Finite Group Databasebeta

← C37×#13871 #22635124

Subgroups — C37×#13871 #22635124

Order 9472.

2590 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
1C22×C4×D4×C37C211yesmaximal, characteristic
2C22×#117×C37C211yesmaximal, characteristic, complemented
3C2×C37×#380C212yesmaximal, complemented
4C2×C37×#380C211yesmaximal, characteristic, complemented
5C37×#1440C212yesmaximal, complemented
6C37×#1438C212yesmaximal
7C37×#1437C212yesmaximal, complemented
8C37×#1436C212yesmaximal, complemented
9C37×C4⋊#95C212yesmaximal, complemented
10C23×D4×C37C2211yescharacteristic
11C24×C4×C37C2211yescharacteristic
12C24×C4×C37C2211yescharacteristic
13C2×C4×D4×C37—24no—
14C2×C4×D4×C37—24no—
15C2×C4×D4×C37C418yescomplemented
16C2×#117×C37—24no—
17C2×#117×C37—28no—
18C22×C4⋊C4×C37C2212yes—
19C22×C4⋊C4×C37C2211yescharacteristic
20C22×C4⋊C4×C37C2212yes—
21C22×C22⋊C4×C37C2212yes—
22C22×C22⋊C4×C37C2214yes—
23C22×C22⋊C4×C37C2211yescharacteristic
24C22×C22⋊C4×C37C2211yescharacteristic
25C22×C22⋊C4×C37C2212yes—
26C22×C42×C37C2212yes—
27C22×C42×C37C2211yescharacteristic
28C37×#380—24no—
29C37×#380—28no—
30C2×#95×C37C2214yes—
31C2×#95×C37C2212yes—
32C2×#95×C37C2214yes—
33C2×#95×C37C2214yes—
34C25×C37C2311yescharacteristic
35C25×C37C2311yescharacteristic
36C22×D4×C37—22no—
37C22×D4×C37—22no—
38C22×D4×C37—24no—
39C22×D4×C37—24no—
40C22×D4×C37C2×C414yes—
41C23×C4×C37—24no—
42C23×C4×C37—24no—
43C23×C4×C37—24no—
44C23×C4×C37—22no—
45C23×C4×C37—22no—
46C23×C4×C37—24no—
47C23×C4×C37C2×C414yes—
48C23×C4×C37C2×C414yes—
49C23×C4×C37D414yes—
50C23×C4×C37D414yes—
51C23×C4×C37C2314yes—
52C23×C4×C37C2311yescharacteristic
53C23×C4×C37C2311yescharacteristic
54C23×C4×C37C2314yes—
55C23×C4×C37C2311yescharacteristic
56C23×C4×C37C2311yescharacteristic
57C23×C4×C37C2311yescharacteristic
58C4×D4×C37—232no—
59#117×C37—232no—
60C2×C4⋊C4×C37—24no—
61C2×C4⋊C4×C37—24no—
62C2×C4⋊C4×C37—22no—
63C2×C4⋊C4×C37—22no—
64C2×C4⋊C4×C37—24no—
65C2×C4⋊C4×C37—24no—
66C2×C4⋊C4×C37—24no—
67C2×C4⋊C4×C37C2×C414yes—
68C2×C4⋊C4×C37D418yescomplemented
69C2×C22⋊C4×C37—24no—
70C2×C22⋊C4×C37—22no—
71C2×C22⋊C4×C37—22no—
72C2×C22⋊C4×C37—28no—
73C2×C22⋊C4×C37—22no—
74C2×C22⋊C4×C37—22no—
75C2×C22⋊C4×C37—24no—
76C2×C22⋊C4×C37—28no—
77C2×C22⋊C4×C37—28no—
78C2×C22⋊C4×C37—44no—
79C2×C22⋊C4×C37—44no—
80C2×C22⋊C4×C37C2×C414yes—
81C2×C22⋊C4×C37C2×C414yes—
82C2×C42×C37—28no—
83C2×C42×C37—24no—
84C2×C42×C37—22no—
85C2×C42×C37—22no—
86C2×C42×C37C2×C414yes—
87#95×C37—28no—
88#95×C37—24no—
89#95×C37—28no—
90#95×C37—44no—
91C24×C37—22no—
92C24×C37—22no—
93C24×C37—21no—
94C24×C37—21no—
95C24×C37—22no—
96C24×C37—22no—
97C24×C37—22no—
98C24×C37—22no—
99C24×C37—22no—
100C24×C37—22no—
101C24×C37—22no—
102C24×C37—22no—
103C24×C37—22no—
104C24×C37C22×C412yes—
105C24×C37C22×C412yes—
106C24×C37C2×D412yes—
107C24×C37C2×D412yes—
108C24×C37#4114yes—
109C24×C37C2411yescharacteristic
110C2×D4×C37—216no—
111C2×D4×C37—216no—
112C2×D4×C37—28no—
113C2×D4×C37—28no—
114C2×D4×C37—28no—
115C22×C4×C37—22no—
116C22×C4×C37—21no—
117C22×C4×C37—21no—
118C22×C4×C37—22no—
119C22×C4×C37—22no—
120C22×C4×C37—216no—
121C22×C4×C37—28no—
122C22×C4×C37—216no—
123C22×C4×C37—28no—
124C22×C4×C37—22no—
125C22×C4×C37—21no—
126C22×C4×C37—21no—
127C22×C4×C37—24no—
128C22×C4×C37—24no—
129C22×C4×C37—21no—
130C22×C4×C37—21no—
131C22×C4×C37—24no—
132C22×C4×C37—24no—
133C22×C4×C37—22no—
134C22×C4×C37—22no—
135C22×C4×C37—24no—
136C22×C4×C37—22no—
137C22×C4×C37—24no—
138C22×C4×C37—28no—
139C22×C4×C37—216no—
140C22×C4×C37—24no—
141C22×C4×C37—24no—
142C22×C4×C37—24no—
143C22×C4×C37—24no—
144C22×C4×C37—24no—
145C22×C4×C37—24no—
146C22×C4×C37—24no—
147C22×C4×C37—44no—
148C22×C4×C37—48no—
149C22×C4×C37—44no—
150C22×C4×C37C22⋊C4116yescomplemented
151C22×C4×C37C22×C412yes—
152C22×C4×C37C22×C412yes—
153C22×C4×C37C22×C412yes—
154C22×C4×C37C22×C412yes—
155C22×C4×C37C22×C412yes—
156C22×C4×C37C2×D418yes—
157C22×C4×C37C2×D412yes—
158C22×C4×C37C2×D412yes—
159C22×C4×C37C2×D412yes—
160C22×C4×C37C2×D412yes—
161C22×C4×C37C2×D414yes—
162C22×C4×C37#4114yes—
163C22×C4×C37#4114yes—
164C4⋊C4×C37—28no—
165C4⋊C4×C37—216no—
166C4⋊C4×C37—48no—
167C22⋊C4×C37—216no—
168C22⋊C4×C37—28no—
169C22⋊C4×C37—28no—
170C22⋊C4×C37—416no—
171C22⋊C4×C37—48no—
172C42×C37—216no—
173C42×C37—28no—
174C23×C37—22no—
175C23×C37—22no—
176C23×C37—22no—
177C23×C37—22no—
178C23×C37—24no—
179C23×C37—24no—
180C23×C37—24no—
181C23×C37—24no—
182C23×C37—22no—
183C23×C37—24no—
184C23×C37—22no—
185C23×C37—24no—
186C23×C37—24no—
187C23×C37—24no—
188C23×C37—24no—
189C23×C37—22no—
190C23×C37—22no—
191C23×C37—24no—
192C23×C37—24no—
193C23×C37—24no—
194C23×C37—24no—
195C23×C37—24no—
196C23×C37—41no—
197C23×C37—42no—
198C23×C37—41no—
199C23×C37—41no—
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—42no—
212C23×C37—42no—
213C23×C37—42no—
214C23×C37C2×C22⋊C414yes—
215C23×C37#11714yescomplemented
216C23×C37C23×C411yescharacteristic
217C23×C37C22×D411yescharacteristic
218C23×C37C22×D411yescharacteristic
219C23×C37C22×D412yes—
220C23×C37C2×#4112yes—
221C23×C37C2×#4112yes—
222C23×C37C2×#4112yes—
223C23×C37H(5,𝔽2)12yes—
224C23×C372−1+412yes—
225D4×C37—232no—
226C2×C4×C37—22no—
227C2×C4×C37—22no—
228C2×C4×C37—24no—
229C2×C4×C37—22no—
230C2×C4×C37—24no—
231C2×C4×C37—22no—
232C2×C4×C37—24no—
233C2×C4×C37—24no—
234C2×C4×C37—232no—
235C2×C4×C37—22no—
236C2×C4×C37—22no—
237C2×C4×C37—24no—
238C2×C4×C37—24no—
239C2×C4×C37—28no—
240C2×C4×C37—28no—
241C2×C4×C37—28no—
242C2×C4×C37—41no—
243C2×C4×C37—42no—
244C2×C4×C37—41no—
245C2×C4×C37—44no—
246C2×C4×C37—41no—
247C2×C4×C37—41no—
248C2×C4×C37—42no—
249C2×C4×C37—44no—
250C2×C4×C37—44no—
251C2×C4×C37—44no—
252C2×C4×C37—416no—
253C2×C4×C37—44no—
254C2×C4×C37—44no—
255C2×C4×C37—44no—
256C2×C4×C37—44no—
257C2×C4×C37—44no—
258C2×C4×C37—44no—
259C2×C4×C37—44no—
260C2×C4×C37C2×C22⋊C414yes—
261C2×C4×C37C2×C22⋊C414yes—
262C2×C4×C37#11714yescomplemented
263C2×C4×C37C4×D418yes—
264C2×C4×C37#12014yes—
265C2×C4×C37#12118yes—
266C2×C4×C37#12314yes—
267#13871C3711yesmaximal, characteristic, direct product factor, Sylow
268C22×C37—24no—
269C22×C37—28no—
270C22×C37—24no—
271C22×C37—24no—
272C22×C37—24no—
273C22×C37—42no—
274C22×C37—44no—
275C22×C37—44no—
276C22×C37—44no—
277C22×C37—44no—
278C22×C37—44no—
279C22×C37—44no—
280C22×C37—44no—
281C22×C37—44no—
282C22×C37—44no—
283C22×C37—44no—
284C22×C37—44no—
285C22×C37—42no—
286C22×C37C22×C22⋊C411yescharacteristic
287C22×C37C2×#11711yescharacteristic
288C22×C37C2×#11711yescharacteristic
289C22×C37C2×C4×D412yes—
290C22×C37#52012yes—
291C22×C37C2×#12011yescharacteristic
292C22×C37C2×#12112yes—
293C22×C37C2×#12311yescharacteristic
294C22×C37#52512yes—
295C22×C37#52512yes—
296C22×C37#53511yescharacteristic
297C22×C37#53611yescharacteristic
298C22×C37#53712yes—
299C22×C37#54612yes—
300C22×C37#54712yes—
301C22×C37#54812yes—
302C22×C37#55012yes—
303C22×C37#55212yes—
304C22×C37#55312yes—
305C22×C37#55512yes—
306C22×C37#55612yes—
307C4×C37—24no—
308C4×C37—24no—
309C4×C37—42no—
310C4×C37—48no—
311C4×C37—42no—
312C4×C37—84no—
313C4×C37#38618yes—
314C22×C4×D4C2×C3711yescharacteristic
315C22×#117C2×C3711yescharacteristic, complemented
316C2×#380C2×C3712yescomplemented
317C2×#380C2×C3711yescharacteristic, complemented
318#1440C2×C3712yescomplemented
319#1438C2×C3712yes—
320#1437C2×C3712yescomplemented
321#1436C2×C3712yescomplemented
322C4⋊#95C2×C3712yescomplemented
323C2×C37—44no—
324C2×C37—44no—
325C2×C37#228011yescharacteristic
326C2×C37C2×#38611yescharacteristic
327C2×C37#231111yescharacteristic
328C2×C37#235212yes—
329C2×C37#235412yes—
330C2×C37#240712yes—
331C2×C37#241412yes—
332C2×C37#241512yes—
333C2×C37#248512yes—
334C23×D4C22×C3711yescharacteristic
335C24×C4C22×C3711yescharacteristic
336C24×C4C22×C3711yescharacteristic
337C2×C4×D4—24no—
338C2×C4×D4—24no—
339C2×C4×D4C4×C3718yescomplemented
340C2×#117—24no—
341C2×#117—28no—
342C22×C4⋊C4C22×C3712yes—
343C22×C4⋊C4C22×C3711yescharacteristic
344C22×C4⋊C4C22×C3712yes—
345C22×C22⋊C4C22×C3712yes—
346C22×C22⋊C4C22×C3714yes—
347C22×C22⋊C4C22×C3711yescharacteristic
348C22×C22⋊C4C22×C3711yescharacteristic
349C22×C22⋊C4C22×C3712yes—
350C22×C42C22×C3712yes—
351C22×C42C22×C3711yescharacteristic
352#380—24no—
353#380—28no—
354C2×#95C22×C3714yes—
355C2×#95C22×C3712yes—
356C2×#95C22×C3714yes—
357C2×#95C22×C3714yes—
358C37#1387111yescharacteristic, direct product factor, Sylow
359C25C23×C3711yescharacteristic
360C25C23×C3711yescharacteristic
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—24no—
364C22×D4—24no—
365C22×D4C2×C4×C3714yes—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—24no—
371C23×C4—24no—
372C23×C4C2×C4×C3714yes—
373C23×C4C2×C4×C3714yes—
374C23×C4D4×C3714yes—
375C23×C4D4×C3714yes—
376C23×C4C23×C3714yes—
377C23×C4C23×C3711yescharacteristic
378C23×C4C23×C3711yescharacteristic
379C23×C4C23×C3714yes—
380C23×C4C23×C3711yescharacteristic
381C23×C4C23×C3711yescharacteristic
382C23×C4C23×C3711yescharacteristic
383C4×D4—232no—
384#117—232no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—24no—
392C2×C4⋊C4C2×C4×C3714yes—
393C2×C4⋊C4D4×C3718yescomplemented
394C2×C22⋊C4—24no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4C2×C4×C3714yes—
406C2×C22⋊C4C2×C4×C3714yes—
407C2×C42—28no—
408C2×C42—24no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42C2×C4×C3714yes—
412#95—28no—
413#95—24no—
414#95—28no—
415#95—44no—
416C24—22no—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24C22×C4×C3712yes—
430C24C22×C4×C3712yes—
431C24C2×D4×C3712yes—
432C24C2×D4×C3712yes—
433C24#41×C3714yes—
434C24C24×C3711yescharacteristic
435C2×D4—216no—
436C2×D4—216no—
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—28no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—216no—
446C22×C4—28no—
447C22×C4—216no—
448C22×C4—28no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—28no—
464C22×C4—216no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—44no—
473C22×C4—48no—
474C22×C4—44no—
475C22×C4C22⋊C4×C37116yescomplemented
476C22×C4C22×C4×C3712yes—
477C22×C4C22×C4×C3712yes—
478C22×C4C22×C4×C3712yes—
479C22×C4C22×C4×C3712yes—
480C22×C4C22×C4×C3712yes—
481C22×C4C2×D4×C3718yes—
482C22×C4C2×D4×C3712yes—
483C22×C4C2×D4×C3712yes—
484C22×C4C2×D4×C3712yes—
485C22×C4C2×D4×C3712yes—
486C22×C4C2×D4×C3714yes—
487C22×C4#41×C3714yes—
488C22×C4#41×C3714yes—
489C4⋊C4—28no—
490C4⋊C4—216no—
491C4⋊C4—48no—
492C22⋊C4—216no—
493C22⋊C4—28no—
494C22⋊C4—28no—
495C22⋊C4—416no—
496C22⋊C4—48no—
497C42—216no—
498C42—28no—
499C23—24no—
500C23—24no—
501C23—22no—
502C23—24no—
503C23—22no—
504C23—24no—
505C23—24no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—24no—
520C23—24no—
521C23—41no—
522C23—42no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—42no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23C2×C22⋊C4×C3714yes—
540C23#117×C3714yescomplemented
541C23C23×C4×C3711yescharacteristic
542C23C22×D4×C3712yes—
543C23C22×D4×C3711yescharacteristic
544C23C22×D4×C3711yescharacteristic
545C23C2×#41×C3712yes—
546C23C2×#41×C3712yes—
547C23C2×#41×C3712yes—
548C23H(5,𝔽2)×C3712yes—
549C232−1+4×C3712yes—
550D4—232no—
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—232no—
560C2×C4—24no—
561C2×C4—28no—
562C2×C4—28no—
563C2×C4—28no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—44no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—416no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—44no—
581C2×C4—44no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—44no—
585C2×C4C2×C22⋊C4×C3714yes—
586C2×C4C2×C22⋊C4×C3714yes—
587C2×C4#117×C3714yescomplemented
588C2×C4C4×D4×C3718yes—
589C2×C4#120×C3714yes—
590C2×C4#121×C3718yes—
591C2×C4#123×C3714yes—
592C22—28no—
593C22—24no—
594C22—24no—
595C22—24no—
596C22—24no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—44no—
607C22—44no—
608C22—42no—
609C22—42no—
610C22C22×C22⋊C4×C3711yescharacteristic
611C22C2×#117×C3711yescharacteristic
612C22C2×#117×C3711yescharacteristic
613C22C2×C4×D4×C3712yes—
614C22C37×#52012yes—
615C22C2×#120×C3711yescharacteristic
616C22C2×#121×C3712yes—
617C22C2×#123×C3711yescharacteristic
618C22C37×#52512yes—
619C22C37×#52512yes—
620C22C37×#53511yescharacteristic
621C22C37×#53611yescharacteristic
622C22C37×#53712yes—
623C22C37×#54612yes—
624C22C37×#54712yes—
625C22C37×#54812yes—
626C22C37×#55012yes—
627C22C37×#55212yes—
628C22C37×#55312yes—
629C22C37×#55512yes—
630C22C37×#55612yes—
631C4—24no—
632C4—24no—
633C4—48no—
634C4—42no—
635C4—42no—
636C4—84no—
637C4C37×#38618yes—
638C2—44no—
639C2—44no—
640C2C37×#228011yescharacteristic
641C2C2×C37×#38611yescharacteristic
642C2C37×#231111yescharacteristic
643C2C37×#235212yes—
644C2C37×#235412yes—
645C2C37×#240712yes—
646C2C37×#241412yes—
647C2C37×#241512yes—
648C2C37×#248512yes—
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. C22×#117×C37C2semidirect
3. C2×C37×#380C2semidirect
4. C2×C37×#380C2semidirect
5. C37×#1440C2semidirect
7. C37×#1437C2semidirect
8. C37×#1436C2semidirect
9. C37×C4⋊#95C2semidirect
15. C2×C4×D4×C37C4semidirect
68. C2×C4⋊C4×C37D4semidirect
150. C22×C4×C37C22⋊C4semidirect
215. C23×C37#117semidirect
262. C2×C4×C37#117semidirect
267. #13871C37direct (N × H)
315. C22×#117C2×C37semidirect
316. C2×#380C2×C37semidirect
317. C2×#380C2×C37semidirect
318. #1440C2×C37semidirect
320. #1437C2×C37semidirect
321. #1436C2×C37semidirect
322. C4⋊#95C2×C37semidirect
339. C2×C4×D4C4×C37semidirect
358. C37#13871direct (N × H)
393. C2×C4⋊C4D4×C37semidirect
475. C22×C4C22⋊C4×C37semidirect
540. C23#117×C37semidirect
587. C2×C4#117×C37semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C372
C22×#117×C372
C2×C37×#3802
C37×#14402
C37×#14382
C37×#14372
C37×#14362
C37×C4⋊#952
#1387137