Finite Group Databasebeta

← C139×#24034 #48018630

Subgroups — C139×#24034 #48018630

Order 35584.

1380 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C139C211yesmaximal, characteristic
2C2×#482×C139C211yesmaximal, characteristic, complemented
3C2×#416×C139C211yesmaximal, characteristic, complemented
4#2485×C139C211yesmaximal, characteristic, complemented
5#2041×C139C211yesmaximal, characteristic, complemented
6#2041×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#1893×C139C211yesmaximal, characteristic, complemented
10#1869×C139C211yesmaximal, characteristic, complemented
11#1865×C139C211yesmaximal, characteristic, complemented
12#1863×C139C211yesmaximal, characteristic, complemented
13#1788×C139C211yesmaximal, characteristic, complemented
14#1788×C139C211yesmaximal, characteristic, complemented
15#1788×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C23×C8×C139C2211yescharacteristic
19#550×C139—24no—
20#550×C139—24no—
21C2×#127×C139—21no—
22C2×#127×C139C2211yescharacteristic
23C2×#121×C139—21no—
24C2×#121×C139—21no—
25C2×#121×C139C2211yescharacteristic
26C2×#121×C139C2211yescharacteristic
27C2×C4×Q8×C139C2211yescharacteristic
28C2×C4×D4×C139—21no—
29C2×C4×D4×C139C2211yescharacteristic
30C2×#117×C139C2211yescharacteristic
31#482×C139—24no—
32C2×#107×C139C2211yescharacteristic
33C2×#106×C139C2211yescharacteristic
34#416×C139—24no—
35C2×#103×C139C2211yescharacteristic
36C2×#103×C139C2211yescharacteristic
37C2×#103×C139C2211yescharacteristic
38C2×#103×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×#102×C139C2211yescharacteristic
47C2×C22⋊C8×C139C2211yescharacteristic
48C2×C22⋊C8×C139C2211yescharacteristic
49C2×C22⋊C8×C139C2211yescharacteristic
50#397×C139—21no—
51#394×C139—21no—
52#389×C139C2211yescharacteristic
53#389×C139C2211yescharacteristic
54#388×C139—21no—
55#387×C139—21no—
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic
58#380×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#336×C139C2211yescharacteristic
62#336×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—41no—
71C2×#41×C139—41no—
72C2×#41×C139—41no—
73C2×#41×C139—41no—
74C2×#41×C139D414yes—
75C22×Q8×C139C2311yescharacteristic
76C22×D4×C139—21no—
77C22×D4×C139—21no—
78C22×D4×C139—21no—
79C22×D4×C139—21no—
80C22×D4×C139—21no—
81C22×D4×C139—21no—
82C22×D4×C139D411yescharacteristic
83C22×D4×C139C2311yescharacteristic
84C22×D4×C139C2311yescharacteristic
85C23×C4×C139—21no—
86C23×C4×C139—21no—
87C23×C4×C139C2311yescharacteristic
88C23×C4×C139C2311yescharacteristic
89C22×C8×C139—22no—
90C22×C8×C139—41no—
91C22×C8×C139—41no—
92C22×C8×C139C2311yescharacteristic
93C22×C8×C139C2311yescharacteristic
94C22×C8×C139C2311yescharacteristic
95C22×C8×C139C2311yescharacteristic
96#127×C139—28no—
97#127×C139—22no—
98#127×C139—22no—
99#121×C139—28no—
100#121×C139—28no—
101#121×C139—22no—
102#121×C139—22no—
103#121×C139—22no—
104#121×C139D414yes—
105C4×Q8×C139—22no—
106C4×Q8×C139—22no—
107C4×D4×C139—28no—
108C4×D4×C139—22no—
109C4×D4×C139—22no—
110#117×C139—22no—
111#117×C139—22no—
112C2×C4⋊C4×C139—21no—
113C2×C4⋊C4×C139—21no—
114C2×C4⋊C4×C139—21no—
115C2×C4⋊C4×C139D411yescharacteristic
116C2×C4⋊C4×C139C2311yescharacteristic
117C2×C4⋊C4×C139C2311yescharacteristic
118C2×C4⋊C4×C139C2311yescharacteristic
119C2×C4⋊C4×C139C2311yescharacteristic
120C2×C4⋊C4×C139C2311yescharacteristic
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×C139D411yescharacteristic
128C2×C22⋊C4×C139D411yescharacteristic
129C2×C42×C139—21no—
130C2×C42×C139—21no—
131C2×C42×C139C2311yescharacteristic
132#107×C139—22no—
133#106×C139—22no—
134#103×C139—22no—
135#103×C139—22no—
136#103×C139—22no—
137#103×C139—22no—
138#102×C139—22no—
139#102×C139—22no—
140#102×C139—22no—
141#102×C139—22no—
142#102×C139—41no—
143#102×C139—41no—
144#102×C139—41no—
145#102×C139—41no—
146C22⋊C8×C139—22no—
147C22⋊C8×C139—41no—
148C22⋊C8×C139—41no—
149#95×C139—21no—
150#95×C139—21no—
151#95×C139—21no—
152#95×C139—21no—
153#95×C139—21no—
154C24×C139—21no—
155C24×C139—21no—
156C24×C139C2×D411yescharacteristic
157C24×C139C2×D411yescharacteristic
158#41×C139—28no—
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—21no—
167C2×Q8×C139—21no—
168C2×Q8×C139—21no—
169C2×Q8×C139C2×D412yes—
170C2×Q8×C139#4112yes—
171C2×Q8×C139#4112yes—
172C2×D4×C139—24no—
173C2×D4×C139—24no—
174C2×D4×C139—22no—
175C2×D4×C139—24no—
176C2×D4×C139—24no—
177C2×D4×C139—24no—
178C2×D4×C139—24no—
179C2×D4×C139—22no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—21no—
183C2×D4×C139—21no—
184C2×D4×C139—21no—
185C2×D4×C139—21no—
186C2×D4×C139—21no—
187C2×D4×C139—21no—
188C2×D4×C139—21no—
189C2×D4×C139—21no—
190C2×D4×C139—41no—
191C2×D4×C139—42no—
192C2×D4×C139—42no—
193C2×D4×C139—42no—
194C2×D4×C139—42no—
195C2×D4×C139—42no—
196C2×D4×C139—42no—
197C2×D4×C139—81no—
198C2×D4×C139—81no—
199C2×D4×C139—81no—
200C2×D4×C139—81no—
201C2×D4×C139—81no—
202C2×D4×C139—81no—
203C2×D4×C139C2×D412yes—
204C2×D4×C139C2×D412yes—
205C22×C4×C139—21no—
206C22×C4×C139—21no—
207C22×C4×C139—21no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—24no—
211C22×C4×C139—21no—
212C22×C4×C139—24no—
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—21no—
223C22×C4×C139—42no—
224C22×C4×C139—42no—
225C22×C4×C139—42no—
226C22×C4×C139—42no—
227C22×C4×C139C2×D411yescharacteristic
228C22×C4×C139C2×D411yescharacteristic
229C22×C4×C139C2×D411yescharacteristic
230C22×C4×C139C2×D412yes—
231C22×C4×C139C2×D412yes—
232C22×C4×C139C2×D411yescharacteristic
233C22×C4×C139C2411yescharacteristic
234C2×C8×C139—21no—
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—44no—
247C4⋊C4×C139—24no—
248C4⋊C4×C139—22no—
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—42no—
259C4⋊C4×C139—81no—
260C4⋊C4×C139C2×D412yes—
261C22⋊C4×C139—24no—
262C22⋊C4×C139—22no—
263C22⋊C4×C139—24no—
264C22⋊C4×C139—22no—
265C22⋊C4×C139—42no—
266C22⋊C4×C139—42no—
267C22⋊C4×C139—81no—
268C22⋊C4×C139—81no—
269C42×C139—24no—
270C42×C139—21no—
271C42×C139—21no—
272C42×C139—42no—
273C23×C139—21no—
274C23×C139—21no—
275C23×C139—21no—
276C23×C139—21no—
277C23×C139—21no—
278C23×C139—21no—
279C23×C139—21no—
280C23×C139—22no—
281C23×C139—22no—
282C23×C139—21no—
283C23×C139—21no—
284C23×C139—21no—
285C23×C139—21no—
286C23×C139—21no—
287C23×C139—21no—
288C23×C139—41no—
289C23×C139—41no—
290C23×C139—41no—
291C23×C139—41no—
292C23×C139—41no—
293C23×C139—41no—
294C23×C139—41no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—41no—
298C23×C139—41no—
299C23×C139—41no—
300C23×C139#12012yes—
301C23×C139C22×D411yescharacteristic
302Q8×C139—22no—
303Q8×C139—22no—
304Q8×C139—22no—
305Q8×C139#12314yes—
306D4×C139—22no—
307D4×C139—22no—
308D4×C139—22no—
309D4×C139—22no—
310D4×C139—44no—
311D4×C139—48no—
312D4×C139—48no—
313D4×C139—48no—
314D4×C139—41no—
315D4×C139—41no—
316D4×C139—41no—
317D4×C139—41no—
318D4×C139—84no—
319D4×C139—84no—
320D4×C139—84no—
321C2×C4×C139—21no—
322C2×C4×C139—22no—
323C2×C4×C139—21no—
324C2×C4×C139—21no—
325C2×C4×C139—22no—
326C2×C4×C139—22no—
327C2×C4×C139—21no—
328C2×C4×C139—22no—
329C2×C4×C139—22no—
330C2×C4×C139—22no—
331C2×C4×C139—22no—
332C2×C4×C139—21no—
333C2×C4×C139—22no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—21no—
337C2×C4×C139—21no—
338C2×C4×C139—21no—
339C2×C4×C139—48no—
340C2×C4×C139—48no—
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#12012yes—
360C2×C4×C139#13512yes—
361C2×C4×C139C22×D411yescharacteristic
362C2×C4×C139C22×D411yescharacteristic
363C2×C4×C139C2×#4111yescharacteristic
364C2×C4×C139C2×#4111yescharacteristic
365C2×C4×C139H(5,𝔽2)11yescharacteristic
366C2×C4×C139H(5,𝔽2)11yescharacteristic
367C8×C139—41no—
368C8×C139—41no—
369C8×C139—41no—
370C8×C139—41no—
371C22×C139—22no—
372C22×C139—22no—
373C22×C139—22no—
374C22×C139—41no—
375C22×C139—41no—
376C22×C139—41no—
377C22×C139—41no—
378C22×C139—42no—
379C22×C139—42no—
380C22×C139—41no—
381C22×C139—41no—
382C22×C139—42no—
383C22×C139—42no—
384C22×C139—41no—
385C22×C139—42no—
386C22×C139—42no—
387C22×C139—41no—
388C22×C139—41no—
389C22×C139—41no—
390C22×C139—41no—
391C22×C139—81no—
392C22×C139—81no—
393C22×C139—81no—
394C22×C139—81no—
395C22×C139—81no—
396C22×C139—81no—
397C22×C139—81no—
398C22×C139—81no—
399C22×C139C2×#12011yescharacteristic
400C22×C139#54611yescharacteristic
401C22×C139#54611yescharacteristic
402C22×C139C2×#13511yescharacteristic
403C22×C139#57511yescharacteristic
404C22×C139#57611yescharacteristic
405C22×C139#57711yescharacteristic
406C4×C139—22no—
407C4×C139—24no—
408C4×C139—22no—
409C4×C139—41no—
410C4×C139—41no—
411C4×C139—42no—
412C4×C139—81no—
413C4×C139—81no—
414C4×C139—81no—
415C4×C139—81no—
416C4×C139C2×#12311yescharacteristic
417C4×C139#53411yescharacteristic
418C4×C139#54611yescharacteristic
419C4×C139#54611yescharacteristic
420C2×C139—42no—
421C2×C139—81no—
422C2×C139—82no—
423C2×C139—82no—
424C2×C139#240511yescharacteristic
425C2×C139#300211yescharacteristic
426C2×C139#301211yescharacteristic
427C2×C139#330411yescharacteristic
428C2×C139#330511yescharacteristic
429C2×C139#330911yescharacteristic
430C2×C139#331711yescharacteristic
431#24034C13911yesmaximal, characteristic, direct product factor, Sylow
432C139#2403411yescharacteristic, direct product factor, Sylow
433C2×#550C2×C13911yescharacteristic
434C2×#482C2×C13911yescharacteristic, complemented
435C2×#416C2×C13911yescharacteristic, complemented
436#2485C2×C13911yescharacteristic, complemented
437#2041C2×C13911yescharacteristic, complemented
438#2041C2×C13911yescharacteristic, complemented
439#2034C2×C13911yescharacteristic, complemented
440#2033C2×C13911yescharacteristic, complemented
441#1893C2×C13911yescharacteristic, complemented
442#1869C2×C13911yescharacteristic, complemented
443#1865C2×C13911yescharacteristic, complemented
444#1863C2×C13911yescharacteristic, complemented
445#1788C2×C13911yescharacteristic, complemented
446#1788C2×C13911yescharacteristic, complemented
447#1788C2×C13911yescharacteristic, complemented
448C22×#41C22×C13911yescharacteristic
449C22×#41C22×C13911yescharacteristic
450C23×C8C22×C13911yescharacteristic
451#550—24no—
452#550—24no—
453C2×#127—21no—
454C2×#127C22×C13911yescharacteristic
455C2×#121—21no—
456C2×#121—21no—
457C2×#121C22×C13911yescharacteristic
458C2×#121C22×C13911yescharacteristic
459C2×C4×Q8C22×C13911yescharacteristic
460C2×C4×D4—21no—
461C2×C4×D4C22×C13911yescharacteristic
462C2×#117C22×C13911yescharacteristic
463#482—24no—
464C2×#107C22×C13911yescharacteristic
465C2×#106C22×C13911yescharacteristic
466#416—24no—
467C2×#103C22×C13911yescharacteristic
468C2×#103C22×C13911yescharacteristic
469C2×#103C22×C13911yescharacteristic
470C2×#103C22×C13911yescharacteristic
471C2×#102C22×C13911yescharacteristic
472C2×#102C22×C13911yescharacteristic
473C2×#102C22×C13911yescharacteristic
474C2×#102C22×C13911yescharacteristic
475C2×#102C22×C13911yescharacteristic
476C2×#102C22×C13911yescharacteristic
477C2×#102C22×C13911yescharacteristic
478C2×#102C22×C13911yescharacteristic
479C2×C22⋊C8C22×C13911yescharacteristic
480C2×C22⋊C8C22×C13911yescharacteristic
481C2×C22⋊C8C22×C13911yescharacteristic
482#397—21no—
483#394—21no—
484#389C22×C13911yescharacteristic
485#389C22×C13911yescharacteristic
486#388—21no—
487#387—21no—
488#380C22×C13911yescharacteristic
489#380C22×C13911yescharacteristic
490#380C22×C13911yescharacteristic
491#340C22×C13911yescharacteristic
492#340C22×C13911yescharacteristic
493#336C22×C13911yescharacteristic
494#336C22×C13911yescharacteristic
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41D4×C13914yes—
507C22×Q8C23×C13911yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4D4×C13911yescharacteristic
515C22×D4C23×C13911yescharacteristic
516C22×D4C23×C13911yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C23×C13911yescharacteristic
520C23×C4C23×C13911yescharacteristic
521C22×C8—22no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C23×C13911yescharacteristic
525C22×C8C23×C13911yescharacteristic
526C22×C8C23×C13911yescharacteristic
527C22×C8C23×C13911yescharacteristic
528#127—28no—
529#127—22no—
530#127—22no—
531#121—28no—
532#121—28no—
533#121—22no—
534#121—22no—
535#121—22no—
536#121D4×C13914yes—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×D4—28no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117—22no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4D4×C13911yescharacteristic
548C2×C4⋊C4C23×C13911yescharacteristic
549C2×C4⋊C4C23×C13911yescharacteristic
550C2×C4⋊C4C23×C13911yescharacteristic
551C2×C4⋊C4C23×C13911yescharacteristic
552C2×C4⋊C4C23×C13911yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4D4×C13911yescharacteristic
560C2×C22⋊C4D4×C13911yescharacteristic
561C2×C42—21no—
562C2×C42—21no—
563C2×C42C23×C13911yescharacteristic
564#107—22no—
565#106—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#102—22no—
571#102—22no—
572#102—22no—
573#102—22no—
574#102—41no—
575#102—41no—
576#102—41no—
577#102—41no—
578C22⋊C8—22no—
579C22⋊C8—41no—
580C22⋊C8—41no—
581#95—21no—
582#95—21no—
583#95—21no—
584#95—21no—
585#95—21no—
586C24—21no—
587C24—21no—
588C24C2×D4×C13911yescharacteristic
589C24C2×D4×C13911yescharacteristic
590#41—28no—
591#41—44no—
592#41—44no—
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8C2×D4×C13912yes—
602C2×Q8#41×C13912yes—
603C2×Q8#41×C13912yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—22no—
607C2×D4—24no—
608C2×D4—24no—
609C2×D4—24no—
610C2×D4—24no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—42no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—81no—
630C2×D4—81no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—81no—
635C2×D4C2×D4×C13912yes—
636C2×D4C2×D4×C13912yes—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
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—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4C2×D4×C13911yescharacteristic
660C22×C4C2×D4×C13911yescharacteristic
661C22×C4C2×D4×C13911yescharacteristic
662C22×C4C2×D4×C13912yes—
663C22×C4C2×D4×C13912yes—
664C22×C4C2×D4×C13911yescharacteristic
665C22×C4C24×C13911yescharacteristic
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—44no—
679C4⋊C4—24no—
680C4⋊C4—22no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—42no—
691C4⋊C4—81no—
692C4⋊C4C2×D4×C13912yes—
693C22⋊C4—24no—
694C22⋊C4—22no—
695C22⋊C4—24no—
696C22⋊C4—22no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—81no—
700C22⋊C4—81no—
701C42—24no—
702C42—21no—
703C42—21no—
704C42—42no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—22no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23#120×C13912yes—
733C23C22×D4×C13911yescharacteristic
734Q8—22no—
735Q8—22no—
736Q8—22no—
737Q8#123×C13914yes—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—44no—
743D4—48no—
744D4—48no—
745D4—48no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—84no—
751D4—84no—
752D4—84no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—48no—
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#120×C13912yes—
792C2×C4#135×C13912yes—
793C2×C4C22×D4×C13911yescharacteristic
794C2×C4C22×D4×C13911yescharacteristic
795C2×C4C2×#41×C13911yescharacteristic
796C2×C4C2×#41×C13911yescharacteristic
797C2×C4H(5,𝔽2)×C13911yescharacteristic
798C2×C4H(5,𝔽2)×C13911yescharacteristic
799C8—41no—
800C8—41no—
801C8—41no—
802C8—41no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—42no—
816C22—41no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—42no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22C2×#120×C13911yescharacteristic
832C22#546×C13911yescharacteristic
833C22#546×C13911yescharacteristic
834C22C2×#135×C13911yescharacteristic
835C22#575×C13911yescharacteristic
836C22#576×C13911yescharacteristic
837C22#577×C13911yescharacteristic
838C4—22no—
839C4—24no—
840C4—22no—
841C4—41no—
842C4—41no—
843C4—42no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—81no—
848C4C2×#123×C13911yescharacteristic
849C4#534×C13911yescharacteristic
850C4#546×C13911yescharacteristic
851C4#546×C13911yescharacteristic
852C2—42no—
853C2—81no—
854C2—82no—
855C2—82no—
856C2#2405×C13911yescharacteristic
857C2#3002×C13911yescharacteristic
858C2#3012×C13911yescharacteristic
859C2#3304×C13911yescharacteristic
860C2#3305×C13911yescharacteristic
861C2#3309×C13911yescharacteristic
862C2#3317×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#550×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C4×D4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#482×C139C2semidirect
3. C2×#416×C139C2semidirect
4. #2485×C139C2semidirect
5. #2041×C139C2semidirect
6. #2041×C139C2semidirect
7. #2034×C139C2semidirect
8. #2033×C139C2semidirect
9. #1893×C139C2semidirect
10. #1869×C139C2semidirect
11. #1865×C139C2semidirect
12. #1863×C139C2semidirect
13. #1788×C139C2semidirect
14. #1788×C139C2semidirect
15. #1788×C139C2semidirect
431. #24034C139direct (N × H)
432. C139#24034direct (N × H)
434. C2×#482C2×C139semidirect
435. C2×#416C2×C139semidirect
436. #2485C2×C139semidirect
437. #2041C2×C139semidirect
438. #2041C2×C139semidirect
439. #2034C2×C139semidirect
440. #2033C2×C139semidirect
441. #1893C2×C139semidirect
442. #1869C2×C139semidirect
443. #1865C2×C139semidirect
444. #1863C2×C139semidirect
445. #1788C2×C139semidirect
446. #1788C2×C139semidirect
447. #1788C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1392
C2×#482×C1392
C2×#416×C1392
#2485×C1392
#2041×C1392
#2034×C1392
#2033×C1392
#1893×C1392
#1869×C1392
#1865×C1392
#1863×C1392
#1788×C1392
#24034139