Finite Group Databasebeta

← C139×#22880 #48017476

Subgroups — C139×#22880 #48017476

Order 35584.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C139C211yesmaximal, characteristic
2C2×C4×D8×C139C211yesmaximal, characteristic, complemented
3C2×#418×C139C211yesmaximal, characteristic, complemented
4#2363×C139C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C139C211yesmaximal, characteristic, complemented
6#1972×C139C211yesmaximal, characteristic, complemented
7#1934×C139C211yesmaximal, characteristic, complemented
8#1925×C139C211yesmaximal, characteristic, complemented
9#1895×C139C211yesmaximal, characteristic, complemented
10#1879×C139C211yesmaximal, characteristic, complemented
11#1879×C139C211yesmaximal, characteristic, complemented
12#1864×C139C211yesmaximal, characteristic, complemented
13#1854×C139C211yesmaximal, characteristic, complemented
14#1762×C139C211yesmaximal, characteristic, complemented
15#1753×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C22×M16×C139C2211yescharacteristic
20C2×#121×C139C2211yescharacteristic
21C2×C4×D4×C139C2211yescharacteristic
22C2×C4×D4×C139C2211yescharacteristic
23C2×C4×D4×C139C2211yescharacteristic, complemented
24C2×#117×C139C2211yescharacteristic
25C22×C22⋊C4×C139—21no—
26#447×C139C418yescomplemented
27C4×D8×C139—24no—
28C2×#107×C139C2211yescharacteristic, complemented
29C2×#106×C139C2211yescharacteristic, complemented
30#418×C139—24no—
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic, complemented
38C2×#102×C139C2211yescharacteristic, complemented
39C2×C22⋊C8×C139C2211yescharacteristic
40C2×#97×C139C2211yescharacteristic, complemented
41C2×C4×C8×C139C2211yescharacteristic, complemented
42#390×C139—21no—
43#390×C139C2211yescharacteristic
44#390×C139C2211yescharacteristic
45#390×C139C2211yescharacteristic, complemented
46#389×C139C2211yescharacteristic, complemented
47#388×C139—21no—
48#386×C139—21no—
49#386×C139—21no—
50#386×C139—21no—
51#380×C139C2211yescharacteristic
52#379×C139—21no—
53C4×C4⋊C4×C139C2211yescharacteristic, complemented
54C4×C22⋊C4×C139—21no—
55C4×C22⋊C4×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic, complemented
57#340×C139C2211yescharacteristic, complemented
58#340×C139C2211yescharacteristic, complemented
59#340×C139C2211yescharacteristic, complemented
60#336×C139C2211yescharacteristic, complemented
61#336×C139C2211yescharacteristic, complemented
62C25×C139—21no—
63C22×D4×C139—22no—
64C22×D4×C139—22no—
65C22×D4×C139—21no—
66C22×D4×C139—21no—
67C22×D4×C139—22no—
68C22×D4×C139—41no—
69C22×D4×C139—41no—
70C22×D4×C139C2×C414yescomplemented
71C22×D4×C139C2311yescharacteristic
72C22×D4×C139C2311yescharacteristic
73C22×D4×C139C2311yescharacteristic
74C23×C4×C139—21no—
75C23×C4×C139—21no—
76C23×C4×C139—21no—
77C23×C4×C139C2311yescharacteristic
78C2×D8×C139—22no—
79C2×D8×C139—22no—
80C2×D8×C139—41no—
81C2×D8×C139—41no—
82C2×D8×C139C2×C414yes—
83C2×D8×C139C2×C414yescomplemented
84C2×M16×C139—22no—
85C2×M16×C139—22no—
86C2×M16×C139—41no—
87C22×C8×C139C2311yescharacteristic
88C22×C8×C139C2311yescharacteristic
89C22×C8×C139C2311yescharacteristic
90C22×C8×C139C2311yescharacteristic
91#121×C139—22no—
92#121×C139C2×C414yescomplemented
93C4×D4×C139—22no—
94C4×D4×C139—22no—
95C4×D4×C139—22no—
96C4×D4×C139—41no—
97C4×D4×C139—41no—
98C4×D4×C139—41no—
99#117×C139—22no—
100#117×C139—41no—
101C2×C4⋊C4×C139—21no—
102C2×C4⋊C4×C139C2311yescharacteristic
103C2×C4⋊C4×C139C2311yescharacteristic
104C2×C4⋊C4×C139C2311yescharacteristic
105C2×C4⋊C4×C139C2311yescharacteristic
106C2×C4⋊C4×C139C2311yescharacteristic
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
109C2×C22⋊C4×C139—21no—
110C2×C22⋊C4×C139—21no—
111C2×C22⋊C4×C139—21no—
112C2×C22⋊C4×C139—21no—
113C2×C22⋊C4×C139—21no—
114C2×C22⋊C4×C139—21no—
115C2×C22⋊C4×C139—21no—
116C2×C22⋊C4×C139—21no—
117C2×C22⋊C4×C139—21no—
118C2×C22⋊C4×C139—21no—
119C2×C22⋊C4×C139—44no—
120C2×C22⋊C4×C139D411yescharacteristic
121C2×C22⋊C4×C139D411yescharacteristic
122C2×C42×C139—21no—
123C2×C42×C139—21no—
124C2×C42×C139C2311yescharacteristic
125C2×C42×C139C2311yescharacteristic
126#107×C139—22no—
127#106×C139—41no—
128#102×C139—22no—
129#102×C139—22no—
130#102×C139—22no—
131#102×C139—22no—
132#102×C139—41no—
133#102×C139C2×C414yescomplemented
134#102×C139C2×C414yescomplemented
135#102×C139D414yescomplemented
136C22⋊C8×C139C2×C414yescomplemented
137#97×C139—41no—
138C4×C8×C139—22no—
139#95×C139—21no—
140#95×C139—21no—
141#95×C139—21no—
142#95×C139D411yescharacteristic
143#95×C139D411yescharacteristic
144C24×C139—21no—
145C24×C139—21no—
146C24×C139—21no—
147C24×C139—24no—
148C24×C139—42no—
149C24×C139—42no—
150C24×C139—42no—
151C24×C139—42no—
152C24×C139—81no—
153C24×C139—81no—
154C24×C139C2×D411yescharacteristic
155C2×D4×C139—28no—
156C2×D4×C139—24no—
157C2×D4×C139—24no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—21no—
165C2×D4×C139—21no—
166C2×D4×C139—21no—
167C2×D4×C139—21no—
168C2×D4×C139—21no—
169C2×D4×C139—21no—
170C2×D4×C139—21no—
171C2×D4×C139—44no—
172C2×D4×C139—44no—
173C2×D4×C139—44no—
174C2×D4×C139—42no—
175C2×D4×C139—42no—
176C2×D4×C139—81no—
177C2×D4×C139—81no—
178C2×D4×C139C22×C412yes—
179C2×D4×C139C22×C412yes—
180C2×D4×C139C22×C412yes—
181C2×D4×C139C2×D412yes—
182C2×D4×C139#4112yes—
183C22×C4×C139—21no—
184C22×C4×C139—21no—
185C22×C4×C139—21no—
186C22×C4×C139—21no—
187C22×C4×C139—21no—
188C22×C4×C139—21no—
189C22×C4×C139—21no—
190C22×C4×C139—21no—
191C22×C4×C139—21no—
192C22×C4×C139—42no—
193C22×C4×C139—42no—
194C22×C4×C139—42no—
195C22×C4×C139—42no—
196C22×C4×C139—42no—
197C22×C4×C139—42no—
198C22×C4×C139—81no—
199C22×C4×C139—81no—
200C22×C4×C139—81no—
201C22×C4×C139C22×C412yes—
202C22×C4×C139C2×D411yescharacteristic
203C22×C4×C139C2×D411yescharacteristic
204C22×C4×C139C2×D411yescharacteristic
205C22×C4×C139C2×D411yescharacteristic
206C22×C4×C139C2×D411yescharacteristic
207C22×C4×C139#4112yes—
208C22×C4×C139C2411yescharacteristic
209D8×C139—28no—
210D8×C139—44no—
211M16×C139—44no—
212C2×C8×C139—21no—
213C2×C8×C139—21no—
214C2×C8×C139—21no—
215C2×C8×C139—21no—
216C2×C8×C139—21no—
217C2×C8×C139—21no—
218C2×C8×C139—21no—
219C2×C8×C139—21no—
220C2×C8×C139—21no—
221C2×C8×C139C22×C412yes—
222C2×C8×C139C22×C412yes—
223C2×C8×C139C2×D412yes—
224C4⋊C4×C139—21no—
225C4⋊C4×C139—21no—
226C4⋊C4×C139—21no—
227C4⋊C4×C139—21no—
228C4⋊C4×C139—21no—
229C4⋊C4×C139—21no—
230C4⋊C4×C139—21no—
231C4⋊C4×C139—21no—
232C4⋊C4×C139—81no—
233C4⋊C4×C139C22×C412yes—
234C4⋊C4×C139C2×D412yes—
235C22⋊C4×C139—24no—
236C22⋊C4×C139—22no—
237C22⋊C4×C139—41no—
238C22⋊C4×C139—42no—
239C22⋊C4×C139—42no—
240C22⋊C4×C139—42no—
241C22⋊C4×C139—42no—
242C22⋊C4×C139—42no—
243C22⋊C4×C139—42no—
244C22⋊C4×C139—42no—
245C22⋊C4×C139—42no—
246C22⋊C4×C139—81no—
247C22⋊C4×C139—81no—
248C22⋊C4×C139—81no—
249C42×C139—21no—
250C42×C139—21no—
251C42×C139—21no—
252C42×C139—21no—
253C42×C139—42no—
254C42×C139—81no—
255C23×C139—22no—
256C23×C139—21no—
257C23×C139—22no—
258C23×C139—22no—
259C23×C139—21no—
260C23×C139—21no—
261C23×C139—21no—
262C23×C139—21no—
263C23×C139—21no—
264C23×C139—22no—
265C23×C139—22no—
266C23×C139—48no—
267C23×C139—48no—
268C23×C139—41no—
269C23×C139—41no—
270C23×C139—41no—
271C23×C139—41no—
272C23×C139—41no—
273C23×C139—41no—
274C23×C139—41no—
275C23×C139—41no—
276C23×C139—41no—
277C23×C139—41no—
278C23×C139—41no—
279C23×C139—41no—
280C23×C139—41no—
281C23×C139—41no—
282C23×C139—41no—
283C23×C139—41no—
284C23×C139—84no—
285C23×C139—84no—
286C23×C139—84no—
287C23×C139—84no—
288C23×C139—84no—
289C23×C139C4×D412yes—
290C23×C139C22×D411yescharacteristic
291D4×C139—22no—
292D4×C139—22no—
293D4×C139—22no—
294D4×C139—22no—
295D4×C139—22no—
296D4×C139—22no—
297D4×C139—22no—
298D4×C139—48no—
299D4×C139—41no—
300D4×C139—41no—
301D4×C139—41no—
302D4×C139—41no—
303D4×C139—84no—
304D4×C139C4×D414yes—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—22no—
310C2×C4×C139—22no—
311C2×C4×C139—22no—
312C2×C4×C139—22no—
313C2×C4×C139—22no—
314C2×C4×C139—21no—
315C2×C4×C139—22no—
316C2×C4×C139—21no—
317C2×C4×C139—21no—
318C2×C4×C139—21no—
319C2×C4×C139—21no—
320C2×C4×C139—21no—
321C2×C4×C139—21no—
322C2×C4×C139—21no—
323C2×C4×C139—21no—
324C2×C4×C139—41no—
325C2×C4×C139—41no—
326C2×C4×C139—41no—
327C2×C4×C139—41no—
328C2×C4×C139—41no—
329C2×C4×C139—41no—
330C2×C4×C139—41no—
331C2×C4×C139—41no—
332C2×C4×C139—41no—
333C2×C4×C139—41no—
334C2×C4×C139—41no—
335C2×C4×C139—41no—
336C2×C4×C139—41no—
337C2×C4×C139—84no—
338C2×C4×C139—84no—
339C2×C4×C139—84no—
340C2×C4×C139C4×D412yes—
341C2×C4×C139AGL(1,ℤ/8)12yes—
342C2×C4×C139C23×C411yescharacteristic
343C2×C4×C139C22×D411yescharacteristic
344C2×C4×C139C2×#4111yescharacteristic
345C2×C4×C139C2×#4111yescharacteristic
346C2×C4×C139H(5,𝔽2)11yescharacteristic
347C2×C4×C139H(5,𝔽2)11yescharacteristic
348C8×C139—22no—
349C8×C139—22no—
350C8×C139—22no—
351C8×C139—41no—
352C22×C139—22no—
353C22×C139—24no—
354C22×C139—22no—
355C22×C139—22no—
356C22×C139—42no—
357C22×C139—42no—
358C22×C139—42no—
359C22×C139—41no—
360C22×C139—41no—
361C22×C139—42no—
362C22×C139—41no—
363C22×C139—42no—
364C22×C139—42no—
365C22×C139—41no—
366C22×C139—42no—
367C22×C139—42no—
368C22×C139—42no—
369C22×C139—42no—
370C22×C139—42no—
371C22×C139—42no—
372C22×C139—816no—
373C22×C139—81no—
374C22×C139—81no—
375C22×C139—81no—
376C22×C139—81no—
377C22×C139—81no—
378C22×C139—81no—
379C22×C139—81no—
380C22×C139—81no—
381C22×C139C2×C4×D411yescharacteristic
382C22×C139D4211yescharacteristic
383C22×C139#54611yescharacteristic
384C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C139#57511yescharacteristic
386C22×C139#57611yescharacteristic
387C22×C139#57611yescharacteristic
388C4×C139—22no—
389C4×C139—22no—
390C4×C139—42no—
391C4×C139—42no—
392C4×C139—41no—
393C4×C139—41no—
394C4×C139—41no—
395C4×C139—81no—
396C4×C139—81no—
397C4×C139—81no—
398C4×C139C2×C4×D411yescharacteristic
399C4×C139#51811yescharacteristic
400C4×C139#54611yescharacteristic
401C4×C139#55111yescharacteristic
402C2×C139—42no—
403C2×C139—44no—
404C2×C139—82no—
405C2×C139—82no—
406C2×C139#235811yescharacteristic
407C2×C139C4×AGL(1,ℤ/8)11yescharacteristic
408C2×C139#294811yescharacteristic
409C2×C139#326411yescharacteristic
410C2×C139#326811yescharacteristic
411C2×C139#332211yescharacteristic
412C2×C139#332511yescharacteristic
413#22880C13911yesmaximal, characteristic, direct product factor, Sylow
414C139#2288011yescharacteristic, direct product factor, Sylow
415C2×#447C2×C13911yescharacteristic
416C2×C4×D8C2×C13911yescharacteristic, complemented
417C2×#418C2×C13911yescharacteristic, complemented
418#2363C2×C13911yescharacteristic, complemented
419D4×C22⋊C4C2×C13911yescharacteristic, complemented
420#1972C2×C13911yescharacteristic, complemented
421#1934C2×C13911yescharacteristic, complemented
422#1925C2×C13911yescharacteristic, complemented
423#1895C2×C13911yescharacteristic, complemented
424#1879C2×C13911yescharacteristic, complemented
425#1879C2×C13911yescharacteristic, complemented
426#1864C2×C13911yescharacteristic, complemented
427#1854C2×C13911yescharacteristic, complemented
428#1762C2×C13911yescharacteristic, complemented
429#1753C2×C13911yescharacteristic, complemented
430C23×D4C22×C13911yescharacteristic
431C22×D8C22×C13911yescharacteristic
432C22×D8C22×C13911yescharacteristic
433C22×M16C22×C13911yescharacteristic
434C2×#121C22×C13911yescharacteristic
435C2×C4×D4C22×C13911yescharacteristic
436C2×C4×D4C22×C13911yescharacteristic
437C2×C4×D4C22×C13911yescharacteristic, complemented
438C2×#117C22×C13911yescharacteristic
439C22×C22⋊C4—21no—
440#447C4×C13918yescomplemented
441C4×D8—24no—
442C2×#107C22×C13911yescharacteristic, complemented
443C2×#106C22×C13911yescharacteristic, complemented
444#418—24no—
445C2×#102C22×C13911yescharacteristic
446C2×#102C22×C13911yescharacteristic
447C2×#102C22×C13911yescharacteristic
448C2×#102C22×C13911yescharacteristic
449C2×#102C22×C13911yescharacteristic
450C2×#102C22×C13911yescharacteristic
451C2×#102C22×C13911yescharacteristic, complemented
452C2×#102C22×C13911yescharacteristic, complemented
453C2×C22⋊C8C22×C13911yescharacteristic
454C2×#97C22×C13911yescharacteristic, complemented
455C2×C4×C8C22×C13911yescharacteristic, complemented
456#390—21no—
457#390C22×C13911yescharacteristic
458#390C22×C13911yescharacteristic
459#390C22×C13911yescharacteristic, complemented
460#389C22×C13911yescharacteristic, complemented
461#388—21no—
462#386—21no—
463#386—21no—
464#386—21no—
465#380C22×C13911yescharacteristic
466#379—21no—
467C4×C4⋊C4C22×C13911yescharacteristic, complemented
468C4×C22⋊C4—21no—
469C4×C22⋊C4C22×C13911yescharacteristic
470#340C22×C13911yescharacteristic, complemented
471#340C22×C13911yescharacteristic, complemented
472#340C22×C13911yescharacteristic, complemented
473#340C22×C13911yescharacteristic, complemented
474#336C22×C13911yescharacteristic, complemented
475#336C22×C13911yescharacteristic, complemented
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—21no—
481C22×D4—22no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C2×C4×C13914yescomplemented
485C22×D4C23×C13911yescharacteristic
486C22×D4C23×C13911yescharacteristic
487C22×D4C23×C13911yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C23×C13911yescharacteristic
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8C2×C4×C13914yes—
497C2×D8C2×C4×C13914yescomplemented
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8C23×C13911yescharacteristic
502C22×C8C23×C13911yescharacteristic
503C22×C8C23×C13911yescharacteristic
504C22×C8C23×C13911yescharacteristic
505#121—22no—
506#121C2×C4×C13914yescomplemented
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513#117—22no—
514#117—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4C23×C13911yescharacteristic
517C2×C4⋊C4C23×C13911yescharacteristic
518C2×C4⋊C4C23×C13911yescharacteristic
519C2×C4⋊C4C23×C13911yescharacteristic
520C2×C4⋊C4C23×C13911yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—44no—
534C2×C22⋊C4D4×C13911yescharacteristic
535C2×C22⋊C4D4×C13911yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42C23×C13911yescharacteristic
539C2×C42C23×C13911yescharacteristic
540#107—22no—
541#106—41no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—41no—
547#102C2×C4×C13914yescomplemented
548#102C2×C4×C13914yescomplemented
549#102D4×C13914yescomplemented
550C22⋊C8C2×C4×C13914yescomplemented
551#97—41no—
552C4×C8—22no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95D4×C13911yescharacteristic
557#95D4×C13911yescharacteristic
558C24—21no—
559C24—21no—
560C24—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24C2×D4×C13911yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C22×C4×C13912yes—
593C2×D4C22×C4×C13912yes—
594C2×D4C22×C4×C13912yes—
595C2×D4C2×D4×C13912yes—
596C2×D4#41×C13912yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C22×C4×C13912yes—
616C22×C4C2×D4×C13911yescharacteristic
617C22×C4C2×D4×C13911yescharacteristic
618C22×C4C2×D4×C13911yescharacteristic
619C22×C4C2×D4×C13911yescharacteristic
620C22×C4C2×D4×C13911yescharacteristic
621C22×C4#41×C13912yes—
622C22×C4C24×C13911yescharacteristic
623D8—28no—
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8C22×C4×C13912yes—
636C2×C8C22×C4×C13912yes—
637C2×C8C2×D4×C13912yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C22×C4×C13912yes—
648C4⋊C4C2×D4×C13912yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—81no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—81no—
669C23—22no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23C4×D4×C13912yes—
704C23C22×D4×C13911yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4C4×D4×C13914yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4C4×D4×C13912yes—
755C2×C4AGL(1,ℤ/8)×C13912yes—
756C2×C4C23×C4×C13911yescharacteristic
757C2×C4C22×D4×C13911yescharacteristic
758C2×C4C2×#41×C13911yescharacteristic
759C2×C4C2×#41×C13911yescharacteristic
760C2×C4H(5,𝔽2)×C13911yescharacteristic
761C2×C4H(5,𝔽2)×C13911yescharacteristic
762C8—22no—
763C8—22no—
764C8—22no—
765C8—41no—
766C22—22no—
767C22—24no—
768C22—22no—
769C22—22no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—41no—
778C22—41no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×C4×D4×C13911yescharacteristic
796C22D42×C13911yescharacteristic
797C22#546×C13911yescharacteristic
798C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
799C22#575×C13911yescharacteristic
800C22#576×C13911yescharacteristic
801C22#576×C13911yescharacteristic
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—42no—
807C4—42no—
808C4—41no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C2×C4×D4×C13911yescharacteristic
813C4#518×C13911yescharacteristic
814C4#546×C13911yescharacteristic
815C4#551×C13911yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2#2358×C13911yescharacteristic
821C2C4×AGL(1,ℤ/8)×C13911yescharacteristic
822C2#2948×C13911yescharacteristic
823C2#3264×C13911yescharacteristic
824C2#3268×C13911yescharacteristic
825C2#3322×C13911yescharacteristic
826C2#3325×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC2×#447×C139C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×D8×C139C2semidirect
3. C2×#418×C139C2semidirect
4. #2363×C139C2semidirect
5. D4×C22⋊C4×C139C2semidirect
6. #1972×C139C2semidirect
7. #1934×C139C2semidirect
8. #1925×C139C2semidirect
9. #1895×C139C2semidirect
10. #1879×C139C2semidirect
11. #1879×C139C2semidirect
12. #1864×C139C2semidirect
13. #1854×C139C2semidirect
14. #1762×C139C2semidirect
15. #1753×C139C2semidirect
23. C2×C4×D4×C139C22semidirect
26. #447×C139C4semidirect
28. C2×#107×C139C22semidirect
29. C2×#106×C139C22semidirect
37. C2×#102×C139C22semidirect
38. C2×#102×C139C22semidirect
40. C2×#97×C139C22semidirect
41. C2×C4×C8×C139C22semidirect
45. #390×C139C22semidirect
46. #389×C139C22semidirect
53. C4×C4⋊C4×C139C22semidirect
56. #340×C139C22semidirect
57. #340×C139C22semidirect
58. #340×C139C22semidirect
59. #340×C139C22semidirect
60. #336×C139C22semidirect
61. #336×C139C22semidirect
70. C22×D4×C139C2×C4semidirect
83. C2×D8×C139C2×C4semidirect
92. #121×C139C2×C4semidirect
133. #102×C139C2×C4semidirect
134. #102×C139C2×C4semidirect
135. #102×C139D4semidirect
136. C22⋊C8×C139C2×C4semidirect
413. #22880C139direct (N × H)
414. C139#22880direct (N × H)
416. C2×C4×D8C2×C139semidirect
417. C2×#418C2×C139semidirect
418. #2363C2×C139semidirect
419. D4×C22⋊C4C2×C139semidirect
420. #1972C2×C139semidirect
421. #1934C2×C139semidirect
422. #1925C2×C139semidirect
423. #1895C2×C139semidirect
424. #1879C2×C139semidirect
425. #1879C2×C139semidirect
426. #1864C2×C139semidirect
427. #1854C2×C139semidirect
428. #1762C2×C139semidirect
429. #1753C2×C139semidirect
437. C2×C4×D4C22×C139semidirect
440. #447C4×C139semidirect
442. C2×#107C22×C139semidirect
443. C2×#106C22×C139semidirect
451. C2×#102C22×C139semidirect
452. C2×#102C22×C139semidirect
454. C2×#97C22×C139semidirect
455. C2×C4×C8C22×C139semidirect
459. #390C22×C139semidirect
460. #389C22×C139semidirect
467. C4×C4⋊C4C22×C139semidirect
470. #340C22×C139semidirect
471. #340C22×C139semidirect
472. #340C22×C139semidirect
473. #340C22×C139semidirect
474. #336C22×C139semidirect
475. #336C22×C139semidirect
484. C22×D4C2×C4×C139semidirect
497. C2×D8C2×C4×C139semidirect
506. #121C2×C4×C139semidirect
547. #102C2×C4×C139semidirect
548. #102C2×C4×C139semidirect
549. #102D4×C139semidirect
550. C22⋊C8C2×C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1392
C2×C4×D8×C1392
C2×#418×C1392
#2363×C1392
D4×C22⋊C4×C1392
#1972×C1392
#1934×C1392
#1925×C1392
#1895×C1392
#1879×C1392
#1864×C1392
#1854×C1392
#1762×C1392
#1753×C1392
#22880139