Finite Group Databasebeta

← C37×#14506 #22635759

Subgroups — C37×#14506 #22635759

Order 9472.

1962 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C37C211yesmaximal, characteristic
2C2×C37×#388C212yesmaximal, complemented
3C37×#1445C212yesmaximal, complemented
4C37×#1439C212yesmaximal, complemented
5C37×#1438C211yesmaximal, characteristic
6C37×#1438C211yesmaximal, characteristic
7C37×#1437C212yesmaximal, complemented
8C37×C4⋊#95C212yesmaximal, complemented
9C37×C22⋊#95C212yesmaximal, complemented
10C23×D4×C37C2211yescharacteristic
11C24×C4×C37C2211yescharacteristic
12C2×#123×C37—28no—
13C2×#123×C37C418yescomplemented
14C22×C4⋊C4×C37C2212yes—
15C22×C4⋊C4×C37C2212yes—
16C22×C22⋊C4×C37C2212yes—
17C22×C22⋊C4×C37C2212yes—
18C22×C22⋊C4×C37C2211yescharacteristic
19C22×C22⋊C4×C37C2212yes—
20C22×C22⋊C4×C37C2212yes—
21C22×C22⋊C4×C37C2211yescharacteristic
22C22×C22⋊C4×C37C2211yescharacteristic
23C22×C42×C37C2212yes—
24C37×#388—28no—
25C2×#95×C37C2212yes—
26C2×#95×C37C2212yes—
27C2×#95×C37C2212yes—
28C2×#95×C37C2212yes—
29C2×#95×C37C2212yes—
30C2×#95×C37C2212yes—
31C2×#95×C37C2211yescharacteristic
32C2×#95×C37C2212yes—
33C2×#95×C37C2211yescharacteristic
34C25×C37C2311yescharacteristic
35C25×C37C2311yescharacteristic
36C22×D4×C37—24no—
37C22×D4×C37—42no—
38C22×D4×C37—41no—
39C22×D4×C37—41no—
40C22×D4×C37C2×C414yes—
41C23×C4×C37—24no—
42C23×C4×C37—42no—
43C23×C4×C37—41no—
44C23×C4×C37—41no—
45C23×C4×C37C2×C414yes—
46C23×C4×C37C2312yes—
47C23×C4×C37C2312yes—
48C23×C4×C37C2312yes—
49C23×C4×C37C2311yescharacteristic
50C23×C4×C37C2312yes—
51C23×C4×C37C2312yes—
52C23×C4×C37C2312yes—
53#123×C37—232no—
54C2×C4⋊C4×C37—24no—
55C2×C4⋊C4×C37—24no—
56C2×C4⋊C4×C37—24no—
57C2×C4⋊C4×C37—24no—
58C2×C4⋊C4×C37—42no—
59C2×C4⋊C4×C37C2×C418yes—
60C2×C22⋊C4×C37—24no—
61C2×C22⋊C4×C37—24no—
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—41no—
69C2×C22⋊C4×C37—42no—
70C2×C22⋊C4×C37—42no—
71C2×C22⋊C4×C37—42no—
72C2×C22⋊C4×C37—42no—
73C2×C22⋊C4×C37—41no—
74C2×C22⋊C4×C37—42no—
75C2×C22⋊C4×C37C2×C418yes—
76C2×C22⋊C4×C37C2×C414yes—
77C2×C22⋊C4×C37D418yes—
78C2×C42×C37—24no—
79C2×C42×C37—24no—
80C2×C42×C37—42no—
81#95×C37—24no—
82#95×C37—24no—
83#95×C37—41no—
84#95×C37—42no—
85#95×C37—42no—
86#95×C37—42no—
87#95×C37—42no—
88#95×C37—42no—
89#95×C37—41no—
90C24×C37—22no—
91C24×C37—22no—
92C24×C37—22no—
93C24×C37—22no—
94C24×C37—21no—
95C24×C37—21no—
96C24×C37—22no—
97C24×C37—22no—
98C24×C37—22no—
99C24×C37—22no—
100C24×C37—22no—
101C24×C37—22no—
102C24×C37—21no—
103C24×C37—21no—
104C24×C37—22no—
105C24×C37C22×C412yes—
106C24×C37C22×C412yes—
107C24×C37C2×D414yes—
108C24×C37C2411yescharacteristic
109C2×D4×C37—28no—
110C2×D4×C37—44no—
111C2×D4×C37—44no—
112C2×D4×C37—48no—
113C2×D4×C37—48no—
114C22×C4×C37—22no—
115C22×C4×C37—22no—
116C22×C4×C37—22no—
117C22×C4×C37—22no—
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—22no—
132C22×C4×C37—22no—
133C22×C4×C37—22no—
134C22×C4×C37—22no—
135C22×C4×C37—21no—
136C22×C4×C37—21no—
137C22×C4×C37—22no—
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×C37—22no—
154C22×C4×C37—22no—
155C22×C4×C37—44no—
156C22×C4×C37—44no—
157C22×C4×C37—48no—
158C22×C4×C37—48no—
159C22×C4×C37C22×C414yes—
160C22×C4×C37C22×C412yes—
161C22×C4×C37C22×C414yes—
162C22×C4×C37C2×D414yes—
163C22×C4×C37C2×D414yes—
164C22×C4×C37#4114yes—
165C22×C4×C37#4114yes—
166C4⋊C4×C37—216no—
167C4⋊C4×C37—48no—
168C22⋊C4×C37—216no—
169C22⋊C4×C37—44no—
170C22⋊C4×C37—48no—
171C22⋊C4×C37—48no—
172C22⋊C4×C37—48no—
173C22⋊C4×C37—44no—
174C22⋊C4×C37C22⋊C4116yescomplemented
175C42×C37—48no—
176C23×C37—24no—
177C23×C37—22no—
178C23×C37—22no—
179C23×C37—24no—
180C23×C37—24no—
181C23×C37—24no—
182C23×C37—24no—
183C23×C37—24no—
184C23×C37—24no—
185C23×C37—24no—
186C23×C37—22no—
187C23×C37—24no—
188C23×C37—22no—
189C23×C37—22no—
190C23×C37—24no—
191C23×C37—42no—
192C23×C37—42no—
193C23×C37—42no—
194C23×C37—42no—
195C23×C37—41no—
196C23×C37—42no—
197C23×C37—41no—
198C23×C37—41no—
199C23×C37—42no—
200C23×C37—41no—
201C23×C37—42no—
202C23×C37—42no—
203C23×C37—42no—
204C23×C37—42no—
205C23×C37—42no—
206C23×C37—42no—
207C23×C37—42no—
208C23×C37—42no—
209C23×C37—42no—
210C23×C37—42no—
211C23×C37—41no—
212C23×C37—42no—
213C23×C37—41no—
214C23×C37—41no—
215C23×C37—42no—
216C23×C37—41no—
217C23×C37C2×C22⋊C414yes—
218C23×C37C23×C411yescharacteristic
219C23×C37C22×D412yes—
220C23×C37C2×#4112yes—
221C23×C37C2×#4112yes—
222C23×C37H(5,𝔽2)12yes—
223C23×C37H(5,𝔽2)11yescharacteristic
224C23×C37H(5,𝔽2)11yescharacteristic
225C23×C37H(5,𝔽2)12yes—
226C23×C372−1+412yes—
227D4×C37—416no—
228C2×C4×C37—24no—
229C2×C4×C37—24no—
230C2×C4×C37—24no—
231C2×C4×C37—24no—
232C2×C4×C37—24no—
233C2×C4×C37—24no—
234C2×C4×C37—24no—
235C2×C4×C37—22no—
236C2×C4×C37—24no—
237C2×C4×C37—24no—
238C2×C4×C37—22no—
239C2×C4×C37—22no—
240C2×C4×C37—24no—
241C2×C4×C37—24no—
242C2×C4×C37—24no—
243C2×C4×C37—24no—
244C2×C4×C37—24no—
245C2×C4×C37—24no—
246C2×C4×C37—416no—
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×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×C37—42no—
275C2×C4×C37C2×C22⋊C418yes—
276#14506C3711yesmaximal, characteristic, direct product factor, Sylow
277C22×C37—24no—
278C22×C37—28no—
279C22×C37—44no—
280C22×C37—42no—
281C22×C37—42no—
282C22×C37—44no—
283C22×C37—44no—
284C22×C37—44no—
285C22×C37—44no—
286C22×C37—42no—
287C22×C37—44no—
288C22×C37—44no—
289C22×C37—42no—
290C22×C37—42no—
291C22×C37—82no—
292C22×C37—82no—
293C22×C37—82no—
294C22×C37—82no—
295C22×C37C22×C22⋊C411yescharacteristic
296C22×C37C4×#4112yes—
297C22×C37#51811yescharacteristic
298C22×C37#51811yescharacteristic
299C22×C37#52012yes—
300C22×C37#53512yes—
301C22×C37#53512yes—
302C22×C37#53812yes—
303C22×C37#53912yes—
304C22×C37#54012yes—
305C22×C37#54212yes—
306C22×C37#54612yes—
307C22×C37#54612yes—
308C22×C37#54712yes—
309C22×C37#54712yes—
310C22×C37#55111yescharacteristic
311C22×C37#55312yes—
312C22×C37#55911yescharacteristic
313C22×C37#56011yescharacteristic
314C22×C37#56212yes—
315C22×C37#56311yescharacteristic
316C4×C37—28no—
317C4×C37—44no—
318C4×C37—42no—
319C4×C37—44no—
320C4×C37—44no—
321C4×C37—82no—
322C4×C37—82no—
323C22×#123C2×C3711yescharacteristic
324C2×#388C2×C3712yescomplemented
325#1445C2×C3712yescomplemented
326#1439C2×C3712yescomplemented
327#1438C2×C3711yescharacteristic
328#1438C2×C3711yescharacteristic
329#1437C2×C3712yescomplemented
330C4⋊#95C2×C3712yescomplemented
331C22⋊#95C2×C3712yescomplemented
332C2×C37—44no—
333C2×C37—82no—
334C2×C37#230911yescharacteristic
335C2×C37#233512yes—
336C2×C37#233912yes—
337C2×C37#237411yescharacteristic
338C2×C37#237611yescharacteristic
339C2×C37#270312yes—
340C2×C37#270612yes—
341C2×C37#271012yes—
342C2×C37#271812yes—
343C23×D4C22×C3711yescharacteristic
344C24×C4C22×C3711yescharacteristic
345C2×#123—28no—
346C2×#123C4×C3718yescomplemented
347C22×C4⋊C4C22×C3712yes—
348C22×C4⋊C4C22×C3712yes—
349C22×C22⋊C4C22×C3712yes—
350C22×C22⋊C4C22×C3712yes—
351C22×C22⋊C4C22×C3711yescharacteristic
352C22×C22⋊C4C22×C3712yes—
353C22×C22⋊C4C22×C3712yes—
354C22×C22⋊C4C22×C3711yescharacteristic
355C22×C22⋊C4C22×C3711yescharacteristic
356C22×C42C22×C3712yes—
357#388—28no—
358C2×#95C22×C3712yes—
359C2×#95C22×C3712yes—
360C2×#95C22×C3712yes—
361C2×#95C22×C3712yes—
362C2×#95C22×C3712yes—
363C2×#95C22×C3712yes—
364C2×#95C22×C3711yescharacteristic
365C2×#95C22×C3712yes—
366C2×#95C22×C3711yescharacteristic
367C37#1450611yescharacteristic, direct product factor, Sylow
368C25C23×C3711yescharacteristic
369C25C23×C3711yescharacteristic
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—41no—
373C22×D4—41no—
374C22×D4C2×C4×C3714yes—
375C23×C4—24no—
376C23×C4—42no—
377C23×C4—41no—
378C23×C4—41no—
379C23×C4C2×C4×C3714yes—
380C23×C4C23×C3712yes—
381C23×C4C23×C3712yes—
382C23×C4C23×C3712yes—
383C23×C4C23×C3711yescharacteristic
384C23×C4C23×C3712yes—
385C23×C4C23×C3712yes—
386C23×C4C23×C3712yes—
387#123—232no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4C2×C4×C3718yes—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—41no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×C4×C3718yes—
410C2×C22⋊C4C2×C4×C3714yes—
411C2×C22⋊C4D4×C3718yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—42no—
415#95—24no—
416#95—24no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—41no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24C22×C4×C3712yes—
440C24C22×C4×C3712yes—
441C24C2×D4×C3714yes—
442C24C24×C3711yescharacteristic
443C2×D4—28no—
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—48no—
447C2×D4—48no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—21no—
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×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—22no—
488C22×C4—22no—
489C22×C4—44no—
490C22×C4—44no—
491C22×C4—48no—
492C22×C4—48no—
493C22×C4C22×C4×C3714yes—
494C22×C4C22×C4×C3712yes—
495C22×C4C22×C4×C3714yes—
496C22×C4C2×D4×C3714yes—
497C22×C4C2×D4×C3714yes—
498C22×C4#41×C3714yes—
499C22×C4#41×C3714yes—
500C4⋊C4—216no—
501C4⋊C4—48no—
502C22⋊C4—216no—
503C22⋊C4—44no—
504C22⋊C4—48no—
505C22⋊C4—48no—
506C22⋊C4—48no—
507C22⋊C4—44no—
508C22⋊C4C22⋊C4×C37116yescomplemented
509C42—48no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—22no—
520C23—24no—
521C23—22no—
522C23—24no—
523C23—22no—
524C23—22no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—41no—
530C23—42no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—41no—
546C23—42no—
547C23—41no—
548C23—41no—
549C23—42no—
550C23—41no—
551C23C2×C22⋊C4×C3714yes—
552C23C23×C4×C3711yescharacteristic
553C23C22×D4×C3712yes—
554C23C2×#41×C3712yes—
555C23C2×#41×C3712yes—
556C23H(5,𝔽2)×C3712yes—
557C23H(5,𝔽2)×C3712yes—
558C23H(5,𝔽2)×C3711yescharacteristic
559C23H(5,𝔽2)×C3711yescharacteristic
560C232−1+4×C3712yes—
561D4—416no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—416no—
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×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×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4C2×C22⋊C4×C3718yes—
610C22—24no—
611C22—28no—
612C22—42no—
613C22—42no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—44no—
623C22—44no—
624C22—82no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22C22×C22⋊C4×C3711yescharacteristic
629C22C4×#41×C3712yes—
630C22C37×#51811yescharacteristic
631C22C37×#51811yescharacteristic
632C22C37×#52012yes—
633C22C37×#53512yes—
634C22C37×#53512yes—
635C22C37×#53812yes—
636C22C37×#53912yes—
637C22C37×#54012yes—
638C22C37×#54212yes—
639C22C37×#54612yes—
640C22C37×#54612yes—
641C22C37×#54712yes—
642C22C37×#54712yes—
643C22C37×#55111yescharacteristic
644C22C37×#55312yes—
645C22C37×#55911yescharacteristic
646C22C37×#56011yescharacteristic
647C22C37×#56212yes—
648C22C37×#56311yescharacteristic
649C4—28no—
650C4—44no—
651C4—44no—
652C4—44no—
653C4—42no—
654C4—82no—
655C4—82no—
656C2—44no—
657C2—82no—
658C2C37×#230911yescharacteristic
659C2C37×#233512yes—
660C2C37×#233912yes—
661C2C37×#237411yescharacteristic
662C2C37×#237611yescharacteristic
663C2C37×#270312yes—
664C2C37×#270612yes—
665C2C37×#271012yes—
666C2C37×#271812yes—
subgroupG/H
center, socleC24×C37C24
commutatorC23C23×C4×C37
Frattini, cosocleC24C24×C37
prime radicalC23×D4×C37C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C37×#388C2semidirect
3. C37×#1445C2semidirect
4. C37×#1439C2semidirect
7. C37×#1437C2semidirect
8. C37×C4⋊#95C2semidirect
9. C37×C22⋊#95C2semidirect
13. C2×#123×C37C4semidirect
174. C22⋊C4×C37C22⋊C4semidirect
276. #14506C37direct (N × H)
324. C2×#388C2×C37semidirect
325. #1445C2×C37semidirect
326. #1439C2×C37semidirect
329. #1437C2×C37semidirect
330. C4⋊#95C2×C37semidirect
331. C22⋊#95C2×C37semidirect
346. C2×#123C4×C37semidirect
367. C37#14506direct (N × H)
508. C22⋊C4C22⋊C4×C37semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C372
C2×C37×#3882
C37×#14452
C37×#14392
C37×#14382
C37×#14372
C37×C4⋊#952
C37×C22⋊#952
#1450637