Finite Group Databasebeta

← C137×#24257 #46873643

Subgroups — C137×#24257 #46873643

Order 35072.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C137C211yesmaximal, characteristic, complemented
2C2×#463×C137C211yesmaximal, characteristic, complemented
3C2×#449×C137C211yesmaximal, characteristic, complemented
4C2×#447×C137C211yesmaximal, characteristic, complemented
5C2×#442×C137C211yesmaximal, characteristic, complemented
6#2537×C137C211yesmaximal, characteristic, complemented
7#2035×C137C211yesmaximal, characteristic, complemented
8#2034×C137C211yesmaximal, characteristic, complemented
9#2000×C137C211yesmaximal, characteristic, complemented
10#1999×C137C211yesmaximal, characteristic, complemented
11#1959×C137C211yesmaximal, characteristic, complemented
12#1955×C137C211yesmaximal, characteristic, complemented
13#1802×C137C211yesmaximal, characteristic, complemented
14#1788×C137C211yesmaximal, characteristic, complemented
15#1786×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C22×SD16×C137C2211yescharacteristic, complemented
19C22×D8×C137C2211yescharacteristic
20C22×D8×C137C2211yescharacteristic
21#546×C137—24no—
22#546×C137—24no—
23C2×#124×C137C2211yescharacteristic
24C2×#123×C137—21no—
25C2×C22⋊Q8×C137C2211yescharacteristic
26C2×#121×C137—21no—
27C2×#121×C137—21no—
28C2×#121×C137C2211yescharacteristic
29C2×#121×C137C2211yescharacteristic
30C2×#121×C137C2211yescharacteristic, complemented
31C2×#120×C137—21no—
32C2×C4×D4×C137C2211yescharacteristic
33C2×C4×D4×C137C2211yescharacteristic
34C2×C4×D4×C137C2211yescharacteristic, complemented
35C22×C22⋊C4×C137—21no—
36#463×C137—24no—
37#449×C137—24no—
38#447×C137—24no—
39#442×C137—24no—
40C2×#106×C137C2211yescharacteristic, complemented
41C2×C4⋊C8×C137C2211yescharacteristic, complemented
42C2×#103×C137C2211yescharacteristic, complemented
43C2×#103×C137C2211yescharacteristic, complemented
44C2×#103×C137C2211yescharacteristic, complemented
45C2×#102×C137C2211yescharacteristic
46C2×#102×C137C2211yescharacteristic
47C2×#102×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic
49C2×#102×C137C2211yescharacteristic
50C2×#102×C137C2211yescharacteristic
51C2×#102×C137C2211yescharacteristic, complemented
52C2×C22⋊C8×C137C2211yescharacteristic
53C2×C22⋊C8×C137C2211yescharacteristic
54C2×C22⋊C8×C137C2211yescharacteristic, complemented
55C2×C22⋊C8×C137C2211yescharacteristic, complemented
56C2×#97×C137C2211yescharacteristic, complemented
57#394×C137—21no—
58#394×C137—21no—
59#384×C137C2211yescharacteristic, complemented
60#380×C137—21no—
61#380×C137C2211yescharacteristic
62#380×C137C2211yescharacteristic, complemented
63#340×C137C2211yescharacteristic, complemented
64#340×C137C2211yescharacteristic, complemented
65C25×C137—21no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—22no—
69C2×#41×C137—22no—
70C2×#41×C137—41no—
71C2×#41×C137—41no—
72C22×Q8×C137C2311yescharacteristic
73C22×D4×C137—21no—
74C22×D4×C137—21no—
75C22×D4×C137—22no—
76C22×D4×C137—22no—
77C22×D4×C137—22no—
78C22×D4×C137—22no—
79C22×D4×C137—21no—
80C22×D4×C137—21no—
81C22×D4×C137—21no—
82C22×D4×C137—41no—
83C22×D4×C137—41no—
84C22×D4×C137D411yescharacteristic
85C22×D4×C137C2311yescharacteristic
86C22×D4×C137C2311yescharacteristic
87C22×D4×C137C2311yescharacteristic
88C23×C4×C137—21no—
89C23×C4×C137—21no—
90C23×C4×C137—21no—
91C23×C4×C137C2311yescharacteristic
92C23×C4×C137C2311yescharacteristic
93C2×SD16×C137—22no—
94C2×SD16×C137—22no—
95C2×SD16×C137—41no—
96C2×D8×C137—22no—
97C2×D8×C137—22no—
98C2×D8×C137—22no—
99C2×D8×C137—22no—
100C2×D8×C137—41no—
101C2×D8×C137D414yescomplemented
102C22×C8×C137C2311yescharacteristic
103C22×C8×C137C2311yescharacteristic
104C22×C8×C137C2311yescharacteristic
105C22×C8×C137C2311yescharacteristic
106#124×C137—22no—
107#124×C137D414yescomplemented
108#123×C137—28no—
109C22⋊Q8×C137—22no—
110C22⋊Q8×C137—22no—
111#121×C137—28no—
112#121×C137—22no—
113#121×C137—22no—
114#121×C137—22no—
115#121×C137—22no—
116#121×C137—41no—
117#121×C137—41no—
118#121×C137—44no—
119#120×C137—28no—
120C4×D4×C137—22no—
121C4×D4×C137—22no—
122C4×D4×C137—22no—
123C4×D4×C137—22no—
124C4×D4×C137—22no—
125C4×D4×C137D414yescomplemented
126C2×C4⋊C4×C137—21no—
127C2×C4⋊C4×C137—21no—
128C2×C4⋊C4×C137—21no—
129C2×C4⋊C4×C137D411yescharacteristic
130C2×C4⋊C4×C137C2311yescharacteristic
131C2×C4⋊C4×C137C2311yescharacteristic
132C2×C4⋊C4×C137C2311yescharacteristic
133C2×C4⋊C4×C137C2311yescharacteristic
134C2×C22⋊C4×C137—28no—
135C2×C22⋊C4×C137—21no—
136C2×C22⋊C4×C137—21no—
137C2×C22⋊C4×C137—21no—
138C2×C22⋊C4×C137—21no—
139C2×C22⋊C4×C137—21no—
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×C137D411yescharacteristic
146C2×C22⋊C4×C137D411yescharacteristic
147C2×C42×C137C2311yescharacteristic
148#106×C137—22no—
149C4⋊C8×C137—22no—
150#103×C137—22no—
151#103×C137—22no—
152#103×C137—41no—
153#102×C137—22no—
154#102×C137—22no—
155#102×C137—22no—
156#102×C137—22no—
157#102×C137—22no—
158#102×C137—22no—
159#102×C137—41no—
160C22⋊C8×C137—22no—
161C22⋊C8×C137—22no—
162C22⋊C8×C137—41no—
163C22⋊C8×C137—41no—
164#97×C137—22no—
165#95×C137—21no—
166#95×C137—21no—
167C24×C137—21no—
168C24×C137—24no—
169C24×C137—21no—
170C24×C137—21no—
171C24×C137—42no—
172C24×C137—42no—
173C24×C137—42no—
174C24×C137—42no—
175C24×C137—81no—
176C24×C137—81no—
177C24×C137C2×D411yescharacteristic
178C24×C137C2×D411yescharacteristic
179#41×C137—44no—
180#41×C137—44no—
181#41×C137—44no—
182#41×C137—44no—
183C2×Q8×C137—21no—
184C2×Q8×C137—21no—
185C2×Q8×C137—21no—
186C2×Q8×C137—21no—
187C2×Q8×C137—21no—
188C2×Q8×C137C2×D412yes—
189C2×D4×C137—24no—
190C2×D4×C137—24no—
191C2×D4×C137—22no—
192C2×D4×C137—24no—
193C2×D4×C137—22no—
194C2×D4×C137—21no—
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—21no—
205C2×D4×C137—21no—
206C2×D4×C137—21no—
207C2×D4×C137—41no—
208C2×D4×C137—42no—
209C2×D4×C137—42no—
210C2×D4×C137—44no—
211C2×D4×C137—44no—
212C2×D4×C137—44no—
213C2×D4×C137—42no—
214C2×D4×C137—42no—
215C2×D4×C137—44no—
216C2×D4×C137—42no—
217C2×D4×C137—42no—
218C2×D4×C137—42no—
219C2×D4×C137—42no—
220C2×D4×C137—81no—
221C2×D4×C137—81no—
222C2×D4×C137—81no—
223C2×D4×C137—81no—
224C2×D4×C137C2×D412yes—
225C2×D4×C137C2×D412yes—
226C2×D4×C137C2×D412yes—
227C2×D4×C137C2×D412yes—
228C2×D4×C137#4112yes—
229C22×C4×C137—24no—
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—21no—
238C22×C4×C137—21no—
239C22×C4×C137—21no—
240C22×C4×C137—21no—
241C22×C4×C137—21no—
242C22×C4×C137—21no—
243C22×C4×C137—21no—
244C22×C4×C137—24no—
245C22×C4×C137—21no—
246C22×C4×C137—21no—
247C22×C4×C137—21no—
248C22×C4×C137—42no—
249C22×C4×C137—42no—
250C22×C4×C137—42no—
251C22×C4×C137—42no—
252C22×C4×C137—42no—
253C22×C4×C137—81no—
254C22×C4×C137—81no—
255C22×C4×C137C2×D411yescharacteristic
256C22×C4×C137C2×D411yescharacteristic
257C22×C4×C137C2×D411yescharacteristic
258C22×C4×C137C2×D411yescharacteristic
259C22×C4×C137C2411yescharacteristic
260SD16×C137—44no—
261D8×C137—28no—
262D8×C137—44no—
263C2×C8×C137—21no—
264C2×C8×C137—21no—
265C2×C8×C137—21no—
266C2×C8×C137—21no—
267C2×C8×C137—21no—
268C2×C8×C137—21no—
269C2×C8×C137—21no—
270C2×C8×C137—21no—
271C2×C8×C137—21no—
272C2×C8×C137—21no—
273C2×C8×C137—21no—
274C2×C8×C137C2×D412yes—
275C4⋊C4×C137—24no—
276C4⋊C4×C137—22no—
277C4⋊C4×C137—21no—
278C4⋊C4×C137—21no—
279C4⋊C4×C137—21no—
280C4⋊C4×C137—21no—
281C4⋊C4×C137—21no—
282C4⋊C4×C137—21no—
283C4⋊C4×C137—21no—
284C4⋊C4×C137—42no—
285C4⋊C4×C137—81no—
286C4⋊C4×C137C2×D412yes—
287C22⋊C4×C137—24no—
288C22⋊C4×C137—24no—
289C22⋊C4×C137—22no—
290C22⋊C4×C137—24no—
291C22⋊C4×C137—24no—
292C22⋊C4×C137—24no—
293C22⋊C4×C137—22no—
294C22⋊C4×C137—42no—
295C22⋊C4×C137—42no—
296C22⋊C4×C137—42no—
297C22⋊C4×C137—42no—
298C22⋊C4×C137—42no—
299C42×C137C2×D412yes—
300C42×C137C2×D412yes—
301C23×C137—21no—
302C23×C137—22no—
303C23×C137—21no—
304C23×C137—22no—
305C23×C137—21no—
306C23×C137—22no—
307C23×C137—21no—
308C23×C137—21no—
309C23×C137—21no—
310C23×C137—22no—
311C23×C137—21no—
312C23×C137—22no—
313C23×C137—21no—
314C23×C137—21no—
315C23×C137—21no—
316C23×C137—21no—
317C23×C137—21no—
318C23×C137—21no—
319C23×C137—48no—
320C23×C137—48no—
321C23×C137—41no—
322C23×C137—41no—
323C23×C137—41no—
324C23×C137—41no—
325C23×C137—41no—
326C23×C137—41no—
327C23×C137—41no—
328C23×C137—41no—
329C23×C137—41no—
330C23×C137—41no—
331C23×C137—41no—
332C23×C137—41no—
333C23×C137—41no—
334C23×C137—41no—
335C23×C137—41no—
336C23×C137—41no—
337C23×C137—84no—
338C23×C137—84no—
339C23×C137—84no—
340C23×C137—84no—
341C23×C137—84no—
342C23×C137AGL(1,ℤ/8)12yes—
343C23×C137C22×D411yescharacteristic
344Q8×C137—22no—
345Q8×C137—22no—
346Q8×C137—41no—
347Q8×C137—41no—
348D4×C137—22no—
349D4×C137—22no—
350D4×C137—22no—
351D4×C137—22no—
352D4×C137—22no—
353D4×C137—22no—
354D4×C137—22no—
355D4×C137—44no—
356D4×C137—48no—
357D4×C137—48no—
358D4×C137—41no—
359D4×C137—41no—
360D4×C137—41no—
361D4×C137—41no—
362D4×C137—84no—
363D4×C137—84no—
364D4×C137—84no—
365D4×C137#12114yescomplemented
366C2×C4×C137—21no—
367C2×C4×C137—21no—
368C2×C4×C137—21no—
369C2×C4×C137—21no—
370C2×C4×C137—22no—
371C2×C4×C137—21no—
372C2×C4×C137—22no—
373C2×C4×C137—21no—
374C2×C4×C137—21no—
375C2×C4×C137—21no—
376C2×C4×C137—21no—
377C2×C4×C137—21no—
378C2×C4×C137—48no—
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—41no—
386C2×C4×C137—41no—
387C2×C4×C137—41no—
388C2×C4×C137—41no—
389C2×C4×C137—41no—
390C2×C4×C137—41no—
391C2×C4×C137—41no—
392C2×C4×C137—41no—
393C2×C4×C137—41no—
394C2×C4×C137—41no—
395C2×C4×C137—41no—
396C2×C4×C137—41no—
397C2×C4×C137—41no—
398C2×C4×C137—41no—
399C2×C4×C137—41no—
400C2×C4×C137—84no—
401C2×C4×C137—84no—
402C2×C4×C137#12012yes—
403C2×C4×C137#12012yes—
404C2×C4×C137C22×D411yescharacteristic
405C2×C4×C137C22×D411yescharacteristic
406C2×C4×C137C22×D411yescharacteristic
407C2×C4×C137C2×#4111yescharacteristic
408C2×C4×C137H(5,𝔽2)11yescharacteristic
409C2×C4×C137H(5,𝔽2)11yescharacteristic
410C8×C137—22no—
411C8×C137—41no—
412C8×C137—41no—
413C8×C137—41no—
414C22×C137—24no—
415C22×C137—22no—
416C22×C137—22no—
417C22×C137—22no—
418C22×C137—41no—
419C22×C137—42no—
420C22×C137—42no—
421C22×C137—41no—
422C22×C137—42no—
423C22×C137—42no—
424C22×C137—41no—
425C22×C137—42no—
426C22×C137—41no—
427C22×C137—42no—
428C22×C137—41no—
429C22×C137—42no—
430C22×C137—42no—
431C22×C137—41no—
432C22×C137—42no—
433C22×C137—41no—
434C22×C137—42no—
435C22×C137—41no—
436C22×C137—42no—
437C22×C137—41no—
438C22×C137—42no—
439C22×C137—41no—
440C22×C137—41no—
441C22×C137—816no—
442C22×C137—81no—
443C22×C137—81no—
444C22×C137—81no—
445C22×C137—81no—
446C22×C137—81no—
447C22×C137—81no—
448C22×C137—81no—
449C22×C137—81no—
450C22×C137C2×#12011yescharacteristic
451C22×C137D4211yescharacteristic
452C22×C137#54611yescharacteristic
453C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
454C22×C137#57511yescharacteristic
455C22×C137#57611yescharacteristic
456C22×C137#57711yescharacteristic
457C4×C137—22no—
458C4×C137—22no—
459C4×C137—41no—
460C4×C137—41no—
461C4×C137—42no—
462C4×C137—42no—
463C4×C137—81no—
464C4×C137—81no—
465C4×C137—81no—
466C4×C137C2×#12111yescharacteristic
467C4×C137#53511yescharacteristic
468C4×C137D4211yescharacteristic
469C4×C137#54611yescharacteristic
470C2×C137—42no—
471C2×C137—44no—
472C2×C137—81no—
473C2×C137—82no—
474C2×C137—82no—
475C2×C137#240811yescharacteristic
476C2×C137#300611yescharacteristic
477C2×C137#301211yescharacteristic
478C2×C137#326411yescharacteristic
479C2×C137#326711yescharacteristic
480C2×C137#330611yescharacteristic
481C2×C137#331911yescharacteristic
482#24257C13711yesmaximal, characteristic, direct product factor, Sylow
483C137#2425711yescharacteristic, direct product factor, Sylow
484C2×#546C2×C13711yescharacteristic, complemented
485C2×#463C2×C13711yescharacteristic, complemented
486C2×#449C2×C13711yescharacteristic, complemented
487C2×#447C2×C13711yescharacteristic, complemented
488C2×#442C2×C13711yescharacteristic, complemented
489#2537C2×C13711yescharacteristic, complemented
490#2035C2×C13711yescharacteristic, complemented
491#2034C2×C13711yescharacteristic, complemented
492#2000C2×C13711yescharacteristic, complemented
493#1999C2×C13711yescharacteristic, complemented
494#1959C2×C13711yescharacteristic, complemented
495#1955C2×C13711yescharacteristic, complemented
496#1802C2×C13711yescharacteristic, complemented
497#1788C2×C13711yescharacteristic, complemented
498#1786C2×C13711yescharacteristic, complemented
499C22×#41C22×C13711yescharacteristic
500C23×D4C22×C13711yescharacteristic
501C22×SD16C22×C13711yescharacteristic, complemented
502C22×D8C22×C13711yescharacteristic
503C22×D8C22×C13711yescharacteristic
504#546—24no—
505#546—24no—
506C2×#124C22×C13711yescharacteristic
507C2×#123—21no—
508C2×C22⋊Q8C22×C13711yescharacteristic
509C2×#121—21no—
510C2×#121—21no—
511C2×#121C22×C13711yescharacteristic
512C2×#121C22×C13711yescharacteristic
513C2×#121C22×C13711yescharacteristic, complemented
514C2×#120—21no—
515C2×C4×D4C22×C13711yescharacteristic
516C2×C4×D4C22×C13711yescharacteristic
517C2×C4×D4C22×C13711yescharacteristic, complemented
518C22×C22⋊C4—21no—
519#463—24no—
520#449—24no—
521#447—24no—
522#442—24no—
523C2×#106C22×C13711yescharacteristic, complemented
524C2×C4⋊C8C22×C13711yescharacteristic, complemented
525C2×#103C22×C13711yescharacteristic, complemented
526C2×#103C22×C13711yescharacteristic, complemented
527C2×#103C22×C13711yescharacteristic, complemented
528C2×#102C22×C13711yescharacteristic
529C2×#102C22×C13711yescharacteristic
530C2×#102C22×C13711yescharacteristic
531C2×#102C22×C13711yescharacteristic
532C2×#102C22×C13711yescharacteristic
533C2×#102C22×C13711yescharacteristic
534C2×#102C22×C13711yescharacteristic, complemented
535C2×C22⋊C8C22×C13711yescharacteristic
536C2×C22⋊C8C22×C13711yescharacteristic
537C2×C22⋊C8C22×C13711yescharacteristic, complemented
538C2×C22⋊C8C22×C13711yescharacteristic, complemented
539C2×#97C22×C13711yescharacteristic, complemented
540#394—21no—
541#394—21no—
542#384C22×C13711yescharacteristic, complemented
543#380—21no—
544#380C22×C13711yescharacteristic
545#380C22×C13711yescharacteristic, complemented
546#340C22×C13711yescharacteristic, complemented
547#340C22×C13711yescharacteristic, complemented
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C23×C13711yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C13711yescharacteristic
568C22×D4C23×C13711yescharacteristic
569C22×D4C23×C13711yescharacteristic
570C22×D4C23×C13711yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C13711yescharacteristic
575C23×C4C23×C13711yescharacteristic
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—41no—
584C2×D8D4×C13714yescomplemented
585C22×C8C23×C13711yescharacteristic
586C22×C8C23×C13711yescharacteristic
587C22×C8C23×C13711yescharacteristic
588C22×C8C23×C13711yescharacteristic
589#124—22no—
590#124D4×C13714yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4D4×C13714yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C13711yescharacteristic
613C2×C4⋊C4C23×C13711yescharacteristic
614C2×C4⋊C4C23×C13711yescharacteristic
615C2×C4⋊C4C23×C13711yescharacteristic
616C2×C4⋊C4C23×C13711yescharacteristic
617C2×C22⋊C4—28no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C13711yescharacteristic
629C2×C22⋊C4D4×C13711yescharacteristic
630C2×C42C23×C13711yescharacteristic
631#106—22no—
632C4⋊C8—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647#97—22no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C13711yescharacteristic
661C24C2×D4×C13711yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C13712yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C13712yes—
708C2×D4C2×D4×C13712yes—
709C2×D4C2×D4×C13712yes—
710C2×D4C2×D4×C13712yes—
711C2×D4#41×C13712yes—
712C22×C4—24no—
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—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C13711yescharacteristic
739C22×C4C2×D4×C13711yescharacteristic
740C22×C4C2×D4×C13711yescharacteristic
741C22×C4C2×D4×C13711yescharacteristic
742C22×C4C24×C13711yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C13712yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C13712yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C13712yes—
783C42C2×D4×C13712yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
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—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23AGL(1,ℤ/8)×C13712yes—
826C23C22×D4×C13711yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4#121×C13714yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4#120×C13712yes—
886C2×C4#120×C13712yes—
887C2×C4C22×D4×C13711yescharacteristic
888C2×C4C22×D4×C13711yescharacteristic
889C2×C4C22×D4×C13711yescharacteristic
890C2×C4C2×#41×C13711yescharacteristic
891C2×C4H(5,𝔽2)×C13711yescharacteristic
892C2×C4H(5,𝔽2)×C13711yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—22no—
898C22—24no—
899C22—22no—
900C22—22no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—42no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—42no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—41no—
923C22—42no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×#120×C13711yescharacteristic
934C22D42×C13711yescharacteristic
935C22#546×C13711yescharacteristic
936C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
937C22#575×C13711yescharacteristic
938C22#576×C13711yescharacteristic
939C22#577×C13711yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×#121×C13711yescharacteristic
950C4#535×C13711yescharacteristic
951C4D42×C13711yescharacteristic
952C4#546×C13711yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2#2408×C13711yescharacteristic
959C2#3006×C13711yescharacteristic
960C2#3012×C13711yescharacteristic
961C2#3264×C13711yescharacteristic
962C2#3267×C13711yescharacteristic
963C2#3306×C13711yescharacteristic
964C2#3319×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×#546×C137C2semidirect
2. C2×#463×C137C2semidirect
3. C2×#449×C137C2semidirect
4. C2×#447×C137C2semidirect
5. C2×#442×C137C2semidirect
6. #2537×C137C2semidirect
7. #2035×C137C2semidirect
8. #2034×C137C2semidirect
9. #2000×C137C2semidirect
10. #1999×C137C2semidirect
11. #1959×C137C2semidirect
12. #1955×C137C2semidirect
13. #1802×C137C2semidirect
14. #1788×C137C2semidirect
15. #1786×C137C2semidirect
18. C22×SD16×C137C22semidirect
30. C2×#121×C137C22semidirect
34. C2×C4×D4×C137C22semidirect
40. C2×#106×C137C22semidirect
41. C2×C4⋊C8×C137C22semidirect
42. C2×#103×C137C22semidirect
43. C2×#103×C137C22semidirect
44. C2×#103×C137C22semidirect
51. C2×#102×C137C22semidirect
54. C2×C22⋊C8×C137C22semidirect
55. C2×C22⋊C8×C137C22semidirect
56. C2×#97×C137C22semidirect
59. #384×C137C22semidirect
62. #380×C137C22semidirect
63. #340×C137C22semidirect
64. #340×C137C22semidirect
101. C2×D8×C137D4semidirect
107. #124×C137D4semidirect
125. C4×D4×C137D4semidirect
365. D4×C137#121semidirect
482. #24257C137direct (N × H)
483. C137#24257direct (N × H)
484. C2×#546C2×C137semidirect
485. C2×#463C2×C137semidirect
486. C2×#449C2×C137semidirect
487. C2×#447C2×C137semidirect
488. C2×#442C2×C137semidirect
489. #2537C2×C137semidirect
490. #2035C2×C137semidirect
491. #2034C2×C137semidirect
492. #2000C2×C137semidirect
493. #1999C2×C137semidirect
494. #1959C2×C137semidirect
495. #1955C2×C137semidirect
496. #1802C2×C137semidirect
497. #1788C2×C137semidirect
498. #1786C2×C137semidirect
501. C22×SD16C22×C137semidirect
513. C2×#121C22×C137semidirect
517. C2×C4×D4C22×C137semidirect
523. C2×#106C22×C137semidirect
524. C2×C4⋊C8C22×C137semidirect
525. C2×#103C22×C137semidirect
526. C2×#103C22×C137semidirect
527. C2×#103C22×C137semidirect
534. C2×#102C22×C137semidirect
537. C2×C22⋊C8C22×C137semidirect
538. C2×C22⋊C8C22×C137semidirect
539. C2×#97C22×C137semidirect
542. #384C22×C137semidirect
545. #380C22×C137semidirect
546. #340C22×C137semidirect
547. #340C22×C137semidirect
584. C2×D8D4×C137semidirect
590. #124D4×C137semidirect
608. C4×D4D4×C137semidirect
848. D4#121×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1372
C2×#463×C1372
C2×#449×C1372
C2×#447×C1372
C2×#442×C1372
#2537×C1372
#2035×C1372
#2034×C1372
#2000×C1372
#1999×C1372
#1959×C1372
#1955×C1372
#1802×C1372
#1788×C1372
#1786×C1372
#24257137