Finite Group Databasebeta

← C139×#14114 #48008710

Subgroups — C139×#14114 #48008710

Order 35584.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C139C211yesmaximal, characteristic
2C2×#388×C139C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C139C211yesmaximal, characteristic
4#1442×C139C211yesmaximal, characteristic, complemented
5#1441×C139C211yesmaximal, characteristic, complemented
6#1439×C139C211yesmaximal, characteristic
7#1439×C139C211yesmaximal, characteristic
8#1436×C139C211yesmaximal, characteristic, complemented
9#1436×C139C211yesmaximal, characteristic, complemented
10#1436×C139C211yesmaximal, characteristic, complemented
11C4⋊#95×C139C211yesmaximal, characteristic, complemented
12#1434×C139C211yesmaximal, characteristic, complemented
13C22⋊#95×C139C211yesmaximal, characteristic
14C22⋊#95×C139C211yesmaximal, characteristic
15C4×#95×C139C211yesmaximal, characteristic, complemented
16C24×C4×C139C2211yescharacteristic
17C22×C4⋊C4×C139C2211yescharacteristic
18C22×C4⋊C4×C139C2211yescharacteristic
19C22×C4⋊C4×C139C2211yescharacteristic
20C22×C4⋊C4×C139C2211yescharacteristic
21C22×C22⋊C4×C139C2211yescharacteristic
22C22×C22⋊C4×C139C2211yescharacteristic
23C22×C22⋊C4×C139C2211yescharacteristic
24C22×C22⋊C4×C139C2211yescharacteristic
25C22×C22⋊C4×C139C2211yescharacteristic
26C22×C22⋊C4×C139C2211yescharacteristic
27C22×C42×C139C2211yescharacteristic
28C22×C42×C139C2211yescharacteristic
29C22×C42×C139C2211yescharacteristic
30C22×C42×C139C2211yescharacteristic
31#388×C139—24no—
32#388×C139C418yescomplemented
33C4×C22⋊C4×C139—24no—
34C2×#95×C139C2211yescharacteristic
35C2×#95×C139C2211yescharacteristic
36C2×#95×C139C2211yescharacteristic
37C2×#95×C139C2211yescharacteristic
38C2×#95×C139C2211yescharacteristic
39C2×#95×C139C2211yescharacteristic
40C2×#95×C139C2211yescharacteristic
41C2×#95×C139C2211yescharacteristic
42C2×#95×C139C2211yescharacteristic
43C2×#95×C139C2211yescharacteristic
44C2×#95×C139C2211yescharacteristic
45C2×#95×C139C2211yescharacteristic
46C2×#95×C139C2211yescharacteristic
47C2×#95×C139C2211yescharacteristic
48C2×#95×C139C2211yescharacteristic
49C2×#95×C139C2211yescharacteristic
50C2×#95×C139C2211yescharacteristic
51C2×#95×C139C2211yescharacteristic
52C2×#95×C139C2211yescharacteristic
53C2×#95×C139C2211yescharacteristic
54C25×C139C2311yescharacteristic
55C23×C4×C139—22no—
56C23×C4×C139—22no—
57C23×C4×C139—22no—
58C23×C4×C139—22no—
59C23×C4×C139—22no—
60C23×C4×C139—41no—
61C23×C4×C139—41no—
62C23×C4×C139C2311yescharacteristic
63C23×C4×C139C2311yescharacteristic
64C23×C4×C139C2311yescharacteristic
65C23×C4×C139C2311yescharacteristic
66C23×C4×C139C2311yescharacteristic
67C23×C4×C139C2311yescharacteristic
68C23×C4×C139C2311yescharacteristic
69C23×C4×C139C2311yescharacteristic
70C23×C4×C139C2311yescharacteristic
71C23×C4×C139C2311yescharacteristic
72C23×C4×C139C2311yescharacteristic
73C23×C4×C139C2311yescharacteristic
74C23×C4×C139C2311yescharacteristic
75C23×C4×C139C2311yescharacteristic
76C2×C4⋊C4×C139—22no—
77C2×C4⋊C4×C139—22no—
78C2×C4⋊C4×C139—22no—
79C2×C4⋊C4×C139—22no—
80C2×C4⋊C4×C139—22no—
81C2×C4⋊C4×C139—41no—
82C2×C4⋊C4×C139—41no—
83C2×C4⋊C4×C139—41no—
84C2×C4⋊C4×C139—41no—
85C2×C4⋊C4×C139—41no—
86C2×C4⋊C4×C139—41no—
87C2×C4⋊C4×C139C2×C414yescomplemented
88C2×C22⋊C4×C139—22no—
89C2×C22⋊C4×C139—22no—
90C2×C22⋊C4×C139—22no—
91C2×C22⋊C4×C139—22no—
92C2×C22⋊C4×C139—22no—
93C2×C22⋊C4×C139—22no—
94C2×C22⋊C4×C139—22no—
95C2×C22⋊C4×C139—41no—
96C2×C22⋊C4×C139—41no—
97C2×C22⋊C4×C139—41no—
98C2×C22⋊C4×C139—41no—
99C2×C22⋊C4×C139—41no—
100C2×C22⋊C4×C139—41no—
101C2×C22⋊C4×C139C2×C414yes—
102C2×C22⋊C4×C139C2×C414yes—
103C2×C22⋊C4×C139C2×C414yes—
104C2×C22⋊C4×C139D414yes—
105C2×C22⋊C4×C139Q814yes—
106C2×C42×C139—22no—
107C2×C42×C139—22no—
108C2×C42×C139—22no—
109C2×C42×C139—22no—
110C2×C42×C139—22no—
111C2×C42×C139—22no—
112C2×C42×C139—41no—
113C2×C42×C139—41no—
114C2×C42×C139—41no—
115C2×C42×C139—41no—
116C2×C42×C139—41no—
117C2×C42×C139C2×C414yescomplemented
118#95×C139—22no—
119#95×C139—22no—
120#95×C139—22no—
121#95×C139—22no—
122#95×C139—22no—
123#95×C139—22no—
124#95×C139—22no—
125#95×C139—22no—
126#95×C139—22no—
127#95×C139—22no—
128#95×C139—22no—
129#95×C139—22no—
130#95×C139—22no—
131#95×C139—41no—
132#95×C139—41no—
133#95×C139—41no—
134#95×C139—41no—
135#95×C139—41no—
136#95×C139C2×C414yescomplemented
137#95×C139C2×C414yescomplemented
138C24×C139—21no—
139C24×C139—21no—
140C24×C139—21no—
141C24×C139—21no—
142C24×C139—21no—
143C24×C139—21no—
144C24×C139—21no—
145C24×C139—21no—
146C24×C139—21no—
147C24×C139—21no—
148C24×C139—21no—
149C24×C139—21no—
150C24×C139C22×C412yes—
151C24×C139C2×D412yes—
152C24×C139C2×Q812yes—
153C24×C139C2411yescharacteristic
154C22×C4×C139—21no—
155C22×C4×C139—21no—
156C22×C4×C139—21no—
157C22×C4×C139—21no—
158C22×C4×C139—21no—
159C22×C4×C139—21no—
160C22×C4×C139—21no—
161C22×C4×C139—21no—
162C22×C4×C139—21no—
163C22×C4×C139—21no—
164C22×C4×C139—21no—
165C22×C4×C139—21no—
166C22×C4×C139—28no—
167C22×C4×C139—21no—
168C22×C4×C139—21no—
169C22×C4×C139—21no—
170C22×C4×C139—21no—
171C22×C4×C139—21no—
172C22×C4×C139—21no—
173C22×C4×C139—21no—
174C22×C4×C139—21no—
175C22×C4×C139—21no—
176C22×C4×C139—21no—
177C22×C4×C139—21no—
178C22×C4×C139—21no—
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—21no—
191C22×C4×C139—21no—
192C22×C4×C139—21no—
193C22×C4×C139—21no—
194C22×C4×C139—21no—
195C22×C4×C139—21no—
196C22×C4×C139—21no—
197C22×C4×C139—21no—
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—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—21no—
224C22×C4×C139—21no—
225C22×C4×C139—21no—
226C22×C4×C139—21no—
227C22×C4×C139—21no—
228C22×C4×C139—21no—
229C22×C4×C139—21no—
230C22×C4×C139—21no—
231C22×C4×C139—21no—
232C22×C4×C139—21no—
233C22×C4×C139—21no—
234C22×C4×C139—21no—
235C22×C4×C139—44no—
236C22×C4×C139—44no—
237C22×C4×C139—44no—
238C22×C4×C139—44no—
239C22×C4×C139—44no—
240C22×C4×C139—44no—
241C22×C4×C139C22×C412yes—
242C22×C4×C139C22×C412yes—
243C22×C4×C139C22×C412yes—
244C22×C4×C139C22×C412yes—
245C22×C4×C139C22×C412yes—
246C22×C4×C139C22×C412yes—
247C22×C4×C139C2×D412yes—
248C22×C4×C139C2×D412yes—
249C22×C4×C139C2×Q812yes—
250C22×C4×C139C2×Q812yes—
251C22×C4×C139#4112yes—
252C22×C4×C139#4112yes—
253C22×C4×C139#4112yes—
254C22×C4×C139#4112yes—
255C22×C4×C139#4112yes—
256C22×C4×C139#4112yes—
257C22×C4×C139#4112yes—
258C22×C4×C139#4112yes—
259C4⋊C4×C139—44no—
260C4⋊C4×C139—44no—
261C4⋊C4×C139—44no—
262C4⋊C4×C139—44no—
263C22⋊C4×C139—28no—
264C22⋊C4×C139—44no—
265C22⋊C4×C139—44no—
266C22⋊C4×C139—44no—
267C22⋊C4×C139—44no—
268C22⋊C4×C139C4⋊C4116yescomplemented
269C42×C139—44no—
270C42×C139—44no—
271C42×C139—44no—
272C42×C139—44no—
273C23×C139—22no—
274C23×C139—22no—
275C23×C139—22no—
276C23×C139—22no—
277C23×C139—22no—
278C23×C139—22no—
279C23×C139—22no—
280C23×C139—22no—
281C23×C139—22no—
282C23×C139—22no—
283C23×C139—22no—
284C23×C139—22no—
285C23×C139—22no—
286C23×C139—22no—
287C23×C139—22no—
288C23×C139—22no—
289C23×C139—22no—
290C23×C139—22no—
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—41no—
301C23×C139—41no—
302C23×C139—41no—
303C23×C139—41no—
304C23×C139—41no—
305C23×C139—41no—
306C23×C139—41no—
307C23×C139C2×C4⋊C414yes—
308C23×C139C23×C411yescharacteristic
309C23×C139C22×D411yescharacteristic
310C23×C139C22×Q811yescharacteristic
311C23×C139C2×#4111yescharacteristic
312C23×C139C2×#4111yescharacteristic
313C23×C139C2×#4111yescharacteristic
314C23×C139C2×#4111yescharacteristic
315C23×C139C2×#4111yescharacteristic
316C23×C139C2×#4111yescharacteristic
317C23×C139C2×#4111yescharacteristic
318C23×C139C2×#4111yescharacteristic
319C23×C139H(5,𝔽2)11yescharacteristic
320C23×C139H(5,𝔽2)11yescharacteristic
321C23×C139H(5,𝔽2)11yescharacteristic
322C23×C139H(5,𝔽2)11yescharacteristic
323C2×C4×C139—22no—
324C2×C4×C139—22no—
325C2×C4×C139—22no—
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—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—22no—
353C2×C4×C139—22no—
354C2×C4×C139—22no—
355C2×C4×C139—22no—
356C2×C4×C139—22no—
357C2×C4×C139—22no—
358C2×C4×C139—22no—
359C2×C4×C139—22no—
360C2×C4×C139—22no—
361C2×C4×C139—22no—
362C2×C4×C139—22no—
363C2×C4×C139—22no—
364C2×C4×C139—22no—
365C2×C4×C139—22no—
366C2×C4×C139—22no—
367C2×C4×C139—22no—
368C2×C4×C139—416no—
369C2×C4×C139—41no—
370C2×C4×C139—41no—
371C2×C4×C139—41no—
372C2×C4×C139—41no—
373C2×C4×C139—41no—
374C2×C4×C139—41no—
375C2×C4×C139—41no—
376C2×C4×C139—41no—
377C2×C4×C139—41no—
378C2×C4×C139—41no—
379C2×C4×C139—41no—
380C2×C4×C139—41no—
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—41no—
402C2×C4×C139—41no—
403C2×C4×C139—41no—
404C2×C4×C139—41no—
405C2×C4×C139—41no—
406C2×C4×C139—41no—
407C2×C4×C139—41no—
408C2×C4×C139—41no—
409C2×C4×C139—41no—
410C2×C4×C139—41no—
411C2×C4×C139—41no—
412C2×C4×C139—41no—
413C2×C4×C139—41no—
414C2×C4×C139—41no—
415C2×C4×C139—41no—
416C2×C4×C139—41no—
417C2×C4×C139—41no—
418C2×C4×C139—41no—
419C2×C4×C139C2×C4⋊C414yes—
420C2×C4×C139C2×C4⋊C414yes—
421C2×C4×C139#12614yes—
422C22×C139—24no—
423C22×C139—24no—
424C22×C139—24no—
425C22×C139—42no—
426C22×C139—42no—
427C22×C139—42no—
428C22×C139—42no—
429C22×C139—42no—
430C22×C139—42no—
431C22×C139—42no—
432C22×C139—42no—
433C22×C139—42no—
434C22×C139—42no—
435C22×C139—42no—
436C22×C139—42no—
437C22×C139C22×C4⋊C411yescharacteristic
438C22×C139C4×#4111yescharacteristic
439C22×C139C4×#4111yescharacteristic
440C22×C139C4×#4111yescharacteristic
441C22×C139C4×#4111yescharacteristic
442C22×C139#51811yescharacteristic
443C22×C139#51811yescharacteristic
444C22×C139#52511yescharacteristic
445C22×C139#52511yescharacteristic
446C22×C139C2×#12611yescharacteristic
447C22×C139#52911yescharacteristic
448C22×C139#52911yescharacteristic
449C22×C139#52911yescharacteristic
450C22×C139#53311yescharacteristic
451C22×C139#53311yescharacteristic
452C22×C139#53811yescharacteristic
453C22×C139#53811yescharacteristic
454C22×C139#54011yescharacteristic
455C22×C139#54011yescharacteristic
456C22×C139#54611yescharacteristic
457C22×C139#54611yescharacteristic
458C22×C139#54611yescharacteristic
459C22×C139#54611yescharacteristic
460C22×C139#55111yescharacteristic
461C22×C139#55111yescharacteristic
462C22×C139#55111yescharacteristic
463C22×C139#55311yescharacteristic
464C22×C139#55311yescharacteristic
465C22×C139#55411yescharacteristic
466C22×C139#55411yescharacteristic
467C22×C139#55411yescharacteristic
468C22×C139#55411yescharacteristic
469C22×C139#55511yescharacteristic
470C22×C139#55511yescharacteristic
471C22×C139#55911yescharacteristic
472C4×C139—24no—
473C4×C139—24no—
474C4×C139—24no—
475C4×C139—42no—
476C4×C139—42no—
477C4×C139—42no—
478C4×C139—42no—
479C4×C139—42no—
480C4×C139—42no—
481C4×C139—42no—
482C4×C139—42no—
483C4×C139—42no—
484C4×C139—81no—
485C4×C139—81no—
486C2×C139—44no—
487C2×C139#229611yescharacteristic
488C2×C139C4×#12611yescharacteristic
489C2×C139#233311yescharacteristic
490C2×C139#234911yescharacteristic
491C2×C139#234911yescharacteristic
492C2×C139#237211yescharacteristic
493C2×C139#237411yescharacteristic
494C2×C139#245711yescharacteristic
495C2×C139#245911yescharacteristic
496C2×C139#247611yescharacteristic
497C2×C139#248011yescharacteristic
498C2×C139#249711yescharacteristic
499C2×C139#252211yescharacteristic
500C2×C139#257411yescharacteristic
501C2×C139#258911yescharacteristic
502#14114C13911yesmaximal, characteristic, direct product factor, Sylow
503C139#1411411yescharacteristic, direct product factor, Sylow
504C2×#388C2×C13911yescharacteristic
505C2×#388C2×C13911yescharacteristic
506C2×C4×C22⋊C4C2×C13911yescharacteristic
507#1442C2×C13911yescharacteristic, complemented
508#1441C2×C13911yescharacteristic, complemented
509#1439C2×C13911yescharacteristic
510#1439C2×C13911yescharacteristic
511#1436C2×C13911yescharacteristic, complemented
512#1436C2×C13911yescharacteristic, complemented
513#1436C2×C13911yescharacteristic, complemented
514C4⋊#95C2×C13911yescharacteristic, complemented
515#1434C2×C13911yescharacteristic, complemented
516C22⋊#95C2×C13911yescharacteristic
517C22⋊#95C2×C13911yescharacteristic
518C4×#95C2×C13911yescharacteristic, complemented
519C24×C4C22×C13911yescharacteristic
520C22×C4⋊C4C22×C13911yescharacteristic
521C22×C4⋊C4C22×C13911yescharacteristic
522C22×C4⋊C4C22×C13911yescharacteristic
523C22×C4⋊C4C22×C13911yescharacteristic
524C22×C22⋊C4C22×C13911yescharacteristic
525C22×C22⋊C4C22×C13911yescharacteristic
526C22×C22⋊C4C22×C13911yescharacteristic
527C22×C22⋊C4C22×C13911yescharacteristic
528C22×C22⋊C4C22×C13911yescharacteristic
529C22×C22⋊C4C22×C13911yescharacteristic
530C22×C42C22×C13911yescharacteristic
531C22×C42C22×C13911yescharacteristic
532C22×C42C22×C13911yescharacteristic
533C22×C42C22×C13911yescharacteristic
534#388—24no—
535#388C4×C13918yescomplemented
536C4×C22⋊C4—24no—
537C2×#95C22×C13911yescharacteristic
538C2×#95C22×C13911yescharacteristic
539C2×#95C22×C13911yescharacteristic
540C2×#95C22×C13911yescharacteristic
541C2×#95C22×C13911yescharacteristic
542C2×#95C22×C13911yescharacteristic
543C2×#95C22×C13911yescharacteristic
544C2×#95C22×C13911yescharacteristic
545C2×#95C22×C13911yescharacteristic
546C2×#95C22×C13911yescharacteristic
547C2×#95C22×C13911yescharacteristic
548C2×#95C22×C13911yescharacteristic
549C2×#95C22×C13911yescharacteristic
550C2×#95C22×C13911yescharacteristic
551C2×#95C22×C13911yescharacteristic
552C2×#95C22×C13911yescharacteristic
553C2×#95C22×C13911yescharacteristic
554C2×#95C22×C13911yescharacteristic
555C2×#95C22×C13911yescharacteristic
556C2×#95C22×C13911yescharacteristic
557C25C23×C13911yescharacteristic
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—41no—
564C23×C4—41no—
565C23×C4C23×C13911yescharacteristic
566C23×C4C23×C13911yescharacteristic
567C23×C4C23×C13911yescharacteristic
568C23×C4C23×C13911yescharacteristic
569C23×C4C23×C13911yescharacteristic
570C23×C4C23×C13911yescharacteristic
571C23×C4C23×C13911yescharacteristic
572C23×C4C23×C13911yescharacteristic
573C23×C4C23×C13911yescharacteristic
574C23×C4C23×C13911yescharacteristic
575C23×C4C23×C13911yescharacteristic
576C23×C4C23×C13911yescharacteristic
577C23×C4C23×C13911yescharacteristic
578C23×C4C23×C13911yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4C2×C4×C13914yescomplemented
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4C2×C4×C13914yes—
605C2×C22⋊C4C2×C4×C13914yes—
606C2×C22⋊C4C2×C4×C13914yes—
607C2×C22⋊C4D4×C13914yes—
608C2×C22⋊C4Q8×C13914yes—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42C2×C4×C13914yescomplemented
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95—41no—
639#95C2×C4×C13914yescomplemented
640#95C2×C4×C13914yescomplemented
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C13912yes—
654C24C2×D4×C13912yes—
655C24C2×Q8×C13912yes—
656C24C24×C13911yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—28no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
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×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4C22×C4×C13912yes—
745C22×C4C22×C4×C13912yes—
746C22×C4C22×C4×C13912yes—
747C22×C4C22×C4×C13912yes—
748C22×C4C22×C4×C13912yes—
749C22×C4C22×C4×C13912yes—
750C22×C4C2×D4×C13912yes—
751C22×C4C2×D4×C13912yes—
752C22×C4C2×Q8×C13912yes—
753C22×C4C2×Q8×C13912yes—
754C22×C4#41×C13912yes—
755C22×C4#41×C13912yes—
756C22×C4#41×C13912yes—
757C22×C4#41×C13912yes—
758C22×C4#41×C13912yes—
759C22×C4#41×C13912yes—
760C22×C4#41×C13912yes—
761C22×C4#41×C13912yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C22⋊C4—28no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4C4⋊C4×C139116yescomplemented
772C42—44no—
773C42—44no—
774C42—44no—
775C42—44no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C13914yes—
811C23C23×C4×C13911yescharacteristic
812C23C22×D4×C13911yescharacteristic
813C23C22×Q8×C13911yescharacteristic
814C23C2×#41×C13911yescharacteristic
815C23C2×#41×C13911yescharacteristic
816C23C2×#41×C13911yescharacteristic
817C23C2×#41×C13911yescharacteristic
818C23C2×#41×C13911yescharacteristic
819C23C2×#41×C13911yescharacteristic
820C23C2×#41×C13911yescharacteristic
821C23C2×#41×C13911yescharacteristic
822C23H(5,𝔽2)×C13911yescharacteristic
823C23H(5,𝔽2)×C13911yescharacteristic
824C23H(5,𝔽2)×C13911yescharacteristic
825C23H(5,𝔽2)×C13911yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
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—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—416no—
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—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4C2×C4⋊C4×C13914yes—
923C2×C4C2×C4⋊C4×C13914yes—
924C2×C4#126×C13914yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C13911yescharacteristic
941C22C4×#41×C13911yescharacteristic
942C22C4×#41×C13911yescharacteristic
943C22C4×#41×C13911yescharacteristic
944C22C4×#41×C13911yescharacteristic
945C22#518×C13911yescharacteristic
946C22#518×C13911yescharacteristic
947C22#525×C13911yescharacteristic
948C22#525×C13911yescharacteristic
949C22C2×#126×C13911yescharacteristic
950C22#529×C13911yescharacteristic
951C22#529×C13911yescharacteristic
952C22#529×C13911yescharacteristic
953C22#533×C13911yescharacteristic
954C22#533×C13911yescharacteristic
955C22#538×C13911yescharacteristic
956C22#538×C13911yescharacteristic
957C22#540×C13911yescharacteristic
958C22#540×C13911yescharacteristic
959C22#546×C13911yescharacteristic
960C22#546×C13911yescharacteristic
961C22#546×C13911yescharacteristic
962C22#546×C13911yescharacteristic
963C22#551×C13911yescharacteristic
964C22#551×C13911yescharacteristic
965C22#551×C13911yescharacteristic
966C22#553×C13911yescharacteristic
967C22#553×C13911yescharacteristic
968C22#554×C13911yescharacteristic
969C22#554×C13911yescharacteristic
970C22#554×C13911yescharacteristic
971C22#554×C13911yescharacteristic
972C22#555×C13911yescharacteristic
973C22#555×C13911yescharacteristic
974C22#559×C13911yescharacteristic
975C4—24no—
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2#2296×C13911yescharacteristic
991C2C4×#126×C13911yescharacteristic
992C2#2333×C13911yescharacteristic
993C2#2349×C13911yescharacteristic
994C2#2349×C13911yescharacteristic
995C2#2372×C13911yescharacteristic
996C2#2374×C13911yescharacteristic
997C2#2457×C13911yescharacteristic
998C2#2459×C13911yescharacteristic
999C2#2476×C13911yescharacteristic
1000C2#2480×C13911yescharacteristic
1001C2#2497×C13911yescharacteristic
1002C2#2522×C13911yescharacteristic
1003C2#2574×C13911yescharacteristic
1004C2#2589×C13911yescharacteristic
subgroupG/H
center, socleC24×C139C24
commutatorC23C23×C4×C139
Frattini, cosocleC24C24×C139
prime radicalC25×C139C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1442×C139C2semidirect
5. #1441×C139C2semidirect
8. #1436×C139C2semidirect
9. #1436×C139C2semidirect
10. #1436×C139C2semidirect
11. C4⋊#95×C139C2semidirect
12. #1434×C139C2semidirect
15. C4×#95×C139C2semidirect
32. #388×C139C4semidirect
87. C2×C4⋊C4×C139C2×C4semidirect
117. C2×C42×C139C2×C4semidirect
136. #95×C139C2×C4semidirect
137. #95×C139C2×C4semidirect
268. C22⋊C4×C139C4⋊C4semidirect
502. #14114C139direct (N × H)
503. C139#14114direct (N × H)
507. #1442C2×C139semidirect
508. #1441C2×C139semidirect
511. #1436C2×C139semidirect
512. #1436C2×C139semidirect
513. #1436C2×C139semidirect
514. C4⋊#95C2×C139semidirect
515. #1434C2×C139semidirect
518. C4×#95C2×C139semidirect
535. #388C4×C139semidirect
590. C2×C4⋊C4C2×C4×C139semidirect
620. C2×C42C2×C4×C139semidirect
639. #95C2×C4×C139semidirect
640. #95C2×C4×C139semidirect
771. C22⋊C4C4⋊C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#388×C1392
C2×C4×C22⋊C4×C1392
#1442×C1392
#1441×C1392
#1439×C1392
#1436×C1392
C4⋊#95×C1392
#1434×C1392
C22⋊#95×C1392
C4×#95×C1392
#14114139