Finite Group Databasebeta

← C37×#18956 #22640209

Subgroups — C37×#18956 #22640209

Order 9472.

950 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3547C211yesmaximal, characteristic, complemented
2C37×#3217C211yesmaximal, characteristic, complemented
3C37×#3208C211yesmaximal, characteristic, complemented
4C37×#3205C211yesmaximal, characteristic, complemented
5C37×#1627C212yesmaximal, complemented
6C37×#1625C212yesmaximal, complemented
7C37×#1624C212yesmaximal, complemented
8C37×#1622C212yesmaximal, complemented
9C37×#1554C211yesmaximal, characteristic, complemented
10C37×#1496C211yesmaximal, characteristic, complemented
11C37×#1482C211yesmaximal, characteristic, complemented
12C37×#562—22no—
13C37×#555—21no—
14C37×#555C2211yescharacteristic, complemented
15C37×#554C2211yescharacteristic, complemented
16C37×#553—21no—
17C37×#552—21no—
18D4×Q8×C37C2211yescharacteristic, complemented
19C37×#548—21no—
20C37×#547C2211yescharacteristic, complemented
21C37×#544—21no—
22C37×#542—22no—
23C37×#540—21no—
24C37×#537—21no—
25C37×#536—21no—
26C37×#533C2211yescharacteristic
27C37×#532C2211yescharacteristic
28C2×#127×C37C2211yescharacteristic
29C37×#529C2211yescharacteristic
30C37×#496—21no—
31C37×#493—21no—
32C37×#492C2212yes—
33C37×#490—21no—
34C37×#486—21no—
35C37×#486C2212yes—
36C37×#460—22no—
37C37×#460C2212yes—
38C37×#459C2212yes—
39C37×#459C2212yes—
40C37×#459C2212yes—
41C37×#450—22no—
42C37×#450—21no—
43C37×#447—21no—
44C37×#447—21no—
45C37×#447—21no—
46C37×#432C2211yescharacteristic
47C37×#431C2211yescharacteristic
48C37×#431C2211yescharacteristic
49C37×#333C2212yescomplemented
50C37×#332C2212yescomplemented
51C37×Q8⋊C8C2212yescomplemented
52C37×D4⋊C8C2212yescomplemented
53C37×D4⋊C8C2212yescomplemented
54C37×D4⋊C8C2212yescomplemented
55C2×#41×C37—21no—
56C2×#41×C37—21no—
57C22×Q8×C37—21no—
58C22×D4×C37—21no—
59C22×D4×C37—21no—
60C22×D4×C37—21no—
61C2×SD16×C37—24no—
62C2×SD16×C37—22no—
63C2×D8×C37—22no—
64C2×D8×C37—22no—
65C2×D8×C37—22no—
66C4⋊Q8×C37—22no—
67C4⋊Q8×C37—21no—
68C4⋊Q8×C37D411yescharacteristic
69C4⋊Q8×C37C2311yescharacteristic
70C4⋊Q8×C37C2311yescharacteristic
71#127×C37—21no—
72#127×C37—21no—
73#127×C37—21no—
74#127×C37D411yescharacteristic
75#127×C37C2312yes—
76#126×C37—22no—
77#126×C37—21no—
78#125×C37—22no—
79#125×C37—21no—
80#125×C37—21no—
81#125×C37D411yescharacteristic
82#124×C37—22no—
83#124×C37—22no—
84#124×C37—22no—
85#124×C37—21no—
86#124×C37D411yescharacteristic
87#123×C37—22no—
88#123×C37—22no—
89#123×C37—22no—
90#123×C37—21no—
91#123×C37—22no—
92C22⋊Q8×C37—22no—
93C22⋊Q8×C37—22no—
94C22⋊Q8×C37—21no—
95C22⋊Q8×C37—22no—
96C22⋊Q8×C37—21no—
97C22⋊Q8×C37—21no—
98C22⋊Q8×C37—21no—
99C22⋊Q8×C37—22no—
100C22⋊Q8×C37D411yescharacteristic
101C22⋊Q8×C37D412yes—
102#121×C37—22no—
103#121×C37—22no—
104#121×C37—22no—
105#121×C37—22no—
106#121×C37—21no—
107#121×C37—21no—
108#121×C37—21no—
109#121×C37—21no—
110#121×C37D411yescharacteristic
111#121×C37D411yescharacteristic
112#121×C37D411yescharacteristic
113C4×Q8×C37—21no—
114C4×Q8×C37D412yes—
115C4×Q8×C37C2311yescharacteristic
116C4×D4×C37—22no—
117C4×D4×C37—21no—
118C4×D4×C37—21no—
119C4×D4×C37—21no—
120C4×D4×C37—21no—
121C4×D4×C37C2311yescharacteristic
122C4×D4×C37C2311yescharacteristic
123C4×D4×C37C2311yescharacteristic
124#117×C37—22no—
125#117×C37—21no—
126#117×C37—21no—
127#117×C37—21no—
128#117×C37—21no—
129C2×C4⋊C4×C37—21no—
130C2×C4⋊C4×C37—21no—
131C2×C42×C37C2311yescharacteristic
132C4⋊C8×C37—21no—
133C4⋊C8×C37C2312yes—
134C4⋊C8×C37C2312yes—
135#102×C37—22no—
136#102×C37—22no—
137#102×C37—22no—
138#102×C37—22no—
139#102×C37—24no—
140C22⋊C8×C37—21no—
141C22⋊C8×C37—21no—
142C22⋊C8×C37—21no—
143#97×C37—21no—
144C4×C8×C37—21no—
145C4×C8×C37C2312yes—
146C24×C37—41no—
147#41×C37—82no—
148#41×C37—82no—
149C2×Q8×C37—22no—
150C2×Q8×C37—21no—
151C2×Q8×C37—21no—
152C2×Q8×C37—82no—
153C2×Q8×C37C2×D411yescharacteristic
154C2×Q8×C37C2×D412yes—
155C2×D4×C37—22no—
156C2×D4×C37—22no—
157C2×D4×C37—21no—
158C2×D4×C37—21no—
159C2×D4×C37—21no—
160C2×D4×C37—21no—
161C2×D4×C37—21no—
162C2×D4×C37—22no—
163C2×D4×C37—22no—
164C2×D4×C37—22no—
165C2×D4×C37—41no—
166C2×D4×C37—41no—
167C2×D4×C37—41no—
168C2×D4×C37—82no—
169C2×D4×C37—82no—
170C2×D4×C37—82no—
171C2×D4×C37C2×D411yescharacteristic
172C2×D4×C37C2×D411yescharacteristic
173C2×D4×C37C2×D411yescharacteristic
174C22×C4×C37—22no—
175C22×C4×C37—22no—
176C22×C4×C37—22no—
177C22×C4×C37—21no—
178C22×C4×C37—21no—
179C22×C4×C37—21no—
180C22×C4×C37C2×D411yescharacteristic
181C22×C4×C37C2×D411yescharacteristic
182C22×C4×C37C2×D411yescharacteristic
183SD16×C37—82no—
184SD16×C37—84no—
185D8×C37—82no—
186D8×C37—82no—
187D8×C37—82no—
188C2×C8×C37—22no—
189C2×C8×C37—22no—
190C2×C8×C37—22no—
191C4⋊C4×C37—22no—
192C4⋊C4×C37—22no—
193C4⋊C4×C37—22no—
194C4⋊C4×C37—22no—
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—21no—
202C4⋊C4×C37—21no—
203C4⋊C4×C37—21no—
204C4⋊C4×C37—21no—
205C4⋊C4×C37C2×D411yescharacteristic
206C4⋊C4×C37C2×D411yescharacteristic
207C4⋊C4×C37C2×D411yescharacteristic
208C4⋊C4×C37C2×D411yescharacteristic
209C4⋊C4×C37C2×D412yes—
210C22⋊C4×C37—22no—
211C22⋊C4×C37—22no—
212C22⋊C4×C37—22no—
213C22⋊C4×C37—22no—
214C22⋊C4×C37—22no—
215C22⋊C4×C37—22no—
216C22⋊C4×C37—21no—
217C22⋊C4×C37—21no—
218C22⋊C4×C37—21no—
219C22⋊C4×C37—21no—
220C22⋊C4×C37—21no—
221C22⋊C4×C37—21no—
222C22⋊C4×C37—21no—
223C22⋊C4×C37—21no—
224C22⋊C4×C37—21no—
225C42×C37—22no—
226C42×C37—22no—
227C42×C37—21no—
228C42×C37C2×D411yescharacteristic
229C42×C37C2×D411yescharacteristic
230C42×C37C2×D411yescharacteristic
231C42×C37C2411yescharacteristic
232C23×C37—21no—
233C23×C37—21no—
234C23×C37—21no—
235C23×C37—42no—
236C23×C37—82no—
237C23×C37—82no—
238C23×C37—82no—
239C23×C37#12011yescharacteristic
240Q8×C37—22no—
241Q8×C37—42no—
242Q8×C37—42no—
243Q8×C37—81no—
244Q8×C37—82no—
245D4×C37—22no—
246D4×C37—22no—
247D4×C37—22no—
248D4×C37—44no—
249D4×C37—42no—
250D4×C37—42no—
251D4×C37—42no—
252D4×C37—42no—
253D4×C37—81no—
254D4×C37—81no—
255D4×C37—82no—
256D4×C37—82no—
257D4×C37—82no—
258D4×C37—81no—
259D4×C37—81no—
260D4×C37—81no—
261D4×C37—82no—
262D4×C37—82no—
263C2×C4×C37—22no—
264C2×C4×C37—22no—
265C2×C4×C37—21no—
266C2×C4×C37—22no—
267C2×C4×C37—21no—
268C2×C4×C37—21no—
269C2×C4×C37—21no—
270C2×C4×C37—22no—
271C2×C4×C37—21no—
272C2×C4×C37—41no—
273C2×C4×C37—42no—
274C2×C4×C37—42no—
275C2×C4×C37—42no—
276C2×C4×C37—82no—
277C2×C4×C37—82no—
278C2×C4×C37—82no—
279C2×C4×C37#12011yescharacteristic
280C2×C4×C37#12011yescharacteristic
281C2×C4×C37#12011yescharacteristic
282C2×C4×C37C22×D411yescharacteristic
283C2×C4×C37C22×D411yescharacteristic
284C2×C4×C37C22×D411yescharacteristic
285C8×C37—42no—
286C8×C37—42no—
287C8×C37—42no—
288#18956C3711yesmaximal, characteristic, direct product factor, Sylow
289C22×C37—21no—
290C22×C37—21no—
291C22×C37—21no—
292C22×C37—41no—
293C22×C37—41no—
294C22×C37—41no—
295C22×C37—41no—
296C22×C37—41no—
297C22×C37—41no—
298C22×C37—41no—
299C22×C37—41no—
300C22×C37—41no—
301C22×C37—82no—
302C22×C37—82no—
303C22×C37—82no—
304C22×C37—164no—
305C22×C37C2×#12011yescharacteristic
306C4×C37—21no—
307C4×C37—21no—
308C4×C37—21no—
309C4×C37—21no—
310C4×C37—41no—
311C4×C37—41no—
312C4×C37—42no—
313C4×C37—41no—
314C4×C37—41no—
315C4×C37—41no—
316C4×C37—42no—
317C4×C37#57612yes—
318C4×C37#57712yes—
319#3547C2×C3711yescharacteristic, complemented
320#3217C2×C3711yescharacteristic, complemented
321#3208C2×C3711yescharacteristic, complemented
322#3205C2×C3711yescharacteristic, complemented
323#1627C2×C3712yescomplemented
324#1625C2×C3712yescomplemented
325#1624C2×C3712yescomplemented
326#1622C2×C3712yescomplemented
327#1554C2×C3711yescharacteristic, complemented
328#1496C2×C3711yescharacteristic, complemented
329#1482C2×C3711yescharacteristic, complemented
330C2×C37—41no—
331C2×C37—81no—
332C2×C37—81no—
333C2×C37—81no—
334C2×C37—162no—
335C2×C37#300811yescharacteristic
336C2×C37#301011yescharacteristic
337C2×C37#302111yescharacteristic
338#562—22no—
339#555—21no—
340#555C22×C3711yescharacteristic, complemented
341#554C22×C3711yescharacteristic, complemented
342#553—21no—
343#552—21no—
344D4×Q8C22×C3711yescharacteristic, complemented
345#548—21no—
346#547C22×C3711yescharacteristic, complemented
347#544—21no—
348#542—22no—
349#540—21no—
350#537—21no—
351#536—21no—
352#533C22×C3711yescharacteristic
353#532C22×C3711yescharacteristic
354C2×#127C22×C3711yescharacteristic
355#529C22×C3711yescharacteristic
356#496—21no—
357#493—21no—
358#492C22×C3712yes—
359#490—21no—
360#486—21no—
361#486C22×C3712yes—
362#460—22no—
363#460C22×C3712yes—
364#459C22×C3712yes—
365#459C22×C3712yes—
366#459C22×C3712yes—
367#450—22no—
368#450—21no—
369#447—21no—
370#447—21no—
371#447—21no—
372#432C22×C3711yescharacteristic
373#431C22×C3711yescharacteristic
374#431C22×C3711yescharacteristic
375#333C22×C3712yescomplemented
376#332C22×C3712yescomplemented
377Q8⋊C8C22×C3712yescomplemented
378D4⋊C8C22×C3712yescomplemented
379D4⋊C8C22×C3712yescomplemented
380D4⋊C8C22×C3712yescomplemented
381C37#1895611yescharacteristic, direct product factor, Sylow
382C2×#41—21no—
383C2×#41—21no—
384C22×Q8—21no—
385C22×D4—21no—
386C22×D4—21no—
387C22×D4—21no—
388C2×SD16—24no—
389C2×SD16—22no—
390C2×D8—22no—
391C2×D8—22no—
392C2×D8—22no—
393C4⋊Q8—22no—
394C4⋊Q8—21no—
395C4⋊Q8D4×C3711yescharacteristic
396C4⋊Q8C23×C3711yescharacteristic
397C4⋊Q8C23×C3711yescharacteristic
398#127—21no—
399#127—21no—
400#127—21no—
401#127D4×C3711yescharacteristic
402#127C23×C3712yes—
403#126—22no—
404#126—21no—
405#125—22no—
406#125—21no—
407#125—21no—
408#125D4×C3711yescharacteristic
409#124—22no—
410#124—22no—
411#124—22no—
412#124—21no—
413#124D4×C3711yescharacteristic
414#123—22no—
415#123—22no—
416#123—22no—
417#123—21no—
418#123—22no—
419C22⋊Q8—22no—
420C22⋊Q8—22no—
421C22⋊Q8—21no—
422C22⋊Q8—22no—
423C22⋊Q8—21no—
424C22⋊Q8—21no—
425C22⋊Q8—21no—
426C22⋊Q8—22no—
427C22⋊Q8D4×C3711yescharacteristic
428C22⋊Q8D4×C3712yes—
429#121—22no—
430#121—22no—
431#121—22no—
432#121—22no—
433#121—21no—
434#121—21no—
435#121—21no—
436#121—21no—
437#121D4×C3711yescharacteristic
438#121D4×C3711yescharacteristic
439#121D4×C3711yescharacteristic
440C4×Q8—21no—
441C4×Q8D4×C3712yes—
442C4×Q8C23×C3711yescharacteristic
443C4×D4—22no—
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4C23×C3711yescharacteristic
449C4×D4C23×C3711yescharacteristic
450C4×D4C23×C3711yescharacteristic
451#117—22no—
452#117—21no—
453#117—21no—
454#117—21no—
455#117—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C42C23×C3711yescharacteristic
459C4⋊C8—21no—
460C4⋊C8C23×C3712yes—
461C4⋊C8C23×C3712yes—
462#102—22no—
463#102—22no—
464#102—22no—
465#102—22no—
466#102—24no—
467C22⋊C8—21no—
468C22⋊C8—21no—
469C22⋊C8—21no—
470#97—21no—
471C4×C8—21no—
472C4×C8C23×C3712yes—
473C24—41no—
474#41—82no—
475#41—82no—
476C2×Q8—22no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—82no—
480C2×Q8C2×D4×C3711yescharacteristic
481C2×Q8C2×D4×C3712yes—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—41no—
493C2×D4—41no—
494C2×D4—41no—
495C2×D4—82no—
496C2×D4—82no—
497C2×D4—82no—
498C2×D4C2×D4×C3711yescharacteristic
499C2×D4C2×D4×C3711yescharacteristic
500C2×D4C2×D4×C3711yescharacteristic
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4C2×D4×C3711yescharacteristic
508C22×C4C2×D4×C3711yescharacteristic
509C22×C4C2×D4×C3711yescharacteristic
510SD16—82no—
511SD16—84no—
512D8—82no—
513D8—82no—
514D8—82no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4C2×D4×C3711yescharacteristic
533C4⋊C4C2×D4×C3711yescharacteristic
534C4⋊C4C2×D4×C3711yescharacteristic
535C4⋊C4C2×D4×C3711yescharacteristic
536C4⋊C4C2×D4×C3712yes—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C42—22no—
553C42—22no—
554C42—21no—
555C42C2×D4×C3711yescharacteristic
556C42C2×D4×C3711yescharacteristic
557C42C2×D4×C3711yescharacteristic
558C42C24×C3711yescharacteristic
559C23—21no—
560C23—21no—
561C23—21no—
562C23—42no—
563C23—82no—
564C23—82no—
565C23—82no—
566C23#120×C3711yescharacteristic
567Q8—22no—
568Q8—42no—
569Q8—42no—
570Q8—81no—
571Q8—82no—
572D4—22no—
573D4—22no—
574D4—22no—
575D4—44no—
576D4—42no—
577D4—42no—
578D4—42no—
579D4—42no—
580D4—81no—
581D4—81no—
582D4—82no—
583D4—82no—
584D4—82no—
585D4—81no—
586D4—81no—
587D4—81no—
588D4—82no—
589D4—82no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4#120×C3711yescharacteristic
607C2×C4#120×C3711yescharacteristic
608C2×C4#120×C3711yescharacteristic
609C2×C4C22×D4×C3711yescharacteristic
610C2×C4C22×D4×C3711yescharacteristic
611C2×C4C22×D4×C3711yescharacteristic
612C8—42no—
613C8—42no—
614C8—42no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—82no—
628C22—82no—
629C22—82no—
630C22—164no—
631C22C2×#120×C3711yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—41no—
637C4—41no—
638C4—42no—
639C4—41no—
640C4—41no—
641C4—41no—
642C4—42no—
643C4C37×#57612yes—
644C4C37×#57712yes—
645C2—41no—
646C2—81no—
647C2—81no—
648C2—81no—
649C2—162no—
650C2C37×#300811yescharacteristic
651C2C37×#301011yescharacteristic
652C2C37×#302111yescharacteristic
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×#3547C2semidirect
2. C37×#3217C2semidirect
3. C37×#3208C2semidirect
4. C37×#3205C2semidirect
5. C37×#1627C2semidirect
6. C37×#1625C2semidirect
7. C37×#1624C2semidirect
8. C37×#1622C2semidirect
9. C37×#1554C2semidirect
10. C37×#1496C2semidirect
11. C37×#1482C2semidirect
14. C37×#555C22semidirect
15. C37×#554C22semidirect
18. D4×Q8×C37C22semidirect
20. C37×#547C22semidirect
49. C37×#333C22semidirect
50. C37×#332C22semidirect
51. C37×Q8⋊C8C22semidirect
52. C37×D4⋊C8C22semidirect
53. C37×D4⋊C8C22semidirect
54. C37×D4⋊C8C22semidirect
288. #18956C37direct (N × H)
319. #3547C2×C37semidirect
320. #3217C2×C37semidirect
321. #3208C2×C37semidirect
322. #3205C2×C37semidirect
323. #1627C2×C37semidirect
324. #1625C2×C37semidirect
325. #1624C2×C37semidirect
326. #1622C2×C37semidirect
327. #1554C2×C37semidirect
328. #1496C2×C37semidirect
329. #1482C2×C37semidirect
340. #555C22×C37semidirect
341. #554C22×C37semidirect
344. D4×Q8C22×C37semidirect
346. #547C22×C37semidirect
375. #333C22×C37semidirect
376. #332C22×C37semidirect
377. Q8⋊C8C22×C37semidirect
378. D4⋊C8C22×C37semidirect
379. D4⋊C8C22×C37semidirect
380. D4⋊C8C22×C37semidirect
381. C37#18956direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#35472
C37×#32172
C37×#32082
C37×#32052
C37×#16272
C37×#16252
C37×#16242
C37×#16222
C37×#15542
C37×#14962
C37×#14822
#1895637