Finite Group Databasebeta

← C139×#26380 #48020976

Subgroups — C139×#26380 #48020976

Order 35584.

932 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C139C211yesmaximal, characteristic, complemented
2C2×C4×D8×C139C211yesmaximal, characteristic
3#2452×C139C211yesmaximal, characteristic, complemented
4#2349×C139C211yesmaximal, characteristic, complemented
5#2092×C139C211yesmaximal, characteristic, complemented
6#2085×C139C211yesmaximal, characteristic, complemented
7#2065×C139C211yesmaximal, characteristic, complemented
8#2057×C139C211yesmaximal, characteristic, complemented
9#1941×C139C211yesmaximal, characteristic, complemented
10#1916×C139C211yesmaximal, characteristic, complemented
11#1879×C139C211yesmaximal, characteristic
12#1879×C139C211yesmaximal, characteristic
13#1864×C139C211yesmaximal, characteristic, complemented
14#1864×C139C211yesmaximal, characteristic, complemented
15#1862×C139C211yesmaximal, characteristic, complemented
16C22×D8×C139C2211yescharacteristic
17C2×C4⋊Q8×C139C2211yescharacteristic
18C2×C22⋊Q8×C139—21no—
19C2×C4×D4×C139C2211yescharacteristic
20C2×C4×D4×C139C2211yescharacteristic
21C2×C4×D4×C139C2211yescharacteristic
22C2×C4×D4×C139C2211yescharacteristic
23#476×C139—24no—
24C4×D8×C139—24no—
25C2×#107×C139C2211yescharacteristic
26C2×#107×C139C2211yescharacteristic
27C2×#106×C139C2211yescharacteristic
28C2×#106×C139C2211yescharacteristic
29C2×#106×C139C2211yescharacteristic
30C2×C4⋊C8×C139C2211yescharacteristic
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic
37C2×C4×C8×C139C2211yescharacteristic
38#396×C139—21no—
39#393×C139—21no—
40#390×C139C2211yescharacteristic
41#390×C139C2211yescharacteristic
42#389×C139C2211yescharacteristic
43#389×C139C2211yescharacteristic
44#389×C139C2211yescharacteristic
45#389×C139C2211yescharacteristic
46#385×C139—21no—
47#385×C139—21no—
48#385×C139—21no—
49#382×C139C2211yescharacteristic
50#380×C139—21no—
51C4×C4⋊C4×C139C2211yescharacteristic
52C2×#95×C139—21no—
53#340×C139C2211yescharacteristic
54#340×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#336×C139C2211yescharacteristic
58#336×C139C2211yescharacteristic
59#336×C139C2211yescharacteristic
60#336×C139C2211yescharacteristic
61C22×Q8×C139—21no—
62C22×D4×C139C2311yescharacteristic
63C22×D4×C139C2311yescharacteristic
64C23×C4×C139—21no—
65C23×C4×C139—21no—
66C23×C4×C139—21no—
67C23×C4×C139—21no—
68C2×D8×C139—22no—
69C2×D8×C139—22no—
70C2×D8×C139Q814yescomplemented
71C22×C8×C139C2311yescharacteristic
72C22×C8×C139C2311yescharacteristic
73C22×C8×C139C2311yescharacteristic
74C22×C8×C139C2311yescharacteristic
75C4⋊Q8×C139—22no—
76C4⋊Q8×C139—41no—
77C22⋊Q8×C139—44no—
78C4×D4×C139—22no—
79C4×D4×C139—22no—
80C4×D4×C139—22no—
81C4×D4×C139—22no—
82C4×D4×C139—22no—
83C4×D4×C139—41no—
84C4×D4×C139—41no—
85C4×D4×C139—41no—
86C2×C4⋊C4×C139—21no—
87C2×C4⋊C4×C139—21no—
88C2×C4⋊C4×C139—21no—
89C2×C4⋊C4×C139—21no—
90C2×C4⋊C4×C139—21no—
91C2×C4⋊C4×C139D411yescharacteristic
92C2×C4⋊C4×C139D411yescharacteristic
93C2×C4⋊C4×C139C2311yescharacteristic
94C2×C4⋊C4×C139C2311yescharacteristic
95C2×C4⋊C4×C139C2311yescharacteristic
96C2×C4⋊C4×C139C2311yescharacteristic
97C2×C4⋊C4×C139C2311yescharacteristic
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C22⋊C4×C139—21no—
100C2×C22⋊C4×C139—21no—
101C2×C22⋊C4×C139—21no—
102C2×C22⋊C4×C139—21no—
103C2×C22⋊C4×C139—21no—
104C2×C22⋊C4×C139—21no—
105C2×C22⋊C4×C139—21no—
106C2×C22⋊C4×C139—21no—
107C2×C42×C139C2311yescharacteristic
108C2×C42×C139C2311yescharacteristic
109C2×C42×C139C2311yescharacteristic
110#107×C139—22no—
111#107×C139—41no—
112#106×C139—22no—
113#106×C139—22no—
114#106×C139—22no—
115C4⋊C8×C139—22no—
116#102×C139—22no—
117#102×C139—22no—
118#102×C139—22no—
119#102×C139—22no—
120#102×C139—41no—
121#102×C139D414yes—
122C4×C8×C139—22no—
123#95×C139—21no—
124#95×C139—21no—
125#95×C139—21no—
126#95×C139—21no—
127#95×C139—21no—
128#95×C139—21no—
129#95×C139D411yescharacteristic
130#95×C139D411yescharacteristic
131C24×C139—21no—
132C24×C139—21no—
133C2×Q8×C139—42no—
134C2×Q8×C139—42no—
135C2×Q8×C139—81no—
136C2×D4×C139—21no—
137C2×D4×C139—21no—
138C2×D4×C139—21no—
139C2×D4×C139—21no—
140C2×D4×C139—21no—
141C2×D4×C139—21no—
142C2×D4×C139—21no—
143C2×D4×C139—21no—
144C2×D4×C139C2×D412yes—
145C2×D4×C139C2×Q812yes—
146C2×D4×C139C2×Q812yes—
147C2×D4×C139#4112yes—
148C22×C4×C139—21no—
149C22×C4×C139—21no—
150C22×C4×C139—24no—
151C22×C4×C139—21no—
152C22×C4×C139—21no—
153C22×C4×C139—21no—
154C22×C4×C139—21no—
155C22×C4×C139—42no—
156C22×C4×C139—42no—
157C22×C4×C139—42no—
158C22×C4×C139—42no—
159C22×C4×C139—42no—
160C22×C4×C139—42no—
161C22×C4×C139—81no—
162C22×C4×C139—81no—
163C22×C4×C139—81no—
164C22×C4×C139—81no—
165C22×C4×C139—81no—
166C22×C4×C139C2×D411yescharacteristic
167C22×C4×C139C2×D411yescharacteristic
168C22×C4×C139C2×D411yescharacteristic
169C22×C4×C139C2×D411yescharacteristic
170C22×C4×C139C2×D411yescharacteristic
171C22×C4×C139C2×D411yescharacteristic
172C22×C4×C139C2411yescharacteristic
173D8×C139—28no—
174C2×C8×C139—21no—
175C2×C8×C139—21no—
176C2×C8×C139—21no—
177C2×C8×C139—21no—
178C2×C8×C139—21no—
179C2×C8×C139—21no—
180C2×C8×C139—21no—
181C2×C8×C139—21no—
182C2×C8×C139—21no—
183C2×C8×C139—21no—
184C2×C8×C139C2×D412yes—
185C2×C8×C139C2×Q812yes—
186C4⋊C4×C139—22no—
187C4⋊C4×C139—22no—
188C4⋊C4×C139—21no—
189C4⋊C4×C139—21no—
190C4⋊C4×C139—21no—
191C4⋊C4×C139—21no—
192C4⋊C4×C139—21no—
193C4⋊C4×C139—21no—
194C4⋊C4×C139—21no—
195C4⋊C4×C139—21no—
196C4⋊C4×C139—21no—
197C4⋊C4×C139—21no—
198C4⋊C4×C139—42no—
199C4⋊C4×C139—42no—
200C4⋊C4×C139—42no—
201C4⋊C4×C139—81no—
202C4⋊C4×C139—81no—
203C4⋊C4×C139C2×D412yes—
204C4⋊C4×C139#4112yes—
205C22⋊C4×C139—24no—
206C22⋊C4×C139—42no—
207C22⋊C4×C139—42no—
208C22⋊C4×C139—42no—
209C22⋊C4×C139—42no—
210C22⋊C4×C139—42no—
211C22⋊C4×C139—42no—
212C22⋊C4×C139—81no—
213C42×C139—21no—
214C42×C139—21no—
215C42×C139—21no—
216C42×C139—21no—
217C42×C139—21no—
218C42×C139—21no—
219C23×C139—22no—
220C23×C139—22no—
221C23×C139—22no—
222C23×C139—22no—
223C23×C139—41no—
224C23×C139—41no—
225C23×C139—41no—
226C23×C139—41no—
227C23×C139—41no—
228C23×C139—41no—
229C23×C139—41no—
230C23×C139—41no—
231C23×C139—41no—
232C23×C139—41no—
233C23×C139C22×D411yescharacteristic
234Q8×C139—84no—
235D4×C139—22no—
236D4×C139—22no—
237D4×C139—22no—
238D4×C139—22no—
239D4×C139—22no—
240D4×C139—41no—
241D4×C139—41no—
242D4×C139C22⋊Q814yescomplemented
243C2×C4×C139—21no—
244C2×C4×C139—21no—
245C2×C4×C139—21no—
246C2×C4×C139—21no—
247C2×C4×C139—21no—
248C2×C4×C139—21no—
249C2×C4×C139—22no—
250C2×C4×C139—21no—
251C2×C4×C139—21no—
252C2×C4×C139—22no—
253C2×C4×C139—21no—
254C2×C4×C139—21no—
255C2×C4×C139—21no—
256C2×C4×C139—21no—
257C2×C4×C139—21no—
258C2×C4×C139—21no—
259C2×C4×C139—21no—
260C2×C4×C139—21no—
261C2×C4×C139—41no—
262C2×C4×C139—41no—
263C2×C4×C139—41no—
264C2×C4×C139—41no—
265C2×C4×C139—41no—
266C2×C4×C139—41no—
267C2×C4×C139—41no—
268C2×C4×C139—41no—
269C2×C4×C139—41no—
270C2×C4×C139—41no—
271C2×C4×C139—41no—
272C2×C4×C139—41no—
273C2×C4×C139—41no—
274C2×C4×C139—41no—
275C2×C4×C139—41no—
276C2×C4×C139—41no—
277C2×C4×C139—84no—
278C2×C4×C139—84no—
279C2×C4×C139—84no—
280C2×C4×C139—84no—
281C2×C4×C139#13512yes—
282C2×C4×C139AGL(1,ℤ/8)12yes—
283C2×C4×C139C22×D411yescharacteristic
284C2×C4×C139C22×Q811yescharacteristic
285C2×C4×C139C2×#4111yescharacteristic
286C2×C4×C139C2×#4111yescharacteristic
287C2×C4×C139H(5,𝔽2)11yescharacteristic
288C2×C4×C1392−1+411yescharacteristic
289C8×C139—22no—
290C8×C139—22no—
291C8×C139—41no—
292C8×C139—41no—
293C22×C139—24no—
294C22×C139—42no—
295C22×C139—42no—
296C22×C139—42no—
297C22×C139—42no—
298C22×C139—42no—
299C22×C139—42no—
300C22×C139—42no—
301C22×C139—42no—
302C22×C139—42no—
303C22×C139—81no—
304C22×C139—81no—
305C22×C139—81no—
306C22×C139—81no—
307C22×C139#52511yescharacteristic
308C22×C139D4211yescharacteristic
309C22×C139D4×Q811yescharacteristic
310C22×C139C2×#13511yescharacteristic
311C22×C139C2×AGL(1,ℤ/8)11yescharacteristic
312C22×C139#57611yescharacteristic
313C22×C139#57711yescharacteristic
314C4×C139—22no—
315C4×C139—22no—
316C4×C139—41no—
317C4×C139—41no—
318C4×C139—42no—
319C4×C139—41no—
320C4×C139—42no—
321C4×C139—41no—
322C4×C139—81no—
323C4×C139—81no—
324C4×C139—81no—
325C4×C139—81no—
326C4×C139C2×C22⋊Q811yescharacteristic
327C4×C139#53911yescharacteristic
328C4×C139#54711yescharacteristic
329C4×C139#55411yescharacteristic
330C2×C139—44no—
331C2×C139—82no—
332C2×C139#244911yescharacteristic
333C2×C139#310611yescharacteristic
334C2×C139#311811yescharacteristic
335C2×C139#326411yescharacteristic
336C2×C139#328211yescharacteristic
337C2×C139#338011yescharacteristic
338C2×C139#338411yescharacteristic
339#26380C13911yesmaximal, characteristic, direct product factor, Sylow
340C139#2638011yescharacteristic, direct product factor, Sylow
341C2×#476C2×C13911yescharacteristic, complemented
342C2×C4×D8C2×C13911yescharacteristic
343#2452C2×C13911yescharacteristic, complemented
344#2349C2×C13911yescharacteristic, complemented
345#2092C2×C13911yescharacteristic, complemented
346#2085C2×C13911yescharacteristic, complemented
347#2065C2×C13911yescharacteristic, complemented
348#2057C2×C13911yescharacteristic, complemented
349#1941C2×C13911yescharacteristic, complemented
350#1916C2×C13911yescharacteristic, complemented
351#1879C2×C13911yescharacteristic
352#1879C2×C13911yescharacteristic
353#1864C2×C13911yescharacteristic, complemented
354#1864C2×C13911yescharacteristic, complemented
355#1862C2×C13911yescharacteristic, complemented
356C22×D8C22×C13911yescharacteristic
357C2×C4⋊Q8C22×C13911yescharacteristic
358C2×C22⋊Q8—21no—
359C2×C4×D4C22×C13911yescharacteristic
360C2×C4×D4C22×C13911yescharacteristic
361C2×C4×D4C22×C13911yescharacteristic
362C2×C4×D4C22×C13911yescharacteristic
363#476—24no—
364C4×D8—24no—
365C2×#107C22×C13911yescharacteristic
366C2×#107C22×C13911yescharacteristic
367C2×#106C22×C13911yescharacteristic
368C2×#106C22×C13911yescharacteristic
369C2×#106C22×C13911yescharacteristic
370C2×C4⋊C8C22×C13911yescharacteristic
371C2×#102C22×C13911yescharacteristic
372C2×#102C22×C13911yescharacteristic
373C2×#102C22×C13911yescharacteristic
374C2×#102C22×C13911yescharacteristic
375C2×#102C22×C13911yescharacteristic
376C2×#102C22×C13911yescharacteristic
377C2×C4×C8C22×C13911yescharacteristic
378#396—21no—
379#393—21no—
380#390C22×C13911yescharacteristic
381#390C22×C13911yescharacteristic
382#389C22×C13911yescharacteristic
383#389C22×C13911yescharacteristic
384#389C22×C13911yescharacteristic
385#389C22×C13911yescharacteristic
386#385—21no—
387#385—21no—
388#385—21no—
389#382C22×C13911yescharacteristic
390#380—21no—
391C4×C4⋊C4C22×C13911yescharacteristic
392C2×#95—21no—
393#340C22×C13911yescharacteristic
394#340C22×C13911yescharacteristic
395#340C22×C13911yescharacteristic
396#340C22×C13911yescharacteristic
397#336C22×C13911yescharacteristic
398#336C22×C13911yescharacteristic
399#336C22×C13911yescharacteristic
400#336C22×C13911yescharacteristic
401C22×Q8—21no—
402C22×D4C23×C13911yescharacteristic
403C22×D4C23×C13911yescharacteristic
404C23×C4—21no—
405C23×C4—21no—
406C23×C4—21no—
407C23×C4—21no—
408C2×D8—22no—
409C2×D8—22no—
410C2×D8Q8×C13914yescomplemented
411C22×C8C23×C13911yescharacteristic
412C22×C8C23×C13911yescharacteristic
413C22×C8C23×C13911yescharacteristic
414C22×C8C23×C13911yescharacteristic
415C4⋊Q8—22no—
416C4⋊Q8—41no—
417C22⋊Q8—44no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—41no—
424C4×D4—41no—
425C4×D4—41no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4D4×C13911yescharacteristic
432C2×C4⋊C4D4×C13911yescharacteristic
433C2×C4⋊C4C23×C13911yescharacteristic
434C2×C4⋊C4C23×C13911yescharacteristic
435C2×C4⋊C4C23×C13911yescharacteristic
436C2×C4⋊C4C23×C13911yescharacteristic
437C2×C4⋊C4C23×C13911yescharacteristic
438C2×C4⋊C4C23×C13911yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C42C23×C13911yescharacteristic
448C2×C42C23×C13911yescharacteristic
449C2×C42C23×C13911yescharacteristic
450#107—22no—
451#107—41no—
452#106—22no—
453#106—22no—
454#106—22no—
455C4⋊C8—22no—
456#102—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460#102—41no—
461#102D4×C13914yes—
462C4×C8—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95D4×C13911yescharacteristic
470#95D4×C13911yescharacteristic
471C24—21no—
472C24—21no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8—81no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4C2×D4×C13912yes—
485C2×D4C2×Q8×C13912yes—
486C2×D4C2×Q8×C13912yes—
487C2×D4#41×C13912yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—24no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—81no—
502C22×C4—81no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4C2×D4×C13911yescharacteristic
507C22×C4C2×D4×C13911yescharacteristic
508C22×C4C2×D4×C13911yescharacteristic
509C22×C4C2×D4×C13911yescharacteristic
510C22×C4C2×D4×C13911yescharacteristic
511C22×C4C2×D4×C13911yescharacteristic
512C22×C4C24×C13911yescharacteristic
513D8—28no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8C2×D4×C13912yes—
525C2×C8C2×Q8×C13912yes—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—81no—
542C4⋊C4—81no—
543C4⋊C4C2×D4×C13912yes—
544C4⋊C4#41×C13912yes—
545C22⋊C4—24no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23C22×D4×C13911yescharacteristic
574Q8—84no—
575D4—22no—
576D4—22no—
577D4—22no—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582D4C22⋊Q8×C13914yescomplemented
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—84no—
618C2×C4—84no—
619C2×C4—84no—
620C2×C4—84no—
621C2×C4#135×C13912yes—
622C2×C4AGL(1,ℤ/8)×C13912yes—
623C2×C4C22×D4×C13911yescharacteristic
624C2×C4C22×Q8×C13911yescharacteristic
625C2×C4C2×#41×C13911yescharacteristic
626C2×C4C2×#41×C13911yescharacteristic
627C2×C4H(5,𝔽2)×C13911yescharacteristic
628C2×C42−1+4×C13911yescharacteristic
629C8—22no—
630C8—22no—
631C8—41no—
632C8—41no—
633C22—24no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—42no—
642C22—42no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22#525×C13911yescharacteristic
648C22D42×C13911yescharacteristic
649C22D4×Q8×C13911yescharacteristic
650C22C2×#135×C13911yescharacteristic
651C22C2×AGL(1,ℤ/8)×C13911yescharacteristic
652C22#576×C13911yescharacteristic
653C22#577×C13911yescharacteristic
654C4—22no—
655C4—22no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—42no—
660C4—41no—
661C4—42no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4C2×C22⋊Q8×C13911yescharacteristic
667C4#539×C13911yescharacteristic
668C4#547×C13911yescharacteristic
669C4#554×C13911yescharacteristic
670C2—44no—
671C2—82no—
672C2#2449×C13911yescharacteristic
673C2#3106×C13911yescharacteristic
674C2#3118×C13911yescharacteristic
675C2#3264×C13911yescharacteristic
676C2#3282×C13911yescharacteristic
677C2#3380×C13911yescharacteristic
678C2#3384×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC22×D8×C139C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C4⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#476×C139C2semidirect
3. #2452×C139C2semidirect
4. #2349×C139C2semidirect
5. #2092×C139C2semidirect
6. #2085×C139C2semidirect
7. #2065×C139C2semidirect
8. #2057×C139C2semidirect
9. #1941×C139C2semidirect
10. #1916×C139C2semidirect
13. #1864×C139C2semidirect
14. #1864×C139C2semidirect
15. #1862×C139C2semidirect
70. C2×D8×C139Q8semidirect
242. D4×C139C22⋊Q8semidirect
339. #26380C139direct (N × H)
340. C139#26380direct (N × H)
341. C2×#476C2×C139semidirect
343. #2452C2×C139semidirect
344. #2349C2×C139semidirect
345. #2092C2×C139semidirect
346. #2085C2×C139semidirect
347. #2065C2×C139semidirect
348. #2057C2×C139semidirect
349. #1941C2×C139semidirect
350. #1916C2×C139semidirect
353. #1864C2×C139semidirect
354. #1864C2×C139semidirect
355. #1862C2×C139semidirect
410. C2×D8Q8×C139semidirect
582. D4C22⋊Q8×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C1392
C2×C4×D8×C1392
#2452×C1392
#2349×C1392
#2092×C1392
#2085×C1392
#2065×C1392
#2057×C1392
#1941×C1392
#1916×C1392
#1879×C1392
#1864×C1392
#1862×C1392
#26380139