Finite Group Databasebeta

← C139×#22424 #48017020

Subgroups — C139×#22424 #48017020

Order 35584.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C139C211yesmaximal, characteristic
2C2×#435×C139C211yesmaximal, characteristic, complemented
3C2×#418×C139C211yesmaximal, characteristic, complemented
4C2×#416×C139C211yesmaximal, characteristic, complemented
5#2354×C139C211yesmaximal, characteristic, complemented
6#1983×C139C211yesmaximal, characteristic, complemented
7#1959×C139C211yesmaximal, characteristic, complemented
8#1894×C139C211yesmaximal, characteristic, complemented
9#1893×C139C211yesmaximal, characteristic, complemented
10#1875×C139C211yesmaximal, characteristic, complemented
11#1873×C139C211yesmaximal, characteristic, complemented
12#1802×C139C211yesmaximal, characteristic, complemented
13#1788×C139C211yesmaximal, characteristic, complemented
14#1786×C139C211yesmaximal, characteristic, complemented
15#1762×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C23×D4×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19C23×C8×C139C2211yescharacteristic, complemented
20#546×C139—24no—
21#546×C139C418yescomplemented
22C2×#124×C139C2211yescharacteristic
23C2×#123×C139—21no—
24C2×C22⋊Q8×C139C2211yescharacteristic
25C2×#121×C139—21no—
26C2×#121×C139C2211yescharacteristic
27C2×#120×C139—21no—
28C2×C4×D4×C139C2211yescharacteristic
29C2×C4×D4×C139C2211yescharacteristic
30C2×#117×C139C2211yescharacteristic
31C2×#117×C139C2211yescharacteristic, complemented
32C22×C22⋊C4×C139—21no—
33#435×C139—24no—
34C2×C4⋊C8×C139C2211yescharacteristic, complemented
35#418×C139—24no—
36#416×C139—24no—
37C2×#103×C139C2211yescharacteristic, complemented
38C2×#103×C139C2211yescharacteristic, complemented
39C2×#103×C139C2211yescharacteristic, complemented
40C2×#103×C139C2211yescharacteristic, complemented
41C2×#102×C139C2211yescharacteristic
42C2×#102×C139C2211yescharacteristic
43C2×#102×C139C2211yescharacteristic
44C2×#102×C139C2211yescharacteristic
45C2×#102×C139C2211yescharacteristic
46C2×#102×C139C2211yescharacteristic
47C2×#102×C139C2211yescharacteristic
48C2×#102×C139C2211yescharacteristic
49C2×C22⋊C8×C139C2211yescharacteristic
50C2×C22⋊C8×C139C2211yescharacteristic, complemented
51C2×#97×C139C2211yescharacteristic, complemented
52#390×C139—21no—
53#388×C139—21no—
54#388×C139—21no—
55#384×C139C2211yescharacteristic, complemented
56#380×C139C2211yescharacteristic
57#380×C139C2211yescharacteristic, complemented
58C4×C4⋊C4×C139—21no—
59C4×C4⋊C4×C139C2211yescharacteristic, complemented
60#340×C139C2211yescharacteristic, complemented
61#340×C139C2211yescharacteristic, complemented
62#340×C139C2211yescharacteristic, complemented
63#340×C139C2211yescharacteristic, complemented
64C25×C139—21no—
65C2×#41×C139—22no—
66C2×#41×C139—22no—
67C2×#41×C139—22no—
68C2×#41×C139—41no—
69C2×#41×C139—41no—
70C2×#41×C139C2×C414yes—
71C22×Q8×C139C2311yescharacteristic
72C22×D4×C139—22no—
73C22×D4×C139—22no—
74C22×D4×C139—21no—
75C22×D4×C139—21no—
76C22×D4×C139—21no—
77C22×D4×C139—22no—
78C22×D4×C139—41no—
79C22×D4×C139—41no—
80C22×D4×C139C2×C414yes—
81C22×D4×C139D411yescharacteristic
82C22×D4×C139C2311yescharacteristic
83C22×D4×C139C2311yescharacteristic
84C23×C4×C139—21no—
85C23×C4×C139—21no—
86C23×C4×C139C2311yescharacteristic
87C23×C4×C139C2311yescharacteristic
88C2×M16×C139—22no—
89C2×M16×C139—22no—
90C2×M16×C139—41no—
91C22×C8×C139—22no—
92C22×C8×C139—22no—
93C22×C8×C139—41no—
94C22×C8×C139C2311yescharacteristic
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97C22×C8×C139C2311yescharacteristic
98#124×C139—22no—
99#124×C139C2×C414yes—
100#123×C139—28no—
101C22⋊Q8×C139—22no—
102C22⋊Q8×C139C2×C414yes—
103#121×C139—22no—
104#121×C139—28no—
105#121×C139C2×C414yes—
106#120×C139—28no—
107C4×D4×C139—22no—
108C4×D4×C139C2×C414yes—
109C4×D4×C139C2×C414yes—
110C4×D4×C139D414yes—
111#117×C139—22no—
112#117×C139—22no—
113#117×C139—41no—
114#117×C139—41no—
115C2×C4⋊C4×C139—21no—
116C2×C4⋊C4×C139—21no—
117C2×C4⋊C4×C139—21no—
118C2×C4⋊C4×C139D411yescharacteristic
119C2×C4⋊C4×C139C2311yescharacteristic
120C2×C4⋊C4×C139C2311yescharacteristic
121C2×C4⋊C4×C139C2311yescharacteristic
122C2×C4⋊C4×C139C2311yescharacteristic
123C2×C4⋊C4×C139C2311yescharacteristic
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—28no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—21no—
134C2×C22⋊C4×C139D411yescharacteristic
135C2×C22⋊C4×C139D411yescharacteristic
136C2×C42×C139—21no—
137C2×C42×C139—21no—
138C2×C42×C139—21no—
139C2×C42×C139C2311yescharacteristic
140C4⋊C8×C139—22no—
141#103×C139—22no—
142#103×C139—22no—
143#103×C139—41no—
144#103×C139—41no—
145#102×C139—22no—
146#102×C139—22no—
147#102×C139—22no—
148#102×C139—22no—
149#102×C139—22no—
150#102×C139—41no—
151#102×C139—41no—
152#102×C139D414yescomplemented
153C22⋊C8×C139—22no—
154C22⋊C8×C139—22no—
155#97×C139—22no—
156#95×C139—21no—
157#95×C139—21no—
158#95×C139—21no—
159C24×C139—21no—
160C24×C139—21no—
161C24×C139—24no—
162C24×C139—42no—
163C24×C139—42no—
164C24×C139—42no—
165C24×C139—42no—
166C24×C139—81no—
167C24×C139—81no—
168C24×C139C2×D411yescharacteristic
169C24×C139C2×D411yescharacteristic
170#41×C139—28no—
171#41×C139—44no—
172#41×C139—44no—
173#41×C139—44no—
174C2×Q8×C139—21no—
175C2×Q8×C139—21no—
176C2×Q8×C139—21no—
177C2×Q8×C139—21no—
178C2×Q8×C139—21no—
179C2×Q8×C139C22×C412yes—
180C2×D4×C139—28no—
181C2×D4×C139—24no—
182C2×D4×C139—24no—
183C2×D4×C139—24no—
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—21no—
191C2×D4×C139—21no—
192C2×D4×C139—44no—
193C2×D4×C139—44no—
194C2×D4×C139—44no—
195C2×D4×C139—41no—
196C2×D4×C139—41no—
197C2×D4×C139—42no—
198C2×D4×C139—42no—
199C2×D4×C139—42no—
200C2×D4×C139—42no—
201C2×D4×C139—81no—
202C2×D4×C139—81no—
203C2×D4×C139C22⋊C414yes—
204C2×D4×C139C22×C412yes—
205C2×D4×C139C22×C412yes—
206C2×D4×C139C2×D412yes—
207C2×D4×C139#4112yes—
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—21no—
219C22×C4×C139—24no—
220C22×C4×C139—24no—
221C22×C4×C139—21no—
222C22×C4×C139—21no—
223C22×C4×C139—21no—
224C22×C4×C139—42no—
225C22×C4×C139—42no—
226C22×C4×C139—81no—
227C22×C4×C139—81no—
228C22×C4×C139C22×C412yes—
229C22×C4×C139C22×C412yes—
230C22×C4×C139C2×D411yescharacteristic
231C22×C4×C139C2×D411yescharacteristic
232C22×C4×C139C2×D411yescharacteristic
233C22×C4×C139C2×D411yescharacteristic
234C22×C4×C139C2×D412yes—
235C22×C4×C139C2×D412yes—
236C22×C4×C139C2411yescharacteristic
237M16×C139—44no—
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—
249C2×C8×C139—44no—
250C2×C8×C139C2×D412yes—
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—42no—
261C4⋊C4×C139—81no—
262C4⋊C4×C139C22⋊C414yes—
263C4⋊C4×C139C22×C412yes—
264C4⋊C4×C139C2×D412yes—
265C22⋊C4×C139—24no—
266C22⋊C4×C139—24no—
267C22⋊C4×C139—24no—
268C22⋊C4×C139—24no—
269C22⋊C4×C139—24no—
270C22⋊C4×C139—42no—
271C22⋊C4×C139—42no—
272C22⋊C4×C139—81no—
273C22⋊C4×C139—81no—
274C22⋊C4×C139C22⋊C414yes—
275C22⋊C4×C139C22⋊C414yes—
276C42×C139—42no—
277C42×C139—42no—
278C42×C139—42no—
279C42×C139C22×C412yes—
280C42×C139C2×D412yes—
281C23×C139—22no—
282C23×C139—21no—
283C23×C139—21no—
284C23×C139—22no—
285C23×C139—21no—
286C23×C139—21no—
287C23×C139—22no—
288C23×C139—21no—
289C23×C139—21no—
290C23×C139—21no—
291C23×C139—21no—
292C23×C139—21no—
293C23×C139—21no—
294C23×C139—21no—
295C23×C139—21no—
296C23×C139—22no—
297C23×C139—48no—
298C23×C139—48no—
299C23×C139—41no—
300C23×C139—41no—
301C23×C139—41no—
302C23×C139—41no—
303C23×C139—41no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—41no—
307C23×C139—41no—
308C23×C139—41no—
309C23×C139—84no—
310C23×C139—84no—
311C23×C139—84no—
312C23×C139—84no—
313C23×C139—84no—
314C23×C139C2×C22⋊C412yes—
315C23×C139C2×C22⋊C412yes—
316C23×C139C22×D411yescharacteristic
317Q8×C139—22no—
318Q8×C139—22no—
319Q8×C139—41no—
320Q8×C139—41no—
321D4×C139—22no—
322D4×C139—22no—
323D4×C139—22no—
324D4×C139—22no—
325D4×C139—22no—
326D4×C139—44no—
327D4×C139—48no—
328D4×C139—48no—
329D4×C139—41no—
330D4×C139—41no—
331D4×C139—84no—
332D4×C139C4×D414yes—
333C2×C4×C139—21no—
334C2×C4×C139—21no—
335C2×C4×C139—21no—
336C2×C4×C139—21no—
337C2×C4×C139—21no—
338C2×C4×C139—21no—
339C2×C4×C139—21no—
340C2×C4×C139—21no—
341C2×C4×C139—22no—
342C2×C4×C139—22no—
343C2×C4×C139—22no—
344C2×C4×C139—22no—
345C2×C4×C139—22no—
346C2×C4×C139—22no—
347C2×C4×C139—22no—
348C2×C4×C139—22no—
349C2×C4×C139—22no—
350C2×C4×C139—22no—
351C2×C4×C139—22no—
352C2×C4×C139—48no—
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—41no—
367C2×C4×C139—41no—
368C2×C4×C139—84no—
369C2×C4×C139C2×C22⋊C412yes—
370C2×C4×C139C2×C22⋊C412yes—
371C2×C4×C139C2×C22⋊C412yes—
372C2×C4×C139C2×C22⋊C412yes—
373C2×C4×C139C23×C411yescharacteristic
374C2×C4×C139C22×D411yescharacteristic
375C2×C4×C139C22×D411yescharacteristic
376C2×C4×C139C2×#4111yescharacteristic
377C2×C4×C139H(5,𝔽2)11yescharacteristic
378C2×C4×C139H(5,𝔽2)11yescharacteristic
379C8×C139—22no—
380C8×C139—41no—
381C8×C139—41no—
382C8×C139—41no—
383C22×C139—22no—
384C22×C139—22no—
385C22×C139—24no—
386C22×C139—22no—
387C22×C139—22no—
388C22×C139—22no—
389C22×C139—22no—
390C22×C139—42no—
391C22×C139—42no—
392C22×C139—41no—
393C22×C139—41no—
394C22×C139—42no—
395C22×C139—41no—
396C22×C139—41no—
397C22×C139—42no—
398C22×C139—41no—
399C22×C139—41no—
400C22×C139—42no—
401C22×C139—41no—
402C22×C139—41no—
403C22×C139—42no—
404C22×C139—42no—
405C22×C139—42no—
406C22×C139—42no—
407C22×C139—816no—
408C22×C139—81no—
409C22×C139—81no—
410C22×C139—81no—
411C22×C139—81no—
412C22×C139C22×C22⋊C411yescharacteristic
413C22×C139D4211yescharacteristic
414C22×C139#54611yescharacteristic
415C22×C139#57511yescharacteristic
416C22×C139#57511yescharacteristic
417C22×C139#57611yescharacteristic
418C22×C139#57711yescharacteristic
419C4×C139—22no—
420C4×C139—22no—
421C4×C139—22no—
422C4×C139—22no—
423C4×C139—42no—
424C4×C139—42no—
425C4×C139—42no—
426C4×C139—81no—
427C4×C139—81no—
428C4×C139—81no—
429C4×C139C2×C4×D411yescharacteristic
430C4×C139#51811yescharacteristic
431C4×C139D4211yescharacteristic
432C4×C139#54611yescharacteristic
433C2×C139—42no—
434C2×C139—42no—
435C2×C139—44no—
436C2×C139—82no—
437C2×C139D4×C22⋊C411yescharacteristic
438C2×C139#289611yescharacteristic
439C2×C139#289711yescharacteristic
440C2×C139#326711yescharacteristic
441C2×C139#326811yescharacteristic
442C2×C139#331111yescharacteristic
443C2×C139#331911yescharacteristic
444#22424C13911yesmaximal, characteristic, direct product factor, Sylow
445C139#2242411yescharacteristic, direct product factor, Sylow
446C2×#546C2×C13911yescharacteristic
447C2×#435C2×C13911yescharacteristic, complemented
448C2×#418C2×C13911yescharacteristic, complemented
449C2×#416C2×C13911yescharacteristic, complemented
450#2354C2×C13911yescharacteristic, complemented
451#1983C2×C13911yescharacteristic, complemented
452#1959C2×C13911yescharacteristic, complemented
453#1894C2×C13911yescharacteristic, complemented
454#1893C2×C13911yescharacteristic, complemented
455#1875C2×C13911yescharacteristic, complemented
456#1873C2×C13911yescharacteristic, complemented
457#1802C2×C13911yescharacteristic, complemented
458#1788C2×C13911yescharacteristic, complemented
459#1786C2×C13911yescharacteristic, complemented
460#1762C2×C13911yescharacteristic, complemented
461C22×#41C22×C13911yescharacteristic
462C23×D4C22×C13911yescharacteristic
463C22×M16C22×C13911yescharacteristic
464C23×C8C22×C13911yescharacteristic, complemented
465#546—24no—
466#546C4×C13918yescomplemented
467C2×#124C22×C13911yescharacteristic
468C2×#123—21no—
469C2×C22⋊Q8C22×C13911yescharacteristic
470C2×#121—21no—
471C2×#121C22×C13911yescharacteristic
472C2×#120—21no—
473C2×C4×D4C22×C13911yescharacteristic
474C2×C4×D4C22×C13911yescharacteristic
475C2×#117C22×C13911yescharacteristic
476C2×#117C22×C13911yescharacteristic, complemented
477C22×C22⋊C4—21no—
478#435—24no—
479C2×C4⋊C8C22×C13911yescharacteristic, complemented
480#418—24no—
481#416—24no—
482C2×#103C22×C13911yescharacteristic, complemented
483C2×#103C22×C13911yescharacteristic, complemented
484C2×#103C22×C13911yescharacteristic, complemented
485C2×#103C22×C13911yescharacteristic, complemented
486C2×#102C22×C13911yescharacteristic
487C2×#102C22×C13911yescharacteristic
488C2×#102C22×C13911yescharacteristic
489C2×#102C22×C13911yescharacteristic
490C2×#102C22×C13911yescharacteristic
491C2×#102C22×C13911yescharacteristic
492C2×#102C22×C13911yescharacteristic
493C2×#102C22×C13911yescharacteristic
494C2×C22⋊C8C22×C13911yescharacteristic
495C2×C22⋊C8C22×C13911yescharacteristic, complemented
496C2×#97C22×C13911yescharacteristic, complemented
497#390—21no—
498#388—21no—
499#388—21no—
500#384C22×C13911yescharacteristic, complemented
501#380C22×C13911yescharacteristic
502#380C22×C13911yescharacteristic, complemented
503C4×C4⋊C4—21no—
504C4×C4⋊C4C22×C13911yescharacteristic, complemented
505#340C22×C13911yescharacteristic, complemented
506#340C22×C13911yescharacteristic, complemented
507#340C22×C13911yescharacteristic, complemented
508#340C22×C13911yescharacteristic, complemented
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C13914yes—
516C22×Q8C23×C13911yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×C4×C13914yes—
526C22×D4D4×C13911yescharacteristic
527C22×D4C23×C13911yescharacteristic
528C22×D4C23×C13911yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C23×C13911yescharacteristic
532C23×C4C23×C13911yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8C23×C13911yescharacteristic
540C22×C8C23×C13911yescharacteristic
541C22×C8C23×C13911yescharacteristic
542C22×C8C23×C13911yescharacteristic
543#124—22no—
544#124C2×C4×C13914yes—
545#123—28no—
546C22⋊Q8—22no—
547C22⋊Q8C2×C4×C13914yes—
548#121—22no—
549#121—28no—
550#121C2×C4×C13914yes—
551#120—28no—
552C4×D4—22no—
553C4×D4C2×C4×C13914yes—
554C4×D4C2×C4×C13914yes—
555C4×D4D4×C13914yes—
556#117—22no—
557#117—22no—
558#117—41no—
559#117—41no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4D4×C13911yescharacteristic
564C2×C4⋊C4C23×C13911yescharacteristic
565C2×C4⋊C4C23×C13911yescharacteristic
566C2×C4⋊C4C23×C13911yescharacteristic
567C2×C4⋊C4C23×C13911yescharacteristic
568C2×C4⋊C4C23×C13911yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4D4×C13911yescharacteristic
580C2×C22⋊C4D4×C13911yescharacteristic
581C2×C42—21no—
582C2×C42—21no—
583C2×C42—21no—
584C2×C42C23×C13911yescharacteristic
585C4⋊C8—22no—
586#103—22no—
587#103—22no—
588#103—41no—
589#103—41no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—22no—
595#102—41no—
596#102—41no—
597#102D4×C13914yescomplemented
598C22⋊C8—22no—
599C22⋊C8—22no—
600#97—22no—
601#95—21no—
602#95—21no—
603#95—21no—
604C24—21no—
605C24—21no—
606C24—24no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—81no—
612C24—81no—
613C24C2×D4×C13911yescharacteristic
614C24C2×D4×C13911yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C22×C4×C13912yes—
625C2×D4—28no—
626C2×D4—24no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—41no—
641C2×D4—41no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—81no—
647C2×D4—81no—
648C2×D4C22⋊C4×C13914yes—
649C2×D4C22×C4×C13912yes—
650C2×D4C22×C4×C13912yes—
651C2×D4C2×D4×C13912yes—
652C2×D4#41×C13912yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4C22×C4×C13912yes—
674C22×C4C22×C4×C13912yes—
675C22×C4C2×D4×C13911yescharacteristic
676C22×C4C2×D4×C13911yescharacteristic
677C22×C4C2×D4×C13911yescharacteristic
678C22×C4C2×D4×C13911yescharacteristic
679C22×C4C2×D4×C13912yes—
680C22×C4C2×D4×C13912yes—
681C22×C4C24×C13911yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—44no—
695C2×C8C2×D4×C13912yes—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—81no—
707C4⋊C4C22⋊C4×C13914yes—
708C4⋊C4C22×C4×C13912yes—
709C4⋊C4C2×D4×C13912yes—
710C22⋊C4—24no—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C22⋊C4C22⋊C4×C13914yes—
720C22⋊C4C22⋊C4×C13914yes—
721C42—42no—
722C42—42no—
723C42—42no—
724C42C22×C4×C13912yes—
725C42C2×D4×C13912yes—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—22no—
742C23—48no—
743C23—48no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23C2×C22⋊C4×C13912yes—
760C23C2×C22⋊C4×C13912yes—
761C23C22×D4×C13911yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—44no—
772D4—48no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—84no—
777D4C4×D4×C13914yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—48no—
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—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—84no—
814C2×C4C2×C22⋊C4×C13912yes—
815C2×C4C2×C22⋊C4×C13912yes—
816C2×C4C2×C22⋊C4×C13912yes—
817C2×C4C2×C22⋊C4×C13912yes—
818C2×C4C23×C4×C13911yescharacteristic
819C2×C4C22×D4×C13911yescharacteristic
820C2×C4C22×D4×C13911yescharacteristic
821C2×C4C2×#41×C13911yescharacteristic
822C2×C4H(5,𝔽2)×C13911yescharacteristic
823C2×C4H(5,𝔽2)×C13911yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C22—22no—
829C22—22no—
830C22—24no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—42no—
846C22—41no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—816no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×C22⋊C4×C13911yescharacteristic
858C22D42×C13911yescharacteristic
859C22#546×C13911yescharacteristic
860C22#575×C13911yescharacteristic
861C22#575×C13911yescharacteristic
862C22#576×C13911yescharacteristic
863C22#577×C13911yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—81no—
872C4—81no—
873C4—81no—
874C4C2×C4×D4×C13911yescharacteristic
875C4#518×C13911yescharacteristic
876C4D42×C13911yescharacteristic
877C4#546×C13911yescharacteristic
878C2—42no—
879C2—42no—
880C2—44no—
881C2—82no—
882C2D4×C22⋊C4×C13911yescharacteristic
883C2#2896×C13911yescharacteristic
884C2#2897×C13911yescharacteristic
885C2#3267×C13911yescharacteristic
886C2#3268×C13911yescharacteristic
887C2#3311×C13911yescharacteristic
888C2#3319×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC2×#546×C139C2
LCSG ▷ C2×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×#435×C139C2semidirect
3. C2×#418×C139C2semidirect
4. C2×#416×C139C2semidirect
5. #2354×C139C2semidirect
6. #1983×C139C2semidirect
7. #1959×C139C2semidirect
8. #1894×C139C2semidirect
9. #1893×C139C2semidirect
10. #1875×C139C2semidirect
11. #1873×C139C2semidirect
12. #1802×C139C2semidirect
13. #1788×C139C2semidirect
14. #1786×C139C2semidirect
15. #1762×C139C2semidirect
19. C23×C8×C139C22semidirect
21. #546×C139C4semidirect
31. C2×#117×C139C22semidirect
34. C2×C4⋊C8×C139C22semidirect
37. C2×#103×C139C22semidirect
38. C2×#103×C139C22semidirect
39. C2×#103×C139C22semidirect
40. C2×#103×C139C22semidirect
50. C2×C22⋊C8×C139C22semidirect
51. C2×#97×C139C22semidirect
55. #384×C139C22semidirect
57. #380×C139C22semidirect
59. C4×C4⋊C4×C139C22semidirect
60. #340×C139C22semidirect
61. #340×C139C22semidirect
62. #340×C139C22semidirect
63. #340×C139C22semidirect
152. #102×C139D4semidirect
444. #22424C139direct (N × H)
445. C139#22424direct (N × H)
447. C2×#435C2×C139semidirect
448. C2×#418C2×C139semidirect
449. C2×#416C2×C139semidirect
450. #2354C2×C139semidirect
451. #1983C2×C139semidirect
452. #1959C2×C139semidirect
453. #1894C2×C139semidirect
454. #1893C2×C139semidirect
455. #1875C2×C139semidirect
456. #1873C2×C139semidirect
457. #1802C2×C139semidirect
458. #1788C2×C139semidirect
459. #1786C2×C139semidirect
460. #1762C2×C139semidirect
464. C23×C8C22×C139semidirect
466. #546C4×C139semidirect
476. C2×#117C22×C139semidirect
479. C2×C4⋊C8C22×C139semidirect
482. C2×#103C22×C139semidirect
483. C2×#103C22×C139semidirect
484. C2×#103C22×C139semidirect
485. C2×#103C22×C139semidirect
495. C2×C22⋊C8C22×C139semidirect
496. C2×#97C22×C139semidirect
500. #384C22×C139semidirect
502. #380C22×C139semidirect
504. C4×C4⋊C4C22×C139semidirect
505. #340C22×C139semidirect
506. #340C22×C139semidirect
507. #340C22×C139semidirect
508. #340C22×C139semidirect
597. #102D4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1392
C2×#435×C1392
C2×#418×C1392
C2×#416×C1392
#2354×C1392
#1983×C1392
#1959×C1392
#1894×C1392
#1893×C1392
#1875×C1392
#1873×C1392
#1802×C1392
#1788×C1392
#1786×C1392
#1762×C1392
#22424139