Finite Group Databasebeta

← C139×#24008 #48018604

Subgroups — C139×#24008 #48018604

Order 35584.

1448 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C139C211yesmaximal, characteristic
2C2×#485×C139C211yesmaximal, characteristic, complemented
3C2×#482×C139C211yesmaximal, characteristic, complemented
4#2280×C139C211yesmaximal, characteristic, complemented
5#2036×C139C211yesmaximal, characteristic, complemented
6#2035×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#1875×C139C211yesmaximal, characteristic, complemented
10#1873×C139C211yesmaximal, characteristic, complemented
11#1854×C139C211yesmaximal, characteristic, complemented
12#1854×C139C211yesmaximal, characteristic, complemented
13#1788×C139C211yesmaximal, characteristic, complemented
14#1788×C139C211yesmaximal, characteristic, complemented
15#1779×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C24×C4×C139C2211yescharacteristic
18#525×C139—24no—
19#525×C139—24no—
20C2×#123×C139—21no—
21C2×C22⋊Q8×C139C2211yescharacteristic
22C2×C22⋊Q8×C139C2211yescharacteristic
23C2×#121×C139C2211yescharacteristic
24C2×#121×C139C2211yescharacteristic
25C2×#120×C139—21no—
26C2×C4×D4×C139—21no—
27C2×C4×D4×C139—21no—
28C2×#117×C139C2211yescharacteristic
29C2×#117×C139C2211yescharacteristic
30C2×#117×C139C2211yescharacteristic
31#485×C139—24no—
32#482×C139—24no—
33C2×#107×C139C2211yescharacteristic, complemented
34C2×#107×C139C2211yescharacteristic, complemented
35C2×#106×C139C2211yescharacteristic, complemented
36C2×#106×C139C2211yescharacteristic, complemented
37C2×#103×C139C2211yescharacteristic, complemented
38C2×#103×C139C2211yescharacteristic, complemented
39C2×#103×C139C2211yescharacteristic, complemented
40C2×#103×C139C2211yescharacteristic, complemented
41C2×#102×C139C2211yescharacteristic, complemented
42C2×#102×C139C2211yescharacteristic, complemented
43C2×#102×C139C2211yescharacteristic, complemented
44C2×#102×C139C2211yescharacteristic, complemented
45C2×C22⋊C8×C139C2211yescharacteristic
46C2×C22⋊C8×C139C2211yescharacteristic
47C2×C22⋊C8×C139C2211yescharacteristic
48C2×C22⋊C8×C139C2211yescharacteristic
49C2×C22⋊C8×C139C2211yescharacteristic
50C2×C22⋊C8×C139C2211yescharacteristic
51#381×C139—21no—
52#380×C139C2211yescharacteristic
53#380×C139C2211yescharacteristic
54#380×C139C2211yescharacteristic
55#380×C139C2211yescharacteristic
56#379×C139—21no—
57C4×C22⋊C4×C139—21no—
58C4×C22⋊C4×C139—21no—
59#340×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63C25×C139D411yescharacteristic
64C2×#41×C139—22no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—41no—
69C2×#41×C139—41no—
70C22×Q8×C139C2311yescharacteristic
71C22×D4×C139—21no—
72C22×D4×C139—21no—
73C22×D4×C139—21no—
74C22×D4×C139C2311yescharacteristic
75C23×C4×C139—21no—
76C23×C4×C139—22no—
77C23×C4×C139—22no—
78C23×C4×C139—22no—
79C23×C4×C139—22no—
80C23×C4×C139—41no—
81C23×C4×C139—41no—
82C23×C4×C139D411yescharacteristic
83C23×C4×C139D411yescharacteristic
84C23×C4×C139D411yescharacteristic
85C23×C4×C139C2311yescharacteristic
86C23×C4×C139C2311yescharacteristic
87C23×C4×C139C2311yescharacteristic
88C22×C8×C139C2311yescharacteristic
89C22×C8×C139C2311yescharacteristic
90C22×C8×C139C2311yescharacteristic
91C22×C8×C139C2311yescharacteristic
92#123×C139—28no—
93C22⋊Q8×C139—22no—
94C22⋊Q8×C139—22no—
95C22⋊Q8×C139—22no—
96C22⋊Q8×C139D414yes—
97#121×C139—22no—
98#121×C139—22no—
99#121×C139—22no—
100#121×C139D414yes—
101#120×C139—28no—
102C4×D4×C139—28no—
103C4×D4×C139—28no—
104#117×C139—22no—
105#117×C139—22no—
106#117×C139—22no—
107#117×C139—22no—
108#117×C139—41no—
109#117×C139—41no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139—21no—
112C2×C4⋊C4×C139C2311yescharacteristic
113C2×C4⋊C4×C139C2311yescharacteristic
114C2×C4⋊C4×C139C2311yescharacteristic
115C2×C4⋊C4×C139C2311yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C22⋊C4×C139—21no—
119C2×C22⋊C4×C139—21no—
120C2×C22⋊C4×C139—21no—
121C2×C22⋊C4×C139—21no—
122C2×C22⋊C4×C139—21no—
123C2×C22⋊C4×C139—21no—
124C2×C22⋊C4×C139—21no—
125C2×C22⋊C4×C139—21no—
126C2×C22⋊C4×C139—21no—
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—21no—
129C2×C42×C139—21no—
130C2×C42×C139—21no—
131C2×C42×C139—21no—
132#107×C139—22no—
133#107×C139—22no—
134#106×C139—22no—
135#106×C139—22no—
136#103×C139—22no—
137#103×C139—22no—
138#103×C139—41no—
139#103×C139—41no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—41no—
143#102×C139—41no—
144C22⋊C8×C139—22no—
145C22⋊C8×C139—22no—
146C22⋊C8×C139—22no—
147C22⋊C8×C139—22no—
148C22⋊C8×C139—41no—
149C22⋊C8×C139—41no—
150#95×C139—21no—
151#95×C139—21no—
152#95×C139—21no—
153#95×C139—21no—
154C24×C139—22no—
155C24×C139—22no—
156C24×C139—22no—
157C24×C139—21no—
158C24×C139—41no—
159C24×C139—41no—
160C24×C139—41no—
161C24×C139—41no—
162C24×C139C2×D411yescharacteristic
163C24×C139C2×D411yescharacteristic
164C24×C139C2×D411yescharacteristic
165#41×C139—44no—
166#41×C139—44no—
167#41×C139—44no—
168#41×C139—44no—
169C2×Q8×C139—21no—
170C2×Q8×C139—21no—
171C2×Q8×C139—21no—
172C2×Q8×C139—21no—
173C2×Q8×C139—21no—
174C2×Q8×C139C2×D412yes—
175C2×D4×C139—24no—
176C2×D4×C139—24no—
177C2×D4×C139—24no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—21no—
183C2×D4×C139—42no—
184C2×D4×C139—42no—
185C2×D4×C139—42no—
186C2×D4×C139—42no—
187C2×D4×C139—42no—
188C2×D4×C139—42no—
189C2×D4×C139C2×D412yes—
190C22×C4×C139—21no—
191C22×C4×C139—21no—
192C22×C4×C139—21no—
193C22×C4×C139—21no—
194C22×C4×C139—21no—
195C22×C4×C139—21no—
196C22×C4×C139—21no—
197C22×C4×C139—21no—
198C22×C4×C139—24no—
199C22×C4×C139—22no—
200C22×C4×C139—22no—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—22no—
205C22×C4×C139—22no—
206C22×C4×C139—22no—
207C22×C4×C139—22no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—21no—
211C22×C4×C139—21no—
212C22×C4×C139—21no—
213C22×C4×C139—21no—
214C22×C4×C139—21no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139—41no—
219C22×C4×C139—41no—
220C22×C4×C139—41no—
221C22×C4×C139—44no—
222C22×C4×C139—44no—
223C22×C4×C139—44no—
224C22×C4×C139—44no—
225C22×C4×C139—42no—
226C22×C4×C139—42no—
227C22×C4×C139C2×D411yescharacteristic
228C22×C4×C139C2×D411yescharacteristic
229C22×C4×C139C2×D412yes—
230C22×C4×C139C2×D412yes—
231C22×C4×C139C2×D411yescharacteristic
232C22×C4×C139#4112yes—
233C22×C4×C139#4112yes—
234C22×C4×C139C2411yescharacteristic
235C2×C8×C139—21no—
236C2×C8×C139—21no—
237C2×C8×C139—21no—
238C2×C8×C139—21no—
239C2×C8×C139—21no—
240C2×C8×C139—21no—
241C2×C8×C139—21no—
242C2×C8×C139—21no—
243C2×C8×C139—21no—
244C2×C8×C139—21no—
245C2×C8×C139—21no—
246C2×C8×C139—21no—
247C4⋊C4×C139—24no—
248C4⋊C4×C139—24no—
249C4⋊C4×C139—21no—
250C4⋊C4×C139—21no—
251C4⋊C4×C139—21no—
252C4⋊C4×C139—21no—
253C4⋊C4×C139—21no—
254C4⋊C4×C139—21no—
255C4⋊C4×C139—21no—
256C4⋊C4×C139—21no—
257C4⋊C4×C139—21no—
258C4⋊C4×C139—21no—
259C4⋊C4×C139C2×D412yes—
260C4⋊C4×C139C2×D412yes—
261C22⋊C4×C139—24no—
262C22⋊C4×C139—24no—
263C22⋊C4×C139—24no—
264C22⋊C4×C139—24no—
265C22⋊C4×C139—24no—
266C22⋊C4×C139—42no—
267C22⋊C4×C139—42no—
268C22⋊C4×C139—42no—
269C22⋊C4×C139—42no—
270C22⋊C4×C139—42no—
271C22⋊C4×C139—42no—
272C42×C139—24no—
273C42×C139—42no—
274C42×C139—42no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—21no—
279C23×C139—21no—
280C23×C139—21no—
281C23×C139—21no—
282C23×C139—21no—
283C23×C139—21no—
284C23×C139—21no—
285C23×C139—21no—
286C23×C139—21no—
287C23×C139—21no—
288C23×C139—21no—
289C23×C139—21no—
290C23×C139—21no—
291C23×C139—21no—
292C23×C139—21no—
293C23×C139—22no—
294C23×C139—44no—
295C23×C139—44no—
296C23×C139—44no—
297C23×C139—44no—
298C23×C139—44no—
299C23×C139—44no—
300C23×C139—44no—
301C23×C139—41no—
302C23×C139—41no—
303C23×C139—41no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—41no—
307C23×C139#12012yes—
308C23×C139#12312yes—
309C23×C139#13512yes—
310C23×C139C22×D411yescharacteristic
311Q8×C139—22no—
312Q8×C139—22no—
313Q8×C139—41no—
314Q8×C139—41no—
315D4×C139—22no—
316D4×C139—22no—
317D4×C139—48no—
318D4×C139—48no—
319D4×C139—48no—
320D4×C139—41no—
321D4×C139—41no—
322C2×C4×C139—21no—
323C2×C4×C139—21no—
324C2×C4×C139—21no—
325C2×C4×C139—21no—
326C2×C4×C139—22no—
327C2×C4×C139—22no—
328C2×C4×C139—22no—
329C2×C4×C139—22no—
330C2×C4×C139—22no—
331C2×C4×C139—22no—
332C2×C4×C139—22no—
333C2×C4×C139—22no—
334C2×C4×C139—22no—
335C2×C4×C139—22no—
336C2×C4×C139—21no—
337C2×C4×C139—22no—
338C2×C4×C139—21no—
339C2×C4×C139—21no—
340C2×C4×C139—44no—
341C2×C4×C139—44no—
342C2×C4×C139—44no—
343C2×C4×C139—48no—
344C2×C4×C139—41no—
345C2×C4×C139—41no—
346C2×C4×C139—41no—
347C2×C4×C139—41no—
348C2×C4×C139—41no—
349C2×C4×C139—41no—
350C2×C4×C139—41no—
351C2×C4×C139—41no—
352C2×C4×C139—41no—
353C2×C4×C139—41no—
354C2×C4×C139—41no—
355C2×C4×C139—41no—
356C2×C4×C139—41no—
357C2×C4×C139—41no—
358C2×C4×C139—41no—
359C2×C4×C139—41no—
360C2×C4×C139—41no—
361C2×C4×C139—41no—
362C2×C4×C139—41no—
363C2×C4×C139—41no—
364C2×C4×C139—41no—
365C2×C4×C139—41no—
366C2×C4×C139#12012yes—
367C2×C4×C139#12312yes—
368C2×C4×C139C22×D411yescharacteristic
369C2×C4×C139C22×D411yescharacteristic
370C2×C4×C139C2×#4111yescharacteristic
371C2×C4×C139C2×#4111yescharacteristic
372C2×C4×C139H(5,𝔽2)11yescharacteristic
373C2×C4×C139H(5,𝔽2)11yescharacteristic
374C8×C139—41no—
375C8×C139—41no—
376C8×C139—41no—
377C8×C139—41no—
378C22×C139—22no—
379C22×C139—22no—
380C22×C139—22no—
381C22×C139—22no—
382C22×C139—22no—
383C22×C139—22no—
384C22×C139—22no—
385C22×C139—22no—
386C22×C139—22no—
387C22×C139—416no—
388C22×C139—41no—
389C22×C139—41no—
390C22×C139—41no—
391C22×C139—41no—
392C22×C139—41no—
393C22×C139—41no—
394C22×C139—41no—
395C22×C139—41no—
396C22×C139—41no—
397C22×C139—41no—
398C22×C139—41no—
399C22×C139—41no—
400C22×C139—42no—
401C22×C139—42no—
402C22×C139—42no—
403C22×C139—81no—
404C22×C139—81no—
405C22×C139—81no—
406C22×C139—81no—
407C22×C139C2×#12011yescharacteristic
408C22×C139C2×#12311yescharacteristic
409C22×C139#53411yescharacteristic
410C22×C139C2×#13511yescharacteristic
411C22×C139#57511yescharacteristic
412C22×C139#57511yescharacteristic
413C22×C139#57511yescharacteristic
414C4×C139—22no—
415C4×C139—22no—
416C4×C139—41no—
417C4×C139—42no—
418C4×C139—42no—
419C4×C139—42no—
420C4×C139—81no—
421C4×C139—81no—
422C4×C139—81no—
423C4×C139—81no—
424C4×C139#54611yescharacteristic
425C4×C139#54611yescharacteristic
426C4×C139#54611yescharacteristic
427C4×C139#54611yescharacteristic
428C2×C139—42no—
429C2×C139—42no—
430C2×C139—42no—
431C2×C139—82no—
432C2×C139#240511yescharacteristic
433C2×C139#300211yescharacteristic
434C2×C139#300511yescharacteristic
435C2×C139#309111yescharacteristic
436C2×C139#309311yescharacteristic
437C2×C139#319111yescharacteristic
438C2×C139#319711yescharacteristic
439#24008C13911yesmaximal, characteristic, direct product factor, Sylow
440C139#2400811yescharacteristic, direct product factor, Sylow
441C2×#525C2×C13911yescharacteristic
442C2×#485C2×C13911yescharacteristic, complemented
443C2×#482C2×C13911yescharacteristic, complemented
444#2280C2×C13911yescharacteristic, complemented
445#2036C2×C13911yescharacteristic, complemented
446#2035C2×C13911yescharacteristic, complemented
447#2034C2×C13911yescharacteristic, complemented
448#2033C2×C13911yescharacteristic, complemented
449#1875C2×C13911yescharacteristic, complemented
450#1873C2×C13911yescharacteristic, complemented
451#1854C2×C13911yescharacteristic, complemented
452#1854C2×C13911yescharacteristic, complemented
453#1788C2×C13911yescharacteristic, complemented
454#1788C2×C13911yescharacteristic, complemented
455#1779C2×C13911yescharacteristic, complemented
456C22×#41C22×C13911yescharacteristic
457C24×C4C22×C13911yescharacteristic
458#525—24no—
459#525—24no—
460C2×#123—21no—
461C2×C22⋊Q8C22×C13911yescharacteristic
462C2×C22⋊Q8C22×C13911yescharacteristic
463C2×#121C22×C13911yescharacteristic
464C2×#121C22×C13911yescharacteristic
465C2×#120—21no—
466C2×C4×D4—21no—
467C2×C4×D4—21no—
468C2×#117C22×C13911yescharacteristic
469C2×#117C22×C13911yescharacteristic
470C2×#117C22×C13911yescharacteristic
471#485—24no—
472#482—24no—
473C2×#107C22×C13911yescharacteristic, complemented
474C2×#107C22×C13911yescharacteristic, complemented
475C2×#106C22×C13911yescharacteristic, complemented
476C2×#106C22×C13911yescharacteristic, complemented
477C2×#103C22×C13911yescharacteristic, complemented
478C2×#103C22×C13911yescharacteristic, complemented
479C2×#103C22×C13911yescharacteristic, complemented
480C2×#103C22×C13911yescharacteristic, complemented
481C2×#102C22×C13911yescharacteristic, complemented
482C2×#102C22×C13911yescharacteristic, complemented
483C2×#102C22×C13911yescharacteristic, complemented
484C2×#102C22×C13911yescharacteristic, complemented
485C2×C22⋊C8C22×C13911yescharacteristic
486C2×C22⋊C8C22×C13911yescharacteristic
487C2×C22⋊C8C22×C13911yescharacteristic
488C2×C22⋊C8C22×C13911yescharacteristic
489C2×C22⋊C8C22×C13911yescharacteristic
490C2×C22⋊C8C22×C13911yescharacteristic
491#381—21no—
492#380C22×C13911yescharacteristic
493#380C22×C13911yescharacteristic
494#380C22×C13911yescharacteristic
495#380C22×C13911yescharacteristic
496#379—21no—
497C4×C22⋊C4—21no—
498C4×C22⋊C4—21no—
499#340C22×C13911yescharacteristic, complemented
500#340C22×C13911yescharacteristic, complemented
501#340C22×C13911yescharacteristic, complemented
502#340C22×C13911yescharacteristic, complemented
503C25D4×C13911yescharacteristic
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8C23×C13911yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4C23×C13911yescharacteristic
515C23×C4—21no—
516C23×C4—22no—
517C23×C4—22no—
518C23×C4—22no—
519C23×C4—22no—
520C23×C4—41no—
521C23×C4—41no—
522C23×C4D4×C13911yescharacteristic
523C23×C4D4×C13911yescharacteristic
524C23×C4D4×C13911yescharacteristic
525C23×C4C23×C13911yescharacteristic
526C23×C4C23×C13911yescharacteristic
527C23×C4C23×C13911yescharacteristic
528C22×C8C23×C13911yescharacteristic
529C22×C8C23×C13911yescharacteristic
530C22×C8C23×C13911yescharacteristic
531C22×C8C23×C13911yescharacteristic
532#123—28no—
533C22⋊Q8—22no—
534C22⋊Q8—22no—
535C22⋊Q8—22no—
536C22⋊Q8D4×C13914yes—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C13914yes—
541#120—28no—
542C4×D4—28no—
543C4×D4—28no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—41no—
549#117—41no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4C23×C13911yescharacteristic
553C2×C4⋊C4C23×C13911yescharacteristic
554C2×C4⋊C4C23×C13911yescharacteristic
555C2×C4⋊C4C23×C13911yescharacteristic
556C2×C4⋊C4C23×C13911yescharacteristic
557C2×C4⋊C4C23×C13911yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42—21no—
572#107—22no—
573#107—22no—
574#106—22no—
575#106—22no—
576#103—22no—
577#103—22no—
578#103—41no—
579#103—41no—
580#102—22no—
581#102—22no—
582#102—41no—
583#102—41no—
584C22⋊C8—22no—
585C22⋊C8—22no—
586C22⋊C8—22no—
587C22⋊C8—22no—
588C22⋊C8—41no—
589C22⋊C8—41no—
590#95—21no—
591#95—21no—
592#95—21no—
593#95—21no—
594C24—22no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—41no—
599C24—41no—
600C24—41no—
601C24—41no—
602C24C2×D4×C13911yescharacteristic
603C24C2×D4×C13911yescharacteristic
604C24C2×D4×C13911yescharacteristic
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8C2×D4×C13912yes—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—24no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4C2×D4×C13912yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—24no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4C2×D4×C13911yescharacteristic
668C22×C4C2×D4×C13911yescharacteristic
669C22×C4C2×D4×C13912yes—
670C22×C4C2×D4×C13912yes—
671C22×C4C2×D4×C13911yescharacteristic
672C22×C4#41×C13912yes—
673C22×C4#41×C13912yes—
674C22×C4C24×C13911yescharacteristic
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4C2×D4×C13912yes—
700C4⋊C4C2×D4×C13912yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C42—24no—
713C42—42no—
714C42—42no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23#120×C13912yes—
748C23#123×C13912yes—
749C23#135×C13912yes—
750C23C22×D4×C13911yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—41no—
754Q8—41no—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—48no—
759D4—48no—
760D4—41no—
761D4—41no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—48no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4#120×C13912yes—
807C2×C4#123×C13912yes—
808C2×C4C22×D4×C13911yescharacteristic
809C2×C4C22×D4×C13911yescharacteristic
810C2×C4C2×#41×C13911yescharacteristic
811C2×C4C2×#41×C13911yescharacteristic
812C2×C4H(5,𝔽2)×C13911yescharacteristic
813C2×C4H(5,𝔽2)×C13911yescharacteristic
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—416no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22C2×#120×C13911yescharacteristic
848C22C2×#123×C13911yescharacteristic
849C22#534×C13911yescharacteristic
850C22C2×#135×C13911yescharacteristic
851C22#575×C13911yescharacteristic
852C22#575×C13911yescharacteristic
853C22#575×C13911yescharacteristic
854C4—22no—
855C4—22no—
856C4—41no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—81no—
864C4#546×C13911yescharacteristic
865C4#546×C13911yescharacteristic
866C4#546×C13911yescharacteristic
867C4#546×C13911yescharacteristic
868C2—42no—
869C2—42no—
870C2—42no—
871C2—82no—
872C2#2405×C13911yescharacteristic
873C2#3002×C13911yescharacteristic
874C2#3005×C13911yescharacteristic
875C2#3091×C13911yescharacteristic
876C2#3093×C13911yescharacteristic
877C2#3191×C13911yescharacteristic
878C2#3197×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#525×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C24×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C139C2semidirect
3. C2×#482×C139C2semidirect
4. #2280×C139C2semidirect
5. #2036×C139C2semidirect
6. #2035×C139C2semidirect
7. #2034×C139C2semidirect
8. #2033×C139C2semidirect
9. #1875×C139C2semidirect
10. #1873×C139C2semidirect
11. #1854×C139C2semidirect
12. #1854×C139C2semidirect
13. #1788×C139C2semidirect
14. #1788×C139C2semidirect
15. #1779×C139C2semidirect
33. C2×#107×C139C22semidirect
34. C2×#107×C139C22semidirect
35. C2×#106×C139C22semidirect
36. C2×#106×C139C22semidirect
37. C2×#103×C139C22semidirect
38. C2×#103×C139C22semidirect
39. C2×#103×C139C22semidirect
40. C2×#103×C139C22semidirect
41. C2×#102×C139C22semidirect
42. C2×#102×C139C22semidirect
43. C2×#102×C139C22semidirect
44. C2×#102×C139C22semidirect
59. #340×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
439. #24008C139direct (N × H)
440. C139#24008direct (N × H)
442. C2×#485C2×C139semidirect
443. C2×#482C2×C139semidirect
444. #2280C2×C139semidirect
445. #2036C2×C139semidirect
446. #2035C2×C139semidirect
447. #2034C2×C139semidirect
448. #2033C2×C139semidirect
449. #1875C2×C139semidirect
450. #1873C2×C139semidirect
451. #1854C2×C139semidirect
452. #1854C2×C139semidirect
453. #1788C2×C139semidirect
454. #1788C2×C139semidirect
455. #1779C2×C139semidirect
473. C2×#107C22×C139semidirect
474. C2×#107C22×C139semidirect
475. C2×#106C22×C139semidirect
476. C2×#106C22×C139semidirect
477. C2×#103C22×C139semidirect
478. C2×#103C22×C139semidirect
479. C2×#103C22×C139semidirect
480. C2×#103C22×C139semidirect
481. C2×#102C22×C139semidirect
482. C2×#102C22×C139semidirect
483. C2×#102C22×C139semidirect
484. C2×#102C22×C139semidirect
499. #340C22×C139semidirect
500. #340C22×C139semidirect
501. #340C22×C139semidirect
502. #340C22×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1392
C2×#485×C1392
C2×#482×C1392
#2280×C1392
#2036×C1392
#2035×C1392
#2034×C1392
#2033×C1392
#1875×C1392
#1873×C1392
#1854×C1392
#1788×C1392
#1779×C1392
#24008139