Finite Group Databasebeta

← C37×#19019 #22640272

Subgroups — C37×#19019 #22640272

Order 9472.

958 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3561C211yesmaximal, characteristic, complemented
2C37×#3235C211yesmaximal, characteristic, complemented
3C37×#3171C211yesmaximal, characteristic, complemented
4C37×#3153C211yesmaximal, characteristic, complemented
5C37×#1661C212yesmaximal, complemented
6C37×#1660C212yesmaximal, complemented
7C37×#1657C212yesmaximal, complemented
8C37×#1656C212yesmaximal, complemented
9C37×#1529C211yesmaximal, characteristic, complemented
10C37×#1527C211yesmaximal, characteristic, complemented
11C37×#1526C211yesmaximal, characteristic, complemented
12C2×#137×C37—21no—
13C2×AGL(1,ℤ/8)×C37—21no—
14C37×#563C2212yes—
15C37×#562C2212yes—
16C37×#556—21no—
17C37×#551—22no—
18D4×Q8×C37—21no—
19C37×#548—21no—
20C37×#546—21no—
21C37×#543—21no—
22C37×#542—21no—
23C37×#542—22no—
24C37×#538—21no—
25C37×#536—21no—
26C37×#533C2211yescharacteristic
27C37×#532C2211yescharacteristic
28C37×#529C2211yescharacteristic
29C2×#124×C37C2211yescharacteristic
30C37×#501C2211yescharacteristic, complemented
31C37×#501C2212yescomplemented
32C37×#497C2212yes—
33C37×#496C2212yes—
34C37×#496C2211yescharacteristic, complemented
35C37×#495—22no—
36C37×#490C2211yescharacteristic, complemented
37C37×#490C2212yescomplemented
38C37×#489C2211yescharacteristic, complemented
39C37×#482—22no—
40C37×#476—21no—
41C37×#474—21no—
42C37×#469—21no—
43C37×#468—21no—
44C4×SD16×C37—21no—
45C4×D8×C37—21no—
46C37×#432C2211yescharacteristic
47C4×M16×C37C2211yescharacteristic
48C4×M16×C37C2211yescharacteristic
49C37×#330C2212yescomplemented
50C37×#330C2212yescomplemented
51C37×#330C2212yescomplemented
52C37×#329C2212yes—
53C37×#329C2212yes—
54C37×#329C2212yescomplemented
55C2×#41×C37—21no—
56C2×#41×C37—21no—
57C22×Q8×C37—21no—
58C22×Q8×C37D411yescharacteristic
59C22×D4×C37D411yescharacteristic
60#137×C37—44no—
61AGL(1,ℤ/8)×C37—44no—
62C2×Q16×C37—22no—
63C2×SD16×C37—22no—
64C2×SD16×C37—21no—
65C2×SD16×C37—22no—
66C2×D8×C37—22no—
67C2×D8×C37—21no—
68C2×M16×C37—21no—
69C2×M16×C37—21no—
70C4⋊Q8×C37—21no—
71C4⋊Q8×C37—22no—
72C4⋊Q8×C37D411yescharacteristic
73C4⋊Q8×C37D411yescharacteristic
74C4⋊Q8×C37C2311yescharacteristic
75#127×C37C2311yescharacteristic
76#126×C37—22no—
77#126×C37—22no—
78#126×C37—22no—
79#126×C37—21no—
80#125×C37C2311yescharacteristic
81#125×C37C2312yes—
82#124×C37—21no—
83#124×C37—22no—
84#124×C37—22no—
85#124×C37—21no—
86#124×C37—21no—
87#124×C37—21no—
88#124×C37D412yes—
89#124×C37C2312yes—
90#124×C37C2311yescharacteristic
91#123×C37—22no—
92#123×C37—22no—
93#123×C37—21no—
94#123×C37—22no—
95#123×C37—22no—
96C22⋊Q8×C37—22no—
97C22⋊Q8×C37—22no—
98C22⋊Q8×C37—21no—
99C22⋊Q8×C37—22no—
100C22⋊Q8×C37—22no—
101C22⋊Q8×C37—22no—
102C22⋊Q8×C37—21no—
103C22⋊Q8×C37—21no—
104C22⋊Q8×C37—22no—
105C22⋊Q8×C37—22no—
106C22⋊Q8×C37D411yescharacteristic
107#121×C37—21no—
108#121×C37—22no—
109#121×C37—22no—
110#121×C37—21no—
111#121×C37—21no—
112#121×C37D411yescharacteristic
113#120×C37—22no—
114C4×Q8×C37—21no—
115C4×Q8×C37—21no—
116C4×Q8×C37—21no—
117C4×Q8×C37D411yescharacteristic
118C4×D4×C37—22no—
119C4×D4×C37—21no—
120C4×D4×C37—22no—
121C4×D4×C37—21no—
122C4×D4×C37—21no—
123C4×D4×C37—21no—
124C4×D4×C37D411yescharacteristic
125#117×C37—22no—
126#117×C37—21no—
127#117×C37D412yes—
128C2×C22⋊C4×C37—22no—
129C2×C22⋊C4×C37—21no—
130C2×C22⋊C4×C37—21no—
131C2×C42×C37C2311yescharacteristic
132#107×C37—21no—
133#107×C37—22no—
134#106×C37—21no—
135#106×C37—22no—
136C4⋊C8×C37—21no—
137#103×C37—21no—
138#102×C37—21no—
139#102×C37—21no—
140#102×C37—21no—
141#102×C37—22no—
142#102×C37—22no—
143C22⋊C8×C37—21no—
144#97×C37C2312yes—
145#97×C37C2311yescharacteristic
146#97×C37C2311yescharacteristic
147#97×C37C2312yes—
148C4×C8×C37—21no—
149C4×C8×C37—21no—
150C24×C37—21no—
151#41×C37—42no—
152#41×C37—42no—
153#41×C37—82no—
154C2×Q8×C37—22no—
155C2×Q8×C37—21no—
156C2×Q8×C37—21no—
157C2×Q8×C37—21no—
158C2×Q8×C37—21no—
159C2×Q8×C37—42no—
160C2×Q8×C37—82no—
161C2×Q8×C37C2×D411yescharacteristic
162C2×Q8×C37C2×D412yes—
163C2×D4×C37—21no—
164C2×D4×C37—22no—
165C2×D4×C37—22no—
166C2×D4×C37—21no—
167C2×D4×C37—21no—
168C2×D4×C37—21no—
169C2×D4×C37—21no—
170C2×D4×C37—42no—
171C2×D4×C37—41no—
172C2×D4×C37C2×D411yescharacteristic
173C2×D4×C37C2×D412yes—
174C22×C4×C37—22no—
175C22×C4×C37—22no—
176C22×C4×C37—22no—
177C22×C4×C37—21no—
178C22×C4×C37—21no—
179C22×C4×C37—41no—
180C22×C4×C37C2×D411yescharacteristic
181C22×C4×C37C2×D411yescharacteristic
182C22×C4×C37C2×D411yescharacteristic
183Q16×C37—44no—
184SD16×C37—42no—
185SD16×C37—44no—
186SD16×C37—44no—
187D8×C37—42no—
188D8×C37—44no—
189M16×C37—24no—
190M16×C37—42no—
191C2×C8×C37—21no—
192C2×C8×C37—22no—
193C2×C8×C37—21no—
194C2×C8×C37—22no—
195C4⋊C4×C37—22no—
196C4⋊C4×C37—22no—
197C4⋊C4×C37—22no—
198C4⋊C4×C37—22no—
199C4⋊C4×C37—21no—
200C4⋊C4×C37—21no—
201C4⋊C4×C37—21no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—21no—
204C4⋊C4×C37—21no—
205C4⋊C4×C37—22no—
206C4⋊C4×C37—22no—
207C4⋊C4×C37—21no—
208C4⋊C4×C37—21no—
209C4⋊C4×C37C2×D412yes—
210C4⋊C4×C37C2×D411yescharacteristic
211C4⋊C4×C37C2×D412yes—
212C4⋊C4×C37C2×D411yescharacteristic
213C22⋊C4×C37—22no—
214C22⋊C4×C37—22no—
215C22⋊C4×C37—22no—
216C22⋊C4×C37—22no—
217C22⋊C4×C37—22no—
218C22⋊C4×C37—21no—
219C22⋊C4×C37—22no—
220C22⋊C4×C37—22no—
221C22⋊C4×C37—22no—
222C22⋊C4×C37—21no—
223C22⋊C4×C37—21no—
224C22⋊C4×C37—22no—
225C22⋊C4×C37—22no—
226C22⋊C4×C37—21no—
227C22⋊C4×C37—21no—
228C22⋊C4×C37—41no—
229C22⋊C4×C37—41no—
230C42×C37—22no—
231C42×C37—22no—
232C42×C37—21no—
233C42×C37C2×D411yescharacteristic
234C42×C37C2×D411yescharacteristic
235C42×C37C2×D411yescharacteristic
236C42×C37C2411yescharacteristic
237C23×C37—22no—
238C23×C37—21no—
239C23×C37—42no—
240C23×C37—41no—
241C23×C37—81no—
242C23×C37—81no—
243C23×C37#12011yescharacteristic
244Q8×C37—42no—
245Q8×C37—41no—
246Q8×C37—41no—
247Q8×C37—41no—
248Q8×C37—42no—
249Q8×C37—42no—
250Q8×C37—81no—
251Q8×C37—82no—
252D4×C37—42no—
253D4×C37—41no—
254D4×C37—41no—
255D4×C37—41no—
256D4×C37—41no—
257D4×C37—41no—
258D4×C37—42no—
259D4×C37—42no—
260D4×C37—42no—
261D4×C37—82no—
262D4×C37—82no—
263D4×C37—82no—
264C2×C4×C37—22no—
265C2×C4×C37—21no—
266C2×C4×C37—22no—
267C2×C4×C37—21no—
268C2×C4×C37—22no—
269C2×C4×C37—22no—
270C2×C4×C37—21no—
271C2×C4×C37—41no—
272C2×C4×C37—41no—
273C2×C4×C37—42no—
274C2×C4×C37—41no—
275C2×C4×C37—81no—
276C2×C4×C37—82no—
277C2×C4×C37—82no—
278C2×C4×C37—82no—
279C2×C4×C37—82no—
280C2×C4×C37#12011yescharacteristic
281C2×C4×C37#12011yescharacteristic
282C2×C4×C37#12011yescharacteristic
283C2×C4×C37C22×D411yescharacteristic
284C2×C4×C37C22×D411yescharacteristic
285C2×C4×C37C22×D411yescharacteristic
286C8×C37—24no—
287C8×C37—22no—
288C8×C37—42no—
289C8×C37—41no—
290#19019C3711yesmaximal, characteristic, direct product factor, Sylow
291C22×C37—21no—
292C22×C37—21no—
293C22×C37—21no—
294C22×C37—41no—
295C22×C37—42no—
296C22×C37—42no—
297C22×C37—41no—
298C22×C37—41no—
299C22×C37—42no—
300C22×C37—81no—
301C22×C37—81no—
302C22×C37—81no—
303C22×C37—162no—
304C22×C37C2×#12011yescharacteristic
305C4×C37—21no—
306C4×C37—21no—
307C4×C37—21no—
308C4×C37—21no—
309C4×C37—21no—
310C4×C37—41no—
311C4×C37—42no—
312C4×C37—42no—
313C4×C37—41no—
314C4×C37—42no—
315C4×C37—41no—
316C4×C37—81no—
317C4×C37#45312yes—
318#3561C2×C3711yescharacteristic, complemented
319#3235C2×C3711yescharacteristic, complemented
320#3171C2×C3711yescharacteristic, complemented
321#3153C2×C3711yescharacteristic, complemented
322#1661C2×C3712yescomplemented
323#1660C2×C3712yescomplemented
324#1657C2×C3712yescomplemented
325#1656C2×C3712yescomplemented
326#1529C2×C3711yescharacteristic, complemented
327#1527C2×C3711yescharacteristic, complemented
328#1526C2×C3711yescharacteristic, complemented
329C2×C37—41no—
330C2×C37—81no—
331C2×C37—82no—
332C2×C37—161no—
333C2×C37C2×#45311yescharacteristic
334C2×C37#301811yescharacteristic
335C2×C37#302011yescharacteristic
336C2×#137—21no—
337C2×AGL(1,ℤ/8)—21no—
338#563C22×C3712yes—
339#562C22×C3712yes—
340#556—21no—
341#551—22no—
342D4×Q8—21no—
343#548—21no—
344#546—21no—
345#543—21no—
346#542—21no—
347#542—22no—
348#538—21no—
349#536—21no—
350#533C22×C3711yescharacteristic
351#532C22×C3711yescharacteristic
352#529C22×C3711yescharacteristic
353C2×#124C22×C3711yescharacteristic
354#501C22×C3711yescharacteristic, complemented
355#501C22×C3712yescomplemented
356#497C22×C3712yes—
357#496C22×C3712yes—
358#496C22×C3711yescharacteristic, complemented
359#495—22no—
360#490C22×C3711yescharacteristic, complemented
361#490C22×C3712yescomplemented
362#489C22×C3711yescharacteristic, complemented
363#482—22no—
364#476—21no—
365#474—21no—
366#469—21no—
367#468—21no—
368C4×SD16—21no—
369C4×D8—21no—
370#432C22×C3711yescharacteristic
371C4×M16C22×C3711yescharacteristic
372C4×M16C22×C3711yescharacteristic
373#330C22×C3712yescomplemented
374#330C22×C3712yescomplemented
375#330C22×C3712yescomplemented
376#329C22×C3712yes—
377#329C22×C3712yes—
378#329C22×C3712yescomplemented
379C37#1901911yescharacteristic, direct product factor, Sylow
380C2×#41—21no—
381C2×#41—21no—
382C22×Q8—21no—
383C22×Q8D4×C3711yescharacteristic
384C22×D4D4×C3711yescharacteristic
385#137—44no—
386AGL(1,ℤ/8)—44no—
387C2×Q16—22no—
388C2×SD16—22no—
389C2×SD16—21no—
390C2×SD16—22no—
391C2×D8—22no—
392C2×D8—21no—
393C2×M16—21no—
394C2×M16—21no—
395C4⋊Q8—21no—
396C4⋊Q8—22no—
397C4⋊Q8D4×C3711yescharacteristic
398C4⋊Q8D4×C3711yescharacteristic
399C4⋊Q8C23×C3711yescharacteristic
400#127C23×C3711yescharacteristic
401#126—22no—
402#126—22no—
403#126—22no—
404#126—21no—
405#125C23×C3711yescharacteristic
406#125C23×C3712yes—
407#124—21no—
408#124—22no—
409#124—22no—
410#124—21no—
411#124—21no—
412#124—21no—
413#124D4×C3712yes—
414#124C23×C3712yes—
415#124C23×C3711yescharacteristic
416#123—22no—
417#123—22no—
418#123—21no—
419#123—22no—
420#123—22no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423C22⋊Q8—21no—
424C22⋊Q8—22no—
425C22⋊Q8—22no—
426C22⋊Q8—22no—
427C22⋊Q8—21no—
428C22⋊Q8—21no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8D4×C3711yescharacteristic
432#121—21no—
433#121—22no—
434#121—22no—
435#121—21no—
436#121—21no—
437#121D4×C3711yescharacteristic
438#120—22no—
439C4×Q8—21no—
440C4×Q8—21no—
441C4×Q8—21no—
442C4×Q8D4×C3711yescharacteristic
443C4×D4—22no—
444C4×D4—21no—
445C4×D4—22no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4D4×C3711yescharacteristic
450#117—22no—
451#117—21no—
452#117D4×C3712yes—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C42C23×C3711yescharacteristic
457#107—21no—
458#107—22no—
459#106—21no—
460#106—22no—
461C4⋊C8—21no—
462#103—21no—
463#102—21no—
464#102—21no—
465#102—21no—
466#102—22no—
467#102—22no—
468C22⋊C8—21no—
469#97C23×C3712yes—
470#97C23×C3711yescharacteristic
471#97C23×C3711yescharacteristic
472#97C23×C3712yes—
473C4×C8—21no—
474C4×C8—21no—
475C24—21no—
476#41—42no—
477#41—42no—
478#41—82no—
479C2×Q8—22no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—42no—
485C2×Q8—82no—
486C2×Q8C2×D4×C3711yescharacteristic
487C2×Q8C2×D4×C3712yes—
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—41no—
497C2×D4C2×D4×C3711yescharacteristic
498C2×D4C2×D4×C3712yes—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—41no—
505C22×C4C2×D4×C3711yescharacteristic
506C22×C4C2×D4×C3711yescharacteristic
507C22×C4C2×D4×C3711yescharacteristic
508Q16—44no—
509SD16—42no—
510SD16—44no—
511SD16—44no—
512D8—42no—
513D8—44no—
514M16—24no—
515M16—42no—
516C2×C8—21no—
517C2×C8—22no—
518C2×C8—21no—
519C2×C8—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4C2×D4×C3712yes—
535C4⋊C4C2×D4×C3711yescharacteristic
536C4⋊C4C2×D4×C3712yes—
537C4⋊C4C2×D4×C3711yescharacteristic
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—21no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—41no—
554C22⋊C4—41no—
555C42—22no—
556C42—22no—
557C42—21no—
558C42C2×D4×C3711yescharacteristic
559C42C2×D4×C3711yescharacteristic
560C42C2×D4×C3711yescharacteristic
561C42C24×C3711yescharacteristic
562C23—22no—
563C23—21no—
564C23—42no—
565C23—41no—
566C23—81no—
567C23—81no—
568C23#120×C3711yescharacteristic
569Q8—42no—
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—42no—
574Q8—42no—
575Q8—81no—
576Q8—82no—
577D4—42no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—42no—
584D4—42no—
585D4—42no—
586D4—82no—
587D4—82no—
588D4—82no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—81no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4#120×C3711yescharacteristic
606C2×C4#120×C3711yescharacteristic
607C2×C4#120×C3711yescharacteristic
608C2×C4C22×D4×C3711yescharacteristic
609C2×C4C22×D4×C3711yescharacteristic
610C2×C4C22×D4×C3711yescharacteristic
611C8—24no—
612C8—22no—
613C8—41no—
614C8—42no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—41no—
619C22—42no—
620C22—42no—
621C22—41no—
622C22—41no—
623C22—42no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—162no—
628C22C2×#120×C3711yescharacteristic
629C4—21no—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—41no—
635C4—42no—
636C4—42no—
637C4—41no—
638C4—42no—
639C4—41no—
640C4—81no—
641C4C37×#45312yes—
642C2—41no—
643C2—82no—
644C2—81no—
645C2—161no—
646C2C2×C37×#45311yescharacteristic
647C2C37×#301811yescharacteristic
648C2C37×#302011yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3561C2semidirect
2. C37×#3235C2semidirect
3. C37×#3171C2semidirect
4. C37×#3153C2semidirect
5. C37×#1661C2semidirect
6. C37×#1660C2semidirect
7. C37×#1657C2semidirect
8. C37×#1656C2semidirect
9. C37×#1529C2semidirect
10. C37×#1527C2semidirect
11. C37×#1526C2semidirect
30. C37×#501C22semidirect
31. C37×#501C22semidirect
34. C37×#496C22semidirect
36. C37×#490C22semidirect
37. C37×#490C22semidirect
38. C37×#489C22semidirect
49. C37×#330C22semidirect
50. C37×#330C22semidirect
51. C37×#330C22semidirect
54. C37×#329C22semidirect
290. #19019C37direct (N × H)
318. #3561C2×C37semidirect
319. #3235C2×C37semidirect
320. #3171C2×C37semidirect
321. #3153C2×C37semidirect
322. #1661C2×C37semidirect
323. #1660C2×C37semidirect
324. #1657C2×C37semidirect
325. #1656C2×C37semidirect
326. #1529C2×C37semidirect
327. #1527C2×C37semidirect
328. #1526C2×C37semidirect
354. #501C22×C37semidirect
355. #501C22×C37semidirect
358. #496C22×C37semidirect
360. #490C22×C37semidirect
361. #490C22×C37semidirect
362. #489C22×C37semidirect
373. #330C22×C37semidirect
374. #330C22×C37semidirect
375. #330C22×C37semidirect
378. #329C22×C37semidirect
379. C37#19019direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35612
C37×#32352
C37×#31712
C37×#31532
C37×#16612
C37×#16602
C37×#16572
C37×#16562
C37×#15292
C37×#15272
C37×#15262
#1901937