Finite Group Databasebeta

← C37×#24086 #22645339

Subgroups — C37×#24086 #22645339

Order 9472.

1014 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3495C211yesmaximal, characteristic
2C37×#3092C211yesmaximal, characteristic
3C2×C37×#428C211yesmaximal, characteristic, complemented
4C37×#2502C211yesmaximal, characteristic, complemented
5C37×#2060C212yesmaximal, complemented
6C37×#2038C212yesmaximal, complemented
7C37×#1901C211yesmaximal, characteristic, complemented
8C37×#1871C211yesmaximal, characteristic
9C37×#1859C212yesmaximal, complemented
10C37×#1857C212yesmaximal, complemented
11C37×#1826C211yesmaximal, characteristic, complemented
12C22×M16×C37C2211yescharacteristic
13C37×#556—21no—
14C37×#554—21no—
15C37×#552—21no—
16C37×#552—22no—
17C37×#552—21no—
18C37×#551—22no—
19C37×#544C2211yescharacteristic
20C37×#542—21no—
21C37×#541—21no—
22C37×#536C2211yescharacteristic
23C37×#533—21no—
24C37×#529—21no—
25C37×#525C2211yescharacteristic
26C2×C22⋊Q8×C37C2211yescharacteristic
27C37×#520C2211yescharacteristic
28C37×#519C2211yescharacteristic
29C2×#117×C37C2211yescharacteristic
30C22×C4⋊C4×C37C2211yescharacteristic
31C37×#484—21no—
32C37×#483—21no—
33C37×#481—21no—
34C37×#480—21no—
35C37×#428—21no—
36C37×#428—21no—
37C37×#428C2212yes—
38C37×#428C2212yes—
39C37×#428C2212yes—
40C2×#107×C37—21no—
41C2×#106×C37—21no—
42C2×#104×C37C2212yes—
43C37×#417C2212yes—
44C2×#101×C37C2212yes—
45C37×#407C2211yescharacteristic
46C37×#398—22no—
47C37×#391C2212yes—
48C37×#385—22no—
49C37×#384C2212yes—
50C4×C22⋊C4×C37C2211yescharacteristic
51C37×#343C2212yes—
52C37×#339C2212yes—
53C37×#339C2212yes—
54C37×#339C2212yes—
55C2×#41×C37C2311yescharacteristic
56C22×Q8×C37C2311yescharacteristic
57C23×C4×C37—21no—
58C23×C4×C37C2311yescharacteristic
59C2×M16×C37—21no—
60C2×M16×C37—24no—
61C2×M16×C37C2312yes—
62C2×M16×C37C2312yes—
63C22×C8×C37—21no—
64C4⋊Q8×C37—21no—
65C4⋊Q8×C37—21no—
66C4⋊Q8×C37—21no—
67#126×C37—22no—
68#126×C37—22no—
69#126×C37—22no—
70#126×C37—22no—
71#125×C37—22no—
72#125×C37—22no—
73#125×C37—22no—
74#125×C37—21no—
75#125×C37—21no—
76#124×C37—22no—
77#124×C37—21no—
78#123×C37—22no—
79#123×C37—22no—
80#123×C37—21no—
81#123×C37—22no—
82C22⋊Q8×C37—22no—
83C22⋊Q8×C37—22no—
84C22⋊Q8×C37—21no—
85C22⋊Q8×C37—21no—
86C22⋊Q8×C37—21no—
87C22⋊Q8×C37—21no—
88C22⋊Q8×C37—22no—
89C22⋊Q8×C37—21no—
90C22⋊Q8×C37—21no—
91C22⋊Q8×C37D411yescharacteristic
92C22⋊Q8×C37D411yescharacteristic
93#121×C37D411yescharacteristic
94#121×C37D411yescharacteristic
95#120×C37—21no—
96C4×Q8×C37—22no—
97C4×Q8×C37—21no—
98C4×Q8×C37—21no—
99C4×Q8×C37—21no—
100C4×Q8×C37—21no—
101C4×Q8×C37—21no—
102C4×D4×C37—22no—
103C4×D4×C37—21no—
104C4×D4×C37—22no—
105C4×D4×C37—21no—
106C4×D4×C37—21no—
107#117×C37—22no—
108#117×C37—22no—
109#117×C37—22no—
110#117×C37—21no—
111#117×C37—21no—
112#117×C37—21no—
113#117×C37D411yescharacteristic
114#117×C37D411yescharacteristic
115#117×C37C2311yescharacteristic
116#117×C37C2311yescharacteristic
117#117×C37C2311yescharacteristic
118C2×C4⋊C4×C37—21no—
119C2×C4⋊C4×C37—21no—
120C2×C4⋊C4×C37—21no—
121C2×C4⋊C4×C37—21no—
122C2×C4⋊C4×C37—21no—
123C2×C4⋊C4×C37—21no—
124C2×C4⋊C4×C37—24no—
125C2×C4⋊C4×C37D412yes—
126C2×C4⋊C4×C37D411yescharacteristic
127C2×C4⋊C4×C37D411yescharacteristic
128C2×C4⋊C4×C37C2312yes—
129C2×C4⋊C4×C37C2311yescharacteristic
130C2×C22⋊C4×C37—21no—
131C2×C22⋊C4×C37—21no—
132C2×C22⋊C4×C37D412yes—
133C2×C42×C37—21no—
134C2×C42×C37C2312yes—
135#107×C37—22no—
136#107×C37—22no—
137#107×C37—22no—
138#106×C37—22no—
139#106×C37—22no—
140#106×C37—22no—
141#104×C37—24no—
142#103×C37—22no—
143#102×C37—22no—
144#101×C37—24no—
145C22⋊C8×C37—21no—
146C22⋊C8×C37—21no—
147#95×C37—21no—
148#95×C37—24no—
149C24×C37C2×D411yescharacteristic
150#41×C37—22no—
151#41×C37—22no—
152C2×Q8×C37—22no—
153C2×Q8×C37—21no—
154C2×Q8×C37—21no—
155C2×Q8×C37—22no—
156C2×Q8×C37—22no—
157C2×Q8×C37C2×D411yescharacteristic
158C2×D4×C37—21no—
159C2×D4×C37—21no—
160C2×D4×C37—21no—
161C2×D4×C37C2×D411yescharacteristic
162C22×C4×C37—22no—
163C22×C4×C37—22no—
164C22×C4×C37—21no—
165C22×C4×C37—22no—
166C22×C4×C37—22no—
167C22×C4×C37—21no—
168C22×C4×C37—21no—
169C22×C4×C37—22no—
170C22×C4×C37—41no—
171C22×C4×C37—41no—
172C22×C4×C37—82no—
173C22×C4×C37C2×D412yes—
174C22×C4×C37C2×D411yescharacteristic
175C22×C4×C37C2×D411yescharacteristic
176C22×C4×C37C2×D411yescharacteristic
177C22×C4×C37C2×D411yescharacteristic
178C22×C4×C37C2×D411yescharacteristic
179C22×C4×C37C2×D412yes—
180C22×C4×C37C2411yescharacteristic
181M16×C37—24no—
182M16×C37—22no—
183M16×C37—22no—
184M16×C37—22no—
185M16×C37#4114yes—
186C2×C8×C37—24no—
187C2×C8×C37—22no—
188C2×C8×C37—22no—
189C4⋊C4×C37—22no—
190C4⋊C4×C37—22no—
191C4⋊C4×C37—22no—
192C4⋊C4×C37—22no—
193C4⋊C4×C37—22no—
194C4⋊C4×C37—22no—
195C4⋊C4×C37—22no—
196C4⋊C4×C37—22no—
197C4⋊C4×C37—21no—
198C4⋊C4×C37—21no—
199C4⋊C4×C37—22no—
200C4⋊C4×C37—22no—
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—41no—
208C4⋊C4×C37—41no—
209C4⋊C4×C37—84no—
210C4⋊C4×C37C2×D411yescharacteristic
211C4⋊C4×C37C2×D411yescharacteristic
212C4⋊C4×C37C2×D411yescharacteristic
213C4⋊C4×C37C2×D411yescharacteristic
214C4⋊C4×C37C2×D411yescharacteristic
215C4⋊C4×C37C2×D411yescharacteristic
216C22⋊C4×C37—24no—
217C22⋊C4×C37—22no—
218C22⋊C4×C37—22no—
219C22⋊C4×C37—22no—
220C22⋊C4×C37—21no—
221C22⋊C4×C37—21no—
222C22⋊C4×C37—22no—
223C22⋊C4×C37—22no—
224C22⋊C4×C37—21no—
225C22⋊C4×C37—21no—
226C22⋊C4×C37—21no—
227C22⋊C4×C37—21no—
228C22⋊C4×C37—21no—
229C22⋊C4×C37—21no—
230C22⋊C4×C37—21no—
231C42×C37—22no—
232C42×C37—22no—
233C42×C37—22no—
234C42×C37—21no—
235C42×C37—21no—
236C42×C37—21no—
237C42×C37—21no—
238C42×C37—21no—
239C42×C37—22no—
240C42×C37—22no—
241C23×C37—22no—
242C23×C37—22no—
243C23×C37—21no—
244C23×C37—41no—
245C23×C37#12011yescharacteristic
246C23×C37#12011yescharacteristic
247C23×C37C22×D411yescharacteristic
248Q8×C37—22no—
249Q8×C37—41no—
250Q8×C37—41no—
251Q8×C37—42no—
252Q8×C37—82no—
253D4×C37—22no—
254D4×C37—42no—
255D4×C37—42no—
256D4×C37—81no—
257C2×C4×C37—22no—
258C2×C4×C37—21no—
259C2×C4×C37—21no—
260C2×C4×C37—21no—
261C2×C4×C37—21no—
262C2×C4×C37—22no—
263C2×C4×C37—22no—
264C2×C4×C37—24no—
265C2×C4×C37—21no—
266C2×C4×C37—21no—
267C2×C4×C37—21no—
268C2×C4×C37—21no—
269C2×C4×C37—21no—
270C2×C4×C37—22no—
271C2×C4×C37—21no—
272C2×C4×C37—21no—
273C2×C4×C37—22no—
274C2×C4×C37—24no—
275C2×C4×C37—42no—
276C2×C4×C37—42no—
277C2×C4×C37—42no—
278C2×C4×C37—41no—
279C2×C4×C37—41no—
280C2×C4×C37—42no—
281C2×C4×C37—44no—
282C2×C4×C37—42no—
283C2×C4×C37—81no—
284C2×C4×C37—82no—
285C2×C4×C37—82no—
286C2×C4×C37—82no—
287C2×C4×C37#12011yescharacteristic
288C2×C4×C37#12011yescharacteristic
289C2×C4×C37C22×D411yescharacteristic
290C2×C4×C37C22×D411yescharacteristic
291C2×C4×C37C2×#4112yes—
292C2×C4×C372−1+412yes—
293C8×C37—24no—
294C8×C37—42no—
295#24086C3711yesmaximal, characteristic, direct product factor, Sylow
296C22×C37—21no—
297C22×C37—21no—
298C22×C37—21no—
299C22×C37—21no—
300C22×C37—21no—
301C22×C37—21no—
302C22×C37—21no—
303C22×C37—44no—
304C22×C37—41no—
305C22×C37—41no—
306C22×C37—41no—
307C22×C37#45612yes—
308C22×C37C2×#12011yescharacteristic
309C22×C37#54712yes—
310C4×C37—21no—
311C4×C37—21no—
312C4×C37—44no—
313C4×C37—42no—
314C4×C37—41no—
315C4×C37—41no—
316C4×C37—41no—
317C4×C37—41no—
318C4×C37—42no—
319C4×C37—41no—
320C4×C37—41no—
321C4×C37—41no—
322C4×C37—82no—
323C4×C37#52511yescharacteristic
324C4×C37#53611yescharacteristic
325C4×C37#54712yes—
326#3495C2×C3711yescharacteristic
327#3092C2×C3711yescharacteristic
328C2×#428C2×C3711yescharacteristic, complemented
329#2502C2×C3711yescharacteristic, complemented
330#2060C2×C3712yescomplemented
331#2038C2×C3712yescomplemented
332#1901C2×C3711yescharacteristic, complemented
333#1871C2×C3711yescharacteristic
334#1859C2×C3712yescomplemented
335#1857C2×C3712yescomplemented
336#1826C2×C3711yescharacteristic, complemented
337C2×C37—22no—
338C2×C37—22no—
339C2×C37—41no—
340C2×C37—81no—
341C2×C37#240611yescharacteristic
342C2×C37C2×#45611yescharacteristic
343C2×C37#302111yescharacteristic
344C22×M16C22×C3711yescharacteristic
345#556—21no—
346#554—21no—
347#552—21no—
348#552—22no—
349#552—21no—
350#551—22no—
351#544C22×C3711yescharacteristic
352#542—21no—
353#541—21no—
354#536C22×C3711yescharacteristic
355#533—21no—
356#529—21no—
357#525C22×C3711yescharacteristic
358C2×C22⋊Q8C22×C3711yescharacteristic
359#520C22×C3711yescharacteristic
360#519C22×C3711yescharacteristic
361C2×#117C22×C3711yescharacteristic
362C22×C4⋊C4C22×C3711yescharacteristic
363#484—21no—
364#483—21no—
365#481—21no—
366#480—21no—
367#428—21no—
368#428—21no—
369#428C22×C3712yes—
370#428C22×C3712yes—
371#428C22×C3712yes—
372C2×#107—21no—
373C2×#106—21no—
374C2×#104C22×C3712yes—
375#417C22×C3712yes—
376C2×#101C22×C3712yes—
377#407C22×C3711yescharacteristic
378#398—22no—
379#391C22×C3712yes—
380#385—22no—
381#384C22×C3712yes—
382C4×C22⋊C4C22×C3711yescharacteristic
383#343C22×C3712yes—
384#339C22×C3712yes—
385#339C22×C3712yes—
386#339C22×C3712yes—
387C37#2408611yescharacteristic, direct product factor, Sylow
388C2×#41C23×C3711yescharacteristic
389C22×Q8C23×C3711yescharacteristic
390C23×C4—21no—
391C23×C4C23×C3711yescharacteristic
392C2×M16—21no—
393C2×M16—24no—
394C2×M16C23×C3712yes—
395C2×M16C23×C3712yes—
396C22×C8—21no—
397C4⋊Q8—21no—
398C4⋊Q8—21no—
399C4⋊Q8—21no—
400#126—22no—
401#126—22no—
402#126—22no—
403#126—22no—
404#125—22no—
405#125—22no—
406#125—22no—
407#125—21no—
408#125—21no—
409#124—22no—
410#124—21no—
411#123—22no—
412#123—22no—
413#123—21no—
414#123—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—22no—
422C22⋊Q8—21no—
423C22⋊Q8—21no—
424C22⋊Q8D4×C3711yescharacteristic
425C22⋊Q8D4×C3711yescharacteristic
426#121D4×C3711yescharacteristic
427#121D4×C3711yescharacteristic
428#120—21no—
429C4×Q8—22no—
430C4×Q8—21no—
431C4×Q8—21no—
432C4×Q8—21no—
433C4×Q8—21no—
434C4×Q8—21no—
435C4×D4—22no—
436C4×D4—21no—
437C4×D4—22no—
438C4×D4—21no—
439C4×D4—21no—
440#117—22no—
441#117—22no—
442#117—21no—
443#117—21no—
444#117—22no—
445#117—21no—
446#117D4×C3711yescharacteristic
447#117D4×C3711yescharacteristic
448#117C23×C3711yescharacteristic
449#117C23×C3711yescharacteristic
450#117C23×C3711yescharacteristic
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4D4×C3712yes—
459C2×C4⋊C4D4×C3711yescharacteristic
460C2×C4⋊C4D4×C3711yescharacteristic
461C2×C4⋊C4C23×C3712yes—
462C2×C4⋊C4C23×C3711yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4D4×C3712yes—
466C2×C42—21no—
467C2×C42C23×C3712yes—
468#107—22no—
469#107—22no—
470#107—22no—
471#106—22no—
472#106—22no—
473#106—22no—
474#104—24no—
475#103—22no—
476#102—22no—
477#101—24no—
478C22⋊C8—21no—
479C22⋊C8—21no—
480#95—21no—
481#95—24no—
482C24C2×D4×C3711yescharacteristic
483#41—22no—
484#41—22no—
485C2×Q8—22no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8C2×D4×C3711yescharacteristic
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4C2×D4×C3711yescharacteristic
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—82no—
506C22×C4C2×D4×C3712yes—
507C22×C4C2×D4×C3711yescharacteristic
508C22×C4C2×D4×C3711yescharacteristic
509C22×C4C2×D4×C3711yescharacteristic
510C22×C4C2×D4×C3711yescharacteristic
511C22×C4C2×D4×C3711yescharacteristic
512C22×C4C2×D4×C3712yes—
513C22×C4C24×C3711yescharacteristic
514M16—24no—
515M16—22no—
516M16—22no—
517M16—22no—
518M16#41×C3714yes—
519C2×C8—24no—
520C2×C8—22no—
521C2×C8—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—84no—
543C4⋊C4C2×D4×C3711yescharacteristic
544C4⋊C4C2×D4×C3711yescharacteristic
545C4⋊C4C2×D4×C3711yescharacteristic
546C4⋊C4C2×D4×C3711yescharacteristic
547C4⋊C4C2×D4×C3711yescharacteristic
548C4⋊C4C2×D4×C3711yescharacteristic
549C22⋊C4—24no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C42—22no—
565C42—22no—
566C42—22no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—22no—
573C42—22no—
574C23—22no—
575C23—22no—
576C23—21no—
577C23—41no—
578C23#120×C3711yescharacteristic
579C23#120×C3711yescharacteristic
580C23C22×D4×C3711yescharacteristic
581Q8—22no—
582Q8—41no—
583Q8—41no—
584Q8—42no—
585Q8—82no—
586D4—22no—
587D4—42no—
588D4—42no—
589D4—81no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—44no—
615C2×C4—42no—
616C2×C4—81no—
617C2×C4—82no—
618C2×C4—82no—
619C2×C4—82no—
620C2×C4#120×C3711yescharacteristic
621C2×C4#120×C3711yescharacteristic
622C2×C4C22×D4×C3711yescharacteristic
623C2×C4C22×D4×C3711yescharacteristic
624C2×C4C2×#41×C3712yes—
625C2×C42−1+4×C3712yes—
626C8—24no—
627C8—42no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—44no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C37×#45612yes—
640C22C2×#120×C3711yescharacteristic
641C22C37×#54712yes—
642C4—21no—
643C4—21no—
644C4—44no—
645C4—42no—
646C4—41no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—42no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—82no—
655C4C37×#52511yescharacteristic
656C4C37×#53611yescharacteristic
657C4C37×#54712yes—
658C2—22no—
659C2—22no—
660C2—41no—
661C2—81no—
662C2C37×#240611yescharacteristic
663C2C2×C37×#45611yescharacteristic
664C2C37×#302111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C37×#428C2semidirect
4. C37×#2502C2semidirect
5. C37×#2060C2semidirect
6. C37×#2038C2semidirect
7. C37×#1901C2semidirect
9. C37×#1859C2semidirect
10. C37×#1857C2semidirect
11. C37×#1826C2semidirect
295. #24086C37direct (N × H)
328. C2×#428C2×C37semidirect
329. #2502C2×C37semidirect
330. #2060C2×C37semidirect
331. #2038C2×C37semidirect
332. #1901C2×C37semidirect
334. #1859C2×C37semidirect
335. #1857C2×C37semidirect
336. #1826C2×C37semidirect
387. C37#24086direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34952
C37×#30922
C2×C37×#4282
C37×#25022
C37×#20602
C37×#20382
C37×#19012
C37×#18712
C37×#18592
C37×#18572
C37×#18262
#2408637