Finite Group Databasebeta

← C137×#24256 #46873642

Subgroups — C137×#24256 #46873642

Order 35072.

1510 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C137C211yesmaximal, characteristic, complemented
2C2×#463×C137C211yesmaximal, characteristic, complemented
3C2×#449×C137C211yesmaximal, characteristic, complemented
4C2×#448×C137C211yesmaximal, characteristic, complemented
5C2×#440×C137C211yesmaximal, characteristic, complemented
6#2537×C137C211yesmaximal, characteristic, complemented
7#2036×C137C211yesmaximal, characteristic, complemented
8#2033×C137C211yesmaximal, characteristic, complemented
9#2000×C137C211yesmaximal, characteristic, complemented
10#1999×C137C211yesmaximal, characteristic, complemented
11#1959×C137C211yesmaximal, characteristic, complemented
12#1955×C137C211yesmaximal, characteristic, complemented
13#1803×C137C211yesmaximal, characteristic, complemented
14#1788×C137C211yesmaximal, characteristic, complemented
15#1787×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C23×Q8×C137C2211yescharacteristic
18C22×SD16×C137C2211yescharacteristic
19C22×SD16×C137C2211yescharacteristic
20C22×D8×C137C2211yescharacteristic
21#548×C137—24no—
22#548×C137—24no—
23C2×#124×C137—21no—
24C2×#124×C137C2211yescharacteristic
25C2×C22⋊Q8×C137—21no—
26C2×C22⋊Q8×C137C2211yescharacteristic
27C2×#121×C137—21no—
28C2×#121×C137—21no—
29C2×#121×C137C2211yescharacteristic
30C2×#121×C137C2211yescharacteristic
31C2×#121×C137C2211yescharacteristic
32C2×C4×Q8×C137C2211yescharacteristic
33C2×C4×D4×C137—21no—
34C2×C4×D4×C137C2211yescharacteristic
35C2×C4×D4×C137C2211yescharacteristic
36#463×C137—24no—
37#449×C137—24no—
38#448×C137—24no—
39#440×C137—24no—
40C2×#107×C137C2211yescharacteristic
41C2×C4⋊C8×C137C2211yescharacteristic
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
55C2×C22⋊C8×C137C2211yescharacteristic
56C2×#97×C137C2211yescharacteristic
57#394×C137—21no—
58#394×C137—21no—
59#384×C137C2211yescharacteristic
60#380×C137—21no—
61#380×C137C2211yescharacteristic
62#380×C137C2211yescharacteristic
63#340×C137C2211yescharacteristic
64#340×C137C2211yescharacteristic
65C2×#41×C137—22no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—22no—
69C2×#41×C137—41no—
70C2×#41×C137—41no—
71C22×Q8×C137—22no—
72C22×Q8×C137—22no—
73C22×Q8×C137—21no—
74C22×Q8×C137—22no—
75C22×Q8×C137—22no—
76C22×Q8×C137—41no—
77C22×Q8×C137—41no—
78C22×Q8×C137C2311yescharacteristic
79C22×Q8×C137C2311yescharacteristic
80C22×D4×C137—21no—
81C22×D4×C137—21no—
82C22×D4×C137—21no—
83C22×D4×C137—21no—
84C22×D4×C137D411yescharacteristic
85C22×D4×C137C2311yescharacteristic
86C22×D4×C137C2311yescharacteristic
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—22no—
96C2×SD16×C137—41no—
97C2×SD16×C137D414yescomplemented
98C2×D8×C137—22no—
99C2×D8×C137—22no—
100C2×D8×C137—41no—
101C22×C8×C137C2311yescharacteristic
102C22×C8×C137C2311yescharacteristic
103C22×C8×C137C2311yescharacteristic
104C22×C8×C137C2311yescharacteristic
105#124×C137—28no—
106#124×C137—22no—
107#124×C137D414yescomplemented
108C22⋊Q8×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—
119C4×Q8×C137—22no—
120C4×Q8×C137D414yescomplemented
121C4×D4×C137—28no—
122C4×D4×C137—22no—
123C4×D4×C137—22no—
124C4×D4×C137—22no—
125C4×D4×C137—22no—
126C2×C4⋊C4×C137—21no—
127C2×C4⋊C4×C137—21no—
128C2×C4⋊C4×C137—21no—
129C2×C4⋊C4×C137—21no—
130C2×C4⋊C4×C137D411yescharacteristic
131C2×C4⋊C4×C137C2311yescharacteristic
132C2×C4⋊C4×C137C2311yescharacteristic
133C2×C4⋊C4×C137C2311yescharacteristic
134C2×C4⋊C4×C137C2311yescharacteristic
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×C137D411yescharacteristic
145C2×C22⋊C4×C137D411yescharacteristic
146C2×C42×C137—21no—
147C2×C42×C137C2311yescharacteristic
148#107×C137—22no—
149C4⋊C8×C137—22no—
150#103×C137—22no—
151#103×C137—22no—
152#103×C137—22no—
153#103×C137—22no—
154#103×C137—22no—
155#103×C137—41no—
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—21no—
169C24×C137C2×D411yescharacteristic
170C24×C137C2×D411yescharacteristic
171#41×C137—44no—
172#41×C137—44no—
173#41×C137—44no—
174#41×C137—44no—
175C2×Q8×C137—24no—
176C2×Q8×C137—21no—
177C2×Q8×C137—21no—
178C2×Q8×C137—21no—
179C2×Q8×C137—21no—
180C2×Q8×C137—21no—
181C2×Q8×C137—21no—
182C2×Q8×C137—21no—
183C2×Q8×C137—21no—
184C2×Q8×C137—42no—
185C2×Q8×C137—42no—
186C2×Q8×C137—44no—
187C2×Q8×C137—44no—
188C2×Q8×C137—44no—
189C2×Q8×C137—44no—
190C2×Q8×C137C2×D412yes—
191C2×Q8×C137C2×D412yes—
192C2×Q8×C137C2×D412yes—
193C2×Q8×C137#4112yes—
194C2×D4×C137—24no—
195C2×D4×C137—24no—
196C2×D4×C137—22no—
197C2×D4×C137—22no—
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—21no—
208C2×D4×C137—41no—
209C2×D4×C137—42no—
210C2×D4×C137—42no—
211C2×D4×C137—42no—
212C2×D4×C137—42no—
213C2×D4×C137—42no—
214C2×D4×C137—42no—
215C2×D4×C137—42no—
216C2×D4×C137—42no—
217C2×D4×C137—81no—
218C2×D4×C137—81no—
219C2×D4×C137C2×D412yes—
220C2×D4×C137C2×D412yes—
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—21no—
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—21no—
238C22×C4×C137—21no—
239C22×C4×C137—21no—
240C22×C4×C137—21no—
241C22×C4×C137—42no—
242C22×C4×C137—42no—
243C22×C4×C137—42no—
244C22×C4×C137—42no—
245C22×C4×C137—42no—
246C22×C4×C137—42no—
247C22×C4×C137—42no—
248C22×C4×C137C2×D411yescharacteristic
249C22×C4×C137C2×D411yescharacteristic
250C22×C4×C137C2×D411yescharacteristic
251C22×C4×C137C2×D411yescharacteristic
252C22×C4×C137C2411yescharacteristic
253SD16×C137—28no—
254SD16×C137—44no—
255D8×C137—44no—
256C2×C8×C137—21no—
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×C137C2×D412yes—
268C4⋊C4×C137—24no—
269C4⋊C4×C137—24no—
270C4⋊C4×C137—22no—
271C4⋊C4×C137—21no—
272C4⋊C4×C137—21no—
273C4⋊C4×C137—21no—
274C4⋊C4×C137—21no—
275C4⋊C4×C137—21no—
276C4⋊C4×C137—21no—
277C4⋊C4×C137—21no—
278C4⋊C4×C137—42no—
279C4⋊C4×C137—81no—
280C4⋊C4×C137C2×D412yes—
281C22⋊C4×C137—24no—
282C22⋊C4×C137—24no—
283C22⋊C4×C137—24no—
284C22⋊C4×C137—24no—
285C22⋊C4×C137—22no—
286C22⋊C4×C137—22no—
287C22⋊C4×C137—42no—
288C22⋊C4×C137—42no—
289C22⋊C4×C137—42no—
290C22⋊C4×C137—42no—
291C22⋊C4×C137—42no—
292C42×C137—24no—
293C42×C137C2×D412yes—
294C42×C137C2×D412yes—
295C23×C137—21no—
296C23×C137—21no—
297C23×C137—21no—
298C23×C137—21no—
299C23×C137—21no—
300C23×C137—21no—
301C23×C137—21no—
302C23×C137—22no—
303C23×C137—22no—
304C23×C137—21no—
305C23×C137—21no—
306C23×C137—21no—
307C23×C137—21no—
308C23×C137—21no—
309C23×C137—21no—
310C23×C137—41no—
311C23×C137—41no—
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×C137AGL(1,ℤ/8)12yes—
323C23×C137C22×D411yescharacteristic
324Q8×C137—22no—
325Q8×C137—22no—
326Q8×C137—22no—
327Q8×C137—22no—
328Q8×C137—22no—
329Q8×C137—48no—
330Q8×C137—41no—
331Q8×C137—41no—
332Q8×C137#12114yescomplemented
333D4×C137—22no—
334D4×C137—22no—
335D4×C137—22no—
336D4×C137—22no—
337D4×C137—44no—
338D4×C137—48no—
339D4×C137—48no—
340D4×C137—41no—
341D4×C137—41no—
342D4×C137—41no—
343D4×C137—41no—
344D4×C137—84no—
345D4×C137—84no—
346C2×C4×C137—22no—
347C2×C4×C137—22no—
348C2×C4×C137—22no—
349C2×C4×C137—21no—
350C2×C4×C137—21no—
351C2×C4×C137—21no—
352C2×C4×C137—21no—
353C2×C4×C137—22no—
354C2×C4×C137—22no—
355C2×C4×C137—21no—
356C2×C4×C137—21no—
357C2×C4×C137—21no—
358C2×C4×C137—21no—
359C2×C4×C137—21no—
360C2×C4×C137—21no—
361C2×C4×C137—48no—
362C2×C4×C137—48no—
363C2×C4×C137—41no—
364C2×C4×C137—41no—
365C2×C4×C137—41no—
366C2×C4×C137—41no—
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—84no—
385C2×C4×C137#12012yes—
386C2×C4×C137#12012yes—
387C2×C4×C137C22×D411yescharacteristic
388C2×C4×C137C22×D411yescharacteristic
389C2×C4×C137C22×D411yescharacteristic
390C2×C4×C137C2×#4111yescharacteristic
391C2×C4×C137H(5,𝔽2)11yescharacteristic
392C2×C4×C137H(5,𝔽2)11yescharacteristic
393C8×C137—22no—
394C8×C137—41no—
395C8×C137—41no—
396C8×C137—41no—
397C22×C137—22no—
398C22×C137—22no—
399C22×C137—22no—
400C22×C137—41no—
401C22×C137—41no—
402C22×C137—41no—
403C22×C137—41no—
404C22×C137—42no—
405C22×C137—41no—
406C22×C137—42no—
407C22×C137—41no—
408C22×C137—42no—
409C22×C137—41no—
410C22×C137—42no—
411C22×C137—41no—
412C22×C137—42no—
413C22×C137—41no—
414C22×C137—42no—
415C22×C137—41no—
416C22×C137—41no—
417C22×C137—81no—
418C22×C137—81no—
419C22×C137—81no—
420C22×C137—81no—
421C22×C137—81no—
422C22×C137—81no—
423C22×C137—81no—
424C22×C137—81no—
425C22×C137C2×#12011yescharacteristic
426C22×C137D4211yescharacteristic
427C22×C137#54611yescharacteristic
428C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C137#57511yescharacteristic
430C22×C137#57711yescharacteristic
431C22×C137#57811yescharacteristic
432C4×C137—24no—
433C4×C137—22no—
434C4×C137—22no—
435C4×C137—41no—
436C4×C137—41no—
437C4×C137—42no—
438C4×C137—42no—
439C4×C137—81no—
440C4×C137—81no—
441C4×C137—81no—
442C4×C137C2×#12111yescharacteristic
443C4×C137#53511yescharacteristic
444C4×C137D4211yescharacteristic
445C4×C137#54611yescharacteristic
446C2×C137—42no—
447C2×C137—81no—
448C2×C137—82no—
449C2×C137—82no—
450C2×C137#240811yescharacteristic
451C2×C137#300611yescharacteristic
452C2×C137#301311yescharacteristic
453C2×C137#326511yescharacteristic
454C2×C137#326911yescharacteristic
455C2×C137#330811yescharacteristic
456C2×C137#332111yescharacteristic
457#24256C13711yesmaximal, characteristic, direct product factor, Sylow
458C137#2425611yescharacteristic, direct product factor, Sylow
459C2×#548C2×C13711yescharacteristic, complemented
460C2×#463C2×C13711yescharacteristic, complemented
461C2×#449C2×C13711yescharacteristic, complemented
462C2×#448C2×C13711yescharacteristic, complemented
463C2×#440C2×C13711yescharacteristic, complemented
464#2537C2×C13711yescharacteristic, complemented
465#2036C2×C13711yescharacteristic, complemented
466#2033C2×C13711yescharacteristic, complemented
467#2000C2×C13711yescharacteristic, complemented
468#1999C2×C13711yescharacteristic, complemented
469#1959C2×C13711yescharacteristic, complemented
470#1955C2×C13711yescharacteristic, complemented
471#1803C2×C13711yescharacteristic, complemented
472#1788C2×C13711yescharacteristic, complemented
473#1787C2×C13711yescharacteristic, complemented
474C22×#41C22×C13711yescharacteristic
475C23×Q8C22×C13711yescharacteristic
476C22×SD16C22×C13711yescharacteristic
477C22×SD16C22×C13711yescharacteristic
478C22×D8C22×C13711yescharacteristic
479#548—24no—
480#548—24no—
481C2×#124—21no—
482C2×#124C22×C13711yescharacteristic
483C2×C22⋊Q8—21no—
484C2×C22⋊Q8C22×C13711yescharacteristic
485C2×#121—21no—
486C2×#121—21no—
487C2×#121C22×C13711yescharacteristic
488C2×#121C22×C13711yescharacteristic
489C2×#121C22×C13711yescharacteristic
490C2×C4×Q8C22×C13711yescharacteristic
491C2×C4×D4—21no—
492C2×C4×D4C22×C13711yescharacteristic
493C2×C4×D4C22×C13711yescharacteristic
494#463—24no—
495#449—24no—
496#448—24no—
497#440—24no—
498C2×#107C22×C13711yescharacteristic
499C2×C4⋊C8C22×C13711yescharacteristic
500C2×#103C22×C13711yescharacteristic
501C2×#103C22×C13711yescharacteristic
502C2×#103C22×C13711yescharacteristic
503C2×#103C22×C13711yescharacteristic
504C2×#103C22×C13711yescharacteristic
505C2×#103C22×C13711yescharacteristic
506C2×#102C22×C13711yescharacteristic
507C2×#102C22×C13711yescharacteristic
508C2×#102C22×C13711yescharacteristic
509C2×#102C22×C13711yescharacteristic
510C2×C22⋊C8C22×C13711yescharacteristic
511C2×C22⋊C8C22×C13711yescharacteristic
512C2×C22⋊C8C22×C13711yescharacteristic
513C2×C22⋊C8C22×C13711yescharacteristic
514C2×#97C22×C13711yescharacteristic
515#394—21no—
516#394—21no—
517#384C22×C13711yescharacteristic
518#380—21no—
519#380C22×C13711yescharacteristic
520#380C22×C13711yescharacteristic
521#340C22×C13711yescharacteristic
522#340C22×C13711yescharacteristic
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—21no—
532C22×Q8—22no—
533C22×Q8—22no—
534C22×Q8—41no—
535C22×Q8—41no—
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×C4C23×C13711yescharacteristic
549C23×C4C23×C13711yescharacteristic
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16D4×C13714yescomplemented
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—41no—
559C22×C8C23×C13711yescharacteristic
560C22×C8C23×C13711yescharacteristic
561C22×C8C23×C13711yescharacteristic
562C22×C8C23×C13711yescharacteristic
563#124—28no—
564#124—22no—
565#124D4×C13714yescomplemented
566C22⋊Q8—28no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569#121—28no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—41no—
575#121—41no—
576#121—44no—
577C4×Q8—22no—
578C4×Q8D4×C13714yescomplemented
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C13711yescharacteristic
589C2×C4⋊C4C23×C13711yescharacteristic
590C2×C4⋊C4C23×C13711yescharacteristic
591C2×C4⋊C4C23×C13711yescharacteristic
592C2×C4⋊C4C23×C13711yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4D4×C13711yescharacteristic
603C2×C22⋊C4D4×C13711yescharacteristic
604C2×C42—21no—
605C2×C42C23×C13711yescharacteristic
606#107—22no—
607C4⋊C8—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—22no—
613#103—41no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—41no—
618C22⋊C8—22no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#97—22no—
623#95—21no—
624#95—21no—
625C24—21no—
626C24—21no—
627C24C2×D4×C13711yescharacteristic
628C24C2×D4×C13711yescharacteristic
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—24no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8—44no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8C2×D4×C13712yes—
649C2×Q8C2×D4×C13712yes—
650C2×Q8C2×D4×C13712yes—
651C2×Q8#41×C13712yes—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C13712yes—
678C2×D4C2×D4×C13712yes—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
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—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4C2×D4×C13711yescharacteristic
707C22×C4C2×D4×C13711yescharacteristic
708C22×C4C2×D4×C13711yescharacteristic
709C22×C4C2×D4×C13711yescharacteristic
710C22×C4C24×C13711yescharacteristic
711SD16—28no—
712SD16—44no—
713D8—44no—
714C2×C8—21no—
715C2×C8—21no—
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×C8C2×D4×C13712yes—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—81no—
738C4⋊C4C2×D4×C13712yes—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C42—24no—
751C42C2×D4×C13712yes—
752C42C2×D4×C13712yes—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23AGL(1,ℤ/8)×C13712yes—
781C23C22×D4×C13711yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—41no—
789Q8—41no—
790Q8#121×C13714yescomplemented
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—84no—
803D4—84no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
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—84no—
843C2×C4#120×C13712yes—
844C2×C4#120×C13712yes—
845C2×C4C22×D4×C13711yescharacteristic
846C2×C4C22×D4×C13711yescharacteristic
847C2×C4C22×D4×C13711yescharacteristic
848C2×C4C2×#41×C13711yescharacteristic
849C2×C4H(5,𝔽2)×C13711yescharacteristic
850C2×C4H(5,𝔽2)×C13711yescharacteristic
851C8—22no—
852C8—41no—
853C8—41no—
854C8—41no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×#120×C13711yescharacteristic
884C22D42×C13711yescharacteristic
885C22#546×C13711yescharacteristic
886C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
887C22#575×C13711yescharacteristic
888C22#577×C13711yescharacteristic
889C22#578×C13711yescharacteristic
890C4—24no—
891C4—22no—
892C4—22no—
893C4—41no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×#121×C13711yescharacteristic
901C4#535×C13711yescharacteristic
902C4D42×C13711yescharacteristic
903C4#546×C13711yescharacteristic
904C2—42no—
905C2—81no—
906C2—82no—
907C2—82no—
908C2#2408×C13711yescharacteristic
909C2#3006×C13711yescharacteristic
910C2#3013×C13711yescharacteristic
911C2#3265×C13711yescharacteristic
912C2#3269×C13711yescharacteristic
913C2#3308×C13711yescharacteristic
914C2#3321×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×#548×C137C2semidirect
2. C2×#463×C137C2semidirect
3. C2×#449×C137C2semidirect
4. C2×#448×C137C2semidirect
5. C2×#440×C137C2semidirect
6. #2537×C137C2semidirect
7. #2036×C137C2semidirect
8. #2033×C137C2semidirect
9. #2000×C137C2semidirect
10. #1999×C137C2semidirect
11. #1959×C137C2semidirect
12. #1955×C137C2semidirect
13. #1803×C137C2semidirect
14. #1788×C137C2semidirect
15. #1787×C137C2semidirect
97. C2×SD16×C137D4semidirect
107. #124×C137D4semidirect
120. C4×Q8×C137D4semidirect
332. Q8×C137#121semidirect
457. #24256C137direct (N × H)
458. C137#24256direct (N × H)
459. C2×#548C2×C137semidirect
460. C2×#463C2×C137semidirect
461. C2×#449C2×C137semidirect
462. C2×#448C2×C137semidirect
463. C2×#440C2×C137semidirect
464. #2537C2×C137semidirect
465. #2036C2×C137semidirect
466. #2033C2×C137semidirect
467. #2000C2×C137semidirect
468. #1999C2×C137semidirect
469. #1959C2×C137semidirect
470. #1955C2×C137semidirect
471. #1803C2×C137semidirect
472. #1788C2×C137semidirect
473. #1787C2×C137semidirect
555. C2×SD16D4×C137semidirect
565. #124D4×C137semidirect
578. C4×Q8D4×C137semidirect
790. Q8#121×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1372
C2×#463×C1372
C2×#449×C1372
C2×#448×C1372
C2×#440×C1372
#2537×C1372
#2036×C1372
#2033×C1372
#2000×C1372
#1999×C1372
#1959×C1372
#1955×C1372
#1803×C1372
#1788×C1372
#1787×C1372
#24256137