C8×C139—21no—
113C22×C8×C139C2311yescharacteristic
114C22×C8×C139C2311yescharacteristic
115C22×C8×C139C2311yescharacteristic
116C22×C8×C139C2311yescharacteristic
117#123×C139—21no—
118C22⋊Q8×C139C2×C411yescharacteristic
119C22⋊Q8×C139C2×C411yescharacteristic
120#121×C139C2×C411yescharacteristic
121#121×C139C2×C411yescharacteristic
122#120×C139—21no—
123C4×D4×C139—21no—
124C4×D4×C139—21no—
125#117×C139C2311yescharacteristic
126C2×C22⋊C4×C139—21no—
127C2×C42×C139C2311yescharacteristic
128C2×C42×C139C2311yescharacteristic
129#108×C139—41no—
130#108×C139—41no—
131C4⋊C8×C139—21no—
132C4⋊C8×C139—21no—
133#104×C139—41no—
134#104×C139—41no—
135#104×C139—41no—
136#104×C139—41no—
137#104×C139—41no—
138#104×C139—41no—
139#103×C139C2×C411yescharacteristic
140#103×C139C2×C411yescharacteristic
141#103×C139C2×C411yescharacteristic
142#103×C139C2×C411yescharacteristic
143#102×C139C2×C411yescharacteristic
144#102×C139C2×C411yescharacteristic
145#102×C139C2×C411yescharacteristic
146#102×C139C2×C411yescharacteristic
147C22⋊C8×C139—21no—
148C22⋊C8×C139—21no—
149C22⋊C8×C139—21no—
150C22⋊C8×C139—21no—
151C22⋊C8×C139—21no—
152C22⋊C8×C139—21no—
153C22⋊C8×C139—21no—
154C22⋊C8×C139—21no—
155C22⋊C8×C139—21no—
156C22⋊C8×C139—21no—
157C22⋊C8×C139—21no—
158C22⋊C8×C139—21no—
159C22⋊C8×C139C2×C411yescharacteristic
160C22⋊C8×C139C2×C411yescharacteristic
161C22⋊C8×C139C2×C411yescharacteristic
162C22⋊C8×C139C2×C411yescharacteristic
163#97×C139—21no—
164#97×C139—41no—
165C4×C8×C139—21no—
166C4×C8×C139—41no—
167#95×C139—21no—
168C24×C139—21no—
169C24×C139#4111yescharacteristic
170#41×C139—21no—
171#41×C139—21no—
172#41×C139—21no—
173#41×C139—21no—
174#41×C139—21no—
175#41×C139—21no—
176#41×C139—21no—
177#41×C139—21no—
178#41×C139—21no—
179#41×C139—21no—
180#41×C139—21no—
181#41×C139—21no—
182#41×C139—41no—
183#41×C139—41no—
184#41×C139—41no—
185#41×C139—41no—
186#41×C139—42no—
187#41×C139—42no—
188#41×C139—42no—
189#41×C139—42no—
190C2×Q8×C139—21no—
191C2×Q8×C139—41no—
192C2×Q8×C139—41no—
193C2×Q8×C139C22×C411yescharacteristic
194C2×Q8×C139C22×C411yescharacteristic
195C2×Q8×C139C22×C411yescharacteristic
196C2×D4×C139—21no—
197C2×D4×C139—21no—
198C2×D4×C139—21no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—41no—
205C2×D4×C139—41no—
206C2×D4×C139—42no—
207C2×D4×C139—42no—
208C2×D4×C139C22×C411yescharacteristic
209C2×D4×C139C22×C411yescharacteristic
210C2×D4×C139C22×C411yescharacteristic
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—21no—
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—42no—
224C22×C4×C139—42no—
225C22×C4×C139C22×C411yescharacteristic
226C22×C4×C139C22×C411yescharacteristic
227C22×C4×C139C2×D411yescharacteristic
228C22×C4×C139C2×D411yescharacteristic
229C22×C4×C139#4111yescharacteristic
230C22×C4×C139C2411yescharacteristic
231Q16×C139—41no—
232Q16×C139—41no—
233SD16×C139—41no—
234SD16×C139—41no—
235SD16×C139—41no—
236SD16×C139—41no—
237D8×C139—41no—
238D8×C139—41no—
239M16×C139—21no—
240M16×C139—21no—
241M16×C139—21no—
242M16×C139—21no—
243M16×C139—21no—
244M16×C139—21no—
245M16×C139—21no—
246M16×C139—21no—
247M16×C139—41no—
248M16×C139—41no—
249M16×C139—41no—
250M16×C139—41no—
251M16×C139—42no—
252M16×C139—42no—
253C2×C8×C139—21no—
254C2×C8×C139—21no—
255C2×C8×C139—21no—
256C2×C8×C139—21no—
257C2×C8×C139—21no—
258C2×C8×C139—21no—
259C2×C8×C139—21no—
260C2×C8×C139—21no—
261C2×C8×C139—21no—
262C2×C8×C139—21no—
263C2×C8×C139—21no—
264C2×C8×C139—21no—
265C2×C8×C139—42no—
266C2×C8×C139—42no—
267C2×C8×C139C22×C411yescharacteristic
268C2×C8×C139C22×C411yescharacteristic
269C2×C8×C139C22×C411yescharacteristic
270C2×C8×C139C22×C411yescharacteristic
271C2×C8×C139C2×D411yescharacteristic
272C2×C8×C139C2×D411yescharacteristic
273C2×C8×C139C2×D411yescharacteristic
274C2×C8×C139C2×D411yescharacteristic
275C4⋊C4×C139—21no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139C22×C411yescharacteristic
278C4⋊C4×C139C22×C411yescharacteristic
279C22⋊C4×C139—21no—
280C22⋊C4×C139—21no—
281C22⋊C4×C139—21no—
282C22⋊C4×C139—21no—
283C22⋊C4×C139—21no—
284C22⋊C4×C139—42no—
285C42×C139—21no—
286C42×C139—21no—
287C42×C139—21no—
288C42×C139—21no—
289C42×C139—21no—
290C23×C139—21no—
291C23×C139—21no—
292C23×C139—21no—
293C23×C139—21no—
294C23×C139—21no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—42no—
298C23×C139—81no—
299C23×C139—81no—
300C23×C139C4×D411yescharacteristic
301C23×C139C4×D411yescharacteristic
302C23×C139C2×#4111yescharacteristic
303Q8×C139—21no—
304Q8×C139—21no—
305Q8×C139—21no—
306Q8×C139—21no—
307Q8×C139—21no—
308Q8×C139—21no—
309Q8×C139—42no—
310D4×C139—21no—
311D4×C139—21no—
312D4×C139—21no—
313D4×C139—21no—
314D4×C139—21no—
315D4×C139—21no—
316D4×C139—42no—
317D4×C139—42no—
318D4×C139—42no—
319D4×C139—41no—
320D4×C139—41no—
321D4×C139—41no—
322D4×C139—41no—
323D4×C139—41no—
324D4×C139—41no—
325D4×C139—81no—
326D4×C139—81no—
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—21no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—21no—
337C2×C4×C139—22no—
338C2×C4×C139—21no—
339C2×C4×C139—21no—
340C2×C4×C139—21no—
341C2×C4×C139—21no—
342C2×C4×C139—21no—
343C2×C4×C139—42no—
344C2×C4×C139—42no—
345C2×C4×C139—41no—
346C2×C4×C139—42no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—41no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
353C2×C4×C139—41no—
354C2×C4×C139—41no—
355C2×C4×C139—41no—
356C2×C4×C139—41no—
357C2×C4×C139C4×D411yescharacteristic
358C2×C4×C139C4×D411yescharacteristic
359C2×C4×C139C23×C411yescharacteristic
360C2×C4×C139C22×D411yescharacteristic
361C2×C4×C139H(5,𝔽2)11yescharacteristic
362C2×C4×C139H(5,𝔽2)11yescharacteristic
363C2×C4×C139H(5,𝔽2)11yescharacteristic
364C2×C4×C139H(5,𝔽2)11yescharacteristic
365C8×C139—21no—
366C8×C139—21no—
367C8×C139—21no—
368C8×C139—21no—
369C8×C139—21no—
370C8×C139—21no—
371C8×C139—21no—
372C8×C139—21no—
373C8×C139—41no—
374C8×C139—41no—
375C8×C139—41no—
376C8×C139—41no—
377C22×C139—21no—
378C22×C139—21no—
379C22×C139—21no—
380C22×C139—21no—
381C22×C139—21no—
382C22×C139—21no—
383C22×C139—21no—
384C22×C139—21no—
385C22×C139—41no—
386C22×C139—41no—
387C22×C139—41no—
388C22×C139—41no—
389C22×C139—41no—
390C22×C139—41no—
391C22×C139—41no—
392C22×C139—41no—
393C22×C139—41no—
394C22×C139—81no—
395C22×C139—81no—
396C22×C139—84no—
397C22×C139C2×C4×D411yescharacteristic
398C22×C139#53811yescharacteristic
399C22×C139#53811yescharacteristic
400C4×C139—21no—
401C4×C139—21no—
402C4×C139—42no—
403C4×C139—41no—
404C4×C139—41no—
405C4×C139—41no—
406C4×C139—41no—
407C4×C139—41no—
408C4×C139—81no—
409C4×C139#51811yescharacteristic
410C4×C139#51811yescharacteristic
411C4×C139#53411yescharacteristic
412C4×C139#53511yescharacteristic
413C2×C139—21no—
414C2×C139—21no—
415C2×C139—41no—
416C2×C139—41no—
417C2×C139—81no—
418C2×C139—81no—
419C2×C139—81no—
420C2×C139#232111yescharacteristic
421C2×C139#295611yescharacteristic
422C2×C139#295711yescharacteristic
423#22062C13911yesmaximal, characteristic, direct product factor, Sylow
424C139#2206211yescharacteristic, direct product factor, Sylow
425#3002C2×C13911yescharacteristic
426#2930C2×C13911yescharacteristic, complemented
427#2879C2×C13911yescharacteristic, complemented
428#1975C2×C13911yescharacteristic, complemented
429#1974C2×C13911yescharacteristic, complemented
430#1938C2×C13911yescharacteristic, complemented
431#1937C2×C13911yescharacteristic, complemented
432#1929C2×C13911yescharacteristic, complemented
433#1929C2×C13911yescharacteristic, complemented
434#1876C2×C13911yescharacteristic, complemented
435#1876C2×C13911yescharacteristic, complemented
436#1871C2×C13911yescharacteristic, complemented
437#1855C2×C13911yescharacteristic, complemented
438#1789C2×C13911yescharacteristic, complemented
439#1753C2×C13911yescharacteristic, complemented
440C22×#41C22×C13911yescharacteristic
441C2×#135C22×C13911yescharacteristic
442C2×#135C22×C13911yescharacteristic
443C2×#131C22×C13911yescharacteristic, complemented
444C22×M16C22×C13911yescharacteristic
445C22×M16C22×C13911yescharacteristic
446#525C22×C13911yescharacteristic
447#452C4×C13911yescharacteristic, complemented
448#452C4×C13911yescharacteristic, complemented
449#451C4×C13911yescharacteristic, complemented
450#450C4×C13911yescharacteristic, complemented
451#449C4×C13911yescharacteristic, complemented
452#449C4×C13911yescharacteristic, complemented
453#448C4×C13911yescharacteristic, complemented
454#447C4×C13911yescharacteristic, complemented
455#436—21no—
456#436—21no—
457#435—21no—
458#435—21no—
459C2×#108C22×C13911yescharacteristic, complemented
460C2×#108C22×C13911yescharacteristic, complemented
461#424C22×C13911yescharacteristic, complemented
462C2×#104C22×C13911yescharacteristic
463C2×#104C22×C13911yescharacteristic
464C2×#104C22×C13911yescharacteristic
465C2×#104C22×C13911yescharacteristic
466C2×#104C22×C13911yescharacteristic, complemented
467C2×#104C22×C13911yescharacteristic, complemented
468#416C22×C13911yescharacteristic
469#416C22×C13911yescharacteristic
470#408—21no—
471#408—21no—
472#408C22×C13911yescharacteristic
473#408C22×C13911yescharacteristic
474#408C22×C13911yescharacteristic
475#408C22×C13911yescharacteristic
476#408C22×C13911yescharacteristic, complemented
477#407—21no—
478#407—21no—
479#407C22×C13911yescharacteristic
480C2×C22⋊C8C22×C13911yescharacteristic
481#405C22×C13911yescharacteristic, complemented
482C2×#97C22×C13911yescharacteristic, complemented
483C2×C4×C8C22×C13911yescharacteristic, complemented
484C4×C22⋊C4C22×C13911yescharacteristic
485#341C22×C13911yescharacteristic, complemented
486#341C22×C13911yescharacteristic, complemented
487#339C22×C13911yescharacteristic, complemented
488#339C22×C13911yescharacteristic, complemented
489#336C22×C13911yescharacteristic, complemented
490#336C22×C13911yescharacteristic, complemented
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41C2×C4×C13911yescharacteristic
498C2×#41C2×C4×C13911yescharacteristic
499C2×#41C23×C13911yescharacteristic
500C2×#41C23×C13911yescharacteristic
501C2×#41C23×C13911yescharacteristic
502C22×Q8C2×C4×C13911yescharacteristic
503C22×D4—21no—
504C22×D4C2×C4×C13911yescharacteristic
505C23×C4—21no—
506C23×C4C23×C13911yescharacteristic
507#135—41no—
508#135—41no—
509#135—41no—
510#135—41no—
511C2×Q16C2×C4×C13911yescharacteristic
512C2×Q16C2×C4×C13911yescharacteristic
513C2×SD16C2×C4×C13911yescharacteristic
514C2×SD16C2×C4×C13911yescharacteristic
515C2×SD16C2×C4×C13911yescharacteristic
516C2×SD16C2×C4×C13911yescharacteristic
517C2×D8C2×C4×C13911yescharacteristic
518C2×D8C2×C4×C13911yescharacteristic
519#131—41no—
520#131—41no—
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16D4×C13911yescharacteristic
528C2×M16D4×C13911yescharacteristic
529C2×M16D4×C13911yescharacteristic
530C2×M16D4×C13911yescharacteristic
531C2×M16C23×C13911yescharacteristic
532C2×M16C23×C13911yescharacteristic
533C2×M16C23×C13911yescharacteristic
534C2×M16C23×C13911yescharacteristic
535C22×C8—21no—
536C22×C8—21no—
537C22×C8C23×C13911yescharacteristic
538C22×C8C23×C13911yescharacteristic
539C22×C8C23×C13911yescharacteristic
540C22×C8C23×C13911yescharacteristic
541#123—21no—
542C22⋊Q8C2×C4×C13911yescharacteristic
543C22⋊Q8C2×C4×C13911yescharacteristic
544#121C2×C4×C13911yescharacteristic
545#121C2×C4×C13911yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C23×C13911yescharacteristic
550C2×C22⋊C4—21no—
551C2×C42C23×C13911yescharacteristic
552C2×C42C23×C13911yescharacteristic
553#108—41no—
554#108—41no—
555C4⋊C8—21no—
556C4⋊C8—21no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—41no—
562#104—41no—
563#103C2×C4×C13911yescharacteristic
564#103C2×C4×C13911yescharacteristic
565#103C2×C4×C13911yescharacteristic
566#103C2×C4×C13911yescharacteristic
567#102C2×C4×C13911yescharacteristic
568#102C2×C4×C13911yescharacteristic
569#102C2×C4×C13911yescharacteristic
570#102C2×C4×C13911yescharacteristic
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—21no—
574C22⋊C8—21no—
575C22⋊C8—21no—
576C22⋊C8—21no—
577C22⋊C8—21no—
578C22⋊C8—21no—
579C22⋊C8—21no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582C22⋊C8—21no—
583C22⋊C8C2×C4×C13911yescharacteristic
584C22⋊C8C2×C4×C13911yescharacteristic
585C22⋊C8C2×C4×C13911yescharacteristic
586C22⋊C8C2×C4×C13911yescharacteristic
587#97—21no—
588#97—41no—
589C4×C8—21no—
590C4×C8—41no—
591#95—21no—
592C24—21no—
593C24#41×C13911yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—21no—
604#41—21no—
605#41—21no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610#41—42no—
611#41—42no—
612#41—42no—
613#41—42no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8C22×C4×C13911yescharacteristic
618C2×Q8C22×C4×C13911yescharacteristic
619C2×Q8C22×C4×C13911yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4C22×C4×C13911yescharacteristic
633C2×D4C22×C4×C13911yescharacteristic
634C2×D4C22×C4×C13911yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4C22×C4×C13911yescharacteristic
650C22×C4C22×C4×C13911yescharacteristic
651C22×C4C2×D4×C13911yescharacteristic
652C22×C4C2×D4×C13911yescharacteristic
653C22×C4#41×C13911yescharacteristic
654C22×C4C24×C13911yescharacteristic
655Q16—41no—
656Q16—41no—
657SD16—41no—
658SD16—41no—
659SD16—41no—
660SD16—41no—
661D8—41no—
662D8—41no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—41no—
672M16—41no—
673M16—41no—
674M16—41no—
675M16—42no—
676M16—42no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8C22×C4×C13911yescharacteristic
692C2×C8C22×C4×C13911yescharacteristic
693C2×C8C22×C4×C13911yescharacteristic
694C2×C8C22×C4×C13911yescharacteristic
695C2×C8C2×D4×C13911yescharacteristic
696C2×C8C2×D4×C13911yescharacteristic
697C2×C8C2×D4×C13911yescharacteristic
698C2×C8C2×D4×C13911yescharacteristic
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C22×C4×C13911yescharacteristic
702C4⋊C4C22×C4×C13911yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—81no—
723C23—81no—
724C23C4×D4×C13911yescharacteristic
725C23C4×D4×C13911yescharacteristic
726C23C2×#41×C13911yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—21no—
739D4—21no—
740D4—42no—
741D4—42no—
742D4—42no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—81no—
750D4—81no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
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—41no—
781C2×C4C4×D4×C13911yescharacteristic
782C2×C4C4×D4×C13911yescharacteristic
783C2×C4C23×C4×C13911yescharacteristic
784C2×C4C22×D4×C13911yescharacteristic
785C2×C4H(5,𝔽2)×C13911yescharacteristic
786C2×C4H(5,𝔽2)×C13911yescharacteristic
787C2×C4H(5,𝔽2)×C13911yescharacteristic
788C2×C4H(5,𝔽2)×C13911yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—41no—
798C8—41no—
799C8—41no—
800C8—41no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—81no—
819C22—81no—
820C22—84no—
821C22C2×C4×D4×C13911yescharacteristic
822C22#538×C13911yescharacteristic
823C22#538×C13911yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—41no—
832C4—81no—
833C4#518×C13911yescharacteristic
834C4#518×C13911yescharacteristic
835C4#534×C13911yescharacteristic
836C4#535×C13911yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—81no—
844C2#2321×C13911yescharacteristic
845C2#2956×C13911yescharacteristic
846C2#2957×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 ◁ C22×M16×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2930×C139C2semidirect
3. #2879×C139C2semidirect
4. #1975×C139C2semidirect
5. #1974×C139C2semidirect
6. #1938×C139C2semidirect
7. #1937×C139C2semidirect
8. #1929×C139C2semidirect
9. #1929×C139C2semidirect
10. #1876×C139C2semidirect
11. #1876×C139C2semidirect
12. #1871×C139C2semidirect
13. #1855×C139C2semidirect
14. #1789×C139C2semidirect
15. #1753×C139C2semidirect
19. C2×#131×C139C22semidirect
23. #452×C139C4semidirect
24. #452×C139C4semidirect
25. #451×C139C4semidirect
26. #450×C139C4semidirect
27. #449×C139C4semidirect
28. #449×C139C4semidirect
29. #448×C139C4semidirect
30. #447×C139C4semidirect
35. C2×#108×C139C22semidirect
36. C2×#108×C139C22semidirect
37. #424×C139C22semidirect
42. C2×#104×C139C22semidirect
43. C2×#104×C139C22semidirect
52. #408×C139C22semidirect
57. #405×C139C22semidirect
58. C2×#97×C139C22semidirect
59. C2×C4×C8×C139C22semidirect
61. #341×C139C22semidirect
62. #341×C139C22semidirect
63. #339×C139C22semidirect
64. #339×C139C22semidirect
65. #336×C139C22semidirect
66. #336×C139C22semidirect
423. #22062C139direct (N × H)
424. C139#22062direct (N × H)
426. #2930C2×C139semidirect
427. #2879C2×C139semidirect
428. #1975C2×C139semidirect
429. #1974C2×C139semidirect
430. #1938C2×C139semidirect
431. #1937C2×C139semidirect
432. #1929C2×C139semidirect
433. #1929C2×C139semidirect
434. #1876C2×C139semidirect
435. #1876C2×C139semidirect
436. #1871C2×C139semidirect
437. #1855C2×C139semidirect
438. #1789C2×C139semidirect
439. #1753C2×C139semidirect
443. C2×#131C22×C139semidirect
447. #452C4×C139semidirect
448. #452C4×C139semidirect
449. #451C4×C139semidirect
450. #450C4×C139semidirect
451. #449C4×C139semidirect
452. #449C4×C139semidirect
453. #448C4×C139semidirect
454. #447C4×C139semidirect
459. C2×#108C22×C139semidirect
460. C2×#108C22×C139semidirect
461. #424C22×C139semidirect
466. C2×#104C22×C139semidirect
467. C2×#104C22×C139semidirect
476. #408C22×C139semidirect
481. #405C22×C139semidirect
482. C2×#97C22×C139semidirect
483. C2×C4×C8C22×C139semidirect
485. #341C22×C139semidirect
486. #341C22×C139semidirect
487. #339C22×C139semidirect
488. #339C22×C139semidirect
489. #336C22×C139semidirect
490. #336C22×C139semidirect

Maximal subgroups

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

subgroupindex
#3002×C1392
#2930×C1392
#2879×C1392
#1975×C1392
#1974×C1392
#1938×C1392
#1937×C1392
#1929×C1392
#1876×C1392
#1871×C1392
#1855×C1392
#1789×C1392
#1753×C1392
#22062139