Finite Group Databasebeta

← C37×#18461 #22639714

Subgroups — C37×#18461 #22639714

Order 9472.

880 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3563C211yesmaximal, characteristic, complemented
2C37×#3215C211yesmaximal, characteristic, complemented
3C37×#3211C211yesmaximal, characteristic
4C37×#2820C211yesmaximal, characteristic, complemented
5C37×#1605C212yesmaximal, complemented
6C37×#1603C212yesmaximal, complemented
7C37×#1599C212yesmaximal, complemented
8C37×#1597C212yesmaximal
9C37×#1518C211yesmaximal, characteristic, complemented
10C37×#1512C211yesmaximal, characteristic, complemented
11C37×#1470C211yesmaximal, characteristic, complemented
12C37×#564—21no—
13C37×#563—21no—
14C37×#557—21no—
15C37×#554—21no—
16C37×#552—21no—
17C37×#552—22no—
18C37×#552—21no—
19C37×#544—21no—
20C37×#544C2212yes—
21C37×#541—21no—
22C37×#541—22no—
23C37×#539C2212yes—
24C37×#533C2211yescharacteristic
25C37×#529C2211yescharacteristic
26C2×#125×C37C2211yescharacteristic
27C2×#124×C37C2211yescharacteristic
28C37×#497—21no—
29C37×#495—21no—
30C37×#489—21no—
31C37×#488—21no—
32C37×#464—21no—
33C37×#464—22no—
34C37×#463—21no—
35C37×#451C2212yes—
36C37×#451C2211yescharacteristic
37C37×#450C2212yes—
38C37×#450C2211yescharacteristic
39C37×#448C2211yescharacteristic
40C37×#447C2211yescharacteristic
41C37×#432C2211yescharacteristic
42C37×#431C2211yescharacteristic
43C37×#399—21no—
44C37×#397—21no—
45C37×#396—22no—
46C37×#395C2212yes—
47C37×#394C2212yes—
48C37×#382C2211yescharacteristic
49C37×#328C2212yes—
50C37×#328C2212yes—
51C37×#328C2212yes—
52C37×#327C2212yes—
53C37×#324C2212yes—
54C37×#324C2212yes—
55C22×Q8×C37C2311yescharacteristic
56C22×D4×C37C2311yescharacteristic
57C2×Q16×C37—21no—
58C2×Q16×C37—22no—
59C2×SD16×C37—21no—
60C2×SD16×C37—22no—
61C2×SD16×C37—21no—
62C2×D8×C37—21no—
63C4⋊Q8×C37—21no—
64C4⋊Q8×C37—22no—
65C4⋊Q8×C37—22no—
66C4⋊Q8×C37D411yescharacteristic
67C4⋊Q8×C37D411yescharacteristic
68#126×C37—22no—
69#126×C37—22no—
70#126×C37—22no—
71#126×C37—22no—
72#126×C37—21no—
73#125×C37—22no—
74#125×C37—22no—
75#125×C37—22no—
76#125×C37—22no—
77#125×C37—21no—
78#125×C37—22no—
79#125×C37—22no—
80#125×C37—22no—
81#125×C37—22no—
82#125×C37—21no—
83#125×C37—21no—
84#125×C37—21no—
85#125×C37—21no—
86#125×C37—21no—
87#125×C37D411yescharacteristic
88#124×C37—21no—
89#124×C37—21no—
90#124×C37—21no—
91#124×C37—21no—
92#124×C37D411yescharacteristic
93#123×C37—22no—
94#123×C37—21no—
95#123×C37—22no—
96C22⋊Q8×C37—21no—
97C22⋊Q8×C37—21no—
98C22⋊Q8×C37—22no—
99C22⋊Q8×C37—22no—
100C22⋊Q8×C37—22no—
101C22⋊Q8×C37—21no—
102C22⋊Q8×C37—22no—
103C22⋊Q8×C37C2311yescharacteristic
104C22⋊Q8×C37C2312yes—
105#121×C37C2311yescharacteristic
106C4×Q8×C37—21no—
107C4×Q8×C37—22no—
108C4×Q8×C37—21no—
109C4×Q8×C37—21no—
110C4×Q8×C37D411yescharacteristic
111C4×Q8×C37D412yes—
112C4×D4×C37—21no—
113C4×D4×C37—22no—
114C4×D4×C37D411yescharacteristic
115#117×C37—22no—
116#117×C37—21no—
117#117×C37—21no—
118#117×C37—22no—
119#117×C37—21no—
120C2×C4⋊C4×C37—21no—
121C2×C4⋊C4×C37—21no—
122C2×C4⋊C4×C37—22no—
123C2×C4⋊C4×C37D412yes—
124C2×C4⋊C4×C37D411yescharacteristic
125C2×C4⋊C4×C37D411yescharacteristic
126C2×C4⋊C4×C37C2312yes—
127C2×C22⋊C4×C37—21no—
128C2×C22⋊C4×C37—21no—
129C2×C22⋊C4×C37—22no—
130C2×C22⋊C4×C37—22no—
131C2×C42×C37C2311yescharacteristic
132C4⋊C8×C37—21no—
133C4⋊C8×C37—21no—
134#103×C37—21no—
135#103×C37—21no—
136#103×C37—22no—
137#102×C37—21no—
138#102×C37—21no—
139#102×C37—22no—
140C22⋊C8×C37C2312yes—
141C22⋊C8×C37C2311yescharacteristic
142C22⋊C8×C37C2311yescharacteristic
143#97×C37—21no—
144C4×C8×C37—21no—
145#95×C37—21no—
146#95×C37—22no—
147#95×C37C2312yes—
148C24×C37—21no—
149C2×Q8×C37—22no—
150C2×Q8×C37—21no—
151C2×Q8×C37—21no—
152C2×Q8×C37—21no—
153C2×Q8×C37—81no—
154C2×Q8×C37C2×D412yes—
155C2×Q8×C37C2×D411yescharacteristic
156C2×D4×C37—21no—
157C2×D4×C37—21no—
158C2×D4×C37—21no—
159C2×D4×C37—81no—
160C2×D4×C37C2×D411yescharacteristic
161C22×C4×C37—22no—
162C22×C4×C37—21no—
163C22×C4×C37—22no—
164C22×C4×C37—21no—
165C22×C4×C37C2×D412yes—
166C22×C4×C37C2×D411yescharacteristic
167C22×C4×C37C2×D412yes—
168C22×C4×C37C2×D411yescharacteristic
169C22×C4×C37C2411yescharacteristic
170Q16×C37—81no—
171Q16×C37—82no—
172SD16×C37—81no—
173SD16×C37—81no—
174SD16×C37—82no—
175D8×C37—81no—
176C2×C8×C37—21no—
177C2×C8×C37—21no—
178C2×C8×C37—22no—
179C4⋊C4×C37—22no—
180C4⋊C4×C37—22no—
181C4⋊C4×C37—22no—
182C4⋊C4×C37—22no—
183C4⋊C4×C37—22no—
184C4⋊C4×C37—22no—
185C4⋊C4×C37—22no—
186C4⋊C4×C37—22no—
187C4⋊C4×C37—21no—
188C4⋊C4×C37—21no—
189C4⋊C4×C37—21no—
190C4⋊C4×C37—22no—
191C4⋊C4×C37—21no—
192C4⋊C4×C37—22no—
193C4⋊C4×C37—21no—
194C4⋊C4×C37—21no—
195C4⋊C4×C37—21no—
196C4⋊C4×C37—21no—
197C4⋊C4×C37—21no—
198C4⋊C4×C37—21no—
199C4⋊C4×C37—22no—
200C4⋊C4×C37—22no—
201C4⋊C4×C37—22no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—22no—
204C4⋊C4×C37—81no—
205C4⋊C4×C37—82no—
206C4⋊C4×C37C2×D411yescharacteristic
207C4⋊C4×C37C2×D411yescharacteristic
208C4⋊C4×C37C2×D412yes—
209C22⋊C4×C37—22no—
210C22⋊C4×C37—22no—
211C22⋊C4×C37—22no—
212C22⋊C4×C37—22no—
213C22⋊C4×C37—21no—
214C22⋊C4×C37—21no—
215C22⋊C4×C37—21no—
216C22⋊C4×C37—21no—
217C22⋊C4×C37—21no—
218C22⋊C4×C37—41no—
219C22⋊C4×C37—41no—
220C22⋊C4×C37—41no—
221C22⋊C4×C37—41no—
222C22⋊C4×C37—82no—
223C22⋊C4×C37—82no—
224C42×C37—22no—
225C42×C37—22no—
226C42×C37—22no—
227C42×C37—22no—
228C42×C37—21no—
229C42×C37C2×D411yescharacteristic
230C42×C37C2×D411yescharacteristic
231C42×C37C2×D411yescharacteristic
232C42×C37C2×D411yescharacteristic
233C23×C37—21no—
234C23×C37—42no—
235C23×C37—42no—
236C23×C37—41no—
237C23×C37—41no—
238C23×C37—41no—
239C23×C37C22×D411yescharacteristic
240Q8×C37—41no—
241Q8×C37—42no—
242Q8×C37—42no—
243Q8×C37—41no—
244Q8×C37—41no—
245Q8×C37—42no—
246Q8×C37—82no—
247D4×C37—41no—
248D4×C37—41no—
249D4×C37—41no—
250D4×C37—42no—
251D4×C37—41no—
252D4×C37—41no—
253C2×C4×C37—21no—
254C2×C4×C37—21no—
255C2×C4×C37—22no—
256C2×C4×C37—21no—
257C2×C4×C37—21no—
258C2×C4×C37—22no—
259C2×C4×C37—21no—
260C2×C4×C37—22no—
261C2×C4×C37—22no—
262C2×C4×C37—22no—
263C2×C4×C37—22no—
264C2×C4×C37—41no—
265C2×C4×C37—41no—
266C2×C4×C37—42no—
267C2×C4×C37—42no—
268C2×C4×C37—42no—
269C2×C4×C37—42no—
270C2×C4×C37—42no—
271C2×C4×C37—41no—
272C2×C4×C37—42no—
273C2×C4×C37—82no—
274C2×C4×C37#12011yescharacteristic
275C2×C4×C37#12011yescharacteristic
276C2×C4×C37#12011yescharacteristic
277C2×C4×C37#12011yescharacteristic
278C2×C4×C37C22×D411yescharacteristic
279C2×C4×C37C22×D411yescharacteristic
280C8×C37—41no—
281C8×C37—41no—
282C8×C37—42no—
283#18461C3711yesmaximal, characteristic, direct product factor, Sylow
284C22×C37—21no—
285C22×C37—21no—
286C22×C37—41no—
287C22×C37—41no—
288C22×C37—41no—
289C22×C37—82no—
290C22×C37—82no—
291C22×C37—81no—
292C22×C37—81no—
293C22×C37—81no—
294C22×C37C2×#12011yescharacteristic
295C22×C37#57711yescharacteristic
296C22×C37#57811yescharacteristic
297C4×C37—21no—
298C4×C37—21no—
299C4×C37—21no—
300C4×C37—21no—
301C4×C37—21no—
302C4×C37—21no—
303C4×C37—42no—
304C4×C37—41no—
305C4×C37—41no—
306C4×C37—42no—
307C4×C37—42no—
308C4×C37—42no—
309C4×C37—41no—
310C4×C37—82no—
311C4×C37—81no—
312#3563C2×C3711yescharacteristic, complemented
313#3215C2×C3711yescharacteristic, complemented
314#3211C2×C3711yescharacteristic
315#2820C2×C3711yescharacteristic, complemented
316#1605C2×C3712yescomplemented
317#1603C2×C3712yescomplemented
318#1599C2×C3712yescomplemented
319#1597C2×C3712yes—
320#1518C2×C3711yescharacteristic, complemented
321#1512C2×C3711yescharacteristic, complemented
322#1470C2×C3711yescharacteristic, complemented
323C2×C37—21no—
324C2×C37—21no—
325C2×C37—81no—
326C2×C37—161no—
327C2×C37#301311yescharacteristic
328C2×C37#302011yescharacteristic
329C2×C37#302711yescharacteristic
330#564—21no—
331#563—21no—
332#557—21no—
333#554—21no—
334#552—21no—
335#552—22no—
336#552—21no—
337#544—21no—
338#544C22×C3712yes—
339#541—21no—
340#541—22no—
341#539C22×C3712yes—
342#533C22×C3711yescharacteristic
343#529C22×C3711yescharacteristic
344C2×#125C22×C3711yescharacteristic
345C2×#124C22×C3711yescharacteristic
346#497—21no—
347#495—21no—
348#489—21no—
349#488—21no—
350#464—21no—
351#464—22no—
352#463—21no—
353#451C22×C3712yes—
354#451C22×C3711yescharacteristic
355#450C22×C3712yes—
356#450C22×C3711yescharacteristic
357#448C22×C3711yescharacteristic
358#447C22×C3711yescharacteristic
359#432C22×C3711yescharacteristic
360#431C22×C3711yescharacteristic
361#399—21no—
362#397—21no—
363#396—22no—
364#395C22×C3712yes—
365#394C22×C3712yes—
366#382C22×C3711yescharacteristic
367#328C22×C3712yes—
368#328C22×C3712yes—
369#328C22×C3712yes—
370#327C22×C3712yes—
371#324C22×C3712yes—
372#324C22×C3712yes—
373C37#1846111yescharacteristic, direct product factor, Sylow
374C22×Q8C23×C3711yescharacteristic
375C22×D4C23×C3711yescharacteristic
376C2×Q16—21no—
377C2×Q16—22no—
378C2×SD16—21no—
379C2×SD16—22no—
380C2×SD16—21no—
381C2×D8—21no—
382C4⋊Q8—21no—
383C4⋊Q8—22no—
384C4⋊Q8—22no—
385C4⋊Q8D4×C3711yescharacteristic
386C4⋊Q8D4×C3711yescharacteristic
387#126—22no—
388#126—22no—
389#126—22no—
390#126—22no—
391#126—21no—
392#125—22no—
393#125—22no—
394#125—22no—
395#125—22no—
396#125—21no—
397#125—22no—
398#125—22no—
399#125—22no—
400#125—22no—
401#125—21no—
402#125—21no—
403#125—21no—
404#125—21no—
405#125—21no—
406#125D4×C3711yescharacteristic
407#124—21no—
408#124—21no—
409#124—21no—
410#124—21no—
411#124D4×C3711yescharacteristic
412#123—22no—
413#123—21no—
414#123—22no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—22no—
418C22⋊Q8—22no—
419C22⋊Q8—22no—
420C22⋊Q8—21no—
421C22⋊Q8—22no—
422C22⋊Q8C23×C3711yescharacteristic
423C22⋊Q8C23×C3712yes—
424#121C23×C3711yescharacteristic
425C4×Q8—21no—
426C4×Q8—22no—
427C4×Q8—21no—
428C4×Q8—21no—
429C4×Q8D4×C3711yescharacteristic
430C4×Q8D4×C3712yes—
431C4×D4—21no—
432C4×D4—22no—
433C4×D4D4×C3711yescharacteristic
434#117—22no—
435#117—21no—
436#117—21no—
437#117—22no—
438#117—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4D4×C3712yes—
443C2×C4⋊C4D4×C3711yescharacteristic
444C2×C4⋊C4D4×C3711yescharacteristic
445C2×C4⋊C4C23×C3712yes—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C42C23×C3711yescharacteristic
451C4⋊C8—21no—
452C4⋊C8—21no—
453#103—21no—
454#103—21no—
455#103—22no—
456#102—21no—
457#102—21no—
458#102—22no—
459C22⋊C8C23×C3712yes—
460C22⋊C8C23×C3711yescharacteristic
461C22⋊C8C23×C3711yescharacteristic
462#97—21no—
463C4×C8—21no—
464#95—21no—
465#95—22no—
466#95C23×C3712yes—
467C24—21no—
468C2×Q8—22no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—81no—
473C2×Q8C2×D4×C3712yes—
474C2×Q8C2×D4×C3711yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—81no—
479C2×D4C2×D4×C3711yescharacteristic
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4C2×D4×C3712yes—
485C22×C4C2×D4×C3711yescharacteristic
486C22×C4C2×D4×C3712yes—
487C22×C4C2×D4×C3711yescharacteristic
488C22×C4C24×C3711yescharacteristic
489Q16—81no—
490Q16—82no—
491SD16—81no—
492SD16—81no—
493SD16—82no—
494D8—81no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—21no—
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—22no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—81no—
524C4⋊C4—82no—
525C4⋊C4C2×D4×C3711yescharacteristic
526C4⋊C4C2×D4×C3711yescharacteristic
527C4⋊C4C2×D4×C3712yes—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—82no—
542C22⋊C4—82no—
543C42—22no—
544C42—22no—
545C42—22no—
546C42—22no—
547C42—21no—
548C42C2×D4×C3711yescharacteristic
549C42C2×D4×C3711yescharacteristic
550C42C2×D4×C3711yescharacteristic
551C42C2×D4×C3711yescharacteristic
552C23—21no—
553C23—42no—
554C23—42no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23C22×D4×C3711yescharacteristic
559Q8—41no—
560Q8—42no—
561Q8—42no—
562Q8—41no—
563Q8—41no—
564Q8—42no—
565Q8—82no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—42no—
570D4—41no—
571D4—41no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—82no—
593C2×C4#120×C3711yescharacteristic
594C2×C4#120×C3711yescharacteristic
595C2×C4#120×C3711yescharacteristic
596C2×C4#120×C3711yescharacteristic
597C2×C4C22×D4×C3711yescharacteristic
598C2×C4C22×D4×C3711yescharacteristic
599C8—41no—
600C8—41no—
601C8—42no—
602C22—21no—
603C22—21no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—82no—
608C22—82no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22C2×#120×C3711yescharacteristic
613C22C37×#57711yescharacteristic
614C22C37×#57811yescharacteristic
615C4—21no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—21no—
620C4—21no—
621C4—42no—
622C4—41no—
623C4—41no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—41no—
628C4—82no—
629C4—81no—
630C2—21no—
631C2—21no—
632C2—81no—
633C2—161no—
634C2C37×#301311yescharacteristic
635C2C37×#302011yescharacteristic
636C2C37×#302711yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#447C22
LCSG ▷ C22×C4 ▷ 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×#3563C2semidirect
2. C37×#3215C2semidirect
4. C37×#2820C2semidirect
5. C37×#1605C2semidirect
6. C37×#1603C2semidirect
7. C37×#1599C2semidirect
9. C37×#1518C2semidirect
10. C37×#1512C2semidirect
11. C37×#1470C2semidirect
283. #18461C37direct (N × H)
312. #3563C2×C37semidirect
313. #3215C2×C37semidirect
315. #2820C2×C37semidirect
316. #1605C2×C37semidirect
317. #1603C2×C37semidirect
318. #1599C2×C37semidirect
320. #1518C2×C37semidirect
321. #1512C2×C37semidirect
322. #1470C2×C37semidirect
373. C37#18461direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35632
C37×#32152
C37×#32112
C37×#28202
C37×#16052
C37×#16032
C37×#15992
C37×#15972
C37×#15182
C37×#15122
C37×#14702
#1846137