Finite Group Databasebeta

← C139×#36299 #48030895

Subgroups — C139×#36299 #48030895

Order 35584.

1794 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2863×C139C212yesmaximal, complemented
2#2859×C139C211yesmaximal, characteristic, complemented
3#2582×C139C211yesmaximal, characteristic, complemented
4#2538×C139C211yesmaximal, characteristic
5#2515×C139C214yesmaximal, complemented
6#2509×C139C212yesmaximal, complemented
7#2495×C139C212yesmaximal, complemented
8#2475×C139C214yesmaximal, complemented
9#2447×C139C212yesmaximal
10#2421×C139C212yesmaximal, complemented
11#2360×C139C212yesmaximal, complemented
12#2355×C139C211yesmaximal, characteristic, complemented
13D4×C4⋊C4×C139C211yesmaximal, characteristic
14#2344×C139C212yesmaximal, complemented
15C4×#124×C139C211yesmaximal, characteristic
16#2293×C139C212yesmaximal
17C42×Q8×C139C211yesmaximal, characteristic, complemented
18C2×#125×C139C2212yes—
19C2×#124×C139C2211yescharacteristic
20C2×C22⋊Q8×C139C2212yes—
21C2×C4×Q8×C139C2211yescharacteristic
22C2×C4×Q8×C139C2211yescharacteristic
23C2×C4×Q8×C139C2211yescharacteristic
24C2×C4×Q8×C139C2211yescharacteristic
25C2×C4×D4×C139C2211yescharacteristic
26C2×C4×D4×C139C2212yes—
27C2×#117×C139C2214yes—
28C22×C4⋊C4×C139C2212yes—
29#400×C139C2214yes—
30#400×C139C2214yes—
31#398×C139C2214yes—
32#397×C139C2214yes—
33#397×C139C2214yes—
34#396×C139C2214yes—
35#391×C139C2211yescharacteristic
36#391×C139C2212yes—
37#391×C139C2212yes—
38#391×C139C2212yes—
39#390×C139C2212yes—
40#390×C139C2211yescharacteristic
41#389×C139C2212yes—
42#389×C139C2212yes—
43#389×C139C2212yes—
44#389×C139C2212yes—
45#389×C139C2212yes—
46#389×C139C2212yes—
47#389×C139C2212yes—
48#389×C139C2212yes—
49#389×C139C2214yes—
50#388×C139C2212yes—
51#388×C139C2214yes—
52#388×C139C2214yes—
53#388×C139C2212yes—
54#387×C139C2214yes—
55#387×C139C2214yes—
56#387×C139C2214yes—
57#387×C139C2214yes—
58#387×C139C2214yes—
59#385×C139C2214yes—
60#385×C139C2214yes—
61#384×C139C2211yescharacteristic
62#384×C139C2211yescharacteristic
63#383×C139C2214yes—
64#382×C139C2212yes—
65#382×C139C2211yescharacteristic
66#382×C139C2212yes—
67#381×C139C2214yes—
68#380×C139C2212yes—
69#380×C139C2212yes—
70C4×C4⋊C4×C139C2212yes—
71C4×C4⋊C4×C139C2211yescharacteristic
72C4×C4⋊C4×C139C2211yescharacteristic
73C4×C4⋊C4×C139C2212yes—
74C4×C4⋊C4×C139C2212yes—
75C4×C4⋊C4×C139C2211yescharacteristic
76C4×C4⋊C4×C139C2212yes—
77C4×C4⋊C4×C139C2212yes—
78C4×C22⋊C4×C139C2214yes—
79C4×C22⋊C4×C139C2212yes—
80C4×C22⋊C4×C139C2212yes—
81C43×C139C2212yes—
82C43×C139C2211yescharacteristic
83C22×Q8×C139C2311yescharacteristic
84C22×Q8×C139C2311yescharacteristic
85C22×D4×C139C2311yescharacteristic
86C23×C4×C139C2312yes—
87C23×C4×C139C2314yes—
88#125×C139—44no—
89#124×C139—24no—
90C22⋊Q8×C139—28no—
91C4×Q8×C139—24no—
92C4×Q8×C139—24no—
93C4×Q8×C139—24no—
94C4×Q8×C139—24no—
95C4×D4×C139—28no—
96C4×D4×C139—24no—
97#117×C139—48no—
98C2×C4⋊C4×C139—28no—
99C2×C4⋊C4×C139C2312yes—
100C2×C4⋊C4×C139C2314yes—
101C2×C4⋊C4×C139C2312yes—
102C2×C4⋊C4×C139C2312yes—
103C2×C4⋊C4×C139C2312yes—
104C2×C4⋊C4×C139C2314yes—
105C2×C4⋊C4×C139C2314yes—
106C2×C4⋊C4×C139C2311yescharacteristic
107C2×C4⋊C4×C139C2312yes—
108C2×C4⋊C4×C139C2311yescharacteristic
109C2×C4⋊C4×C139C2311yescharacteristic
110C2×C4⋊C4×C139C2311yescharacteristic
111C2×C4⋊C4×C139C2312yes—
112C2×C4⋊C4×C139C2312yes—
113C2×C4⋊C4×C139C2312yes—
114C2×C4⋊C4×C139C2312yes—
115C2×C4⋊C4×C139C2314yes—
116C2×C4⋊C4×C139C2312yes—
117C2×C4⋊C4×C139C2314yes—
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C22⋊C4×C139C2312yes—
120C2×C22⋊C4×C139C2314yes—
121C2×C22⋊C4×C139C2314yes—
122C2×C22⋊C4×C139C2312yes—
123C2×C22⋊C4×C139C2312yes—
124C2×C22⋊C4×C139C2312yes—
125C2×C22⋊C4×C139C2312yes—
126C2×C22⋊C4×C139C2314yes—
127C2×C42×C139C2312yes—
128C2×C42×C139C2312yes—
129C2×C42×C139C2312yes—
130C2×C42×C139C2311yescharacteristic
131C2×C42×C139C2311yescharacteristic
132C2×C42×C139C2312yes—
133C2×C42×C139C2312yes—
134C2×C42×C139C2312yes—
135C2×C42×C139C2311yescharacteristic
136C2×C42×C139C2311yescharacteristic
137C2×C42×C139C2311yescharacteristic
138C2×C42×C139C2311yescharacteristic
139C2×C42×C139C2312yes—
140C2×C42×C139C2314yes—
141C2×C42×C139C2311yescharacteristic
142#95×C139C2314yes—
143#95×C139C2312yes—
144#95×C139C2314yes—
145#95×C139C2314yes—
146#95×C139C2314yes—
147#95×C139C2314yes—
148#95×C139C2314yes—
149#95×C139C2312yes—
150#95×C139C2312yes—
151#95×C139C2314yes—
152#95×C139C2314yes—
153#95×C139C2314yes—
154#95×C139C2312yes—
155#95×C139C2312yes—
156#95×C139C2312yes—
157#95×C139C2312yes—
158#95×C139C2314yes—
159C24×C139C2412yes—
160C2×Q8×C139—22no—
161C2×Q8×C139—22no—
162C2×Q8×C139—22no—
163C2×Q8×C139—22no—
164C2×Q8×C139—22no—
165C2×Q8×C139#4114yes—
166C2×D4×C139—22no—
167C2×D4×C139—22no—
168C2×D4×C139#4114yes—
169C22×C4×C139—28no—
170C22×C4×C139—28no—
171C22×C4×C139—24no—
172C22×C4×C139—24no—
173C22×C4×C139—24no—
174C22×C4×C139—44no—
175C22×C4×C139C2412yes—
176C22×C4×C139C2412yes—
177C22×C4×C139C2411yescharacteristic
178C22×C4×C139C2412yes—
179C22×C4×C139C2412yes—
180C22×C4×C139C2412yes—
181C22×C4×C139C2414yes—
182C22×C4×C139C2414yes—
183C22×C4×C139C2411yescharacteristic
184C22×C4×C139C2412yes—
185C22×C4×C139C2412yes—
186C22×C4×C139C2411yescharacteristic
187C22×C4×C139C2411yescharacteristic
188C22×C4×C139C2411yescharacteristic
189C22×C4×C139C2411yescharacteristic
190C22×C4×C139C2411yescharacteristic
191C4⋊C4×C139—28no—
192C4⋊C4×C139—24no—
193C4⋊C4×C139—24no—
194C4⋊C4×C139—22no—
195C4⋊C4×C139—24no—
196C4⋊C4×C139—24no—
197C4⋊C4×C139—24no—
198C4⋊C4×C139—22no—
199C4⋊C4×C139—22no—
200C4⋊C4×C139—22no—
201C4⋊C4×C139—24no—
202C4⋊C4×C139—24no—
203C4⋊C4×C139—28no—
204C4⋊C4×C139—28no—
205C4⋊C4×C139—24no—
206C4⋊C4×C139—44no—
207C4⋊C4×C139—42no—
208C4⋊C4×C139—42no—
209C4⋊C4×C139—44no—
210C4⋊C4×C139#4114yes—
211C22⋊C4×C139—28no—
212C22⋊C4×C139—24no—
213C22⋊C4×C139—24no—
214C22⋊C4×C139—24no—
215C22⋊C4×C139—28no—
216C22⋊C4×C139—24no—
217C22⋊C4×C139—24no—
218C22⋊C4×C139—44no—
219C42×C139—24no—
220C42×C139—24no—
221C42×C139—24no—
222C42×C139—22no—
223C42×C139—22no—
224C42×C139—24no—
225C42×C139—24no—
226C42×C139—22no—
227C42×C139—24no—
228C42×C139—22no—
229C42×C139—22no—
230C42×C139—22no—
231C42×C139—24no—
232C42×C139—44no—
233C42×C139#4114yes—
234C23×C139—22no—
235C23×C139—22no—
236C23×C139—22no—
237C23×C139—22no—
238C23×C139—22no—
239C23×C139—22no—
240C23×C139C2×#4114yes—
241C23×C139C2511yescharacteristic
242Q8×C139—28no—
243Q8×C139—44no—
244D4×C139—28no—
245C2×C4×C139—21no—
246C2×C4×C139—21no—
247C2×C4×C139—22no—
248C2×C4×C139—22no—
249C2×C4×C139—22no—
250C2×C4×C139—22no—
251C2×C4×C139—21no—
252C2×C4×C139—21no—
253C2×C4×C139—21no—
254C2×C4×C139—21no—
255C2×C4×C139—21no—
256C2×C4×C139—22no—
257C2×C4×C139—21no—
258C2×C4×C139—21no—
259C2×C4×C139—22no—
260C2×C4×C139—21no—
261C2×C4×C139—22no—
262C2×C4×C139—22no—
263C2×C4×C139—22no—
264C2×C4×C139—22no—
265C2×C4×C139—24no—
266C2×C4×C139—22no—
267C2×C4×C139—24no—
268C2×C4×C139—22no—
269C2×C4×C139—22no—
270C2×C4×C139—24no—
271C2×C4×C139—22no—
272C2×C4×C139—21no—
273C2×C4×C139—22no—
274C2×C4×C139—24no—
275C2×C4×C139—24no—
276C2×C4×C139—21no—
277C2×C4×C139—22no—
278C2×C4×C139—22no—
279C2×C4×C139—22no—
280C2×C4×C139—24no—
281C2×C4×C139—22no—
282C2×C4×C139—416no—
283C2×C4×C139—48no—
284C2×C4×C139C2×#4114yes—
285C2×C4×C139C2×#4114yes—
286C2×C4×C139C2×#4112yes—
287C2×C4×C139C2×#4112yes—
288C2×C4×C139C2×#4112yes—
289C2×C4×C139C2×#4112yes—
290C2×C4×C139C2×#4112yes—
291C2×C4×C139C2×#4112yes—
292C2×C4×C139H(5,𝔽2)12yes—
293C2×C4×C1392−1+412yes—
294C2×C4×C1392−1+412yes—
295C22×C139—24no—
296C22×C139—24no—
297C22×C139—24no—
298C22×C139—42no—
299C22×C139—42no—
300C22×C139—42no—
301C22×C139—42no—
302C22×C139C22×#4111yescharacteristic
303C22×C139C22×#4111yescharacteristic
304C22×C139C22×#4111yescharacteristic
305C22×C139C22×#4111yescharacteristic
306C22×C139C2×H(5,𝔽2)11yescharacteristic
307C22×C139C2×2−1+411yescharacteristic
308C22×C139C2×2−1+411yescharacteristic
309C4×C139—24no—
310C4×C139—24no—
311C4×C139—22no—
312C4×C139—22no—
313C4×C139—22no—
314C4×C139—42no—
315C4×C139—42no—
316C4×C139—41no—
317C4×C139—44no—
318C4×C139—42no—
319C4×C139—41no—
320C4×C139—42no—
321C4×C139—42no—
322C4×C139—44no—
323C4×C139#52914yes—
324C4×C139#55214yes—
325C2×C139—44no—
326C2×C139C2×#52911yescharacteristic
327C2×C139C2×#55211yescharacteristic
328C2×C139#348111yescharacteristic
329C2×C139#348211yescharacteristic
330C2×C139#351111yescharacteristic
331C2×C139#352211yescharacteristic
332C2×C139#352311yescharacteristic
333#36299C13911yesmaximal, characteristic, direct product factor, Sylow
334C139#3629911yescharacteristic, direct product factor, Sylow
335#2863C2×C13912yescomplemented
336#2859C2×C13911yescharacteristic, complemented
337#2582C2×C13911yescharacteristic, complemented
338#2538C2×C13911yescharacteristic
339#2515C2×C13914yescomplemented
340#2509C2×C13912yescomplemented
341#2495C2×C13912yescomplemented
342#2475C2×C13914yescomplemented
343#2447C2×C13912yes—
344#2421C2×C13912yescomplemented
345#2360C2×C13912yescomplemented
346#2355C2×C13911yescharacteristic, complemented
347D4×C4⋊C4C2×C13911yescharacteristic
348#2344C2×C13912yescomplemented
349C4×#124C2×C13911yescharacteristic
350#2293C2×C13912yes—
351C42×Q8C2×C13911yescharacteristic, complemented
352C2×#125C22×C13912yes—
353C2×#124C22×C13911yescharacteristic
354C2×C22⋊Q8C22×C13912yes—
355C2×C4×Q8C22×C13911yescharacteristic
356C2×C4×Q8C22×C13911yescharacteristic
357C2×C4×Q8C22×C13911yescharacteristic
358C2×C4×Q8C22×C13911yescharacteristic
359C2×C4×D4C22×C13912yes—
360C2×C4×D4C22×C13911yescharacteristic
361C2×#117C22×C13914yes—
362C22×C4⋊C4C22×C13912yes—
363#400C22×C13914yes—
364#400C22×C13914yes—
365#398C22×C13914yes—
366#397C22×C13914yes—
367#397C22×C13914yes—
368#396C22×C13914yes—
369#391C22×C13912yes—
370#391C22×C13912yes—
371#391C22×C13911yescharacteristic
372#391C22×C13912yes—
373#390C22×C13912yes—
374#390C22×C13911yescharacteristic
375#389C22×C13912yes—
376#389C22×C13912yes—
377#389C22×C13912yes—
378#389C22×C13912yes—
379#389C22×C13912yes—
380#389C22×C13912yes—
381#389C22×C13912yes—
382#389C22×C13912yes—
383#389C22×C13914yes—
384#388C22×C13914yes—
385#388C22×C13912yes—
386#388C22×C13914yes—
387#388C22×C13912yes—
388#387C22×C13914yes—
389#387C22×C13914yes—
390#387C22×C13914yes—
391#387C22×C13914yes—
392#387C22×C13914yes—
393#385C22×C13914yes—
394#385C22×C13914yes—
395#384C22×C13911yescharacteristic
396#384C22×C13911yescharacteristic
397#383C22×C13914yes—
398#382C22×C13912yes—
399#382C22×C13912yes—
400#382C22×C13911yescharacteristic
401#381C22×C13914yes—
402#380C22×C13912yes—
403#380C22×C13912yes—
404C4×C4⋊C4C22×C13911yescharacteristic
405C4×C4⋊C4C22×C13912yes—
406C4×C4⋊C4C22×C13911yescharacteristic
407C4×C4⋊C4C22×C13912yes—
408C4×C4⋊C4C22×C13912yes—
409C4×C4⋊C4C22×C13912yes—
410C4×C4⋊C4C22×C13911yescharacteristic
411C4×C4⋊C4C22×C13912yes—
412C4×C22⋊C4C22×C13912yes—
413C4×C22⋊C4C22×C13912yes—
414C4×C22⋊C4C22×C13914yes—
415C43C22×C13911yescharacteristic
416C43C22×C13912yes—
417C22×Q8C23×C13911yescharacteristic
418C22×Q8C23×C13911yescharacteristic
419C22×D4C23×C13911yescharacteristic
420C23×C4C23×C13912yes—
421C23×C4C23×C13914yes—
422#125—44no—
423#124—24no—
424C22⋊Q8—28no—
425C4×Q8—24no—
426C4×Q8—24no—
427C4×Q8—24no—
428C4×Q8—24no—
429C4×D4—28no—
430C4×D4—24no—
431#117—48no—
432C2×C4⋊C4—28no—
433C2×C4⋊C4C23×C13912yes—
434C2×C4⋊C4C23×C13914yes—
435C2×C4⋊C4C23×C13914yes—
436C2×C4⋊C4C23×C13911yescharacteristic
437C2×C4⋊C4C23×C13912yes—
438C2×C4⋊C4C23×C13911yescharacteristic
439C2×C4⋊C4C23×C13911yescharacteristic
440C2×C4⋊C4C23×C13911yescharacteristic
441C2×C4⋊C4C23×C13912yes—
442C2×C4⋊C4C23×C13912yes—
443C2×C4⋊C4C23×C13912yes—
444C2×C4⋊C4C23×C13912yes—
445C2×C4⋊C4C23×C13912yes—
446C2×C4⋊C4C23×C13914yes—
447C2×C4⋊C4C23×C13912yes—
448C2×C4⋊C4C23×C13914yes—
449C2×C4⋊C4C23×C13912yes—
450C2×C4⋊C4C23×C13912yes—
451C2×C4⋊C4C23×C13914yes—
452C2×C4⋊C4C23×C13911yescharacteristic
453C2×C22⋊C4C23×C13912yes—
454C2×C22⋊C4C23×C13914yes—
455C2×C22⋊C4C23×C13912yes—
456C2×C22⋊C4C23×C13914yes—
457C2×C22⋊C4C23×C13912yes—
458C2×C22⋊C4C23×C13912yes—
459C2×C22⋊C4C23×C13912yes—
460C2×C22⋊C4C23×C13914yes—
461C2×C42C23×C13912yes—
462C2×C42C23×C13912yes—
463C2×C42C23×C13912yes—
464C2×C42C23×C13911yescharacteristic
465C2×C42C23×C13911yescharacteristic
466C2×C42C23×C13912yes—
467C2×C42C23×C13912yes—
468C2×C42C23×C13912yes—
469C2×C42C23×C13911yescharacteristic
470C2×C42C23×C13911yescharacteristic
471C2×C42C23×C13911yescharacteristic
472C2×C42C23×C13911yescharacteristic
473C2×C42C23×C13912yes—
474C2×C42C23×C13914yes—
475C2×C42C23×C13911yescharacteristic
476#95C23×C13914yes—
477#95C23×C13912yes—
478#95C23×C13912yes—
479#95C23×C13912yes—
480#95C23×C13912yes—
481#95C23×C13914yes—
482#95C23×C13912yes—
483#95C23×C13912yes—
484#95C23×C13912yes—
485#95C23×C13914yes—
486#95C23×C13914yes—
487#95C23×C13914yes—
488#95C23×C13914yes—
489#95C23×C13914yes—
490#95C23×C13914yes—
491#95C23×C13914yes—
492#95C23×C13914yes—
493C24C24×C13912yes—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8#41×C13914yes—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4#41×C13914yes—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—44no—
509C22×C4C24×C13912yes—
510C22×C4C24×C13911yescharacteristic
511C22×C4C24×C13912yes—
512C22×C4C24×C13912yes—
513C22×C4C24×C13912yes—
514C22×C4C24×C13912yes—
515C22×C4C24×C13914yes—
516C22×C4C24×C13914yes—
517C22×C4C24×C13911yescharacteristic
518C22×C4C24×C13912yes—
519C22×C4C24×C13912yes—
520C22×C4C24×C13911yescharacteristic
521C22×C4C24×C13911yescharacteristic
522C22×C4C24×C13911yescharacteristic
523C22×C4C24×C13911yescharacteristic
524C22×C4C24×C13911yescharacteristic
525C4⋊C4—28no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—22no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—28no—
538C4⋊C4—28no—
539C4⋊C4—24no—
540C4⋊C4—44no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—44no—
544C4⋊C4#41×C13914yes—
545C22⋊C4—28no—
546C22⋊C4—24no—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—28no—
550C22⋊C4—24no—
551C22⋊C4—24no—
552C22⋊C4—44no—
553C42—24no—
554C42—24no—
555C42—24no—
556C42—22no—
557C42—22no—
558C42—24no—
559C42—24no—
560C42—22no—
561C42—24no—
562C42—22no—
563C42—22no—
564C42—22no—
565C42—24no—
566C42—44no—
567C42#41×C13914yes—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—22no—
574C23C2×#41×C13914yes—
575C23C25×C13911yescharacteristic
576Q8—28no—
577Q8—44no—
578D4—28no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—22no—
616C2×C4—416no—
617C2×C4—48no—
618C2×C4C2×#41×C13914yes—
619C2×C4C2×#41×C13914yes—
620C2×C4C2×#41×C13912yes—
621C2×C4C2×#41×C13912yes—
622C2×C4C2×#41×C13912yes—
623C2×C4C2×#41×C13912yes—
624C2×C4C2×#41×C13912yes—
625C2×C4C2×#41×C13912yes—
626C2×C4H(5,𝔽2)×C13912yes—
627C2×C42−1+4×C13912yes—
628C2×C42−1+4×C13912yes—
629C22—24no—
630C22—24no—
631C22—24no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22C22×#41×C13911yescharacteristic
637C22C22×#41×C13911yescharacteristic
638C22C22×#41×C13911yescharacteristic
639C22C22×#41×C13911yescharacteristic
640C22C2×H(5,𝔽2)×C13911yescharacteristic
641C22C2×2−1+4×C13911yescharacteristic
642C22C2×2−1+4×C13911yescharacteristic
643C4—24no—
644C4—24no—
645C4—22no—
646C4—22no—
647C4—22no—
648C4—42no—
649C4—42no—
650C4—44no—
651C4—41no—
652C4—42no—
653C4—41no—
654C4—42no—
655C4—42no—
656C4—44no—
657C4#529×C13914yes—
658C4#552×C13914yes—
659C2—44no—
660C2C2×#529×C13911yescharacteristic
661C2C2×#552×C13911yescharacteristic
662C2#3481×C13911yescharacteristic
663C2#3482×C13911yescharacteristic
664C2#3511×C13911yescharacteristic
665C2#3522×C13911yescharacteristic
666C2#3523×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C25
commutator, Frattini, cosocleC23C25×C139
prime radicalC22×D4×C139C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2863×C139C2semidirect
2. #2859×C139C2semidirect
3. #2582×C139C2semidirect
5. #2515×C139C2semidirect
6. #2509×C139C2semidirect
7. #2495×C139C2semidirect
8. #2475×C139C2semidirect
10. #2421×C139C2semidirect
11. #2360×C139C2semidirect
12. #2355×C139C2semidirect
14. #2344×C139C2semidirect
17. C42×Q8×C139C2semidirect
333. #36299C139direct (N × H)
334. C139#36299direct (N × H)
335. #2863C2×C139semidirect
336. #2859C2×C139semidirect
337. #2582C2×C139semidirect
339. #2515C2×C139semidirect
340. #2509C2×C139semidirect
341. #2495C2×C139semidirect
342. #2475C2×C139semidirect
344. #2421C2×C139semidirect
345. #2360C2×C139semidirect
346. #2355C2×C139semidirect
348. #2344C2×C139semidirect
351. C42×Q8C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2863×C1392
#2859×C1392
#2582×C1392
#2538×C1392
#2515×C1392
#2509×C1392
#2495×C1392
#2475×C1392
#2447×C1392
#2421×C1392
#2360×C1392
#2355×C1392
D4×C4⋊C4×C1392
#2344×C1392
C4×#124×C1392
#2293×C1392
C42×Q8×C1392
#36299139