Finite Group Databasebeta

← C139×#24394 #48018990

Subgroups — C139×#24394 #48018990

Order 35584.

1578 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C139C211yesmaximal, characteristic
2C2×#468×C139C211yesmaximal, characteristic, complemented
3C2×#465×C139C211yesmaximal, characteristic, complemented
4C2×#450×C139C211yesmaximal, characteristic, complemented
5C2×#408×C139C211yesmaximal, characteristic, complemented
6#2616×C139C211yesmaximal, characteristic, complemented
7#2034×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#2000×C139C211yesmaximal, characteristic, complemented
10#2000×C139C211yesmaximal, characteristic, complemented
11#1895×C139C211yesmaximal, characteristic, complemented
12#1893×C139C211yesmaximal, characteristic, complemented
13#1873×C139C211yesmaximal, characteristic, complemented
14#1854×C139C211yesmaximal, characteristic, complemented
15#1786×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×D4×C139C2211yescharacteristic
18C22×SD16×C139C2211yescharacteristic
19C22×SD16×C139C2211yescharacteristic
20C22×M16×C139C2211yescharacteristic, complemented
21C23×C8×C139C2211yescharacteristic, complemented
22#535×C139—24no—
23#535×C139—24no—
24C2×#127×C139—21no—
25C2×#124×C139—21no—
26C2×C22⋊Q8×C139C2211yescharacteristic
27C2×C22⋊Q8×C139C2211yescharacteristic, complemented
28C2×C22⋊Q8×C139C2211yescharacteristic, complemented
29C2×#121×C139C2211yescharacteristic
30C2×#121×C139C2211yescharacteristic
31C2×#121×C139C2211yescharacteristic
32C2×#121×C139C2211yescharacteristic
33C2×#120×C139—21no—
34C2×#120×C139—21no—
35C2×#117×C139C2211yescharacteristic
36#468×C139—24no—
37#465×C139—24no—
38#450×C139—24no—
39C2×#107×C139C2211yescharacteristic, complemented
40C2×#106×C139C2211yescharacteristic, complemented
41C2×#103×C139C2211yescharacteristic, complemented
42C2×#103×C139C2211yescharacteristic, complemented
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×#102×C139C2211yescharacteristic
47C2×#102×C139C2211yescharacteristic
48C2×#102×C139C2211yescharacteristic
49#408×C139—24no—
50C2×C22⋊C8×C139C2211yescharacteristic
51C2×C22⋊C8×C139C2211yescharacteristic
52C2×C22⋊C8×C139C2211yescharacteristic, complemented
53C2×C22⋊C8×C139C2211yescharacteristic, complemented
54#395×C139—21no—
55#394×C139—21no—
56#394×C139—21no—
57#394×C139—21no—
58#380×C139C2211yescharacteristic
59#380×C139C2211yescharacteristic, complemented
60#380×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63#340×C139C2211yescharacteristic, complemented
64#340×C139C2211yescharacteristic, complemented
65C25×C139—21no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—22no—
69C2×#41×C139—22no—
70C2×#41×C139—41no—
71C2×#41×C139—41no—
72C22×Q8×C139D411yescharacteristic
73C22×Q8×C139C2311yescharacteristic
74C22×D4×C139—21no—
75C22×D4×C139—21no—
76C22×D4×C139—21no—
77C22×D4×C139—21no—
78C22×D4×C139—22no—
79C22×D4×C139—22no—
80C22×D4×C139—21no—
81C22×D4×C139—22no—
82C22×D4×C139—22no—
83C22×D4×C139—41no—
84C22×D4×C139—41no—
85C22×D4×C139D411yescharacteristic
86C22×D4×C139D411yescharacteristic
87C22×D4×C139D411yescharacteristic
88C22×D4×C139C2311yescharacteristic
89C22×D4×C139C2311yescharacteristic
90C23×C4×C139C2311yescharacteristic
91C23×C4×C139C2311yescharacteristic
92C23×C4×C139C2311yescharacteristic
93C2×SD16×C139—22no—
94C2×SD16×C139—22no—
95C2×SD16×C139—22no—
96C2×SD16×C139—22no—
97C2×SD16×C139—41no—
98C2×SD16×C139—41no—
99C2×M16×C139—22no—
100C2×M16×C139—22no—
101C2×M16×C139—41no—
102C22×C8×C139—22no—
103C22×C8×C139—22no—
104C22×C8×C139—41no—
105C22×C8×C139C2311yescharacteristic
106C22×C8×C139C2311yescharacteristic
107C22×C8×C139C2311yescharacteristic
108C22×C8×C139C2311yescharacteristic
109#127×C139—28no—
110#124×C139—28no—
111C22⋊Q8×C139—22no—
112C22⋊Q8×C139—22no—
113C22⋊Q8×C139—22no—
114C22⋊Q8×C139—22no—
115C22⋊Q8×C139—41no—
116C22⋊Q8×C139—41no—
117#121×C139—22no—
118#121×C139—22no—
119#121×C139—22no—
120#121×C139—22no—
121#121×C139—22no—
122#121×C139—22no—
123#121×C139D414yes—
124#121×C139D414yes—
125#120×C139—28no—
126#120×C139—28no—
127#117×C139—22no—
128#117×C139—22no—
129C2×C4⋊C4×C139—21no—
130C2×C4⋊C4×C139—21no—
131C2×C4⋊C4×C139—21no—
132C2×C4⋊C4×C139C2311yescharacteristic
133C2×C4⋊C4×C139C2311yescharacteristic
134C2×C4⋊C4×C139C2311yescharacteristic
135C2×C4⋊C4×C139C2311yescharacteristic
136C2×C4⋊C4×C139C2311yescharacteristic
137C2×C22⋊C4×C139—21no—
138C2×C22⋊C4×C139—21no—
139C2×C22⋊C4×C139—21no—
140C2×C22⋊C4×C139—21no—
141C2×C22⋊C4×C139—21no—
142C2×C22⋊C4×C139—21no—
143C2×C22⋊C4×C139—21no—
144C2×C22⋊C4×C139—21no—
145C2×C22⋊C4×C139—21no—
146C2×C22⋊C4×C139—21no—
147C2×C22⋊C4×C139—21no—
148C2×C42×C139—21no—
149#107×C139—22no—
150#106×C139—22no—
151#103×C139—22no—
152#103×C139—22no—
153#102×C139—22no—
154#102×C139—22no—
155#102×C139—22no—
156#102×C139—22no—
157#102×C139—41no—
158#102×C139—41no—
159C22⋊C8×C139—22no—
160C22⋊C8×C139—22no—
161C22⋊C8×C139—22no—
162C22⋊C8×C139D414yescomplemented
163#95×C139—21no—
164#95×C139—21no—
165#95×C139—21no—
166C24×C139—24no—
167C24×C139—21no—
168C24×C139—21no—
169C24×C139—42no—
170C24×C139—42no—
171C24×C139—81no—
172C24×C139—81no—
173C24×C139—81no—
174C24×C139—81no—
175C24×C139C2×D411yescharacteristic
176C24×C139C2×D411yescharacteristic
177C24×C139C2×D411yescharacteristic
178#41×C139—44no—
179#41×C139—44no—
180#41×C139—44no—
181#41×C139—44no—
182C2×Q8×C139—22no—
183C2×Q8×C139—22no—
184C2×Q8×C139—21no—
185C2×Q8×C139—21no—
186C2×Q8×C139—21no—
187C2×Q8×C139—21no—
188C2×Q8×C139—21no—
189C2×Q8×C139—21no—
190C2×Q8×C139—41no—
191C2×D4×C139—24no—
192C2×D4×C139—22no—
193C2×D4×C139—22no—
194C2×D4×C139—22no—
195C2×D4×C139—22no—
196C2×D4×C139—24no—
197C2×D4×C139—24no—
198C2×D4×C139—24no—
199C2×D4×C139—24no—
200C2×D4×C139—22no—
201C2×D4×C139—22no—
202C2×D4×C139—21no—
203C2×D4×C139—21no—
204C2×D4×C139—21no—
205C2×D4×C139—21no—
206C2×D4×C139—21no—
207C2×D4×C139—21no—
208C2×D4×C139—21no—
209C2×D4×C139—21no—
210C2×D4×C139—21no—
211C2×D4×C139—21no—
212C2×D4×C139—44no—
213C2×D4×C139—44no—
214C2×D4×C139—44no—
215C2×D4×C139—44no—
216C2×D4×C139—41no—
217C2×D4×C139—41no—
218C2×D4×C139—41no—
219C2×D4×C139—42no—
220C2×D4×C139—42no—
221C2×D4×C139—81no—
222C2×D4×C139—81no—
223C2×D4×C139—81no—
224C2×D4×C139—81no—
225C2×D4×C139—81no—
226C2×D4×C139—81no—
227C2×D4×C139—81no—
228C2×D4×C139—81no—
229C2×D4×C139C2×D412yes—
230C2×D4×C139C2×D412yes—
231C22×C4×C139—21no—
232C22×C4×C139—21no—
233C22×C4×C139—21no—
234C22×C4×C139—21no—
235C22×C4×C139—21no—
236C22×C4×C139—21no—
237C22×C4×C139—21no—
238C22×C4×C139—21no—
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—21no—
242C22×C4×C139—21no—
243C22×C4×C139—21no—
244C22×C4×C139—21no—
245C22×C4×C139—21no—
246C22×C4×C139—21no—
247C22×C4×C139—21no—
248C22×C4×C139—21no—
249C22×C4×C139—21no—
250C22×C4×C139—21no—
251C22×C4×C139C2×D411yescharacteristic
252C22×C4×C139C2×D411yescharacteristic
253C22×C4×C139C2×D412yes—
254C22×C4×C139C2×D412yes—
255C22×C4×C139C2×D411yescharacteristic
256C22×C4×C139C2×D412yes—
257C22×C4×C139#4112yes—
258C22×C4×C139C2411yescharacteristic
259SD16×C139—44no—
260SD16×C139—44no—
261M16×C139—44no—
262C2×C8×C139—21no—
263C2×C8×C139—21no—
264C2×C8×C139—21no—
265C2×C8×C139—21no—
266C2×C8×C139—21no—
267C2×C8×C139—21no—
268C2×C8×C139—21no—
269C2×C8×C139—21no—
270C2×C8×C139—21no—
271C2×C8×C139—21no—
272C2×C8×C139—44no—
273C2×C8×C139C2×D412yes—
274C2×C8×C139C2×D412yes—
275C4⋊C4×C139—21no—
276C4⋊C4×C139—21no—
277C4⋊C4×C139—21no—
278C4⋊C4×C139—21no—
279C4⋊C4×C139—21no—
280C4⋊C4×C139—21no—
281C4⋊C4×C139—21no—
282C4⋊C4×C139—21no—
283C4⋊C4×C139—42no—
284C4⋊C4×C139—42no—
285C4⋊C4×C139—42no—
286C4⋊C4×C139C2×D412yes—
287C4⋊C4×C139C2×D412yes—
288C22⋊C4×C139—24no—
289C22⋊C4×C139—24no—
290C22⋊C4×C139—24no—
291C22⋊C4×C139—24no—
292C22⋊C4×C139—24no—
293C22⋊C4×C139—42no—
294C22⋊C4×C139—42no—
295C22⋊C4×C139—42no—
296C22⋊C4×C139—81no—
297C22⋊C4×C139—81no—
298C22⋊C4×C139—81no—
299C42×C139—24no—
300C23×C139—21no—
301C23×C139—21no—
302C23×C139—21no—
303C23×C139—21no—
304C23×C139—21no—
305C23×C139—21no—
306C23×C139—21no—
307C23×C139—21no—
308C23×C139—21no—
309C23×C139—21no—
310C23×C139—21no—
311C23×C139—21no—
312C23×C139—22no—
313C23×C139—22no—
314C23×C139—21no—
315C23×C139—21no—
316C23×C139—21no—
317C23×C139—21no—
318C23×C139—21no—
319C23×C139—21no—
320C23×C139—21no—
321C23×C139—48no—
322C23×C139—41no—
323C23×C139—41no—
324C23×C139—41no—
325C23×C139—41no—
326C23×C139—41no—
327C23×C139—41no—
328C23×C139—41no—
329C23×C139—41no—
330C23×C139—41no—
331C23×C139—41no—
332C23×C139—41no—
333C23×C139—41no—
334C23×C139—84no—
335C23×C139—84no—
336C23×C139—84no—
337C23×C139—84no—
338C23×C139—84no—
339C23×C139—84no—
340C23×C139#12012yes—
341C23×C139#12112yes—
342C23×C139C22×D411yescharacteristic
343Q8×C139—44no—
344Q8×C139—41no—
345Q8×C139—41no—
346Q8×C139—41no—
347Q8×C139—41no—
348D4×C139—22no—
349D4×C139—22no—
350D4×C139—22no—
351D4×C139—22no—
352D4×C139—44no—
353D4×C139—44no—
354D4×C139—48no—
355D4×C139—44no—
356D4×C139—41no—
357D4×C139—41no—
358D4×C139—41no—
359D4×C139—41no—
360D4×C139—84no—
361D4×C139—84no—
362D4×C139—84no—
363D4×C139—84no—
364C2×C4×C139—21no—
365C2×C4×C139—21no—
366C2×C4×C139—21no—
367C2×C4×C139—21no—
368C2×C4×C139—22no—
369C2×C4×C139—22no—
370C2×C4×C139—22no—
371C2×C4×C139—22no—
372C2×C4×C139—22no—
373C2×C4×C139—22no—
374C2×C4×C139—22no—
375C2×C4×C139—22no—
376C2×C4×C139—22no—
377C2×C4×C139—22no—
378C2×C4×C139—21no—
379C2×C4×C139—21no—
380C2×C4×C139—21no—
381C2×C4×C139—41no—
382C2×C4×C139—41no—
383C2×C4×C139—41no—
384C2×C4×C139—41no—
385C2×C4×C139—41no—
386C2×C4×C139—41no—
387C2×C4×C139—41no—
388C2×C4×C139—41no—
389C2×C4×C139—41no—
390C2×C4×C139—41no—
391C2×C4×C139—41no—
392C2×C4×C139—41no—
393C2×C4×C139—41no—
394C2×C4×C139—41no—
395C2×C4×C139—41no—
396C2×C4×C139—41no—
397C2×C4×C139—41no—
398C2×C4×C139—41no—
399C2×C4×C139—41no—
400C2×C4×C139—41no—
401C2×C4×C139#12012yes—
402C2×C4×C139#12112yes—
403C2×C4×C139C22×D411yescharacteristic
404C2×C4×C139C22×D411yescharacteristic
405C2×C4×C139C22×D411yescharacteristic
406C2×C4×C139C2×#4111yescharacteristic
407C2×C4×C139H(5,𝔽2)11yescharacteristic
408C2×C4×C139H(5,𝔽2)11yescharacteristic
409C8×C139—22no—
410C8×C139—22no—
411C8×C139—41no—
412C8×C139—41no—
413C22×C139—22no—
414C22×C139—22no—
415C22×C139—22no—
416C22×C139—22no—
417C22×C139—22no—
418C22×C139—22no—
419C22×C139—41no—
420C22×C139—41no—
421C22×C139—41no—
422C22×C139—41no—
423C22×C139—41no—
424C22×C139—41no—
425C22×C139—41no—
426C22×C139—41no—
427C22×C139—41no—
428C22×C139—42no—
429C22×C139—42no—
430C22×C139—41no—
431C22×C139—41no—
432C22×C139—41no—
433C22×C139—42no—
434C22×C139—42no—
435C22×C139—41no—
436C22×C139—42no—
437C22×C139—42no—
438C22×C139—41no—
439C22×C139—41no—
440C22×C139—816no—
441C22×C139—81no—
442C22×C139—81no—
443C22×C139—81no—
444C22×C139—81no—
445C22×C139—81no—
446C22×C139—81no—
447C22×C139—81no—
448C22×C139—81no—
449C22×C139C2×#12011yescharacteristic
450C22×C139C2×#12111yescharacteristic
451C22×C139#53411yescharacteristic
452C22×C139#57611yescharacteristic
453C22×C139#57711yescharacteristic
454C22×C139#57711yescharacteristic
455C22×C139#57711yescharacteristic
456C4×C139—22no—
457C4×C139—22no—
458C4×C139—41no—
459C4×C139—42no—
460C4×C139—42no—
461C4×C139—81no—
462C4×C139—81no—
463C4×C139—81no—
464C4×C139—81no—
465C4×C139D4211yescharacteristic
466C4×C139D4211yescharacteristic
467C4×C139#54611yescharacteristic
468C4×C139#54611yescharacteristic
469C2×C139—42no—
470C2×C139—42no—
471C2×C139—81no—
472C2×C139—82no—
473C2×C139—82no—
474C2×C139#241011yescharacteristic
475C2×C139#300911yescharacteristic
476C2×C139#301211yescharacteristic
477C2×C139#305711yescharacteristic
478C2×C139#306211yescharacteristic
479C2×C139#319811yescharacteristic
480C2×C139#320011yescharacteristic
481#24394C13911yesmaximal, characteristic, direct product factor, Sylow
482C139#2439411yescharacteristic, direct product factor, Sylow
483C2×#535C2×C13911yescharacteristic
484C2×#468C2×C13911yescharacteristic, complemented
485C2×#465C2×C13911yescharacteristic, complemented
486C2×#450C2×C13911yescharacteristic, complemented
487C2×#408C2×C13911yescharacteristic, complemented
488#2616C2×C13911yescharacteristic, complemented
489#2034C2×C13911yescharacteristic, complemented
490#2033C2×C13911yescharacteristic, complemented
491#2000C2×C13911yescharacteristic, complemented
492#2000C2×C13911yescharacteristic, complemented
493#1895C2×C13911yescharacteristic, complemented
494#1893C2×C13911yescharacteristic, complemented
495#1873C2×C13911yescharacteristic, complemented
496#1854C2×C13911yescharacteristic, complemented
497#1786C2×C13911yescharacteristic, complemented
498C22×#41C22×C13911yescharacteristic
499C23×D4C22×C13911yescharacteristic
500C22×SD16C22×C13911yescharacteristic
501C22×SD16C22×C13911yescharacteristic
502C22×M16C22×C13911yescharacteristic, complemented
503C23×C8C22×C13911yescharacteristic, complemented
504#535—24no—
505#535—24no—
506C2×#127—21no—
507C2×#124—21no—
508C2×C22⋊Q8C22×C13911yescharacteristic
509C2×C22⋊Q8C22×C13911yescharacteristic, complemented
510C2×C22⋊Q8C22×C13911yescharacteristic, complemented
511C2×#121C22×C13911yescharacteristic
512C2×#121C22×C13911yescharacteristic
513C2×#121C22×C13911yescharacteristic
514C2×#121C22×C13911yescharacteristic
515C2×#120—21no—
516C2×#120—21no—
517C2×#117C22×C13911yescharacteristic
518#468—24no—
519#465—24no—
520#450—24no—
521C2×#107C22×C13911yescharacteristic, complemented
522C2×#106C22×C13911yescharacteristic, complemented
523C2×#103C22×C13911yescharacteristic, complemented
524C2×#103C22×C13911yescharacteristic, complemented
525C2×#102C22×C13911yescharacteristic
526C2×#102C22×C13911yescharacteristic
527C2×#102C22×C13911yescharacteristic
528C2×#102C22×C13911yescharacteristic
529C2×#102C22×C13911yescharacteristic
530C2×#102C22×C13911yescharacteristic
531#408—24no—
532C2×C22⋊C8C22×C13911yescharacteristic
533C2×C22⋊C8C22×C13911yescharacteristic
534C2×C22⋊C8C22×C13911yescharacteristic, complemented
535C2×C22⋊C8C22×C13911yescharacteristic, complemented
536#395—21no—
537#394—21no—
538#394—21no—
539#394—21no—
540#380C22×C13911yescharacteristic
541#380C22×C13911yescharacteristic, complemented
542#380C22×C13911yescharacteristic, complemented
543#340C22×C13911yescharacteristic, complemented
544#340C22×C13911yescharacteristic, complemented
545#340C22×C13911yescharacteristic, complemented
546#340C22×C13911yescharacteristic, complemented
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C13911yescharacteristic
555C22×Q8C23×C13911yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—22no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C13911yescharacteristic
568C22×D4D4×C13911yescharacteristic
569C22×D4D4×C13911yescharacteristic
570C22×D4C23×C13911yescharacteristic
571C22×D4C23×C13911yescharacteristic
572C23×C4C23×C13911yescharacteristic
573C23×C4C23×C13911yescharacteristic
574C23×C4C23×C13911yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16—41no—
584C22×C8—22no—
585C22×C8—22no—
586C22×C8—41no—
587C22×C8C23×C13911yescharacteristic
588C22×C8C23×C13911yescharacteristic
589C22×C8C23×C13911yescharacteristic
590C22×C8C23×C13911yescharacteristic
591#127—28no—
592#124—28no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121D4×C13914yes—
606#121D4×C13914yes—
607#120—28no—
608#120—28no—
609#117—22no—
610#117—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4C23×C13911yescharacteristic
615C2×C4⋊C4C23×C13911yescharacteristic
616C2×C4⋊C4C23×C13911yescharacteristic
617C2×C4⋊C4C23×C13911yescharacteristic
618C2×C4⋊C4C23×C13911yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C42—21no—
631#107—22no—
632#106—22no—
633#103—22no—
634#103—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—22no—
644C22⋊C8D4×C13914yescomplemented
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—42no—
652C24—42no—
653C24—81no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24C2×D4×C13911yescharacteristic
658C24C2×D4×C13911yescharacteristic
659C24C2×D4×C13911yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—22no—
665C2×Q8—22no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—41no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—24no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—41no—
699C2×D4—41no—
700C2×D4—41no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C13912yes—
712C2×D4C2×D4×C13912yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4C2×D4×C13911yescharacteristic
734C22×C4C2×D4×C13911yescharacteristic
735C22×C4C2×D4×C13912yes—
736C22×C4C2×D4×C13912yes—
737C22×C4C2×D4×C13911yescharacteristic
738C22×C4C2×D4×C13912yes—
739C22×C4#41×C13912yes—
740C22×C4C24×C13911yescharacteristic
741SD16—44no—
742SD16—44no—
743M16—44no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—44no—
755C2×C8C2×D4×C13912yes—
756C2×C8C2×D4×C13912yes—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4—42no—
768C4⋊C4C2×D4×C13912yes—
769C4⋊C4C2×D4×C13912yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—42no—
778C22⋊C4—81no—
779C22⋊C4—81no—
780C22⋊C4—81no—
781C42—24no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23#120×C13912yes—
823C23#121×C13912yes—
824C23C22×D4×C13911yescharacteristic
825Q8—44no—
826Q8—41no—
827Q8—41no—
828Q8—41no—
829Q8—41no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—44no—
835D4—44no—
836D4—48no—
837D4—44no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—84no—
843D4—84no—
844D4—84no—
845D4—84no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4#120×C13912yes—
884C2×C4#121×C13912yes—
885C2×C4C22×D4×C13911yescharacteristic
886C2×C4C22×D4×C13911yescharacteristic
887C2×C4C22×D4×C13911yescharacteristic
888C2×C4C2×#41×C13911yescharacteristic
889C2×C4H(5,𝔽2)×C13911yescharacteristic
890C2×C4H(5,𝔽2)×C13911yescharacteristic
891C8—22no—
892C8—22no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—42no—
918C22—42no—
919C22—41no—
920C22—42no—
921C22—42no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C13911yescharacteristic
932C22C2×#121×C13911yescharacteristic
933C22#534×C13911yescharacteristic
934C22#576×C13911yescharacteristic
935C22#577×C13911yescharacteristic
936C22#577×C13911yescharacteristic
937C22#577×C13911yescharacteristic
938C4—22no—
939C4—22no—
940C4—41no—
941C4—42no—
942C4—42no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—81no—
947C4D42×C13911yescharacteristic
948C4D42×C13911yescharacteristic
949C4#546×C13911yescharacteristic
950C4#546×C13911yescharacteristic
951C2—42no—
952C2—42no—
953C2—81no—
954C2—82no—
955C2—82no—
956C2#2410×C13911yescharacteristic
957C2#3009×C13911yescharacteristic
958C2#3012×C13911yescharacteristic
959C2#3057×C13911yescharacteristic
960C2#3062×C13911yescharacteristic
961C2#3198×C13911yescharacteristic
962C2#3200×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#535×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×#468×C139C2semidirect
3. C2×#465×C139C2semidirect
4. C2×#450×C139C2semidirect
5. C2×#408×C139C2semidirect
6. #2616×C139C2semidirect
7. #2034×C139C2semidirect
8. #2033×C139C2semidirect
9. #2000×C139C2semidirect
10. #2000×C139C2semidirect
11. #1895×C139C2semidirect
12. #1893×C139C2semidirect
13. #1873×C139C2semidirect
14. #1854×C139C2semidirect
15. #1786×C139C2semidirect
20. C22×M16×C139C22semidirect
21. C23×C8×C139C22semidirect
27. C2×C22⋊Q8×C139C22semidirect
28. C2×C22⋊Q8×C139C22semidirect
39. C2×#107×C139C22semidirect
40. C2×#106×C139C22semidirect
41. C2×#103×C139C22semidirect
42. C2×#103×C139C22semidirect
52. C2×C22⋊C8×C139C22semidirect
53. C2×C22⋊C8×C139C22semidirect
59. #380×C139C22semidirect
60. #380×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
63. #340×C139C22semidirect
64. #340×C139C22semidirect
162. C22⋊C8×C139D4semidirect
481. #24394C139direct (N × H)
482. C139#24394direct (N × H)
484. C2×#468C2×C139semidirect
485. C2×#465C2×C139semidirect
486. C2×#450C2×C139semidirect
487. C2×#408C2×C139semidirect
488. #2616C2×C139semidirect
489. #2034C2×C139semidirect
490. #2033C2×C139semidirect
491. #2000C2×C139semidirect
492. #2000C2×C139semidirect
493. #1895C2×C139semidirect
494. #1893C2×C139semidirect
495. #1873C2×C139semidirect
496. #1854C2×C139semidirect
497. #1786C2×C139semidirect
502. C22×M16C22×C139semidirect
503. C23×C8C22×C139semidirect
509. C2×C22⋊Q8C22×C139semidirect
510. C2×C22⋊Q8C22×C139semidirect
521. C2×#107C22×C139semidirect
522. C2×#106C22×C139semidirect
523. C2×#103C22×C139semidirect
524. C2×#103C22×C139semidirect
534. C2×C22⋊C8C22×C139semidirect
535. C2×C22⋊C8C22×C139semidirect
541. #380C22×C139semidirect
542. #380C22×C139semidirect
543. #340C22×C139semidirect
544. #340C22×C139semidirect
545. #340C22×C139semidirect
546. #340C22×C139semidirect
644. C22⋊C8D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1392
C2×#468×C1392
C2×#465×C1392
C2×#450×C1392
C2×#408×C1392
#2616×C1392
#2034×C1392
#2033×C1392
#2000×C1392
#1895×C1392
#1893×C1392
#1873×C1392
#1854×C1392
#1786×C1392
#24394139