Finite Group Databasebeta

← C139×#24435 #48019031

Subgroups — C139×#24435 #48019031

Order 35584.

1550 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C139C211yesmaximal, characteristic, complemented
2C2×#466×C139C211yesmaximal, characteristic, complemented
3C2×#449×C139C211yesmaximal, characteristic, complemented
4C2×#449×C139C211yesmaximal, characteristic, complemented
5C2×#416×C139C211yesmaximal, characteristic, complemented
6#2414×C139C211yesmaximal, characteristic, complemented
7#2041×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#2011×C139C211yesmaximal, characteristic, complemented
10#1999×C139C211yesmaximal, characteristic, complemented
11#1880×C139C211yesmaximal, characteristic, complemented
12#1875×C139C211yesmaximal, characteristic, complemented
13#1869×C139C211yesmaximal, characteristic, complemented
14#1863×C139C211yesmaximal, characteristic, complemented
15#1788×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×D8×C139C2211yescharacteristic
20C22×D8×C139C2211yescharacteristic
21C23×C8×C139C2211yescharacteristic
22#550×C139—24no—
23#550×C139—24no—
24C2×#127×C139—21no—
25C2×#127×C139C2211yescharacteristic
26C2×#121×C139—21no—
27C2×#121×C139—21no—
28C2×#121×C139C2211yescharacteristic
29C2×#121×C139C2211yescharacteristic
30C2×#121×C139C2211yescharacteristic
31C2×#121×C139C2211yescharacteristic
32C2×C4×Q8×C139C2211yescharacteristic
33C2×C4×D4×C139—21no—
34C2×C4×D4×C139C2211yescharacteristic
35C2×#117×C139C2211yescharacteristic
36#466×C139—24no—
37#449×C139—24no—
38#449×C139—24no—
39C2×#107×C139C2211yescharacteristic
40#416×C139—24no—
41C2×#103×C139C2211yescharacteristic
42C2×#103×C139C2211yescharacteristic
43C2×#103×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×#102×C139C2211yescharacteristic
47C2×#102×C139C2211yescharacteristic
48C2×#102×C139C2211yescharacteristic
49C2×#102×C139C2211yescharacteristic
50C2×#102×C139C2211yescharacteristic
51C2×C22⋊C8×C139C2211yescharacteristic
52C2×C22⋊C8×C139C2211yescharacteristic
53C2×C22⋊C8×C139C2211yescharacteristic
54#394×C139—21no—
55#392×C139—21no—
56#390×C139—21no—
57#390×C139C2211yescharacteristic
58#389×C139C2211yescharacteristic
59#388×C139—21no—
60#380×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62#340×C139C2211yescharacteristic
63#336×C139C2211yescharacteristic
64#336×C139C2211yescharacteristic
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—22no—
69C2×#41×C139—22no—
70C2×#41×C139—22no—
71C2×#41×C139—22no—
72C2×#41×C139—41no—
73C2×#41×C139—41no—
74C2×#41×C139—41no—
75C2×#41×C139—41no—
76C2×#41×C139D414yescomplemented
77C22×Q8×C139C2311yescharacteristic
78C22×D4×C139—21no—
79C22×D4×C139—21no—
80C22×D4×C139—21no—
81C22×D4×C139—21no—
82C22×D4×C139—21no—
83C22×D4×C139—21no—
84C22×D4×C139—21no—
85C22×D4×C139—21no—
86C22×D4×C139D411yescharacteristic
87C22×D4×C139C2311yescharacteristic
88C22×D4×C139C2311yescharacteristic
89C22×D4×C139C2311yescharacteristic
90C23×C4×C139—21no—
91C23×C4×C139—21no—
92C23×C4×C139C2311yescharacteristic
93C23×C4×C139C2311yescharacteristic
94C2×SD16×C139—22no—
95C2×SD16×C139—22no—
96C2×SD16×C139—22no—
97C2×D8×C139—22no—
98C2×D8×C139—22no—
99C2×D8×C139—22no—
100C2×D8×C139—41no—
101C2×D8×C139—41no—
102C2×D8×C139—41no—
103C22×C8×C139—22no—
104C22×C8×C139—22no—
105C22×C8×C139—41no—
106C22×C8×C139C2311yescharacteristic
107C22×C8×C139C2311yescharacteristic
108C22×C8×C139C2311yescharacteristic
109C22×C8×C139C2311yescharacteristic
110#127×C139—28no—
111#127×C139—22no—
112#127×C139—22no—
113#121×C139—28no—
114#121×C139—28no—
115#121×C139—22no—
116#121×C139—22no—
117#121×C139—22no—
118#121×C139—22no—
119#121×C139—22no—
120#121×C139—22no—
121#121×C139—41no—
122#121×C139D414yescomplemented
123C4×Q8×C139—22no—
124C4×Q8×C139—22no—
125C4×D4×C139—28no—
126C4×D4×C139—22no—
127C4×D4×C139—22no—
128#117×C139—22no—
129#117×C139—41no—
130C2×C4⋊C4×C139—21no—
131C2×C4⋊C4×C139—21no—
132C2×C4⋊C4×C139D411yescharacteristic
133C2×C4⋊C4×C139C2311yescharacteristic
134C2×C4⋊C4×C139C2311yescharacteristic
135C2×C4⋊C4×C139C2311yescharacteristic
136C2×C4⋊C4×C139C2311yescharacteristic
137C2×C22⋊C4×C139—21no—
138C2×C22⋊C4×C139—21no—
139C2×C22⋊C4×C139—21no—
140C2×C22⋊C4×C139—21no—
141C2×C22⋊C4×C139—21no—
142C2×C22⋊C4×C139—21no—
143C2×C22⋊C4×C139—21no—
144C2×C22⋊C4×C139—21no—
145C2×C22⋊C4×C139D411yescharacteristic
146C2×C22⋊C4×C139D411yescharacteristic
147C2×C42×C139—21no—
148C2×C42×C139—21no—
149C2×C42×C139C2311yescharacteristic
150#107×C139—22no—
151#103×C139—22no—
152#103×C139—22no—
153#103×C139D414yescomplemented
154#102×C139—22no—
155#102×C139—22no—
156#102×C139—22no—
157#102×C139—22no—
158#102×C139—22no—
159#102×C139—22no—
160#102×C139—41no—
161C22⋊C8×C139—22no—
162C22⋊C8×C139—22no—
163C22⋊C8×C139—41no—
164#95×C139—21no—
165#95×C139—21no—
166C24×C139—21no—
167C24×C139—21no—
168C24×C139—21no—
169C24×C139C2×D411yescharacteristic
170C24×C139C2×D411yescharacteristic
171#41×C139—28no—
172#41×C139—44no—
173#41×C139—44no—
174#41×C139—44no—
175#41×C139—44no—
176#41×C139—44no—
177#41×C139—44no—
178#41×C139—44no—
179C2×Q8×C139—21no—
180C2×Q8×C139—21no—
181C2×Q8×C139—21no—
182C2×Q8×C139C2×D412yes—
183C2×Q8×C139C2×D412yes—
184C2×Q8×C139#4112yes—
185C2×D4×C139—24no—
186C2×D4×C139—24no—
187C2×D4×C139—22no—
188C2×D4×C139—24no—
189C2×D4×C139—24no—
190C2×D4×C139—24no—
191C2×D4×C139—24no—
192C2×D4×C139—22no—
193C2×D4×C139—21no—
194C2×D4×C139—21no—
195C2×D4×C139—21no—
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—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—21no—
208C2×D4×C139—21no—
209C2×D4×C139—41no—
210C2×D4×C139—42no—
211C2×D4×C139—42no—
212C2×D4×C139—42no—
213C2×D4×C139—42no—
214C2×D4×C139—42no—
215C2×D4×C139—42no—
216C2×D4×C139—42no—
217C2×D4×C139—42no—
218C2×D4×C139—42no—
219C2×D4×C139—81no—
220C2×D4×C139—81no—
221C2×D4×C139—81no—
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×C139C2×D412yes—
229C2×D4×C139C2×D412yes—
230C22×C4×C139—21no—
231C22×C4×C139—21no—
232C22×C4×C139—21no—
233C22×C4×C139—21no—
234C22×C4×C139—21no—
235C22×C4×C139—24no—
236C22×C4×C139—21no—
237C22×C4×C139—21no—
238C22×C4×C139—24no—
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—21no—
242C22×C4×C139—21no—
243C22×C4×C139—21no—
244C22×C4×C139—21no—
245C22×C4×C139—21no—
246C22×C4×C139—21no—
247C22×C4×C139—42no—
248C22×C4×C139—42no—
249C22×C4×C139—42no—
250C22×C4×C139—42no—
251C22×C4×C139C2×D411yescharacteristic
252C22×C4×C139C2×D411yescharacteristic
253C22×C4×C139C2×D411yescharacteristic
254C22×C4×C139C2×D412yes—
255C22×C4×C139C2×D412yes—
256C22×C4×C139C2×D411yescharacteristic
257C22×C4×C139C2411yescharacteristic
258SD16×C139—44no—
259D8×C139—44no—
260D8×C139—44no—
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—44no—
273C2×C8×C139C2×D412yes—
274C4⋊C4×C139—24no—
275C4⋊C4×C139—22no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139—21no—
278C4⋊C4×C139—21no—
279C4⋊C4×C139—21no—
280C4⋊C4×C139—21no—
281C4⋊C4×C139—21no—
282C4⋊C4×C139—81no—
283C4⋊C4×C139C2×D412yes—
284C4⋊C4×C139C2×D412yes—
285C22⋊C4×C139—24no—
286C22⋊C4×C139—22no—
287C22⋊C4×C139—24no—
288C22⋊C4×C139—22no—
289C22⋊C4×C139—42no—
290C22⋊C4×C139—42no—
291C22⋊C4×C139—42no—
292C22⋊C4×C139—42no—
293C22⋊C4×C139—81no—
294C22⋊C4×C139—81no—
295C42×C139—24no—
296C42×C139—21no—
297C42×C139—21no—
298C42×C139—42no—
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—22no—
308C23×C139—21no—
309C23×C139—21no—
310C23×C139—21no—
311C23×C139—21no—
312C23×C139—21no—
313C23×C139—21no—
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—41no—
323C23×C139—41no—
324C23×C139—41no—
325C23×C139—41no—
326C23×C139—41no—
327C23×C139—41no—
328C23×C139—41no—
329C23×C139—41no—
330C23×C139—41no—
331C23×C139—41no—
332C23×C139—41no—
333C23×C139#12012yes—
334C23×C139C22×D411yescharacteristic
335Q8×C139—22no—
336Q8×C139—22no—
337Q8×C139—22no—
338Q8×C139#12114yes—
339D4×C139—22no—
340D4×C139—22no—
341D4×C139—22no—
342D4×C139—22no—
343D4×C139—44no—
344D4×C139—48no—
345D4×C139—48no—
346D4×C139—48no—
347D4×C139—41no—
348D4×C139—41no—
349D4×C139—41no—
350D4×C139—41no—
351D4×C139—41no—
352D4×C139—41no—
353D4×C139—41no—
354D4×C139—41no—
355D4×C139—84no—
356D4×C139—84no—
357D4×C139—84no—
358D4×C139—84no—
359D4×C139—84no—
360C2×C4×C139—21no—
361C2×C4×C139—22no—
362C2×C4×C139—21no—
363C2×C4×C139—22no—
364C2×C4×C139—21no—
365C2×C4×C139—22no—
366C2×C4×C139—21no—
367C2×C4×C139—22no—
368C2×C4×C139—22no—
369C2×C4×C139—22no—
370C2×C4×C139—22no—
371C2×C4×C139—21no—
372C2×C4×C139—22no—
373C2×C4×C139—21no—
374C2×C4×C139—22no—
375C2×C4×C139—21no—
376C2×C4×C139—21no—
377C2×C4×C139—21no—
378C2×C4×C139—21no—
379C2×C4×C139—48no—
380C2×C4×C139—48no—
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—41no—
389C2×C4×C139—41no—
390C2×C4×C139—41no—
391C2×C4×C139—41no—
392C2×C4×C139—41no—
393C2×C4×C139—41no—
394C2×C4×C139—41no—
395C2×C4×C139#12012yes—
396C2×C4×C139#13512yes—
397C2×C4×C139C22×D411yescharacteristic
398C2×C4×C139C22×D411yescharacteristic
399C2×C4×C139C22×D411yescharacteristic
400C2×C4×C139C2×#4111yescharacteristic
401C2×C4×C139H(5,𝔽2)11yescharacteristic
402C2×C4×C139H(5,𝔽2)11yescharacteristic
403C8×C139—22no—
404C8×C139—41no—
405C8×C139—41no—
406C8×C139—41no—
407C22×C139—22no—
408C22×C139—22no—
409C22×C139—22no—
410C22×C139—41no—
411C22×C139—41no—
412C22×C139—41no—
413C22×C139—41no—
414C22×C139—42no—
415C22×C139—42no—
416C22×C139—41no—
417C22×C139—41no—
418C22×C139—42no—
419C22×C139—42no—
420C22×C139—41no—
421C22×C139—42no—
422C22×C139—42no—
423C22×C139—41no—
424C22×C139—41no—
425C22×C139—41no—
426C22×C139—41no—
427C22×C139—81no—
428C22×C139—81no—
429C22×C139—81no—
430C22×C139—81no—
431C22×C139—81no—
432C22×C139—81no—
433C22×C139—81no—
434C22×C139—81no—
435C22×C139—81no—
436C22×C139—81no—
437C22×C139—81no—
438C22×C139—81no—
439C22×C139—81no—
440C22×C139—81no—
441C22×C139—81no—
442C22×C139C2×#12011yescharacteristic
443C22×C139D4211yescharacteristic
444C22×C139#54611yescharacteristic
445C22×C139C2×#13511yescharacteristic
446C22×C139#57511yescharacteristic
447C22×C139#57611yescharacteristic
448C22×C139#57611yescharacteristic
449C4×C139—22no—
450C4×C139—24no—
451C4×C139—22no—
452C4×C139—41no—
453C4×C139—41no—
454C4×C139—42no—
455C4×C139—42no—
456C4×C139—81no—
457C4×C139—81no—
458C4×C139C2×#12111yescharacteristic
459C4×C139#53411yescharacteristic
460C4×C139D4211yescharacteristic
461C4×C139#54611yescharacteristic
462C2×C139—42no—
463C2×C139—81no—
464C2×C139—82no—
465C2×C139—82no—
466C2×C139—161no—
467C2×C139#241011yescharacteristic
468C2×C139#300211yescharacteristic
469C2×C139#300811yescharacteristic
470C2×C139#326811yescharacteristic
471C2×C139#328711yescharacteristic
472C2×C139#330511yescharacteristic
473C2×C139#330911yescharacteristic
474#24435C13911yesmaximal, characteristic, direct product factor, Sylow
475C139#2443511yescharacteristic, direct product factor, Sylow
476C2×#550C2×C13911yescharacteristic, complemented
477C2×#466C2×C13911yescharacteristic, complemented
478C2×#449C2×C13911yescharacteristic, complemented
479C2×#449C2×C13911yescharacteristic, complemented
480C2×#416C2×C13911yescharacteristic, complemented
481#2414C2×C13911yescharacteristic, complemented
482#2041C2×C13911yescharacteristic, complemented
483#2033C2×C13911yescharacteristic, complemented
484#2011C2×C13911yescharacteristic, complemented
485#1999C2×C13911yescharacteristic, complemented
486#1880C2×C13911yescharacteristic, complemented
487#1875C2×C13911yescharacteristic, complemented
488#1869C2×C13911yescharacteristic, complemented
489#1863C2×C13911yescharacteristic, complemented
490#1788C2×C13911yescharacteristic, complemented
491C22×#41C22×C13911yescharacteristic
492C22×#41C22×C13911yescharacteristic
493C22×SD16C22×C13911yescharacteristic
494C22×D8C22×C13911yescharacteristic
495C22×D8C22×C13911yescharacteristic
496C23×C8C22×C13911yescharacteristic
497#550—24no—
498#550—24no—
499C2×#127—21no—
500C2×#127C22×C13911yescharacteristic
501C2×#121—21no—
502C2×#121—21no—
503C2×#121C22×C13911yescharacteristic
504C2×#121C22×C13911yescharacteristic
505C2×#121C22×C13911yescharacteristic
506C2×#121C22×C13911yescharacteristic
507C2×C4×Q8C22×C13911yescharacteristic
508C2×C4×D4—21no—
509C2×C4×D4C22×C13911yescharacteristic
510C2×#117C22×C13911yescharacteristic
511#466—24no—
512#449—24no—
513#449—24no—
514C2×#107C22×C13911yescharacteristic
515#416—24no—
516C2×#103C22×C13911yescharacteristic
517C2×#103C22×C13911yescharacteristic
518C2×#103C22×C13911yescharacteristic
519C2×#102C22×C13911yescharacteristic
520C2×#102C22×C13911yescharacteristic
521C2×#102C22×C13911yescharacteristic
522C2×#102C22×C13911yescharacteristic
523C2×#102C22×C13911yescharacteristic
524C2×#102C22×C13911yescharacteristic
525C2×#102C22×C13911yescharacteristic
526C2×C22⋊C8C22×C13911yescharacteristic
527C2×C22⋊C8C22×C13911yescharacteristic
528C2×C22⋊C8C22×C13911yescharacteristic
529#394—21no—
530#392—21no—
531#390—21no—
532#390C22×C13911yescharacteristic
533#389C22×C13911yescharacteristic
534#388—21no—
535#380C22×C13911yescharacteristic
536#340C22×C13911yescharacteristic
537#340C22×C13911yescharacteristic
538#336C22×C13911yescharacteristic
539#336C22×C13911yescharacteristic
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—41no—
548C2×#41—41no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41D4×C13914yescomplemented
552C22×Q8C23×C13911yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4D4×C13911yescharacteristic
562C22×D4C23×C13911yescharacteristic
563C22×D4C23×C13911yescharacteristic
564C22×D4C23×C13911yescharacteristic
565C23×C4—21no—
566C23×C4—21no—
567C23×C4C23×C13911yescharacteristic
568C23×C4C23×C13911yescharacteristic
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—22no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—41no—
576C2×D8—41no—
577C2×D8—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C23×C13911yescharacteristic
582C22×C8C23×C13911yescharacteristic
583C22×C8C23×C13911yescharacteristic
584C22×C8C23×C13911yescharacteristic
585#127—28no—
586#127—22no—
587#127—22no—
588#121—28no—
589#121—28no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121D4×C13914yescomplemented
598C4×Q8—22no—
599C4×Q8—22no—
600C4×D4—28no—
601C4×D4—22no—
602C4×D4—22no—
603#117—22no—
604#117—41no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4D4×C13911yescharacteristic
608C2×C4⋊C4C23×C13911yescharacteristic
609C2×C4⋊C4C23×C13911yescharacteristic
610C2×C4⋊C4C23×C13911yescharacteristic
611C2×C4⋊C4C23×C13911yescharacteristic
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4D4×C13911yescharacteristic
621C2×C22⋊C4D4×C13911yescharacteristic
622C2×C42—21no—
623C2×C42—21no—
624C2×C42C23×C13911yescharacteristic
625#107—22no—
626#103—22no—
627#103—22no—
628#103D4×C13914yescomplemented
629#102—22no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—41no—
639#95—21no—
640#95—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24C2×D4×C13911yescharacteristic
645C24C2×D4×C13911yescharacteristic
646#41—28no—
647#41—44no—
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C13912yes—
658C2×Q8C2×D4×C13912yes—
659C2×Q8#41×C13912yes—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
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—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—41no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C13912yes—
704C2×D4C2×D4×C13912yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—24no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4C2×D4×C13911yescharacteristic
727C22×C4C2×D4×C13911yescharacteristic
728C22×C4C2×D4×C13911yescharacteristic
729C22×C4C2×D4×C13912yes—
730C22×C4C2×D4×C13912yes—
731C22×C4C2×D4×C13911yescharacteristic
732C22×C4C24×C13911yescharacteristic
733SD16—44no—
734D8—44no—
735D8—44no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—44no—
748C2×C8C2×D4×C13912yes—
749C4⋊C4—24no—
750C4⋊C4—22no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—81no—
758C4⋊C4C2×D4×C13912yes—
759C4⋊C4C2×D4×C13912yes—
760C22⋊C4—24no—
761C22⋊C4—22no—
762C22⋊C4—24no—
763C22⋊C4—22no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C42—24no—
771C42—21no—
772C42—21no—
773C42—42no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23#120×C13912yes—
809C23C22×D4×C13911yescharacteristic
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8#121×C13914yes—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—22no—
818D4—44no—
819D4—48no—
820D4—48no—
821D4—48no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—48no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4#120×C13912yes—
871C2×C4#135×C13912yes—
872C2×C4C22×D4×C13911yescharacteristic
873C2×C4C22×D4×C13911yescharacteristic
874C2×C4C22×D4×C13911yescharacteristic
875C2×C4C2×#41×C13911yescharacteristic
876C2×C4H(5,𝔽2)×C13911yescharacteristic
877C2×C4H(5,𝔽2)×C13911yescharacteristic
878C8—22no—
879C8—41no—
880C8—41no—
881C8—41no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—41no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—41no—
895C22—41no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×#120×C13911yescharacteristic
918C22D42×C13911yescharacteristic
919C22#546×C13911yescharacteristic
920C22C2×#135×C13911yescharacteristic
921C22#575×C13911yescharacteristic
922C22#576×C13911yescharacteristic
923C22#576×C13911yescharacteristic
924C4—22no—
925C4—24no—
926C4—22no—
927C4—41no—
928C4—41no—
929C4—42no—
930C4—42no—
931C4—81no—
932C4—81no—
933C4C2×#121×C13911yescharacteristic
934C4#534×C13911yescharacteristic
935C4D42×C13911yescharacteristic
936C4#546×C13911yescharacteristic
937C2—42no—
938C2—81no—
939C2—82no—
940C2—82no—
941C2—161no—
942C2#2410×C13911yescharacteristic
943C2#3002×C13911yescharacteristic
944C2#3008×C13911yescharacteristic
945C2#3268×C13911yescharacteristic
946C2#3287×C13911yescharacteristic
947C2#3305×C13911yescharacteristic
948C2#3309×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#550×C139C2semidirect
2. C2×#466×C139C2semidirect
3. C2×#449×C139C2semidirect
4. C2×#449×C139C2semidirect
5. C2×#416×C139C2semidirect
6. #2414×C139C2semidirect
7. #2041×C139C2semidirect
8. #2033×C139C2semidirect
9. #2011×C139C2semidirect
10. #1999×C139C2semidirect
11. #1880×C139C2semidirect
12. #1875×C139C2semidirect
13. #1869×C139C2semidirect
14. #1863×C139C2semidirect
15. #1788×C139C2semidirect
76. C2×#41×C139D4semidirect
122. #121×C139D4semidirect
153. #103×C139D4semidirect
474. #24435C139direct (N × H)
475. C139#24435direct (N × H)
476. C2×#550C2×C139semidirect
477. C2×#466C2×C139semidirect
478. C2×#449C2×C139semidirect
479. C2×#449C2×C139semidirect
480. C2×#416C2×C139semidirect
481. #2414C2×C139semidirect
482. #2041C2×C139semidirect
483. #2033C2×C139semidirect
484. #2011C2×C139semidirect
485. #1999C2×C139semidirect
486. #1880C2×C139semidirect
487. #1875C2×C139semidirect
488. #1869C2×C139semidirect
489. #1863C2×C139semidirect
490. #1788C2×C139semidirect
551. C2×#41D4×C139semidirect
597. #121D4×C139semidirect
628. #103D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1392
C2×#466×C1392
C2×#449×C1392
C2×#416×C1392
#2414×C1392
#2041×C1392
#2033×C1392
#2011×C1392
#1999×C1392
#1880×C1392
#1875×C1392
#1869×C1392
#1863×C1392
#1788×C1392
#24435139