Finite Group Databasebeta

← C137×#23860 #46873246

Subgroups — C137×#23860 #46873246

Order 35072.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 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×D42×C137C211yesmaximal, characteristic, complemented
3C2×#449×C137C211yesmaximal, characteristic, complemented
4C2×#450×C137C211yesmaximal, characteristic, complemented
5C2×#447×C137C211yesmaximal, characteristic, complemented
6#2407×C137C211yesmaximal, characteristic, complemented
7#2014×C137C211yesmaximal, characteristic, complemented
8#2011×C137C211yesmaximal, characteristic, complemented
9#2000×C137C211yesmaximal, characteristic, complemented
10#1999×C137C211yesmaximal, characteristic, complemented
11#1895×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, complemented
17C23×D4×C137—21no—
18C23×D4×C137C2211yescharacteristic
19C23×D4×C137C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C137—24no—
21C2×AGL(1,ℤ/8)×C137—24no—
22C2×AGL(1,ℤ/8)×C137—24no—
23C22×SD16×C137C2211yescharacteristic
24C22×SD16×C137C2211yescharacteristic, complemented
25C22×SD16×C137C2211yescharacteristic, complemented
26C22×D8×C137C2211yescharacteristic
27C22×D8×C137C2211yescharacteristic, complemented
28C22×D8×C137C2211yescharacteristic, complemented
29C22×M16×C137C2211yescharacteristic, complemented
30D42×C137—24no—
31D42×C137—24no—
32C2×#127×C137C2211yescharacteristic
33C2×C22⋊Q8×C137C2211yescharacteristic, complemented
34C2×#121×C137—21no—
35C2×#121×C137C2211yescharacteristic
36C2×#121×C137C2211yescharacteristic
37C2×#121×C137C2211yescharacteristic, complemented
38C2×#120×C137—21no—
39C2×#120×C137—21no—
40C2×C4×D4×C137C2211yescharacteristic
41C2×C4×D4×C137C2211yescharacteristic
42#450×C137—24no—
43#449×C137—24no—
44#447×C137—24no—
45C2×#103×C137C2211yescharacteristic, complemented
46C2×#102×C137C2211yescharacteristic
47C2×#102×C137C2211yescharacteristic
48C2×#102×C137C2211yescharacteristic, complemented
49C2×#102×C137C2211yescharacteristic, complemented
50C2×#102×C137C2211yescharacteristic, complemented
51C2×#102×C137C2211yescharacteristic, complemented
52C2×#102×C137C2211yescharacteristic, complemented
53C2×C22⋊C8×C137C2211yescharacteristic, complemented
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, complemented
63#340×C137C2211yescharacteristic, complemented
64#340×C137C2211yescharacteristic, complemented
65#336×C137C2211yescharacteristic, complemented
66#336×C137C2211yescharacteristic, complemented
67C25×C137—21no—
68C25×C137—21no—
69C2×#41×C137—22no—
70C2×#41×C137—22no—
71C2×#41×C137—22no—
72C2×#41×C137—22no—
73C2×#41×C137—41no—
74C2×#41×C137—41no—
75C22×Q8×C137C2311yescharacteristic
76C22×D4×C137—22no—
77C22×D4×C137—22no—
78C22×D4×C137—28no—
79C22×D4×C137—21no—
80C22×D4×C137—21no—
81C22×D4×C137—22no—
82C22×D4×C137—22no—
83C22×D4×C137—22no—
84C22×D4×C137—22no—
85C22×D4×C137—21no—
86C22×D4×C137—21no—
87C22×D4×C137—21no—
88C22×D4×C137—21no—
89C22×D4×C137—21no—
90C22×D4×C137—22no—
91C22×D4×C137—21no—
92C22×D4×C137—41no—
93C22×D4×C137—41no—
94C22×D4×C137—41no—
95C22×D4×C137—41no—
96C22×D4×C137—44no—
97C22×D4×C137—44no—
98C22×D4×C137D411yescharacteristic
99C22×D4×C137D414yescomplemented
100C22×D4×C137C2311yescharacteristic
101C22×D4×C137C2311yescharacteristic
102C22×D4×C137C2311yescharacteristic
103C22×D4×C137C2311yescharacteristic
104C23×C4×C137—21no—
105C23×C4×C137—21no—
106C23×C4×C137C2311yescharacteristic
107C23×C4×C137C2311yescharacteristic
108AGL(1,ℤ/8)×C137—232no—
109C2×SD16×C137—22no—
110C2×SD16×C137—22no—
111C2×SD16×C137—22no—
112C2×SD16×C137—22no—
113C2×SD16×C137—22no—
114C2×SD16×C137—22no—
115C2×SD16×C137—22no—
116C2×SD16×C137—41no—
117C2×SD16×C137D414yescomplemented
118C2×D8×C137—22no—
119C2×D8×C137—22no—
120C2×D8×C137—22no—
121C2×D8×C137—22no—
122C2×D8×C137—22no—
123C2×D8×C137—22no—
124C2×D8×C137—22no—
125C2×D8×C137—41no—
126C2×D8×C137D414yescomplemented
127C2×M16×C137—22no—
128C2×M16×C137—22no—
129C2×M16×C137—22no—
130C22×C8×C137C2311yescharacteristic
131C22×C8×C137C2311yescharacteristic
132C22×C8×C137C2311yescharacteristic
133C22×C8×C137C2311yescharacteristic
134#127×C137—22no—
135#127×C137—22no—
136C22⋊Q8×C137—22no—
137C22⋊Q8×C137—41no—
138#121×C137—28no—
139#121×C137—22no—
140#121×C137—22no—
141#121×C137—22no—
142#121×C137—22no—
143#121×C137—41no—
144#121×C137D414yescomplemented
145#120×C137—28no—
146#120×C137—28no—
147C4×D4×C137—22no—
148C4×D4×C137—22no—
149C4×D4×C137—22no—
150C4×D4×C137—22no—
151C2×C4⋊C4×C137—21no—
152C2×C4⋊C4×C137D411yescharacteristic
153C2×C4⋊C4×C137C2311yescharacteristic
154C2×C4⋊C4×C137C2311yescharacteristic
155C2×C4⋊C4×C137C2311yescharacteristic
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×C137—21no—
163C2×C22⋊C4×C137—21no—
164C2×C22⋊C4×C137D411yescharacteristic
165C2×C22⋊C4×C137D411yescharacteristic
166C2×C42×C137C2311yescharacteristic
167#103×C137—22no—
168#102×C137—22no—
169#102×C137—22no—
170#102×C137—22no—
171#102×C137—22no—
172#102×C137—22no—
173#102×C137—41no—
174#102×C137—41no—
175C22⋊C8×C137—22no—
176C22⋊C8×C137—22no—
177C22⋊C8×C137—22no—
178#95×C137—21no—
179#95×C137—21no—
180#95×C137—21no—
181C24×C137—21no—
182C24×C137—24no—
183C24×C137—21no—
184C24×C137—21no—
185C24×C137—21no—
186C24×C137—24no—
187C24×C137—42no—
188C24×C137—42no—
189C24×C137—42no—
190C24×C137—42no—
191C24×C137—42no—
192C24×C137—42no—
193C24×C137—42no—
194C24×C137—42no—
195C24×C137—81no—
196C24×C137—81no—
197C24×C137—81no—
198C24×C137—81no—
199C24×C137C2×D411yescharacteristic
200C24×C137C2×D411yescharacteristic
201#41×C137—28no—
202#41×C137—44no—
203#41×C137—44no—
204#41×C137—44no—
205C2×Q8×C137—21no—
206C2×Q8×C137—21no—
207C2×Q8×C137—21no—
208C2×Q8×C137—21no—
209C2×Q8×C137—21no—
210C2×Q8×C137C2×D412yescomplemented
211C2×D4×C137—22no—
212C2×D4×C137—22no—
213C2×D4×C137—28no—
214C2×D4×C137—24no—
215C2×D4×C137—24no—
216C2×D4×C137—24no—
217C2×D4×C137—24no—
218C2×D4×C137—24no—
219C2×D4×C137—24no—
220C2×D4×C137—22no—
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—21no—
230C2×D4×C137—21no—
231C2×D4×C137—21no—
232C2×D4×C137—21no—
233C2×D4×C137—21no—
234C2×D4×C137—21no—
235C2×D4×C137—21no—
236C2×D4×C137—21no—
237C2×D4×C137—21no—
238C2×D4×C137—21no—
239C2×D4×C137—44no—
240C2×D4×C137—44no—
241C2×D4×C137—44no—
242C2×D4×C137—42no—
243C2×D4×C137—42no—
244C2×D4×C137—42no—
245C2×D4×C137—42no—
246C2×D4×C137—42no—
247C2×D4×C137—42no—
248C2×D4×C137—44no—
249C2×D4×C137—44no—
250C2×D4×C137—432no—
251C2×D4×C137—44no—
252C2×D4×C137—42no—
253C2×D4×C137—42no—
254C2×D4×C137—42no—
255C2×D4×C137—42no—
256C2×D4×C137—42no—
257C2×D4×C137—42no—
258C2×D4×C137—44no—
259C2×D4×C137—42no—
260C2×D4×C137—42no—
261C2×D4×C137—42no—
262C2×D4×C137—81no—
263C2×D4×C137—81no—
264C2×D4×C137—81no—
265C2×D4×C137C2×D412yes—
266C2×D4×C137C2×D412yes—
267C2×D4×C137C2×D412yes—
268C2×D4×C137C2×D412yes—
269C2×D4×C137C2×D412yes—
270C2×D4×C137C2×D412yescomplemented
271C22×C4×C137—21no—
272C22×C4×C137—21no—
273C22×C4×C137—21no—
274C22×C4×C137—21no—
275C22×C4×C137—24no—
276C22×C4×C137—21no—
277C22×C4×C137—21no—
278C22×C4×C137—21no—
279C22×C4×C137—21no—
280C22×C4×C137—21no—
281C22×C4×C137—21no—
282C22×C4×C137—21no—
283C22×C4×C137—21no—
284C22×C4×C137—21no—
285C22×C4×C137—21no—
286C22×C4×C137—42no—
287C22×C4×C137—42no—
288C22×C4×C137—42no—
289C22×C4×C137—42no—
290C22×C4×C137—42no—
291C22×C4×C137C2×D411yescharacteristic
292C22×C4×C137C2×D411yescharacteristic
293C22×C4×C137C2×D411yescharacteristic
294C22×C4×C137C2×D412yes—
295C22×C4×C137C2×D412yes—
296C22×C4×C137C2×D411yescharacteristic
297C22×C4×C137C2411yescharacteristic
298SD16×C137—28no—
299SD16×C137—28no—
300SD16×C137—44no—
301D8×C137—28no—
302D8×C137—28no—
303D8×C137—44no—
304M16×C137—28no—
305C2×C8×C137—21no—
306C2×C8×C137—21no—
307C2×C8×C137—21no—
308C2×C8×C137—21no—
309C2×C8×C137—21no—
310C2×C8×C137—21no—
311C2×C8×C137—21no—
312C2×C8×C137—21no—
313C2×C8×C137—21no—
314C2×C8×C137—21no—
315C2×C8×C137C2×D412yescomplemented
316C2×C8×C137C2×D412yescomplemented
317C4⋊C4×C137—22no—
318C4⋊C4×C137—21no—
319C4⋊C4×C137—21no—
320C4⋊C4×C137—21no—
321C4⋊C4×C137—21no—
322C4⋊C4×C137—21no—
323C4⋊C4×C137—42no—
324C4⋊C4×C137C2×D412yes—
325C22⋊C4×C137—24no—
326C22⋊C4×C137—24no—
327C22⋊C4×C137—22no—
328C22⋊C4×C137—24no—
329C22⋊C4×C137—22no—
330C22⋊C4×C137—42no—
331C22⋊C4×C137—42no—
332C22⋊C4×C137—42no—
333C22⋊C4×C137—81no—
334C22⋊C4×C137—81no—
335C42×C137—21no—
336C42×C137—21no—
337C23×C137—21no—
338C23×C137—22no—
339C23×C137—21no—
340C23×C137—21no—
341C23×C137—21no—
342C23×C137—21no—
343C23×C137—22no—
344C23×C137—22no—
345C23×C137—21no—
346C23×C137—21no—
347C23×C137—21no—
348C23×C137—21no—
349C23×C137—21no—
350C23×C137—21no—
351C23×C137—21no—
352C23×C137—22no—
353C23×C137—22no—
354C23×C137—22no—
355C23×C137—48no—
356C23×C137—48no—
357C23×C137—48no—
358C23×C137—48no—
359C23×C137—41no—
360C23×C137—41no—
361C23×C137—41no—
362C23×C137—41no—
363C23×C137—41no—
364C23×C137—41no—
365C23×C137—41no—
366C23×C137—41no—
367C23×C137—41no—
368C23×C137—41no—
369C23×C137—41no—
370C23×C137—41no—
371C23×C137—41no—
372C23×C137—41no—
373C23×C137—41no—
374C23×C137—41no—
375C23×C137—41no—
376C23×C137—41no—
377C23×C137—41no—
378C23×C137—41no—
379C23×C137—41no—
380C23×C137—41no—
381C23×C137—84no—
382C23×C137—84no—
383C23×C137—84no—
384C23×C137—84no—
385C23×C137—84no—
386C23×C137—84no—
387C23×C137—84no—
388C23×C137—84no—
389C23×C137—84no—
390C23×C137—84no—
391C23×C137#12012yes—
392C23×C137AGL(1,ℤ/8)12yescomplemented
393C23×C137C22×D411yescharacteristic
394Q8×C137—22no—
395Q8×C137—22no—
396Q8×C137—41no—
397Q8×C137—41no—
398D4×C137—28no—
399D4×C137—22no—
400D4×C137—22no—
401D4×C137—22no—
402D4×C137—22no—
403D4×C137—22no—
404D4×C137—22no—
405D4×C137—22no—
406D4×C137—22no—
407D4×C137—22no—
408D4×C137—48no—
409D4×C137—48no—
410D4×C137—48no—
411D4×C137—48no—
412D4×C137—48no—
413D4×C137—48no—
414D4×C137—41no—
415D4×C137—41no—
416D4×C137—41no—
417D4×C137—41no—
418D4×C137—41no—
419D4×C137—41no—
420D4×C137—84no—
421D4×C137—84no—
422D4×C137#12014yes—
423C2×C4×C137—21no—
424C2×C4×C137—21no—
425C2×C4×C137—21no—
426C2×C4×C137—21no—
427C2×C4×C137—22no—
428C2×C4×C137—22no—
429C2×C4×C137—22no—
430C2×C4×C137—22no—
431C2×C4×C137—21no—
432C2×C4×C137—21no—
433C2×C4×C137—22no—
434C2×C4×C137—21no—
435C2×C4×C137—22no—
436C2×C4×C137—21no—
437C2×C4×C137—21no—
438C2×C4×C137—21no—
439C2×C4×C137—48no—
440C2×C4×C137—48no—
441C2×C4×C137—41no—
442C2×C4×C137—41no—
443C2×C4×C137—41no—
444C2×C4×C137—41no—
445C2×C4×C137—41no—
446C2×C4×C137—41no—
447C2×C4×C137—41no—
448C2×C4×C137—41no—
449C2×C4×C137—41no—
450C2×C4×C137—41no—
451C2×C4×C137—41no—
452C2×C4×C137—41no—
453C2×C4×C137—41no—
454C2×C4×C137—41no—
455C2×C4×C137#12012yes—
456C2×C4×C137AGL(1,ℤ/8)12yescomplemented
457C2×C4×C137C22×D411yescharacteristic
458C2×C4×C137C22×D411yescharacteristic
459C2×C4×C137C22×D411yescharacteristic
460C2×C4×C137C22×D411yescharacteristic
461C2×C4×C137H(5,𝔽2)11yescharacteristic
462C2×C4×C137H(5,𝔽2)11yescharacteristic
463C8×C137—22no—
464C8×C137—22no—
465C8×C137—41no—
466C8×C137—41no—
467C22×C137—22no—
468C22×C137—24no—
469C22×C137—22no—
470C22×C137—22no—
471C22×C137—22no—
472C22×C137—22no—
473C22×C137—22no—
474C22×C137—41no—
475C22×C137—42no—
476C22×C137—41no—
477C22×C137—42no—
478C22×C137—41no—
479C22×C137—42no—
480C22×C137—41no—
481C22×C137—42no—
482C22×C137—41no—
483C22×C137—41no—
484C22×C137—42no—
485C22×C137—41no—
486C22×C137—41no—
487C22×C137—42no—
488C22×C137—42no—
489C22×C137—42no—
490C22×C137—42no—
491C22×C137—42no—
492C22×C137—42no—
493C22×C137—42no—
494C22×C137—42no—
495C22×C137—42no—
496C22×C137—42no—
497C22×C137—816no—
498C22×C137—816no—
499C22×C137—81no—
500C22×C137—81no—
501C22×C137—81no—
502C22×C137—81no—
503C22×C137—81no—
504C22×C137—81no—
505C22×C137—81no—
506C22×C137—81no—
507C22×C137—81no—
508C22×C137—81no—
509C22×C137—81no—
510C22×C137—81no—
511C22×C137C2×#12011yescharacteristic
512C22×C137D4211yescharacteristic
513C22×C137D4211yescharacteristic
514C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
515C22×C137C2×AGL(1,ℤ/8)11yescharacteristic
516C22×C137#57611yescharacteristic
517C22×C137#57711yescharacteristic
518C4×C137—22no—
519C4×C137—22no—
520C4×C137—41no—
521C4×C137—42no—
522C4×C137—42no—
523C4×C137—41no—
524C4×C137—81no—
525C4×C137—81no—
526C4×C137C2×#12011yescharacteristic
527C4×C137#53411yescharacteristic
528C4×C137D4211yescharacteristic
529C4×C137D4211yescharacteristic
530C2×C137—42no—
531C2×C137—42no—
532C2×C137—44no—
533C2×C137—82no—
534C2×C137—82no—
535C2×C137—82no—
536C2×C137#240311yescharacteristic
537C2×C137#300311yescharacteristic
538C2×C137#301211yescharacteristic
539C2×C137#326411yescharacteristic
540C2×C137#326511yescharacteristic
541C2×C137#327211yescharacteristic
542C2×C137#327411yescharacteristic
543#23860C13711yesmaximal, characteristic, direct product factor, Sylow
544C137#2386011yescharacteristic, direct product factor, Sylow
545C22×AGL(1,ℤ/8)C2×C13711yescharacteristic, complemented
546C2×D42C2×C13711yescharacteristic, complemented
547C2×#449C2×C13711yescharacteristic, complemented
548C2×#450C2×C13711yescharacteristic, complemented
549C2×#447C2×C13711yescharacteristic, complemented
550#2407C2×C13711yescharacteristic, complemented
551#2014C2×C13711yescharacteristic, complemented
552#2011C2×C13711yescharacteristic, complemented
553#2000C2×C13711yescharacteristic, complemented
554#1999C2×C13711yescharacteristic, complemented
555#1895C2×C13711yescharacteristic, complemented
556#1879C2×C13711yescharacteristic, complemented
557#1877C2×C13711yescharacteristic, complemented
558#1870C2×C13711yescharacteristic, complemented
559#1786C2×C13711yescharacteristic, complemented
560C22×#41C22×C13711yescharacteristic, complemented
561C23×D4—21no—
562C23×D4C22×C13711yescharacteristic
563C23×D4C22×C13711yescharacteristic
564C2×AGL(1,ℤ/8)—24no—
565C2×AGL(1,ℤ/8)—24no—
566C2×AGL(1,ℤ/8)—24no—
567C22×SD16C22×C13711yescharacteristic
568C22×SD16C22×C13711yescharacteristic, complemented
569C22×SD16C22×C13711yescharacteristic, complemented
570C22×D8C22×C13711yescharacteristic
571C22×D8C22×C13711yescharacteristic, complemented
572C22×D8C22×C13711yescharacteristic, complemented
573C22×M16C22×C13711yescharacteristic, complemented
574D42—24no—
575D42—24no—
576C2×#127C22×C13711yescharacteristic
577C2×C22⋊Q8C22×C13711yescharacteristic, complemented
578C2×#121—21no—
579C2×#121C22×C13711yescharacteristic
580C2×#121C22×C13711yescharacteristic
581C2×#121C22×C13711yescharacteristic, complemented
582C2×#120—21no—
583C2×#120—21no—
584C2×C4×D4C22×C13711yescharacteristic
585C2×C4×D4C22×C13711yescharacteristic
586#450—24no—
587#449—24no—
588#447—24no—
589C2×#103C22×C13711yescharacteristic, complemented
590C2×#102C22×C13711yescharacteristic
591C2×#102C22×C13711yescharacteristic
592C2×#102C22×C13711yescharacteristic, complemented
593C2×#102C22×C13711yescharacteristic, complemented
594C2×#102C22×C13711yescharacteristic, complemented
595C2×#102C22×C13711yescharacteristic, complemented
596C2×#102C22×C13711yescharacteristic, complemented
597C2×C22⋊C8C22×C13711yescharacteristic, complemented
598C2×C22⋊C8C22×C13711yescharacteristic, complemented
599C2×C22⋊C8C22×C13711yescharacteristic, complemented
600#394—21no—
601#392—21no—
602#391C22×C13711yescharacteristic, complemented
603#390C22×C13711yescharacteristic, complemented
604#386—21no—
605#385—21no—
606#380C22×C13711yescharacteristic, complemented
607#340C22×C13711yescharacteristic, complemented
608#340C22×C13711yescharacteristic, complemented
609#336C22×C13711yescharacteristic, complemented
610#336C22×C13711yescharacteristic, complemented
611C25—21no—
612C25—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C22×Q8C23×C13711yescharacteristic
620C22×D4—22no—
621C22×D4—22no—
622C22×D4—28no—
623C22×D4—21no—
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4—21no—
632C22×D4—21no—
633C22×D4—21no—
634C22×D4—22no—
635C22×D4—21no—
636C22×D4—41no—
637C22×D4—41no—
638C22×D4—41no—
639C22×D4—41no—
640C22×D4—44no—
641C22×D4—44no—
642C22×D4D4×C13711yescharacteristic
643C22×D4D4×C13714yescomplemented
644C22×D4C23×C13711yescharacteristic
645C22×D4C23×C13711yescharacteristic
646C22×D4C23×C13711yescharacteristic
647C22×D4C23×C13711yescharacteristic
648C23×C4—21no—
649C23×C4—21no—
650C23×C4C23×C13711yescharacteristic
651C23×C4C23×C13711yescharacteristic
652AGL(1,ℤ/8)—232no—
653C2×SD16—22no—
654C2×SD16—22no—
655C2×SD16—22no—
656C2×SD16—22no—
657C2×SD16—22no—
658C2×SD16—22no—
659C2×SD16—22no—
660C2×SD16—41no—
661C2×SD16D4×C13714yescomplemented
662C2×D8—22no—
663C2×D8—22no—
664C2×D8—22no—
665C2×D8—22no—
666C2×D8—22no—
667C2×D8—22no—
668C2×D8—22no—
669C2×D8—41no—
670C2×D8D4×C13714yescomplemented
671C2×M16—22no—
672C2×M16—22no—
673C2×M16—22no—
674C22×C8C23×C13711yescharacteristic
675C22×C8C23×C13711yescharacteristic
676C22×C8C23×C13711yescharacteristic
677C22×C8C23×C13711yescharacteristic
678#127—22no—
679#127—22no—
680C22⋊Q8—22no—
681C22⋊Q8—41no—
682#121—28no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—41no—
688#121D4×C13714yescomplemented
689#120—28no—
690#120—28no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4D4×C13711yescharacteristic
697C2×C4⋊C4C23×C13711yescharacteristic
698C2×C4⋊C4C23×C13711yescharacteristic
699C2×C4⋊C4C23×C13711yescharacteristic
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4D4×C13711yescharacteristic
709C2×C22⋊C4D4×C13711yescharacteristic
710C2×C42C23×C13711yescharacteristic
711#103—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—41no—
718#102—41no—
719C22⋊C8—22no—
720C22⋊C8—22no—
721C22⋊C8—22no—
722#95—21no—
723#95—21no—
724#95—21no—
725C24—21no—
726C24—24no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—24no—
731C24—42no—
732C24—42no—
733C24—42no—
734C24—42no—
735C24—42no—
736C24—42no—
737C24—42no—
738C24—42no—
739C24—81no—
740C24—81no—
741C24—81no—
742C24—81no—
743C24C2×D4×C13711yescharacteristic
744C24C2×D4×C13711yescharacteristic
745#41—28no—
746#41—44no—
747#41—44no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8C2×D4×C13712yescomplemented
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—28no—
758C2×D4—24no—
759C2×D4—24no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—24no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—44no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—432no—
795C2×D4—44no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—44no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4C2×D4×C13712yes—
810C2×D4C2×D4×C13712yes—
811C2×D4C2×D4×C13712yes—
812C2×D4C2×D4×C13712yes—
813C2×D4C2×D4×C13712yes—
814C2×D4C2×D4×C13712yescomplemented
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—24no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4C2×D4×C13711yescharacteristic
836C22×C4C2×D4×C13711yescharacteristic
837C22×C4C2×D4×C13711yescharacteristic
838C22×C4C2×D4×C13712yes—
839C22×C4C2×D4×C13712yes—
840C22×C4C2×D4×C13711yescharacteristic
841C22×C4C24×C13711yescharacteristic
842SD16—28no—
843SD16—28no—
844SD16—44no—
845D8—28no—
846D8—28no—
847D8—44no—
848M16—28no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C13712yescomplemented
860C2×C8C2×D4×C13712yescomplemented
861C4⋊C4—22no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4C2×D4×C13712yes—
869C22⋊C4—24no—
870C22⋊C4—24no—
871C22⋊C4—22no—
872C22⋊C4—24no—
873C22⋊C4—22no—
874C22⋊C4—42no—
875C22⋊C4—42no—
876C22⋊C4—42no—
877C22⋊C4—81no—
878C22⋊C4—81no—
879C42—21no—
880C42—21no—
881C23—21no—
882C23—22no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—22no—
888C23—22no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—48no—
900C23—48no—
901C23—48no—
902C23—48no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—84no—
926C23—84no—
927C23—84no—
928C23—84no—
929C23—84no—
930C23—84no—
931C23—84no—
932C23—84no—
933C23—84no—
934C23—84no—
935C23#120×C13712yes—
936C23AGL(1,ℤ/8)×C13712yescomplemented
937C23C22×D4×C13711yescharacteristic
938Q8—22no—
939Q8—22no—
940Q8—41no—
941Q8—41no—
942D4—28no—
943D4—22no—
944D4—22no—
945D4—22no—
946D4—22no—
947D4—22no—
948D4—22no—
949D4—22no—
950D4—22no—
951D4—22no—
952D4—48no—
953D4—48no—
954D4—48no—
955D4—48no—
956D4—48no—
957D4—48no—
958D4—41no—
959D4—41no—
960D4—41no—
961D4—41no—
962D4—41no—
963D4—41no—
964D4—84no—
965D4—84no—
966D4#120×C13714yes—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—22no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4#120×C13712yes—
1000C2×C4AGL(1,ℤ/8)×C13712yescomplemented
1001C2×C4C22×D4×C13711yescharacteristic
1002C2×C4C22×D4×C13711yescharacteristic
1003C2×C4C22×D4×C13711yescharacteristic
1004C2×C4C22×D4×C13711yescharacteristic
1005C2×C4H(5,𝔽2)×C13711yescharacteristic
1006C2×C4H(5,𝔽2)×C13711yescharacteristic
1007C8—22no—
1008C8—22no—
1009C8—41no—
1010C8—41no—
1011C22—22no—
1012C22—24no—
1013C22—22no—
1014C22—22no—
1015C22—22no—
1016C22—22no—
1017C22—22no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—42no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—42no—
1026C22—41no—
1027C22—41no—
1028C22—42no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—42no—
1038C22—42no—
1039C22—42no—
1040C22—42no—
1041C22—816no—
1042C22—816no—
1043C22—81no—
1044C22—81no—
1045C22—81no—
1046C22—81no—
1047C22—81no—
1048C22—81no—
1049C22—81no—
1050C22—81no—
1051C22—81no—
1052C22—81no—
1053C22—81no—
1054C22—81no—
1055C22C2×#120×C13711yescharacteristic
1056C22D42×C13711yescharacteristic
1057C22D42×C13711yescharacteristic
1058C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
1059C22C2×AGL(1,ℤ/8)×C13711yescharacteristic
1060C22#576×C13711yescharacteristic
1061C22#577×C13711yescharacteristic
1062C4—22no—
1063C4—22no—
1064C4—41no—
1065C4—42no—
1066C4—42no—
1067C4—41no—
1068C4—81no—
1069C4—81no—
1070C4C2×#120×C13711yescharacteristic
1071C4#534×C13711yescharacteristic
1072C4D42×C13711yescharacteristic
1073C4D42×C13711yescharacteristic
1074C2—42no—
1075C2—42no—
1076C2—44no—
1077C2—82no—
1078C2—82no—
1079C2—82no—
1080C2#2403×C13711yescharacteristic
1081C2#3003×C13711yescharacteristic
1082C2#3012×C13711yescharacteristic
1083C2#3264×C13711yescharacteristic
1084C2#3265×C13711yescharacteristic
1085C2#3272×C13711yescharacteristic
1086C2#3274×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×D42×C137C2semidirect
3. C2×#449×C137C2semidirect
4. C2×#450×C137C2semidirect
5. C2×#447×C137C2semidirect
6. #2407×C137C2semidirect
7. #2014×C137C2semidirect
8. #2011×C137C2semidirect
9. #2000×C137C2semidirect
10. #1999×C137C2semidirect
11. #1895×C137C2semidirect
12. #1879×C137C2semidirect
13. #1877×C137C2semidirect
14. #1870×C137C2semidirect
15. #1786×C137C2semidirect
16. C22×#41×C137C22semidirect
24. C22×SD16×C137C22semidirect
25. C22×SD16×C137C22semidirect
27. C22×D8×C137C22semidirect
28. C22×D8×C137C22semidirect
29. C22×M16×C137C22semidirect
33. C2×C22⋊Q8×C137C22semidirect
37. C2×#121×C137C22semidirect
45. C2×#103×C137C22semidirect
48. C2×#102×C137C22semidirect
49. C2×#102×C137C22semidirect
50. C2×#102×C137C22semidirect
51. C2×#102×C137C22semidirect
52. C2×#102×C137C22semidirect
53. C2×C22⋊C8×C137C22semidirect
54. C2×C22⋊C8×C137C22semidirect
55. C2×C22⋊C8×C137C22semidirect
58. #391×C137C22semidirect
59. #390×C137C22semidirect
62. #380×C137C22semidirect
63. #340×C137C22semidirect
64. #340×C137C22semidirect
65. #336×C137C22semidirect
66. #336×C137C22semidirect
99. C22×D4×C137D4semidirect
117. C2×SD16×C137D4semidirect
126. C2×D8×C137D4semidirect
144. #121×C137D4semidirect
210. C2×Q8×C137C2×D4semidirect
270. C2×D4×C137C2×D4semidirect
315. C2×C8×C137C2×D4semidirect
316. C2×C8×C137C2×D4semidirect
392. C23×C137AGL(1,ℤ/8)semidirect
456. C2×C4×C137AGL(1,ℤ/8)semidirect
543. #23860C137direct (N × H)
544. C137#23860direct (N × H)
545. C22×AGL(1,ℤ/8)C2×C137semidirect
546. C2×D42C2×C137semidirect
547. C2×#449C2×C137semidirect
548. C2×#450C2×C137semidirect
549. C2×#447C2×C137semidirect
550. #2407C2×C137semidirect
551. #2014C2×C137semidirect
552. #2011C2×C137semidirect
553. #2000C2×C137semidirect
554. #1999C2×C137semidirect
555. #1895C2×C137semidirect
556. #1879C2×C137semidirect
557. #1877C2×C137semidirect
558. #1870C2×C137semidirect
559. #1786C2×C137semidirect
560. C22×#41C22×C137semidirect
568. C22×SD16C22×C137semidirect
569. C22×SD16C22×C137semidirect
571. C22×D8C22×C137semidirect
572. C22×D8C22×C137semidirect
573. C22×M16C22×C137semidirect
577. C2×C22⋊Q8C22×C137semidirect
581. C2×#121C22×C137semidirect
589. C2×#103C22×C137semidirect
592. C2×#102C22×C137semidirect
593. C2×#102C22×C137semidirect
594. C2×#102C22×C137semidirect
595. C2×#102C22×C137semidirect
596. C2×#102C22×C137semidirect
597. C2×C22⋊C8C22×C137semidirect
598. C2×C22⋊C8C22×C137semidirect
599. C2×C22⋊C8C22×C137semidirect
602. #391C22×C137semidirect
603. #390C22×C137semidirect
606. #380C22×C137semidirect
607. #340C22×C137semidirect
608. #340C22×C137semidirect
609. #336C22×C137semidirect
610. #336C22×C137semidirect
643. C22×D4D4×C137semidirect
661. C2×SD16D4×C137semidirect
670. C2×D8D4×C137semidirect
688. #121D4×C137semidirect
754. C2×Q8C2×D4×C137semidirect
814. C2×D4C2×D4×C137semidirect
859. C2×C8C2×D4×C137semidirect
860. C2×C8C2×D4×C137semidirect
936. C23AGL(1,ℤ/8)×C137semidirect
1000. C2×C4AGL(1,ℤ/8)×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×D42×C1372
C2×#449×C1372
C2×#450×C1372
C2×#447×C1372
#2407×C1372
#2014×C1372
#2011×C1372
#2000×C1372
#1999×C1372
#1895×C1372
#1879×C1372
#1877×C1372
#1870×C1372
#1786×C1372
#23860137