Finite Group Databasebeta

← C37×#13944 #22635197

Subgroups — C37×#13944 #22635197

Order 9472.

1846 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C37C211yesmaximal, characteristic
2C2×C37×#387C212yesmaximal, complemented
3C37×#1445C212yesmaximal, complemented
4C37×#1439C212yesmaximal
5C37×#1437C212yesmaximal
6C37×C4⋊#95C211yesmaximal, characteristic, complemented
7C37×#1434C211yesmaximal, characteristic, complemented
8C37×#1434C211yesmaximal, characteristic, complemented
9C37×C22⋊#95C211yesmaximal, characteristic
10C37×C22⋊#95C211yesmaximal, characteristic
11C4×#95×C37C211yesmaximal, characteristic, complemented
12C24×C4×C37C2211yescharacteristic
13C2×#117×C37—28no—
14C2×#117×C37C418yescomplemented
15C22×C4⋊C4×C37C2212yes—
16C22×C4⋊C4×C37C2211yescharacteristic
17C22×C4⋊C4×C37C2211yescharacteristic
18C22×C22⋊C4×C37C2212yes—
19C22×C22⋊C4×C37C2212yes—
20C22×C22⋊C4×C37C2211yescharacteristic
21C22×C22⋊C4×C37C2211yescharacteristic
22C22×C42×C37C2212yes—
23C22×C42×C37C2211yescharacteristic
24C22×C42×C37C2211yescharacteristic
25C37×#387—28no—
26C2×#95×C37C2211yescharacteristic
27C2×#95×C37C2211yescharacteristic
28C2×#95×C37C2212yes—
29C2×#95×C37C2211yescharacteristic
30C2×#95×C37C2211yescharacteristic
31C2×#95×C37C2212yes—
32C2×#95×C37C2212yes—
33C2×#95×C37C2212yes—
34C2×#95×C37C2212yes—
35C2×#95×C37C2212yes—
36C2×#95×C37C2212yes—
37C2×#95×C37C2212yes—
38C25×C37C2311yescharacteristic
39C23×C4×C37—24no—
40C23×C4×C37—24no—
41C23×C4×C37—22no—
42C23×C4×C37—22no—
43C23×C4×C37C2×C414yes—
44C23×C4×C37C2312yes—
45C23×C4×C37C2312yes—
46C23×C4×C37C2311yescharacteristic
47C23×C4×C37C2311yescharacteristic
48C23×C4×C37C2312yes—
49C23×C4×C37C2312yes—
50C23×C4×C37C2311yescharacteristic
51C23×C4×C37C2311yescharacteristic
52C23×C4×C37C2311yescharacteristic
53C23×C4×C37C2311yescharacteristic
54#117×C37—232no—
55C2×C4⋊C4×C37—24no—
56C2×C4⋊C4×C37—24no—
57C2×C4⋊C4×C37—24no—
58C2×C4⋊C4×C37—42no—
59C2×C4⋊C4×C37C2×C414yes—
60C2×C4⋊C4×C37C2×C414yes—
61C2×C4⋊C4×C37D418yes—
62C2×C22⋊C4×C37—24no—
63C2×C22⋊C4×C37—24no—
64C2×C22⋊C4×C37—24no—
65C2×C22⋊C4×C37—24no—
66C2×C22⋊C4×C37—24no—
67C2×C22⋊C4×C37—24no—
68C2×C22⋊C4×C37—42no—
69C2×C22⋊C4×C37—42no—
70C2×C22⋊C4×C37C2×C414yes—
71C2×C22⋊C4×C37C2×C414yes—
72C2×C42×C37—24no—
73C2×C42×C37—24no—
74C2×C42×C37—24no—
75C2×C42×C37—24no—
76C2×C42×C37—42no—
77C2×C42×C37C2×C414yes—
78C2×C42×C37C2×C414yes—
79#95×C37—24no—
80#95×C37—24no—
81#95×C37—24no—
82#95×C37—24no—
83#95×C37—24no—
84#95×C37—22no—
85#95×C37—22no—
86#95×C37—24no—
87#95×C37—22no—
88#95×C37—22no—
89#95×C37—42no—
90#95×C37—42no—
91C24×C37—22no—
92C24×C37—22no—
93C24×C37—22no—
94C24×C37—21no—
95C24×C37—21no—
96C24×C37—21no—
97C24×C37—21no—
98C24×C37—21no—
99C24×C37—21no—
100C24×C37C22×C412yes—
101C24×C37#4114yes—
102C24×C37C2411yescharacteristic
103C22×C4×C37—216no—
104C22×C4×C37—216no—
105C22×C4×C37—28no—
106C22×C4×C37—22no—
107C22×C4×C37—22no—
108C22×C4×C37—22no—
109C22×C4×C37—21no—
110C22×C4×C37—21no—
111C22×C4×C37—22no—
112C22×C4×C37—22no—
113C22×C4×C37—21no—
114C22×C4×C37—21no—
115C22×C4×C37—21no—
116C22×C4×C37—21no—
117C22×C4×C37—28no—
118C22×C4×C37—28no—
119C22×C4×C37—22no—
120C22×C4×C37—22no—
121C22×C4×C37—22no—
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—22no—
130C22×C4×C37—22no—
131C22×C4×C37—21no—
132C22×C4×C37—21no—
133C22×C4×C37—22no—
134C22×C4×C37—22no—
135C22×C4×C37—22no—
136C22×C4×C37—21no—
137C22×C4×C37—21no—
138C22×C4×C37—22no—
139C22×C4×C37—22no—
140C22×C4×C37—22no—
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×C37C22×C412yes—
154C22×C4×C37C22×C412yes—
155C22×C4×C37C22×C412yes—
156C22×C4×C37C22×C412yes—
157C22×C4×C37C22×C412yes—
158C22×C4×C37C22×C412yes—
159C22×C4×C37C2×D414yes—
160C22×C4×C37C2×D414yes—
161C22×C4×C37C2×D414yes—
162C22×C4×C37#4114yes—
163C22×C4×C37#4114yes—
164C22×C4×C37#4112yes—
165C22×C4×C37#4112yes—
166C4⋊C4×C37—28no—
167C4⋊C4×C37—48no—
168C4⋊C4×C37C22⋊C4116yescomplemented
169C22⋊C4×C37—28no—
170C22⋊C4×C37—28no—
171C22⋊C4×C37—48no—
172C22⋊C4×C37—48no—
173C42×C37—28no—
174C42×C37—28no—
175C42×C37—48no—
176C23×C37—22no—
177C23×C37—22no—
178C23×C37—22no—
179C23×C37—22no—
180C23×C37—22no—
181C23×C37—22no—
182C23×C37—24no—
183C23×C37—24no—
184C23×C37—24no—
185C23×C37—24no—
186C23×C37—24no—
187C23×C37—24no—
188C23×C37—42no—
189C23×C37—42no—
190C23×C37—41no—
191C23×C37—41no—
192C23×C37—41no—
193C23×C37—41no—
194C23×C37—42no—
195C23×C37—42no—
196C23×C37—42no—
197C23×C37—42no—
198C23×C37#11714yes—
199C23×C37C23×C411yescharacteristic
200C23×C37C22×D412yes—
201C23×C37C2×#4111yescharacteristic
202C23×C37C2×#4111yescharacteristic
203C23×C37C2×#4112yes—
204C23×C37C2×#4112yes—
205C23×C37C2×#4112yes—
206C23×C37H(5,𝔽2)11yescharacteristic
207C23×C37H(5,𝔽2)11yescharacteristic
208C23×C372−1+411yescharacteristic
209C23×C372−1+411yescharacteristic
210C2×C4×C37—232no—
211C2×C4×C37—22no—
212C2×C4×C37—22no—
213C2×C4×C37—22no—
214C2×C4×C37—22no—
215C2×C4×C37—22no—
216C2×C4×C37—22no—
217C2×C4×C37—22no—
218C2×C4×C37—22no—
219C2×C4×C37—24no—
220C2×C4×C37—24no—
221C2×C4×C37—24no—
222C2×C4×C37—24no—
223C2×C4×C37—24no—
224C2×C4×C37—24no—
225C2×C4×C37—24no—
226C2×C4×C37—24no—
227C2×C4×C37—22no—
228C2×C4×C37—22no—
229C2×C4×C37—22no—
230C2×C4×C37—22no—
231C2×C4×C37—22no—
232C2×C4×C37—22no—
233C2×C4×C37—24no—
234C2×C4×C37—24no—
235C2×C4×C37—24no—
236C2×C4×C37—24no—
237C2×C4×C37—24no—
238C2×C4×C37—24no—
239C2×C4×C37—42no—
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—42no—
249C2×C4×C37—42no—
250C2×C4×C37—42no—
251C2×C4×C37—42no—
252C2×C4×C37—42no—
253C2×C4×C37—42no—
254C2×C4×C37—42no—
255C2×C4×C37—42no—
256C2×C4×C37—42no—
257C2×C4×C37—42no—
258C2×C4×C37—42no—
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×C37C2×C22⋊C414yes—
266C2×C4×C37C2×C22⋊C414yes—
267C2×C4×C37C2×C22⋊C414yes—
268C2×C4×C37#11714yes—
269#13944C3711yesmaximal, characteristic, direct product factor, Sylow
270C22×C37—24no—
271C22×C37—24no—
272C22×C37—24no—
273C22×C37—42no—
274C22×C37—42no—
275C22×C37—42no—
276C22×C37—44no—
277C22×C37—44no—
278C22×C37—44no—
279C22×C37—44no—
280C22×C37—42no—
281C22×C37C22×C22⋊C411yescharacteristic
282C22×C37C2×#11711yescharacteristic
283C22×C37C2×#11711yescharacteristic
284C22×C37C4×#4111yescharacteristic
285C22×C37C4×#4111yescharacteristic
286C22×C37#52011yescharacteristic
287C22×C37#52011yescharacteristic
288C22×C37#52512yes—
289C22×C37#52512yes—
290C22×C37#52912yes—
291C22×C37#52912yes—
292C22×C37#54011yescharacteristic
293C22×C37#54111yescharacteristic
294C22×C37#54211yescharacteristic
295C22×C37#54211yescharacteristic
296C22×C37#54612yes—
297C22×C37#54712yes—
298C22×C37#54812yes—
299C22×C37#55012yes—
300C22×C37#55112yes—
301C22×C37#55112yes—
302C22×C37#55212yes—
303C22×C37#55212yes—
304C4×C37—24no—
305C4×C37—24no—
306C4×C37—24no—
307C4×C37—24no—
308C4×C37—42no—
309C4×C37—42no—
310C4×C37—44no—
311C4×C37—44no—
312C4×C37—82no—
313C4×C37—82no—
314C22×#117C2×C3711yescharacteristic
315C2×#387C2×C3712yescomplemented
316#1445C2×C3712yescomplemented
317#1439C2×C3712yes—
318#1437C2×C3712yes—
319C4⋊#95C2×C3711yescharacteristic, complemented
320#1434C2×C3711yescharacteristic, complemented
321#1434C2×C3711yescharacteristic, complemented
322C22⋊#95C2×C3711yescharacteristic
323C22⋊#95C2×C3711yescharacteristic
324C4×#95C2×C3711yescharacteristic, complemented
325C2×C37—44no—
326C2×C37#228011yescharacteristic
327C2×C37#229811yescharacteristic
328C2×C37#231411yescharacteristic
329C2×C37#233911yescharacteristic
330C2×C37#234111yescharacteristic
331C2×C37#234311yescharacteristic
332C2×C37#234311yescharacteristic
333C2×C37#247112yes—
334C2×C37#247512yes—
335C2×C37#247712yes—
336C2×C37#247912yes—
337C24×C4C22×C3711yescharacteristic
338C2×#117—28no—
339C2×#117C4×C3718yescomplemented
340C22×C4⋊C4C22×C3712yes—
341C22×C4⋊C4C22×C3711yescharacteristic
342C22×C4⋊C4C22×C3711yescharacteristic
343C22×C22⋊C4C22×C3712yes—
344C22×C22⋊C4C22×C3712yes—
345C22×C22⋊C4C22×C3711yescharacteristic
346C22×C22⋊C4C22×C3711yescharacteristic
347C22×C42C22×C3712yes—
348C22×C42C22×C3711yescharacteristic
349C22×C42C22×C3711yescharacteristic
350#387—28no—
351C2×#95C22×C3711yescharacteristic
352C2×#95C22×C3711yescharacteristic
353C2×#95C22×C3712yes—
354C2×#95C22×C3711yescharacteristic
355C2×#95C22×C3711yescharacteristic
356C2×#95C22×C3712yes—
357C2×#95C22×C3712yes—
358C2×#95C22×C3712yes—
359C2×#95C22×C3712yes—
360C2×#95C22×C3712yes—
361C2×#95C22×C3712yes—
362C2×#95C22×C3712yes—
363C37#1394411yescharacteristic, direct product factor, Sylow
364C25C23×C3711yescharacteristic
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4C2×C4×C3714yes—
370C23×C4C23×C3712yes—
371C23×C4C23×C3712yes—
372C23×C4C23×C3711yescharacteristic
373C23×C4C23×C3711yescharacteristic
374C23×C4C23×C3712yes—
375C23×C4C23×C3712yes—
376C23×C4C23×C3711yescharacteristic
377C23×C4C23×C3711yescharacteristic
378C23×C4C23×C3711yescharacteristic
379C23×C4C23×C3711yescharacteristic
380#117—232no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—24no—
383C2×C4⋊C4—24no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4C2×C4×C3714yes—
386C2×C4⋊C4C2×C4×C3714yes—
387C2×C4⋊C4D4×C3718yes—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4C2×C4×C3714yes—
397C2×C22⋊C4C2×C4×C3714yes—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—42no—
403C2×C42C2×C4×C3714yes—
404C2×C42C2×C4×C3714yes—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—22no—
411#95—22no—
412#95—24no—
413#95—22no—
414#95—22no—
415#95—42no—
416#95—42no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24C22×C4×C3712yes—
427C24#41×C3714yes—
428C24C24×C3711yescharacteristic
429C22×C4—216no—
430C22×C4—216no—
431C22×C4—28no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4C22×C4×C3712yes—
480C22×C4C22×C4×C3712yes—
481C22×C4C22×C4×C3712yes—
482C22×C4C22×C4×C3712yes—
483C22×C4C22×C4×C3712yes—
484C22×C4C22×C4×C3712yes—
485C22×C4C2×D4×C3714yes—
486C22×C4C2×D4×C3714yes—
487C22×C4C2×D4×C3714yes—
488C22×C4#41×C3714yes—
489C22×C4#41×C3714yes—
490C22×C4#41×C3712yes—
491C22×C4#41×C3712yes—
492C4⋊C4—28no—
493C4⋊C4—48no—
494C4⋊C4C22⋊C4×C37116yescomplemented
495C22⋊C4—28no—
496C22⋊C4—28no—
497C22⋊C4—48no—
498C22⋊C4—48no—
499C42—28no—
500C42—28no—
501C42—48no—
502C23—22no—
503C23—22no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—42no—
515C23—42no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23#117×C3714yes—
525C23C23×C4×C3711yescharacteristic
526C23C22×D4×C3712yes—
527C23C2×#41×C3711yescharacteristic
528C23C2×#41×C3711yescharacteristic
529C23C2×#41×C3712yes—
530C23C2×#41×C3712yes—
531C23C2×#41×C3712yes—
532C23H(5,𝔽2)×C3711yescharacteristic
533C23H(5,𝔽2)×C3711yescharacteristic
534C232−1+4×C3711yescharacteristic
535C232−1+4×C3711yescharacteristic
536C2×C4—232no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
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—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4C2×C22⋊C4×C3714yes—
592C2×C4C2×C22⋊C4×C3714yes—
593C2×C4C2×C22⋊C4×C3714yes—
594C2×C4#117×C3714yes—
595C22—24no—
596C22—24no—
597C22—24no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—44no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22C22×C22⋊C4×C3711yescharacteristic
607C22C2×#117×C3711yescharacteristic
608C22C2×#117×C3711yescharacteristic
609C22C4×#41×C3711yescharacteristic
610C22C4×#41×C3711yescharacteristic
611C22C37×#52011yescharacteristic
612C22C37×#52011yescharacteristic
613C22C37×#52512yes—
614C22C37×#52512yes—
615C22C37×#52912yes—
616C22C37×#52912yes—
617C22C37×#54011yescharacteristic
618C22C37×#54111yescharacteristic
619C22C37×#54211yescharacteristic
620C22C37×#54211yescharacteristic
621C22C37×#54612yes—
622C22C37×#54712yes—
623C22C37×#54812yes—
624C22C37×#55012yes—
625C22C37×#55112yes—
626C22C37×#55112yes—
627C22C37×#55212yes—
628C22C37×#55212yes—
629C4—24no—
630C4—24no—
631C4—24no—
632C4—24no—
633C4—44no—
634C4—44no—
635C4—42no—
636C4—42no—
637C4—82no—
638C4—82no—
639C2—44no—
640C2C37×#228011yescharacteristic
641C2C37×#229811yescharacteristic
642C2C37×#231411yescharacteristic
643C2C37×#233911yescharacteristic
644C2C37×#234111yescharacteristic
645C2C37×#234311yescharacteristic
646C2C37×#234311yescharacteristic
647C2C37×#247112yes—
648C2C37×#247512yes—
649C2C37×#247712yes—
650C2C37×#247912yes—
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
2. C2×C37×#387C2semidirect
3. C37×#1445C2semidirect
6. C37×C4⋊#95C2semidirect
7. C37×#1434C2semidirect
8. C37×#1434C2semidirect
11. C4×#95×C37C2semidirect
14. C2×#117×C37C4semidirect
168. C4⋊C4×C37C22⋊C4semidirect
269. #13944C37direct (N × H)
315. C2×#387C2×C37semidirect
316. #1445C2×C37semidirect
319. C4⋊#95C2×C37semidirect
320. #1434C2×C37semidirect
321. #1434C2×C37semidirect
324. C4×#95C2×C37semidirect
339. C2×#117C4×C37semidirect
363. C37#13944direct (N × H)
494. C4⋊C4C22⋊C4×C37semidirect

Maximal subgroups

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

subgroupindex
C22×#117×C372
C2×C37×#3872
C37×#14452
C37×#14392
C37×#14372
C37×C4⋊#952
C37×#14342
C37×C22⋊#952
C4×#95×C372
#1394437