Finite Group Databasebeta

← C139×#29601 #48024197

Subgroups — C139×#29601 #48024197

Order 35584.

1462 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C139C211yesmaximal, characteristic
2C2×#485×C139C211yesmaximal, characteristic, complemented
3C2×#452×C139C211yesmaximal, characteristic, complemented
4#2848×C139C211yesmaximal, characteristic, complemented
5#2036×C139C211yesmaximal, characteristic, complemented
6#2035×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#2001×C139C211yesmaximal, characteristic, complemented
10#2001×C139C211yesmaximal, characteristic, complemented
11#2000×C139C211yesmaximal, characteristic, complemented
12#2000×C139C211yesmaximal, characteristic, complemented
13#1825×C139C211yesmaximal, characteristic, complemented
14#1788×C139C211yesmaximal, characteristic, complemented
15#1779×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C24×C4×C139C2211yescharacteristic
18C22×Q16×C139C2211yescharacteristic, complemented
19C22×SD16×C139C2211yescharacteristic, complemented
20#525×C139—24no—
21#525×C139—24no—
22C2×#123×C139—21no—
23C2×C22⋊Q8×C139C2211yescharacteristic
24C2×C22⋊Q8×C139C2211yescharacteristic
25C2×C22⋊Q8×C139C2211yescharacteristic
26C2×C22⋊Q8×C139C2211yescharacteristic
27C2×C22⋊Q8×C139C2211yescharacteristic
28C2×#121×C139C2211yescharacteristic
29C2×#121×C139C2211yescharacteristic
30C2×#120×C139—21no—
31C2×C4×D4×C139—21no—
32C2×C4×D4×C139—21no—
33C2×#117×C139C2211yescharacteristic
34#485×C139—24no—
35#452×C139—24no—
36C2×#107×C139C2211yescharacteristic, complemented
37C2×#106×C139C2211yescharacteristic, complemented
38C2×#103×C139C2211yescharacteristic, complemented
39C2×#103×C139C2211yescharacteristic, complemented
40C2×#103×C139C2211yescharacteristic, complemented
41C2×#103×C139C2211yescharacteristic, complemented
42C2×#103×C139C2211yescharacteristic, complemented
43C2×#102×C139C2211yescharacteristic, complemented
44C2×#102×C139C2211yescharacteristic, complemented
45C2×#102×C139C2211yescharacteristic, complemented
46C2×C22⋊C8×C139C2211yescharacteristic
47C2×C22⋊C8×C139C2211yescharacteristic
48C2×C22⋊C8×C139C2211yescharacteristic
49C2×C22⋊C8×C139C2211yescharacteristic
50C2×C22⋊C8×C139C2211yescharacteristic
51C2×C22⋊C8×C139C2211yescharacteristic
52#385×C139—21no—
53#385×C139—21no—
54#385×C139—21no—
55#380×C139C2211yescharacteristic
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic
58#379×C139—21no—
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63C25×C139D411yescharacteristic
64C2×#41×C139—22no—
65C2×#41×C139—41no—
66C2×#41×C139—41no—
67C2×#41×C139—41no—
68C2×#41×C139—41no—
69C2×#41×C139D414yes—
70C22×Q8×C139C2311yescharacteristic
71C22×Q8×C139C2311yescharacteristic
72C22×D4×C139—21no—
73C22×D4×C139—21no—
74C22×D4×C139—21no—
75C22×D4×C139C2311yescharacteristic
76C23×C4×C139—21no—
77C23×C4×C139—22no—
78C23×C4×C139—22no—
79C23×C4×C139—41no—
80C23×C4×C139—41no—
81C23×C4×C139—41no—
82C23×C4×C139—41no—
83C23×C4×C139D411yescharacteristic
84C23×C4×C139D411yescharacteristic
85C23×C4×C139D411yescharacteristic
86C23×C4×C139C2311yescharacteristic
87C23×C4×C139C2311yescharacteristic
88C23×C4×C139C2311yescharacteristic
89C2×Q16×C139—22no—
90C2×Q16×C139—41no—
91C2×Q16×C139—41no—
92C2×SD16×C139—22no—
93C2×SD16×C139—41no—
94C2×SD16×C139—41no—
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97C22×C8×C139C2311yescharacteristic
98C22×C8×C139C2311yescharacteristic
99#123×C139—28no—
100C22⋊Q8×C139—22no—
101C22⋊Q8×C139—22no—
102C22⋊Q8×C139—22no—
103C22⋊Q8×C139—22no—
104C22⋊Q8×C139—22no—
105C22⋊Q8×C139—22no—
106C22⋊Q8×C139—41no—
107C22⋊Q8×C139—41no—
108C22⋊Q8×C139—41no—
109C22⋊Q8×C139—41no—
110#121×C139—22no—
111#121×C139—22no—
112#121×C139—22no—
113#121×C139—22no—
114#120×C139—28no—
115C4×D4×C139—28no—
116C4×D4×C139—28no—
117#117×C139—22no—
118#117×C139D414yes—
119C2×C4⋊C4×C139—21no—
120C2×C4⋊C4×C139—21no—
121C2×C4⋊C4×C139—21no—
122C2×C4⋊C4×C139—21no—
123C2×C4⋊C4×C139—21no—
124C2×C4⋊C4×C139C2311yescharacteristic
125C2×C4⋊C4×C139C2311yescharacteristic
126C2×C4⋊C4×C139C2311yescharacteristic
127C2×C4⋊C4×C139C2311yescharacteristic
128C2×C4⋊C4×C139C2311yescharacteristic
129C2×C22⋊C4×C139—21no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—21no—
134C2×C22⋊C4×C139—21no—
135C2×C22⋊C4×C139—21no—
136C2×C22⋊C4×C139—21no—
137C2×C22⋊C4×C139—21no—
138C2×C22⋊C4×C139—21no—
139C2×C22⋊C4×C139—21no—
140C2×C42×C139—21no—
141#107×C139—22no—
142#106×C139—22no—
143#103×C139—22no—
144#103×C139—22no—
145#103×C139—22no—
146#103×C139—41no—
147#103×C139—41no—
148#102×C139—22no—
149#102×C139—41no—
150#102×C139—41no—
151C22⋊C8×C139—22no—
152C22⋊C8×C139—22no—
153C22⋊C8×C139—41no—
154C22⋊C8×C139—41no—
155C22⋊C8×C139—41no—
156C22⋊C8×C139—41no—
157#95×C139—21no—
158#95×C139—21no—
159#95×C139—21no—
160C24×C139—22no—
161C24×C139—22no—
162C24×C139—22no—
163C24×C139—21no—
164C24×C139—41no—
165C24×C139—41no—
166C24×C139—41no—
167C24×C139—41no—
168C24×C139C2×D411yescharacteristic
169C24×C139C2×D411yescharacteristic
170C24×C139C2×D411yescharacteristic
171#41×C139—44no—
172#41×C139—44no—
173#41×C139—44no—
174#41×C139—44no—
175C2×Q8×C139—21no—
176C2×Q8×C139—21no—
177C2×Q8×C139—21no—
178C2×Q8×C139—21no—
179C2×Q8×C139—21no—
180C2×Q8×C139—21no—
181C2×Q8×C139—21no—
182C2×Q8×C139—21no—
183C2×Q8×C139—21no—
184C2×Q8×C139—21no—
185C2×Q8×C139—21no—
186C2×Q8×C139C2×D412yes—
187C2×D4×C139—24no—
188C2×D4×C139—24no—
189C2×D4×C139—24no—
190C2×D4×C139—21no—
191C2×D4×C139—21no—
192C2×D4×C139—21no—
193C2×D4×C139—21no—
194C2×D4×C139—21no—
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×C139C2×D412yes—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—21no—
205C22×C4×C139—21no—
206C22×C4×C139—22no—
207C22×C4×C139—21no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—22no—
211C22×C4×C139—22no—
212C22×C4×C139—24no—
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—21no—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
229C22×C4×C139—41no—
230C22×C4×C139—41no—
231C22×C4×C139—41no—
232C22×C4×C139—41no—
233C22×C4×C139—41no—
234C22×C4×C139—41no—
235C22×C4×C139—44no—
236C22×C4×C139—44no—
237C22×C4×C139—44no—
238C22×C4×C139—44no—
239C22×C4×C139—42no—
240C22×C4×C139—42no—
241C22×C4×C139C2×D411yescharacteristic
242C22×C4×C139C2×D411yescharacteristic
243C22×C4×C139C2×D411yescharacteristic
244C22×C4×C139C2×D412yes—
245C22×C4×C139C2×D412yes—
246C22×C4×C139C2411yescharacteristic
247Q16×C139—44no—
248SD16×C139—44no—
249C2×C8×C139—21no—
250C2×C8×C139—21no—
251C2×C8×C139—21no—
252C2×C8×C139—21no—
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—
261C4⋊C4×C139—24no—
262C4⋊C4×C139—24no—
263C4⋊C4×C139—21no—
264C4⋊C4×C139—21no—
265C4⋊C4×C139—21no—
266C4⋊C4×C139—21no—
267C4⋊C4×C139—21no—
268C4⋊C4×C139—21no—
269C4⋊C4×C139—21no—
270C4⋊C4×C139—21no—
271C4⋊C4×C139—42no—
272C4⋊C4×C139—42no—
273C4⋊C4×C139—42no—
274C4⋊C4×C139C2×D412yes—
275C4⋊C4×C139C2×D412yes—
276C22⋊C4×C139—24no—
277C22⋊C4×C139—24no—
278C22⋊C4×C139—24no—
279C22⋊C4×C139—24no—
280C22⋊C4×C139—24no—
281C22⋊C4×C139—42no—
282C22⋊C4×C139—42no—
283C22⋊C4×C139—42no—
284C22⋊C4×C139—42no—
285C22⋊C4×C139—42no—
286C22⋊C4×C139—42no—
287C42×C139—24no—
288C23×C139—21no—
289C23×C139—21no—
290C23×C139—21no—
291C23×C139—21no—
292C23×C139—21no—
293C23×C139—21no—
294C23×C139—21no—
295C23×C139—21no—
296C23×C139—21no—
297C23×C139—21no—
298C23×C139—21no—
299C23×C139—21no—
300C23×C139—21no—
301C23×C139—21no—
302C23×C139—21no—
303C23×C139—21no—
304C23×C139—21no—
305C23×C139—21no—
306C23×C139—22no—
307C23×C139—44no—
308C23×C139—44no—
309C23×C139—44no—
310C23×C139—44no—
311C23×C139—44no—
312C23×C139—44no—
313C23×C139—44no—
314C23×C139—41no—
315C23×C139—41no—
316C23×C139—41no—
317C23×C139—41no—
318C23×C139—41no—
319C23×C139—41no—
320C23×C139#12012yes—
321C23×C139#13512yes—
322C23×C139#13712yes—
323C23×C139C22×D411yescharacteristic
324Q8×C139—22no—
325Q8×C139—22no—
326Q8×C139—41no—
327Q8×C139—41no—
328Q8×C139—41no—
329Q8×C139—41no—
330Q8×C139—41no—
331Q8×C139—41no—
332D4×C139—22no—
333D4×C139—22no—
334D4×C139—48no—
335D4×C139—48no—
336D4×C139—48no—
337D4×C139—41no—
338D4×C139—41no—
339C2×C4×C139—21no—
340C2×C4×C139—21no—
341C2×C4×C139—22no—
342C2×C4×C139—22no—
343C2×C4×C139—22no—
344C2×C4×C139—22no—
345C2×C4×C139—22no—
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—44no—
355C2×C4×C139—44no—
356C2×C4×C139—48no—
357C2×C4×C139—44no—
358C2×C4×C139—41no—
359C2×C4×C139—41no—
360C2×C4×C139—41no—
361C2×C4×C139—41no—
362C2×C4×C139—41no—
363C2×C4×C139—41no—
364C2×C4×C139—41no—
365C2×C4×C139—41no—
366C2×C4×C139—41no—
367C2×C4×C139—41no—
368C2×C4×C139—41no—
369C2×C4×C139—41no—
370C2×C4×C139—41no—
371C2×C4×C139—41no—
372C2×C4×C139—41no—
373C2×C4×C139—41no—
374C2×C4×C139—41no—
375C2×C4×C139—41no—
376C2×C4×C139—41no—
377C2×C4×C139—41no—
378C2×C4×C139—41no—
379C2×C4×C139—41no—
380C2×C4×C139—41no—
381C2×C4×C139—41no—
382C2×C4×C139—41no—
383C2×C4×C139—41no—
384C2×C4×C139#12012yes—
385C2×C4×C139C22×D411yescharacteristic
386C2×C4×C139C22×D411yescharacteristic
387C2×C4×C139H(5,𝔽2)11yescharacteristic
388C2×C4×C139H(5,𝔽2)11yescharacteristic
389C2×C4×C139H(5,𝔽2)11yescharacteristic
390C2×C4×C139H(5,𝔽2)11yescharacteristic
391C8×C139—41no—
392C8×C139—41no—
393C8×C139—41no—
394C8×C139—41no—
395C22×C139—22no—
396C22×C139—22no—
397C22×C139—22no—
398C22×C139—22no—
399C22×C139—22no—
400C22×C139—22no—
401C22×C139—22no—
402C22×C139—22no—
403C22×C139—22no—
404C22×C139—416no—
405C22×C139—41no—
406C22×C139—41no—
407C22×C139—41no—
408C22×C139—41no—
409C22×C139—41no—
410C22×C139—41no—
411C22×C139—41no—
412C22×C139—41no—
413C22×C139—41no—
414C22×C139—41no—
415C22×C139—41no—
416C22×C139—41no—
417C22×C139—42no—
418C22×C139—42no—
419C22×C139—42no—
420C22×C139—81no—
421C22×C139—81no—
422C22×C139—81no—
423C22×C139—81no—
424C22×C139C2×#12011yescharacteristic
425C22×C139#53411yescharacteristic
426C22×C139#53411yescharacteristic
427C22×C139C2×#13511yescharacteristic
428C22×C139C2×#13711yescharacteristic
429C22×C139#57511yescharacteristic
430C22×C139#57511yescharacteristic
431C4×C139—22no—
432C4×C139—41no—
433C4×C139—41no—
434C4×C139—42no—
435C4×C139—42no—
436C4×C139—42no—
437C4×C139—81no—
438C4×C139—81no—
439C4×C139—81no—
440C4×C139—81no—
441C4×C139#53411yescharacteristic
442C4×C139#53411yescharacteristic
443C4×C139#53511yescharacteristic
444C4×C139#53511yescharacteristic
445C2×C139—42no—
446C2×C139—42no—
447C2×C139—42no—
448C2×C139—82no—
449C2×C139#261311yescharacteristic
450C2×C139#300211yescharacteristic
451C2×C139#300711yescharacteristic
452C2×C139#319011yescharacteristic
453C2×C139#319111yescharacteristic
454C2×C139#319611yescharacteristic
455C2×C139#319711yescharacteristic
456#29601C13911yesmaximal, characteristic, direct product factor, Sylow
457C139#2960111yescharacteristic, direct product factor, Sylow
458C2×#525C2×C13911yescharacteristic
459C2×#485C2×C13911yescharacteristic, complemented
460C2×#452C2×C13911yescharacteristic, complemented
461#2848C2×C13911yescharacteristic, complemented
462#2036C2×C13911yescharacteristic, complemented
463#2035C2×C13911yescharacteristic, complemented
464#2034C2×C13911yescharacteristic, complemented
465#2033C2×C13911yescharacteristic, complemented
466#2001C2×C13911yescharacteristic, complemented
467#2001C2×C13911yescharacteristic, complemented
468#2000C2×C13911yescharacteristic, complemented
469#2000C2×C13911yescharacteristic, complemented
470#1825C2×C13911yescharacteristic, complemented
471#1788C2×C13911yescharacteristic, complemented
472#1779C2×C13911yescharacteristic, complemented
473C22×#41C22×C13911yescharacteristic
474C24×C4C22×C13911yescharacteristic
475C22×Q16C22×C13911yescharacteristic, complemented
476C22×SD16C22×C13911yescharacteristic, complemented
477#525—24no—
478#525—24no—
479C2×#123—21no—
480C2×C22⋊Q8C22×C13911yescharacteristic
481C2×C22⋊Q8C22×C13911yescharacteristic
482C2×C22⋊Q8C22×C13911yescharacteristic
483C2×C22⋊Q8C22×C13911yescharacteristic
484C2×C22⋊Q8C22×C13911yescharacteristic
485C2×#121C22×C13911yescharacteristic
486C2×#121C22×C13911yescharacteristic
487C2×#120—21no—
488C2×C4×D4—21no—
489C2×C4×D4—21no—
490C2×#117C22×C13911yescharacteristic
491#485—24no—
492#452—24no—
493C2×#107C22×C13911yescharacteristic, complemented
494C2×#106C22×C13911yescharacteristic, complemented
495C2×#103C22×C13911yescharacteristic, complemented
496C2×#103C22×C13911yescharacteristic, complemented
497C2×#103C22×C13911yescharacteristic, complemented
498C2×#103C22×C13911yescharacteristic, complemented
499C2×#103C22×C13911yescharacteristic, complemented
500C2×#102C22×C13911yescharacteristic, complemented
501C2×#102C22×C13911yescharacteristic, complemented
502C2×#102C22×C13911yescharacteristic, complemented
503C2×C22⋊C8C22×C13911yescharacteristic
504C2×C22⋊C8C22×C13911yescharacteristic
505C2×C22⋊C8C22×C13911yescharacteristic
506C2×C22⋊C8C22×C13911yescharacteristic
507C2×C22⋊C8C22×C13911yescharacteristic
508C2×C22⋊C8C22×C13911yescharacteristic
509#385—21no—
510#385—21no—
511#385—21no—
512#380C22×C13911yescharacteristic
513#380C22×C13911yescharacteristic
514#380C22×C13911yescharacteristic
515#379—21no—
516#340C22×C13911yescharacteristic, complemented
517#340C22×C13911yescharacteristic, complemented
518#340C22×C13911yescharacteristic, complemented
519#340C22×C13911yescharacteristic, complemented
520C25D4×C13911yescharacteristic
521C2×#41—22no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41D4×C13914yes—
527C22×Q8C23×C13911yescharacteristic
528C22×Q8C23×C13911yescharacteristic
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4C23×C13911yescharacteristic
533C23×C4—21no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—41no—
537C23×C4—41no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4D4×C13911yescharacteristic
541C23×C4D4×C13911yescharacteristic
542C23×C4D4×C13911yescharacteristic
543C23×C4C23×C13911yescharacteristic
544C23×C4C23×C13911yescharacteristic
545C23×C4C23×C13911yescharacteristic
546C2×Q16—22no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×SD16—22no—
550C2×SD16—41no—
551C2×SD16—41no—
552C22×C8C23×C13911yescharacteristic
553C22×C8C23×C13911yescharacteristic
554C22×C8C23×C13911yescharacteristic
555C22×C8C23×C13911yescharacteristic
556#123—28no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—41no—
564C22⋊Q8—41no—
565C22⋊Q8—41no—
566C22⋊Q8—41no—
567#121—22no—
568#121—22no—
569#121—22no—
570#121—22no—
571#120—28no—
572C4×D4—28no—
573C4×D4—28no—
574#117—22no—
575#117D4×C13914yes—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4C23×C13911yescharacteristic
582C2×C4⋊C4C23×C13911yescharacteristic
583C2×C4⋊C4C23×C13911yescharacteristic
584C2×C4⋊C4C23×C13911yescharacteristic
585C2×C4⋊C4C23×C13911yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C42—21no—
598#107—22no—
599#106—22no—
600#103—22no—
601#103—22no—
602#103—22no—
603#103—41no—
604#103—41no—
605#102—22no—
606#102—41no—
607#102—41no—
608C22⋊C8—22no—
609C22⋊C8—22no—
610C22⋊C8—41no—
611C22⋊C8—41no—
612C22⋊C8—41no—
613C22⋊C8—41no—
614#95—21no—
615#95—21no—
616#95—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—41no—
622C24—41no—
623C24—41no—
624C24—41no—
625C24C2×D4×C13911yescharacteristic
626C24C2×D4×C13911yescharacteristic
627C24C2×D4×C13911yescharacteristic
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C13912yes—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4C2×D4×C13912yes—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—22no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—24no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—41no—
687C22×C4—41no—
688C22×C4—41no—
689C22×C4—41no—
690C22×C4—41no—
691C22×C4—41no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4C2×D4×C13911yescharacteristic
699C22×C4C2×D4×C13911yescharacteristic
700C22×C4C2×D4×C13911yescharacteristic
701C22×C4C2×D4×C13912yes—
702C22×C4C2×D4×C13912yes—
703C22×C4C24×C13911yescharacteristic
704Q16—44no—
705SD16—44no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C4⋊C4—24no—
719C4⋊C4—24no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C4⋊C4C2×D4×C13912yes—
732C4⋊C4C2×D4×C13912yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—24no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C42—24no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—44no—
768C23—44no—
769C23—44no—
770C23—44no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C13912yes—
778C23#135×C13912yes—
779C23#137×C13912yes—
780C23C22×D4×C13911yescharacteristic
781Q8—22no—
782Q8—22no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—48no—
814C2×C4—44no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4#120×C13912yes—
842C2×C4C22×D4×C13911yescharacteristic
843C2×C4C22×D4×C13911yescharacteristic
844C2×C4H(5,𝔽2)×C13911yescharacteristic
845C2×C4H(5,𝔽2)×C13911yescharacteristic
846C2×C4H(5,𝔽2)×C13911yescharacteristic
847C2×C4H(5,𝔽2)×C13911yescharacteristic
848C8—41no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—416no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C13911yescharacteristic
882C22#534×C13911yescharacteristic
883C22#534×C13911yescharacteristic
884C22C2×#135×C13911yescharacteristic
885C22C2×#137×C13911yescharacteristic
886C22#575×C13911yescharacteristic
887C22#575×C13911yescharacteristic
888C4—22no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4#534×C13911yescharacteristic
899C4#534×C13911yescharacteristic
900C4#535×C13911yescharacteristic
901C4#535×C13911yescharacteristic
902C2—42no—
903C2—42no—
904C2—42no—
905C2—82no—
906C2#2613×C13911yescharacteristic
907C2#3002×C13911yescharacteristic
908C2#3007×C13911yescharacteristic
909C2#3190×C13911yescharacteristic
910C2#3191×C13911yescharacteristic
911C2#3196×C13911yescharacteristic
912C2#3197×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#525×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C24×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C139C2semidirect
3. C2×#452×C139C2semidirect
4. #2848×C139C2semidirect
5. #2036×C139C2semidirect
6. #2035×C139C2semidirect
7. #2034×C139C2semidirect
8. #2033×C139C2semidirect
9. #2001×C139C2semidirect
10. #2001×C139C2semidirect
11. #2000×C139C2semidirect
12. #2000×C139C2semidirect
13. #1825×C139C2semidirect
14. #1788×C139C2semidirect
15. #1779×C139C2semidirect
18. C22×Q16×C139C22semidirect
19. C22×SD16×C139C22semidirect
36. C2×#107×C139C22semidirect
37. C2×#106×C139C22semidirect
38. C2×#103×C139C22semidirect
39. C2×#103×C139C22semidirect
40. C2×#103×C139C22semidirect
41. C2×#103×C139C22semidirect
42. C2×#103×C139C22semidirect
43. C2×#102×C139C22semidirect
44. C2×#102×C139C22semidirect
45. C2×#102×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
456. #29601C139direct (N × H)
457. C139#29601direct (N × H)
459. C2×#485C2×C139semidirect
460. C2×#452C2×C139semidirect
461. #2848C2×C139semidirect
462. #2036C2×C139semidirect
463. #2035C2×C139semidirect
464. #2034C2×C139semidirect
465. #2033C2×C139semidirect
466. #2001C2×C139semidirect
467. #2001C2×C139semidirect
468. #2000C2×C139semidirect
469. #2000C2×C139semidirect
470. #1825C2×C139semidirect
471. #1788C2×C139semidirect
472. #1779C2×C139semidirect
475. C22×Q16C22×C139semidirect
476. C22×SD16C22×C139semidirect
493. C2×#107C22×C139semidirect
494. C2×#106C22×C139semidirect
495. C2×#103C22×C139semidirect
496. C2×#103C22×C139semidirect
497. C2×#103C22×C139semidirect
498. C2×#103C22×C139semidirect
499. C2×#103C22×C139semidirect
500. C2×#102C22×C139semidirect
501. C2×#102C22×C139semidirect
502. C2×#102C22×C139semidirect
516. #340C22×C139semidirect
517. #340C22×C139semidirect
518. #340C22×C139semidirect
519. #340C22×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1392
C2×#485×C1392
C2×#452×C1392
#2848×C1392
#2036×C1392
#2035×C1392
#2034×C1392
#2033×C1392
#2001×C1392
#2000×C1392
#1825×C1392
#1788×C1392
#1779×C1392
#29601139