Finite Group Databasebeta

← C139×#24017 #48018613

Subgroups — C139×#24017 #48018613

Order 35584.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C139C211yesmaximal, characteristic
2C2×#485×C139C211yesmaximal, characteristic, complemented
3C2×#482×C139C211yesmaximal, characteristic, complemented
4#2311×C139C211yesmaximal, characteristic, complemented
5#2036×C139C211yesmaximal, characteristic, complemented
6#2035×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#1874×C139C211yesmaximal, characteristic, complemented
10#1872×C139C211yesmaximal, characteristic, complemented
11#1853×C139C211yesmaximal, characteristic, complemented
12#1852×C139C211yesmaximal, characteristic, complemented
13#1788×C139C211yesmaximal, characteristic, complemented
14#1788×C139C211yesmaximal, characteristic, complemented
15#1780×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18#537×C139—24no—
19#537×C139—24no—
20C2×C22⋊Q8×C139—21no—
21C2×C22⋊Q8×C139C2211yescharacteristic
22C2×C22⋊Q8×C139C2211yescharacteristic
23C2×#121×C139—21no—
24C2×#121×C139—21no—
25C2×#121×C139—21no—
26C2×#121×C139C2211yescharacteristic
27C2×#121×C139C2211yescharacteristic
28C2×#117×C139C2211yescharacteristic
29C22×C4⋊C4×C139C2211yescharacteristic
30C22×C4⋊C4×C139C2211yescharacteristic
31#485×C139—24no—
32#482×C139—24no—
33C2×#107×C139C2211yescharacteristic
34C2×#107×C139C2211yescharacteristic
35C2×#106×C139C2211yescharacteristic
36C2×#106×C139C2211yescharacteristic
37C2×#103×C139C2211yescharacteristic
38C2×#103×C139C2211yescharacteristic
39C2×#103×C139C2211yescharacteristic
40C2×#103×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
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#391×C139—21no—
52#390×C139—21no—
53#386×C139—21no—
54#386×C139—21no—
55#380×C139C2211yescharacteristic
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic
58#380×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62#340×C139C2211yescharacteristic
63C2×#41×C139—22no—
64C2×#41×C139—22no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—22no—
69C2×#41×C139—22no—
70C2×#41×C139—22no—
71C2×#41×C139—41no—
72C2×#41×C139—41no—
73C2×#41×C139—41no—
74C2×#41×C139—41no—
75C22×Q8×C139D411yescharacteristic
76C22×Q8×C139C2311yescharacteristic
77C22×D4×C139—21no—
78C22×D4×C139—21no—
79C22×D4×C139—21no—
80C22×D4×C139D411yescharacteristic
81C22×D4×C139D411yescharacteristic
82C22×D4×C139D411yescharacteristic
83C22×D4×C139C2311yescharacteristic
84C23×C4×C139—21no—
85C23×C4×C139—21no—
86C23×C4×C139—21no—
87C23×C4×C139C2311yescharacteristic
88C23×C4×C139C2311yescharacteristic
89C23×C4×C139C2311yescharacteristic
90C22×C8×C139C2311yescharacteristic
91C22×C8×C139C2311yescharacteristic
92C22×C8×C139C2311yescharacteristic
93C22×C8×C139C2311yescharacteristic
94C22⋊Q8×C139—28no—
95C22⋊Q8×C139—22no—
96C22⋊Q8×C139—22no—
97C22⋊Q8×C139—22no—
98C22⋊Q8×C139D414yes—
99#121×C139—28no—
100#121×C139—28no—
101#121×C139—28no—
102#121×C139—22no—
103#121×C139—22no—
104#121×C139—22no—
105#121×C139D414yes—
106#117×C139—22no—
107#117×C139—22no—
108C2×C4⋊C4×C139—21no—
109C2×C4⋊C4×C139—21no—
110C2×C4⋊C4×C139—21no—
111C2×C4⋊C4×C139—22no—
112C2×C4⋊C4×C139—22no—
113C2×C4⋊C4×C139—21no—
114C2×C4⋊C4×C139—41no—
115C2×C4⋊C4×C139—41no—
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C4⋊C4×C139C2311yescharacteristic
120C2×C4⋊C4×C139C2311yescharacteristic
121C2×C4⋊C4×C139C2311yescharacteristic
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×C22⋊C4×C139—21no—
130C2×C22⋊C4×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—21no—
155C24×C139C2×D411yescharacteristic
156C24×C139C2×D411yescharacteristic
157C24×C139C2×D411yescharacteristic
158#41×C139—44no—
159#41×C139—44no—
160#41×C139—44no—
161#41×C139—44no—
162#41×C139—44no—
163#41×C139—44no—
164#41×C139—44no—
165#41×C139—44no—
166C2×Q8×C139—22no—
167C2×Q8×C139—22no—
168C2×Q8×C139—21no—
169C2×Q8×C139—21no—
170C2×Q8×C139—21no—
171C2×Q8×C139—21no—
172C2×Q8×C139—21no—
173C2×Q8×C139—41no—
174C2×Q8×C139C2×D412yes—
175C2×D4×C139—24no—
176C2×D4×C139—22no—
177C2×D4×C139—22no—
178C2×D4×C139—22no—
179C2×D4×C139—22no—
180C2×D4×C139—24no—
181C2×D4×C139—24no—
182C2×D4×C139—22no—
183C2×D4×C139—22no—
184C2×D4×C139—21no—
185C2×D4×C139—21no—
186C2×D4×C139—21no—
187C2×D4×C139—21no—
188C2×D4×C139—21no—
189C2×D4×C139—41no—
190C2×D4×C139—41no—
191C2×D4×C139—41no—
192C2×D4×C139—42no—
193C2×D4×C139—42no—
194C2×D4×C139—81no—
195C2×D4×C139—81no—
196C2×D4×C139—81no—
197C2×D4×C139—81no—
198C2×D4×C139C2×D412yes—
199C22×C4×C139—21no—
200C22×C4×C139—21no—
201C22×C4×C139—21no—
202C22×C4×C139—21no—
203C22×C4×C139—21no—
204C22×C4×C139—21no—
205C22×C4×C139—21no—
206C22×C4×C139—21no—
207C22×C4×C139—24no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—21no—
211C22×C4×C139—24no—
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—21no—
219C22×C4×C139—21no—
220C22×C4×C139—21no—
221C22×C4×C139—21no—
222C22×C4×C139—42no—
223C22×C4×C139—42no—
224C22×C4×C139—42no—
225C22×C4×C139—81no—
226C22×C4×C139—81no—
227C22×C4×C139—81no—
228C22×C4×C139—81no—
229C22×C4×C139C2×D411yescharacteristic
230C22×C4×C139C2×D411yescharacteristic
231C22×C4×C139C2×D412yes—
232C22×C4×C139C2×D412yes—
233C22×C4×C139C2×D411yescharacteristic
234C22×C4×C139#4112yes—
235C22×C4×C139#4112yes—
236C22×C4×C139C2411yescharacteristic
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—
247C2×C8×C139—21no—
248C2×C8×C139—21no—
249C4⋊C4×C139—24no—
250C4⋊C4×C139—24no—
251C4⋊C4×C139—24no—
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×C139—21no—
260C4⋊C4×C139—21no—
261C4⋊C4×C139—21no—
262C4⋊C4×C139—42no—
263C4⋊C4×C139C2×D412yes—
264C4⋊C4×C139C2×D412yes—
265C22⋊C4×C139—24no—
266C22⋊C4×C139—24no—
267C22⋊C4×C139—24no—
268C22⋊C4×C139—24no—
269C22⋊C4×C139—42no—
270C22⋊C4×C139—81no—
271C22⋊C4×C139—81no—
272C22⋊C4×C139—81no—
273C22⋊C4×C139—81no—
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—22no—
289C23×C139—21no—
290C23×C139—21no—
291C23×C139—21no—
292C23×C139—21no—
293C23×C139—21no—
294C23×C139—21no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—41no—
298C23×C139—41no—
299C23×C139—41no—
300C23×C139—41no—
301C23×C139#12012yes—
302C23×C139#12312yes—
303C23×C139C22×D411yescharacteristic
304Q8×C139—22no—
305Q8×C139—22no—
306Q8×C139—44no—
307Q8×C139—41no—
308Q8×C139—41no—
309D4×C139—22no—
310D4×C139—22no—
311D4×C139—44no—
312D4×C139—44no—
313D4×C139—44no—
314D4×C139—48no—
315D4×C139—41no—
316D4×C139—41no—
317D4×C139—84no—
318D4×C139—84no—
319C2×C4×C139—21no—
320C2×C4×C139—21no—
321C2×C4×C139—21no—
322C2×C4×C139—21no—
323C2×C4×C139—22no—
324C2×C4×C139—22no—
325C2×C4×C139—22no—
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—21no—
335C2×C4×C139—21no—
336C2×C4×C139—21no—
337C2×C4×C139—48no—
338C2×C4×C139—41no—
339C2×C4×C139—41no—
340C2×C4×C139—41no—
341C2×C4×C139—41no—
342C2×C4×C139—41no—
343C2×C4×C139—41no—
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—84no—
361C2×C4×C139—84no—
362C2×C4×C139#12012yes—
363C2×C4×C139#12312yes—
364C2×C4×C139C22×D411yescharacteristic
365C2×C4×C139C22×D411yescharacteristic
366C2×C4×C139C2×#4111yescharacteristic
367C2×C4×C139C2×#4111yescharacteristic
368C2×C4×C139H(5,𝔽2)11yescharacteristic
369C2×C4×C139H(5,𝔽2)11yescharacteristic
370C8×C139—41no—
371C8×C139—41no—
372C8×C139—41no—
373C8×C139—41no—
374C22×C139—22no—
375C22×C139—22no—
376C22×C139—22no—
377C22×C139—22no—
378C22×C139—22no—
379C22×C139—22no—
380C22×C139—41no—
381C22×C139—41no—
382C22×C139—41no—
383C22×C139—41no—
384C22×C139—41no—
385C22×C139—41no—
386C22×C139—41no—
387C22×C139—41no—
388C22×C139—41no—
389C22×C139—41no—
390C22×C139—42no—
391C22×C139—41no—
392C22×C139—41no—
393C22×C139—41no—
394C22×C139—41no—
395C22×C139—42no—
396C22×C139—41no—
397C22×C139—42no—
398C22×C139—81no—
399C22×C139—81no—
400C22×C139—81no—
401C22×C139—81no—
402C22×C139C2×#12011yescharacteristic
403C22×C139C2×#12311yescharacteristic
404C22×C139#53411yescharacteristic
405C22×C139#57611yescharacteristic
406C22×C139#57711yescharacteristic
407C22×C139#57711yescharacteristic
408C22×C139#57811yescharacteristic
409C4×C139—22no—
410C4×C139—22no—
411C4×C139—41no—
412C4×C139—42no—
413C4×C139—42no—
414C4×C139—42no—
415C4×C139—81no—
416C4×C139—81no—
417C4×C139—81no—
418C4×C139—81no—
419C4×C139#54611yescharacteristic
420C4×C139#54611yescharacteristic
421C4×C139#54611yescharacteristic
422C4×C139#54611yescharacteristic
423C2×C139—42no—
424C2×C139—42no—
425C2×C139—81no—
426C2×C139—82no—
427C2×C139#240511yescharacteristic
428C2×C139#301211yescharacteristic
429C2×C139#301311yescharacteristic
430C2×C139#309811yescharacteristic
431C2×C139#309911yescharacteristic
432C2×C139#319811yescharacteristic
433C2×C139#320111yescharacteristic
434#24017C13911yesmaximal, characteristic, direct product factor, Sylow
435C139#2401711yescharacteristic, direct product factor, Sylow
436C2×#537C2×C13911yescharacteristic
437C2×#485C2×C13911yescharacteristic, complemented
438C2×#482C2×C13911yescharacteristic, complemented
439#2311C2×C13911yescharacteristic, complemented
440#2036C2×C13911yescharacteristic, complemented
441#2035C2×C13911yescharacteristic, complemented
442#2034C2×C13911yescharacteristic, complemented
443#2033C2×C13911yescharacteristic, complemented
444#1874C2×C13911yescharacteristic, complemented
445#1872C2×C13911yescharacteristic, complemented
446#1853C2×C13911yescharacteristic, complemented
447#1852C2×C13911yescharacteristic, complemented
448#1788C2×C13911yescharacteristic, complemented
449#1788C2×C13911yescharacteristic, complemented
450#1780C2×C13911yescharacteristic, complemented
451C22×#41C22×C13911yescharacteristic
452C22×#41C22×C13911yescharacteristic
453#537—24no—
454#537—24no—
455C2×C22⋊Q8—21no—
456C2×C22⋊Q8C22×C13911yescharacteristic
457C2×C22⋊Q8C22×C13911yescharacteristic
458C2×#121—21no—
459C2×#121—21no—
460C2×#121—21no—
461C2×#121C22×C13911yescharacteristic
462C2×#121C22×C13911yescharacteristic
463C2×#117C22×C13911yescharacteristic
464C22×C4⋊C4C22×C13911yescharacteristic
465C22×C4⋊C4C22×C13911yescharacteristic
466#485—24no—
467#482—24no—
468C2×#107C22×C13911yescharacteristic
469C2×#107C22×C13911yescharacteristic
470C2×#106C22×C13911yescharacteristic
471C2×#106C22×C13911yescharacteristic
472C2×#103C22×C13911yescharacteristic
473C2×#103C22×C13911yescharacteristic
474C2×#103C22×C13911yescharacteristic
475C2×#103C22×C13911yescharacteristic
476C2×#102C22×C13911yescharacteristic
477C2×#102C22×C13911yescharacteristic
478C2×#102C22×C13911yescharacteristic
479C2×#102C22×C13911yescharacteristic
480C2×C22⋊C8C22×C13911yescharacteristic
481C2×C22⋊C8C22×C13911yescharacteristic
482C2×C22⋊C8C22×C13911yescharacteristic
483C2×C22⋊C8C22×C13911yescharacteristic
484C2×C22⋊C8C22×C13911yescharacteristic
485C2×C22⋊C8C22×C13911yescharacteristic
486#391—21no—
487#390—21no—
488#386—21no—
489#386—21no—
490#380C22×C13911yescharacteristic
491#380C22×C13911yescharacteristic
492#380C22×C13911yescharacteristic
493#380C22×C13911yescharacteristic
494#340C22×C13911yescharacteristic
495#340C22×C13911yescharacteristic
496#340C22×C13911yescharacteristic
497#340C22×C13911yescharacteristic
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C22×Q8D4×C13911yescharacteristic
511C22×Q8C23×C13911yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C13911yescharacteristic
516C22×D4D4×C13911yescharacteristic
517C22×D4D4×C13911yescharacteristic
518C22×D4C23×C13911yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C13911yescharacteristic
523C23×C4C23×C13911yescharacteristic
524C23×C4C23×C13911yescharacteristic
525C22×C8C23×C13911yescharacteristic
526C22×C8C23×C13911yescharacteristic
527C22×C8C23×C13911yescharacteristic
528C22×C8C23×C13911yescharacteristic
529C22⋊Q8—28no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8D4×C13914yes—
534#121—28no—
535#121—28no—
536#121—28no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121D4×C13914yes—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4C23×C13911yescharacteristic
552C2×C4⋊C4C23×C13911yescharacteristic
553C2×C4⋊C4C23×C13911yescharacteristic
554C2×C4⋊C4C23×C13911yescharacteristic
555C2×C4⋊C4C23×C13911yescharacteristic
556C2×C4⋊C4C23×C13911yescharacteristic
557C2×C22⋊C4—21no—
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×C42—21no—
567#107—22no—
568#107—22no—
569#106—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—41no—
578#102—41no—
579C22⋊C8—22no—
580C22⋊C8—22no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—41no—
584C22⋊C8—41no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C13911yescharacteristic
591C24C2×D4×C13911yescharacteristic
592C24C2×D4×C13911yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—41no—
609C2×Q8C2×D4×C13912yes—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—22no—
618C2×D4—22no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4C2×D4×C13912yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—24no—
647C22×C4—21no—
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—42no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4—81no—
663C22×C4—81no—
664C22×C4C2×D4×C13911yescharacteristic
665C22×C4C2×D4×C13911yescharacteristic
666C22×C4C2×D4×C13912yes—
667C22×C4C2×D4×C13912yes—
668C22×C4C2×D4×C13911yescharacteristic
669C22×C4#41×C13912yes—
670C22×C4#41×C13912yes—
671C22×C4C24×C13911yescharacteristic
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
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—
684C4⋊C4—24no—
685C4⋊C4—24no—
686C4⋊C4—24no—
687C4⋊C4—21no—
688C4⋊C4—21no—
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—42no—
698C4⋊C4C2×D4×C13912yes—
699C4⋊C4C2×D4×C13912yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23#120×C13912yes—
737C23#123×C13912yes—
738C23C22×D4×C13911yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—44no—
742Q8—41no—
743Q8—41no—
744D4—22no—
745D4—22no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—48no—
750D4—41no—
751D4—41no—
752D4—84no—
753D4—84no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—48no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
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—84no—
796C2×C4—84no—
797C2×C4#120×C13912yes—
798C2×C4#123×C13912yes—
799C2×C4C22×D4×C13911yescharacteristic
800C2×C4C22×D4×C13911yescharacteristic
801C2×C4C2×#41×C13911yescharacteristic
802C2×C4C2×#41×C13911yescharacteristic
803C2×C4H(5,𝔽2)×C13911yescharacteristic
804C2×C4H(5,𝔽2)×C13911yescharacteristic
805C8—41no—
806C8—41no—
807C8—41no—
808C8—41no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22C2×#120×C13911yescharacteristic
838C22C2×#123×C13911yescharacteristic
839C22#534×C13911yescharacteristic
840C22#576×C13911yescharacteristic
841C22#577×C13911yescharacteristic
842C22#577×C13911yescharacteristic
843C22#578×C13911yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—42no—
848C4—42no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—81no—
853C4—81no—
854C4#546×C13911yescharacteristic
855C4#546×C13911yescharacteristic
856C4#546×C13911yescharacteristic
857C4#546×C13911yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—82no—
862C2#2405×C13911yescharacteristic
863C2#3012×C13911yescharacteristic
864C2#3013×C13911yescharacteristic
865C2#3098×C13911yescharacteristic
866C2#3099×C13911yescharacteristic
867C2#3198×C13911yescharacteristic
868C2#3201×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#537×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C22×#41×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. #2311×C139C2semidirect
5. #2036×C139C2semidirect
6. #2035×C139C2semidirect
7. #2034×C139C2semidirect
8. #2033×C139C2semidirect
9. #1874×C139C2semidirect
10. #1872×C139C2semidirect
11. #1853×C139C2semidirect
12. #1852×C139C2semidirect
13. #1788×C139C2semidirect
14. #1788×C139C2semidirect
15. #1780×C139C2semidirect
434. #24017C139direct (N × H)
435. C139#24017direct (N × H)
437. C2×#485C2×C139semidirect
438. C2×#482C2×C139semidirect
439. #2311C2×C139semidirect
440. #2036C2×C139semidirect
441. #2035C2×C139semidirect
442. #2034C2×C139semidirect
443. #2033C2×C139semidirect
444. #1874C2×C139semidirect
445. #1872C2×C139semidirect
446. #1853C2×C139semidirect
447. #1852C2×C139semidirect
448. #1788C2×C139semidirect
449. #1788C2×C139semidirect
450. #1780C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1392
C2×#485×C1392
C2×#482×C1392
#2311×C1392
#2036×C1392
#2035×C1392
#2034×C1392
#2033×C1392
#1874×C1392
#1872×C1392
#1853×C1392
#1852×C1392
#1788×C1392
#1780×C1392
#24017139