Finite Group Databasebeta

← C139×#24893 #48019489

Subgroups — C139×#24893 #48019489

Order 35584.

1232 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C139C211yesmaximal, characteristic
2C2×C4×D8×C139C211yesmaximal, characteristic, complemented
3#2422×C139C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C139C211yesmaximal, characteristic, complemented
5#2093×C139C211yesmaximal, characteristic, complemented
6#2075×C139C211yesmaximal, characteristic, complemented
7#2054×C139C211yesmaximal, characteristic, complemented
8#2033×C139C211yesmaximal, characteristic, complemented
9#1934×C139C211yesmaximal, characteristic, complemented
10#1923×C139C211yesmaximal, characteristic, complemented
11#1879×C139C211yesmaximal, characteristic, complemented
12#1879×C139C211yesmaximal, characteristic, complemented
13#1862×C139C211yesmaximal, characteristic, complemented
14#1802×C139C211yesmaximal, characteristic, complemented
15#1786×C139C211yesmaximal, characteristic, complemented
16C23×D4×C139C2211yescharacteristic
17C22×D8×C139C2211yescharacteristic
18C22×D8×C139C2211yescharacteristic
19C2×#123×C139—21no—
20C2×#121×C139C2211yescharacteristic
21C2×C4×D4×C139C2211yescharacteristic
22C2×C4×D4×C139C2211yescharacteristic
23C2×C4×D4×C139C2211yescharacteristic, complemented
24C22×C22⋊C4×C139—21no—
25#447×C139—24no—
26C4×D8×C139—24no—
27C2×#107×C139C2211yescharacteristic, complemented
28C2×#107×C139C2211yescharacteristic, complemented
29C2×C4⋊C8×C139C2211yescharacteristic, complemented
30C2×#102×C139C2211yescharacteristic
31C2×#102×C139C2211yescharacteristic
32C2×#102×C139C2211yescharacteristic
33C2×#102×C139C2211yescharacteristic
34C2×#102×C139C2211yescharacteristic
35C2×#102×C139C2211yescharacteristic
36C2×#102×C139C2211yescharacteristic, complemented
37C2×#102×C139C2211yescharacteristic, complemented
38C2×C22⋊C8×C139C2211yescharacteristic
39C2×C22⋊C8×C139C2211yescharacteristic
40C2×C4×C8×C139C2211yescharacteristic, complemented
41#397×C139—21no—
42#394×C139—21no—
43#390×C139C2211yescharacteristic
44#390×C139C2211yescharacteristic
45#390×C139C2211yescharacteristic, complemented
46#389×C139C2211yescharacteristic, complemented
47#386×C139—21no—
48#386×C139—21no—
49#385×C139—21no—
50#384×C139C2211yescharacteristic, complemented
51#380×C139C2211yescharacteristic
52#380×C139C2211yescharacteristic
53#379×C139—21no—
54C4×C22⋊C4×C139C2211yescharacteristic
55#340×C139C2211yescharacteristic, complemented
56#340×C139C2211yescharacteristic, complemented
57#340×C139C2211yescharacteristic, complemented
58#340×C139C2211yescharacteristic, complemented
59#336×C139C2211yescharacteristic, complemented
60#336×C139C2211yescharacteristic, complemented
61C25×C139—21no—
62C22×D4×C139—22no—
63C22×D4×C139—22no—
64C22×D4×C139—22no—
65C22×D4×C139—22no—
66C22×D4×C139—21no—
67C22×D4×C139—21no—
68C22×D4×C139—41no—
69C22×D4×C139—41no—
70C22×D4×C139C2311yescharacteristic
71C22×D4×C139C2311yescharacteristic
72C22×D4×C139C2311yescharacteristic
73C23×C4×C139—21no—
74C23×C4×C139—21no—
75C23×C4×C139—21no—
76C23×C4×C139C2311yescharacteristic
77C2×D8×C139—22no—
78C2×D8×C139—22no—
79C2×D8×C139—22no—
80C2×D8×C139—22no—
81C2×D8×C139—41no—
82C2×D8×C139D414yes—
83C22×C8×C139C2311yescharacteristic
84C22×C8×C139C2311yescharacteristic
85C22×C8×C139C2311yescharacteristic
86C22×C8×C139C2311yescharacteristic
87#123×C139—44no—
88#121×C139—22no—
89#121×C139—41no—
90C4×D4×C139—22no—
91C4×D4×C139—22no—
92C4×D4×C139—22no—
93C4×D4×C139—41no—
94C4×D4×C139—41no—
95C4×D4×C139—41no—
96C2×C4⋊C4×C139—21no—
97C2×C4⋊C4×C139—21no—
98C2×C4⋊C4×C139—21no—
99C2×C4⋊C4×C139C2311yescharacteristic
100C2×C4⋊C4×C139C2311yescharacteristic
101C2×C4⋊C4×C139C2311yescharacteristic
102C2×C4⋊C4×C139C2311yescharacteristic
103C2×C4⋊C4×C139C2311yescharacteristic
104C2×C22⋊C4×C139—21no—
105C2×C22⋊C4×C139—21no—
106C2×C22⋊C4×C139—21no—
107C2×C22⋊C4×C139—21no—
108C2×C22⋊C4×C139—21no—
109C2×C22⋊C4×C139—21no—
110C2×C22⋊C4×C139—21no—
111C2×C22⋊C4×C139—21no—
112C2×C22⋊C4×C139—21no—
113C2×C22⋊C4×C139—21no—
114C2×C22⋊C4×C139—21no—
115C2×C22⋊C4×C139—21no—
116C2×C22⋊C4×C139—44no—
117C2×C22⋊C4×C139D411yescharacteristic
118C2×C22⋊C4×C139D411yescharacteristic
119C2×C42×C139C2311yescharacteristic
120C2×C42×C139C2311yescharacteristic
121#107×C139—22no—
122#107×C139—41no—
123C4⋊C8×C139—41no—
124#102×C139—22no—
125#102×C139—22no—
126#102×C139—22no—
127#102×C139—22no—
128#102×C139—22no—
129#102×C139—22no—
130#102×C139—41no—
131#102×C139—41no—
132C22⋊C8×C139—22no—
133C22⋊C8×C139—41no—
134C4×C8×C139—22no—
135#95×C139—21no—
136#95×C139—21no—
137#95×C139—21no—
138#95×C139D411yescharacteristic
139#95×C139D411yescharacteristic
140C24×C139—21no—
141C24×C139—24no—
142C24×C139—21no—
143C24×C139—21no—
144C24×C139—42no—
145C24×C139—42no—
146C24×C139—42no—
147C24×C139—42no—
148C24×C139—81no—
149C24×C139—81no—
150C24×C139C2×D411yescharacteristic
151C2×D4×C139—24no—
152C2×D4×C139—21no—
153C2×D4×C139—21no—
154C2×D4×C139—21no—
155C2×D4×C139—21no—
156C2×D4×C139—21no—
157C2×D4×C139—21no—
158C2×D4×C139—21no—
159C2×D4×C139—21no—
160C2×D4×C139—21no—
161C2×D4×C139—21no—
162C2×D4×C139—21no—
163C2×D4×C139—21no—
164C2×D4×C139—21no—
165C2×D4×C139—42no—
166C2×D4×C139—42no—
167C2×D4×C139—44no—
168C2×D4×C139—44no—
169C2×D4×C139—44no—
170C2×D4×C139—44no—
171C2×D4×C139—42no—
172C2×D4×C139—42no—
173C2×D4×C139—81no—
174C2×D4×C139C2×D412yes—
175C2×D4×C139C2×D412yes—
176C2×D4×C139#4112yes—
177C2×D4×C139#4112yes—
178C2×D4×C139#4112yes—
179C22×C4×C139—21no—
180C22×C4×C139—21no—
181C22×C4×C139—21no—
182C22×C4×C139—21no—
183C22×C4×C139—21no—
184C22×C4×C139—21no—
185C22×C4×C139—21no—
186C22×C4×C139—21no—
187C22×C4×C139—21no—
188C22×C4×C139—21no—
189C22×C4×C139—21no—
190C22×C4×C139—42no—
191C22×C4×C139—42no—
192C22×C4×C139—42no—
193C22×C4×C139—42no—
194C22×C4×C139—42no—
195C22×C4×C139—42no—
196C22×C4×C139—81no—
197C22×C4×C139—81no—
198C22×C4×C139—81no—
199C22×C4×C139C2×D411yescharacteristic
200C22×C4×C139C2×D411yescharacteristic
201C22×C4×C139C2×D411yescharacteristic
202C22×C4×C139C2×D411yescharacteristic
203C22×C4×C139C2×D411yescharacteristic
204C22×C4×C139C2411yescharacteristic
205D8×C139—28no—
206D8×C139—44no—
207C2×C8×C139—21no—
208C2×C8×C139—21no—
209C2×C8×C139—21no—
210C2×C8×C139—21no—
211C2×C8×C139—21no—
212C2×C8×C139—21no—
213C2×C8×C139—21no—
214C2×C8×C139—21no—
215C2×C8×C139—21no—
216C2×C8×C139—21no—
217C2×C8×C139—21no—
218C2×C8×C139C2×D412yes—
219C4⋊C4×C139—21no—
220C4⋊C4×C139—21no—
221C4⋊C4×C139—21no—
222C4⋊C4×C139—21no—
223C4⋊C4×C139—21no—
224C4⋊C4×C139—21no—
225C4⋊C4×C139—21no—
226C4⋊C4×C139—21no—
227C4⋊C4×C139—21no—
228C4⋊C4×C139—21no—
229C4⋊C4×C139—42no—
230C4⋊C4×C139—42no—
231C4⋊C4×C139—81no—
232C22⋊C4×C139—41no—
233C22⋊C4×C139—42no—
234C22⋊C4×C139—42no—
235C22⋊C4×C139—42no—
236C22⋊C4×C139—42no—
237C22⋊C4×C139—42no—
238C22⋊C4×C139—42no—
239C22⋊C4×C139—42no—
240C22⋊C4×C139—42no—
241C22⋊C4×C139—42no—
242C22⋊C4×C139—42no—
243C22⋊C4×C139—81no—
244C22⋊C4×C139—81no—
245C22⋊C4×C139D814yescomplemented
246C42×C139—21no—
247C42×C139—21no—
248C42×C139—21no—
249C42×C139—21no—
250C23×C139—21no—
251C23×C139—22no—
252C23×C139—22no—
253C23×C139—21no—
254C23×C139—22no—
255C23×C139—21no—
256C23×C139—21no—
257C23×C139—21no—
258C23×C139—21no—
259C23×C139—22no—
260C23×C139—22no—
261C23×C139—48no—
262C23×C139—48no—
263C23×C139—41no—
264C23×C139—41no—
265C23×C139—41no—
266C23×C139—41no—
267C23×C139—41no—
268C23×C139—41no—
269C23×C139—41no—
270C23×C139—41no—
271C23×C139—41no—
272C23×C139—41no—
273C23×C139—41no—
274C23×C139—41no—
275C23×C139—41no—
276C23×C139—41no—
277C23×C139—41no—
278C23×C139—41no—
279C23×C139—84no—
280C23×C139—84no—
281C23×C139—84no—
282C23×C139—84no—
283C23×C139—84no—
284C23×C139C2×D812yes—
285C23×C139C22×D411yescharacteristic
286D4×C139—22no—
287D4×C139—22no—
288D4×C139—22no—
289D4×C139—22no—
290D4×C139—22no—
291D4×C139—22no—
292D4×C139—22no—
293D4×C139—48no—
294D4×C139—41no—
295D4×C139—41no—
296D4×C139—41no—
297D4×C139—41no—
298D4×C139—84no—
299D4×C139#12314yescomplemented
300C2×C4×C139—21no—
301C2×C4×C139—21no—
302C2×C4×C139—21no—
303C2×C4×C139—21no—
304C2×C4×C139—21no—
305C2×C4×C139—21no—
306C2×C4×C139—21no—
307C2×C4×C139—21no—
308C2×C4×C139—21no—
309C2×C4×C139—21no—
310C2×C4×C139—21no—
311C2×C4×C139—21no—
312C2×C4×C139—21no—
313C2×C4×C139—41no—
314C2×C4×C139—41no—
315C2×C4×C139—41no—
316C2×C4×C139—41no—
317C2×C4×C139—41no—
318C2×C4×C139—41no—
319C2×C4×C139—41no—
320C2×C4×C139—41no—
321C2×C4×C139—41no—
322C2×C4×C139—41no—
323C2×C4×C139—41no—
324C2×C4×C139—41no—
325C2×C4×C139—41no—
326C2×C4×C139—41no—
327C2×C4×C139—41no—
328C2×C4×C139—41no—
329C2×C4×C139—41no—
330C2×C4×C139—41no—
331C2×C4×C139—41no—
332C2×C4×C139—84no—
333C2×C4×C139—84no—
334C2×C4×C139—84no—
335C2×C4×C139C2×D812yes—
336C2×C4×C139C2×D812yes—
337C2×C4×C139C22×D411yescharacteristic
338C2×C4×C139C2×#4111yescharacteristic
339C2×C4×C139C2×#4111yescharacteristic
340C2×C4×C139C2×#4111yescharacteristic
341C2×C4×C139H(5,𝔽2)11yescharacteristic
342C2×C4×C139H(5,𝔽2)11yescharacteristic
343C8×C139—22no—
344C8×C139—41no—
345C8×C139—41no—
346C8×C139—41no—
347C22×C139—22no—
348C22×C139—24no—
349C22×C139—22no—
350C22×C139—22no—
351C22×C139—42no—
352C22×C139—41no—
353C22×C139—42no—
354C22×C139—41no—
355C22×C139—41no—
356C22×C139—42no—
357C22×C139—42no—
358C22×C139—42no—
359C22×C139—41no—
360C22×C139—42no—
361C22×C139—42no—
362C22×C139—42no—
363C22×C139—42no—
364C22×C139—42no—
365C22×C139—42no—
366C22×C139—42no—
367C22×C139—816no—
368C22×C139—81no—
369C22×C139—81no—
370C22×C139—81no—
371C22×C139—81no—
372C22×C139—81no—
373C22×C139—81no—
374C22×C139—81no—
375C22×C139—81no—
376C22×C139#52511yescharacteristic
377C22×C139D4211yescharacteristic
378C22×C139#54611yescharacteristic
379C22×C139C22×D811yescharacteristic
380C22×C139#57511yescharacteristic
381C22×C139#57611yescharacteristic
382C22×C139#57711yescharacteristic
383C4×C139—22no—
384C4×C139—22no—
385C4×C139—41no—
386C4×C139—41no—
387C4×C139—41no—
388C4×C139—81no—
389C4×C139—81no—
390C4×C139—81no—
391C4×C139—81no—
392C4×C139—81no—
393C4×C139C2×#12311yescharacteristic
394C4×C139#53811yescharacteristic
395C4×C139#54611yescharacteristic
396C4×C139#55111yescharacteristic
397C2×C139—42no—
398C2×C139—44no—
399C2×C139—82no—
400C2×C139—82no—
401C2×C139#241811yescharacteristic
402C2×C139#310011yescharacteristic
403C2×C139#311811yescharacteristic
404C2×C139#326711yescharacteristic
405C2×C139D4×D811yescharacteristic
406C2×C139#329411yescharacteristic
407C2×C139#332211yescharacteristic
408#24893C13911yesmaximal, characteristic, direct product factor, Sylow
409C139#2489311yescharacteristic, direct product factor, Sylow
410C2×#447C2×C13911yescharacteristic
411C2×C4×D8C2×C13911yescharacteristic, complemented
412#2422C2×C13911yescharacteristic, complemented
413D4×C22⋊C4C2×C13911yescharacteristic, complemented
414#2093C2×C13911yescharacteristic, complemented
415#2075C2×C13911yescharacteristic, complemented
416#2054C2×C13911yescharacteristic, complemented
417#2033C2×C13911yescharacteristic, complemented
418#1934C2×C13911yescharacteristic, complemented
419#1923C2×C13911yescharacteristic, complemented
420#1879C2×C13911yescharacteristic, complemented
421#1879C2×C13911yescharacteristic, complemented
422#1862C2×C13911yescharacteristic, complemented
423#1802C2×C13911yescharacteristic, complemented
424#1786C2×C13911yescharacteristic, complemented
425C23×D4C22×C13911yescharacteristic
426C22×D8C22×C13911yescharacteristic
427C22×D8C22×C13911yescharacteristic
428C2×#123—21no—
429C2×#121C22×C13911yescharacteristic
430C2×C4×D4C22×C13911yescharacteristic
431C2×C4×D4C22×C13911yescharacteristic
432C2×C4×D4C22×C13911yescharacteristic, complemented
433C22×C22⋊C4—21no—
434#447—24no—
435C4×D8—24no—
436C2×#107C22×C13911yescharacteristic, complemented
437C2×#107C22×C13911yescharacteristic, complemented
438C2×C4⋊C8C22×C13911yescharacteristic, complemented
439C2×#102C22×C13911yescharacteristic
440C2×#102C22×C13911yescharacteristic
441C2×#102C22×C13911yescharacteristic
442C2×#102C22×C13911yescharacteristic
443C2×#102C22×C13911yescharacteristic
444C2×#102C22×C13911yescharacteristic
445C2×#102C22×C13911yescharacteristic, complemented
446C2×#102C22×C13911yescharacteristic, complemented
447C2×C22⋊C8C22×C13911yescharacteristic
448C2×C22⋊C8C22×C13911yescharacteristic
449C2×C4×C8C22×C13911yescharacteristic, complemented
450#397—21no—
451#394—21no—
452#390C22×C13911yescharacteristic
453#390C22×C13911yescharacteristic
454#390C22×C13911yescharacteristic, complemented
455#389C22×C13911yescharacteristic, complemented
456#386—21no—
457#386—21no—
458#385—21no—
459#384C22×C13911yescharacteristic, complemented
460#380C22×C13911yescharacteristic
461#380C22×C13911yescharacteristic
462#379—21no—
463C4×C22⋊C4C22×C13911yescharacteristic
464#340C22×C13911yescharacteristic, complemented
465#340C22×C13911yescharacteristic, complemented
466#340C22×C13911yescharacteristic, complemented
467#340C22×C13911yescharacteristic, complemented
468#336C22×C13911yescharacteristic, complemented
469#336C22×C13911yescharacteristic, complemented
470C25—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—41no—
478C22×D4—41no—
479C22×D4C23×C13911yescharacteristic
480C22×D4C23×C13911yescharacteristic
481C22×D4C23×C13911yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C13911yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—41no—
491C2×D8D4×C13914yes—
492C22×C8C23×C13911yescharacteristic
493C22×C8C23×C13911yescharacteristic
494C22×C8C23×C13911yescharacteristic
495C22×C8C23×C13911yescharacteristic
496#123—44no—
497#121—22no—
498#121—41no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—41no—
503C4×D4—41no—
504C4×D4—41no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4C23×C13911yescharacteristic
509C2×C4⋊C4C23×C13911yescharacteristic
510C2×C4⋊C4C23×C13911yescharacteristic
511C2×C4⋊C4C23×C13911yescharacteristic
512C2×C4⋊C4C23×C13911yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—44no—
526C2×C22⋊C4D4×C13911yescharacteristic
527C2×C22⋊C4D4×C13911yescharacteristic
528C2×C42C23×C13911yescharacteristic
529C2×C42C23×C13911yescharacteristic
530#107—22no—
531#107—41no—
532C4⋊C8—41no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—22no—
539#102—41no—
540#102—41no—
541C22⋊C8—22no—
542C22⋊C8—41no—
543C4×C8—22no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95D4×C13911yescharacteristic
548#95D4×C13911yescharacteristic
549C24—21no—
550C24—24no—
551C24—21no—
552C24—21no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—81no—
558C24—81no—
559C24C2×D4×C13911yescharacteristic
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—44no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4C2×D4×C13912yes—
584C2×D4C2×D4×C13912yes—
585C2×D4#41×C13912yes—
586C2×D4#41×C13912yes—
587C2×D4#41×C13912yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C2×D4×C13911yescharacteristic
609C22×C4C2×D4×C13911yescharacteristic
610C22×C4C2×D4×C13911yescharacteristic
611C22×C4C2×D4×C13911yescharacteristic
612C22×C4C2×D4×C13911yescharacteristic
613C22×C4C24×C13911yescharacteristic
614D8—28no—
615D8—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8C2×D4×C13912yes—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—81no—
641C22⋊C4—41no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—81no—
653C22⋊C4—81no—
654C22⋊C4D8×C13914yescomplemented
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—48no—
671C23—48no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23C2×D8×C13912yes—
694C23C22×D4×C13911yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4#123×C13914yescomplemented
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—84no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4C2×D8×C13912yes—
745C2×C4C2×D8×C13912yes—
746C2×C4C22×D4×C13911yescharacteristic
747C2×C4C2×#41×C13911yescharacteristic
748C2×C4C2×#41×C13911yescharacteristic
749C2×C4C2×#41×C13911yescharacteristic
750C2×C4H(5,𝔽2)×C13911yescharacteristic
751C2×C4H(5,𝔽2)×C13911yescharacteristic
752C8—22no—
753C8—41no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—42no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—41no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—816no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22#525×C13911yescharacteristic
786C22D42×C13911yescharacteristic
787C22#546×C13911yescharacteristic
788C22C22×D8×C13911yescharacteristic
789C22#575×C13911yescharacteristic
790C22#576×C13911yescharacteristic
791C22#577×C13911yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C2×#123×C13911yescharacteristic
803C4#538×C13911yescharacteristic
804C4#546×C13911yescharacteristic
805C4#551×C13911yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—82no—
810C2#2418×C13911yescharacteristic
811C2#3100×C13911yescharacteristic
812C2#3118×C13911yescharacteristic
813C2#3267×C13911yescharacteristic
814C2D4×D8×C13911yescharacteristic
815C2#3294×C13911yescharacteristic
816C2#3322×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C22×D4
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#447×C139C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C139 ◁ C4×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×D8×C139C2semidirect
3. #2422×C139C2semidirect
4. D4×C22⋊C4×C139C2semidirect
5. #2093×C139C2semidirect
6. #2075×C139C2semidirect
7. #2054×C139C2semidirect
8. #2033×C139C2semidirect
9. #1934×C139C2semidirect
10. #1923×C139C2semidirect
11. #1879×C139C2semidirect
12. #1879×C139C2semidirect
13. #1862×C139C2semidirect
14. #1802×C139C2semidirect
15. #1786×C139C2semidirect
23. C2×C4×D4×C139C22semidirect
27. C2×#107×C139C22semidirect
28. C2×#107×C139C22semidirect
29. C2×C4⋊C8×C139C22semidirect
36. C2×#102×C139C22semidirect
37. C2×#102×C139C22semidirect
40. C2×C4×C8×C139C22semidirect
45. #390×C139C22semidirect
46. #389×C139C22semidirect
50. #384×C139C22semidirect
55. #340×C139C22semidirect
56. #340×C139C22semidirect
57. #340×C139C22semidirect
58. #340×C139C22semidirect
59. #336×C139C22semidirect
60. #336×C139C22semidirect
245. C22⋊C4×C139D8semidirect
299. D4×C139#123semidirect
408. #24893C139direct (N × H)
409. C139#24893direct (N × H)
411. C2×C4×D8C2×C139semidirect
412. #2422C2×C139semidirect
413. D4×C22⋊C4C2×C139semidirect
414. #2093C2×C139semidirect
415. #2075C2×C139semidirect
416. #2054C2×C139semidirect
417. #2033C2×C139semidirect
418. #1934C2×C139semidirect
419. #1923C2×C139semidirect
420. #1879C2×C139semidirect
421. #1879C2×C139semidirect
422. #1862C2×C139semidirect
423. #1802C2×C139semidirect
424. #1786C2×C139semidirect
432. C2×C4×D4C22×C139semidirect
436. C2×#107C22×C139semidirect
437. C2×#107C22×C139semidirect
438. C2×C4⋊C8C22×C139semidirect
445. C2×#102C22×C139semidirect
446. C2×#102C22×C139semidirect
449. C2×C4×C8C22×C139semidirect
454. #390C22×C139semidirect
455. #389C22×C139semidirect
459. #384C22×C139semidirect
464. #340C22×C139semidirect
465. #340C22×C139semidirect
466. #340C22×C139semidirect
467. #340C22×C139semidirect
468. #336C22×C139semidirect
469. #336C22×C139semidirect
654. C22⋊C4D8×C139semidirect
708. D4#123×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1392
C2×C4×D8×C1392
#2422×C1392
D4×C22⋊C4×C1392
#2093×C1392
#2075×C1392
#2054×C1392
#2033×C1392
#1934×C1392
#1923×C1392
#1879×C1392
#1862×C1392
#1802×C1392
#1786×C1392
#24893139