Finite Group Databasebeta

← C37×#13901 #22635154

Subgroups — C37×#13901 #22635154

Order 9472.

1818 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#383C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊C4×C37C211yesmaximal, characteristic
3C22×#95×C37C211yesmaximal, characteristic
4C37×#1443C212yesmaximal, complemented
5C37×#1443C212yesmaximal, complemented
6C37×#1434C211yesmaximal, characteristic, complemented
7C37×#1434C211yesmaximal, characteristic, complemented
8C37×#1434C211yesmaximal, characteristic, complemented
9C37×C22⋊#95C212yesmaximal
10C37×C22⋊#95C212yesmaximal
11C37×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C37C2212yes—
13C24×C4×C37C2211yescharacteristic
14C22×C22⋊C4×C37C2212yes—
15C22×C22⋊C4×C37C2211yescharacteristic
16C22×C22⋊C4×C37C2211yescharacteristic
17C22×C42×C37C2211yescharacteristic
18C22×C42×C37C2211yescharacteristic
19C37×#383—24no—
20C4×C22⋊C4×C37C418yescomplemented
21C2×#95×C37—24no—
22C2×#95×C37C2211yescharacteristic
23C2×#95×C37C2212yes—
24C2×#95×C37C2212yes—
25C2×#95×C37C2211yescharacteristic
26C2×#95×C37C2212yes—
27C2×#95×C37C2212yes—
28C2×#95×C37C2211yescharacteristic
29C2×#95×C37C2212yes—
30C2×#95×C37C2212yes—
31C2×#95×C37C2212yes—
32C2×#95×C37C2212yes—
33C2×#95×C37C2212yes—
34C2×#95×C37C2212yes—
35C2×#95×C37C2211yescharacteristic
36C2×#95×C37C2211yescharacteristic
37C2×#95×C37C2211yescharacteristic
38C25×C37C2311yescharacteristic
39C23×C4×C37—24no—
40C23×C4×C37—24no—
41C23×C4×C37—24no—
42C23×C4×C37—22no—
43C23×C4×C37—24no—
44C23×C4×C37—22no—
45C23×C4×C37—24no—
46C23×C4×C37—24no—
47C23×C4×C37—42no—
48C23×C4×C37—42no—
49C23×C4×C37—42no—
50C23×C4×C37C2×C414yes—
51C23×C4×C37C2312yes—
52C23×C4×C37C2312yes—
53C23×C4×C37C2311yescharacteristic
54C23×C4×C37C2311yescharacteristic
55C23×C4×C37C2311yescharacteristic
56C23×C4×C37C2311yescharacteristic
57C23×C4×C37C2311yescharacteristic
58C23×C4×C37C2312yes—
59C23×C4×C37C2312yes—
60C23×C4×C37C2311yescharacteristic
61C2×C22⋊C4×C37—22no—
62C2×C22⋊C4×C37—24no—
63C2×C22⋊C4×C37—22no—
64C2×C22⋊C4×C37—24no—
65C2×C22⋊C4×C37—24no—
66C2×C22⋊C4×C37—24no—
67C2×C22⋊C4×C37C2×C414yes—
68C2×C22⋊C4×C37C2×C414yes—
69C2×C42×C37—22no—
70C2×C42×C37—22no—
71C2×C42×C37—42no—
72C2×C42×C37C2×C414yescomplemented
73C2×C42×C37C2×C414yescomplemented
74#95×C37—24no—
75#95×C37—22no—
76#95×C37—24no—
77#95×C37—24no—
78#95×C37—22no—
79#95×C37—24no—
80#95×C37—24no—
81#95×C37—22no—
82#95×C37—42no—
83#95×C37—42no—
84#95×C37—42no—
85#95×C37—42no—
86#95×C37—42no—
87#95×C37C2×C414yescomplemented
88#95×C37C2×C414yescomplemented
89#95×C37D414yes—
90C24×C37—21no—
91C24×C37—21no—
92C24×C37—22no—
93C24×C37—22no—
94C24×C37—21no—
95C24×C37—21no—
96C24×C37C22×C412yes—
97C24×C37#4112yes—
98C24×C37#4114yes—
99C24×C37#4112yes—
100C24×C37#4114yes—
101C24×C37C2411yescharacteristic
102C22×C4×C37—22no—
103C22×C4×C37—22no—
104C22×C4×C37—216no—
105C22×C4×C37—28no—
106C22×C4×C37—21no—
107C22×C4×C37—21no—
108C22×C4×C37—21no—
109C22×C4×C37—22no—
110C22×C4×C37—22no—
111C22×C4×C37—22no—
112C22×C4×C37—21no—
113C22×C4×C37—21no—
114C22×C4×C37—22no—
115C22×C4×C37—22no—
116C22×C4×C37—21no—
117C22×C4×C37—21no—
118C22×C4×C37—21no—
119C22×C4×C37—21no—
120C22×C4×C37—22no—
121C22×C4×C37—21no—
122C22×C4×C37—22no—
123C22×C4×C37—22no—
124C22×C4×C37—22no—
125C22×C4×C37—22no—
126C22×C4×C37—22no—
127C22×C4×C37—22no—
128C22×C4×C37—22no—
129C22×C4×C37—21no—
130C22×C4×C37—21no—
131C22×C4×C37—22no—
132C22×C4×C37—22no—
133C22×C4×C37—22no—
134C22×C4×C37—22no—
135C22×C4×C37—22no—
136C22×C4×C37—22no—
137C22×C4×C37—22no—
138C22×C4×C37—21no—
139C22×C4×C37—21no—
140C22×C4×C37—28no—
141C22×C4×C37—22no—
142C22×C4×C37—22no—
143C22×C4×C37—22no—
144C22×C4×C37—22no—
145C22×C4×C37—22no—
146C22×C4×C37—22no—
147C22×C4×C37—22no—
148C22×C4×C37—22no—
149C22×C4×C37—22no—
150C22×C4×C37—22no—
151C22×C4×C37—22no—
152C22×C4×C37—22no—
153C22×C4×C37—22no—
154C22×C4×C37—22no—
155C22×C4×C37—44no—
156C22×C4×C37—48no—
157C22×C4×C37—48no—
158C22×C4×C37—48no—
159C22×C4×C37—48no—
160C22×C4×C37—48no—
161C22×C4×C37—48no—
162C22×C4×C37—48no—
163C22×C4×C37—48no—
164C22×C4×C37C22×C412yes—
165C22×C4×C37C22×C412yes—
166C22×C4×C37C22×C412yes—
167C22×C4×C37C22×C412yes—
168C22×C4×C37C22×C412yes—
169C22×C4×C37C22×C412yes—
170C22×C4×C37C2×D414yes—
171C22×C4×C37C2×D412yes—
172C22×C4×C37#4114yes—
173C22×C4×C37#4112yes—
174C22⋊C4×C37—28no—
175C22⋊C4×C37—28no—
176C22⋊C4×C37—48no—
177C42×C37—28no—
178C42×C37—44no—
179C23×C37—22no—
180C23×C37—22no—
181C23×C37—22no—
182C23×C37—22no—
183C23×C37—24no—
184C23×C37—24no—
185C23×C37—24no—
186C23×C37—24no—
187C23×C37—24no—
188C23×C37—22no—
189C23×C37—22no—
190C23×C37—24no—
191C23×C37—24no—
192C23×C37—24no—
193C23×C37—24no—
194C23×C37—22no—
195C23×C37—22no—
196C23×C37—24no—
197C23×C37#11714yes—
198C23×C37#11714yes—
199C23×C37#11714yes—
200C23×C37#12618yes—
201C23×C37#12618yes—
202C23×C37C23×C411yescharacteristic
203C23×C37C22×D411yescharacteristic
204C23×C37C2×#4112yes—
205C23×C37C2×#4112yes—
206C23×C37C2×#4111yescharacteristic
207C23×C37C2×#4111yescharacteristic
208C23×C37C2×#4111yescharacteristic
209C23×C37C2×#4112yes—
210C23×C37H(5,𝔽2)12yes—
211C23×C37H(5,𝔽2)11yescharacteristic
212C23×C372−1+411yescharacteristic
213C2×C4×C37—22no—
214C2×C4×C37—22no—
215C2×C4×C37—24no—
216C2×C4×C37—24no—
217C2×C4×C37—22no—
218C2×C4×C37—22no—
219C2×C4×C37—22no—
220C2×C4×C37—22no—
221C2×C4×C37—22no—
222C2×C4×C37—22no—
223C2×C4×C37—22no—
224C2×C4×C37—22no—
225C2×C4×C37—22no—
226C2×C4×C37—22no—
227C2×C4×C37—22no—
228C2×C4×C37—22no—
229C2×C4×C37—22no—
230C2×C4×C37—22no—
231C2×C4×C37—22no—
232C2×C4×C37—24no—
233C2×C4×C37—24no—
234C2×C4×C37—24no—
235C2×C4×C37—24no—
236C2×C4×C37—24no—
237C2×C4×C37—24no—
238C2×C4×C37—416no—
239C2×C4×C37—432no—
240C2×C4×C37—42no—
241C2×C4×C37—42no—
242C2×C4×C37—42no—
243C2×C4×C37—42no—
244C2×C4×C37—42no—
245C2×C4×C37—42no—
246C2×C4×C37—42no—
247C2×C4×C37—42no—
248C2×C4×C37—41no—
249C2×C4×C37—42no—
250C2×C4×C37—42no—
251C2×C4×C37—42no—
252C2×C4×C37—41no—
253C2×C4×C37—42no—
254C2×C4×C37—42no—
255C2×C4×C37—42no—
256C2×C4×C37—42no—
257C2×C4×C37—41no—
258C2×C4×C37—41no—
259C2×C4×C37—42no—
260C2×C4×C37—42no—
261C2×C4×C37—42no—
262C2×C4×C37—42no—
263C2×C4×C37—42no—
264C2×C4×C37—42no—
265C2×C4×C37—42no—
266C2×C4×C37—42no—
267C2×C4×C37—42no—
268C2×C4×C37—42no—
269C2×C4×C37—42no—
270C2×C4×C37—42no—
271C2×C4×C37—42no—
272C2×C4×C37—42no—
273C2×C4×C37—42no—
274C2×C4×C37C4×D414yes—
275#13901C3711yesmaximal, characteristic, direct product factor, Sylow
276C22×C37—24no—
277C22×C37—24no—
278C22×C37—24no—
279C22×C37—24no—
280C22×C37—24no—
281C22×C37—28no—
282C22×C37—28no—
283C22×C37—28no—
284C22×C37—28no—
285C22×C37—24no—
286C22×C37#38318yescomplemented
287C22×C37C2×#11711yescharacteristic
288C22×C37C2×#11711yescharacteristic
289C22×C37C2×#11711yescharacteristic
290C22×C37C2×C4×D411yescharacteristic
291C22×C37C4×#4111yescharacteristic
292C22×C37#51811yescharacteristic
293C22×C37#52011yescharacteristic
294C22×C37#52512yes—
295C22×C37C2×#12612yes—
296C22×C37C2×#12612yes—
297C22×C37#52912yes—
298C22×C37#53812yes—
299C22×C37#53912yes—
300C22×C37#54612yes—
301C22×C37#54611yescharacteristic
302C22×C37#54811yescharacteristic
303C22×C37#55112yes—
304C22×C37#55112yes—
305C22×C37#55112yes—
306C22×C37#55212yes—
307C22×C37#55211yescharacteristic
308C22×C37#55311yescharacteristic
309C22×C37#55312yes—
310C4×C37—24no—
311C4×C37—42no—
312C4×C37—42no—
313C4×C37—42no—
314C4×C37—42no—
315C4×C37—44no—
316C4×C37—44no—
317C4×C37—42no—
318C4×C37—82no—
319C4×C37—82no—
320C2×#383C2×C3711yescharacteristic, complemented
321C2×C4×C22⋊C4C2×C3711yescharacteristic
322C22×#95C2×C3711yescharacteristic
323#1443C2×C3712yescomplemented
324#1443C2×C3712yescomplemented
325#1434C2×C3711yescharacteristic, complemented
326#1434C2×C3711yescharacteristic, complemented
327#1434C2×C3711yescharacteristic, complemented
328C22⋊#95C2×C3711yescharacteristic
329C22⋊#95C2×C3712yes—
330C22⋊#95C2×C3712yes—
331C2×C37—28no—
332C2×C37C2×#38311yescharacteristic
333C2×C37#229011yescharacteristic
334C2×C37#231811yescharacteristic
335C2×C37#234211yescharacteristic
336C2×C37#234311yescharacteristic
337C2×C37#235211yescharacteristic
338C2×C37#235311yescharacteristic
339C2×C37#248012yes—
340C2×C37#248112yes—
341C2×C37#249312yes—
342C2×C37#251012yes—
343C24×C4C22×C3712yes—
344C24×C4C22×C3711yescharacteristic
345C22×C22⋊C4C22×C3712yes—
346C22×C22⋊C4C22×C3711yescharacteristic
347C22×C22⋊C4C22×C3711yescharacteristic
348C22×C42C22×C3711yescharacteristic
349C22×C42C22×C3711yescharacteristic
350#383—24no—
351C4×C22⋊C4C4×C3718yescomplemented
352C2×#95—24no—
353C2×#95C22×C3711yescharacteristic
354C2×#95C22×C3712yes—
355C2×#95C22×C3712yes—
356C2×#95C22×C3711yescharacteristic
357C2×#95C22×C3712yes—
358C2×#95C22×C3712yes—
359C2×#95C22×C3711yescharacteristic
360C2×#95C22×C3712yes—
361C2×#95C22×C3712yes—
362C2×#95C22×C3712yes—
363C2×#95C22×C3712yes—
364C2×#95C22×C3712yes—
365C2×#95C22×C3712yes—
366C2×#95C22×C3711yescharacteristic
367C2×#95C22×C3711yescharacteristic
368C2×#95C22×C3711yescharacteristic
369C37#1390111yescharacteristic, direct product factor, Sylow
370C25C23×C3711yescharacteristic
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—24no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4C2×C4×C3714yes—
383C23×C4C23×C3712yes—
384C23×C4C23×C3712yes—
385C23×C4C23×C3711yescharacteristic
386C23×C4C23×C3711yescharacteristic
387C23×C4C23×C3711yescharacteristic
388C23×C4C23×C3711yescharacteristic
389C23×C4C23×C3711yescharacteristic
390C23×C4C23×C3712yes—
391C23×C4C23×C3712yes—
392C23×C4C23×C3711yescharacteristic
393C2×C22⋊C4—22no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4C2×C4×C3714yes—
400C2×C22⋊C4C2×C4×C3714yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—42no—
404C2×C42C2×C4×C3714yescomplemented
405C2×C42C2×C4×C3714yescomplemented
406#95—24no—
407#95—22no—
408#95—24no—
409#95—24no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—22no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
419#95C2×C4×C3714yescomplemented
420#95C2×C4×C3714yescomplemented
421#95D4×C3714yes—
422C24—21no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24—22no—
427C24—21no—
428C24C22×C4×C3712yes—
429C24#41×C3712yes—
430C24#41×C3714yes—
431C24#41×C3712yes—
432C24#41×C3714yes—
433C24C24×C3711yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—216no—
437C22×C4—28no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—44no—
488C22×C4—48no—
489C22×C4—48no—
490C22×C4—48no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4—48no—
494C22×C4—48no—
495C22×C4—48no—
496C22×C4C22×C4×C3712yes—
497C22×C4C22×C4×C3712yes—
498C22×C4C22×C4×C3712yes—
499C22×C4C22×C4×C3712yes—
500C22×C4C22×C4×C3712yes—
501C22×C4C22×C4×C3712yes—
502C22×C4C2×D4×C3714yes—
503C22×C4C2×D4×C3712yes—
504C22×C4#41×C3714yes—
505C22×C4#41×C3712yes—
506C22⋊C4—28no—
507C22⋊C4—28no—
508C22⋊C4—48no—
509C42—28no—
510C42—44no—
511C23—22no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—22no—
517C23—24no—
518C23—22no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—22no—
523C23—24no—
524C23—22no—
525C23—24no—
526C23—22no—
527C23—22no—
528C23—22no—
529C23#117×C3714yes—
530C23#117×C3714yes—
531C23#117×C3714yes—
532C23#126×C3718yes—
533C23#126×C3718yes—
534C23C23×C4×C3711yescharacteristic
535C23C22×D4×C3711yescharacteristic
536C23C2×#41×C3712yes—
537C23C2×#41×C3712yes—
538C23C2×#41×C3711yescharacteristic
539C23C2×#41×C3712yes—
540C23C2×#41×C3711yescharacteristic
541C23C2×#41×C3711yescharacteristic
542C23H(5,𝔽2)×C3711yescharacteristic
543C23H(5,𝔽2)×C3712yes—
544C232−1+4×C3711yescharacteristic
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—416no—
571C2×C4—432no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4C4×D4×C3714yes—
607C22—24no—
608C22—24no—
609C22—28no—
610C22—28no—
611C22—28no—
612C22—28no—
613C22—24no—
614C22—24no—
615C22—24no—
616C22—24no—
617C22C37×#38318yescomplemented
618C22C2×#117×C3711yescharacteristic
619C22C2×#117×C3711yescharacteristic
620C22C2×#117×C3711yescharacteristic
621C22C2×C4×D4×C3711yescharacteristic
622C22C4×#41×C3711yescharacteristic
623C22C37×#51811yescharacteristic
624C22C37×#52011yescharacteristic
625C22C37×#52512yes—
626C22C2×#126×C3712yes—
627C22C2×#126×C3712yes—
628C22C37×#52912yes—
629C22C37×#53812yes—
630C22C37×#53912yes—
631C22C37×#54611yescharacteristic
632C22C37×#54612yes—
633C22C37×#54811yescharacteristic
634C22C37×#55112yes—
635C22C37×#55112yes—
636C22C37×#55112yes—
637C22C37×#55211yescharacteristic
638C22C37×#55212yes—
639C22C37×#55311yescharacteristic
640C22C37×#55312yes—
641C4—24no—
642C4—42no—
643C4—42no—
644C4—44no—
645C4—44no—
646C4—42no—
647C4—42no—
648C4—42no—
649C4—82no—
650C4—82no—
651C2—28no—
652C2C2×C37×#38311yescharacteristic
653C2C37×#229011yescharacteristic
654C2C37×#231811yescharacteristic
655C2C37×#234211yescharacteristic
656C2C37×#234311yescharacteristic
657C2C37×#235211yescharacteristic
658C2C37×#235311yescharacteristic
659C2C37×#248012yes—
660C2C37×#248112yes—
661C2C37×#249312yes—
662C2C37×#251012yes—
subgroupG/H
center, socleC24×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC24C24×C37
prime radicalC25×C37C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C37×#383C2semidirect
4. C37×#1443C2semidirect
5. C37×#1443C2semidirect
6. C37×#1434C2semidirect
7. C37×#1434C2semidirect
8. C37×#1434C2semidirect
20. C4×C22⋊C4×C37C4semidirect
72. C2×C42×C37C2×C4semidirect
73. C2×C42×C37C2×C4semidirect
87. #95×C37C2×C4semidirect
88. #95×C37C2×C4semidirect
275. #13901C37direct (N × H)
286. C22×C37#383semidirect
320. C2×#383C2×C37semidirect
323. #1443C2×C37semidirect
324. #1443C2×C37semidirect
325. #1434C2×C37semidirect
326. #1434C2×C37semidirect
327. #1434C2×C37semidirect
351. C4×C22⋊C4C4×C37semidirect
369. C37#13901direct (N × H)
404. C2×C42C2×C4×C37semidirect
405. C2×C42C2×C4×C37semidirect
419. #95C2×C4×C37semidirect
420. #95C2×C4×C37semidirect
617. C22C37×#383semidirect

Maximal subgroups

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

subgroupindex
C2×C37×#3832
C2×C4×C22⋊C4×C372
C22×#95×C372
C37×#14432
C37×#14342
C37×C22⋊#952
#1390137