Finite Group Databasebeta

← C37×#19048 #22640301

Subgroups — C37×#19048 #22640301

Order 9472.

908 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3561C211yesmaximal, characteristic, complemented
2C37×#3213C211yesmaximal, characteristic, complemented
3C37×#3180C211yesmaximal, characteristic, complemented
4C37×#3135C211yesmaximal, characteristic, complemented
5C37×#1664C212yesmaximal, complemented
6C37×#1662C212yesmaximal, complemented
7C37×#1657C212yesmaximal, complemented
8C37×#1656C212yesmaximal, complemented
9C37×#1532C211yesmaximal, characteristic, complemented
10C37×#1531C211yesmaximal, characteristic, complemented
11C2×C37×#329C211yesmaximal, characteristic, complemented
12C37×#563C2212yes—
13C37×#562C2212yes—
14C37×#556—21no—
15C37×#551—22no—
16D4×Q8×C37—21no—
17C37×#548—21no—
18C37×#546—21no—
19C37×#543—21no—
20C37×#542—21no—
21C37×#542—22no—
22C37×#538—21no—
23C37×#536—21no—
24C37×#533C2211yescharacteristic
25C37×#532C2211yescharacteristic
26C37×#529C2211yescharacteristic
27C2×#124×C37C2211yescharacteristic
28C37×#501C2211yescharacteristic, complemented
29C37×#496C2212yes—
30C37×#496C2211yescharacteristic, complemented
31C37×#491C2212yescomplemented
32C37×#490C2212yescomplemented
33C37×#490C2211yescharacteristic, complemented
34C37×#489—21no—
35C37×#489—21no—
36C37×#489C2212yes—
37C37×#489C2211yescharacteristic, complemented
38C37×#466—21no—
39C37×#465—21no—
40C37×#463—22no—
41C37×#448—21no—
42C37×#447—21no—
43C37×#442—21no—
44C37×#440—21no—
45C37×#432C2211yescharacteristic
46C37×#416—22no—
47C2×#97×C37C2211yescharacteristic
48C2×#97×C37C2211yescharacteristic
49C37×#330C2212yescomplemented
50C37×#330C2212yescomplemented
51C37×#330C2212yescomplemented
52C37×#329C2212yes—
53C37×#329C2212yes—
54C37×#329C2212yescomplemented
55C2×#41×C37—21no—
56C2×#41×C37—21no—
57C22×Q8×C37—21no—
58C22×Q8×C37D411yescharacteristic
59C22×D4×C37D411yescharacteristic
60C2×SD16×C37—21no—
61C2×SD16×C37—22no—
62C2×D8×C37—21no—
63C2×D8×C37—22no—
64C22×C8×C37—21no—
65C22×C8×C37—21no—
66C4⋊Q8×C37—21no—
67C4⋊Q8×C37—22no—
68C4⋊Q8×C37D411yescharacteristic
69C4⋊Q8×C37D411yescharacteristic
70C4⋊Q8×C37C2311yescharacteristic
71#127×C37C2311yescharacteristic
72#126×C37—22no—
73#126×C37—22no—
74#126×C37—22no—
75#126×C37—21no—
76#125×C37C2311yescharacteristic
77#125×C37C2312yes—
78#124×C37—21no—
79#124×C37—22no—
80#124×C37—22no—
81#124×C37—21no—
82#124×C37—21no—
83#124×C37—21no—
84#124×C37D412yes—
85#124×C37C2312yes—
86#124×C37C2311yescharacteristic
87#123×C37—22no—
88#123×C37—22no—
89#123×C37—21no—
90#123×C37—22no—
91#123×C37—22no—
92C22⋊Q8×C37—22no—
93C22⋊Q8×C37—22no—
94C22⋊Q8×C37—21no—
95C22⋊Q8×C37—22no—
96C22⋊Q8×C37—22no—
97C22⋊Q8×C37—22no—
98C22⋊Q8×C37—21no—
99C22⋊Q8×C37—21no—
100C22⋊Q8×C37—22no—
101C22⋊Q8×C37—22no—
102C22⋊Q8×C37D411yescharacteristic
103#121×C37—21no—
104#121×C37—22no—
105#121×C37—22no—
106#121×C37—21no—
107#121×C37—21no—
108#121×C37D411yescharacteristic
109#120×C37—22no—
110C4×Q8×C37—21no—
111C4×Q8×C37—21no—
112C4×Q8×C37—21no—
113C4×Q8×C37D411yescharacteristic
114C4×D4×C37—22no—
115C4×D4×C37—21no—
116C4×D4×C37—22no—
117C4×D4×C37—21no—
118C4×D4×C37—21no—
119C4×D4×C37—21no—
120C4×D4×C37D411yescharacteristic
121#117×C37—22no—
122#117×C37—21no—
123#117×C37D412yes—
124C2×C22⋊C4×C37—22no—
125C2×C22⋊C4×C37—21no—
126C2×C22⋊C4×C37—21no—
127C2×C42×C37C2311yescharacteristic
128#107×C37—21no—
129#106×C37—21no—
130C4⋊C8×C37—21no—
131#103×C37—21no—
132#103×C37—22no—
133#103×C37—22no—
134#103×C37—22no—
135#102×C37—21no—
136#102×C37—22no—
137#102×C37—22no—
138#102×C37—22no—
139#102×C37—21no—
140#102×C37—21no—
141C22⋊C8×C37—21no—
142#97×C37—21no—
143#97×C37—21no—
144#97×C37C2312yes—
145#97×C37C2311yescharacteristic
146#97×C37C2311yescharacteristic
147#97×C37C2312yes—
148C24×C37—21no—
149#41×C37—44no—
150#41×C37—82no—
151C2×Q8×C37—22no—
152C2×Q8×C37—21no—
153C2×Q8×C37—21no—
154C2×Q8×C37—21no—
155C2×Q8×C37—21no—
156C2×Q8×C37—82no—
157C2×Q8×C37—81no—
158C2×Q8×C37C2×D411yescharacteristic
159C2×Q8×C37C2×D412yes—
160C2×D4×C37—21no—
161C2×D4×C37—22no—
162C2×D4×C37—22no—
163C2×D4×C37—21no—
164C2×D4×C37—21no—
165C2×D4×C37—21no—
166C2×D4×C37—21no—
167C2×D4×C37—41no—
168C2×D4×C37—81no—
169C2×D4×C37C2×D411yescharacteristic
170C2×D4×C37C2×D412yes—
171C22×C4×C37—22no—
172C22×C4×C37—22no—
173C22×C4×C37—22no—
174C22×C4×C37—21no—
175C22×C4×C37—21no—
176C22×C4×C37—41no—
177C22×C4×C37C2×D411yescharacteristic
178C22×C4×C37C2×D411yescharacteristic
179C22×C4×C37C2×D411yescharacteristic
180SD16×C37—42no—
181SD16×C37—82no—
182D8×C37—42no—
183D8×C37—82no—
184C2×C8×C37—21no—
185C2×C8×C37—21no—
186C2×C8×C37—22no—
187C2×C8×C37—22no—
188C2×C8×C37—42no—
189C2×C8×C37—42no—
190C4⋊C4×C37—22no—
191C4⋊C4×C37—22no—
192C4⋊C4×C37—22no—
193C4⋊C4×C37—22no—
194C4⋊C4×C37—21no—
195C4⋊C4×C37—21no—
196C4⋊C4×C37—21no—
197C4⋊C4×C37—21no—
198C4⋊C4×C37—21no—
199C4⋊C4×C37—21no—
200C4⋊C4×C37—22no—
201C4⋊C4×C37—22no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—21no—
204C4⋊C4×C37C2×D412yes—
205C4⋊C4×C37C2×D412yes—
206C4⋊C4×C37C2×D411yescharacteristic
207C4⋊C4×C37C2×D411yescharacteristic
208C22⋊C4×C37—22no—
209C22⋊C4×C37—22no—
210C22⋊C4×C37—22no—
211C22⋊C4×C37—22no—
212C22⋊C4×C37—22no—
213C22⋊C4×C37—21no—
214C22⋊C4×C37—22no—
215C22⋊C4×C37—22no—
216C22⋊C4×C37—22no—
217C22⋊C4×C37—21no—
218C22⋊C4×C37—21no—
219C22⋊C4×C37—22no—
220C22⋊C4×C37—22no—
221C22⋊C4×C37—21no—
222C22⋊C4×C37—21no—
223C22⋊C4×C37—41no—
224C22⋊C4×C37—41no—
225C42×C37—22no—
226C42×C37—22no—
227C42×C37—21no—
228C42×C37C2×D411yescharacteristic
229C42×C37C2×D411yescharacteristic
230C42×C37C2×D411yescharacteristic
231C42×C37C2411yescharacteristic
232C23×C37—22no—
233C23×C37—21no—
234C23×C37—42no—
235C23×C37—41no—
236C23×C37—81no—
237C23×C37—81no—
238C23×C37#12011yescharacteristic
239Q8×C37—41no—
240Q8×C37—42no—
241Q8×C37—42no—
242Q8×C37—42no—
243Q8×C37—42no—
244Q8×C37—81no—
245Q8×C37—82no—
246D4×C37—41no—
247D4×C37—42no—
248D4×C37—42no—
249D4×C37—41no—
250D4×C37—42no—
251D4×C37—41no—
252D4×C37—42no—
253D4×C37—42no—
254D4×C37—82no—
255D4×C37—82no—
256D4×C37—82no—
257C2×C4×C37—22no—
258C2×C4×C37—21no—
259C2×C4×C37—22no—
260C2×C4×C37—21no—
261C2×C4×C37—22no—
262C2×C4×C37—22no—
263C2×C4×C37—21no—
264C2×C4×C37—41no—
265C2×C4×C37—41no—
266C2×C4×C37—42no—
267C2×C4×C37—41no—
268C2×C4×C37—82no—
269C2×C4×C37—81no—
270C2×C4×C37—82no—
271C2×C4×C37—82no—
272C2×C4×C37—82no—
273C2×C4×C37#12011yescharacteristic
274C2×C4×C37#12011yescharacteristic
275C2×C4×C37#12011yescharacteristic
276C2×C4×C37C22×D411yescharacteristic
277C2×C4×C37C22×D411yescharacteristic
278C2×C4×C37C22×D411yescharacteristic
279C8×C37—22no—
280C8×C37—42no—
281C8×C37—41no—
282C8×C37—42no—
283#19048C3711yesmaximal, characteristic, direct product factor, Sylow
284C22×C37—21no—
285C22×C37—21no—
286C22×C37—41no—
287C22×C37—42no—
288C22×C37—42no—
289C22×C37—41no—
290C22×C37—41no—
291C22×C37—42no—
292C22×C37—81no—
293C22×C37—81no—
294C22×C37—81no—
295C22×C37—162no—
296C22×C37#45412yes—
297C22×C37C2×#12011yescharacteristic
298C4×C37—21no—
299C4×C37—21no—
300C4×C37—21no—
301C4×C37—21no—
302C4×C37—21no—
303C4×C37—21no—
304C4×C37—41no—
305C4×C37—41no—
306C4×C37—42no—
307C4×C37—41no—
308C4×C37—42no—
309C4×C37—42no—
310C4×C37—81no—
311#3561C2×C3711yescharacteristic, complemented
312#3213C2×C3711yescharacteristic, complemented
313#3180C2×C3711yescharacteristic, complemented
314#3135C2×C3711yescharacteristic, complemented
315#1664C2×C3712yescomplemented
316#1662C2×C3712yescomplemented
317#1657C2×C3712yescomplemented
318#1656C2×C3712yescomplemented
319#1532C2×C3711yescharacteristic, complemented
320#1531C2×C3711yescharacteristic, complemented
321C2×#329C2×C3711yescharacteristic, complemented
322C2×C37—22no—
323C2×C37—81no—
324C2×C37—82no—
325C2×C37—161no—
326C2×C37C2×#45411yescharacteristic
327C2×C37#301811yescharacteristic
328C2×C37#301911yescharacteristic
329#563C22×C3712yes—
330#562C22×C3712yes—
331#556—21no—
332#551—22no—
333D4×Q8—21no—
334#548—21no—
335#546—21no—
336#543—21no—
337#542—21no—
338#542—22no—
339#538—21no—
340#536—21no—
341#533C22×C3711yescharacteristic
342#532C22×C3711yescharacteristic
343#529C22×C3711yescharacteristic
344C2×#124C22×C3711yescharacteristic
345#501C22×C3711yescharacteristic, complemented
346#496C22×C3712yes—
347#496C22×C3711yescharacteristic, complemented
348#491C22×C3712yescomplemented
349#490C22×C3712yescomplemented
350#490C22×C3711yescharacteristic, complemented
351#489—21no—
352#489—21no—
353#489C22×C3712yes—
354#489C22×C3711yescharacteristic, complemented
355#466—21no—
356#465—21no—
357#463—22no—
358#448—21no—
359#447—21no—
360#442—21no—
361#440—21no—
362#432C22×C3711yescharacteristic
363#416—22no—
364C2×#97C22×C3711yescharacteristic
365C2×#97C22×C3711yescharacteristic
366#330C22×C3712yescomplemented
367#330C22×C3712yescomplemented
368#330C22×C3712yescomplemented
369#329C22×C3712yes—
370#329C22×C3712yes—
371#329C22×C3712yescomplemented
372C37#1904811yescharacteristic, direct product factor, Sylow
373C2×#41—21no—
374C2×#41—21no—
375C22×Q8—21no—
376C22×Q8D4×C3711yescharacteristic
377C22×D4D4×C3711yescharacteristic
378C2×SD16—21no—
379C2×SD16—22no—
380C2×D8—21no—
381C2×D8—22no—
382C22×C8—21no—
383C22×C8—21no—
384C4⋊Q8—21no—
385C4⋊Q8—22no—
386C4⋊Q8D4×C3711yescharacteristic
387C4⋊Q8D4×C3711yescharacteristic
388C4⋊Q8C23×C3711yescharacteristic
389#127C23×C3711yescharacteristic
390#126—22no—
391#126—22no—
392#126—22no—
393#126—21no—
394#125C23×C3711yescharacteristic
395#125C23×C3712yes—
396#124—21no—
397#124—22no—
398#124—22no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124D4×C3712yes—
403#124C23×C3712yes—
404#124C23×C3711yescharacteristic
405#123—22no—
406#123—22no—
407#123—21no—
408#123—22no—
409#123—22no—
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8D4×C3711yescharacteristic
421#121—21no—
422#121—22no—
423#121—22no—
424#121—21no—
425#121—21no—
426#121D4×C3711yescharacteristic
427#120—22no—
428C4×Q8—21no—
429C4×Q8—21no—
430C4×Q8—21no—
431C4×Q8D4×C3711yescharacteristic
432C4×D4—22no—
433C4×D4—21no—
434C4×D4—22no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4D4×C3711yescharacteristic
439#117—22no—
440#117—21no—
441#117D4×C3712yes—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C42C23×C3711yescharacteristic
446#107—21no—
447#106—21no—
448C4⋊C8—21no—
449#103—21no—
450#103—22no—
451#103—22no—
452#103—22no—
453#102—21no—
454#102—22no—
455#102—22no—
456#102—22no—
457#102—21no—
458#102—21no—
459C22⋊C8—21no—
460#97—21no—
461#97—21no—
462#97C23×C3712yes—
463#97C23×C3711yescharacteristic
464#97C23×C3711yescharacteristic
465#97C23×C3712yes—
466C24—21no—
467#41—44no—
468#41—82no—
469C2×Q8—22no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—82no—
475C2×Q8—81no—
476C2×Q8C2×D4×C3711yescharacteristic
477C2×Q8C2×D4×C3712yes—
478C2×D4—21no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—41no—
486C2×D4—81no—
487C2×D4C2×D4×C3711yescharacteristic
488C2×D4C2×D4×C3712yes—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4C2×D4×C3711yescharacteristic
496C22×C4C2×D4×C3711yescharacteristic
497C22×C4C2×D4×C3711yescharacteristic
498SD16—42no—
499SD16—82no—
500D8—42no—
501D8—82no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—42no—
507C2×C8—42no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4C2×D4×C3712yes—
523C4⋊C4C2×D4×C3712yes—
524C4⋊C4C2×D4×C3711yescharacteristic
525C4⋊C4C2×D4×C3711yescharacteristic
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—41no—
542C22⋊C4—41no—
543C42—22no—
544C42—22no—
545C42—21no—
546C42C2×D4×C3711yescharacteristic
547C42C2×D4×C3711yescharacteristic
548C42C2×D4×C3711yescharacteristic
549C42C24×C3711yescharacteristic
550C23—22no—
551C23—21no—
552C23—42no—
553C23—41no—
554C23—81no—
555C23—81no—
556C23#120×C3711yescharacteristic
557Q8—41no—
558Q8—42no—
559Q8—42no—
560Q8—42no—
561Q8—42no—
562Q8—81no—
563Q8—82no—
564D4—41no—
565D4—42no—
566D4—42no—
567D4—41no—
568D4—42no—
569D4—41no—
570D4—42no—
571D4—42no—
572D4—82no—
573D4—82no—
574D4—82no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—82no—
587C2×C4—81no—
588C2×C4—82no—
589C2×C4—82no—
590C2×C4—82no—
591C2×C4#120×C3711yescharacteristic
592C2×C4#120×C3711yescharacteristic
593C2×C4#120×C3711yescharacteristic
594C2×C4C22×D4×C3711yescharacteristic
595C2×C4C22×D4×C3711yescharacteristic
596C2×C4C22×D4×C3711yescharacteristic
597C8—22no—
598C8—42no—
599C8—41no—
600C8—42no—
601C22—21no—
602C22—21no—
603C22—41no—
604C22—42no—
605C22—42no—
606C22—41no—
607C22—41no—
608C22—42no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—162no—
613C22C37×#45412yes—
614C22C2×#120×C3711yescharacteristic
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—41no—
622C4—41no—
623C4—42no—
624C4—41no—
625C4—42no—
626C4—42no—
627C4—81no—
628C2—22no—
629C2—82no—
630C2—81no—
631C2—161no—
632C2C2×C37×#45411yescharacteristic
633C2C37×#301811yescharacteristic
634C2C37×#301911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C37×#3561C2semidirect
2. C37×#3213C2semidirect
3. C37×#3180C2semidirect
4. C37×#3135C2semidirect
5. C37×#1664C2semidirect
6. C37×#1662C2semidirect
7. C37×#1657C2semidirect
8. C37×#1656C2semidirect
9. C37×#1532C2semidirect
10. C37×#1531C2semidirect
11. C2×C37×#329C2semidirect
28. C37×#501C22semidirect
30. C37×#496C22semidirect
31. C37×#491C22semidirect
32. C37×#490C22semidirect
33. C37×#490C22semidirect
37. C37×#489C22semidirect
49. C37×#330C22semidirect
50. C37×#330C22semidirect
51. C37×#330C22semidirect
54. C37×#329C22semidirect
283. #19048C37direct (N × H)
311. #3561C2×C37semidirect
312. #3213C2×C37semidirect
313. #3180C2×C37semidirect
314. #3135C2×C37semidirect
315. #1664C2×C37semidirect
316. #1662C2×C37semidirect
317. #1657C2×C37semidirect
318. #1656C2×C37semidirect
319. #1532C2×C37semidirect
320. #1531C2×C37semidirect
321. C2×#329C2×C37semidirect
345. #501C22×C37semidirect
347. #496C22×C37semidirect
348. #491C22×C37semidirect
349. #490C22×C37semidirect
350. #490C22×C37semidirect
354. #489C22×C37semidirect
366. #330C22×C37semidirect
367. #330C22×C37semidirect
368. #330C22×C37semidirect
371. #329C22×C37semidirect
372. C37#19048direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35612
C37×#32132
C37×#31802
C37×#31352
C37×#16642
C37×#16622
C37×#16572
C37×#16562
C37×#15322
C37×#15312
C2×C37×#3292
#1904837