Finite Group Databasebeta

← C139×#24220 #48018816

Subgroups — C139×#24220 #48018816

Order 35584.

1556 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C139C211yesmaximal, characteristic
2C2×#464×C139C211yesmaximal, characteristic, complemented
3C2×#460×C139C211yesmaximal, characteristic, complemented
4C2×#452×C139C211yesmaximal, characteristic, complemented
5C2×#450×C139C211yesmaximal, characteristic, complemented
6#2323×C139C211yesmaximal, characteristic, complemented
7#2042×C139C211yesmaximal, characteristic, complemented
8#2041×C139C211yesmaximal, characteristic, complemented
9#2015×C139C211yesmaximal, characteristic, complemented
10#2014×C139C211yesmaximal, characteristic, complemented
11#1983×C139C211yesmaximal, characteristic, complemented
12#1982×C139C211yesmaximal, characteristic, complemented
13#1798×C139C211yesmaximal, characteristic, complemented
14#1788×C139C211yesmaximal, characteristic, complemented
15#1786×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×D4×C139C2211yescharacteristic
18C22×Q16×C139C2211yescharacteristic, complemented
19C22×SD16×C139C2211yescharacteristic
20C22×SD16×C139C2211yescharacteristic
21C22×SD16×C139C2211yescharacteristic, complemented
22#535×C139—24no—
23#535×C139—24no—
24C2×#127×C139C2211yescharacteristic
25C2×#127×C139C2211yescharacteristic
26C2×#124×C139C2211yescharacteristic
27C2×#124×C139C2211yescharacteristic
28C2×C22⋊Q8×C139C2211yescharacteristic
29C2×#121×C139—21no—
30C2×#121×C139—21no—
31C2×#120×C139—21no—
32C2×#120×C139—21no—
33C2×C4×Q8×C139C2211yescharacteristic, complemented
34C2×#117×C139C2211yescharacteristic
35#464×C139—24no—
36#460×C139—24no—
37#452×C139—24no—
38#450×C139—24no—
39C2×C4⋊C8×C139C2211yescharacteristic, complemented
40C2×C4⋊C8×C139C2211yescharacteristic, complemented
41C2×#103×C139C2211yescharacteristic, complemented
42C2×#103×C139C2211yescharacteristic, complemented
43C2×#103×C139C2211yescharacteristic, complemented
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×#102×C139C2211yescharacteristic
47C2×#102×C139C2211yescharacteristic
48C2×#102×C139C2211yescharacteristic
49C2×#102×C139C2211yescharacteristic
50C2×#102×C139C2211yescharacteristic, complemented
51C2×#102×C139C2211yescharacteristic, complemented
52C2×#102×C139C2211yescharacteristic, complemented
53C2×C22⋊C8×C139C2211yescharacteristic
54C2×C22⋊C8×C139C2211yescharacteristic
55#391×C139C2211yescharacteristic, complemented
56#389×C139—21no—
57#389×C139C2211yescharacteristic, complemented
58#388×C139—21no—
59#388×C139—21no—
60#387×C139—21no—
61#380×C139C2211yescharacteristic
62C4×C4⋊C4×C139C2211yescharacteristic, complemented
63#336×C139C2211yescharacteristic, complemented
64#336×C139C2211yescharacteristic, complemented
65C25×C139—21no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—22no—
69C2×#41×C139—22no—
70C2×#41×C139—41no—
71C2×#41×C139—41no—
72C22×Q8×C139C2311yescharacteristic
73C22×Q8×C139C2311yescharacteristic
74C22×D4×C139—21no—
75C22×D4×C139—22no—
76C22×D4×C139—22no—
77C22×D4×C139—21no—
78C22×D4×C139—21no—
79C22×D4×C139—21no—
80C22×D4×C139—21no—
81C22×D4×C139—21no—
82C22×D4×C139—22no—
83C22×D4×C139—22no—
84C22×D4×C139—41no—
85C22×D4×C139—41no—
86C22×D4×C139C2311yescharacteristic
87C22×D4×C139C2311yescharacteristic
88C22×D4×C139C2311yescharacteristic
89C23×C4×C139—21no—
90C23×C4×C139C2311yescharacteristic
91C2×Q16×C139—22no—
92C2×Q16×C139—22no—
93C2×Q16×C139—41no—
94C2×SD16×C139—22no—
95C2×SD16×C139—22no—
96C2×SD16×C139—22no—
97C2×SD16×C139—22no—
98C2×SD16×C139—22no—
99C2×SD16×C139—22no—
100C2×SD16×C139—41no—
101C2×SD16×C139—41no—
102C2×SD16×C139—41no—
103C22×C8×C139C2311yescharacteristic
104C22×C8×C139C2311yescharacteristic
105C22×C8×C139C2311yescharacteristic
106C22×C8×C139C2311yescharacteristic
107#127×C139—22no—
108#127×C139—22no—
109#127×C139—22no—
110#127×C139D414yes—
111#124×C139—22no—
112#124×C139—22no—
113#124×C139—22no—
114#124×C139D414yes—
115C22⋊Q8×C139—22no—
116C22⋊Q8×C139D414yescomplemented
117#121×C139—28no—
118#121×C139—28no—
119#120×C139—28no—
120#120×C139—28no—
121C4×Q8×C139—22no—
122C4×Q8×C139—22no—
123#117×C139—22no—
124#117×C139—22no—
125C2×C4⋊C4×C139—21no—
126C2×C4⋊C4×C139—21no—
127C2×C4⋊C4×C139—21no—
128C2×C4⋊C4×C139D411yescharacteristic
129C2×C4⋊C4×C139D411yescharacteristic
130C2×C4⋊C4×C139C2311yescharacteristic
131C2×C4⋊C4×C139C2311yescharacteristic
132C2×C4⋊C4×C139C2311yescharacteristic
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×C139D411yescharacteristic
140C2×C22⋊C4×C139D411yescharacteristic
141C2×C42×C139—21no—
142C2×C42×C139—21no—
143C2×C42×C139C2311yescharacteristic
144C2×C42×C139C2311yescharacteristic
145C4⋊C8×C139—22no—
146C4⋊C8×C139—22no—
147#103×C139—22no—
148#103×C139—22no—
149#103×C139—41no—
150#102×C139—22no—
151#102×C139—22no—
152#102×C139—22no—
153#102×C139—22no—
154#102×C139—22no—
155#102×C139—22no—
156#102×C139—41no—
157#102×C139—41no—
158#102×C139—41no—
159C22⋊C8×C139—22no—
160C22⋊C8×C139—22no—
161#95×C139—21no—
162#95×C139—21no—
163#95×C139—21no—
164#95×C139—21no—
165#95×C139—21no—
166C24×C139—24no—
167C24×C139—21no—
168C24×C139—21no—
169C24×C139—21no—
170C24×C139—42no—
171C24×C139—42no—
172C24×C139—81no—
173C24×C139—81no—
174C24×C139—81no—
175C24×C139—81no—
176C24×C139C2×D411yescharacteristic
177#41×C139—44no—
178#41×C139—44no—
179#41×C139—44no—
180#41×C139—44no—
181C2×Q8×C139—21no—
182C2×Q8×C139—21no—
183C2×Q8×C139—21no—
184C2×Q8×C139—21no—
185C2×Q8×C139—21no—
186C2×Q8×C139—21no—
187C2×Q8×C139—21no—
188C2×Q8×C139—21no—
189C2×Q8×C139—21no—
190C2×Q8×C139—21no—
191C2×Q8×C139C2×D412yes—
192C2×Q8×C139C2×D412yes—
193C2×D4×C139—24no—
194C2×D4×C139—24no—
195C2×D4×C139—24no—
196C2×D4×C139—24no—
197C2×D4×C139—24no—
198C2×D4×C139—24no—
199C2×D4×C139—21no—
200C2×D4×C139—21no—
201C2×D4×C139—21no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
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—21no—
212C2×D4×C139—21no—
213C2×D4×C139—21no—
214C2×D4×C139—44no—
215C2×D4×C139—44no—
216C2×D4×C139—44no—
217C2×D4×C139—44no—
218C2×D4×C139—42no—
219C2×D4×C139—42no—
220C2×D4×C139—42no—
221C2×D4×C139—42no—
222C2×D4×C139—81no—
223C2×D4×C139—81no—
224C2×D4×C139—81no—
225C2×D4×C139—81no—
226C2×D4×C139—81no—
227C2×D4×C139—81no—
228C2×D4×C139—81no—
229C2×D4×C139—81no—
230C2×D4×C139C2×D412yes—
231C2×D4×C139C2×D412yes—
232C2×D4×C139C2×D412yes—
233C22×C4×C139—21no—
234C22×C4×C139—21no—
235C22×C4×C139—21no—
236C22×C4×C139—21no—
237C22×C4×C139—24no—
238C22×C4×C139—21no—
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—21no—
242C22×C4×C139—21no—
243C22×C4×C139—42no—
244C22×C4×C139—42no—
245C22×C4×C139C2×D411yescharacteristic
246C22×C4×C139C2×D411yescharacteristic
247C22×C4×C139C2×D411yescharacteristic
248C22×C4×C139C2×D411yescharacteristic
249C22×C4×C139C2×D411yescharacteristic
250C22×C4×C139C2×D412yes—
251C22×C4×C139#4112yes—
252C22×C4×C139C2411yescharacteristic
253Q16×C139—44no—
254SD16×C139—44no—
255SD16×C139—44no—
256SD16×C139—44no—
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—21no—
266C2×C8×C139—21no—
267C2×C8×C139—21no—
268C2×C8×C139—21no—
269C4⋊C4×C139—22no—
270C4⋊C4×C139—22no—
271C4⋊C4×C139—24no—
272C4⋊C4×C139—21no—
273C4⋊C4×C139—21no—
274C4⋊C4×C139—21no—
275C4⋊C4×C139—21no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139—42no—
278C4⋊C4×C139—81no—
279C4⋊C4×C139C2×D412yes—
280C22⋊C4×C139—24no—
281C22⋊C4×C139—24no—
282C22⋊C4×C139—24no—
283C22⋊C4×C139—24no—
284C22⋊C4×C139—24no—
285C22⋊C4×C139—22no—
286C22⋊C4×C139—22no—
287C22⋊C4×C139—81no—
288C42×C139—21no—
289C42×C139—21no—
290C42×C139—42no—
291C42×C139—81no—
292C42×C139C2×D412yes—
293C42×C139C2×D412yes—
294C23×C139—21no—
295C23×C139—21no—
296C23×C139—21no—
297C23×C139—21no—
298C23×C139—21no—
299C23×C139—21no—
300C23×C139—22no—
301C23×C139—22no—
302C23×C139—22no—
303C23×C139—48no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—41no—
307C23×C139—41no—
308C23×C139—41no—
309C23×C139—41no—
310C23×C139—41no—
311C23×C139—41no—
312C23×C139—41no—
313C23×C139—41no—
314C23×C139—41no—
315C23×C139—41no—
316C23×C139—41no—
317C23×C139—41no—
318C23×C139—41no—
319C23×C139—41no—
320C23×C139—41no—
321C23×C139—41no—
322C23×C139—84no—
323C23×C139—84no—
324C23×C139—84no—
325C23×C139—84no—
326C23×C139—84no—
327C23×C139—84no—
328C23×C139#12112yes—
329C23×C139C22×D411yescharacteristic
330Q8×C139—22no—
331Q8×C139—22no—
332Q8×C139—22no—
333Q8×C139—22no—
334Q8×C139—41no—
335Q8×C139—41no—
336Q8×C139—41no—
337Q8×C139—41no—
338D4×C139—22no—
339D4×C139—22no—
340D4×C139—22no—
341D4×C139—22no—
342D4×C139—22no—
343D4×C139—22no—
344D4×C139—48no—
345D4×C139—48no—
346D4×C139—41no—
347D4×C139—41no—
348D4×C139—41no—
349D4×C139—41no—
350D4×C139—41no—
351D4×C139—41no—
352D4×C139—84no—
353D4×C139—84no—
354D4×C139—84no—
355D4×C139—84no—
356C2×C4×C139—21no—
357C2×C4×C139—21no—
358C2×C4×C139—21no—
359C2×C4×C139—21no—
360C2×C4×C139—21no—
361C2×C4×C139—21no—
362C2×C4×C139—22no—
363C2×C4×C139—22no—
364C2×C4×C139—22no—
365C2×C4×C139—22no—
366C2×C4×C139—21no—
367C2×C4×C139—21no—
368C2×C4×C139—22no—
369C2×C4×C139—22no—
370C2×C4×C139—22no—
371C2×C4×C139—21no—
372C2×C4×C139—21no—
373C2×C4×C139—21no—
374C2×C4×C139—21no—
375C2×C4×C139—48no—
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—41no—
385C2×C4×C139—41no—
386C2×C4×C139—41no—
387C2×C4×C139—41no—
388C2×C4×C139#12012yes—
389C2×C4×C139#12012yes—
390C2×C4×C139#12112yes—
391C2×C4×C139C22×D411yescharacteristic
392C2×C4×C139C22×D411yescharacteristic
393C2×C4×C139C22×D411yescharacteristic
394C2×C4×C139C2×#4111yescharacteristic
395C2×C4×C139H(5,𝔽2)11yescharacteristic
396C2×C4×C139H(5,𝔽2)11yescharacteristic
397C8×C139—41no—
398C8×C139—41no—
399C8×C139—41no—
400C8×C139—41no—
401C22×C139—22no—
402C22×C139—22no—
403C22×C139—22no—
404C22×C139—41no—
405C22×C139—41no—
406C22×C139—41no—
407C22×C139—41no—
408C22×C139—42no—
409C22×C139—42no—
410C22×C139—42no—
411C22×C139—42no—
412C22×C139—42no—
413C22×C139—42no—
414C22×C139—42no—
415C22×C139—42no—
416C22×C139—42no—
417C22×C139—816no—
418C22×C139—81no—
419C22×C139—81no—
420C22×C139—81no—
421C22×C139—81no—
422C22×C139—81no—
423C22×C139—81no—
424C22×C139—81no—
425C22×C139—81no—
426C22×C139—81no—
427C22×C139—81no—
428C22×C139—81no—
429C22×C139—81no—
430C22×C139C2×#12011yescharacteristic
431C22×C139C2×#12111yescharacteristic
432C22×C139#53511yescharacteristic
433C22×C139#57611yescharacteristic
434C22×C139#57711yescharacteristic
435C22×C139#57711yescharacteristic
436C22×C139#57711yescharacteristic
437C4×C139—22no—
438C4×C139—22no—
439C4×C139—22no—
440C4×C139—42no—
441C4×C139—42no—
442C4×C139—41no—
443C4×C139—41no—
444C4×C139—42no—
445C4×C139—81no—
446C4×C139—81no—
447C4×C139D4211yescharacteristic
448C4×C139D4211yescharacteristic
449C4×C139#54611yescharacteristic
450C4×C139#54611yescharacteristic
451C2×C139—42no—
452C2×C139—82no—
453C2×C139—82no—
454C2×C139—82no—
455C2×C139#240811yescharacteristic
456C2×C139#300911yescharacteristic
457C2×C139#301211yescharacteristic
458C2×C139#304311yescharacteristic
459C2×C139#304511yescharacteristic
460C2×C139#322211yescharacteristic
461C2×C139#322411yescharacteristic
462#24220C13911yesmaximal, characteristic, direct product factor, Sylow
463C139#2422011yescharacteristic, direct product factor, Sylow
464C2×#535C2×C13911yescharacteristic
465C2×#464C2×C13911yescharacteristic, complemented
466C2×#460C2×C13911yescharacteristic, complemented
467C2×#452C2×C13911yescharacteristic, complemented
468C2×#450C2×C13911yescharacteristic, complemented
469#2323C2×C13911yescharacteristic, complemented
470#2042C2×C13911yescharacteristic, complemented
471#2041C2×C13911yescharacteristic, complemented
472#2015C2×C13911yescharacteristic, complemented
473#2014C2×C13911yescharacteristic, complemented
474#1983C2×C13911yescharacteristic, complemented
475#1982C2×C13911yescharacteristic, complemented
476#1798C2×C13911yescharacteristic, complemented
477#1788C2×C13911yescharacteristic, complemented
478#1786C2×C13911yescharacteristic, complemented
479C22×#41C22×C13911yescharacteristic
480C23×D4C22×C13911yescharacteristic
481C22×Q16C22×C13911yescharacteristic, complemented
482C22×SD16C22×C13911yescharacteristic
483C22×SD16C22×C13911yescharacteristic
484C22×SD16C22×C13911yescharacteristic, complemented
485#535—24no—
486#535—24no—
487C2×#127C22×C13911yescharacteristic
488C2×#127C22×C13911yescharacteristic
489C2×#124C22×C13911yescharacteristic
490C2×#124C22×C13911yescharacteristic
491C2×C22⋊Q8C22×C13911yescharacteristic
492C2×#121—21no—
493C2×#121—21no—
494C2×#120—21no—
495C2×#120—21no—
496C2×C4×Q8C22×C13911yescharacteristic, complemented
497C2×#117C22×C13911yescharacteristic
498#464—24no—
499#460—24no—
500#452—24no—
501#450—24no—
502C2×C4⋊C8C22×C13911yescharacteristic, complemented
503C2×C4⋊C8C22×C13911yescharacteristic, complemented
504C2×#103C22×C13911yescharacteristic, complemented
505C2×#103C22×C13911yescharacteristic, complemented
506C2×#103C22×C13911yescharacteristic, complemented
507C2×#102C22×C13911yescharacteristic
508C2×#102C22×C13911yescharacteristic
509C2×#102C22×C13911yescharacteristic
510C2×#102C22×C13911yescharacteristic
511C2×#102C22×C13911yescharacteristic
512C2×#102C22×C13911yescharacteristic
513C2×#102C22×C13911yescharacteristic, complemented
514C2×#102C22×C13911yescharacteristic, complemented
515C2×#102C22×C13911yescharacteristic, complemented
516C2×C22⋊C8C22×C13911yescharacteristic
517C2×C22⋊C8C22×C13911yescharacteristic
518#391C22×C13911yescharacteristic, complemented
519#389—21no—
520#389C22×C13911yescharacteristic, complemented
521#388—21no—
522#388—21no—
523#387—21no—
524#380C22×C13911yescharacteristic
525C4×C4⋊C4C22×C13911yescharacteristic, complemented
526#336C22×C13911yescharacteristic, complemented
527#336C22×C13911yescharacteristic, complemented
528C25—21no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—41no—
534C2×#41—41no—
535C22×Q8C23×C13911yescharacteristic
536C22×Q8C23×C13911yescharacteristic
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—41no—
548C22×D4—41no—
549C22×D4C23×C13911yescharacteristic
550C22×D4C23×C13911yescharacteristic
551C22×D4C23×C13911yescharacteristic
552C23×C4—21no—
553C23×C4C23×C13911yescharacteristic
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—41no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C22×C8C23×C13911yescharacteristic
567C22×C8C23×C13911yescharacteristic
568C22×C8C23×C13911yescharacteristic
569C22×C8C23×C13911yescharacteristic
570#127—22no—
571#127—22no—
572#127—22no—
573#127D4×C13914yes—
574#124—22no—
575#124—22no—
576#124—22no—
577#124D4×C13914yes—
578C22⋊Q8—22no—
579C22⋊Q8D4×C13914yescomplemented
580#121—28no—
581#121—28no—
582#120—28no—
583#120—28no—
584C4×Q8—22no—
585C4×Q8—22no—
586#117—22no—
587#117—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4D4×C13911yescharacteristic
592C2×C4⋊C4D4×C13911yescharacteristic
593C2×C4⋊C4C23×C13911yescharacteristic
594C2×C4⋊C4C23×C13911yescharacteristic
595C2×C4⋊C4C23×C13911yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4D4×C13911yescharacteristic
603C2×C22⋊C4D4×C13911yescharacteristic
604C2×C42—21no—
605C2×C42—21no—
606C2×C42C23×C13911yescharacteristic
607C2×C42C23×C13911yescharacteristic
608C4⋊C8—22no—
609C4⋊C8—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—22no—
619#102—41no—
620#102—41no—
621#102—41no—
622C22⋊C8—22no—
623C22⋊C8—22no—
624#95—21no—
625#95—21no—
626#95—21no—
627#95—21no—
628#95—21no—
629C24—24no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—81no—
636C24—81no—
637C24—81no—
638C24—81no—
639C24C2×D4×C13911yescharacteristic
640#41—44no—
641#41—44no—
642#41—44no—
643#41—44no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8C2×D4×C13912yes—
655C2×Q8C2×D4×C13912yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—81no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4—81no—
690C2×D4—81no—
691C2×D4—81no—
692C2×D4—81no—
693C2×D4C2×D4×C13912yes—
694C2×D4C2×D4×C13912yes—
695C2×D4C2×D4×C13912yes—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—24no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4C2×D4×C13911yescharacteristic
709C22×C4C2×D4×C13911yescharacteristic
710C22×C4C2×D4×C13911yescharacteristic
711C22×C4C2×D4×C13911yescharacteristic
712C22×C4C2×D4×C13911yescharacteristic
713C22×C4C2×D4×C13912yes—
714C22×C4#41×C13912yes—
715C22×C4C24×C13911yescharacteristic
716Q16—44no—
717SD16—44no—
718SD16—44no—
719SD16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—22no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—42no—
741C4⋊C4—81no—
742C4⋊C4C2×D4×C13912yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—81no—
751C42—21no—
752C42—21no—
753C42—42no—
754C42—81no—
755C42C2×D4×C13912yes—
756C42C2×D4×C13912yes—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—48no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#121×C13912yes—
792C23C22×D4×C13911yescharacteristic
793Q8—22no—
794Q8—22no—
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—84no—
816D4—84no—
817D4—84no—
818D4—84no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—48no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4#120×C13912yes—
852C2×C4#120×C13912yes—
853C2×C4#121×C13912yes—
854C2×C4C22×D4×C13911yescharacteristic
855C2×C4C22×D4×C13911yescharacteristic
856C2×C4C22×D4×C13911yescharacteristic
857C2×C4C2×#41×C13911yescharacteristic
858C2×C4H(5,𝔽2)×C13911yescharacteristic
859C2×C4H(5,𝔽2)×C13911yescharacteristic
860C8—41no—
861C8—41no—
862C8—41no—
863C8—41no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—816no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22C2×#120×C13911yescharacteristic
894C22C2×#121×C13911yescharacteristic
895C22#535×C13911yescharacteristic
896C22#576×C13911yescharacteristic
897C22#577×C13911yescharacteristic
898C22#577×C13911yescharacteristic
899C22#577×C13911yescharacteristic
900C4—22no—
901C4—22no—
902C4—22no—
903C4—42no—
904C4—42no—
905C4—42no—
906C4—41no—
907C4—41no—
908C4—81no—
909C4—81no—
910C4D42×C13911yescharacteristic
911C4D42×C13911yescharacteristic
912C4#546×C13911yescharacteristic
913C4#546×C13911yescharacteristic
914C2—42no—
915C2—82no—
916C2—82no—
917C2—82no—
918C2#2408×C13911yescharacteristic
919C2#3009×C13911yescharacteristic
920C2#3012×C13911yescharacteristic
921C2#3043×C13911yescharacteristic
922C2#3045×C13911yescharacteristic
923C2#3222×C13911yescharacteristic
924C2#3224×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#535×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×#117×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#464×C139C2semidirect
3. C2×#460×C139C2semidirect
4. C2×#452×C139C2semidirect
5. C2×#450×C139C2semidirect
6. #2323×C139C2semidirect
7. #2042×C139C2semidirect
8. #2041×C139C2semidirect
9. #2015×C139C2semidirect
10. #2014×C139C2semidirect
11. #1983×C139C2semidirect
12. #1982×C139C2semidirect
13. #1798×C139C2semidirect
14. #1788×C139C2semidirect
15. #1786×C139C2semidirect
18. C22×Q16×C139C22semidirect
21. C22×SD16×C139C22semidirect
33. C2×C4×Q8×C139C22semidirect
39. C2×C4⋊C8×C139C22semidirect
40. C2×C4⋊C8×C139C22semidirect
41. C2×#103×C139C22semidirect
42. C2×#103×C139C22semidirect
43. C2×#103×C139C22semidirect
50. C2×#102×C139C22semidirect
51. C2×#102×C139C22semidirect
52. C2×#102×C139C22semidirect
55. #391×C139C22semidirect
57. #389×C139C22semidirect
62. C4×C4⋊C4×C139C22semidirect
63. #336×C139C22semidirect
64. #336×C139C22semidirect
116. C22⋊Q8×C139D4semidirect
462. #24220C139direct (N × H)
463. C139#24220direct (N × H)
465. C2×#464C2×C139semidirect
466. C2×#460C2×C139semidirect
467. C2×#452C2×C139semidirect
468. C2×#450C2×C139semidirect
469. #2323C2×C139semidirect
470. #2042C2×C139semidirect
471. #2041C2×C139semidirect
472. #2015C2×C139semidirect
473. #2014C2×C139semidirect
474. #1983C2×C139semidirect
475. #1982C2×C139semidirect
476. #1798C2×C139semidirect
477. #1788C2×C139semidirect
478. #1786C2×C139semidirect
481. C22×Q16C22×C139semidirect
484. C22×SD16C22×C139semidirect
496. C2×C4×Q8C22×C139semidirect
502. C2×C4⋊C8C22×C139semidirect
503. C2×C4⋊C8C22×C139semidirect
504. C2×#103C22×C139semidirect
505. C2×#103C22×C139semidirect
506. C2×#103C22×C139semidirect
513. C2×#102C22×C139semidirect
514. C2×#102C22×C139semidirect
515. C2×#102C22×C139semidirect
518. #391C22×C139semidirect
520. #389C22×C139semidirect
525. C4×C4⋊C4C22×C139semidirect
526. #336C22×C139semidirect
527. #336C22×C139semidirect
579. C22⋊Q8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1392
C2×#464×C1392
C2×#460×C1392
C2×#452×C1392
C2×#450×C1392
#2323×C1392
#2042×C1392
#2041×C1392
#2015×C1392
#2014×C1392
#1983×C1392
#1982×C1392
#1798×C1392
#1788×C1392
#1786×C1392
#24220139