Finite Group Databasebeta

← C139×#13789 #48008385

Subgroups — C139×#13789 #48008385

Order 35584.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1022 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×#385×C139C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C139C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C139C211yesmaximal, characteristic
6#1437×C139C211yesmaximal, characteristic
7#1437×C139C211yesmaximal, characteristic
8#1436×C139C211yesmaximal, characteristic, complemented
9#1436×C139C211yesmaximal, characteristic, complemented
10#1436×C139C211yesmaximal, characteristic, complemented
11#1436×C139C211yesmaximal, characteristic, complemented
12C4⋊#95×C139C211yesmaximal, characteristic, complemented
13#1434×C139C211yesmaximal, characteristic, complemented
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
31C22×C42×C139C2211yescharacteristic
32C22×C42×C139C2211yescharacteristic
33#388×C139C418yescomplemented
34#388×C139C418yescomplemented
35#385×C139C418yescomplemented
36C4×C4⋊C4×C139—24no—
37C4×C22⋊C4×C139—24no—
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
54C2×#95×C139C2211yescharacteristic
55C2×#95×C139C2211yescharacteristic
56C25×C139C2311yescharacteristic
57C23×C4×C139—22no—
58C23×C4×C139—22no—
59C23×C4×C139—41no—
60C23×C4×C139—41no—
61C23×C4×C139—41no—
62C23×C4×C139—41no—
63C23×C4×C139C2×C414yes—
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
76C23×C4×C139C2311yescharacteristic
77C23×C4×C139C2311yescharacteristic
78C2×C4⋊C4×C139—22no—
79C2×C4⋊C4×C139—22no—
80C2×C4⋊C4×C139—22no—
81C2×C4⋊C4×C139—22no—
82C2×C4⋊C4×C139—41no—
83C2×C4⋊C4×C139—41no—
84C2×C4⋊C4×C139—41no—
85C2×C4⋊C4×C139—41no—
86C2×C4⋊C4×C139C2×C414yes—
87C2×C4⋊C4×C139C2×C414yes—
88C2×C4⋊C4×C139C2×C414yescomplemented
89C2×C4⋊C4×C139C2×C414yescomplemented
90C2×C22⋊C4×C139—22no—
91C2×C22⋊C4×C139—22no—
92C2×C22⋊C4×C139—22no—
93C2×C22⋊C4×C139—22no—
94C2×C22⋊C4×C139—41no—
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×C139C2×C414yes—
101C2×C22⋊C4×C139C2×C414yes—
102C2×C22⋊C4×C139C2×C414yes—
103C2×C22⋊C4×C139C2×C414yes—
104C2×C22⋊C4×C139C2×C414yes—
105C2×C22⋊C4×C139C2×C414yes—
106C2×C22⋊C4×C139C2×C414yes—
107C2×C22⋊C4×C139C2×C414yes—
108C2×C42×C139—22no—
109C2×C42×C139—22no—
110C2×C42×C139—22no—
111C2×C42×C139—22no—
112C2×C42×C139—22no—
113C2×C42×C139—41no—
114C2×C42×C139—41no—
115C2×C42×C139—41no—
116C2×C42×C139—41no—
117C2×C42×C139—41no—
118C2×C42×C139—41no—
119C2×C42×C139—41no—
120C2×C42×C139—41no—
121C2×C42×C139—41no—
122C2×C42×C139—41no—
123C2×C42×C139C2×C414yescomplemented
124C2×C42×C139C2×C414yescomplemented
125C2×C42×C139D414yes—
126#95×C139—22no—
127#95×C139—22no—
128#95×C139—22no—
129#95×C139—22no—
130#95×C139—22no—
131#95×C139—22no—
132#95×C139—41no—
133#95×C139—41no—
134#95×C139—41no—
135#95×C139—41no—
136#95×C139—41no—
137#95×C139—41no—
138#95×C139C2×C414yes—
139#95×C139C2×C414yes—
140#95×C139C2×C414yescomplemented
141#95×C139C2×C414yescomplemented
142#95×C139C2×C414yescomplemented
143#95×C139C2×C414yescomplemented
144C24×C139—21no—
145C24×C139—21no—
146C24×C139—21no—
147C24×C139—21no—
148C24×C139—21no—
149C24×C139—21no—
150C24×C139—21no—
151C24×C139—21no—
152C24×C139—21no—
153C24×C139—21no—
154C24×C139—21no—
155C24×C139—21no—
156C24×C139C22×C412yes—
157C24×C139C22×C412yes—
158C24×C139C22×C412yes—
159C24×C139C2411yescharacteristic
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—21no—
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—28no—
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×C139C22×C412yes—
248C22×C4×C139C22×C412yes—
249C22×C4×C139C22×C412yes—
250C22×C4×C139C22×C412yes—
251C22×C4×C139C22×C412yes—
252C22×C4×C139C22×C412yes—
253C22×C4×C139C22×C412yes—
254C22×C4×C139C22×C412yes—
255C22×C4×C139C22×C412yes—
256C22×C4×C139C22×C412yes—
257C22×C4×C139C22×C412yes—
258C22×C4×C139C22×C412yes—
259C22×C4×C139C2×D412yes—
260C22×C4×C139C2×D412yes—
261C22×C4×C139C2×D412yes—
262C22×C4×C139#4112yes—
263C22×C4×C139#4112yes—
264C22×C4×C139#4112yes—
265C4⋊C4×C139—28no—
266C4⋊C4×C139—28no—
267C4⋊C4×C139—44no—
268C4⋊C4×C139—44no—
269C22⋊C4×C139—28no—
270C22⋊C4×C139—28no—
271C22⋊C4×C139—44no—
272C22⋊C4×C139—44no—
273C22⋊C4×C139—44no—
274C22⋊C4×C139C42116yescomplemented
275C42×C139—28no—
276C42×C139—44no—
277C42×C139—44no—
278C42×C139—44no—
279C42×C139—44no—
280C42×C139—44no—
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—22no—
292C23×C139—22no—
293C23×C139—22no—
294C23×C139—22no—
295C23×C139—22no—
296C23×C139—22no—
297C23×C139—22no—
298C23×C139—22no—
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—41no—
310C23×C139—41no—
311C23×C139—41no—
312C23×C139—41no—
313C23×C139—41no—
314C23×C139—41no—
315C23×C139C2×C4214yes—
316C23×C139C23×C411yescharacteristic
317C23×C139C23×C411yescharacteristic
318C23×C139C23×C411yescharacteristic
319C23×C139C22×D411yescharacteristic
320C23×C139C2×#4111yescharacteristic
321C23×C139C2×#4111yescharacteristic
322C23×C139C2×#4111yescharacteristic
323C23×C139H(5,𝔽2)11yescharacteristic
324C23×C139H(5,𝔽2)11yescharacteristic
325C23×C139H(5,𝔽2)11yescharacteristic
326C23×C139H(5,𝔽2)11yescharacteristic
327C23×C139H(5,𝔽2)11yescharacteristic
328C23×C1392−1+411yescharacteristic
329C23×C1392−1+411yescharacteristic
330C23×C1392−1+411yescharacteristic
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—22no—
369C2×C4×C139—22no—
370C2×C4×C139—22no—
371C2×C4×C139—22no—
372C2×C4×C139—22no—
373C2×C4×C139—22no—
374C2×C4×C139—22no—
375C2×C4×C139—22no—
376C2×C4×C139—22no—
377C2×C4×C139—22no—
378C2×C4×C139—22no—
379C2×C4×C139—22no—
380C2×C4×C139—22no—
381C2×C4×C139—22no—
382C2×C4×C139—22no—
383C2×C4×C139—22no—
384C2×C4×C139—22no—
385C2×C4×C139—22no—
386C2×C4×C139—22no—
387C2×C4×C139—22no—
388C2×C4×C139—416no—
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×C139—41no—
420C2×C4×C139—41no—
421C2×C4×C139—41no—
422C2×C4×C139—41no—
423C2×C4×C139—41no—
424C2×C4×C139—41no—
425C2×C4×C139C2×C4214yes—
426C2×C4×C139C2×C4214yes—
427C2×C4×C139C4×D414yes—
428C2×C4×C139C4×D414yes—
429C2×C4×C139C4×D414yes—
430C22×C139—24no—
431C22×C139—24no—
432C22×C139—24no—
433C22×C139—42no—
434C22×C139—42no—
435C22×C139—42no—
436C22×C139—42no—
437C22×C139—42no—
438C22×C139—42no—
439C22×C139—42no—
440C22×C139—42no—
441C22×C139—42no—
442C22×C139—42no—
443C22×C139—42no—
444C22×C139—42no—
445C22×C139C22×C4211yescharacteristic
446C22×C139C2×C4×D411yescharacteristic
447C22×C139C2×C4×D411yescharacteristic
448C22×C139C2×C4×D411yescharacteristic
449C22×C139C4×#4111yescharacteristic
450C22×C139C4×#4111yescharacteristic
451C22×C139C4×#4111yescharacteristic
452C22×C139#51811yescharacteristic
453C22×C139#51811yescharacteristic
454C22×C139#51811yescharacteristic
455C22×C139#51811yescharacteristic
456C22×C139#51911yescharacteristic
457C22×C139#52011yescharacteristic
458C22×C139#52011yescharacteristic
459C22×C139#52011yescharacteristic
460C22×C139#52011yescharacteristic
461C22×C139#52011yescharacteristic
462C22×C139#52011yescharacteristic
463C22×C139#52011yescharacteristic
464C22×C139#53411yescharacteristic
465C22×C139#53511yescharacteristic
466C22×C139#53611yescharacteristic
467C22×C139#53711yescharacteristic
468C22×C139#53811yescharacteristic
469C22×C139#53811yescharacteristic
470C22×C139#53811yescharacteristic
471C22×C139#53911yescharacteristic
472C22×C139#53911yescharacteristic
473C22×C139#53911yescharacteristic
474C22×C139#54011yescharacteristic
475C22×C139#54111yescharacteristic
476C22×C139#54211yescharacteristic
477C22×C139#54211yescharacteristic
478C22×C139#54211yescharacteristic
479C22×C139#54211yescharacteristic
480C4×C139—24no—
481C4×C139—24no—
482C4×C139—24no—
483C4×C139—24no—
484C4×C139—24no—
485C4×C139—42no—
486C4×C139—42no—
487C4×C139—42no—
488C4×C139—42no—
489C4×C139—42no—
490C4×C139—42no—
491C4×C139—42no—
492C4×C139—42no—
493C4×C139—42no—
494C2×C139—44no—
495C2×C139C42×D411yescharacteristic
496C2×C139#227411yescharacteristic
497C2×C139#227511yescharacteristic
498C2×C139#232111yescharacteristic
499C2×C139#232211yescharacteristic
500C2×C139#232311yescharacteristic
501C2×C139#232411yescharacteristic
502C2×C139#232511yescharacteristic
503C2×C139#232611yescharacteristic
504C2×C139#233211yescharacteristic
505C2×C139#233411yescharacteristic
506C2×C139#233411yescharacteristic
507C2×C139#233511yescharacteristic
508C2×C139#233511yescharacteristic
509C2×C139#233711yescharacteristic
510#13789C13911yesmaximal, characteristic, direct product factor, Sylow
511C139#1378911yescharacteristic, direct product factor, Sylow
512C2×#388C2×C13911yescharacteristic
513C2×#388C2×C13911yescharacteristic
514C2×#385C2×C13911yescharacteristic
515C2×C4×C4⋊C4C2×C13911yescharacteristic, complemented
516C2×C4×C22⋊C4C2×C13911yescharacteristic
517#1437C2×C13911yescharacteristic
518#1437C2×C13911yescharacteristic
519#1436C2×C13911yescharacteristic, complemented
520#1436C2×C13911yescharacteristic, complemented
521#1436C2×C13911yescharacteristic, complemented
522#1436C2×C13911yescharacteristic, complemented
523C4⋊#95C2×C13911yescharacteristic, complemented
524#1434C2×C13911yescharacteristic, complemented
525C22⋊#95C2×C13911yescharacteristic
526C4×#95C2×C13911yescharacteristic, complemented
527C24×C4C22×C13911yescharacteristic
528C22×C4⋊C4C22×C13911yescharacteristic
529C22×C4⋊C4C22×C13911yescharacteristic
530C22×C4⋊C4C22×C13911yescharacteristic
531C22×C4⋊C4C22×C13911yescharacteristic
532C22×C22⋊C4C22×C13911yescharacteristic
533C22×C22⋊C4C22×C13911yescharacteristic
534C22×C22⋊C4C22×C13911yescharacteristic
535C22×C22⋊C4C22×C13911yescharacteristic
536C22×C22⋊C4C22×C13911yescharacteristic
537C22×C22⋊C4C22×C13911yescharacteristic
538C22×C42C22×C13911yescharacteristic
539C22×C42C22×C13911yescharacteristic
540C22×C42C22×C13911yescharacteristic
541C22×C42C22×C13911yescharacteristic
542C22×C42C22×C13911yescharacteristic
543C22×C42C22×C13911yescharacteristic
544#388C4×C13918yescomplemented
545#388C4×C13918yescomplemented
546#385C4×C13918yescomplemented
547C4×C4⋊C4—24no—
548C4×C22⋊C4—24no—
549C2×#95C22×C13911yescharacteristic
550C2×#95C22×C13911yescharacteristic
551C2×#95C22×C13911yescharacteristic
552C2×#95C22×C13911yescharacteristic
553C2×#95C22×C13911yescharacteristic
554C2×#95C22×C13911yescharacteristic
555C2×#95C22×C13911yescharacteristic
556C2×#95C22×C13911yescharacteristic
557C2×#95C22×C13911yescharacteristic
558C2×#95C22×C13911yescharacteristic
559C2×#95C22×C13911yescharacteristic
560C2×#95C22×C13911yescharacteristic
561C2×#95C22×C13911yescharacteristic
562C2×#95C22×C13911yescharacteristic
563C2×#95C22×C13911yescharacteristic
564C2×#95C22×C13911yescharacteristic
565C2×#95C22×C13911yescharacteristic
566C2×#95C22×C13911yescharacteristic
567C25C23×C13911yescharacteristic
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4C2×C4×C13914yes—
575C23×C4C23×C13911yescharacteristic
576C23×C4C23×C13911yescharacteristic
577C23×C4C23×C13911yescharacteristic
578C23×C4C23×C13911yescharacteristic
579C23×C4C23×C13911yescharacteristic
580C23×C4C23×C13911yescharacteristic
581C23×C4C23×C13911yescharacteristic
582C23×C4C23×C13911yescharacteristic
583C23×C4C23×C13911yescharacteristic
584C23×C4C23×C13911yescharacteristic
585C23×C4C23×C13911yescharacteristic
586C23×C4C23×C13911yescharacteristic
587C23×C4C23×C13911yescharacteristic
588C23×C4C23×C13911yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4C2×C4×C13914yes—
598C2×C4⋊C4C2×C4×C13914yes—
599C2×C4⋊C4C2×C4×C13914yescomplemented
600C2×C4⋊C4C2×C4×C13914yescomplemented
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4C2×C4×C13914yes—
612C2×C22⋊C4C2×C4×C13914yes—
613C2×C22⋊C4C2×C4×C13914yes—
614C2×C22⋊C4C2×C4×C13914yes—
615C2×C22⋊C4C2×C4×C13914yes—
616C2×C22⋊C4C2×C4×C13914yes—
617C2×C22⋊C4C2×C4×C13914yes—
618C2×C22⋊C4C2×C4×C13914yes—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—22no—
624C2×C42—41no—
625C2×C42—41no—
626C2×C42—41no—
627C2×C42—41no—
628C2×C42—41no—
629C2×C42—41no—
630C2×C42—41no—
631C2×C42—41no—
632C2×C42—41no—
633C2×C42—41no—
634C2×C42C2×C4×C13914yescomplemented
635C2×C42C2×C4×C13914yescomplemented
636C2×C42D4×C13914yes—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—41no—
644#95—41no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95C2×C4×C13914yes—
650#95C2×C4×C13914yes—
651#95C2×C4×C13914yescomplemented
652#95C2×C4×C13914yescomplemented
653#95C2×C4×C13914yescomplemented
654#95C2×C4×C13914yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×C4×C13912yes—
668C24C22×C4×C13912yes—
669C24C22×C4×C13912yes—
670C24C24×C13911yescharacteristic
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—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—28no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4C22×C4×C13912yes—
753C22×C4C22×C4×C13912yes—
754C22×C4C22×C4×C13912yes—
755C22×C4C22×C4×C13912yes—
756C22×C4C22×C4×C13912yes—
757C22×C4C22×C4×C13912yes—
758C22×C4C22×C4×C13912yes—
759C22×C4C22×C4×C13912yes—
760C22×C4C22×C4×C13912yes—
761C22×C4C22×C4×C13912yes—
762C22×C4C22×C4×C13912yes—
763C22×C4C22×C4×C13912yes—
764C22×C4C22×C4×C13912yes—
765C22×C4C22×C4×C13912yes—
766C22×C4C22×C4×C13912yes—
767C22×C4C22×C4×C13912yes—
768C22×C4C22×C4×C13912yes—
769C22×C4C22×C4×C13912yes—
770C22×C4C2×D4×C13912yes—
771C22×C4C2×D4×C13912yes—
772C22×C4C2×D4×C13912yes—
773C22×C4#41×C13912yes—
774C22×C4#41×C13912yes—
775C22×C4#41×C13912yes—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C22⋊C4—28no—
781C22⋊C4—28no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C22⋊C4—44no—
785C22⋊C4C42×C139116yescomplemented
786C42—28no—
787C42—44no—
788C42—44no—
789C42—44no—
790C42—44no—
791C42—44no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C42×C13914yes—
827C23C23×C4×C13911yescharacteristic
828C23C23×C4×C13911yescharacteristic
829C23C23×C4×C13911yescharacteristic
830C23C22×D4×C13911yescharacteristic
831C23C2×#41×C13911yescharacteristic
832C23C2×#41×C13911yescharacteristic
833C23C2×#41×C13911yescharacteristic
834C23H(5,𝔽2)×C13911yescharacteristic
835C23H(5,𝔽2)×C13911yescharacteristic
836C23H(5,𝔽2)×C13911yescharacteristic
837C23H(5,𝔽2)×C13911yescharacteristic
838C23H(5,𝔽2)×C13911yescharacteristic
839C232−1+4×C13911yescharacteristic
840C232−1+4×C13911yescharacteristic
841C232−1+4×C13911yescharacteristic
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—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—416no—
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×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4C2×C42×C13914yes—
937C2×C4C2×C42×C13914yes—
938C2×C4C4×D4×C13914yes—
939C2×C4C4×D4×C13914yes—
940C2×C4C4×D4×C13914yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C42×C13911yescharacteristic
957C22C2×C4×D4×C13911yescharacteristic
958C22C2×C4×D4×C13911yescharacteristic
959C22C2×C4×D4×C13911yescharacteristic
960C22C4×#41×C13911yescharacteristic
961C22C4×#41×C13911yescharacteristic
962C22C4×#41×C13911yescharacteristic
963C22#518×C13911yescharacteristic
964C22#518×C13911yescharacteristic
965C22#518×C13911yescharacteristic
966C22#518×C13911yescharacteristic
967C22#519×C13911yescharacteristic
968C22#520×C13911yescharacteristic
969C22#520×C13911yescharacteristic
970C22#520×C13911yescharacteristic
971C22#520×C13911yescharacteristic
972C22#520×C13911yescharacteristic
973C22#520×C13911yescharacteristic
974C22#520×C13911yescharacteristic
975C22#534×C13911yescharacteristic
976C22#535×C13911yescharacteristic
977C22#536×C13911yescharacteristic
978C22#537×C13911yescharacteristic
979C22#538×C13911yescharacteristic
980C22#538×C13911yescharacteristic
981C22#538×C13911yescharacteristic
982C22#539×C13911yescharacteristic
983C22#539×C13911yescharacteristic
984C22#539×C13911yescharacteristic
985C22#540×C13911yescharacteristic
986C22#541×C13911yescharacteristic
987C22#542×C13911yescharacteristic
988C22#542×C13911yescharacteristic
989C22#542×C13911yescharacteristic
990C22#542×C13911yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—24no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C2—44no—
1006C2C42×D4×C13911yescharacteristic
1007C2#2274×C13911yescharacteristic
1008C2#2275×C13911yescharacteristic
1009C2#2321×C13911yescharacteristic
1010C2#2322×C13911yescharacteristic
1011C2#2323×C13911yescharacteristic
1012C2#2324×C13911yescharacteristic
1013C2#2325×C13911yescharacteristic
1014C2#2326×C13911yescharacteristic
1015C2#2332×C13911yescharacteristic
1016C2#2334×C13911yescharacteristic
1017C2#2334×C13911yescharacteristic
1018C2#2335×C13911yescharacteristic
1019C2#2335×C13911yescharacteristic
1020C2#2337×C13911yescharacteristic
subgroupG/H
center, socleC24×C139C24
commutatorC22C22×C42×C139
Frattini, cosocleC24C24×C139
prime radicalC25×C139C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C4×C4⋊C4×C139C2semidirect
8. #1436×C139C2semidirect
9. #1436×C139C2semidirect
10. #1436×C139C2semidirect
11. #1436×C139C2semidirect
12. C4⋊#95×C139C2semidirect
13. #1434×C139C2semidirect
15. C4×#95×C139C2semidirect
33. #388×C139C4semidirect
34. #388×C139C4semidirect
35. #385×C139C4semidirect
88. C2×C4⋊C4×C139C2×C4semidirect
89. C2×C4⋊C4×C139C2×C4semidirect
123. C2×C42×C139C2×C4semidirect
124. C2×C42×C139C2×C4semidirect
140. #95×C139C2×C4semidirect
141. #95×C139C2×C4semidirect
142. #95×C139C2×C4semidirect
143. #95×C139C2×C4semidirect
274. C22⋊C4×C139C42semidirect
510. #13789C139direct (N × H)
511. C139#13789direct (N × H)
515. C2×C4×C4⋊C4C2×C139semidirect
519. #1436C2×C139semidirect
520. #1436C2×C139semidirect
521. #1436C2×C139semidirect
522. #1436C2×C139semidirect
523. C4⋊#95C2×C139semidirect
524. #1434C2×C139semidirect
526. C4×#95C2×C139semidirect
544. #388C4×C139semidirect
545. #388C4×C139semidirect
546. #385C4×C139semidirect
599. C2×C4⋊C4C2×C4×C139semidirect
600. C2×C4⋊C4C2×C4×C139semidirect
634. C2×C42C2×C4×C139semidirect
635. C2×C42C2×C4×C139semidirect
651. #95C2×C4×C139semidirect
652. #95C2×C4×C139semidirect
653. #95C2×C4×C139semidirect
654. #95C2×C4×C139semidirect
785. C22⋊C4C42×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×#385×C1392
C2×C4×C4⋊C4×C1392
C2×C4×C22⋊C4×C1392
#1437×C1392
#1436×C1392
C4⋊#95×C1392
#1434×C1392
C22⋊#95×C1392
C4×#95×C1392
#13789139