Finite Group Databasebeta

← C139×#22549 #48017145

Subgroups — C139×#22549 #48017145

Order 35584.

1118 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#559×C139C211yesmaximal, characteristic
2C2×#446×C139C211yesmaximal, characteristic, complemented
3#2355×C139C211yesmaximal, characteristic, complemented
4#1983×C139C211yesmaximal, characteristic, complemented
5#1983×C139C211yesmaximal, characteristic, complemented
6#1982×C139C211yesmaximal, characteristic
7#1961×C139C211yesmaximal, characteristic
8#1959×C139C211yesmaximal, characteristic, complemented
9#1958×C139C211yesmaximal, characteristic, complemented
10#1805×C139C211yesmaximal, characteristic, complemented
11#1804×C139C211yesmaximal, characteristic, complemented
12#1802×C139C211yesmaximal, characteristic, complemented
13#1763×C139C211yesmaximal, characteristic, complemented
14#1762×C139C211yesmaximal, characteristic, complemented
15C4×#102×C139C211yesmaximal, characteristic, complemented
16#559×C139—24no—
17#559×C139C418yescomplemented
18C2×#127×C139C2211yescharacteristic
19C2×#124×C139—21no—
20C2×#124×C139C2211yescharacteristic
21C2×#124×C139C2211yescharacteristic
22C2×#123×C139—21no—
23C2×#123×C139—21no—
24C2×C4×Q8×C139C2211yescharacteristic
25C2×C4×Q8×C139C2211yescharacteristic
26C2×C4×D4×C139—21no—
27C2×C4×D4×C139C2211yescharacteristic
28C2×C4×D4×C139C2211yescharacteristic
29#446×C139—24no—
30C2×C4⋊C8×C139C2211yescharacteristic
31C2×C4⋊C8×C139C2211yescharacteristic
32C2×C4⋊C8×C139C2211yescharacteristic
33C2×#103×C139C2211yescharacteristic
34C2×#103×C139C2211yescharacteristic
35C2×#103×C139C2211yescharacteristic
36C2×#103×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#97×C139C2211yescharacteristic
46C2×#97×C139C2211yescharacteristic
47C2×C4×C8×C139C2211yescharacteristic
48#391×C139—21no—
49#387×C139—21no—
50#387×C139—21no—
51#384×C139C2211yescharacteristic
52#382×C139C2211yescharacteristic
53#382×C139C2211yescharacteristic
54C4×C4⋊C4×C139—21no—
55C4×C4⋊C4×C139C2211yescharacteristic
56C4×C4⋊C4×C139C2211yescharacteristic
57C4×C4⋊C4×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62C22×Q8×C139D411yescharacteristic
63C22×Q8×C139C2311yescharacteristic
64C22×D4×C139—21no—
65C22×D4×C139—21no—
66C22×D4×C139C2311yescharacteristic
67C22×D4×C139C2311yescharacteristic
68C23×C4×C139—21no—
69C23×C4×C139—21no—
70C22×C8×C139C2311yescharacteristic
71C22×C8×C139C2311yescharacteristic
72C22×C8×C139C2311yescharacteristic
73C22×C8×C139C2311yescharacteristic
74#127×C139—22no—
75#127×C139C2×C414yes—
76#124×C139—28no—
77#124×C139—22no—
78#124×C139—22no—
79#124×C139C2×C414yes—
80#124×C139C2×C414yes—
81#123×C139—28no—
82#123×C139—28no—
83C4×Q8×C139—22no—
84C4×Q8×C139C2×C414yes—
85C4×Q8×C139C2×C414yes—
86C4×Q8×C139D414yes—
87C4×D4×C139—28no—
88C4×D4×C139—22no—
89C4×D4×C139—22no—
90C4×D4×C139C2×C414yes—
91C4×D4×C139C2×C414yes—
92C2×C4⋊C4×C139—21no—
93C2×C4⋊C4×C139—21no—
94C2×C4⋊C4×C139—21no—
95C2×C4⋊C4×C139D411yescharacteristic
96C2×C4⋊C4×C139D411yescharacteristic
97C2×C4⋊C4×C139D411yescharacteristic
98C2×C4⋊C4×C139C2311yescharacteristic
99C2×C4⋊C4×C139C2311yescharacteristic
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C4⋊C4×C139C2311yescharacteristic
102C2×C4⋊C4×C139C2311yescharacteristic
103C2×C22⋊C4×C139—21no—
104C2×C22⋊C4×C139—21no—
105C2×C22⋊C4×C139—21no—
106C2×C22⋊C4×C139—21no—
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
109C2×C42×C139—21no—
110C2×C42×C139—21no—
111C2×C42×C139—21no—
112C2×C42×C139—21no—
113C2×C42×C139C2311yescharacteristic
114C2×C42×C139C2311yescharacteristic
115C2×C42×C139C2311yescharacteristic
116C4⋊C8×C139—22no—
117C4⋊C8×C139—22no—
118C4⋊C8×C139—22no—
119#103×C139—22no—
120#103×C139—22no—
121#103×C139—41no—
122#103×C139—41no—
123#102×C139—22no—
124#102×C139—22no—
125#102×C139—22no—
126#102×C139—22no—
127#102×C139—41no—
128#102×C139—41no—
129#102×C139—41no—
130#102×C139—41no—
131#97×C139—22no—
132#97×C139—22no—
133C4×C8×C139—22no—
134#95×C139—21no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139—21no—
138#95×C139—21no—
139#95×C139—21no—
140#95×C139—21no—
141C24×C139—21no—
142C24×C139—21no—
143C2×Q8×C139—21no—
144C2×Q8×C139—21no—
145C2×Q8×C139—21no—
146C2×Q8×C139—21no—
147C2×Q8×C139—21no—
148C2×Q8×C139—41no—
149C2×Q8×C139—41no—
150C2×Q8×C139C22⋊C414yes—
151C2×Q8×C139C22×C412yes—
152C2×D4×C139—24no—
153C2×D4×C139—24no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
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—42no—
165C2×D4×C139—42no—
166C2×D4×C139—81no—
167C2×D4×C139—81no—
168C2×D4×C139C22×C412yes—
169C2×D4×C139C22×C412yes—
170C22×C4×C139—21no—
171C22×C4×C139—21no—
172C22×C4×C139—21no—
173C22×C4×C139—24no—
174C22×C4×C139—24no—
175C22×C4×C139—21no—
176C22×C4×C139—21no—
177C22×C4×C139—21no—
178C22×C4×C139—81no—
179C22×C4×C139—81no—
180C22×C4×C139—81no—
181C22×C4×C139—81no—
182C22×C4×C139C2×D411yescharacteristic
183C22×C4×C139C2×D411yescharacteristic
184C22×C4×C139C2×D411yescharacteristic
185C22×C4×C139C2×D411yescharacteristic
186C22×C4×C139C2×D411yescharacteristic
187C22×C4×C139C2×D411yescharacteristic
188C22×C4×C139C2411yescharacteristic
189C2×C8×C139—21no—
190C2×C8×C139—21no—
191C2×C8×C139—21no—
192C2×C8×C139—21no—
193C2×C8×C139—21no—
194C2×C8×C139—21no—
195C2×C8×C139—21no—
196C2×C8×C139—21no—
197C2×C8×C139—21no—
198C2×C8×C139—21no—
199C2×C8×C139—21no—
200C2×C8×C139#4112yes—
201C4⋊C4×C139—24no—
202C4⋊C4×C139—21no—
203C4⋊C4×C139—21no—
204C4⋊C4×C139—21no—
205C4⋊C4×C139—21no—
206C4⋊C4×C139—21no—
207C4⋊C4×C139—21no—
208C4⋊C4×C139—21no—
209C4⋊C4×C139—21no—
210C4⋊C4×C139—42no—
211C4⋊C4×C139—81no—
212C4⋊C4×C139C22⋊C414yes—
213C4⋊C4×C139C22⋊C414yes—
214C4⋊C4×C139C22⋊C414yes—
215C4⋊C4×C139C22×C412yes—
216C4⋊C4×C139#4112yes—
217C22⋊C4×C139—24no—
218C22⋊C4×C139—24no—
219C22⋊C4×C139—24no—
220C22⋊C4×C139—24no—
221C22⋊C4×C139—24no—
222C22⋊C4×C139—24no—
223C42×C139—24no—
224C42×C139—42no—
225C42×C139—81no—
226C42×C139—81no—
227C42×C139C22×C412yes—
228C42×C139C22×C412yes—
229C42×C139C22×C412yes—
230C42×C139C2×D412yes—
231C42×C139C2×D412yes—
232C42×C139C2×D412yes—
233C23×C139—22no—
234C23×C139—22no—
235C23×C139—41no—
236C23×C139—41no—
237C23×C139—41no—
238C23×C139—41no—
239C23×C139—41no—
240C23×C139—41no—
241C23×C139—41no—
242C23×C139—41no—
243C23×C139—41no—
244C23×C139—41no—
245C23×C139—41no—
246C23×C139—41no—
247C23×C139C22×D411yescharacteristic
248Q8×C139—22no—
249Q8×C139—22no—
250Q8×C139—44no—
251Q8×C139—41no—
252Q8×C139—41no—
253D4×C139—22no—
254D4×C139—22no—
255D4×C139—22no—
256D4×C139—22no—
257D4×C139—48no—
258D4×C139—41no—
259D4×C139—41no—
260D4×C139—41no—
261D4×C139—41no—
262D4×C139—84no—
263C2×C4×C139—21no—
264C2×C4×C139—21no—
265C2×C4×C139—21no—
266C2×C4×C139—21no—
267C2×C4×C139—21no—
268C2×C4×C139—21no—
269C2×C4×C139—21no—
270C2×C4×C139—21no—
271C2×C4×C139—21no—
272C2×C4×C139—21no—
273C2×C4×C139—21no—
274C2×C4×C139—21no—
275C2×C4×C139—22no—
276C2×C4×C139—22no—
277C2×C4×C139—22no—
278C2×C4×C139—41no—
279C2×C4×C139—41no—
280C2×C4×C139—41no—
281C2×C4×C139—41no—
282C2×C4×C139—41no—
283C2×C4×C139—41no—
284C2×C4×C139—41no—
285C2×C4×C139—41no—
286C2×C4×C139—41no—
287C2×C4×C139—41no—
288C2×C4×C139—41no—
289C2×C4×C139—41no—
290C2×C4×C139—41no—
291C2×C4×C139—41no—
292C2×C4×C139—41no—
293C2×C4×C139—84no—
294C2×C4×C139—84no—
295C2×C4×C139C2×C22⋊C412yes—
296C2×C4×C139C2×C22⋊C412yes—
297C2×C4×C139C2×C22⋊C412yes—
298C2×C4×C139C2×C22⋊C412yes—
299C2×C4×C139C2×C22⋊C412yes—
300C2×C4×C139C2×C22⋊C412yes—
301C2×C4×C139C23×C411yescharacteristic
302C2×C4×C139C22×D411yescharacteristic
303C2×C4×C139C2×#4111yescharacteristic
304C2×C4×C139C2×#4111yescharacteristic
305C2×C4×C139H(5,𝔽2)11yescharacteristic
306C2×C4×C1392−1+411yescharacteristic
307C8×C139—22no—
308C8×C139—41no—
309C8×C139—41no—
310C8×C139—41no—
311C22×C139—42no—
312C22×C139—42no—
313C22×C139—42no—
314C22×C139—42no—
315C22×C139—42no—
316C22×C139—42no—
317C22×C139—81no—
318C22×C139—81no—
319C22×C139—81no—
320C22×C139—81no—
321C22×C139—81no—
322C22×C139—81no—
323C22×C139—81no—
324C22×C139—81no—
325C22×C139C22×C22⋊C411yescharacteristic
326C22×C139#54811yescharacteristic
327C22×C139#55011yescharacteristic
328C22×C139#57511yescharacteristic
329C22×C139#57511yescharacteristic
330C22×C139#57611yescharacteristic
331C22×C139#57711yescharacteristic
332C4×C139—22no—
333C4×C139—22no—
334C4×C139—22no—
335C4×C139—22no—
336C4×C139—22no—
337C4×C139—22no—
338C4×C139—42no—
339C4×C139—42no—
340C4×C139—42no—
341C4×C139—81no—
342C4×C139—81no—
343C4×C139—81no—
344C4×C139C4×#4111yescharacteristic
345C4×C139#52011yescharacteristic
346C4×C139#54811yescharacteristic
347C4×C139#55011yescharacteristic
348C2×C139—82no—
349C2×C139—82no—
350C2×C139#234111yescharacteristic
351C2×C139#289611yescharacteristic
352C2×C139#289711yescharacteristic
353C2×C139#337011yescharacteristic
354C2×C139#337111yescharacteristic
355C2×C139#340111yescharacteristic
356C2×C139#340311yescharacteristic
357#22549C13911yesmaximal, characteristic, direct product factor, Sylow
358C139#2254911yescharacteristic, direct product factor, Sylow
359C2×#559C2×C13911yescharacteristic
360C2×#446C2×C13911yescharacteristic, complemented
361#2355C2×C13911yescharacteristic, complemented
362#1983C2×C13911yescharacteristic, complemented
363#1983C2×C13911yescharacteristic, complemented
364#1982C2×C13911yescharacteristic
365#1961C2×C13911yescharacteristic
366#1959C2×C13911yescharacteristic, complemented
367#1958C2×C13911yescharacteristic, complemented
368#1805C2×C13911yescharacteristic, complemented
369#1804C2×C13911yescharacteristic, complemented
370#1802C2×C13911yescharacteristic, complemented
371#1763C2×C13911yescharacteristic, complemented
372#1762C2×C13911yescharacteristic, complemented
373C4×#102C2×C13911yescharacteristic, complemented
374#559—24no—
375#559C4×C13918yescomplemented
376C2×#127C22×C13911yescharacteristic
377C2×#124—21no—
378C2×#124C22×C13911yescharacteristic
379C2×#124C22×C13911yescharacteristic
380C2×#123—21no—
381C2×#123—21no—
382C2×C4×Q8C22×C13911yescharacteristic
383C2×C4×Q8C22×C13911yescharacteristic
384C2×C4×D4—21no—
385C2×C4×D4C22×C13911yescharacteristic
386C2×C4×D4C22×C13911yescharacteristic
387#446—24no—
388C2×C4⋊C8C22×C13911yescharacteristic
389C2×C4⋊C8C22×C13911yescharacteristic
390C2×C4⋊C8C22×C13911yescharacteristic
391C2×#103C22×C13911yescharacteristic
392C2×#103C22×C13911yescharacteristic
393C2×#103C22×C13911yescharacteristic
394C2×#103C22×C13911yescharacteristic
395C2×#102C22×C13911yescharacteristic
396C2×#102C22×C13911yescharacteristic
397C2×#102C22×C13911yescharacteristic
398C2×#102C22×C13911yescharacteristic
399C2×#102C22×C13911yescharacteristic
400C2×#102C22×C13911yescharacteristic
401C2×#102C22×C13911yescharacteristic
402C2×#102C22×C13911yescharacteristic
403C2×#97C22×C13911yescharacteristic
404C2×#97C22×C13911yescharacteristic
405C2×C4×C8C22×C13911yescharacteristic
406#391—21no—
407#387—21no—
408#387—21no—
409#384C22×C13911yescharacteristic
410#382C22×C13911yescharacteristic
411#382C22×C13911yescharacteristic
412C4×C4⋊C4—21no—
413C4×C4⋊C4C22×C13911yescharacteristic
414C4×C4⋊C4C22×C13911yescharacteristic
415C4×C4⋊C4C22×C13911yescharacteristic
416#340C22×C13911yescharacteristic
417#340C22×C13911yescharacteristic
418#340C22×C13911yescharacteristic
419#340C22×C13911yescharacteristic
420C22×Q8D4×C13911yescharacteristic
421C22×Q8C23×C13911yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C23×C13911yescharacteristic
425C22×D4C23×C13911yescharacteristic
426C23×C4—21no—
427C23×C4—21no—
428C22×C8C23×C13911yescharacteristic
429C22×C8C23×C13911yescharacteristic
430C22×C8C23×C13911yescharacteristic
431C22×C8C23×C13911yescharacteristic
432#127—22no—
433#127C2×C4×C13914yes—
434#124—28no—
435#124—22no—
436#124—22no—
437#124C2×C4×C13914yes—
438#124C2×C4×C13914yes—
439#123—28no—
440#123—28no—
441C4×Q8—22no—
442C4×Q8C2×C4×C13914yes—
443C4×Q8C2×C4×C13914yes—
444C4×Q8D4×C13914yes—
445C4×D4—28no—
446C4×D4—22no—
447C4×D4—22no—
448C4×D4C2×C4×C13914yes—
449C4×D4C2×C4×C13914yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4D4×C13911yescharacteristic
454C2×C4⋊C4D4×C13911yescharacteristic
455C2×C4⋊C4D4×C13911yescharacteristic
456C2×C4⋊C4C23×C13911yescharacteristic
457C2×C4⋊C4C23×C13911yescharacteristic
458C2×C4⋊C4C23×C13911yescharacteristic
459C2×C4⋊C4C23×C13911yescharacteristic
460C2×C4⋊C4C23×C13911yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42C23×C13911yescharacteristic
472C2×C42C23×C13911yescharacteristic
473C2×C42C23×C13911yescharacteristic
474C4⋊C8—22no—
475C4⋊C8—22no—
476C4⋊C8—22no—
477#103—22no—
478#103—22no—
479#103—41no—
480#103—41no—
481#102—22no—
482#102—22no—
483#102—22no—
484#102—22no—
485#102—41no—
486#102—41no—
487#102—41no—
488#102—41no—
489#97—22no—
490#97—22no—
491C4×C8—22no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24—21no—
500C24—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8C22⋊C4×C13914yes—
509C2×Q8C22×C4×C13912yes—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—42no—
523C2×D4—42no—
524C2×D4—81no—
525C2×D4—81no—
526C2×D4C22×C4×C13912yes—
527C2×D4C22×C4×C13912yes—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—81no—
537C22×C4—81no—
538C22×C4—81no—
539C22×C4—81no—
540C22×C4C2×D4×C13911yescharacteristic
541C22×C4C2×D4×C13911yescharacteristic
542C22×C4C2×D4×C13911yescharacteristic
543C22×C4C2×D4×C13911yescharacteristic
544C22×C4C2×D4×C13911yescharacteristic
545C22×C4C2×D4×C13911yescharacteristic
546C22×C4C24×C13911yescharacteristic
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8#41×C13912yes—
559C4⋊C4—24no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—81no—
570C4⋊C4C22⋊C4×C13914yes—
571C4⋊C4C22⋊C4×C13914yes—
572C4⋊C4C22⋊C4×C13914yes—
573C4⋊C4C22×C4×C13912yes—
574C4⋊C4#41×C13912yes—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—24no—
581C42—24no—
582C42—42no—
583C42—81no—
584C42—81no—
585C42C22×C4×C13912yes—
586C42C22×C4×C13912yes—
587C42C22×C4×C13912yes—
588C42C2×D4×C13912yes—
589C42C2×D4×C13912yes—
590C42C2×D4×C13912yes—
591C23—22no—
592C23—22no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C22×D4×C13911yescharacteristic
606Q8—22no—
607Q8—22no—
608Q8—44no—
609Q8—41no—
610Q8—41no—
611D4—22no—
612D4—22no—
613D4—22no—
614D4—22no—
615D4—48no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—84no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—84no—
652C2×C4—84no—
653C2×C4C2×C22⋊C4×C13912yes—
654C2×C4C2×C22⋊C4×C13912yes—
655C2×C4C2×C22⋊C4×C13912yes—
656C2×C4C2×C22⋊C4×C13912yes—
657C2×C4C2×C22⋊C4×C13912yes—
658C2×C4C2×C22⋊C4×C13912yes—
659C2×C4C23×C4×C13911yescharacteristic
660C2×C4C22×D4×C13911yescharacteristic
661C2×C4C2×#41×C13911yescharacteristic
662C2×C4C2×#41×C13911yescharacteristic
663C2×C4H(5,𝔽2)×C13911yescharacteristic
664C2×C42−1+4×C13911yescharacteristic
665C8—22no—
666C8—41no—
667C8—41no—
668C8—41no—
669C22—42no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—42no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C22×C22⋊C4×C13911yescharacteristic
684C22#548×C13911yescharacteristic
685C22#550×C13911yescharacteristic
686C22#575×C13911yescharacteristic
687C22#575×C13911yescharacteristic
688C22#576×C13911yescharacteristic
689C22#577×C13911yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—22no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4C4×#41×C13911yescharacteristic
703C4#520×C13911yescharacteristic
704C4#548×C13911yescharacteristic
705C4#550×C13911yescharacteristic
706C2—82no—
707C2—82no—
708C2#2341×C13911yescharacteristic
709C2#2896×C13911yescharacteristic
710C2#2897×C13911yescharacteristic
711C2#3370×C13911yescharacteristic
712C2#3371×C13911yescharacteristic
713C2#3401×C13911yescharacteristic
714C2#3403×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC2×#127×C139C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C4×Q8×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#446×C139C2semidirect
3. #2355×C139C2semidirect
4. #1983×C139C2semidirect
5. #1983×C139C2semidirect
8. #1959×C139C2semidirect
9. #1958×C139C2semidirect
10. #1805×C139C2semidirect
11. #1804×C139C2semidirect
12. #1802×C139C2semidirect
13. #1763×C139C2semidirect
14. #1762×C139C2semidirect
15. C4×#102×C139C2semidirect
17. #559×C139C4semidirect
357. #22549C139direct (N × H)
358. C139#22549direct (N × H)
360. C2×#446C2×C139semidirect
361. #2355C2×C139semidirect
362. #1983C2×C139semidirect
363. #1983C2×C139semidirect
366. #1959C2×C139semidirect
367. #1958C2×C139semidirect
368. #1805C2×C139semidirect
369. #1804C2×C139semidirect
370. #1802C2×C139semidirect
371. #1763C2×C139semidirect
372. #1762C2×C139semidirect
373. C4×#102C2×C139semidirect
375. #559C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#559×C1392
C2×#446×C1392
#2355×C1392
#1983×C1392
#1982×C1392
#1961×C1392
#1959×C1392
#1958×C1392
#1805×C1392
#1804×C1392
#1802×C1392
#1763×C1392
#1762×C1392
C4×#102×C1392
#22549139