Finite Group Databasebeta

← C137×#23863 #46873249

Subgroups — C137×#23863 #46873249

Order 35072.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C137C211yesmaximal, characteristic, complemented
2C2×#546×C137C211yesmaximal, characteristic, complemented
3C2×#452×C137C211yesmaximal, characteristic, complemented
4C2×#452×C137C211yesmaximal, characteristic, complemented
5C2×#449×C137C211yesmaximal, characteristic, complemented
6#2407×C137C211yesmaximal, characteristic, complemented
7#2015×C137C211yesmaximal, characteristic, complemented
8#2012×C137C211yesmaximal, characteristic, complemented
9#2000×C137C211yesmaximal, characteristic, complemented
10#1999×C137C211yesmaximal, characteristic, complemented
11#1894×C137C211yesmaximal, characteristic, complemented
12#1879×C137C211yesmaximal, characteristic, complemented
13#1877×C137C211yesmaximal, characteristic, complemented
14#1870×C137C211yesmaximal, characteristic, complemented
15#1786×C137C211yesmaximal, characteristic, complemented
16C22×#41×C137C2211yescharacteristic
17C22×#41×C137C2211yescharacteristic
18C23×D4×C137C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C137—24no—
20C2×AGL(1,ℤ/8)×C137—24no—
21C2×AGL(1,ℤ/8)×C137—24no—
22C22×Q16×C137C2211yescharacteristic, complemented
23C22×SD16×C137C2211yescharacteristic
24C22×SD16×C137C2211yescharacteristic
25C22×SD16×C137C2211yescharacteristic, complemented
26C22×D8×C137C2211yescharacteristic
27C22×D8×C137C2211yescharacteristic
28C22×M16×C137C2211yescharacteristic
29#546×C137—24no—
30#546×C137—24no—
31C2×#124×C137C2211yescharacteristic
32C2×#123×C137—21no—
33C2×C22⋊Q8×C137C2211yescharacteristic
34C2×C22⋊Q8×C137C2211yescharacteristic, complemented
35C2×#121×C137—21no—
36C2×#121×C137C2211yescharacteristic
37C2×#121×C137C2211yescharacteristic, complemented
38C2×#120×C137—21no—
39C2×C4×D4×C137C2211yescharacteristic
40C2×C4×D4×C137C2211yescharacteristic
41C22×C22⋊C4×C137—21no—
42#452×C137—24no—
43#452×C137—24no—
44#449×C137—24no—
45C2×#103×C137C2211yescharacteristic, complemented
46C2×#103×C137C2211yescharacteristic, complemented
47C2×#103×C137C2211yescharacteristic, complemented
48C2×#102×C137C2211yescharacteristic
49C2×#102×C137C2211yescharacteristic
50C2×#102×C137C2211yescharacteristic
51C2×#102×C137C2211yescharacteristic
52C2×#102×C137C2211yescharacteristic, complemented
53C2×C22⋊C8×C137C2211yescharacteristic
54C2×C22⋊C8×C137C2211yescharacteristic, complemented
55C2×C22⋊C8×C137C2211yescharacteristic, complemented
56#394×C137—21no—
57#392×C137—21no—
58#391×C137C2211yescharacteristic, complemented
59#390×C137C2211yescharacteristic, complemented
60#386×C137—21no—
61#385×C137—21no—
62#380×C137C2211yescharacteristic
63#340×C137C2211yescharacteristic, complemented
64#340×C137C2211yescharacteristic, complemented
65#336×C137C2211yescharacteristic, complemented
66#336×C137C2211yescharacteristic, complemented
67C25×C137—21no—
68C2×#41×C137—22no—
69C2×#41×C137—22no—
70C2×#41×C137—22no—
71C2×#41×C137—22no—
72C2×#41×C137—22no—
73C2×#41×C137—22no—
74C2×#41×C137—22no—
75C2×#41×C137—22no—
76C2×#41×C137—41no—
77C2×#41×C137—41no—
78C2×#41×C137—41no—
79C2×#41×C137—41no—
80C22×Q8×C137C2311yescharacteristic
81C22×Q8×C137C2311yescharacteristic
82C22×D4×C137—22no—
83C22×D4×C137—22no—
84C22×D4×C137—21no—
85C22×D4×C137—21no—
86C22×D4×C137—21no—
87C22×D4×C137—21no—
88C22×D4×C137—21no—
89C22×D4×C137—22no—
90C22×D4×C137—41no—
91C22×D4×C137—41no—
92C22×D4×C137D411yescharacteristic
93C22×D4×C137D414yescomplemented
94C22×D4×C137C2311yescharacteristic
95C22×D4×C137C2311yescharacteristic
96C22×D4×C137C2311yescharacteristic
97C23×C4×C137—21no—
98C23×C4×C137—21no—
99C23×C4×C137—21no—
100C23×C4×C137C2311yescharacteristic
101C23×C4×C137C2311yescharacteristic
102AGL(1,ℤ/8)×C137—232no—
103C2×Q16×C137—22no—
104C2×Q16×C137—22no—
105C2×Q16×C137—41no—
106C2×SD16×C137—22no—
107C2×SD16×C137—22no—
108C2×SD16×C137—22no—
109C2×SD16×C137—22no—
110C2×SD16×C137—22no—
111C2×SD16×C137—22no—
112C2×SD16×C137—22no—
113C2×SD16×C137—41no—
114C2×SD16×C137D414yescomplemented
115C2×D8×C137—22no—
116C2×D8×C137—22no—
117C2×D8×C137—22no—
118C2×D8×C137—22no—
119C2×D8×C137—22no—
120C2×D8×C137D414yescomplemented
121C2×M16×C137—22no—
122C2×M16×C137—22no—
123C2×M16×C137—22no—
124C22×C8×C137C2311yescharacteristic
125C22×C8×C137C2311yescharacteristic
126C22×C8×C137C2311yescharacteristic
127C22×C8×C137C2311yescharacteristic
128#124×C137—22no—
129#124×C137—22no—
130#123×C137—28no—
131C22⋊Q8×C137—22no—
132C22⋊Q8×C137—22no—
133C22⋊Q8×C137—41no—
134C22⋊Q8×C137D414yescomplemented
135#121×C137—28no—
136#121×C137—22no—
137#121×C137—22no—
138#121×C137—22no—
139#121×C137—41no—
140#120×C137—28no—
141C4×D4×C137—22no—
142C4×D4×C137—22no—
143C4×D4×C137—22no—
144C4×D4×C137—22no—
145C2×C4⋊C4×C137—21no—
146C2×C4⋊C4×C137—21no—
147C2×C4⋊C4×C137D411yescharacteristic
148C2×C4⋊C4×C137C2311yescharacteristic
149C2×C4⋊C4×C137C2311yescharacteristic
150C2×C4⋊C4×C137C2311yescharacteristic
151C2×C22⋊C4×C137—28no—
152C2×C22⋊C4×C137—21no—
153C2×C22⋊C4×C137—21no—
154C2×C22⋊C4×C137—21no—
155C2×C22⋊C4×C137—21no—
156C2×C22⋊C4×C137—21no—
157C2×C22⋊C4×C137—21no—
158C2×C22⋊C4×C137—21no—
159C2×C22⋊C4×C137—21no—
160C2×C22⋊C4×C137—21no—
161C2×C22⋊C4×C137—21no—
162C2×C22⋊C4×C137D411yescharacteristic
163C2×C22⋊C4×C137D411yescharacteristic
164C2×C42×C137C2311yescharacteristic
165#103×C137—22no—
166#103×C137—22no—
167#103×C137—22no—
168#102×C137—22no—
169#102×C137—22no—
170#102×C137—22no—
171#102×C137—41no—
172#102×C137—41no—
173C22⋊C8×C137—22no—
174C22⋊C8×C137—22no—
175C22⋊C8×C137—22no—
176#95×C137—21no—
177#95×C137—21no—
178#95×C137—21no—
179C24×C137—21no—
180C24×C137—21no—
181C24×C137—21no—
182C24×C137—24no—
183C24×C137—42no—
184C24×C137—42no—
185C24×C137—42no—
186C24×C137—42no—
187C24×C137—81no—
188C24×C137—81no—
189C24×C137C2×D411yescharacteristic
190C24×C137C2×D411yescharacteristic
191#41×C137—28no—
192#41×C137—44no—
193#41×C137—44no—
194#41×C137—44no—
195#41×C137—44no—
196#41×C137—44no—
197#41×C137—44no—
198#41×C137—44no—
199C2×Q8×C137—21no—
200C2×Q8×C137—21no—
201C2×Q8×C137—21no—
202C2×Q8×C137—21no—
203C2×Q8×C137—21no—
204C2×Q8×C137—21no—
205C2×Q8×C137—21no—
206C2×Q8×C137—21no—
207C2×Q8×C137—21no—
208C2×Q8×C137—21no—
209C2×Q8×C137C2×D412yes—
210C2×Q8×C137C2×D412yes—
211C2×D4×C137—28no—
212C2×D4×C137—24no—
213C2×D4×C137—22no—
214C2×D4×C137—24no—
215C2×D4×C137—24no—
216C2×D4×C137—21no—
217C2×D4×C137—21no—
218C2×D4×C137—21no—
219C2×D4×C137—21no—
220C2×D4×C137—21no—
221C2×D4×C137—21no—
222C2×D4×C137—21no—
223C2×D4×C137—21no—
224C2×D4×C137—21no—
225C2×D4×C137—21no—
226C2×D4×C137—21no—
227C2×D4×C137—21no—
228C2×D4×C137—21no—
229C2×D4×C137—44no—
230C2×D4×C137—44no—
231C2×D4×C137—44no—
232C2×D4×C137—41no—
233C2×D4×C137—41no—
234C2×D4×C137—42no—
235C2×D4×C137—42no—
236C2×D4×C137—42no—
237C2×D4×C137—42no—
238C2×D4×C137—42no—
239C2×D4×C137—42no—
240C2×D4×C137—42no—
241C2×D4×C137—42no—
242C2×D4×C137—42no—
243C2×D4×C137—81no—
244C2×D4×C137—81no—
245C2×D4×C137—81no—
246C2×D4×C137C2×D412yes—
247C2×D4×C137C2×D412yes—
248C2×D4×C137C2×D412yes—
249C2×D4×C137C2×D412yes—
250C2×D4×C137C2×D412yes—
251C22×C4×C137—21no—
252C22×C4×C137—21no—
253C22×C4×C137—21no—
254C22×C4×C137—21no—
255C22×C4×C137—24no—
256C22×C4×C137—21no—
257C22×C4×C137—21no—
258C22×C4×C137—21no—
259C22×C4×C137—24no—
260C22×C4×C137—21no—
261C22×C4×C137—21no—
262C22×C4×C137—21no—
263C22×C4×C137—21no—
264C22×C4×C137—21no—
265C22×C4×C137—21no—
266C22×C4×C137—21no—
267C22×C4×C137—21no—
268C22×C4×C137—42no—
269C22×C4×C137—42no—
270C22×C4×C137—42no—
271C22×C4×C137—42no—
272C22×C4×C137—42no—
273C22×C4×C137—81no—
274C22×C4×C137—81no—
275C22×C4×C137C2×D411yescharacteristic
276C22×C4×C137C2×D411yescharacteristic
277C22×C4×C137C2×D411yescharacteristic
278C22×C4×C137C2×D411yescharacteristic
279C22×C4×C137C2×D412yes—
280C22×C4×C137C2×D412yes—
281C22×C4×C137C2411yescharacteristic
282Q16×C137—44no—
283SD16×C137—28no—
284SD16×C137—28no—
285SD16×C137—44no—
286D8×C137—28no—
287D8×C137—28no—
288M16×C137—28no—
289C2×C8×C137—21no—
290C2×C8×C137—21no—
291C2×C8×C137—21no—
292C2×C8×C137—21no—
293C2×C8×C137—21no—
294C2×C8×C137—21no—
295C2×C8×C137—21no—
296C2×C8×C137—21no—
297C2×C8×C137—21no—
298C2×C8×C137—21no—
299C2×C8×C137C2×D412yes—
300C2×C8×C137C2×D412yes—
301C4⋊C4×C137—24no—
302C4⋊C4×C137—22no—
303C4⋊C4×C137—21no—
304C4⋊C4×C137—21no—
305C4⋊C4×C137—21no—
306C4⋊C4×C137—21no—
307C4⋊C4×C137—21no—
308C4⋊C4×C137—42no—
309C4⋊C4×C137C2×D412yes—
310C22⋊C4×C137—24no—
311C22⋊C4×C137—24no—
312C22⋊C4×C137—24no—
313C22⋊C4×C137—24no—
314C22⋊C4×C137—22no—
315C22⋊C4×C137—24no—
316C22⋊C4×C137—22no—
317C22⋊C4×C137—42no—
318C22⋊C4×C137—42no—
319C22⋊C4×C137—42no—
320C22⋊C4×C137—81no—
321C22⋊C4×C137—81no—
322C42×C137—21no—
323C42×C137—21no—
324C23×C137—22no—
325C23×C137—21no—
326C23×C137—21no—
327C23×C137—22no—
328C23×C137—22no—
329C23×C137—21no—
330C23×C137—21no—
331C23×C137—21no—
332C23×C137—21no—
333C23×C137—22no—
334C23×C137—21no—
335C23×C137—21no—
336C23×C137—22no—
337C23×C137—21no—
338C23×C137—21no—
339C23×C137—21no—
340C23×C137—21no—
341C23×C137—21no—
342C23×C137—48no—
343C23×C137—48no—
344C23×C137—41no—
345C23×C137—41no—
346C23×C137—41no—
347C23×C137—41no—
348C23×C137—41no—
349C23×C137—41no—
350C23×C137—41no—
351C23×C137—41no—
352C23×C137—41no—
353C23×C137—41no—
354C23×C137—41no—
355C23×C137—41no—
356C23×C137—41no—
357C23×C137—41no—
358C23×C137—41no—
359C23×C137—41no—
360C23×C137—84no—
361C23×C137—84no—
362C23×C137—84no—
363C23×C137—84no—
364C23×C137—84no—
365C23×C137#12012yes—
366C23×C137C22×D411yescharacteristic
367Q8×C137—22no—
368Q8×C137—22no—
369Q8×C137—22no—
370Q8×C137—22no—
371Q8×C137—41no—
372Q8×C137—41no—
373Q8×C137—41no—
374Q8×C137—41no—
375D4×C137—22no—
376D4×C137—22no—
377D4×C137—22no—
378D4×C137—22no—
379D4×C137—22no—
380D4×C137—22no—
381D4×C137—22no—
382D4×C137—48no—
383D4×C137—44no—
384D4×C137—48no—
385D4×C137—48no—
386D4×C137—41no—
387D4×C137—41no—
388D4×C137—41no—
389D4×C137—41no—
390D4×C137—84no—
391D4×C137—84no—
392D4×C137#12014yes—
393C2×C4×C137—21no—
394C2×C4×C137—21no—
395C2×C4×C137—22no—
396C2×C4×C137—22no—
397C2×C4×C137—22no—
398C2×C4×C137—22no—
399C2×C4×C137—21no—
400C2×C4×C137—21no—
401C2×C4×C137—22no—
402C2×C4×C137—21no—
403C2×C4×C137—22no—
404C2×C4×C137—21no—
405C2×C4×C137—22no—
406C2×C4×C137—21no—
407C2×C4×C137—21no—
408C2×C4×C137—21no—
409C2×C4×C137—21no—
410C2×C4×C137—21no—
411C2×C4×C137—48no—
412C2×C4×C137—48no—
413C2×C4×C137—41no—
414C2×C4×C137—41no—
415C2×C4×C137—41no—
416C2×C4×C137—41no—
417C2×C4×C137—41no—
418C2×C4×C137—41no—
419C2×C4×C137—41no—
420C2×C4×C137—41no—
421C2×C4×C137—41no—
422C2×C4×C137—41no—
423C2×C4×C137—41no—
424C2×C4×C137—41no—
425C2×C4×C137—41no—
426C2×C4×C137—41no—
427C2×C4×C137—41no—
428C2×C4×C137—41no—
429C2×C4×C137—84no—
430C2×C4×C137#12012yes—
431C2×C4×C137C22×D411yescharacteristic
432C2×C4×C137C22×D411yescharacteristic
433C2×C4×C137C22×D411yescharacteristic
434C2×C4×C137C22×D411yescharacteristic
435C2×C4×C137H(5,𝔽2)11yescharacteristic
436C2×C4×C137H(5,𝔽2)11yescharacteristic
437C8×C137—22no—
438C8×C137—22no—
439C8×C137—41no—
440C8×C137—41no—
441C22×C137—22no—
442C22×C137—24no—
443C22×C137—22no—
444C22×C137—22no—
445C22×C137—42no—
446C22×C137—41no—
447C22×C137—42no—
448C22×C137—42no—
449C22×C137—41no—
450C22×C137—42no—
451C22×C137—41no—
452C22×C137—42no—
453C22×C137—41no—
454C22×C137—42no—
455C22×C137—42no—
456C22×C137—41no—
457C22×C137—42no—
458C22×C137—41no—
459C22×C137—42no—
460C22×C137—41no—
461C22×C137—42no—
462C22×C137—41no—
463C22×C137—42no—
464C22×C137—41no—
465C22×C137—41no—
466C22×C137—42no—
467C22×C137—41no—
468C22×C137—816no—
469C22×C137—81no—
470C22×C137—81no—
471C22×C137—81no—
472C22×C137—81no—
473C22×C137—81no—
474C22×C137—81no—
475C22×C137—81no—
476C22×C137—81no—
477C22×C137C2×#12011yescharacteristic
478C22×C137D4211yescharacteristic
479C22×C137D4211yescharacteristic
480C22×C137#57511yescharacteristic
481C22×C137#57511yescharacteristic
482C22×C137#57611yescharacteristic
483C22×C137#57711yescharacteristic
484C4×C137—22no—
485C4×C137—41no—
486C4×C137—42no—
487C4×C137—42no—
488C4×C137—41no—
489C4×C137—41no—
490C4×C137—42no—
491C4×C137—81no—
492C4×C137—81no—
493C4×C137C2×#12011yescharacteristic
494C4×C137#53411yescharacteristic
495C4×C137D4211yescharacteristic
496C4×C137D4211yescharacteristic
497C2×C137—42no—
498C2×C137—44no—
499C2×C137—81no—
500C2×C137—82no—
501C2×C137—82no—
502C2×C137#240311yescharacteristic
503C2×C137#300511yescharacteristic
504C2×C137#301211yescharacteristic
505C2×C137#326711yescharacteristic
506C2×C137#326811yescharacteristic
507C2×C137#327311yescharacteristic
508C2×C137#327511yescharacteristic
509#23863C13711yesmaximal, characteristic, direct product factor, Sylow
510C137#2386311yescharacteristic, direct product factor, Sylow
511C22×AGL(1,ℤ/8)C2×C13711yescharacteristic, complemented
512C2×#546C2×C13711yescharacteristic, complemented
513C2×#452C2×C13711yescharacteristic, complemented
514C2×#452C2×C13711yescharacteristic, complemented
515C2×#449C2×C13711yescharacteristic, complemented
516#2407C2×C13711yescharacteristic, complemented
517#2015C2×C13711yescharacteristic, complemented
518#2012C2×C13711yescharacteristic, complemented
519#2000C2×C13711yescharacteristic, complemented
520#1999C2×C13711yescharacteristic, complemented
521#1894C2×C13711yescharacteristic, complemented
522#1879C2×C13711yescharacteristic, complemented
523#1877C2×C13711yescharacteristic, complemented
524#1870C2×C13711yescharacteristic, complemented
525#1786C2×C13711yescharacteristic, complemented
526C22×#41C22×C13711yescharacteristic
527C22×#41C22×C13711yescharacteristic
528C23×D4C22×C13711yescharacteristic
529C2×AGL(1,ℤ/8)—24no—
530C2×AGL(1,ℤ/8)—24no—
531C2×AGL(1,ℤ/8)—24no—
532C22×Q16C22×C13711yescharacteristic, complemented
533C22×SD16C22×C13711yescharacteristic
534C22×SD16C22×C13711yescharacteristic
535C22×SD16C22×C13711yescharacteristic, complemented
536C22×D8C22×C13711yescharacteristic
537C22×D8C22×C13711yescharacteristic
538C22×M16C22×C13711yescharacteristic
539#546—24no—
540#546—24no—
541C2×#124C22×C13711yescharacteristic
542C2×#123—21no—
543C2×C22⋊Q8C22×C13711yescharacteristic
544C2×C22⋊Q8C22×C13711yescharacteristic, complemented
545C2×#121—21no—
546C2×#121C22×C13711yescharacteristic
547C2×#121C22×C13711yescharacteristic, complemented
548C2×#120—21no—
549C2×C4×D4C22×C13711yescharacteristic
550C2×C4×D4C22×C13711yescharacteristic
551C22×C22⋊C4—21no—
552#452—24no—
553#452—24no—
554#449—24no—
555C2×#103C22×C13711yescharacteristic, complemented
556C2×#103C22×C13711yescharacteristic, complemented
557C2×#103C22×C13711yescharacteristic, complemented
558C2×#102C22×C13711yescharacteristic
559C2×#102C22×C13711yescharacteristic
560C2×#102C22×C13711yescharacteristic
561C2×#102C22×C13711yescharacteristic
562C2×#102C22×C13711yescharacteristic, complemented
563C2×C22⋊C8C22×C13711yescharacteristic
564C2×C22⋊C8C22×C13711yescharacteristic, complemented
565C2×C22⋊C8C22×C13711yescharacteristic, complemented
566#394—21no—
567#392—21no—
568#391C22×C13711yescharacteristic, complemented
569#390C22×C13711yescharacteristic, complemented
570#386—21no—
571#385—21no—
572#380C22×C13711yescharacteristic
573#340C22×C13711yescharacteristic, complemented
574#340C22×C13711yescharacteristic, complemented
575#336C22×C13711yescharacteristic, complemented
576#336C22×C13711yescharacteristic, complemented
577C25—21no—
578C2×#41—22no—
579C2×#41—22no—
580C2×#41—22no—
581C2×#41—22no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—22no—
586C2×#41—41no—
587C2×#41—41no—
588C2×#41—41no—
589C2×#41—41no—
590C22×Q8C23×C13711yescharacteristic
591C22×Q8C23×C13711yescharacteristic
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—41no—
601C22×D4—41no—
602C22×D4D4×C13711yescharacteristic
603C22×D4D4×C13714yescomplemented
604C22×D4C23×C13711yescharacteristic
605C22×D4C23×C13711yescharacteristic
606C22×D4C23×C13711yescharacteristic
607C23×C4—21no—
608C23×C4—21no—
609C23×C4—21no—
610C23×C4C23×C13711yescharacteristic
611C23×C4C23×C13711yescharacteristic
612AGL(1,ℤ/8)—232no—
613C2×Q16—22no—
614C2×Q16—22no—
615C2×Q16—41no—
616C2×SD16—22no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—22no—
620C2×SD16—22no—
621C2×SD16—22no—
622C2×SD16—22no—
623C2×SD16—41no—
624C2×SD16D4×C13714yescomplemented
625C2×D8—22no—
626C2×D8—22no—
627C2×D8—22no—
628C2×D8—22no—
629C2×D8—22no—
630C2×D8D4×C13714yescomplemented
631C2×M16—22no—
632C2×M16—22no—
633C2×M16—22no—
634C22×C8C23×C13711yescharacteristic
635C22×C8C23×C13711yescharacteristic
636C22×C8C23×C13711yescharacteristic
637C22×C8C23×C13711yescharacteristic
638#124—22no—
639#124—22no—
640#123—28no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—41no—
644C22⋊Q8D4×C13714yescomplemented
645#121—28no—
646#121—22no—
647#121—22no—
648#121—22no—
649#121—41no—
650#120—28no—
651C4×D4—22no—
652C4×D4—22no—
653C4×D4—22no—
654C4×D4—22no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4D4×C13711yescharacteristic
658C2×C4⋊C4C23×C13711yescharacteristic
659C2×C4⋊C4C23×C13711yescharacteristic
660C2×C4⋊C4C23×C13711yescharacteristic
661C2×C22⋊C4—28no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4D4×C13711yescharacteristic
673C2×C22⋊C4D4×C13711yescharacteristic
674C2×C42C23×C13711yescharacteristic
675#103—22no—
676#103—22no—
677#103—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—41no—
682#102—41no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—22no—
686#95—21no—
687#95—21no—
688#95—21no—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—24no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—81no—
698C24—81no—
699C24C2×D4×C13711yescharacteristic
700C24C2×D4×C13711yescharacteristic
701#41—28no—
702#41—44no—
703#41—44no—
704#41—44no—
705#41—44no—
706#41—44no—
707#41—44no—
708#41—44no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8—21no—
719C2×Q8C2×D4×C13712yes—
720C2×Q8C2×D4×C13712yes—
721C2×D4—28no—
722C2×D4—24no—
723C2×D4—22no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—44no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—41no—
743C2×D4—41no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—42no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4C2×D4×C13712yes—
757C2×D4C2×D4×C13712yes—
758C2×D4C2×D4×C13712yes—
759C2×D4C2×D4×C13712yes—
760C2×D4C2×D4×C13712yes—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—24no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—24no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—42no—
779C22×C4—42no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—42no—
783C22×C4—81no—
784C22×C4—81no—
785C22×C4C2×D4×C13711yescharacteristic
786C22×C4C2×D4×C13711yescharacteristic
787C22×C4C2×D4×C13711yescharacteristic
788C22×C4C2×D4×C13711yescharacteristic
789C22×C4C2×D4×C13712yes—
790C22×C4C2×D4×C13712yes—
791C22×C4C24×C13711yescharacteristic
792Q16—44no—
793SD16—28no—
794SD16—28no—
795SD16—44no—
796D8—28no—
797D8—28no—
798M16—28no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8C2×D4×C13712yes—
810C2×C8C2×D4×C13712yes—
811C4⋊C4—24no—
812C4⋊C4—22no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C13712yes—
820C22⋊C4—24no—
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—24no—
824C22⋊C4—22no—
825C22⋊C4—24no—
826C22⋊C4—22no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C22⋊C4—81no—
832C42—21no—
833C42—21no—
834C23—22no—
835C23—21no—
836C23—21no—
837C23—22no—
838C23—22no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—21no—
843C23—22no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—48no—
853C23—48no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23#120×C13712yes—
876C23C22×D4×C13711yescharacteristic
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—22no—
881Q8—41no—
882Q8—41no—
883Q8—41no—
884Q8—41no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—22no—
892D4—48no—
893D4—48no—
894D4—44no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—84no—
901D4—84no—
902D4#120×C13714yes—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—22no—
912C2×C4—21no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—21no—
921C2×C4—48no—
922C2×C4—48no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—84no—
940C2×C4#120×C13712yes—
941C2×C4C22×D4×C13711yescharacteristic
942C2×C4C22×D4×C13711yescharacteristic
943C2×C4C22×D4×C13711yescharacteristic
944C2×C4C22×D4×C13711yescharacteristic
945C2×C4H(5,𝔽2)×C13711yescharacteristic
946C2×C4H(5,𝔽2)×C13711yescharacteristic
947C8—22no—
948C8—22no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—24no—
953C22—22no—
954C22—22no—
955C22—42no—
956C22—41no—
957C22—42no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—42no—
965C22—42no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—41no—
973C22—42no—
974C22—41no—
975C22—41no—
976C22—42no—
977C22—41no—
978C22—816no—
979C22—81no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22C2×#120×C13711yescharacteristic
988C22D42×C13711yescharacteristic
989C22D42×C13711yescharacteristic
990C22#575×C13711yescharacteristic
991C22#575×C13711yescharacteristic
992C22#576×C13711yescharacteristic
993C22#577×C13711yescharacteristic
994C4—22no—
995C4—41no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C13711yescharacteristic
1004C4#534×C13711yescharacteristic
1005C4D42×C13711yescharacteristic
1006C4D42×C13711yescharacteristic
1007C2—42no—
1008C2—44no—
1009C2—81no—
1010C2—82no—
1011C2—82no—
1012C2#2403×C13711yescharacteristic
1013C2#3005×C13711yescharacteristic
1014C2#3012×C13711yescharacteristic
1015C2#3267×C13711yescharacteristic
1016C2#3268×C13711yescharacteristic
1017C2#3273×C13711yescharacteristic
1018C2#3275×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. C22×AGL(1,ℤ/8)×C137C2semidirect
2. C2×#546×C137C2semidirect
3. C2×#452×C137C2semidirect
4. C2×#452×C137C2semidirect
5. C2×#449×C137C2semidirect
6. #2407×C137C2semidirect
7. #2015×C137C2semidirect
8. #2012×C137C2semidirect
9. #2000×C137C2semidirect
10. #1999×C137C2semidirect
11. #1894×C137C2semidirect
12. #1879×C137C2semidirect
13. #1877×C137C2semidirect
14. #1870×C137C2semidirect
15. #1786×C137C2semidirect
22. C22×Q16×C137C22semidirect
25. C22×SD16×C137C22semidirect
34. C2×C22⋊Q8×C137C22semidirect
37. C2×#121×C137C22semidirect
45. C2×#103×C137C22semidirect
46. C2×#103×C137C22semidirect
47. C2×#103×C137C22semidirect
52. C2×#102×C137C22semidirect
54. C2×C22⋊C8×C137C22semidirect
55. C2×C22⋊C8×C137C22semidirect
58. #391×C137C22semidirect
59. #390×C137C22semidirect
63. #340×C137C22semidirect
64. #340×C137C22semidirect
65. #336×C137C22semidirect
66. #336×C137C22semidirect
93. C22×D4×C137D4semidirect
114. C2×SD16×C137D4semidirect
120. C2×D8×C137D4semidirect
134. C22⋊Q8×C137D4semidirect
509. #23863C137direct (N × H)
510. C137#23863direct (N × H)
511. C22×AGL(1,ℤ/8)C2×C137semidirect
512. C2×#546C2×C137semidirect
513. C2×#452C2×C137semidirect
514. C2×#452C2×C137semidirect
515. C2×#449C2×C137semidirect
516. #2407C2×C137semidirect
517. #2015C2×C137semidirect
518. #2012C2×C137semidirect
519. #2000C2×C137semidirect
520. #1999C2×C137semidirect
521. #1894C2×C137semidirect
522. #1879C2×C137semidirect
523. #1877C2×C137semidirect
524. #1870C2×C137semidirect
525. #1786C2×C137semidirect
532. C22×Q16C22×C137semidirect
535. C22×SD16C22×C137semidirect
544. C2×C22⋊Q8C22×C137semidirect
547. C2×#121C22×C137semidirect
555. C2×#103C22×C137semidirect
556. C2×#103C22×C137semidirect
557. C2×#103C22×C137semidirect
562. C2×#102C22×C137semidirect
564. C2×C22⋊C8C22×C137semidirect
565. C2×C22⋊C8C22×C137semidirect
568. #391C22×C137semidirect
569. #390C22×C137semidirect
573. #340C22×C137semidirect
574. #340C22×C137semidirect
575. #336C22×C137semidirect
576. #336C22×C137semidirect
603. C22×D4D4×C137semidirect
624. C2×SD16D4×C137semidirect
630. C2×D8D4×C137semidirect
644. C22⋊Q8D4×C137semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1372
C2×#546×C1372
C2×#452×C1372
C2×#449×C1372
#2407×C1372
#2015×C1372
#2012×C1372
#2000×C1372
#1999×C1372
#1894×C1372
#1879×C1372
#1877×C1372
#1870×C1372
#1786×C1372
#23863137