Finite Group Databasebeta

← C139×#21772 #48016368

Subgroups — C139×#21772 #48016368

Order 35584.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C139C211yesmaximal, characteristic
2C2×#408×C139C211yesmaximal, characteristic, complemented
3#2311×C139C211yesmaximal, characteristic, complemented
4#1895×C139C211yesmaximal, characteristic, complemented
5#1894×C139C211yesmaximal, characteristic, complemented
6#1893×C139C211yesmaximal, characteristic, complemented
7#1892×C139C211yesmaximal, characteristic, complemented
8#1875×C139C211yesmaximal, characteristic, complemented
9#1874×C139C211yesmaximal, characteristic, complemented
10#1873×C139C211yesmaximal, characteristic, complemented
11#1872×C139C211yesmaximal, characteristic, complemented
12#1824×C139C211yesmaximal, characteristic, complemented
13#1823×C139C211yesmaximal, characteristic, complemented
14#1788×C139C211yesmaximal, characteristic, complemented
15#1788×C139C211yesmaximal, characteristic, complemented
16C22×#41×C139C2211yescharacteristic
17C22×#41×C139C2211yescharacteristic
18C22×M16×C139C2211yescharacteristic
19C23×C8×C139C2211yescharacteristic
20#537×C139—24no—
21#537×C139C418yescomplemented
22C2×C22⋊Q8×C139—21no—
23C2×C22⋊Q8×C139C2211yescharacteristic
24C2×C22⋊Q8×C139C2211yescharacteristic
25C2×#121×C139—21no—
26C2×#121×C139—21no—
27C2×#121×C139—21no—
28C2×#121×C139C2211yescharacteristic
29C2×#121×C139C2211yescharacteristic
30C2×#117×C139C2211yescharacteristic
31C22×C4⋊C4×C139C2211yescharacteristic
32C22×C4⋊C4×C139C2211yescharacteristic
33C2×#103×C139C2211yescharacteristic
34C2×#103×C139C2211yescharacteristic
35C2×#103×C139C2211yescharacteristic
36C2×#103×C139C2211yescharacteristic
37C2×#102×C139C2211yescharacteristic
38C2×#102×C139C2211yescharacteristic
39C2×#102×C139C2211yescharacteristic
40C2×#102×C139C2211yescharacteristic
41#408×C139—24no—
42C2×C22⋊C8×C139C2211yescharacteristic
43C2×C22⋊C8×C139C2211yescharacteristic
44C2×C22⋊C8×C139C2211yescharacteristic
45C2×C22⋊C8×C139C2211yescharacteristic
46#391×C139—21no—
47#390×C139—21no—
48#386×C139—21no—
49#386×C139—21no—
50#380×C139C2211yescharacteristic
51#380×C139C2211yescharacteristic
52#380×C139C2211yescharacteristic
53#380×C139C2211yescharacteristic
54#340×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic
56#340×C139C2211yescharacteristic
57#340×C139C2211yescharacteristic
58#340×C139C2211yescharacteristic
59#340×C139C2211yescharacteristic
60#340×C139C2211yescharacteristic
61#340×C139C2211yescharacteristic
62C2×#41×C139—22no—
63C2×#41×C139—41no—
64C2×#41×C139—41no—
65C2×#41×C139—41no—
66C2×#41×C139—41no—
67C2×#41×C139—41no—
68C2×#41×C139—41no—
69C2×#41×C139—41no—
70C2×#41×C139—41no—
71C2×#41×C139C2×C414yes—
72C2×#41×C139C2×C414yescomplemented
73C2×#41×C139D414yes—
74C22×Q8×C139D411yescharacteristic
75C22×Q8×C139C2311yescharacteristic
76C22×D4×C139—21no—
77C22×D4×C139—21no—
78C22×D4×C139—21no—
79C22×D4×C139D411yescharacteristic
80C22×D4×C139D411yescharacteristic
81C22×D4×C139D411yescharacteristic
82C22×D4×C139C2311yescharacteristic
83C23×C4×C139—21no—
84C23×C4×C139—21no—
85C23×C4×C139—21no—
86C23×C4×C139C2311yescharacteristic
87C23×C4×C139C2311yescharacteristic
88C23×C4×C139C2311yescharacteristic
89C2×M16×C139—22no—
90C2×M16×C139—41no—
91C2×M16×C139—41no—
92C22×C8×C139—22no—
93C22×C8×C139—41no—
94C22×C8×C139—41no—
95C22×C8×C139C2311yescharacteristic
96C22×C8×C139C2311yescharacteristic
97C22×C8×C139C2311yescharacteristic
98C22×C8×C139C2311yescharacteristic
99C22⋊Q8×C139—28no—
100C22⋊Q8×C139—22no—
101C22⋊Q8×C139—22no—
102C22⋊Q8×C139C2×C414yes—
103C22⋊Q8×C139C2×C414yescomplemented
104#121×C139—28no—
105#121×C139—28no—
106#121×C139—28no—
107#121×C139—22no—
108#121×C139—22no—
109#121×C139C2×C414yes—
110#121×C139C2×C414yescomplemented
111#117×C139—41no—
112#117×C139—41no—
113C2×C4⋊C4×C139—21no—
114C2×C4⋊C4×C139—22no—
115C2×C4⋊C4×C139—21no—
116C2×C4⋊C4×C139—21no—
117C2×C4⋊C4×C139—21no—
118C2×C4⋊C4×C139—41no—
119C2×C4⋊C4×C139—41no—
120C2×C4⋊C4×C139C2×C414yescomplemented
121C2×C4⋊C4×C139C2311yescharacteristic
122C2×C4⋊C4×C139C2311yescharacteristic
123C2×C4⋊C4×C139C2311yescharacteristic
124C2×C4⋊C4×C139C2311yescharacteristic
125C2×C4⋊C4×C139C2311yescharacteristic
126C2×C4⋊C4×C139C2311yescharacteristic
127C2×C22⋊C4×C139—21no—
128C2×C22⋊C4×C139—21no—
129C2×C22⋊C4×C139—21no—
130C2×C22⋊C4×C139—21no—
131C2×C22⋊C4×C139—21no—
132C2×C22⋊C4×C139—21no—
133C2×C22⋊C4×C139—21no—
134C2×C22⋊C4×C139—21no—
135C2×C22⋊C4×C139—21no—
136C2×C42×C139—21no—
137#103×C139—41no—
138#103×C139—41no—
139#103×C139—41no—
140#103×C139—41no—
141#102×C139—41no—
142#102×C139—41no—
143#102×C139—41no—
144#102×C139—41no—
145C22⋊C8×C139—22no—
146C22⋊C8×C139—22no—
147C22⋊C8×C139—22no—
148C22⋊C8×C139—22no—
149#95×C139—21no—
150#95×C139—21no—
151#95×C139—21no—
152#95×C139—21no—
153C24×C139—21no—
154C24×C139C2×D411yescharacteristic
155C24×C139C2×D411yescharacteristic
156C24×C139C2×D411yescharacteristic
157#41×C139—44no—
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—
165C2×Q8×C139—21no—
166C2×Q8×C139—21no—
167C2×Q8×C139—21no—
168C2×Q8×C139—21no—
169C2×Q8×C139—21no—
170C2×Q8×C139—41no—
171C2×Q8×C139—41no—
172C2×Q8×C139C22⋊C414yes—
173C2×Q8×C139C22×C412yes—
174C2×D4×C139—24no—
175C2×D4×C139—24no—
176C2×D4×C139—24no—
177C2×D4×C139—21no—
178C2×D4×C139—21no—
179C2×D4×C139—21no—
180C2×D4×C139—21no—
181C2×D4×C139—21no—
182C2×D4×C139—41no—
183C2×D4×C139—41no—
184C2×D4×C139—41no—
185C2×D4×C139—41no—
186C2×D4×C139—41no—
187C2×D4×C139—41no—
188C2×D4×C139—42no—
189C2×D4×C139—42no—
190C2×D4×C139—81no—
191C2×D4×C139—81no—
192C2×D4×C139—81no—
193C2×D4×C139—81no—
194C2×D4×C139C22⋊C414yes—
195C2×D4×C139C22⋊C414yes—
196C2×D4×C139C22⋊C414yes—
197C2×D4×C139C22×C412yes—
198C22×C4×C139—21no—
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—21no—
208C22×C4×C139—21no—
209C22×C4×C139—21no—
210C22×C4×C139—21no—
211C22×C4×C139—21no—
212C22×C4×C139—21no—
213C22×C4×C139—24no—
214C22×C4×C139—24no—
215C22×C4×C139—21no—
216C22×C4×C139—21no—
217C22×C4×C139—21no—
218C22×C4×C139—21no—
219C22×C4×C139—42no—
220C22×C4×C139—42no—
221C22×C4×C139—42no—
222C22×C4×C139—81no—
223C22×C4×C139—81no—
224C22×C4×C139—81no—
225C22×C4×C139—81no—
226C22×C4×C139C22×C412yes—
227C22×C4×C139C22×C412yes—
228C22×C4×C139C22×C412yes—
229C22×C4×C139C2×D411yescharacteristic
230C22×C4×C139C2×D411yescharacteristic
231C22×C4×C139C2×D411yescharacteristic
232C22×C4×C139C2×D412yes—
233C22×C4×C139C2×D412yes—
234C22×C4×C139C2×D412yes—
235C22×C4×C139C2411yescharacteristic
236M16×C139—44no—
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—
249C2×C8×C139—44no—
250C4⋊C4×C139—24no—
251C4⋊C4×C139—24no—
252C4⋊C4×C139—24no—
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—21no—
263C4⋊C4×C139—42no—
264C4⋊C4×C139C22×C412yes—
265C4⋊C4×C139C22×C412yes—
266C22⋊C4×C139—24no—
267C22⋊C4×C139—24no—
268C22⋊C4×C139—24no—
269C22⋊C4×C139—24no—
270C22⋊C4×C139—42no—
271C22⋊C4×C139—81no—
272C22⋊C4×C139—81no—
273C22⋊C4×C139—81no—
274C22⋊C4×C139—81no—
275C42×C139—42no—
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—21no—
294C23×C139—22no—
295C23×C139—41no—
296C23×C139—41no—
297C23×C139—41no—
298C23×C139—41no—
299C23×C139—41no—
300C23×C139—41no—
301C23×C139C2×C22⋊C412yes—
302C23×C139C2×C22⋊C412yes—
303C23×C139C2×C22⋊C412yes—
304C23×C139C22×D411yescharacteristic
305Q8×C139—22no—
306Q8×C139—22no—
307Q8×C139—44no—
308Q8×C139—41no—
309Q8×C139—41no—
310D4×C139—22no—
311D4×C139—22no—
312D4×C139—44no—
313D4×C139—44no—
314D4×C139—44no—
315D4×C139—48no—
316D4×C139—41no—
317D4×C139—41no—
318D4×C139—84no—
319D4×C139—84no—
320C2×C4×C139—21no—
321C2×C4×C139—21no—
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—22no—
337C2×C4×C139—22no—
338C2×C4×C139—22no—
339C2×C4×C139—22no—
340C2×C4×C139—22no—
341C2×C4×C139—48no—
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×C139C2×C22⋊C412yes—
363C2×C4×C139C2×C22⋊C412yes—
364C2×C4×C139C2×C22⋊C412yes—
365C2×C4×C139C23×C411yescharacteristic
366C2×C4×C139C22×D411yescharacteristic
367C2×C4×C139H(5,𝔽2)11yescharacteristic
368C2×C4×C139H(5,𝔽2)11yescharacteristic
369C2×C4×C139H(5,𝔽2)11yescharacteristic
370C2×C4×C139H(5,𝔽2)11yescharacteristic
371C8×C139—41no—
372C8×C139—41no—
373C8×C139—41no—
374C8×C139—41no—
375C22×C139—22no—
376C22×C139—22no—
377C22×C139—22no—
378C22×C139—22no—
379C22×C139—22no—
380C22×C139—22no—
381C22×C139—22no—
382C22×C139—22no—
383C22×C139—22no—
384C22×C139—41no—
385C22×C139—41no—
386C22×C139—41no—
387C22×C139—41no—
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—42no—
397C22×C139—42no—
398C22×C139—42no—
399C22×C139—81no—
400C22×C139—81no—
401C22×C139—81no—
402C22×C139—81no—
403C22×C139C22×C22⋊C411yescharacteristic
404C22×C139#53411yescharacteristic
405C22×C139#53411yescharacteristic
406C22×C139#57611yescharacteristic
407C22×C139#57711yescharacteristic
408C22×C139#57711yescharacteristic
409C22×C139#57811yescharacteristic
410C4×C139—22no—
411C4×C139—22no—
412C4×C139—22no—
413C4×C139—42no—
414C4×C139—42no—
415C4×C139—42no—
416C4×C139—81no—
417C4×C139—81no—
418C4×C139—81no—
419C4×C139—81no—
420C4×C139#51811yescharacteristic
421C4×C139#51811yescharacteristic
422C4×C139#53411yescharacteristic
423C4×C139#53411yescharacteristic
424C2×C139—42no—
425C2×C139—42no—
426C2×C139—42no—
427C2×C139—82no—
428C2×C139#230811yescharacteristic
429C2×C139#289711yescharacteristic
430C2×C139#289811yescharacteristic
431C2×C139#319811yescharacteristic
432C2×C139#320111yescharacteristic
433C2×C139#320311yescharacteristic
434C2×C139#320411yescharacteristic
435#21772C13911yesmaximal, characteristic, direct product factor, Sylow
436C139#2177211yescharacteristic, direct product factor, Sylow
437C2×#537C2×C13911yescharacteristic
438C2×#408C2×C13911yescharacteristic, complemented
439#2311C2×C13911yescharacteristic, complemented
440#1895C2×C13911yescharacteristic, complemented
441#1894C2×C13911yescharacteristic, complemented
442#1893C2×C13911yescharacteristic, complemented
443#1892C2×C13911yescharacteristic, complemented
444#1875C2×C13911yescharacteristic, complemented
445#1874C2×C13911yescharacteristic, complemented
446#1873C2×C13911yescharacteristic, complemented
447#1872C2×C13911yescharacteristic, complemented
448#1824C2×C13911yescharacteristic, complemented
449#1823C2×C13911yescharacteristic, complemented
450#1788C2×C13911yescharacteristic, complemented
451#1788C2×C13911yescharacteristic, complemented
452C22×#41C22×C13911yescharacteristic
453C22×#41C22×C13911yescharacteristic
454C22×M16C22×C13911yescharacteristic
455C23×C8C22×C13911yescharacteristic
456#537—24no—
457#537C4×C13918yescomplemented
458C2×C22⋊Q8—21no—
459C2×C22⋊Q8C22×C13911yescharacteristic
460C2×C22⋊Q8C22×C13911yescharacteristic
461C2×#121—21no—
462C2×#121—21no—
463C2×#121—21no—
464C2×#121C22×C13911yescharacteristic
465C2×#121C22×C13911yescharacteristic
466C2×#117C22×C13911yescharacteristic
467C22×C4⋊C4C22×C13911yescharacteristic
468C22×C4⋊C4C22×C13911yescharacteristic
469C2×#103C22×C13911yescharacteristic
470C2×#103C22×C13911yescharacteristic
471C2×#103C22×C13911yescharacteristic
472C2×#103C22×C13911yescharacteristic
473C2×#102C22×C13911yescharacteristic
474C2×#102C22×C13911yescharacteristic
475C2×#102C22×C13911yescharacteristic
476C2×#102C22×C13911yescharacteristic
477#408—24no—
478C2×C22⋊C8C22×C13911yescharacteristic
479C2×C22⋊C8C22×C13911yescharacteristic
480C2×C22⋊C8C22×C13911yescharacteristic
481C2×C22⋊C8C22×C13911yescharacteristic
482#391—21no—
483#390—21no—
484#386—21no—
485#386—21no—
486#380C22×C13911yescharacteristic
487#380C22×C13911yescharacteristic
488#380C22×C13911yescharacteristic
489#380C22×C13911yescharacteristic
490#340C22×C13911yescharacteristic
491#340C22×C13911yescharacteristic
492#340C22×C13911yescharacteristic
493#340C22×C13911yescharacteristic
494#340C22×C13911yescharacteristic
495#340C22×C13911yescharacteristic
496#340C22×C13911yescharacteristic
497#340C22×C13911yescharacteristic
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×C4×C13914yes—
508C2×#41C2×C4×C13914yescomplemented
509C2×#41D4×C13914yes—
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
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C23×C13911yescharacteristic
532C22×C8C23×C13911yescharacteristic
533C22×C8C23×C13911yescharacteristic
534C22×C8C23×C13911yescharacteristic
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×C4×C13914yes—
539C22⋊Q8C2×C4×C13914yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×C4×C13914yes—
546#121C2×C4×C13914yescomplemented
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4C2×C4×C13914yescomplemented
557C2×C4⋊C4C23×C13911yescharacteristic
558C2×C4⋊C4C23×C13911yescharacteristic
559C2×C4⋊C4C23×C13911yescharacteristic
560C2×C4⋊C4C23×C13911yescharacteristic
561C2×C4⋊C4C23×C13911yescharacteristic
562C2×C4⋊C4C23×C13911yescharacteristic
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×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C42—21no—
573#103—41no—
574#103—41no—
575#103—41no—
576#103—41no—
577#102—41no—
578#102—41no—
579#102—41no—
580#102—41no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
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—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊C4×C13914yes—
609C2×Q8C22×C4×C13912yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊C4×C13914yes—
631C2×D4C22⋊C4×C13914yes—
632C2×D4C22⋊C4×C13914yes—
633C2×D4C22×C4×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—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C22×C4×C13912yes—
663C22×C4C22×C4×C13912yes—
664C22×C4C22×C4×C13912yes—
665C22×C4C2×D4×C13911yescharacteristic
666C22×C4C2×D4×C13911yescharacteristic
667C22×C4C2×D4×C13911yescharacteristic
668C22×C4C2×D4×C13912yes—
669C22×C4C2×D4×C13912yes—
670C22×C4C2×D4×C13912yes—
671C22×C4C24×C13911yescharacteristic
672M16—44no—
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—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—24no—
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⋊C4—42no—
700C4⋊C4C22×C4×C13912yes—
701C4⋊C4C22×C4×C13912yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
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—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊C4×C13912yes—
738C23C2×C22⋊C4×C13912yes—
739C23C2×C22⋊C4×C13912yes—
740C23C22×D4×C13911yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
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—22no—
777C2×C4—48no—
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—41no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4C2×C22⋊C4×C13912yes—
799C2×C4C2×C22⋊C4×C13912yes—
800C2×C4C2×C22⋊C4×C13912yes—
801C2×C4C23×C4×C13911yescharacteristic
802C2×C4C22×D4×C13911yescharacteristic
803C2×C4H(5,𝔽2)×C13911yescharacteristic
804C2×C4H(5,𝔽2)×C13911yescharacteristic
805C2×C4H(5,𝔽2)×C13911yescharacteristic
806C2×C4H(5,𝔽2)×C13911yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊C4×C13911yescharacteristic
840C22#534×C13911yescharacteristic
841C22#534×C13911yescharacteristic
842C22#576×C13911yescharacteristic
843C22#577×C13911yescharacteristic
844C22#577×C13911yescharacteristic
845C22#578×C13911yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4#518×C13911yescharacteristic
857C4#518×C13911yescharacteristic
858C4#534×C13911yescharacteristic
859C4#534×C13911yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2#2308×C13911yescharacteristic
865C2#2897×C13911yescharacteristic
866C2#2898×C13911yescharacteristic
867C2#3198×C13911yescharacteristic
868C2#3201×C13911yescharacteristic
869C2#3203×C13911yescharacteristic
870C2#3204×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
prime radicalC2×#537×C139C2
LCSG ▷ C2×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×#408×C139C2semidirect
3. #2311×C139C2semidirect
4. #1895×C139C2semidirect
5. #1894×C139C2semidirect
6. #1893×C139C2semidirect
7. #1892×C139C2semidirect
8. #1875×C139C2semidirect
9. #1874×C139C2semidirect
10. #1873×C139C2semidirect
11. #1872×C139C2semidirect
12. #1824×C139C2semidirect
13. #1823×C139C2semidirect
14. #1788×C139C2semidirect
15. #1788×C139C2semidirect
21. #537×C139C4semidirect
72. C2×#41×C139C2×C4semidirect
103. C22⋊Q8×C139C2×C4semidirect
110. #121×C139C2×C4semidirect
120. C2×C4⋊C4×C139C2×C4semidirect
435. #21772C139direct (N × H)
436. C139#21772direct (N × H)
438. C2×#408C2×C139semidirect
439. #2311C2×C139semidirect
440. #1895C2×C139semidirect
441. #1894C2×C139semidirect
442. #1893C2×C139semidirect
443. #1892C2×C139semidirect
444. #1875C2×C139semidirect
445. #1874C2×C139semidirect
446. #1873C2×C139semidirect
447. #1872C2×C139semidirect
448. #1824C2×C139semidirect
449. #1823C2×C139semidirect
450. #1788C2×C139semidirect
451. #1788C2×C139semidirect
457. #537C4×C139semidirect
508. C2×#41C2×C4×C139semidirect
539. C22⋊Q8C2×C4×C139semidirect
546. #121C2×C4×C139semidirect
556. C2×C4⋊C4C2×C4×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×#408×C1392
#2311×C1392
#1895×C1392
#1894×C1392
#1893×C1392
#1892×C1392
#1875×C1392
#1874×C1392
#1873×C1392
#1872×C1392
#1824×C1392
#1823×C1392
#1788×C1392
#21772139