Finite Group Databasebeta

← C137×#23894 #46873280

Subgroups — C137×#23894 #46873280

Order 35072.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3586×C137C211yesmaximal, characteristic, complemented
2#3585×C137C211yesmaximal, characteristic, complemented
3#3020×C137C211yesmaximal, characteristic, complemented
4#3019×C137C211yesmaximal, characteristic, complemented
5#3010×C137C211yesmaximal, characteristic, complemented
6#3009×C137C211yesmaximal, characteristic, complemented
7#2019×C137C211yesmaximal, characteristic, complemented
8#2017×C137C211yesmaximal, characteristic, complemented
9#2009×C137C211yesmaximal, characteristic, complemented
10#2008×C137C211yesmaximal, characteristic, complemented
11#1903×C137C211yesmaximal, characteristic, complemented
12#1902×C137C211yesmaximal, characteristic, complemented
13#1881×C137C211yesmaximal, characteristic, complemented
14#1881×C137C211yesmaximal, characteristic, complemented
15#1794×C137C211yesmaximal, characteristic, complemented
16#585×C137C2211yescharacteristic
17C2×2−1+4×C137C2211yescharacteristic, complemented
18C2×H(5,𝔽2)×C137C2211yescharacteristic
19#578×C137—22no—
20#578×C137—22no—
21#577×C137—22no—
22#577×C137—22no—
23#577×C137—22no—
24#577×C137—22no—
25#576×C137—22no—
26#576×C137—22no—
27#575×C137—22no—
28#575×C137—22no—
29#575×C137C2211yescharacteristic
30#575×C137C2211yescharacteristic
31#575×C137C2211yescharacteristic
32#575×C137C2211yescharacteristic, complemented
33#575×C137C2211yescharacteristic, complemented
34C2×#137×C137—22no—
35C2×#137×C137C2211yescharacteristic
36C2×#137×C137C2211yescharacteristic, complemented
37C2×AGL(1,ℤ/8)×C137—22no—
38C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
39C2×AGL(1,ℤ/8)×C137C2211yescharacteristic
40C22×SD16×C137C2211yescharacteristic, complemented
41#568×C137C2211yescharacteristic
42#568×C137C2211yescharacteristic, complemented
43#536×C137C2211yescharacteristic, complemented
44#535×C137C2211yescharacteristic, complemented
45#456×C137—22no—
46#455×C137—22no—
47#454×C137—22no—
48#453×C137—22no—
49#452×C137—22no—
50#450×C137—22no—
51#449×C137—22no—
52#448×C137—22no—
53#421×C137C2211yescharacteristic
54#421×C137C2211yescharacteristic, complemented
55#421×C137C2211yescharacteristic, complemented
56#421×C137C2211yescharacteristic, complemented
57#419×C137C2211yescharacteristic, complemented
58#418×C137C2211yescharacteristic, complemented
59#416×C137C2211yescharacteristic
60#416×C137C2211yescharacteristic, complemented
61C2×#101×C137C2211yescharacteristic, complemented
62C2×#100×C137C2211yescharacteristic, complemented
63#410×C137C2211yescharacteristic, complemented
64#408×C137C2211yescharacteristic, complemented
65#408×C137C2211yescharacteristic, complemented
66#408×C137C2211yescharacteristic, complemented
67#344×C137C2211yescharacteristic, complemented
68#344×C137C2211yescharacteristic, complemented
69#341×C137C2211yescharacteristic, complemented
70#338×C137C2211yescharacteristic, complemented
712−1+4×C137—22no—
722−1+4×C137—21no—
732−1+4×C137—22no—
742−1+4×C137—21no—
752−1+4×C137—22no—
762−1+4×C137—41no—
772−1+4×C137D412yescomplemented
78H(5,𝔽2)×C137—22no—
79H(5,𝔽2)×C137—21no—
80H(5,𝔽2)×C137—22no—
81H(5,𝔽2)×C137—21no—
82H(5,𝔽2)×C137—22no—
83H(5,𝔽2)×C137—41no—
84H(5,𝔽2)×C137—41no—
85H(5,𝔽2)×C137D412yescomplemented
86C2×#41×C137—22no—
87C2×#41×C137—22no—
88C2×#41×C137—21no—
89C2×#41×C137—21no—
90C2×#41×C137—21no—
91C2×#41×C137—21no—
92C2×#41×C137—41no—
93C2×#41×C137—41no—
94C2×#41×C137C2311yescharacteristic
95C2×#41×C137C2311yescharacteristic
96C2×#41×C137C2311yescharacteristic
97C2×#41×C137C2311yescharacteristic
98C2×#41×C137C2311yescharacteristic
99C22×Q8×C137—21no—
100C22×Q8×C137—21no—
101C22×Q8×C137C2311yescharacteristic
102C22×D4×C137—21no—
103C22×D4×C137—21no—
104C22×D4×C137—41no—
105C22×D4×C137C2311yescharacteristic
106#137×C137—24no—
107#137×C137—24no—
108#137×C137—24no—
109#137×C137—24no—
110#137×C137—22no—
111#137×C137—22no—
112#137×C137—21no—
113#137×C137—22no—
114#137×C137—21no—
115#137×C137—21no—
116#137×C137—21no—
117#137×C137—21no—
118#137×C137—21no—
119#137×C137—21no—
120#137×C137—21no—
121#137×C137—22no—
122#137×C137D412yes—
123#137×C137D412yescomplemented
124AGL(1,ℤ/8)×C137—24no—
125AGL(1,ℤ/8)×C137—24no—
126AGL(1,ℤ/8)×C137—24no—
127AGL(1,ℤ/8)×C137—24no—
128AGL(1,ℤ/8)×C137—22no—
129AGL(1,ℤ/8)×C137—22no—
130AGL(1,ℤ/8)×C137—21no—
131AGL(1,ℤ/8)×C137—22no—
132AGL(1,ℤ/8)×C137—21no—
133AGL(1,ℤ/8)×C137—21no—
134AGL(1,ℤ/8)×C137—21no—
135AGL(1,ℤ/8)×C137—21no—
136AGL(1,ℤ/8)×C137—21no—
137AGL(1,ℤ/8)×C137—21no—
138AGL(1,ℤ/8)×C137—21no—
139AGL(1,ℤ/8)×C137—22no—
140AGL(1,ℤ/8)×C137D412yes—
141AGL(1,ℤ/8)×C137D412yescomplemented
142#135×C137—24no—
143#135×C137—24no—
144#135×C137—24no—
145#135×C137—24no—
146#135×C137—22no—
147#135×C137—22no—
148#135×C137—22no—
149#135×C137—22no—
150#135×C137—41no—
151C2×Q16×C137—24no—
152C2×Q16×C137—21no—
153C2×Q16×C137D412yescomplemented
154C2×SD16×C137—24no—
155C2×SD16×C137—24no—
156C2×SD16×C137—21no—
157C2×SD16×C137—21no—
158C2×SD16×C137—22no—
159C2×SD16×C137—22no—
160C2×SD16×C137—41no—
161C2×SD16×C137D412yes—
162C2×SD16×C137D412yescomplemented
163C2×D8×C137—24no—
164C2×D8×C137—21no—
165C2×D8×C137D412yes—
166#131×C137—22no—
167#131×C137—22no—
168#131×C137—22no—
169#131×C137—22no—
170C2×M16×C137—22no—
171C2×M16×C137—22no—
172C2×M16×C137C2311yescharacteristic
173C2×M16×C137C2311yescharacteristic
174C2×M16×C137C2311yescharacteristic
175C2×M16×C137C2311yescharacteristic
176C2×M16×C137C2311yescharacteristic
177C22×C8×C137C2311yescharacteristic
178C4⋊Q8×C137—21no—
179#127×C137—21no—
180#124×C137—21no—
181#124×C137—21no—
182#123×C137—41no—
183C22⋊Q8×C137—22no—
184#121×C137—22no—
185#120×C137—41no—
186#117×C137C2311yescharacteristic
187#117×C137C2311yescharacteristic
188#104×C137—22no—
189#104×C137—22no—
190#104×C137—22no—
191#104×C137—22no—
192#103×C137—21no—
193#103×C137—21no—
194#103×C137—22no—
195#102×C137—21no—
196#102×C137—21no—
197#102×C137—22no—
198#101×C137—22no—
199#100×C137—22no—
200#99×C137—41no—
201C22⋊C8×C137—22no—
202C22⋊C8×C137—22no—
203C22⋊C8×C137—41no—
204C24×C137—21no—
205C24×C137—41no—
206#41×C137—21no—
207#41×C137—21no—
208#41×C137—21no—
209#41×C137—21no—
210#41×C137—24no—
211#41×C137—24no—
212#41×C137—22no—
213#41×C137—22no—
214#41×C137—22no—
215#41×C137—22no—
216#41×C137—21no—
217#41×C137—21no—
218#41×C137—21no—
219#41×C137—21no—
220#41×C137—21no—
221#41×C137—21no—
222#41×C137—21no—
223#41×C137—21no—
224#41×C137—21no—
225#41×C137—21no—
226#41×C137—21no—
227#41×C137—21no—
228#41×C137—42no—
229#41×C137—42no—
230#41×C137—42no—
231#41×C137—42no—
232#41×C137—42no—
233#41×C137—44no—
234#41×C137—42no—
235#41×C137—42no—
236#41×C137—42no—
237#41×C137—41no—
238#41×C137—41no—
239#41×C137—44no—
240#41×C137—42no—
241#41×C137—42no—
242#41×C137C2×D412yes—
243#41×C137C2×D412yes—
244#41×C137C2×D412yes—
245#41×C137C2×D412yes—
246C2×Q8×C137—21no—
247C2×Q8×C137—24no—
248C2×Q8×C137—22no—
249C2×Q8×C137—22no—
250C2×Q8×C137—21no—
251C2×Q8×C137—21no—
252C2×Q8×C137—21no—
253C2×Q8×C137—21no—
254C2×Q8×C137—41no—
255C2×Q8×C137—42no—
256C2×Q8×C137—42no—
257C2×Q8×C137—41no—
258C2×Q8×C137—42no—
259C2×Q8×C137C2×D412yes—
260C2×Q8×C137C2×D411yescharacteristic
261C2×Q8×C137C2×D411yescharacteristic
262C2×Q8×C137C2×D411yescharacteristic
263C2×Q8×C137C2×D411yescharacteristic
264C2×Q8×C137C2×D411yescharacteristic
265C2×D4×C137—21no—
266C2×D4×C137—21no—
267C2×D4×C137—24no—
268C2×D4×C137—22no—
269C2×D4×C137—22no—
270C2×D4×C137—21no—
271C2×D4×C137—21no—
272C2×D4×C137—21no—
273C2×D4×C137—21no—
274C2×D4×C137—21no—
275C2×D4×C137—21no—
276C2×D4×C137—21no—
277C2×D4×C137—21no—
278C2×D4×C137—42no—
279C2×D4×C137—41no—
280C2×D4×C137—41no—
281C2×D4×C137—42no—
282C2×D4×C137—42no—
283C2×D4×C137—41no—
284C2×D4×C137—44no—
285C2×D4×C137—42no—
286C2×D4×C137—42no—
287C2×D4×C137—44no—
288C2×D4×C137—41no—
289C2×D4×C137—42no—
290C2×D4×C137—42no—
291C2×D4×C137C2×D412yes—
292C2×D4×C137C2×D411yescharacteristic
293C2×D4×C137C2×D411yescharacteristic
294C2×D4×C137C2×D411yescharacteristic
295C2×D4×C137C2×D411yescharacteristic
296C2×D4×C137C2×D411yescharacteristic
297C22×C4×C137—21no—
298C22×C4×C137—21no—
299C22×C4×C137—21no—
300C22×C4×C137—21no—
301C22×C4×C137—21no—
302C22×C4×C137—21no—
303C22×C4×C137—41no—
304C22×C4×C137—42no—
305C22×C4×C137—41no—
306C22×C4×C137—41no—
307C22×C4×C137C2411yescharacteristic
308Q16×C137—24no—
309Q16×C137—22no—
310Q16×C137—22no—
311Q16×C137—22no—
312Q16×C137—24no—
313Q16×C137—22no—
314Q16×C137—41no—
315SD16×C137—24no—
316SD16×C137—22no—
317SD16×C137—24no—
318SD16×C137—22no—
319SD16×C137—22no—
320SD16×C137—22no—
321SD16×C137—22no—
322SD16×C137—24no—
323SD16×C137—22no—
324SD16×C137—22no—
325SD16×C137—24no—
326SD16×C137—22no—
327SD16×C137—44no—
328SD16×C137—41no—
329SD16×C137—41no—
330D8×C137—24no—
331D8×C137—22no—
332D8×C137—22no—
333D8×C137—22no—
334D8×C137—24no—
335D8×C137—22no—
336D8×C137—41no—
337M16×C137—24no—
338M16×C137—24no—
339M16×C137—21no—
340M16×C137—21no—
341M16×C137—21no—
342M16×C137—21no—
343M16×C137—21no—
344M16×C137—21no—
345M16×C137—21no—
346M16×C137—21no—
347M16×C137C2×D412yes—
348M16×C137C2×D412yes—
349C2×C8×C137—24no—
350C2×C8×C137—24no—
351C2×C8×C137—21no—
352C2×C8×C137—21no—
353C2×C8×C137—21no—
354C2×C8×C137—21no—
355C2×C8×C137—21no—
356C2×C8×C137—21no—
357C2×C8×C137C2×D412yes—
358C2×C8×C137C2×D412yes—
359C4⋊C4×C137—21no—
360C4⋊C4×C137—21no—
361C4⋊C4×C137—42no—
362C22⋊C4×C137—21no—
363C22⋊C4×C137—21no—
364C22⋊C4×C137—42no—
365C22⋊C4×C137—42no—
366C42×C137—21no—
367C42×C137—21no—
368C23×C137—21no—
369C23×C137—21no—
370C23×C137—21no—
371C23×C137—21no—
372C23×C137—21no—
373C23×C137—22no—
374C23×C137—42no—
375C23×C137—44no—
376C23×C137—41no—
377C23×C137—41no—
378C23×C137—161no—
379C23×C137—162no—
380C23×C137H(5,𝔽2)11yescharacteristic
381Q8×C137—21no—
382Q8×C137—21no—
383Q8×C137—21no—
384Q8×C137—21no—
385Q8×C137—22no—
386Q8×C137—21no—
387Q8×C137—21no—
388Q8×C137—22no—
389Q8×C137—21no—
390Q8×C137—21no—
391Q8×C137—42no—
392Q8×C137—44no—
393Q8×C137—41no—
394Q8×C137—41no—
395Q8×C137#12012yes—
396Q8×C137#12012yes—
397D4×C137—22no—
398D4×C137—22no—
399D4×C137—22no—
400D4×C137—22no—
401D4×C137—21no—
402D4×C137—21no—
403D4×C137—22no—
404D4×C137—21no—
405D4×C137—21no—
406D4×C137—21no—
407D4×C137—21no—
408D4×C137—21no—
409D4×C137—21no—
410D4×C137—22no—
411D4×C137—42no—
412D4×C137—42no—
413D4×C137—44no—
414D4×C137—42no—
415D4×C137—44no—
416D4×C137—44no—
417D4×C137—41no—
418D4×C137—41no—
419D4×C137—41no—
420D4×C137—41no—
421D4×C137—41no—
422D4×C137—41no—
423D4×C137—41no—
424D4×C137—41no—
425D4×C137—162no—
426D4×C137#12012yes—
427D4×C137#12012yes—
428C2×C4×C137—21no—
429C2×C4×C137—21no—
430C2×C4×C137—22no—
431C2×C4×C137—22no—
432C2×C4×C137—22no—
433C2×C4×C137—22no—
434C2×C4×C137—21no—
435C2×C4×C137—21no—
436C2×C4×C137—22no—
437C2×C4×C137—21no—
438C2×C4×C137—42no—
439C2×C4×C137—42no—
440C2×C4×C137—42no—
441C2×C4×C137—44no—
442C2×C4×C137—44no—
443C2×C4×C137—44no—
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×C137C22×D411yescharacteristic
455C2×C4×C137C22×D411yescharacteristic
456C2×C4×C137C22×D411yescharacteristic
457C2×C4×C137C22×D411yescharacteristic
458C2×C4×C137C22×D411yescharacteristic
459C2×C4×C137H(5,𝔽2)11yescharacteristic
460C8×C137—22no—
461C8×C137—22no—
462C8×C137—22no—
463C8×C137—22no—
464C8×C137—41no—
465C8×C137—41no—
466C22×C137—22no—
467C22×C137—22no—
468C22×C137—41no—
469C22×C137—42no—
470C22×C137—42no—
471C22×C137—41no—
472C22×C137—41no—
473C22×C137—41no—
474C22×C137—42no—
475C22×C137—81no—
476C22×C137—81no—
477C22×C137—82no—
478C22×C137—81no—
479C22×C137—82no—
480C22×C137—161no—
481C22×C137—162no—
482C22×C137—164no—
483C22×C137#53411yescharacteristic
484C22×C137D4211yescharacteristic
485C22×C137D4211yescharacteristic
486C4×C137—22no—
487C4×C137—22no—
488C4×C137—41no—
489C4×C137—41no—
490C4×C137—41no—
491C4×C137—42no—
492C4×C137—81no—
493C4×C137—81no—
494C4×C137C2×#12011yescharacteristic
495C4×C137C2×#12011yescharacteristic
496C4×C137D4211yescharacteristic
497C4×C137D4211yescharacteristic
498C2×C137—21no—
499C2×C137—21no—
500C2×C137—21no—
501C2×C137—42no—
502C2×C137—42no—
503C2×C137—81no—
504C2×C137—81no—
505C2×C137—82no—
506C2×C137—81no—
507C2×C137#240311yescharacteristic
508#23894C13711yesmaximal, characteristic, direct product factor, Sylow
509C137#2389411yescharacteristic, direct product factor, Sylow
510#3586C2×C13711yescharacteristic, complemented
511#3585C2×C13711yescharacteristic, complemented
512#3020C2×C13711yescharacteristic, complemented
513#3019C2×C13711yescharacteristic, complemented
514#3010C2×C13711yescharacteristic, complemented
515#3009C2×C13711yescharacteristic, complemented
516#2019C2×C13711yescharacteristic, complemented
517#2017C2×C13711yescharacteristic, complemented
518#2009C2×C13711yescharacteristic, complemented
519#2008C2×C13711yescharacteristic, complemented
520#1903C2×C13711yescharacteristic, complemented
521#1902C2×C13711yescharacteristic, complemented
522#1881C2×C13711yescharacteristic, complemented
523#1881C2×C13711yescharacteristic, complemented
524#1794C2×C13711yescharacteristic, complemented
525#585C22×C13711yescharacteristic
526C2×2−1+4C22×C13711yescharacteristic, complemented
527C2×H(5,𝔽2)C22×C13711yescharacteristic
528#578—22no—
529#578—22no—
530#577—22no—
531#577—22no—
532#577—22no—
533#577—22no—
534#576—22no—
535#576—22no—
536#575—22no—
537#575—22no—
538#575C22×C13711yescharacteristic
539#575C22×C13711yescharacteristic
540#575C22×C13711yescharacteristic
541#575C22×C13711yescharacteristic, complemented
542#575C22×C13711yescharacteristic, complemented
543C2×#137—22no—
544C2×#137C22×C13711yescharacteristic
545C2×#137C22×C13711yescharacteristic, complemented
546C2×AGL(1,ℤ/8)—22no—
547C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
548C2×AGL(1,ℤ/8)C22×C13711yescharacteristic
549C22×SD16C22×C13711yescharacteristic, complemented
550#568C22×C13711yescharacteristic
551#568C22×C13711yescharacteristic, complemented
552#536C22×C13711yescharacteristic, complemented
553#535C22×C13711yescharacteristic, complemented
554#456—22no—
555#455—22no—
556#454—22no—
557#453—22no—
558#452—22no—
559#450—22no—
560#449—22no—
561#448—22no—
562#421C22×C13711yescharacteristic
563#421C22×C13711yescharacteristic, complemented
564#421C22×C13711yescharacteristic, complemented
565#421C22×C13711yescharacteristic, complemented
566#419C22×C13711yescharacteristic, complemented
567#418C22×C13711yescharacteristic, complemented
568#416C22×C13711yescharacteristic
569#416C22×C13711yescharacteristic, complemented
570C2×#101C22×C13711yescharacteristic, complemented
571C2×#100C22×C13711yescharacteristic, complemented
572#410C22×C13711yescharacteristic, complemented
573#408C22×C13711yescharacteristic, complemented
574#408C22×C13711yescharacteristic, complemented
575#408C22×C13711yescharacteristic, complemented
576#344C22×C13711yescharacteristic, complemented
577#344C22×C13711yescharacteristic, complemented
578#341C22×C13711yescharacteristic, complemented
579#338C22×C13711yescharacteristic, complemented
5802−1+4—22no—
5812−1+4—21no—
5822−1+4—22no—
5832−1+4—21no—
5842−1+4—22no—
5852−1+4—41no—
5862−1+4D4×C13712yescomplemented
587H(5,𝔽2)—22no—
588H(5,𝔽2)—21no—
589H(5,𝔽2)—22no—
590H(5,𝔽2)—21no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—41no—
593H(5,𝔽2)—41no—
594H(5,𝔽2)D4×C13712yescomplemented
595C2×#41—22no—
596C2×#41—22no—
597C2×#41—21no—
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—41no—
602C2×#41—41no—
603C2×#41C23×C13711yescharacteristic
604C2×#41C23×C13711yescharacteristic
605C2×#41C23×C13711yescharacteristic
606C2×#41C23×C13711yescharacteristic
607C2×#41C23×C13711yescharacteristic
608C22×Q8—21no—
609C22×Q8—21no—
610C22×Q8C23×C13711yescharacteristic
611C22×D4—21no—
612C22×D4—21no—
613C22×D4—41no—
614C22×D4C23×C13711yescharacteristic
615#137—24no—
616#137—24no—
617#137—24no—
618#137—24no—
619#137—22no—
620#137—22no—
621#137—21no—
622#137—22no—
623#137—21no—
624#137—21no—
625#137—21no—
626#137—21no—
627#137—21no—
628#137—21no—
629#137—21no—
630#137—22no—
631#137D4×C13712yes—
632#137D4×C13712yescomplemented
633AGL(1,ℤ/8)—24no—
634AGL(1,ℤ/8)—24no—
635AGL(1,ℤ/8)—24no—
636AGL(1,ℤ/8)—24no—
637AGL(1,ℤ/8)—22no—
638AGL(1,ℤ/8)—22no—
639AGL(1,ℤ/8)—21no—
640AGL(1,ℤ/8)—22no—
641AGL(1,ℤ/8)—21no—
642AGL(1,ℤ/8)—21no—
643AGL(1,ℤ/8)—21no—
644AGL(1,ℤ/8)—21no—
645AGL(1,ℤ/8)—21no—
646AGL(1,ℤ/8)—21no—
647AGL(1,ℤ/8)—21no—
648AGL(1,ℤ/8)—22no—
649AGL(1,ℤ/8)D4×C13712yes—
650AGL(1,ℤ/8)D4×C13712yescomplemented
651#135—24no—
652#135—24no—
653#135—24no—
654#135—24no—
655#135—22no—
656#135—22no—
657#135—22no—
658#135—22no—
659#135—41no—
660C2×Q16—24no—
661C2×Q16—21no—
662C2×Q16D4×C13712yescomplemented
663C2×SD16—24no—
664C2×SD16—24no—
665C2×SD16—21no—
666C2×SD16—21no—
667C2×SD16—22no—
668C2×SD16—22no—
669C2×SD16—41no—
670C2×SD16D4×C13712yes—
671C2×SD16D4×C13712yescomplemented
672C2×D8—24no—
673C2×D8—21no—
674C2×D8D4×C13712yes—
675#131—22no—
676#131—22no—
677#131—22no—
678#131—22no—
679C2×M16—22no—
680C2×M16—22no—
681C2×M16C23×C13711yescharacteristic
682C2×M16C23×C13711yescharacteristic
683C2×M16C23×C13711yescharacteristic
684C2×M16C23×C13711yescharacteristic
685C2×M16C23×C13711yescharacteristic
686C22×C8C23×C13711yescharacteristic
687C4⋊Q8—21no—
688#127—21no—
689#124—21no—
690#124—21no—
691#123—41no—
692C22⋊Q8—22no—
693#121—22no—
694#120—41no—
695#117C23×C13711yescharacteristic
696#117C23×C13711yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—22no—
704#102—21no—
705#102—21no—
706#102—22no—
707#101—22no—
708#100—22no—
709#99—41no—
710C22⋊C8—22no—
711C22⋊C8—22no—
712C22⋊C8—41no—
713C24—21no—
714C24—41no—
715#41—21no—
716#41—21no—
717#41—21no—
718#41—21no—
719#41—24no—
720#41—24no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—21no—
726#41—21no—
727#41—21no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—21no—
737#41—42no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—44no—
743#41—42no—
744#41—42no—
745#41—42no—
746#41—41no—
747#41—41no—
748#41—44no—
749#41—42no—
750#41—42no—
751#41C2×D4×C13712yes—
752#41C2×D4×C13712yes—
753#41C2×D4×C13712yes—
754#41C2×D4×C13712yes—
755C2×Q8—21no—
756C2×Q8—24no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8C2×D4×C13712yes—
769C2×Q8C2×D4×C13711yescharacteristic
770C2×Q8C2×D4×C13711yescharacteristic
771C2×Q8C2×D4×C13711yescharacteristic
772C2×Q8C2×D4×C13711yescharacteristic
773C2×Q8C2×D4×C13711yescharacteristic
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—24no—
777C2×D4—22no—
778C2×D4—22no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—42no—
788C2×D4—41no—
789C2×D4—41no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—41no—
793C2×D4—44no—
794C2×D4—42no—
795C2×D4—42no—
796C2×D4—44no—
797C2×D4—41no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4C2×D4×C13712yes—
801C2×D4C2×D4×C13711yescharacteristic
802C2×D4C2×D4×C13711yescharacteristic
803C2×D4C2×D4×C13711yescharacteristic
804C2×D4C2×D4×C13711yescharacteristic
805C2×D4C2×D4×C13711yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4C24×C13711yescharacteristic
817Q16—24no—
818Q16—22no—
819Q16—22no—
820Q16—22no—
821Q16—24no—
822Q16—22no—
823Q16—41no—
824SD16—24no—
825SD16—22no—
826SD16—24no—
827SD16—22no—
828SD16—22no—
829SD16—22no—
830SD16—22no—
831SD16—24no—
832SD16—22no—
833SD16—22no—
834SD16—24no—
835SD16—22no—
836SD16—44no—
837SD16—41no—
838SD16—41no—
839D8—24no—
840D8—22no—
841D8—22no—
842D8—22no—
843D8—24no—
844D8—22no—
845D8—41no—
846M16—24no—
847M16—24no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16C2×D4×C13712yes—
857M16C2×D4×C13712yes—
858C2×C8—24no—
859C2×C8—24no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8C2×D4×C13712yes—
867C2×C8C2×D4×C13712yes—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—42no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—42no—
874C22⋊C4—42no—
875C42—21no—
876C42—21no—
877C23—21no—
878C23—21no—
879C23—21no—
880C23—21no—
881C23—21no—
882C23—22no—
883C23—42no—
884C23—44no—
885C23—41no—
886C23—41no—
887C23—161no—
888C23—162no—
889C23H(5,𝔽2)×C13711yescharacteristic
890Q8—21no—
891Q8—21no—
892Q8—21no—
893Q8—21no—
894Q8—22no—
895Q8—21no—
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—21no—
900Q8—42no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C13712yes—
905Q8#120×C13712yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—21no—
911D4—21no—
912D4—22no—
913D4—21no—
914D4—21no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—21no—
919D4—22no—
920D4—42no—
921D4—42no—
922D4—44no—
923D4—42no—
924D4—44no—
925D4—44no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—162no—
935D4#120×C13712yes—
936D4#120×C13712yes—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—22no—
946C2×C4—21no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—44no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4C22×D4×C13711yescharacteristic
964C2×C4C22×D4×C13711yescharacteristic
965C2×C4C22×D4×C13711yescharacteristic
966C2×C4C22×D4×C13711yescharacteristic
967C2×C4C22×D4×C13711yescharacteristic
968C2×C4H(5,𝔽2)×C13711yescharacteristic
969C8—22no—
970C8—22no—
971C8—22no—
972C8—22no—
973C8—41no—
974C8—41no—
975C22—22no—
976C22—22no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—42no—
984C22—81no—
985C22—81no—
986C22—82no—
987C22—81no—
988C22—82no—
989C22—161no—
990C22—162no—
991C22—164no—
992C22#534×C13711yescharacteristic
993C22D42×C13711yescharacteristic
994C22D42×C13711yescharacteristic
995C4—22no—
996C4—22no—
997C4—41no—
998C4—41no—
999C4—41no—
1000C4—42no—
1001C4—81no—
1002C4—81no—
1003C4C2×#120×C13711yescharacteristic
1004C4C2×#120×C13711yescharacteristic
1005C4D42×C13711yescharacteristic
1006C4D42×C13711yescharacteristic
1007C2—21no—
1008C2—21no—
1009C2—21no—
1010C2—42no—
1011C2—42no—
1012C2—81no—
1013C2—81no—
1014C2—82no—
1015C2—81no—
1016C2#2403×C13711yescharacteristic
subgroupG/H
center, socleC2×C137#2403
commutator, Frattini, cosocleC22×C4C24×C137
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C137 ◁ C22×C4×C137 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3586×C137C2semidirect
2. #3585×C137C2semidirect
3. #3020×C137C2semidirect
4. #3019×C137C2semidirect
5. #3010×C137C2semidirect
6. #3009×C137C2semidirect
7. #2019×C137C2semidirect
8. #2017×C137C2semidirect
9. #2009×C137C2semidirect
10. #2008×C137C2semidirect
11. #1903×C137C2semidirect
12. #1902×C137C2semidirect
13. #1881×C137C2semidirect
14. #1881×C137C2semidirect
15. #1794×C137C2semidirect
17. C2×2−1+4×C137C22semidirect
32. #575×C137C22semidirect
33. #575×C137C22semidirect
36. C2×#137×C137C22semidirect
40. C22×SD16×C137C22semidirect
42. #568×C137C22semidirect
43. #536×C137C22semidirect
44. #535×C137C22semidirect
54. #421×C137C22semidirect
55. #421×C137C22semidirect
56. #421×C137C22semidirect
57. #419×C137C22semidirect
58. #418×C137C22semidirect
60. #416×C137C22semidirect
61. C2×#101×C137C22semidirect
62. C2×#100×C137C22semidirect
63. #410×C137C22semidirect
64. #408×C137C22semidirect
65. #408×C137C22semidirect
66. #408×C137C22semidirect
67. #344×C137C22semidirect
68. #344×C137C22semidirect
69. #341×C137C22semidirect
70. #338×C137C22semidirect
77. 2−1+4×C137D4semidirect
85. H(5,𝔽2)×C137D4semidirect
123. #137×C137D4semidirect
141. AGL(1,ℤ/8)×C137D4semidirect
153. C2×Q16×C137D4semidirect
162. C2×SD16×C137D4semidirect
508. #23894C137direct (N × H)
509. C137#23894direct (N × H)
510. #3586C2×C137semidirect
511. #3585C2×C137semidirect
512. #3020C2×C137semidirect
513. #3019C2×C137semidirect
514. #3010C2×C137semidirect
515. #3009C2×C137semidirect
516. #2019C2×C137semidirect
517. #2017C2×C137semidirect
518. #2009C2×C137semidirect
519. #2008C2×C137semidirect
520. #1903C2×C137semidirect
521. #1902C2×C137semidirect
522. #1881C2×C137semidirect
523. #1881C2×C137semidirect
524. #1794C2×C137semidirect
526. C2×2−1+4C22×C137semidirect
541. #575C22×C137semidirect
542. #575C22×C137semidirect
545. C2×#137C22×C137semidirect
549. C22×SD16C22×C137semidirect
551. #568C22×C137semidirect
552. #536C22×C137semidirect
553. #535C22×C137semidirect
563. #421C22×C137semidirect
564. #421C22×C137semidirect
565. #421C22×C137semidirect
566. #419C22×C137semidirect
567. #418C22×C137semidirect
569. #416C22×C137semidirect
570. C2×#101C22×C137semidirect
571. C2×#100C22×C137semidirect
572. #410C22×C137semidirect
573. #408C22×C137semidirect
574. #408C22×C137semidirect
575. #408C22×C137semidirect
576. #344C22×C137semidirect
577. #344C22×C137semidirect
578. #341C22×C137semidirect
579. #338C22×C137semidirect
586. 2−1+4D4×C137semidirect
594. H(5,𝔽2)D4×C137semidirect
632. #137D4×C137semidirect
650. AGL(1,ℤ/8)D4×C137semidirect
662. C2×Q16D4×C137semidirect
671. C2×SD16D4×C137semidirect

Maximal subgroups

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

subgroupindex
#3586×C1372
#3585×C1372
#3020×C1372
#3019×C1372
#3010×C1372
#3009×C1372
#2019×C1372
#2017×C1372
#2009×C1372
#2008×C1372
#1903×C1372
#1902×C1372
#1881×C1372
#1794×C1372
#23894137