Finite Group Databasebeta

← C2×#2418×C139 #48029244

Subgroups — C2×#2418×C139 #48029244

Order 35584.

5054 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C139C211yesmaximal, characteristic, complemented
2C22×#120×C139C211yesmaximal, characteristic
3C22×C4×D4×C139C211yesmaximal, characteristic, complemented
4C23×C22⋊C4×C139C211yesmaximal, characteristic, complemented
5#2418×C139C2116yesmaximal, direct product factor
6C2×#399×C139C211yesmaximal, characteristic, complemented
7C2×#397×C139C211yesmaximal, characteristic, complemented
8C2×#394×C139C211yesmaximal, characteristic, complemented
9C2×#394×C139C211yesmaximal, characteristic, complemented
10C2×#388×C139C211yesmaximal, characteristic, complemented
11C2×#388×C139C211yesmaximal, characteristic, complemented
12C2×#386×C139C211yesmaximal, characteristic, complemented
13C2×#386×C139C211yesmaximal, characteristic, complemented
14C2×#385×C139C211yesmaximal, characteristic, complemented
15C2×#380×C139C211yesmaximal, characteristic, complemented
16C2×#379×C139C211yesmaximal, characteristic, complemented
17C26×C139C2211yescharacteristic
18C23×D4×C139C2211yescharacteristic
19C23×D4×C139C2211yescharacteristic
20C23×D4×C139C2211yescharacteristic
21C24×C4×C139C2211yescharacteristic
22C24×C4×C139C2211yescharacteristic
23C24×C4×C139C2211yescharacteristic, complemented
24C2×#123×C139—28no—
25C2×#123×C139C2218yescomplemented
26C2×#120×C139—28no—
27C2×#120×C139C2218yes—
28C2×C4×D4×C139—28no—
29C2×C4×D4×C139C2218yescomplemented
30C22×C4⋊C4×C139C2211yescharacteristic, complemented
31C22×C4⋊C4×C139C2211yescharacteristic, complemented
32C22×C4⋊C4×C139C2211yescharacteristic, complemented
33C22×C4⋊C4×C139C2211yescharacteristic, complemented
34C22×C4⋊C4×C139C2211yescharacteristic, complemented
35C22×C22⋊C4×C139—28no—
36C22×C22⋊C4×C139C2211yescharacteristic
37C22×C22⋊C4×C139C2211yescharacteristic
38C22×C22⋊C4×C139C2211yescharacteristic
39C22×C22⋊C4×C139C2211yescharacteristic
40C22×C22⋊C4×C139C2211yescharacteristic
41C22×C22⋊C4×C139C2211yescharacteristic
42C22×C22⋊C4×C139C2211yescharacteristic
43C22×C22⋊C4×C139C2211yescharacteristic
44C22×C22⋊C4×C139C2211yescharacteristic
45C22×C22⋊C4×C139C2211yescharacteristic
46C22×C22⋊C4×C139C2211yescharacteristic
47C22×C22⋊C4×C139C2211yescharacteristic
48C22×C22⋊C4×C139C2211yescharacteristic
49C22×C22⋊C4×C139C2218yescomplemented
50C22×C22⋊C4×C139C2211yescharacteristic, complemented
51C22×C22⋊C4×C139C2211yescharacteristic, complemented
52C22×C22⋊C4×C139C2211yescharacteristic, complemented
53C22×C42×C139C2211yescharacteristic, complemented
54#399×C139C2218yescomplemented
55#397×C139C2218yescomplemented
56#394×C139C2218yescomplemented
57#394×C139C2218yescomplemented
58#388×C139C2218yescomplemented
59#388×C139C2218yescomplemented
60#386×C139C2218yescomplemented
61#386×C139C2218yescomplemented
62#385×C139C2218yescomplemented
63#380×C139C2218yescomplemented
64#379×C139C2218yescomplemented
65C2×#95×C139C2211yescharacteristic, complemented
66C2×#95×C139C2211yescharacteristic, complemented
67C2×#95×C139C2211yescharacteristic, complemented
68C2×#95×C139C2211yescharacteristic, complemented
69C2×#95×C139C2211yescharacteristic, complemented
70C2×#95×C139C2211yescharacteristic, complemented
71C25×C139—24no—
72C25×C139—24no—
73C25×C139—24no—
74C25×C139—24no—
75C25×C139—24no—
76C25×C139—42no—
77C25×C139—42no—
78C25×C139C2311yescharacteristic
79C25×C139C2311yescharacteristic
80C25×C139C2311yescharacteristic
81C25×C139C2314yes—
82C25×C139C2311yescharacteristic
83C22×D4×C139—24no—
84C22×D4×C139—24no—
85C22×D4×C139—24no—
86C22×D4×C139—24no—
87C22×D4×C139—24no—
88C22×D4×C139—24no—
89C22×D4×C139—42no—
90C22×D4×C139—42no—
91C22×D4×C139D418yes—
92C22×D4×C139C2314yes—
93C22×D4×C139C2314yes—
94C22×D4×C139C2314yes—
95C23×C4×C139—24no—
96C23×C4×C139—24no—
97C23×C4×C139—24no—
98C23×C4×C139—24no—
99C23×C4×C139—24no—
100C23×C4×C139—24no—
101C23×C4×C139—42no—
102C23×C4×C139—42no—
103C23×C4×C139—42no—
104C23×C4×C139C2311yescharacteristic
105C23×C4×C139C2311yescharacteristic
106C23×C4×C139C2311yescharacteristic
107C23×C4×C139C2311yescharacteristic
108C23×C4×C139C2311yescharacteristic
109C23×C4×C139C2311yescharacteristic
110C23×C4×C139C2311yescharacteristic
111C23×C4×C139C2311yescharacteristic
112C23×C4×C139C2314yes—
113C23×C4×C139C2314yes—
114C23×C4×C139C2311yescharacteristic
115C23×C4×C139C2311yescharacteristic
116C23×C4×C139C2311yescharacteristic
117C23×C4×C139C2314yescomplemented
118#123×C139—232no—
119#120×C139—232no—
120C4×D4×C139—232no—
121C2×C4⋊C4×C139—24no—
122C2×C4⋊C4×C139—24no—
123C2×C4⋊C4×C139—24no—
124C2×C4⋊C4×C139—42no—
125C2×C4⋊C4×C139—42no—
126C2×C4⋊C4×C139C2314yescomplemented
127C2×C4⋊C4×C139C2314yescomplemented
128C2×C4⋊C4×C139C2314yescomplemented
129C2×C4⋊C4×C139C2314yescomplemented
130C2×C4⋊C4×C139C2314yescomplemented
131C2×C22⋊C4×C139—24no—
132C2×C22⋊C4×C139—24no—
133C2×C22⋊C4×C139—24no—
134C2×C22⋊C4×C139—24no—
135C2×C22⋊C4×C139—24no—
136C2×C22⋊C4×C139—24no—
137C2×C22⋊C4×C139—24no—
138C2×C22⋊C4×C139—24no—
139C2×C22⋊C4×C139—24no—
140C2×C22⋊C4×C139—24no—
141C2×C22⋊C4×C139—24no—
142C2×C22⋊C4×C139—24no—
143C2×C22⋊C4×C139—232no—
144C2×C22⋊C4×C139—42no—
145C2×C22⋊C4×C139—42no—
146C2×C22⋊C4×C139—42no—
147C2×C22⋊C4×C139D418yescomplemented
148C2×C22⋊C4×C139C2314yes—
149C2×C22⋊C4×C139C2314yes—
150C2×C22⋊C4×C139C2314yes—
151C2×C22⋊C4×C139C2314yes—
152C2×C22⋊C4×C139C2314yes—
153C2×C22⋊C4×C139C2314yes—
154C2×C22⋊C4×C139C2314yes—
155C2×C22⋊C4×C139C2314yes—
156C2×C22⋊C4×C139C2314yes—
157C2×C22⋊C4×C139C2314yes—
158C2×C22⋊C4×C139C2314yes—
159C2×C22⋊C4×C139C2314yes—
160C2×C22⋊C4×C139C2314yes—
161C2×C22⋊C4×C139C2314yescomplemented
162C2×C22⋊C4×C139C2314yescomplemented
163C2×C22⋊C4×C139C2314yescomplemented
164C2×C42×C139—24no—
165C2×C42×C139C2314yescomplemented
166#95×C139C2314yescomplemented
167#95×C139C2314yescomplemented
168#95×C139C2314yescomplemented
169#95×C139C2314yescomplemented
170#95×C139C2314yescomplemented
171#95×C139C2314yescomplemented
172C24×C139—22no—
173C24×C139—22no—
174C24×C139—22no—
175C24×C139—22no—
176C24×C139—232no—
177C24×C139—28no—
178C24×C139—22no—
179C24×C139—22no—
180C24×C139—22no—
181C24×C139—22no—
182C24×C139—22no—
183C24×C139—22no—
184C24×C139—22no—
185C24×C139—28no—
186C24×C139—28no—
187C24×C139—22no—
188C24×C139—22no—
189C24×C139—22no—
190C24×C139—22no—
191C24×C139—22no—
192C24×C139—22no—
193C24×C139—22no—
194C24×C139—22no—
195C24×C139—22no—
196C24×C139—22no—
197C24×C139—22no—
198C24×C139—28no—
199C24×C139—28no—
200C24×C139—44no—
201C24×C139—44no—
202C24×C139—416no—
203C24×C139—416no—
204C24×C139—416no—
205C24×C139—416no—
206C24×C139—416no—
207C24×C139—416no—
208C24×C139C2×D414yes—
209C24×C139C2×D414yes—
210C24×C139C2×D414yes—
211C24×C139#4114yes—
212C24×C139#4114yes—
213C24×C139#4114yes—
214C24×C139C2412yes—
215C24×C139C2412yes—
216C24×C139C2412yes—
217C24×C139C2412yes—
218C24×C139C2411yescharacteristic
219C2×D4×C139—232no—
220C2×D4×C139—28no—
221C2×D4×C139—28no—
222C2×D4×C139—28no—
223C2×D4×C139—28no—
224C2×D4×C139—28no—
225C2×D4×C139—28no—
226C2×D4×C139—44no—
227C2×D4×C139—44no—
228C2×D4×C139—416no—
229C2×D4×C139—416no—
230C2×D4×C139C2×D4116yes—
231C22×C4×C139—22no—
232C22×C4×C139—22no—
233C22×C4×C139—22no—
234C22×C4×C139—22no—
235C22×C4×C139—22no—
236C22×C4×C139—22no—
237C22×C4×C139—22no—
238C22×C4×C139—22no—
239C22×C4×C139—22no—
240C22×C4×C139—22no—
241C22×C4×C139—22no—
242C22×C4×C139—22no—
243C22×C4×C139—22no—
244C22×C4×C139—22no—
245C22×C4×C139—22no—
246C22×C4×C139—22no—
247C22×C4×C139—28no—
248C22×C4×C139—28no—
249C22×C4×C139—22no—
250C22×C4×C139—22no—
251C22×C4×C139—22no—
252C22×C4×C139—22no—
253C22×C4×C139—28no—
254C22×C4×C139—22no—
255C22×C4×C139—22no—
256C22×C4×C139—22no—
257C22×C4×C139—22no—
258C22×C4×C139—22no—
259C22×C4×C139—22no—
260C22×C4×C139—22no—
261C22×C4×C139—22no—
262C22×C4×C139—22no—
263C22×C4×C139—22no—
264C22×C4×C139—28no—
265C22×C4×C139—28no—
266C22×C4×C139—28no—
267C22×C4×C139—44no—
268C22×C4×C139—44no—
269C22×C4×C139—44no—
270C22×C4×C139—416no—
271C22×C4×C139—416no—
272C22×C4×C139—416no—
273C22×C4×C139C2×D414yes—
274C22×C4×C139C2×D414yes—
275C22×C4×C139C2×D414yes—
276C22×C4×C139C2412yes—
277C22×C4×C139C2412yes—
278C22×C4×C139C2412yes—
279C22×C4×C139C2412yes—
280C22×C4×C139C2412yes—
281C22×C4×C139C2412yes—
282C22×C4×C139C2412yes—
283C22×C4×C139C2412yes—
284C22×C4×C139C2412yes—
285C22×C4×C139C2412yes—
286C22×C4×C139C2412yes—
287C4⋊C4×C139—28no—
288C4⋊C4×C139—28no—
289C4⋊C4×C139—28no—
290C4⋊C4×C139—44no—
291C4⋊C4×C139—44no—
292C22⋊C4×C139—28no—
293C22⋊C4×C139—28no—
294C22⋊C4×C139—28no—
295C22⋊C4×C139—28no—
296C22⋊C4×C139—28no—
297C22⋊C4×C139—28no—
298C22⋊C4×C139—28no—
299C22⋊C4×C139—28no—
300C22⋊C4×C139—28no—
301C22⋊C4×C139—28no—
302C22⋊C4×C139—28no—
303C22⋊C4×C139—28no—
304C22⋊C4×C139—44no—
305C22⋊C4×C139—44no—
306C22⋊C4×C139—44no—
307C22⋊C4×C139C2×D4116yescomplemented
308C42×C139—28no—
309C23×C139—28no—
310C23×C139—28no—
311C23×C139—28no—
312C23×C139—28no—
313C23×C139—28no—
314C23×C139—28no—
315C23×C139—22no—
316C23×C139—22no—
317C23×C139—22no—
318C23×C139—22no—
319C23×C139—232no—
320C23×C139—28no—
321C23×C139—28no—
322C23×C139—28no—
323C23×C139—28no—
324C23×C139—28no—
325C23×C139—28no—
326C23×C139—28no—
327C23×C139—28no—
328C23×C139—28no—
329C23×C139—22no—
330C23×C139—22no—
331C23×C139—22no—
332C23×C139—22no—
333C23×C139—22no—
334C23×C139—22no—
335C23×C139—22no—
336C23×C139—22no—
337C23×C139—22no—
338C23×C139—22no—
339C23×C139—22no—
340C23×C139—22no—
341C23×C139—22no—
342C23×C139—22no—
343C23×C139—22no—
344C23×C139—22no—
345C23×C139—22no—
346C23×C139—22no—
347C23×C139—416no—
348C23×C139—416no—
349C23×C139—416no—
350C23×C139—416no—
351C23×C139—4128no—
352C23×C139—416no—
353C23×C139—44no—
354C23×C139—44no—
355C23×C139—416no—
356C23×C139—44no—
357C23×C139—44no—
358C23×C139—44no—
359C23×C139—44no—
360C23×C139—44no—
361C23×C139—44no—
362C23×C139—44no—
363C23×C139—44no—
364C23×C139—44no—
365C23×C139—44no—
366C23×C139#123116yescomplemented
367C23×C139C22×D414yes—
368C23×C139C22×D414yes—
369C23×C139C22×D414yes—
370C23×C139C22×D412yes—
371C23×C139C22×D412yes—
372C23×C139C2×#4114yes—
373C23×C139C2×#4114yes—
374C23×C139C2×#4114yes—
375C23×C139C2×#4112yes—
376C23×C139C2×#4112yes—
377C23×C139C2×#4112yes—
378C23×C139H(5,𝔽2)12yes—
379C23×C139H(5,𝔽2)12yes—
380C23×C139C2511yescharacteristic
381D4×C139—232no—
382D4×C139—416no—
383D4×C139—416no—
384C2×C4×C139—28no—
385C2×C4×C139—28no—
386C2×C4×C139—28no—
387C2×C4×C139—22no—
388C2×C4×C139—22no—
389C2×C4×C139—22no—
390C2×C4×C139—22no—
391C2×C4×C139—22no—
392C2×C4×C139—22no—
393C2×C4×C139—22no—
394C2×C4×C139—22no—
395C2×C4×C139—22no—
396C2×C4×C139—22no—
397C2×C4×C139—22no—
398C2×C4×C139—22no—
399C2×C4×C139—22no—
400C2×C4×C139—22no—
401C2×C4×C139—22no—
402C2×C4×C139—22no—
403C2×C4×C139—22no—
404C2×C4×C139—22no—
405C2×C4×C139—22no—
406C2×C4×C139—22no—
407C2×C4×C139—22no—
408C2×C4×C139—22no—
409C2×C4×C139—22no—
410C2×C4×C139—22no—
411C2×C4×C139—22no—
412C2×C4×C139—22no—
413C2×C4×C139—22no—
414C2×C4×C139—22no—
415C2×C4×C139—22no—
416C2×C4×C139—22no—
417C2×C4×C139—416no—
418C2×C4×C139—416no—
419C2×C4×C139—416no—
420C2×C4×C139—44no—
421C2×C4×C139—44no—
422C2×C4×C139—44no—
423C2×C4×C139—44no—
424C2×C4×C139—44no—
425C2×C4×C139—44no—
426C2×C4×C139—44no—
427C2×C4×C139—44no—
428C2×C4×C139C22×D414yes—
429C2×C4×C139C22×D414yes—
430C2×C4×C139C22×D414yes—
431C22×C139—24no—
432C22×C139—232no—
433C22×C139—24no—
434C22×C139—24no—
435C22×C139—24no—
436C22×C139—24no—
437C22×C139—24no—
438C22×C139—24no—
439C22×C139—24no—
440C22×C139—24no—
441C22×C139—24no—
442C22×C139—24no—
443C22×C139—24no—
444C22×C139—24no—
445C22×C139—24no—
446C22×C139—24no—
447C22×C139—464no—
448C22×C139—42no—
449C22×C139—42no—
450C22×C139—42no—
451C22×C139—416no—
452C22×C139—416no—
453C22×C139—416no—
454C22×C139—42no—
455C22×C139—42no—
456C22×C139—42no—
457C22×C139—42no—
458C22×C139—42no—
459C22×C139—42no—
460C22×C139—42no—
461C22×C139—42no—
462C22×C139—42no—
463C22×C139C2×#12314yes—
464C22×C139C2×#12318yescomplemented
465C22×C139#52514yes—
466C22×C139#53814yes—
467C22×C139D4214yes—
468C22×C139#54614yes—
469C22×C139#54614yes—
470C22×C139#55114yes—
471C22×C139C23×D411yescharacteristic
472C22×C139C23×D411yescharacteristic
473C22×C139C22×#4111yescharacteristic
474C22×C139C22×#4111yescharacteristic
475C22×C139C22×#4111yescharacteristic
476C22×C139C2×H(5,𝔽2)11yescharacteristic
477C22×C139C2×H(5,𝔽2)11yescharacteristic
478C4×C139—24no—
479C4×C139—24no—
480C4×C139—24no—
481C4×C139—42no—
482C4×C139—42no—
483C4×C139—42no—
484C4×C139—42no—
485C4×C139—42no—
486C4×C139—42no—
487C4×C139—42no—
488C4×C139—42no—
489C2×C139—28no—
490C2×C139—44no—
491C2×C139—44no—
492C2×C139—44no—
493C2×C139#241818yesdirect product factor
494C2×C139C22×#12311yescharacteristic
495C2×C139C2×#52511yescharacteristic
496C2×C139C2×#53811yescharacteristic
497C2×C139C2×D4211yescharacteristic
498C2×C139C2×#54611yescharacteristic
499C2×C139C2×#54611yescharacteristic
500C2×C139C2×#55111yescharacteristic
501C2×#2418C13911yesmaximal, characteristic, direct product factor, Sylow
502C139C2×#241811yescharacteristic, direct product factor, Sylow
503C22×#123C2×C13911yescharacteristic, complemented
504C22×#120C2×C13911yescharacteristic
505C22×C4×D4C2×C13911yescharacteristic, complemented
506C23×C22⋊C4C2×C13911yescharacteristic, complemented
507#2418C2×C139116yesdirect product factor
508C2×#399C2×C13911yescharacteristic, complemented
509C2×#397C2×C13911yescharacteristic, complemented
510C2×#394C2×C13911yescharacteristic, complemented
511C2×#394C2×C13911yescharacteristic, complemented
512C2×#388C2×C13911yescharacteristic, complemented
513C2×#388C2×C13911yescharacteristic, complemented
514C2×#386C2×C13911yescharacteristic, complemented
515C2×#386C2×C13911yescharacteristic, complemented
516C2×#385C2×C13911yescharacteristic, complemented
517C2×#380C2×C13911yescharacteristic, complemented
518C2×#379C2×C13911yescharacteristic, complemented
519C26C22×C13911yescharacteristic
520C23×D4C22×C13911yescharacteristic
521C23×D4C22×C13911yescharacteristic
522C23×D4C22×C13911yescharacteristic
523C24×C4C22×C13911yescharacteristic
524C24×C4C22×C13911yescharacteristic
525C24×C4C22×C13911yescharacteristic, complemented
526C2×#123—28no—
527C2×#123C22×C13918yescomplemented
528C2×#120—28no—
529C2×#120C22×C13918yes—
530C2×C4×D4—28no—
531C2×C4×D4C22×C13918yescomplemented
532C22×C4⋊C4C22×C13911yescharacteristic, complemented
533C22×C4⋊C4C22×C13911yescharacteristic, complemented
534C22×C4⋊C4C22×C13911yescharacteristic, complemented
535C22×C4⋊C4C22×C13911yescharacteristic, complemented
536C22×C4⋊C4C22×C13911yescharacteristic, complemented
537C22×C22⋊C4—28no—
538C22×C22⋊C4C22×C13911yescharacteristic
539C22×C22⋊C4C22×C13911yescharacteristic
540C22×C22⋊C4C22×C13911yescharacteristic
541C22×C22⋊C4C22×C13911yescharacteristic
542C22×C22⋊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×C22⋊C4C22×C13911yescharacteristic
551C22×C22⋊C4C22×C13918yescomplemented
552C22×C22⋊C4C22×C13911yescharacteristic, complemented
553C22×C22⋊C4C22×C13911yescharacteristic, complemented
554C22×C22⋊C4C22×C13911yescharacteristic, complemented
555C22×C42C22×C13911yescharacteristic, complemented
556#399C22×C13918yescomplemented
557#397C22×C13918yescomplemented
558#394C22×C13918yescomplemented
559#394C22×C13918yescomplemented
560#388C22×C13918yescomplemented
561#388C22×C13918yescomplemented
562#386C22×C13918yescomplemented
563#386C22×C13918yescomplemented
564#385C22×C13918yescomplemented
565#380C22×C13918yescomplemented
566#379C22×C13918yescomplemented
567C2×#95C22×C13911yescharacteristic, complemented
568C2×#95C22×C13911yescharacteristic, complemented
569C2×#95C22×C13911yescharacteristic, complemented
570C2×#95C22×C13911yescharacteristic, complemented
571C2×#95C22×C13911yescharacteristic, complemented
572C2×#95C22×C13911yescharacteristic, complemented
573C25—24no—
574C25—24no—
575C25—24no—
576C25—24no—
577C25—24no—
578C25—42no—
579C25—42no—
580C25C23×C13911yescharacteristic
581C25C23×C13911yescharacteristic
582C25C23×C13911yescharacteristic
583C25C23×C13914yes—
584C25C23×C13911yescharacteristic
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—24no—
588C22×D4—24no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—42no—
593C22×D4D4×C13918yes—
594C22×D4C23×C13914yes—
595C22×D4C23×C13914yes—
596C22×D4C23×C13914yes—
597C23×C4—24no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—24no—
601C23×C4—24no—
602C23×C4—24no—
603C23×C4—42no—
604C23×C4—42no—
605C23×C4—42no—
606C23×C4C23×C13911yescharacteristic
607C23×C4C23×C13911yescharacteristic
608C23×C4C23×C13911yescharacteristic
609C23×C4C23×C13911yescharacteristic
610C23×C4C23×C13911yescharacteristic
611C23×C4C23×C13911yescharacteristic
612C23×C4C23×C13911yescharacteristic
613C23×C4C23×C13911yescharacteristic
614C23×C4C23×C13914yes—
615C23×C4C23×C13914yes—
616C23×C4C23×C13911yescharacteristic
617C23×C4C23×C13911yescharacteristic
618C23×C4C23×C13911yescharacteristic
619C23×C4C23×C13914yescomplemented
620#123—232no—
621#120—232no—
622C4×D4—232no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—24no—
626C2×C4⋊C4—42no—
627C2×C4⋊C4—42no—
628C2×C4⋊C4C23×C13914yescomplemented
629C2×C4⋊C4C23×C13914yescomplemented
630C2×C4⋊C4C23×C13914yescomplemented
631C2×C4⋊C4C23×C13914yescomplemented
632C2×C4⋊C4C23×C13914yescomplemented
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—232no—
646C2×C22⋊C4—42no—
647C2×C22⋊C4—42no—
648C2×C22⋊C4—42no—
649C2×C22⋊C4D4×C13918yescomplemented
650C2×C22⋊C4C23×C13914yes—
651C2×C22⋊C4C23×C13914yes—
652C2×C22⋊C4C23×C13914yes—
653C2×C22⋊C4C23×C13914yes—
654C2×C22⋊C4C23×C13914yes—
655C2×C22⋊C4C23×C13914yes—
656C2×C22⋊C4C23×C13914yes—
657C2×C22⋊C4C23×C13914yes—
658C2×C22⋊C4C23×C13914yes—
659C2×C22⋊C4C23×C13914yes—
660C2×C22⋊C4C23×C13914yes—
661C2×C22⋊C4C23×C13914yes—
662C2×C22⋊C4C23×C13914yes—
663C2×C22⋊C4C23×C13914yescomplemented
664C2×C22⋊C4C23×C13914yescomplemented
665C2×C22⋊C4C23×C13914yescomplemented
666C2×C42—24no—
667C2×C42C23×C13914yescomplemented
668#95C23×C13914yescomplemented
669#95C23×C13914yescomplemented
670#95C23×C13914yescomplemented
671#95C23×C13914yescomplemented
672#95C23×C13914yescomplemented
673#95C23×C13914yescomplemented
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—232no—
679C24—28no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—28no—
688C24—28no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—28no—
701C24—28no—
702C24—44no—
703C24—44no—
704C24—416no—
705C24—416no—
706C24—416no—
707C24—416no—
708C24—416no—
709C24—416no—
710C24C2×D4×C13914yes—
711C24C2×D4×C13914yes—
712C24C2×D4×C13914yes—
713C24#41×C13914yes—
714C24#41×C13914yes—
715C24#41×C13914yes—
716C24C24×C13912yes—
717C24C24×C13912yes—
718C24C24×C13912yes—
719C24C24×C13912yes—
720C24C24×C13911yescharacteristic
721C2×D4—232no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—416no—
731C2×D4—416no—
732C2×D4C2×D4×C139116yes—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—28no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—28no—
767C22×C4—28no—
768C22×C4—28no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—416no—
773C22×C4—416no—
774C22×C4—416no—
775C22×C4C2×D4×C13914yes—
776C22×C4C2×D4×C13914yes—
777C22×C4C2×D4×C13914yes—
778C22×C4C24×C13912yes—
779C22×C4C24×C13912yes—
780C22×C4C24×C13912yes—
781C22×C4C24×C13912yes—
782C22×C4C24×C13912yes—
783C22×C4C24×C13912yes—
784C22×C4C24×C13912yes—
785C22×C4C24×C13912yes—
786C22×C4C24×C13912yes—
787C22×C4C24×C13912yes—
788C22×C4C24×C13912yes—
789C4⋊C4—28no—
790C4⋊C4—28no—
791C4⋊C4—28no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C22⋊C4C2×D4×C139116yescomplemented
810C42—28no—
811C23—28no—
812C23—28no—
813C23—28no—
814C23—28no—
815C23—28no—
816C23—28no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—232no—
822C23—28no—
823C23—28no—
824C23—28no—
825C23—28no—
826C23—28no—
827C23—28no—
828C23—28no—
829C23—28no—
830C23—28no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—416no—
850C23—416no—
851C23—416no—
852C23—416no—
853C23—4128no—
854C23—416no—
855C23—44no—
856C23—44no—
857C23—416no—
858C23—44no—
859C23—44no—
860C23—44no—
861C23—44no—
862C23—44no—
863C23—44no—
864C23—44no—
865C23—44no—
866C23—44no—
867C23—44no—
868C23#123×C139116yescomplemented
869C23C22×D4×C13914yes—
870C23C22×D4×C13914yes—
871C23C22×D4×C13914yes—
872C23C22×D4×C13912yes—
873C23C22×D4×C13912yes—
874C23C2×#41×C13914yes—
875C23C2×#41×C13914yes—
876C23C2×#41×C13914yes—
877C23C2×#41×C13912yes—
878C23C2×#41×C13912yes—
879C23C2×#41×C13912yes—
880C23H(5,𝔽2)×C13912yes—
881C23H(5,𝔽2)×C13912yes—
882C23C25×C13911yescharacteristic
883D4—232no—
884D4—416no—
885D4—416no—
886C2×C4—28no—
887C2×C4—28no—
888C2×C4—28no—
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—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—416no—
920C2×C4—416no—
921C2×C4—416no—
922C2×C4—44no—
923C2×C4—44no—
924C2×C4—44no—
925C2×C4—44no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4C22×D4×C13914yes—
931C2×C4C22×D4×C13914yes—
932C2×C4C22×D4×C13914yes—
933C22—24no—
934C22—232no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—24no—
946C22—24no—
947C22—24no—
948C22—24no—
949C22—464no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—416no—
954C22—416no—
955C22—416no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22C2×#123×C13914yes—
966C22C2×#123×C13918yescomplemented
967C22#525×C13914yes—
968C22#538×C13914yes—
969C22D42×C13914yes—
970C22#546×C13914yes—
971C22#546×C13914yes—
972C22#551×C13914yes—
973C22C23×D4×C13911yescharacteristic
974C22C23×D4×C13911yescharacteristic
975C22C22×#41×C13911yescharacteristic
976C22C22×#41×C13911yescharacteristic
977C22C22×#41×C13911yescharacteristic
978C22C2×H(5,𝔽2)×C13911yescharacteristic
979C22C2×H(5,𝔽2)×C13911yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C2—28no—
992C2—44no—
993C2—44no—
994C2—44no—
995C2#2418×C13918yesdirect product factor
996C2C22×#123×C13911yescharacteristic
997C2C2×#525×C13911yescharacteristic
998C2C2×#538×C13911yescharacteristic
999C2C2×D42×C13911yescharacteristic
1000C2C2×#546×C13911yescharacteristic
1001C2C2×#546×C13911yescharacteristic
1002C2C2×#551×C13911yescharacteristic
subgroupG/H
center, socleC24×C139C24
commutator, Frattini, cosocleC23C25×C139
prime radicalC22×#120×C139C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#123×C139C2semidirect
3. C22×C4×D4×C139C2semidirect
4. C23×C22⋊C4×C139C2semidirect
5. #2418×C139C2direct (N × H)
6. C2×#399×C139C2semidirect
7. C2×#397×C139C2semidirect
8. C2×#394×C139C2semidirect
9. C2×#394×C139C2semidirect
10. C2×#388×C139C2semidirect
11. C2×#388×C139C2semidirect
12. C2×#386×C139C2semidirect
13. C2×#386×C139C2semidirect
14. C2×#385×C139C2semidirect
15. C2×#380×C139C2semidirect
16. C2×#379×C139C2semidirect
23. C24×C4×C139C22semidirect
25. C2×#123×C139C22semidirect
29. C2×C4×D4×C139C22semidirect
30. C22×C4⋊C4×C139C22semidirect
31. C22×C4⋊C4×C139C22semidirect
32. C22×C4⋊C4×C139C22semidirect
33. C22×C4⋊C4×C139C22semidirect
34. C22×C4⋊C4×C139C22semidirect
49. C22×C22⋊C4×C139C22semidirect
50. C22×C22⋊C4×C139C22semidirect
51. C22×C22⋊C4×C139C22semidirect
52. C22×C22⋊C4×C139C22semidirect
53. C22×C42×C139C22semidirect
54. #399×C139C22semidirect
55. #397×C139C22semidirect
56. #394×C139C22semidirect
57. #394×C139C22semidirect
58. #388×C139C22semidirect
59. #388×C139C22semidirect
60. #386×C139C22semidirect
61. #386×C139C22semidirect
62. #385×C139C22semidirect
63. #380×C139C22semidirect
64. #379×C139C22semidirect
65. C2×#95×C139C22semidirect
66. C2×#95×C139C22semidirect
67. C2×#95×C139C22semidirect
68. C2×#95×C139C22semidirect
69. C2×#95×C139C22semidirect
70. C2×#95×C139C22semidirect
117. C23×C4×C139C23semidirect
126. C2×C4⋊C4×C139C23semidirect
127. C2×C4⋊C4×C139C23semidirect
128. C2×C4⋊C4×C139C23semidirect
129. C2×C4⋊C4×C139C23semidirect
130. C2×C4⋊C4×C139C23semidirect
147. C2×C22⋊C4×C139D4semidirect
161. C2×C22⋊C4×C139C23semidirect
162. C2×C22⋊C4×C139C23semidirect
163. C2×C22⋊C4×C139C23semidirect
165. C2×C42×C139C23semidirect
166. #95×C139C23semidirect
167. #95×C139C23semidirect
168. #95×C139C23semidirect
169. #95×C139C23semidirect
170. #95×C139C23semidirect
171. #95×C139C23semidirect
307. C22⋊C4×C139C2×D4semidirect
366. C23×C139#123semidirect
464. C22×C139C2×#123semidirect
493. C2×C139#2418direct (N × H)
501. C2×#2418C139direct (N × H)
502. C139C2×#2418direct (N × H)
503. C22×#123C2×C139semidirect
505. C22×C4×D4C2×C139semidirect
506. C23×C22⋊C4C2×C139semidirect
507. #2418C2×C139direct (N × H)
508. C2×#399C2×C139semidirect
509. C2×#397C2×C139semidirect
510. C2×#394C2×C139semidirect
511. C2×#394C2×C139semidirect
512. C2×#388C2×C139semidirect
513. C2×#388C2×C139semidirect
514. C2×#386C2×C139semidirect
515. C2×#386C2×C139semidirect
516. C2×#385C2×C139semidirect
517. C2×#380C2×C139semidirect
518. C2×#379C2×C139semidirect
525. C24×C4C22×C139semidirect
527. C2×#123C22×C139semidirect
531. C2×C4×D4C22×C139semidirect
532. C22×C4⋊C4C22×C139semidirect
533. C22×C4⋊C4C22×C139semidirect
534. C22×C4⋊C4C22×C139semidirect
535. C22×C4⋊C4C22×C139semidirect
536. C22×C4⋊C4C22×C139semidirect
551. C22×C22⋊C4C22×C139semidirect
552. C22×C22⋊C4C22×C139semidirect
553. C22×C22⋊C4C22×C139semidirect
554. C22×C22⋊C4C22×C139semidirect
555. C22×C42C22×C139semidirect
556. #399C22×C139semidirect
557. #397C22×C139semidirect
558. #394C22×C139semidirect
559. #394C22×C139semidirect
560. #388C22×C139semidirect
561. #388C22×C139semidirect
562. #386C22×C139semidirect
563. #386C22×C139semidirect
564. #385C22×C139semidirect
565. #380C22×C139semidirect
566. #379C22×C139semidirect
567. C2×#95C22×C139semidirect
568. C2×#95C22×C139semidirect
569. C2×#95C22×C139semidirect
570. C2×#95C22×C139semidirect
571. C2×#95C22×C139semidirect
572. C2×#95C22×C139semidirect
619. C23×C4C23×C139semidirect
628. C2×C4⋊C4C23×C139semidirect
629. C2×C4⋊C4C23×C139semidirect
630. C2×C4⋊C4C23×C139semidirect
631. C2×C4⋊C4C23×C139semidirect
632. C2×C4⋊C4C23×C139semidirect
649. C2×C22⋊C4D4×C139semidirect
663. C2×C22⋊C4C23×C139semidirect
664. C2×C22⋊C4C23×C139semidirect
665. C2×C22⋊C4C23×C139semidirect
667. C2×C42C23×C139semidirect
668. #95C23×C139semidirect
669. #95C23×C139semidirect
670. #95C23×C139semidirect
671. #95C23×C139semidirect
672. #95C23×C139semidirect
673. #95C23×C139semidirect
809. C22⋊C4C2×D4×C139semidirect
868. C23#123×C139semidirect
966. C22C2×#123×C139semidirect
995. C2#2418×C139direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#123×C1392
C22×#120×C1392
C22×C4×D4×C1392
C23×C22⋊C4×C1392
#2418×C1392
C2×#399×C1392
C2×#397×C1392
C2×#394×C1392
C2×#388×C1392
C2×#386×C1392
C2×#385×C1392
C2×#380×C1392
C2×#379×C1392
C2×#2418139