Finite Group Databasebeta

← C139×#15765 #48010361

Subgroups — C139×#15765 #48010361

Order 35584.

1598 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C139C211yesmaximal, characteristic
2C2×#399×C139C211yesmaximal, characteristic
3C2×#398×C139C211yesmaximal, characteristic, complemented
4C2×#396×C139C211yesmaximal, characteristic
5C2×#389×C139C211yesmaximal, characteristic, complemented
6C2×#388×C139C211yesmaximal, characteristic
7C2×#387×C139C211yesmaximal, characteristic, complemented
8C2×#384×C139C211yesmaximal, characteristic, complemented
9#1445×C139C211yesmaximal, characteristic, complemented
10#1444×C139C211yesmaximal, characteristic, complemented
11#1444×C139C211yesmaximal, characteristic, complemented
12#1439×C139C211yesmaximal, characteristic
13#1439×C139C211yesmaximal, characteristic
14#1437×C139C211yesmaximal, characteristic
15#1436×C139C211yesmaximal, characteristic, complemented
16C22×C4⋊C4×C139C2211yescharacteristic
17C22×C4⋊C4×C139C2211yescharacteristic
18C22×C4⋊C4×C139C2211yescharacteristic
19C22×C4⋊C4×C139C2211yescharacteristic
20C22×C4⋊C4×C139C2211yescharacteristic
21C22×C4⋊C4×C139C2211yescharacteristic
22C22×C4⋊C4×C139C2211yescharacteristic
23C22×C4⋊C4×C139C2211yescharacteristic
24C22×C4⋊C4×C139C2211yescharacteristic
25C22×C4⋊C4×C139C2211yescharacteristic
26C22×C4⋊C4×C139C2211yescharacteristic
27C22×C4⋊C4×C139C2211yescharacteristic
28C22×C22⋊C4×C139C2211yescharacteristic
29C22×C22⋊C4×C139C2211yescharacteristic
30C22×C22⋊C4×C139C2211yescharacteristic
31C22×C22⋊C4×C139C2211yescharacteristic
32C22×C22⋊C4×C139C2211yescharacteristic
33C22×C22⋊C4×C139C2211yescharacteristic
34C22×C22⋊C4×C139C2211yescharacteristic
35C22×C42×C139C2211yescharacteristic
36C22×C42×C139C2211yescharacteristic
37#399×C139—24no—
38#399×C139—24no—
39#398×C139—24no—
40#396×C139—24no—
41#389×C139—24no—
42#388×C139—24no—
43#387×C139—24no—
44#384×C139—24no—
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
56C2×#95×C139C2211yescharacteristic
57C2×#95×C139C2211yescharacteristic
58C2×#95×C139C2211yescharacteristic
59C25×C139C2311yescharacteristic
60C23×C4×C139C2311yescharacteristic
61C23×C4×C139C2311yescharacteristic
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
74C2×C4⋊C4×C139—22no—
75C2×C4⋊C4×C139—22no—
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—22no—
82C2×C4⋊C4×C139—22no—
83C2×C4⋊C4×C139—22no—
84C2×C4⋊C4×C139—22no—
85C2×C4⋊C4×C139—22no—
86C2×C4⋊C4×C139—22no—
87C2×C4⋊C4×C139—22no—
88C2×C4⋊C4×C139—22no—
89C2×C4⋊C4×C139—22no—
90C2×C4⋊C4×C139—22no—
91C2×C4⋊C4×C139—22no—
92C2×C4⋊C4×C139—22no—
93C2×C4⋊C4×C139—22no—
94C2×C4⋊C4×C139—22no—
95C2×C4⋊C4×C139—22no—
96C2×C4⋊C4×C139—22no—
97C2×C4⋊C4×C139—22no—
98C2×C4⋊C4×C139—22no—
99C2×C4⋊C4×C139—22no—
100C2×C4⋊C4×C139—41no—
101C2×C4⋊C4×C139—41no—
102C2×C4⋊C4×C139—41no—
103C2×C4⋊C4×C139—41no—
104C2×C4⋊C4×C139—41no—
105C2×C4⋊C4×C139—41no—
106C2×C4⋊C4×C139—41no—
107C2×C4⋊C4×C139—41no—
108C2×C4⋊C4×C139D414yes—
109C2×C4⋊C4×C139D414yes—
110C2×C22⋊C4×C139—22no—
111C2×C22⋊C4×C139—22no—
112C2×C22⋊C4×C139—22no—
113C2×C22⋊C4×C139—22no—
114C2×C22⋊C4×C139—22no—
115C2×C22⋊C4×C139—22no—
116C2×C22⋊C4×C139—22no—
117C2×C22⋊C4×C139—22no—
118C2×C22⋊C4×C139—22no—
119C2×C22⋊C4×C139—22no—
120C2×C22⋊C4×C139—22no—
121C2×C22⋊C4×C139—22no—
122C2×C22⋊C4×C139—22no—
123C2×C22⋊C4×C139—22no—
124C2×C22⋊C4×C139—22no—
125C2×C22⋊C4×C139—22no—
126C2×C22⋊C4×C139—41no—
127C2×C22⋊C4×C139—41no—
128C2×C22⋊C4×C139—41no—
129C2×C22⋊C4×C139—41no—
130C2×C22⋊C4×C139Q814yes—
131C2×C42×C139—22no—
132C2×C42×C139—22no—
133C2×C42×C139—22no—
134C2×C42×C139—22no—
135C2×C42×C139—22no—
136C2×C42×C139—22no—
137#95×C139—22no—
138#95×C139—22no—
139#95×C139—22no—
140#95×C139—22no—
141#95×C139—22no—
142#95×C139—22no—
143#95×C139—22no—
144#95×C139—22no—
145#95×C139—22no—
146#95×C139—22no—
147#95×C139—22no—
148#95×C139—22no—
149#95×C139D414yes—
150#95×C139D414yes—
151C24×C139—21no—
152C24×C139—21no—
153C24×C139—21no—
154C24×C139—21no—
155C24×C139—21no—
156C24×C139—21no—
157C24×C139—21no—
158C24×C139—21no—
159C24×C139—21no—
160C24×C139—21no—
161C24×C139—21no—
162C24×C139—21no—
163C24×C139—21no—
164C24×C139—21no—
165C24×C139C2×Q812yes—
166C24×C139C2411yescharacteristic
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—21no—
236C22×C4×C139—21no—
237C22×C4×C139—21no—
238C22×C4×C139—21no—
239C22×C4×C139—21no—
240C22×C4×C139—21no—
241C22×C4×C139—21no—
242C22×C4×C139—21no—
243C22×C4×C139—21no—
244C22×C4×C139—21no—
245C22×C4×C139—21no—
246C22×C4×C139—21no—
247C22×C4×C139C2×D412yes—
248C22×C4×C139C2×D412yes—
249C22×C4×C139C2×D412yes—
250C22×C4×C139C2×D412yes—
251C22×C4×C139C2×D412yes—
252C22×C4×C139C2×D412yes—
253C22×C4×C139C2×D412yes—
254C22×C4×C139C2×D412yes—
255C22×C4×C139C2×D412yes—
256C22×C4×C139C2×D412yes—
257C22×C4×C139C2×D412yes—
258C22×C4×C139C2×D412yes—
259C22×C4×C139C2×Q812yes—
260C22×C4×C139C2×Q812yes—
261C22×C4×C139#4112yes—
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—
269C4⋊C4×C139—44no—
270C4⋊C4×C139—44no—
271C4⋊C4×C139—44no—
272C4⋊C4×C139—44no—
273C4⋊C4×C139—44no—
274C4⋊C4×C139—44no—
275C4⋊C4×C139—44no—
276C4⋊C4×C139—44no—
277C22⋊C4×C139—28no—
278C22⋊C4×C139—44no—
279C22⋊C4×C139—44no—
280C22⋊C4×C139—44no—
281C22⋊C4×C139—44no—
282C22⋊C4×C139—44no—
283C22⋊C4×C139—44no—
284C42×C139—28no—
285C42×C139—44no—
286C23×C139—22no—
287C23×C139—22no—
288C23×C139—22no—
289C23×C139—22no—
290C23×C139—22no—
291C23×C139—22no—
292C23×C139—22no—
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×C139—41no—
308C23×C139—41no—
309C23×C139—41no—
310C23×C139—41no—
311C23×C139—41no—
312C23×C139—41no—
313C23×C139—41no—
314C23×C139—41no—
315C23×C139—41no—
316C23×C139—41no—
317C23×C139—41no—
318C23×C139—41no—
319C23×C139—41no—
320C23×C139—41no—
321C23×C139C22×D411yescharacteristic
322C23×C139C22×D411yescharacteristic
323C23×C139C22×D411yescharacteristic
324C23×C139C22×D411yescharacteristic
325C23×C139C22×Q811yescharacteristic
326C23×C139C2×#4111yescharacteristic
327C23×C139C2×#4111yescharacteristic
328C23×C139C2×#4111yescharacteristic
329C23×C139C2×#4111yescharacteristic
330C23×C139H(5,𝔽2)11yescharacteristic
331C23×C139H(5,𝔽2)11yescharacteristic
332C23×C1392−1+411yescharacteristic
333C23×C1392−1+411yescharacteristic
334C23×C1392−1+411yescharacteristic
335C23×C1392−1+411yescharacteristic
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—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×C139—41no—
420C2×C4×C139—41no—
421C2×C4×C139—41no—
422C2×C4×C139—41no—
423C2×C4×C139—41no—
424C2×C4×C139—41no—
425C2×C4×C139—41no—
426C2×C4×C139—41no—
427C2×C4×C139—41no—
428C2×C4×C139—41no—
429C2×C4×C139—41no—
430C2×C4×C139#12114yes—
431C2×C4×C139C22⋊Q814yes—
432C2×C4×C139#12314yes—
433C2×C4×C139#12714yes—
434C22×C139—42no—
435C22×C139—42no—
436C22×C139—42no—
437C22×C139—42no—
438C22×C139—42no—
439C22×C139—42no—
440C22×C139—42no—
441C22×C139—81no—
442C22×C139—81no—
443C22×C139—81no—
444C22×C139—81no—
445C22×C139—81no—
446C22×C139—81no—
447C22×C139—81no—
448C22×C139—81no—
449C22×C139C2×#12111yescharacteristic
450C22×C139C2×C22⋊Q811yescharacteristic
451C22×C139C2×#12311yescharacteristic
452C22×C139#52511yescharacteristic
453C22×C139C2×#12711yescharacteristic
454C22×C139#53311yescharacteristic
455C22×C139#53511yescharacteristic
456C22×C139#53611yescharacteristic
457C22×C139#53611yescharacteristic
458C22×C139#53611yescharacteristic
459C22×C139#53911yescharacteristic
460C22×C139#53911yescharacteristic
461C22×C139#54111yescharacteristic
462C22×C139#54211yescharacteristic
463C22×C139#54411yescharacteristic
464C22×C139D4211yescharacteristic
465C22×C139D4211yescharacteristic
466C22×C139#54711yescharacteristic
467C22×C139#54711yescharacteristic
468C22×C139#54711yescharacteristic
469C22×C139#54711yescharacteristic
470C22×C139#54711yescharacteristic
471C22×C139#54711yescharacteristic
472C22×C139#54811yescharacteristic
473C22×C139D4×Q811yescharacteristic
474C22×C139D4×Q811yescharacteristic
475C22×C139D4×Q811yescharacteristic
476C22×C139#55011yescharacteristic
477C22×C139#55011yescharacteristic
478C22×C139#55211yescharacteristic
479C22×C139#55211yescharacteristic
480C22×C139#55311yescharacteristic
481C22×C139#55411yescharacteristic
482C22×C139#56311yescharacteristic
483C22×C139#56311yescharacteristic
484C4×C139—24no—
485C4×C139—24no—
486C4×C139—24no—
487C4×C139—24no—
488C4×C139—42no—
489C4×C139—42no—
490C4×C139—42no—
491C4×C139—42no—
492C4×C139—42no—
493C4×C139—42no—
494C4×C139—81no—
495C4×C139—81no—
496C4×C139—81no—
497C4×C139—81no—
498C2×C139—82no—
499C2×C139#241311yescharacteristic
500C2×C139#242311yescharacteristic
501C2×C139#242911yescharacteristic
502C2×C139#244111yescharacteristic
503C2×C139#244311yescharacteristic
504C2×C139#244911yescharacteristic
505C2×C139#250111yescharacteristic
506C2×C139#254111yescharacteristic
507C2×C139#254211yescharacteristic
508C2×C139#267411yescharacteristic
509C2×C139#267711yescharacteristic
510C2×C139#271811yescharacteristic
511C2×C139#272011yescharacteristic
512C2×C139#272111yescharacteristic
513C2×C139#272111yescharacteristic
514#15765C13911yesmaximal, characteristic, direct product factor, Sylow
515C139#1576511yescharacteristic, direct product factor, Sylow
516C2×#399C2×C13911yescharacteristic
517C2×#399C2×C13911yescharacteristic
518C2×#398C2×C13911yescharacteristic, complemented
519C2×#396C2×C13911yescharacteristic
520C2×#389C2×C13911yescharacteristic, complemented
521C2×#388C2×C13911yescharacteristic
522C2×#387C2×C13911yescharacteristic, complemented
523C2×#384C2×C13911yescharacteristic, complemented
524#1445C2×C13911yescharacteristic, complemented
525#1444C2×C13911yescharacteristic, complemented
526#1444C2×C13911yescharacteristic, complemented
527#1439C2×C13911yescharacteristic
528#1439C2×C13911yescharacteristic
529#1437C2×C13911yescharacteristic
530#1436C2×C13911yescharacteristic, complemented
531C22×C4⋊C4C22×C13911yescharacteristic
532C22×C4⋊C4C22×C13911yescharacteristic
533C22×C4⋊C4C22×C13911yescharacteristic
534C22×C4⋊C4C22×C13911yescharacteristic
535C22×C4⋊C4C22×C13911yescharacteristic
536C22×C4⋊C4C22×C13911yescharacteristic
537C22×C4⋊C4C22×C13911yescharacteristic
538C22×C4⋊C4C22×C13911yescharacteristic
539C22×C4⋊C4C22×C13911yescharacteristic
540C22×C4⋊C4C22×C13911yescharacteristic
541C22×C4⋊C4C22×C13911yescharacteristic
542C22×C4⋊C4C22×C13911yescharacteristic
543C22×C22⋊C4C22×C13911yescharacteristic
544C22×C22⋊C4C22×C13911yescharacteristic
545C22×C22⋊C4C22×C13911yescharacteristic
546C22×C22⋊C4C22×C13911yescharacteristic
547C22×C22⋊C4C22×C13911yescharacteristic
548C22×C22⋊C4C22×C13911yescharacteristic
549C22×C22⋊C4C22×C13911yescharacteristic
550C22×C42C22×C13911yescharacteristic
551C22×C42C22×C13911yescharacteristic
552#399—24no—
553#399—24no—
554#398—24no—
555#396—24no—
556#389—24no—
557#388—24no—
558#387—24no—
559#384—24no—
560C2×#95C22×C13911yescharacteristic
561C2×#95C22×C13911yescharacteristic
562C2×#95C22×C13911yescharacteristic
563C2×#95C22×C13911yescharacteristic
564C2×#95C22×C13911yescharacteristic
565C2×#95C22×C13911yescharacteristic
566C2×#95C22×C13911yescharacteristic
567C2×#95C22×C13911yescharacteristic
568C2×#95C22×C13911yescharacteristic
569C2×#95C22×C13911yescharacteristic
570C2×#95C22×C13911yescharacteristic
571C2×#95C22×C13911yescharacteristic
572C2×#95C22×C13911yescharacteristic
573C2×#95C22×C13911yescharacteristic
574C25C23×C13911yescharacteristic
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—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4D4×C13914yes—
624C2×C4⋊C4D4×C13914yes—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—22no—
641C2×C22⋊C4—41no—
642C2×C22⋊C4—41no—
643C2×C22⋊C4—41no—
644C2×C22⋊C4—41no—
645C2×C22⋊C4Q8×C13914yes—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—22no—
651C2×C42—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95D4×C13914yes—
665#95D4×C13914yes—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C2×Q8×C13912yes—
681C24C24×C13911yescharacteristic
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—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4C2×D4×C13912yes—
763C22×C4C2×D4×C13912yes—
764C22×C4C2×D4×C13912yes—
765C22×C4C2×D4×C13912yes—
766C22×C4C2×D4×C13912yes—
767C22×C4C2×D4×C13912yes—
768C22×C4C2×D4×C13912yes—
769C22×C4C2×D4×C13912yes—
770C22×C4C2×D4×C13912yes—
771C22×C4C2×D4×C13912yes—
772C22×C4C2×D4×C13912yes—
773C22×C4C2×D4×C13912yes—
774C22×C4C2×Q8×C13912yes—
775C22×C4C2×Q8×C13912yes—
776C22×C4#41×C13912yes—
777C22×C4#41×C13912yes—
778C22×C4#41×C13912yes—
779C22×C4#41×C13912yes—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—44no—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4—44no—
786C4⋊C4—44no—
787C4⋊C4—44no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C22⋊C4—28no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—44no—
798C22⋊C4—44no—
799C42—28no—
800C42—44no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—41no—
809C23—41no—
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—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23C22×D4×C13911yescharacteristic
837C23C22×D4×C13911yescharacteristic
838C23C22×D4×C13911yescharacteristic
839C23C22×D4×C13911yescharacteristic
840C23C22×Q8×C13911yescharacteristic
841C23C2×#41×C13911yescharacteristic
842C23C2×#41×C13911yescharacteristic
843C23C2×#41×C13911yescharacteristic
844C23C2×#41×C13911yescharacteristic
845C23H(5,𝔽2)×C13911yescharacteristic
846C23H(5,𝔽2)×C13911yescharacteristic
847C232−1+4×C13911yescharacteristic
848C232−1+4×C13911yescharacteristic
849C232−1+4×C13911yescharacteristic
850C232−1+4×C13911yescharacteristic
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—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×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×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4#121×C13914yes—
946C2×C4C22⋊Q8×C13914yes—
947C2×C4#123×C13914yes—
948C2×C4#127×C13914yes—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22C2×#121×C13911yescharacteristic
965C22C2×C22⋊Q8×C13911yescharacteristic
966C22C2×#123×C13911yescharacteristic
967C22#525×C13911yescharacteristic
968C22C2×#127×C13911yescharacteristic
969C22#533×C13911yescharacteristic
970C22#535×C13911yescharacteristic
971C22#536×C13911yescharacteristic
972C22#536×C13911yescharacteristic
973C22#536×C13911yescharacteristic
974C22#539×C13911yescharacteristic
975C22#539×C13911yescharacteristic
976C22#541×C13911yescharacteristic
977C22#542×C13911yescharacteristic
978C22#544×C13911yescharacteristic
979C22D42×C13911yescharacteristic
980C22D42×C13911yescharacteristic
981C22#547×C13911yescharacteristic
982C22#547×C13911yescharacteristic
983C22#547×C13911yescharacteristic
984C22#547×C13911yescharacteristic
985C22#547×C13911yescharacteristic
986C22#547×C13911yescharacteristic
987C22#548×C13911yescharacteristic
988C22D4×Q8×C13911yescharacteristic
989C22D4×Q8×C13911yescharacteristic
990C22D4×Q8×C13911yescharacteristic
991C22#550×C13911yescharacteristic
992C22#550×C13911yescharacteristic
993C22#552×C13911yescharacteristic
994C22#552×C13911yescharacteristic
995C22#553×C13911yescharacteristic
996C22#554×C13911yescharacteristic
997C22#563×C13911yescharacteristic
998C22#563×C13911yescharacteristic
999C4—24no—
1000C4—24no—
1001C4—24no—
1002C4—24no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—81no—
1010C4—81no—
1011C4—81no—
1012C4—81no—
1013C2—82no—
1014C2#2413×C13911yescharacteristic
1015C2#2423×C13911yescharacteristic
1016C2#2429×C13911yescharacteristic
1017C2#2441×C13911yescharacteristic
1018C2#2443×C13911yescharacteristic
1019C2#2449×C13911yescharacteristic
1020C2#2501×C13911yescharacteristic
1021C2#2541×C13911yescharacteristic
1022C2#2542×C13911yescharacteristic
1023C2#2674×C13911yescharacteristic
1024C2#2677×C13911yescharacteristic
1025C2#2718×C13911yescharacteristic
1026C2#2720×C13911yescharacteristic
1027C2#2721×C13911yescharacteristic
1028C2#2721×C13911yescharacteristic
subgroupG/H
center, socleC24×C139C24
commutator, Frattini, cosocleC24C24×C139
prime radicalC25×C139C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#398×C139C2semidirect
5. C2×#389×C139C2semidirect
7. C2×#387×C139C2semidirect
8. C2×#384×C139C2semidirect
9. #1445×C139C2semidirect
10. #1444×C139C2semidirect
11. #1444×C139C2semidirect
15. #1436×C139C2semidirect
514. #15765C139direct (N × H)
515. C139#15765direct (N × H)
518. C2×#398C2×C139semidirect
520. C2×#389C2×C139semidirect
522. C2×#387C2×C139semidirect
523. C2×#384C2×C139semidirect
524. #1445C2×C139semidirect
525. #1444C2×C139semidirect
526. #1444C2×C139semidirect
530. #1436C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1392
C2×#398×C1392
C2×#396×C1392
C2×#389×C1392
C2×#388×C1392
C2×#387×C1392
C2×#384×C1392
#1445×C1392
#1444×C1392
#1439×C1392
#1437×C1392
#1436×C1392
#15765139