Finite Group Databasebeta

← C137×#19069 #46868455

Subgroups — C137×#19069 #46868455

Order 35072.

886 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3545×C137C211yesmaximal, characteristic
2#3240×C137C211yesmaximal, characteristic, complemented
3#3215×C137C211yesmaximal, characteristic, complemented
4#3172×C137C211yesmaximal, characteristic, complemented
5#1664×C137C211yesmaximal, characteristic, complemented
6#1662×C137C211yesmaximal, characteristic, complemented
7#1661×C137C211yesmaximal, characteristic, complemented
8#1661×C137C211yesmaximal, characteristic, complemented
9#1661×C137C211yesmaximal, characteristic, complemented
10#1660×C137C211yesmaximal, characteristic, complemented
11#1659×C137C211yesmaximal, characteristic, complemented
12#1659×C137C211yesmaximal, characteristic, complemented
13#1535×C137C211yesmaximal, characteristic, complemented
14#1529×C137C211yesmaximal, characteristic, complemented
15#1527×C137C211yesmaximal, characteristic, complemented
16#563×C137C2211yescharacteristic
17#562×C137C2211yescharacteristic
18#562×C137C2211yescharacteristic
19H(3,𝔽4)×C137C2211yescharacteristic
20#555×C137—21no—
21#551×C137—21no—
22#551×C137—21no—
23#551×C137—21no—
24#546×C137—21no—
25#546×C137—21no—
26#542×C137—21no—
27#542×C137—21no—
28#538×C137—21no—
29#538×C137—21no—
30#536×C137—21no—
31#534×C137—21no—
32#533×C137C2211yescharacteristic, complemented
33#529×C137C2211yescharacteristic
34#529×C137C2211yescharacteristic
35C2×#124×C137C2211yescharacteristic
36#501×C137C2211yescharacteristic, complemented
37#501×C137C2211yescharacteristic, complemented
38#501×C137C2211yescharacteristic, complemented
39#497×C137C2211yescharacteristic
40#497×C137C2211yescharacteristic, complemented
41#497×C137C2211yescharacteristic, complemented
42#491×C137C2211yescharacteristic, complemented
43#489×C137C2211yescharacteristic
44#489×C137C2211yescharacteristic, complemented
45#489×C137C2211yescharacteristic, complemented
46#489×C137C2211yescharacteristic, complemented
47#489×C137C2211yescharacteristic, complemented
48#485×C137—21no—
49#482×C137—21no—
50#479×C137—21no—
51#478×C137—21no—
52#470×C137—21no—
53#468×C137—21no—
54#464×C137—21no—
55#464×C137—21no—
56#451×C137—21no—
57#450×C137—21no—
58C4×Q16×C137—21no—
59C4×SD16×C137—21no—
60#432×C137C2211yescharacteristic, complemented
61#432×C137C2211yescharacteristic, complemented
62C4×M16×C137C2211yescharacteristic, complemented
63#330×C137C2211yescharacteristic, complemented
64#330×C137C2211yescharacteristic, complemented
65#330×C137C2211yescharacteristic, complemented
66#330×C137C2211yescharacteristic, complemented
67#329×C137C2211yescharacteristic
68#329×C137C2211yescharacteristic
69#329×C137C2211yescharacteristic, complemented
70#329×C137C2211yescharacteristic, complemented
71#329×C137C2211yescharacteristic, complemented
72#329×C137C2211yescharacteristic, complemented
73#329×C137C2211yescharacteristic, complemented
74#329×C137C2211yescharacteristic, complemented
75C2×#41×C137—21no—
76C22×Q8×C137D411yescharacteristic
77C22×D4×C137—21no—
78C22×D4×C137D411yescharacteristic
79C2×Q16×C137—21no—
80C2×Q16×C137—21no—
81C2×Q16×C137—21no—
82C2×SD16×C137—21no—
83C2×SD16×C137—21no—
84C2×SD16×C137—21no—
85C2×M16×C137—21no—
86C4⋊Q8×C137—21no—
87C4⋊Q8×C137—21no—
88C4⋊Q8×C137C2311yescharacteristic
89C4⋊Q8×C137C2311yescharacteristic
90#126×C137—21no—
91#126×C137—21no—
92#126×C137—21no—
93#126×C137—21no—
94#126×C137—21no—
95#126×C137—21no—
96#125×C137—21no—
97#125×C137C2311yescharacteristic
98#125×C137C2311yescharacteristic
99#124×C137—21no—
100#124×C137—21no—
101#124×C137—21no—
102#124×C137—21no—
103#124×C137—21no—
104#124×C137—21no—
105#124×C137—21no—
106#124×C137—21no—
107#124×C137D411yescharacteristic
108#124×C137D411yescharacteristic
109#124×C137C2311yescharacteristic
110#124×C137C2311yescharacteristic
111#124×C137C2311yescharacteristic
112#124×C137C2311yescharacteristic
113#123×C137—21no—
114#123×C137—21no—
115#123×C137—21no—
116#123×C137—21no—
117#123×C137—21no—
118#123×C137—21no—
119#123×C137—21no—
120#123×C137—21no—
121#123×C137—21no—
122#123×C137—21no—
123#123×C137—21no—
124#123×C137—21no—
125C22⋊Q8×C137—21no—
126C22⋊Q8×C137—21no—
127C22⋊Q8×C137—21no—
128C22⋊Q8×C137—21no—
129C22⋊Q8×C137—21no—
130C22⋊Q8×C137—21no—
131C22⋊Q8×C137—21no—
132C22⋊Q8×C137—21no—
133C22⋊Q8×C137—21no—
134C22⋊Q8×C137—21no—
135C22⋊Q8×C137D411yescharacteristic
136C22⋊Q8×C137D411yescharacteristic
137#121×C137—21no—
138#121×C137—21no—
139#121×C137—21no—
140#121×C137—21no—
141#121×C137—21no—
142#121×C137—21no—
143#121×C137—21no—
144#121×C137—21no—
145#121×C137D411yescharacteristic
146#121×C137D411yescharacteristic
147#120×C137—21no—
148#120×C137—21no—
149#120×C137—21no—
150#120×C137—21no—
151#120×C137—21no—
152#120×C137—21no—
153C4×Q8×C137—21no—
154C4×Q8×C137—21no—
155C4×Q8×C137D411yescharacteristic
156C4×Q8×C137D411yescharacteristic
157C4×D4×C137—21no—
158C4×D4×C137—21no—
159C4×D4×C137—21no—
160C4×D4×C137—21no—
161C4×D4×C137—21no—
162C4×D4×C137—21no—
163C4×D4×C137D411yescharacteristic
164C4×D4×C137D411yescharacteristic
165#117×C137—21no—
166#117×C137—21no—
167#117×C137—21no—
168#117×C137—21no—
169#117×C137—21no—
170#117×C137—21no—
171C2×C22⋊C4×C137—21no—
172C2×C22⋊C4×C137—21no—
173C2×C22⋊C4×C137—21no—
174C2×C22⋊C4×C137—21no—
175C2×C22⋊C4×C137—21no—
176C2×C42×C137C2311yescharacteristic
177#107×C137—21no—
178#107×C137—21no—
179#107×C137—21no—
180#106×C137—21no—
181#106×C137—21no—
182#106×C137—21no—
183C4⋊C8×C137—21no—
184C4⋊C8×C137—21no—
185#103×C137—21no—
186#103×C137—21no—
187#103×C137—21no—
188#103×C137—21no—
189#103×C137—21no—
190#103×C137—21no—
191#103×C137—21no—
192#102×C137—21no—
193#102×C137—21no—
194#102×C137—21no—
195#102×C137—21no—
196#102×C137—21no—
197C22⋊C8×C137—21no—
198C22⋊C8×C137—21no—
199#97×C137C2311yescharacteristic
200#97×C137C2311yescharacteristic
201#97×C137C2311yescharacteristic
202#97×C137C2311yescharacteristic
203#97×C137C2311yescharacteristic
204#97×C137C2311yescharacteristic
205C4×C8×C137—21no—
206C24×C137—21no—
207C24×C137—21no—
208#41×C137—82no—
209C2×Q8×C137—21no—
210C2×Q8×C137—21no—
211C2×Q8×C137—21no—
212C2×Q8×C137—21no—
213C2×Q8×C137—81no—
214C2×Q8×C137C2×D411yescharacteristic
215C2×Q8×C137C2×D411yescharacteristic
216C2×Q8×C137C2×D411yescharacteristic
217C2×Q8×C137C2×D411yescharacteristic
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—81no—
229C2×D4×C137—82no—
230C2×D4×C137C2×D411yescharacteristic
231C2×D4×C137C2×D411yescharacteristic
232C2×D4×C137C2×D411yescharacteristic
233C2×D4×C137C2×D411yescharacteristic
234C22×C4×C137—21no—
235C22×C4×C137—21no—
236C22×C4×C137—21no—
237C22×C4×C137—21no—
238C22×C4×C137—21no—
239C22×C4×C137—21no—
240C22×C4×C137—21no—
241C22×C4×C137—21no—
242C22×C4×C137C2×D411yescharacteristic
243C22×C4×C137C2×D411yescharacteristic
244C22×C4×C137C2×D411yescharacteristic
245Q16×C137—42no—
246Q16×C137—81no—
247Q16×C137—81no—
248SD16×C137—42no—
249SD16×C137—81no—
250SD16×C137—81no—
251M16×C137—42no—
252C2×C8×C137—21no—
253C2×C8×C137—21no—
254C2×C8×C137—21no—
255C2×C8×C137—21no—
256C2×C8×C137—21no—
257C2×C8×C137—21no—
258C4⋊C4×C137—21no—
259C4⋊C4×C137—21no—
260C4⋊C4×C137—21no—
261C4⋊C4×C137—21no—
262C4⋊C4×C137—21no—
263C4⋊C4×C137—21no—
264C4⋊C4×C137—21no—
265C4⋊C4×C137—21no—
266C4⋊C4×C137—21no—
267C4⋊C4×C137—21no—
268C4⋊C4×C137—21no—
269C4⋊C4×C137—21no—
270C4⋊C4×C137—21no—
271C4⋊C4×C137—21no—
272C4⋊C4×C137—21no—
273C4⋊C4×C137—21no—
274C4⋊C4×C137—21no—
275C4⋊C4×C137—21no—
276C4⋊C4×C137—41no—
277C4⋊C4×C137—41no—
278C4⋊C4×C137C2×D411yescharacteristic
279C4⋊C4×C137C2×D411yescharacteristic
280C4⋊C4×C137C2×D411yescharacteristic
281C4⋊C4×C137C2×D411yescharacteristic
282C22⋊C4×C137—21no—
283C22⋊C4×C137—21no—
284C22⋊C4×C137—21no—
285C22⋊C4×C137—21no—
286C22⋊C4×C137—21no—
287C22⋊C4×C137—21no—
288C22⋊C4×C137—21no—
289C22⋊C4×C137—21no—
290C22⋊C4×C137—21no—
291C22⋊C4×C137—21no—
292C22⋊C4×C137—21no—
293C22⋊C4×C137—21no—
294C22⋊C4×C137—21no—
295C22⋊C4×C137—21no—
296C22⋊C4×C137—21no—
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—21no—
304C22⋊C4×C137—21no—
305C22⋊C4×C137—21no—
306C22⋊C4×C137—21no—
307C22⋊C4×C137—21no—
308C22⋊C4×C137—21no—
309C22⋊C4×C137—21no—
310C22⋊C4×C137—41no—
311C42×C137—21no—
312C42×C137—21no—
313C42×C137—21no—
314C42×C137—21no—
315C42×C137—41no—
316C42×C137C2×D411yescharacteristic
317C42×C137C2×D411yescharacteristic
318C42×C137C2×D411yescharacteristic
319C42×C137C2411yescharacteristic
320C23×C137—21no—
321C23×C137—21no—
322C23×C137—21no—
323C23×C137—21no—
324C23×C137—42no—
325C23×C137—81no—
326C23×C137—81no—
327C23×C137—81no—
328C23×C137—81no—
329C23×C137—81no—
330C23×C137#12011yescharacteristic
331Q8×C137—41no—
332Q8×C137—41no—
333Q8×C137—41no—
334Q8×C137—41no—
335Q8×C137—41no—
336Q8×C137—41no—
337Q8×C137—41no—
338Q8×C137—41no—
339Q8×C137—81no—
340Q8×C137—81no—
341D4×C137—41no—
342D4×C137—41no—
343D4×C137—41no—
344D4×C137—41no—
345D4×C137—42no—
346D4×C137—42no—
347D4×C137—81no—
348D4×C137—81no—
349D4×C137—81no—
350D4×C137—81no—
351D4×C137—81no—
352D4×C137—81no—
353D4×C137—81no—
354D4×C137—81no—
355C2×C4×C137—21no—
356C2×C4×C137—21no—
357C2×C4×C137—21no—
358C2×C4×C137—21no—
359C2×C4×C137—21no—
360C2×C4×C137—21no—
361C2×C4×C137—21no—
362C2×C4×C137—21no—
363C2×C4×C137—41no—
364C2×C4×C137—41no—
365C2×C4×C137—41no—
366C2×C4×C137—42no—
367C2×C4×C137—41no—
368C2×C4×C137—41no—
369C2×C4×C137—81no—
370C2×C4×C137—81no—
371C2×C4×C137—81no—
372C2×C4×C137—81no—
373C2×C4×C137—81no—
374C2×C4×C137—81no—
375C2×C4×C137—81no—
376C2×C4×C137#12011yescharacteristic
377C2×C4×C137#12011yescharacteristic
378C2×C4×C137#12011yescharacteristic
379C2×C4×C137C22×D411yescharacteristic
380C2×C4×C137C22×D411yescharacteristic
381C2×C4×C137C22×D411yescharacteristic
382C8×C137—22no—
383C8×C137—41no—
384C8×C137—41no—
385C8×C137—41no—
386C8×C137—41no—
387C8×C137—41no—
388C22×C137—21no—
389C22×C137—21no—
390C22×C137—21no—
391C22×C137—41no—
392C22×C137—41no—
393C22×C137—41no—
394C22×C137—41no—
395C22×C137—41no—
396C22×C137—41no—
397C22×C137—41no—
398C22×C137—41no—
399C22×C137—41no—
400C22×C137—41no—
401C22×C137—41no—
402C22×C137—41no—
403C22×C137—162no—
404C22×C137—162no—
405C22×C137C2×#12011yescharacteristic
406C4×C137—21no—
407C4×C137—21no—
408C4×C137—21no—
409C4×C137—21no—
410C4×C137—21no—
411C4×C137—21no—
412C4×C137—41no—
413C4×C137—41no—
414C4×C137—41no—
415C4×C137—41no—
416C4×C137—41no—
417C4×C137—41no—
418C4×C137—41no—
419C4×C137—41no—
420C4×C137—81no—
421C4×C137—81no—
422C2×C137—41no—
423C2×C137—81no—
424C2×C137—81no—
425C2×C137—81no—
426C2×C137—81no—
427C2×C137#301811yescharacteristic
428C2×C137#301911yescharacteristic
429C2×C137#302211yescharacteristic
430#19069C13711yesmaximal, characteristic, direct product factor, Sylow
431C137#1906911yescharacteristic, direct product factor, Sylow
432#3545C2×C13711yescharacteristic
433#3240C2×C13711yescharacteristic, complemented
434#3215C2×C13711yescharacteristic, complemented
435#3172C2×C13711yescharacteristic, complemented
436#1664C2×C13711yescharacteristic, complemented
437#1662C2×C13711yescharacteristic, complemented
438#1661C2×C13711yescharacteristic, complemented
439#1661C2×C13711yescharacteristic, complemented
440#1661C2×C13711yescharacteristic, complemented
441#1660C2×C13711yescharacteristic, complemented
442#1659C2×C13711yescharacteristic, complemented
443#1659C2×C13711yescharacteristic, complemented
444#1535C2×C13711yescharacteristic, complemented
445#1529C2×C13711yescharacteristic, complemented
446#1527C2×C13711yescharacteristic, complemented
447#563C22×C13711yescharacteristic
448#562C22×C13711yescharacteristic
449#562C22×C13711yescharacteristic
450H(3,𝔽4)C22×C13711yescharacteristic
451#555—21no—
452#551—21no—
453#551—21no—
454#551—21no—
455#546—21no—
456#546—21no—
457#542—21no—
458#542—21no—
459#538—21no—
460#538—21no—
461#536—21no—
462#534—21no—
463#533C22×C13711yescharacteristic, complemented
464#529C22×C13711yescharacteristic
465#529C22×C13711yescharacteristic
466C2×#124C22×C13711yescharacteristic
467#501C22×C13711yescharacteristic, complemented
468#501C22×C13711yescharacteristic, complemented
469#501C22×C13711yescharacteristic, complemented
470#497C22×C13711yescharacteristic
471#497C22×C13711yescharacteristic, complemented
472#497C22×C13711yescharacteristic, complemented
473#491C22×C13711yescharacteristic, complemented
474#489C22×C13711yescharacteristic
475#489C22×C13711yescharacteristic, complemented
476#489C22×C13711yescharacteristic, complemented
477#489C22×C13711yescharacteristic, complemented
478#489C22×C13711yescharacteristic, complemented
479#485—21no—
480#482—21no—
481#479—21no—
482#478—21no—
483#470—21no—
484#468—21no—
485#464—21no—
486#464—21no—
487#451—21no—
488#450—21no—
489C4×Q16—21no—
490C4×SD16—21no—
491#432C22×C13711yescharacteristic, complemented
492#432C22×C13711yescharacteristic, complemented
493C4×M16C22×C13711yescharacteristic, complemented
494#330C22×C13711yescharacteristic, complemented
495#330C22×C13711yescharacteristic, complemented
496#330C22×C13711yescharacteristic, complemented
497#330C22×C13711yescharacteristic, complemented
498#329C22×C13711yescharacteristic
499#329C22×C13711yescharacteristic
500#329C22×C13711yescharacteristic, complemented
501#329C22×C13711yescharacteristic, complemented
502#329C22×C13711yescharacteristic, complemented
503#329C22×C13711yescharacteristic, complemented
504#329C22×C13711yescharacteristic, complemented
505#329C22×C13711yescharacteristic, complemented
506C2×#41—21no—
507C22×Q8D4×C13711yescharacteristic
508C22×D4—21no—
509C22×D4D4×C13711yescharacteristic
510C2×Q16—21no—
511C2×Q16—21no—
512C2×Q16—21no—
513C2×SD16—21no—
514C2×SD16—21no—
515C2×SD16—21no—
516C2×M16—21no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519C4⋊Q8C23×C13711yescharacteristic
520C4⋊Q8C23×C13711yescharacteristic
521#126—21no—
522#126—21no—
523#126—21no—
524#126—21no—
525#126—21no—
526#126—21no—
527#125—21no—
528#125C23×C13711yescharacteristic
529#125C23×C13711yescharacteristic
530#124—21no—
531#124—21no—
532#124—21no—
533#124—21no—
534#124—21no—
535#124—21no—
536#124—21no—
537#124—21no—
538#124D4×C13711yescharacteristic
539#124D4×C13711yescharacteristic
540#124C23×C13711yescharacteristic
541#124C23×C13711yescharacteristic
542#124C23×C13711yescharacteristic
543#124C23×C13711yescharacteristic
544#123—21no—
545#123—21no—
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553#123—21no—
554#123—21no—
555#123—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566C22⋊Q8D4×C13711yescharacteristic
567C22⋊Q8D4×C13711yescharacteristic
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121—21no—
576#121D4×C13711yescharacteristic
577#121D4×C13711yescharacteristic
578#120—21no—
579#120—21no—
580#120—21no—
581#120—21no—
582#120—21no—
583#120—21no—
584C4×Q8—21no—
585C4×Q8—21no—
586C4×Q8D4×C13711yescharacteristic
587C4×Q8D4×C13711yescharacteristic
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4D4×C13711yescharacteristic
595C4×D4D4×C13711yescharacteristic
596#117—21no—
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C42C23×C13711yescharacteristic
608#107—21no—
609#107—21no—
610#107—21no—
611#106—21no—
612#106—21no—
613#106—21no—
614C4⋊C8—21no—
615C4⋊C8—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103—21no—
620#103—21no—
621#103—21no—
622#103—21no—
623#102—21no—
624#102—21no—
625#102—21no—
626#102—21no—
627#102—21no—
628C22⋊C8—21no—
629C22⋊C8—21no—
630#97C23×C13711yescharacteristic
631#97C23×C13711yescharacteristic
632#97C23×C13711yescharacteristic
633#97C23×C13711yescharacteristic
634#97C23×C13711yescharacteristic
635#97C23×C13711yescharacteristic
636C4×C8—21no—
637C24—21no—
638C24—21no—
639#41—82no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—81no—
645C2×Q8C2×D4×C13711yescharacteristic
646C2×Q8C2×D4×C13711yescharacteristic
647C2×Q8C2×D4×C13711yescharacteristic
648C2×Q8C2×D4×C13711yescharacteristic
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—81no—
660C2×D4—82no—
661C2×D4C2×D4×C13711yescharacteristic
662C2×D4C2×D4×C13711yescharacteristic
663C2×D4C2×D4×C13711yescharacteristic
664C2×D4C2×D4×C13711yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4C2×D4×C13711yescharacteristic
674C22×C4C2×D4×C13711yescharacteristic
675C22×C4C2×D4×C13711yescharacteristic
676Q16—42no—
677Q16—81no—
678Q16—81no—
679SD16—42no—
680SD16—81no—
681SD16—81no—
682M16—42no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—41no—
708C4⋊C4—41no—
709C4⋊C4C2×D4×C13711yescharacteristic
710C4⋊C4C2×D4×C13711yescharacteristic
711C4⋊C4C2×D4×C13711yescharacteristic
712C4⋊C4C2×D4×C13711yescharacteristic
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
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—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—41no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—21no—
746C42—41no—
747C42C2×D4×C13711yescharacteristic
748C42C2×D4×C13711yescharacteristic
749C42C2×D4×C13711yescharacteristic
750C42C24×C13711yescharacteristic
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—42no—
756C23—81no—
757C23—81no—
758C23—81no—
759C23—81no—
760C23—81no—
761C23#120×C13711yescharacteristic
762Q8—41no—
763Q8—41no—
764Q8—41no—
765Q8—41no—
766Q8—41no—
767Q8—41no—
768Q8—41no—
769Q8—41no—
770Q8—81no—
771Q8—81no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—42no—
777D4—42no—
778D4—81no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—81no—
783D4—81no—
784D4—81no—
785D4—81no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4#120×C13711yescharacteristic
808C2×C4#120×C13711yescharacteristic
809C2×C4#120×C13711yescharacteristic
810C2×C4C22×D4×C13711yescharacteristic
811C2×C4C22×D4×C13711yescharacteristic
812C2×C4C22×D4×C13711yescharacteristic
813C8—22no—
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C8—41no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—162no—
835C22—162no—
836C22C2×#120×C13711yescharacteristic
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—81no—
852C4—81no—
853C2—41no—
854C2—81no—
855C2—81no—
856C2—81no—
857C2—81no—
858C2#3018×C13711yescharacteristic
859C2#3019×C13711yescharacteristic
860C2#3022×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC42C24×C137
prime radical#3545×C137C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3240×C137C2semidirect
3. #3215×C137C2semidirect
4. #3172×C137C2semidirect
5. #1664×C137C2semidirect
6. #1662×C137C2semidirect
7. #1661×C137C2semidirect
8. #1661×C137C2semidirect
9. #1661×C137C2semidirect
10. #1660×C137C2semidirect
11. #1659×C137C2semidirect
12. #1659×C137C2semidirect
13. #1535×C137C2semidirect
14. #1529×C137C2semidirect
15. #1527×C137C2semidirect
32. #533×C137C22semidirect
36. #501×C137C22semidirect
37. #501×C137C22semidirect
38. #501×C137C22semidirect
40. #497×C137C22semidirect
41. #497×C137C22semidirect
42. #491×C137C22semidirect
44. #489×C137C22semidirect
45. #489×C137C22semidirect
46. #489×C137C22semidirect
47. #489×C137C22semidirect
60. #432×C137C22semidirect
61. #432×C137C22semidirect
62. C4×M16×C137C22semidirect
63. #330×C137C22semidirect
64. #330×C137C22semidirect
65. #330×C137C22semidirect
66. #330×C137C22semidirect
69. #329×C137C22semidirect
70. #329×C137C22semidirect
71. #329×C137C22semidirect
72. #329×C137C22semidirect
73. #329×C137C22semidirect
74. #329×C137C22semidirect
430. #19069C137direct (N × H)
431. C137#19069direct (N × H)
433. #3240C2×C137semidirect
434. #3215C2×C137semidirect
435. #3172C2×C137semidirect
436. #1664C2×C137semidirect
437. #1662C2×C137semidirect
438. #1661C2×C137semidirect
439. #1661C2×C137semidirect
440. #1661C2×C137semidirect
441. #1660C2×C137semidirect
442. #1659C2×C137semidirect
443. #1659C2×C137semidirect
444. #1535C2×C137semidirect
445. #1529C2×C137semidirect
446. #1527C2×C137semidirect
463. #533C22×C137semidirect
467. #501C22×C137semidirect
468. #501C22×C137semidirect
469. #501C22×C137semidirect
471. #497C22×C137semidirect
472. #497C22×C137semidirect
473. #491C22×C137semidirect
475. #489C22×C137semidirect
476. #489C22×C137semidirect
477. #489C22×C137semidirect
478. #489C22×C137semidirect
491. #432C22×C137semidirect
492. #432C22×C137semidirect
493. C4×M16C22×C137semidirect
494. #330C22×C137semidirect
495. #330C22×C137semidirect
496. #330C22×C137semidirect
497. #330C22×C137semidirect
500. #329C22×C137semidirect
501. #329C22×C137semidirect
502. #329C22×C137semidirect
503. #329C22×C137semidirect
504. #329C22×C137semidirect
505. #329C22×C137semidirect

Maximal subgroups

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

subgroupindex
#3545×C1372
#3240×C1372
#3215×C1372
#3172×C1372
#1664×C1372
#1662×C1372
#1661×C1372
#1660×C1372
#1659×C1372
#1535×C1372
#1529×C1372
#1527×C1372
#19069137