Finite Group Databasebeta

← C137×#24454 #46873840

Subgroups — C137×#24454 #46873840

Order 35072.

1528 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C137C211yesmaximal, characteristic, complemented
2C2×#468×C137C211yesmaximal, characteristic, complemented
3C2×#449×C137C211yesmaximal, characteristic, complemented
4C2×#449×C137C211yesmaximal, characteristic, complemented
5C2×#417×C137C211yesmaximal, characteristic, complemented
6#2416×C137C211yesmaximal, characteristic, complemented
7#2043×C137C211yesmaximal, characteristic, complemented
8#2036×C137C211yesmaximal, characteristic, complemented
9#2013×C137C211yesmaximal, characteristic, complemented
10#2000×C137C211yesmaximal, characteristic, complemented
11#1879×C137C211yesmaximal, characteristic, complemented
12#1872×C137C211yesmaximal, characteristic, complemented
13#1870×C137C211yesmaximal, characteristic, complemented
14#1862×C137C211yesmaximal, characteristic, complemented
15#1788×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C22×#41×C137C2211yescharacteristic
18C22×SD16×C137C2211yescharacteristic
19C22×SD16×C137C2211yescharacteristic
20C22×D8×C137C2211yescharacteristic
21C22×M16×C137C2211yescharacteristic
22#547×C137—24no—
23#547×C137—24no—
24C2×C4⋊Q8×C137C2211yescharacteristic
25C2×#123×C137—21no—
26C2×#123×C137—21no—
27C2×C22⋊Q8×C137C2211yescharacteristic
28C2×C22⋊Q8×C137C2211yescharacteristic
29C2×#121×C137—21no—
30C2×#121×C137—21no—
31C2×#121×C137C2211yescharacteristic
32C2×#121×C137C2211yescharacteristic
33C2×C4×D4×C137C2211yescharacteristic
34C2×C4×D4×C137C2211yescharacteristic
35C22×C4⋊C4×C137—21no—
36C22×C4⋊C4×C137C2211yescharacteristic
37#468×C137—24no—
38#449×C137—24no—
39#449×C137—24no—
40C2×#107×C137C2211yescharacteristic
41#417×C137—24no—
42C2×#103×C137C2211yescharacteristic
43C2×#103×C137C2211yescharacteristic
44C2×#103×C137C2211yescharacteristic
45C2×#103×C137C2211yescharacteristic
46C2×#103×C137C2211yescharacteristic
47C2×#103×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic
49C2×#102×C137C2211yescharacteristic
50C2×#102×C137C2211yescharacteristic
51C2×#102×C137C2211yescharacteristic
52C2×C22⋊C8×C137C2211yescharacteristic
53C2×C22⋊C8×C137C2211yescharacteristic
54C2×C22⋊C8×C137C2211yescharacteristic
55#396×C137—21no—
56#394×C137—21no—
57#390×C137C2211yescharacteristic
58#389×C137C2211yescharacteristic
59#386×C137—21no—
60#380×C137C2211yescharacteristic
61#340×C137C2211yescharacteristic
62#340×C137C2211yescharacteristic
63#336×C137C2211yescharacteristic
64#336×C137C2211yescharacteristic
65C2×#41×C137—22no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—22no—
69C2×#41×C137—22no—
70C2×#41×C137—22no—
71C2×#41×C137—22no—
72C2×#41×C137—41no—
73C2×#41×C137—41no—
74C2×#41×C137—41no—
75C2×#41×C137—41no—
76C2×#41×C137D414yescomplemented
77C22×Q8×C137C2311yescharacteristic
78C22×Q8×C137C2311yescharacteristic
79C22×D4×C137—21no—
80C22×D4×C137—21no—
81C22×D4×C137—21no—
82C22×D4×C137—21no—
83C22×D4×C137D411yescharacteristic
84C22×D4×C137C2311yescharacteristic
85C22×D4×C137C2311yescharacteristic
86C23×C4×C137—21no—
87C23×C4×C137—21no—
88C23×C4×C137—21no—
89C23×C4×C137—21no—
90C23×C4×C137C2311yescharacteristic
91C23×C4×C137C2311yescharacteristic
92C2×SD16×C137—22no—
93C2×SD16×C137—22no—
94C2×SD16×C137—22no—
95C2×SD16×C137—41no—
96C2×SD16×C137—41no—
97C2×SD16×C137—41no—
98C2×D8×C137—22no—
99C2×D8×C137—22no—
100C2×D8×C137—22no—
101C2×M16×C137—22no—
102C2×M16×C137—22no—
103C2×M16×C137—41no—
104C22×C8×C137C2311yescharacteristic
105C22×C8×C137C2311yescharacteristic
106C22×C8×C137C2311yescharacteristic
107C22×C8×C137C2311yescharacteristic
108C4⋊Q8×C137—22no—
109C4⋊Q8×C137—22no—
110#123×C137—28no—
111#123×C137—28no—
112C22⋊Q8×C137—22no—
113C22⋊Q8×C137—22no—
114C22⋊Q8×C137—22no—
115C22⋊Q8×C137D414yescomplemented
116#121×C137—28no—
117#121×C137—22no—
118#121×C137—22no—
119#121×C137—22no—
120#121×C137—41no—
121#121×C137—44no—
122C4×D4×C137—22no—
123C4×D4×C137—22no—
124C4×D4×C137—22no—
125C4×D4×C137—22no—
126C2×C4⋊C4×C137—28no—
127C2×C4⋊C4×C137—21no—
128C2×C4⋊C4×C137—21no—
129C2×C4⋊C4×C137—21no—
130C2×C4⋊C4×C137—21no—
131C2×C4⋊C4×C137—22no—
132C2×C4⋊C4×C137—21no—
133C2×C4⋊C4×C137—21no—
134C2×C4⋊C4×C137—41no—
135C2×C4⋊C4×C137D411yescharacteristic
136C2×C4⋊C4×C137C2311yescharacteristic
137C2×C4⋊C4×C137C2311yescharacteristic
138C2×C4⋊C4×C137C2311yescharacteristic
139C2×C4⋊C4×C137C2311yescharacteristic
140C2×C22⋊C4×C137—21no—
141C2×C22⋊C4×C137—21no—
142C2×C22⋊C4×C137—21no—
143C2×C22⋊C4×C137—21no—
144C2×C22⋊C4×C137—21no—
145C2×C22⋊C4×C137—21no—
146C2×C22⋊C4×C137—21no—
147C2×C22⋊C4×C137—21no—
148C2×C22⋊C4×C137D411yescharacteristic
149C2×C22⋊C4×C137D411yescharacteristic
150C2×C42×C137C2311yescharacteristic
151#107×C137—22no—
152#103×C137—22no—
153#103×C137—22no—
154#103×C137—22no—
155#103×C137—22no—
156#103×C137—22no—
157#103×C137—41no—
158#102×C137—22no—
159#102×C137—22no—
160#102×C137—22no—
161#102×C137D414yescomplemented
162C22⋊C8×C137—22no—
163C22⋊C8×C137—22no—
164C22⋊C8×C137—41no—
165#95×C137—21no—
166#95×C137—21no—
167C24×C137—21no—
168C24×C137—21no—
169C24×C137C2×D411yescharacteristic
170C24×C137C2×D411yescharacteristic
171#41×C137—28no—
172#41×C137—44no—
173#41×C137—44no—
174#41×C137—44no—
175#41×C137—44no—
176#41×C137—44no—
177#41×C137—44no—
178#41×C137—44no—
179C2×Q8×C137—21no—
180C2×Q8×C137—21no—
181C2×Q8×C137—21no—
182C2×Q8×C137—21no—
183C2×Q8×C137—21no—
184C2×Q8×C137—21no—
185C2×Q8×C137—21no—
186C2×Q8×C137—21no—
187C2×Q8×C137—21no—
188C2×Q8×C137—21no—
189C2×Q8×C137C2×D412yes—
190C2×Q8×C137C2×D412yes—
191C2×D4×C137—24no—
192C2×D4×C137—22no—
193C2×D4×C137—24no—
194C2×D4×C137—22no—
195C2×D4×C137—21no—
196C2×D4×C137—21no—
197C2×D4×C137—21no—
198C2×D4×C137—21no—
199C2×D4×C137—21no—
200C2×D4×C137—21no—
201C2×D4×C137—21no—
202C2×D4×C137—21no—
203C2×D4×C137—21no—
204C2×D4×C137—41no—
205C2×D4×C137—42no—
206C2×D4×C137—42no—
207C2×D4×C137—42no—
208C2×D4×C137—42no—
209C2×D4×C137—42no—
210C2×D4×C137—42no—
211C2×D4×C137—42no—
212C2×D4×C137—42no—
213C2×D4×C137—42no—
214C2×D4×C137—81no—
215C2×D4×C137C2×D412yes—
216C2×D4×C137C2×D412yes—
217C2×D4×C137#4112yes—
218C22×C4×C137—21no—
219C22×C4×C137—21no—
220C22×C4×C137—21no—
221C22×C4×C137—21no—
222C22×C4×C137—24no—
223C22×C4×C137—24no—
224C22×C4×C137—21no—
225C22×C4×C137—21no—
226C22×C4×C137—21no—
227C22×C4×C137—21no—
228C22×C4×C137—24no—
229C22×C4×C137—21no—
230C22×C4×C137—21no—
231C22×C4×C137—21no—
232C22×C4×C137—21no—
233C22×C4×C137—21no—
234C22×C4×C137—21no—
235C22×C4×C137—21no—
236C22×C4×C137—21no—
237C22×C4×C137—42no—
238C22×C4×C137—42no—
239C22×C4×C137—42no—
240C22×C4×C137—42no—
241C22×C4×C137—42no—
242C22×C4×C137—42no—
243C22×C4×C137—42no—
244C22×C4×C137—42no—
245C22×C4×C137—81no—
246C22×C4×C137C2×D411yescharacteristic
247C22×C4×C137C2×D411yescharacteristic
248C22×C4×C137C2×D411yescharacteristic
249C22×C4×C137C2×D412yes—
250C22×C4×C137C2×D412yes—
251C22×C4×C137C2×D411yescharacteristic
252C22×C4×C137C2411yescharacteristic
253SD16×C137—44no—
254SD16×C137—44no—
255D8×C137—44no—
256M16×C137—44no—
257C2×C8×C137—21no—
258C2×C8×C137—21no—
259C2×C8×C137—21no—
260C2×C8×C137—21no—
261C2×C8×C137—21no—
262C2×C8×C137—21no—
263C2×C8×C137—21no—
264C2×C8×C137—21no—
265C2×C8×C137—21no—
266C2×C8×C137—21no—
267C2×C8×C137—21no—
268C2×C8×C137C2×D412yes—
269C4⋊C4×C137—24no—
270C4⋊C4×C137—24no—
271C4⋊C4×C137—24no—
272C4⋊C4×C137—22no—
273C4⋊C4×C137—24no—
274C4⋊C4×C137—21no—
275C4⋊C4×C137—21no—
276C4⋊C4×C137—21no—
277C4⋊C4×C137—21no—
278C4⋊C4×C137—21no—
279C4⋊C4×C137—21no—
280C4⋊C4×C137—42no—
281C4⋊C4×C137—42no—
282C4⋊C4×C137C2×D412yes—
283C4⋊C4×C137C2×D412yes—
284C22⋊C4×C137—24no—
285C22⋊C4×C137—24no—
286C22⋊C4×C137—24no—
287C22⋊C4×C137—22no—
288C22⋊C4×C137—22no—
289C22⋊C4×C137—42no—
290C22⋊C4×C137—42no—
291C22⋊C4×C137—42no—
292C22⋊C4×C137—42no—
293C22⋊C4×C137—81no—
294C42×C137—21no—
295C42×C137—21no—
296C23×C137—22no—
297C23×C137—21no—
298C23×C137—22no—
299C23×C137—21no—
300C23×C137—22no—
301C23×C137—21no—
302C23×C137—21no—
303C23×C137—21no—
304C23×C137—21no—
305C23×C137—21no—
306C23×C137—21no—
307C23×C137—21no—
308C23×C137—21no—
309C23×C137—21no—
310C23×C137—21no—
311C23×C137—21no—
312C23×C137—41no—
313C23×C137—41no—
314C23×C137—41no—
315C23×C137—41no—
316C23×C137—41no—
317C23×C137—41no—
318C23×C137—41no—
319C23×C137—41no—
320C23×C137—41no—
321C23×C137—41no—
322C23×C137—41no—
323C23×C137#12012yes—
324C23×C137C22×D411yescharacteristic
325Q8×C137—22no—
326Q8×C137—22no—
327Q8×C137—22no—
328Q8×C137—22no—
329Q8×C137—41no—
330Q8×C137—41no—
331Q8×C137—41no—
332Q8×C137—41no—
333D4×C137—22no—
334D4×C137—22no—
335D4×C137—22no—
336D4×C137—44no—
337D4×C137—48no—
338D4×C137—48no—
339D4×C137—41no—
340D4×C137—41no—
341D4×C137—41no—
342D4×C137—41no—
343D4×C137—84no—
344D4×C137—84no—
345D4×C137#12114yescomplemented
346C2×C4×C137—21no—
347C2×C4×C137—21no—
348C2×C4×C137—21no—
349C2×C4×C137—21no—
350C2×C4×C137—22no—
351C2×C4×C137—22no—
352C2×C4×C137—22no—
353C2×C4×C137—22no—
354C2×C4×C137—21no—
355C2×C4×C137—22no—
356C2×C4×C137—21no—
357C2×C4×C137—22no—
358C2×C4×C137—22no—
359C2×C4×C137—21no—
360C2×C4×C137—22no—
361C2×C4×C137—21no—
362C2×C4×C137—21no—
363C2×C4×C137—21no—
364C2×C4×C137—48no—
365C2×C4×C137—48no—
366C2×C4×C137—48no—
367C2×C4×C137—41no—
368C2×C4×C137—41no—
369C2×C4×C137—41no—
370C2×C4×C137—41no—
371C2×C4×C137—41no—
372C2×C4×C137—41no—
373C2×C4×C137—41no—
374C2×C4×C137—41no—
375C2×C4×C137—41no—
376C2×C4×C137—41no—
377C2×C4×C137—41no—
378C2×C4×C137—41no—
379C2×C4×C137—41no—
380C2×C4×C137—41no—
381C2×C4×C137—41no—
382C2×C4×C137—41no—
383C2×C4×C137—41no—
384C2×C4×C137—41no—
385C2×C4×C137—84no—
386C2×C4×C137#12012yes—
387C2×C4×C137AGL(1,ℤ/8)12yes—
388C2×C4×C137C22×D411yescharacteristic
389C2×C4×C137C22×D411yescharacteristic
390C2×C4×C137C22×D411yescharacteristic
391C2×C4×C137C2×#4111yescharacteristic
392C2×C4×C137H(5,𝔽2)11yescharacteristic
393C2×C4×C137H(5,𝔽2)11yescharacteristic
394C8×C137—22no—
395C8×C137—41no—
396C8×C137—41no—
397C8×C137—41no—
398C22×C137—22no—
399C22×C137—24no—
400C22×C137—22no—
401C22×C137—22no—
402C22×C137—41no—
403C22×C137—42no—
404C22×C137—42no—
405C22×C137—42no—
406C22×C137—41no—
407C22×C137—42no—
408C22×C137—41no—
409C22×C137—42no—
410C22×C137—41no—
411C22×C137—42no—
412C22×C137—41no—
413C22×C137—41no—
414C22×C137—41no—
415C22×C137—41no—
416C22×C137—41no—
417C22×C137—41no—
418C22×C137—41no—
419C22×C137—81no—
420C22×C137—81no—
421C22×C137—81no—
422C22×C137—81no—
423C22×C137—81no—
424C22×C137—81no—
425C22×C137—81no—
426C22×C137C2×#12011yescharacteristic
427C22×C137D4211yescharacteristic
428C22×C137#54611yescharacteristic
429C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C137#57511yescharacteristic
431C22×C137#57711yescharacteristic
432C22×C137#57811yescharacteristic
433C4×C137—22no—
434C4×C137—22no—
435C4×C137—41no—
436C4×C137—42no—
437C4×C137—42no—
438C4×C137—42no—
439C4×C137—41no—
440C4×C137—42no—
441C4×C137—81no—
442C4×C137—81no—
443C4×C137C2×#12111yescharacteristic
444C4×C137#53411yescharacteristic
445C4×C137D4211yescharacteristic
446C4×C137#54611yescharacteristic
447C2×C137—42no—
448C2×C137—44no—
449C2×C137—81no—
450C2×C137—161no—
451C2×C137#241011yescharacteristic
452C2×C137#300611yescharacteristic
453C2×C137#301311yescharacteristic
454C2×C137#326911yescharacteristic
455C2×C137#327211yescharacteristic
456C2×C137#330711yescharacteristic
457C2×C137#333011yescharacteristic
458#24454C13711yesmaximal, characteristic, direct product factor, Sylow
459C137#2445411yescharacteristic, direct product factor, Sylow
460C2×#547C2×C13711yescharacteristic, complemented
461C2×#468C2×C13711yescharacteristic, complemented
462C2×#449C2×C13711yescharacteristic, complemented
463C2×#449C2×C13711yescharacteristic, complemented
464C2×#417C2×C13711yescharacteristic, complemented
465#2416C2×C13711yescharacteristic, complemented
466#2043C2×C13711yescharacteristic, complemented
467#2036C2×C13711yescharacteristic, complemented
468#2013C2×C13711yescharacteristic, complemented
469#2000C2×C13711yescharacteristic, complemented
470#1879C2×C13711yescharacteristic, complemented
471#1872C2×C13711yescharacteristic, complemented
472#1870C2×C13711yescharacteristic, complemented
473#1862C2×C13711yescharacteristic, complemented
474#1788C2×C13711yescharacteristic, complemented
475C22×#41C22×C13711yescharacteristic
476C22×#41C22×C13711yescharacteristic
477C22×SD16C22×C13711yescharacteristic
478C22×SD16C22×C13711yescharacteristic
479C22×D8C22×C13711yescharacteristic
480C22×M16C22×C13711yescharacteristic
481#547—24no—
482#547—24no—
483C2×C4⋊Q8C22×C13711yescharacteristic
484C2×#123—21no—
485C2×#123—21no—
486C2×C22⋊Q8C22×C13711yescharacteristic
487C2×C22⋊Q8C22×C13711yescharacteristic
488C2×#121—21no—
489C2×#121—21no—
490C2×#121C22×C13711yescharacteristic
491C2×#121C22×C13711yescharacteristic
492C2×C4×D4C22×C13711yescharacteristic
493C2×C4×D4C22×C13711yescharacteristic
494C22×C4⋊C4—21no—
495C22×C4⋊C4C22×C13711yescharacteristic
496#468—24no—
497#449—24no—
498#449—24no—
499C2×#107C22×C13711yescharacteristic
500#417—24no—
501C2×#103C22×C13711yescharacteristic
502C2×#103C22×C13711yescharacteristic
503C2×#103C22×C13711yescharacteristic
504C2×#103C22×C13711yescharacteristic
505C2×#103C22×C13711yescharacteristic
506C2×#103C22×C13711yescharacteristic
507C2×#102C22×C13711yescharacteristic
508C2×#102C22×C13711yescharacteristic
509C2×#102C22×C13711yescharacteristic
510C2×#102C22×C13711yescharacteristic
511C2×C22⋊C8C22×C13711yescharacteristic
512C2×C22⋊C8C22×C13711yescharacteristic
513C2×C22⋊C8C22×C13711yescharacteristic
514#396—21no—
515#394—21no—
516#390C22×C13711yescharacteristic
517#389C22×C13711yescharacteristic
518#386—21no—
519#380C22×C13711yescharacteristic
520#340C22×C13711yescharacteristic
521#340C22×C13711yescharacteristic
522#336C22×C13711yescharacteristic
523#336C22×C13711yescharacteristic
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C2×#41—41no—
535C2×#41D4×C13714yescomplemented
536C22×Q8C23×C13711yescharacteristic
537C22×Q8C23×C13711yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4D4×C13711yescharacteristic
543C22×D4C23×C13711yescharacteristic
544C22×D4C23×C13711yescharacteristic
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C23×C13711yescharacteristic
550C23×C4C23×C13711yescharacteristic
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×M16—22no—
561C2×M16—22no—
562C2×M16—41no—
563C22×C8C23×C13711yescharacteristic
564C22×C8C23×C13711yescharacteristic
565C22×C8C23×C13711yescharacteristic
566C22×C8C23×C13711yescharacteristic
567C4⋊Q8—22no—
568C4⋊Q8—22no—
569#123—28no—
570#123—28no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8D4×C13714yescomplemented
575#121—28no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—41no—
580#121—44no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C2×C4⋊C4—28no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4D4×C13711yescharacteristic
595C2×C4⋊C4C23×C13711yescharacteristic
596C2×C4⋊C4C23×C13711yescharacteristic
597C2×C4⋊C4C23×C13711yescharacteristic
598C2×C4⋊C4C23×C13711yescharacteristic
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4D4×C13711yescharacteristic
608C2×C22⋊C4D4×C13711yescharacteristic
609C2×C42C23×C13711yescharacteristic
610#107—22no—
611#103—22no—
612#103—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#103—41no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102D4×C13714yescomplemented
621C22⋊C8—22no—
622C22⋊C8—22no—
623C22⋊C8—41no—
624#95—21no—
625#95—21no—
626C24—21no—
627C24—21no—
628C24C2×D4×C13711yescharacteristic
629C24C2×D4×C13711yescharacteristic
630#41—28no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635#41—44no—
636#41—44no—
637#41—44no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8C2×D4×C13712yes—
649C2×Q8C2×D4×C13712yes—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—24no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—41no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—81no—
674C2×D4C2×D4×C13712yes—
675C2×D4C2×D4×C13712yes—
676C2×D4#41×C13712yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—24no—
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—42no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—81no—
705C22×C4C2×D4×C13711yescharacteristic
706C22×C4C2×D4×C13711yescharacteristic
707C22×C4C2×D4×C13711yescharacteristic
708C22×C4C2×D4×C13712yes—
709C22×C4C2×D4×C13712yes—
710C22×C4C2×D4×C13711yescharacteristic
711C22×C4C24×C13711yescharacteristic
712SD16—44no—
713SD16—44no—
714D8—44no—
715M16—44no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8C2×D4×C13712yes—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—42no—
740C4⋊C4—42no—
741C4⋊C4C2×D4×C13712yes—
742C4⋊C4C2×D4×C13712yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C42—21no—
754C42—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—21no—
759C23—22no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23#120×C13712yes—
783C23C22×D4×C13711yescharacteristic
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—22no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—84no—
803D4—84no—
804D4#121×C13714yescomplemented
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—48no—
824C2×C4—48no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—84no—
845C2×C4#120×C13712yes—
846C2×C4AGL(1,ℤ/8)×C13712yes—
847C2×C4C22×D4×C13711yescharacteristic
848C2×C4C22×D4×C13711yescharacteristic
849C2×C4C22×D4×C13711yescharacteristic
850C2×C4C2×#41×C13711yescharacteristic
851C2×C4H(5,𝔽2)×C13711yescharacteristic
852C2×C4H(5,𝔽2)×C13711yescharacteristic
853C8—22no—
854C8—41no—
855C8—41no—
856C8—41no—
857C22—22no—
858C22—24no—
859C22—22no—
860C22—22no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22C2×#120×C13711yescharacteristic
886C22D42×C13711yescharacteristic
887C22#546×C13711yescharacteristic
888C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
889C22#575×C13711yescharacteristic
890C22#577×C13711yescharacteristic
891C22#578×C13711yescharacteristic
892C4—22no—
893C4—22no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—42no—
898C4—41no—
899C4—42no—
900C4—81no—
901C4—81no—
902C4C2×#121×C13711yescharacteristic
903C4#534×C13711yescharacteristic
904C4D42×C13711yescharacteristic
905C4#546×C13711yescharacteristic
906C2—42no—
907C2—44no—
908C2—81no—
909C2—161no—
910C2#2410×C13711yescharacteristic
911C2#3006×C13711yescharacteristic
912C2#3013×C13711yescharacteristic
913C2#3269×C13711yescharacteristic
914C2#3272×C13711yescharacteristic
915C2#3307×C13711yescharacteristic
916C2#3330×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C22×D4
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C4×D4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#547×C137C2semidirect
2. C2×#468×C137C2semidirect
3. C2×#449×C137C2semidirect
4. C2×#449×C137C2semidirect
5. C2×#417×C137C2semidirect
6. #2416×C137C2semidirect
7. #2043×C137C2semidirect
8. #2036×C137C2semidirect
9. #2013×C137C2semidirect
10. #2000×C137C2semidirect
11. #1879×C137C2semidirect
12. #1872×C137C2semidirect
13. #1870×C137C2semidirect
14. #1862×C137C2semidirect
15. #1788×C137C2semidirect
76. C2×#41×C137D4semidirect
115. C22⋊Q8×C137D4semidirect
161. #102×C137D4semidirect
345. D4×C137#121semidirect
458. #24454C137direct (N × H)
459. C137#24454direct (N × H)
460. C2×#547C2×C137semidirect
461. C2×#468C2×C137semidirect
462. C2×#449C2×C137semidirect
463. C2×#449C2×C137semidirect
464. C2×#417C2×C137semidirect
465. #2416C2×C137semidirect
466. #2043C2×C137semidirect
467. #2036C2×C137semidirect
468. #2013C2×C137semidirect
469. #2000C2×C137semidirect
470. #1879C2×C137semidirect
471. #1872C2×C137semidirect
472. #1870C2×C137semidirect
473. #1862C2×C137semidirect
474. #1788C2×C137semidirect
535. C2×#41D4×C137semidirect
574. C22⋊Q8D4×C137semidirect
620. #102D4×C137semidirect
804. D4#121×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1372
C2×#468×C1372
C2×#449×C1372
C2×#417×C1372
#2416×C1372
#2043×C1372
#2036×C1372
#2013×C1372
#2000×C1372
#1879×C1372
#1872×C1372
#1870×C1372
#1862×C1372
#1788×C1372
#24454137