Finite Group Databasebeta

← C137×#24444 #46873830

Subgroups — C137×#24444 #46873830

Order 35072.

1662 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C137C211yesmaximal, characteristic, complemented
2C2×#469×C137C211yesmaximal, characteristic, complemented
3C2×#449×C137C211yesmaximal, characteristic, complemented
4C2×#447×C137C211yesmaximal, characteristic, complemented
5C2×#417×C137C211yesmaximal, characteristic, complemented
6#2416×C137C211yesmaximal, characteristic, complemented
7#2042×C137C211yesmaximal, characteristic, complemented
8#2035×C137C211yesmaximal, characteristic, complemented
9#2012×C137C211yesmaximal, characteristic, complemented
10#2000×C137C211yesmaximal, characteristic, complemented
11#1879×C137C211yesmaximal, characteristic, complemented
12#1874×C137C211yesmaximal, characteristic, complemented
13#1870×C137C211yesmaximal, characteristic, complemented
14#1864×C137C211yesmaximal, characteristic, complemented
15#1786×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C23×D4×C137C2211yescharacteristic
18C22×SD16×C137C2211yescharacteristic, complemented
19C22×D8×C137C2211yescharacteristic
20C22×D8×C137C2211yescharacteristic
21C22×M16×C137C2211yescharacteristic, complemented
22#546×C137—24no—
23#546×C137—24no—
24C2×#124×C137C2211yescharacteristic
25C2×#123×C137—21no—
26C2×C22⋊Q8×C137C2211yescharacteristic
27C2×#121×C137—21no—
28C2×#121×C137—21no—
29C2×#121×C137C2211yescharacteristic
30C2×#121×C137C2211yescharacteristic
31C2×#121×C137C2211yescharacteristic, complemented
32C2×#120×C137—21no—
33C2×C4×D4×C137C2211yescharacteristic
34C2×C4×D4×C137C2211yescharacteristic
35C22×C4⋊C4×C137C2211yescharacteristic, complemented
36C22×C22⋊C4×C137—21no—
37#469×C137—24no—
38#449×C137—24no—
39#447×C137—24no—
40C2×#106×C137C2211yescharacteristic, complemented
41#417×C137—24no—
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
55#396×C137—21no—
56#394×C137—21no—
57#390×C137C2211yescharacteristic, complemented
58#389×C137C2211yescharacteristic, complemented
59#386×C137—21no—
60#380×C137C2211yescharacteristic
61#340×C137C2211yescharacteristic, complemented
62#340×C137C2211yescharacteristic, complemented
63#336×C137C2211yescharacteristic, complemented
64#336×C137C2211yescharacteristic, complemented
65C25×C137—21no—
66C2×#41×C137—22no—
67C2×#41×C137—22no—
68C2×#41×C137—22no—
69C2×#41×C137—41no—
70C2×#41×C137—41no—
71C2×#41×C137D414yescomplemented
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—41no—
95C2×SD16×C137—41no—
96C2×D8×C137—22no—
97C2×D8×C137—22no—
98C2×D8×C137—22no—
99C2×D8×C137—22no—
100C2×D8×C137—22no—
101C2×D8×C137—41no—
102C2×M16×C137—22no—
103C2×M16×C137—22no—
104C2×M16×C137—41no—
105C22×C8×C137C2311yescharacteristic
106C22×C8×C137C2311yescharacteristic
107C22×C8×C137C2311yescharacteristic
108C22×C8×C137C2311yescharacteristic
109#124×C137—22no—
110#124×C137—22no—
111#123×C137—28no—
112C22⋊Q8×C137—22no—
113C22⋊Q8×C137—22no—
114#121×C137—28no—
115#121×C137—22no—
116#121×C137—22no—
117#121×C137—22no—
118#121×C137—22no—
119#121×C137—41no—
120#121×C137—44no—
121#121×C137D414yescomplemented
122#120×C137—28no—
123C4×D4×C137—22no—
124C4×D4×C137—22no—
125C4×D4×C137—22no—
126C4×D4×C137—22no—
127C2×C4⋊C4×C137—21no—
128C2×C4⋊C4×C137—22no—
129C2×C4⋊C4×C137—21no—
130C2×C4⋊C4×C137—21no—
131C2×C4⋊C4×C137—41no—
132C2×C4⋊C4×C137D411yescharacteristic
133C2×C4⋊C4×C137C2311yescharacteristic
134C2×C4⋊C4×C137C2311yescharacteristic
135C2×C4⋊C4×C137C2311yescharacteristic
136C2×C4⋊C4×C137C2311yescharacteristic
137C2×C22⋊C4×C137—28no—
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×C137—21no—
146C2×C22⋊C4×C137—21no—
147C2×C22⋊C4×C137—21no—
148C2×C22⋊C4×C137D411yescharacteristic
149C2×C22⋊C4×C137D411yescharacteristic
150C2×C42×C137C2311yescharacteristic
151#106×C137—22no—
152#103×C137—22no—
153#103×C137—22no—
154#103×C137—22no—
155#102×C137—22no—
156#102×C137—22no—
157#102×C137—22no—
158#102×C137—22no—
159#102×C137—22no—
160#102×C137—41no—
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—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—28no—
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—22no—
191C2×D4×C137—24no—
192C2×D4×C137—22no—
193C2×D4×C137—24no—
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—21no—
208C2×D4×C137—41no—
209C2×D4×C137—42no—
210C2×D4×C137—42no—
211C2×D4×C137—42no—
212C2×D4×C137—44no—
213C2×D4×C137—44no—
214C2×D4×C137—44no—
215C2×D4×C137—42no—
216C2×D4×C137—42no—
217C2×D4×C137—44no—
218C2×D4×C137—42no—
219C2×D4×C137—42no—
220C2×D4×C137—42no—
221C2×D4×C137—42no—
222C2×D4×C137—81no—
223C2×D4×C137—81no—
224C2×D4×C137—81no—
225C2×D4×C137C2×D412yes—
226C2×D4×C137C2×D412yes—
227C2×D4×C137C2×D412yes—
228C2×D4×C137#4112yes—
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—24no—
237C22×C4×C137—24no—
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—21no—
245C22×C4×C137—21no—
246C22×C4×C137—42no—
247C22×C4×C137—42no—
248C22×C4×C137—42no—
249C22×C4×C137—42no—
250C22×C4×C137—81no—
251C22×C4×C137—81no—
252C22×C4×C137—81no—
253C22×C4×C137C2×D411yescharacteristic
254C22×C4×C137C2×D411yescharacteristic
255C22×C4×C137C2×D411yescharacteristic
256C22×C4×C137C2×D411yescharacteristic
257C22×C4×C137C2×D412yes—
258C22×C4×C137C2×D412yes—
259C22×C4×C137C2411yescharacteristic
260SD16×C137—44no—
261D8×C137—44no—
262D8×C137—44no—
263M16×C137—44no—
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×C137—21no—
275C2×C8×C137C2×D412yes—
276C4⋊C4×C137—24no—
277C4⋊C4×C137—22no—
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—42no—
286C4⋊C4×C137C2×D412yes—
287C4⋊C4×C137C2×D412yes—
288C22⋊C4×C137—24no—
289C22⋊C4×C137—24no—
290C22⋊C4×C137—24no—
291C22⋊C4×C137—24no—
292C22⋊C4×C137—22no—
293C22⋊C4×C137—22no—
294C22⋊C4×C137—24no—
295C22⋊C4×C137—42no—
296C22⋊C4×C137—42no—
297C22⋊C4×C137—42no—
298C22⋊C4×C137—42no—
299C22⋊C4×C137—81no—
300C42×C137—21no—
301C42×C137—21no—
302C23×C137—21no—
303C23×C137—22no—
304C23×C137—21no—
305C23×C137—21no—
306C23×C137—22no—
307C23×C137—21no—
308C23×C137—21no—
309C23×C137—22no—
310C23×C137—21no—
311C23×C137—21no—
312C23×C137—21no—
313C23×C137—21no—
314C23×C137—21no—
315C23×C137—21no—
316C23×C137—21no—
317C23×C137—22no—
318C23×C137—48no—
319C23×C137—48no—
320C23×C137—41no—
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×C137#12012yes—
343C23×C137AGL(1,ℤ/8)12yes—
344C23×C137C22×D411yescharacteristic
345Q8×C137—22no—
346Q8×C137—22no—
347Q8×C137—41no—
348Q8×C137—41no—
349D4×C137—22no—
350D4×C137—22no—
351D4×C137—22no—
352D4×C137—22no—
353D4×C137—22no—
354D4×C137—44no—
355D4×C137—48no—
356D4×C137—48no—
357D4×C137—41no—
358D4×C137—41no—
359D4×C137—41no—
360D4×C137—41no—
361D4×C137—41no—
362D4×C137—41no—
363D4×C137—84no—
364D4×C137—84no—
365D4×C137—84no—
366D4×C137#12114yescomplemented
367C2×C4×C137—21no—
368C2×C4×C137—21no—
369C2×C4×C137—22no—
370C2×C4×C137—22no—
371C2×C4×C137—22no—
372C2×C4×C137—22no—
373C2×C4×C137—21no—
374C2×C4×C137—21no—
375C2×C4×C137—22no—
376C2×C4×C137—22no—
377C2×C4×C137—21no—
378C2×C4×C137—21no—
379C2×C4×C137—22no—
380C2×C4×C137—21no—
381C2×C4×C137—21no—
382C2×C4×C137—21no—
383C2×C4×C137—21no—
384C2×C4×C137—21no—
385C2×C4×C137—48no—
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—41no—
401C2×C4×C137—41no—
402C2×C4×C137—84no—
403C2×C4×C137—84no—
404C2×C4×C137#12012yes—
405C2×C4×C137C22×D411yescharacteristic
406C2×C4×C137C22×D411yescharacteristic
407C2×C4×C137C22×D411yescharacteristic
408C2×C4×C137C2×#4111yescharacteristic
409C2×C4×C137H(5,𝔽2)11yescharacteristic
410C2×C4×C137H(5,𝔽2)11yescharacteristic
411C8×C137—22no—
412C8×C137—41no—
413C8×C137—41no—
414C8×C137—41no—
415C22×C137—22no—
416C22×C137—24no—
417C22×C137—22no—
418C22×C137—22no—
419C22×C137—22no—
420C22×C137—22no—
421C22×C137—22no—
422C22×C137—41no—
423C22×C137—42no—
424C22×C137—41no—
425C22×C137—42no—
426C22×C137—42no—
427C22×C137—41no—
428C22×C137—41no—
429C22×C137—41no—
430C22×C137—42no—
431C22×C137—41no—
432C22×C137—42no—
433C22×C137—41no—
434C22×C137—41no—
435C22×C137—42no—
436C22×C137—42no—
437C22×C137—42no—
438C22×C137—42no—
439C22×C137—816no—
440C22×C137—81no—
441C22×C137—81no—
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×C137—81no—
451C22×C137C2×#12011yescharacteristic
452C22×C137D4211yescharacteristic
453C22×C137#54611yescharacteristic
454C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C137#57511yescharacteristic
456C22×C137#57611yescharacteristic
457C22×C137#57711yescharacteristic
458C4×C137—22no—
459C4×C137—41no—
460C4×C137—42no—
461C4×C137—41no—
462C4×C137—42no—
463C4×C137—41no—
464C4×C137—42no—
465C4×C137—81no—
466C4×C137—81no—
467C4×C137C2×#12111yescharacteristic
468C4×C137#53411yescharacteristic
469C4×C137D4211yescharacteristic
470C4×C137#54611yescharacteristic
471C2×C137—42no—
472C2×C137—42no—
473C2×C137—44no—
474C2×C137—82no—
475C2×C137—161no—
476C2×C137#241011yescharacteristic
477C2×C137#300611yescharacteristic
478C2×C137#301211yescharacteristic
479C2×C137#326411yescharacteristic
480C2×C137#327511yescharacteristic
481C2×C137#330611yescharacteristic
482C2×C137#332211yescharacteristic
483#24444C13711yesmaximal, characteristic, direct product factor, Sylow
484C137#2444411yescharacteristic, direct product factor, Sylow
485C2×#546C2×C13711yescharacteristic, complemented
486C2×#469C2×C13711yescharacteristic, complemented
487C2×#449C2×C13711yescharacteristic, complemented
488C2×#447C2×C13711yescharacteristic, complemented
489C2×#417C2×C13711yescharacteristic, complemented
490#2416C2×C13711yescharacteristic, complemented
491#2042C2×C13711yescharacteristic, complemented
492#2035C2×C13711yescharacteristic, complemented
493#2012C2×C13711yescharacteristic, complemented
494#2000C2×C13711yescharacteristic, complemented
495#1879C2×C13711yescharacteristic, complemented
496#1874C2×C13711yescharacteristic, complemented
497#1870C2×C13711yescharacteristic, complemented
498#1864C2×C13711yescharacteristic, complemented
499#1786C2×C13711yescharacteristic, complemented
500C22×#41C22×C13711yescharacteristic
501C23×D4C22×C13711yescharacteristic
502C22×SD16C22×C13711yescharacteristic, complemented
503C22×D8C22×C13711yescharacteristic
504C22×D8C22×C13711yescharacteristic
505C22×M16C22×C13711yescharacteristic, complemented
506#546—24no—
507#546—24no—
508C2×#124C22×C13711yescharacteristic
509C2×#123—21no—
510C2×C22⋊Q8C22×C13711yescharacteristic
511C2×#121—21no—
512C2×#121—21no—
513C2×#121C22×C13711yescharacteristic
514C2×#121C22×C13711yescharacteristic
515C2×#121C22×C13711yescharacteristic, complemented
516C2×#120—21no—
517C2×C4×D4C22×C13711yescharacteristic
518C2×C4×D4C22×C13711yescharacteristic
519C22×C4⋊C4C22×C13711yescharacteristic, complemented
520C22×C22⋊C4—21no—
521#469—24no—
522#449—24no—
523#447—24no—
524C2×#106C22×C13711yescharacteristic, complemented
525#417—24no—
526C2×#103C22×C13711yescharacteristic, complemented
527C2×#103C22×C13711yescharacteristic, complemented
528C2×#103C22×C13711yescharacteristic, complemented
529C2×#102C22×C13711yescharacteristic
530C2×#102C22×C13711yescharacteristic
531C2×#102C22×C13711yescharacteristic
532C2×#102C22×C13711yescharacteristic
533C2×#102C22×C13711yescharacteristic
534C2×#102C22×C13711yescharacteristic
535C2×#102C22×C13711yescharacteristic, complemented
536C2×C22⋊C8C22×C13711yescharacteristic
537C2×C22⋊C8C22×C13711yescharacteristic
538C2×C22⋊C8C22×C13711yescharacteristic, complemented
539#396—21no—
540#394—21no—
541#390C22×C13711yescharacteristic, complemented
542#389C22×C13711yescharacteristic, complemented
543#386—21no—
544#380C22×C13711yescharacteristic
545#340C22×C13711yescharacteristic, complemented
546#340C22×C13711yescharacteristic, complemented
547#336C22×C13711yescharacteristic, complemented
548#336C22×C13711yescharacteristic, complemented
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41D4×C13714yescomplemented
556C22×Q8C23×C13711yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—22no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4D4×C13711yescharacteristic
569C22×D4C23×C13711yescharacteristic
570C22×D4C23×C13711yescharacteristic
571C22×D4C23×C13711yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—21no—
575C23×C4C23×C13711yescharacteristic
576C23×C4C23×C13711yescharacteristic
577C2×SD16—22no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—41no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—41no—
589C22×C8C23×C13711yescharacteristic
590C22×C8C23×C13711yescharacteristic
591C22×C8C23×C13711yescharacteristic
592C22×C8C23×C13711yescharacteristic
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598#121—28no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—44no—
605#121D4×C13714yescomplemented
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4D4×C13711yescharacteristic
617C2×C4⋊C4C23×C13711yescharacteristic
618C2×C4⋊C4C23×C13711yescharacteristic
619C2×C4⋊C4C23×C13711yescharacteristic
620C2×C4⋊C4C23×C13711yescharacteristic
621C2×C22⋊C4—28no—
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⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4D4×C13711yescharacteristic
633C2×C22⋊C4D4×C13711yescharacteristic
634C2×C42C23×C13711yescharacteristic
635#106—22no—
636#103—22no—
637#103—22no—
638#103—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—41no—
645#102D4×C13714yescomplemented
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—41no—
649#95—21no—
650#95—21no—
651C24—21no—
652C24—24no—
653C24—21no—
654C24—21no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C2×D4×C13711yescharacteristic
662C24C2×D4×C13711yescharacteristic
663#41—28no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×D4×C13712yes—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—24no—
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—21no—
691C2×D4—21no—
692C2×D4—41no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—44no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4C2×D4×C13712yes—
710C2×D4C2×D4×C13712yes—
711C2×D4C2×D4×C13712yes—
712C2×D4#41×C13712yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4C2×D4×C13711yescharacteristic
738C22×C4C2×D4×C13711yescharacteristic
739C22×C4C2×D4×C13711yescharacteristic
740C22×C4C2×D4×C13711yescharacteristic
741C22×C4C2×D4×C13712yes—
742C22×C4C2×D4×C13712yes—
743C22×C4C24×C13711yescharacteristic
744SD16—44no—
745D8—44no—
746D8—44no—
747M16—44no—
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×C8—21no—
758C2×C8—21no—
759C2×C8C2×D4×C13712yes—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4C2×D4×C13712yes—
771C4⋊C4C2×D4×C13712yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—22no—
778C22⋊C4—24no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—81no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—22no—
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—41no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23—84no—
826C23#120×C13712yes—
827C23AGL(1,ℤ/8)×C13712yes—
828C23C22×D4×C13711yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
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—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4#121×C13714yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
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—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4#120×C13712yes—
889C2×C4C22×D4×C13711yescharacteristic
890C2×C4C22×D4×C13711yescharacteristic
891C2×C4C22×D4×C13711yescharacteristic
892C2×C4C2×#41×C13711yescharacteristic
893C2×C4H(5,𝔽2)×C13711yescharacteristic
894C2×C4H(5,𝔽2)×C13711yescharacteristic
895C8—22no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—22no—
900C22—22no—
901C22—24no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—41no—
914C22—42no—
915C22—42no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—816no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22C2×#120×C13711yescharacteristic
936C22D42×C13711yescharacteristic
937C22#546×C13711yescharacteristic
938C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
939C22#575×C13711yescharacteristic
940C22#576×C13711yescharacteristic
941C22#577×C13711yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4C2×#121×C13711yescharacteristic
952C4#534×C13711yescharacteristic
953C4D42×C13711yescharacteristic
954C4#546×C13711yescharacteristic
955C2—42no—
956C2—42no—
957C2—44no—
958C2—82no—
959C2—161no—
960C2#2410×C13711yescharacteristic
961C2#3006×C13711yescharacteristic
962C2#3012×C13711yescharacteristic
963C2#3264×C13711yescharacteristic
964C2#3275×C13711yescharacteristic
965C2#3306×C13711yescharacteristic
966C2#3322×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×#469×C137C2semidirect
3. C2×#449×C137C2semidirect
4. C2×#447×C137C2semidirect
5. C2×#417×C137C2semidirect
6. #2416×C137C2semidirect
7. #2042×C137C2semidirect
8. #2035×C137C2semidirect
9. #2012×C137C2semidirect
10. #2000×C137C2semidirect
11. #1879×C137C2semidirect
12. #1874×C137C2semidirect
13. #1870×C137C2semidirect
14. #1864×C137C2semidirect
15. #1786×C137C2semidirect
18. C22×SD16×C137C22semidirect
21. C22×M16×C137C22semidirect
31. C2×#121×C137C22semidirect
35. C22×C4⋊C4×C137C22semidirect
40. C2×#106×C137C22semidirect
42. C2×#103×C137C22semidirect
43. C2×#103×C137C22semidirect
44. C2×#103×C137C22semidirect
51. C2×#102×C137C22semidirect
54. C2×C22⋊C8×C137C22semidirect
57. #390×C137C22semidirect
58. #389×C137C22semidirect
61. #340×C137C22semidirect
62. #340×C137C22semidirect
63. #336×C137C22semidirect
64. #336×C137C22semidirect
71. C2×#41×C137D4semidirect
121. #121×C137D4semidirect
161. #102×C137D4semidirect
366. D4×C137#121semidirect
483. #24444C137direct (N × H)
484. C137#24444direct (N × H)
485. C2×#546C2×C137semidirect
486. C2×#469C2×C137semidirect
487. C2×#449C2×C137semidirect
488. C2×#447C2×C137semidirect
489. C2×#417C2×C137semidirect
490. #2416C2×C137semidirect
491. #2042C2×C137semidirect
492. #2035C2×C137semidirect
493. #2012C2×C137semidirect
494. #2000C2×C137semidirect
495. #1879C2×C137semidirect
496. #1874C2×C137semidirect
497. #1870C2×C137semidirect
498. #1864C2×C137semidirect
499. #1786C2×C137semidirect
502. C22×SD16C22×C137semidirect
505. C22×M16C22×C137semidirect
515. C2×#121C22×C137semidirect
519. C22×C4⋊C4C22×C137semidirect
524. C2×#106C22×C137semidirect
526. C2×#103C22×C137semidirect
527. C2×#103C22×C137semidirect
528. C2×#103C22×C137semidirect
535. C2×#102C22×C137semidirect
538. C2×C22⋊C8C22×C137semidirect
541. #390C22×C137semidirect
542. #389C22×C137semidirect
545. #340C22×C137semidirect
546. #340C22×C137semidirect
547. #336C22×C137semidirect
548. #336C22×C137semidirect
555. C2×#41D4×C137semidirect
605. #121D4×C137semidirect
645. #102D4×C137semidirect
850. 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×#469×C1372
C2×#449×C1372
C2×#447×C1372
C2×#417×C1372
#2416×C1372
#2042×C1372
#2035×C1372
#2012×C1372
#2000×C1372
#1879×C1372
#1874×C1372
#1870×C1372
#1864×C1372
#1786×C1372
#24444137