Finite Group Databasebeta

← C37×#19025 #22640278

Subgroups — C37×#19025 #22640278

Order 9472.

872 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3561C211yesmaximal, characteristic
2C37×#3237C211yesmaximal, characteristic, complemented
3C37×#3172C211yesmaximal, characteristic, complemented
4C37×#3140C211yesmaximal, characteristic, complemented
5C37×#1664C212yesmaximal, complemented
6C37×#1664C212yesmaximal, complemented
7C37×#1662C212yesmaximal, complemented
8C37×#1661C212yesmaximal, complemented
9C37×#1529C211yesmaximal, characteristic, complemented
10C37×#1527C211yesmaximal, characteristic, complemented
11C37×#1526C211yesmaximal, 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×#533C2211yescharacteristic
26C37×#529C2211yescharacteristic
27C2×#124×C37C2211yescharacteristic
28C37×#501C2211yescharacteristic, complemented
29C37×#501C2212yescomplemented
30C37×#497C2211yescharacteristic, complemented
31C37×#491C2211yescharacteristic, complemented
32C37×#491C2212yescomplemented
33C37×#489C2212yes—
34C37×#489C2212yes—
35C37×#489C2211yescharacteristic, complemented
36C37×#488—22no—
37C37×#485—22no—
38C37×#477—21no—
39C37×#475—21no—
40C37×#470—21no—
41C37×#468—21no—
42C4×Q16×C37—21no—
43C4×SD16×C37—21no—
44C37×#432C2211yescharacteristic
45C37×#419—21no—
46C37×#418—21no—
47C4×M16×C37C2211yescharacteristic
48C4×M16×C37C2211yescharacteristic
49C37×#330C2212yescomplemented
50C37×#330C2212yescomplemented
51C37×#330C2212yescomplemented
52C37×#329C2212yes—
53C37×#329C2212yes—
54C37×#329C2212yescomplemented
55C2×#41×C37—21no—
56C22×Q8×C37—21no—
57C22×Q8×C37D411yescharacteristic
58C22×D4×C37D411yescharacteristic
59C2×Q16×C37—21no—
60C2×SD16×C37—21no—
61C2×M16×C37—21no—
62C2×M16×C37—21no—
63C4⋊Q8×C37—21no—
64C4⋊Q8×C37—22no—
65C4⋊Q8×C37D411yescharacteristic
66C4⋊Q8×C37D411yescharacteristic
67C4⋊Q8×C37C2311yescharacteristic
68C4⋊Q8×C37C2311yescharacteristic
69#126×C37—22no—
70#126×C37—22no—
71#126×C37—22no—
72#126×C37—21no—
73#125×C37—21no—
74#125×C37C2311yescharacteristic
75#125×C37C2312yes—
76#124×C37—21no—
77#124×C37—22no—
78#124×C37—22no—
79#124×C37—21no—
80#124×C37—21no—
81#124×C37D412yes—
82#124×C37C2312yes—
83#124×C37C2311yescharacteristic
84#123×C37—22no—
85#123×C37—22no—
86#123×C37—21no—
87#123×C37—22no—
88#123×C37—22no—
89C22⋊Q8×C37—22no—
90C22⋊Q8×C37—22no—
91C22⋊Q8×C37—21no—
92C22⋊Q8×C37—22no—
93C22⋊Q8×C37—22no—
94C22⋊Q8×C37—22no—
95C22⋊Q8×C37—21no—
96C22⋊Q8×C37—21no—
97C22⋊Q8×C37—22no—
98C22⋊Q8×C37—22no—
99C22⋊Q8×C37—21no—
100C22⋊Q8×C37—21no—
101C22⋊Q8×C37D411yescharacteristic
102#121×C37—21no—
103#121×C37—22no—
104#121×C37—22no—
105#121×C37D411yescharacteristic
106#120×C37—22no—
107C4×Q8×C37—21no—
108C4×Q8×C37—21no—
109C4×Q8×C37—21no—
110C4×Q8×C37—21no—
111C4×Q8×C37—21no—
112C4×Q8×C37D411yescharacteristic
113C4×D4×C37—22no—
114C4×D4×C37—21no—
115C4×D4×C37—22no—
116C4×D4×C37—21no—
117C4×D4×C37D411yescharacteristic
118#117×C37—22no—
119#117×C37—21no—
120#117×C37—21no—
121#117×C37D412yes—
122C2×C22⋊C4×C37—22no—
123C2×C22⋊C4×C37—21no—
124C2×C22⋊C4×C37—21no—
125C2×C42×C37C2311yescharacteristic
126#107×C37—21no—
127#107×C37—22no—
128#106×C37—21no—
129#106×C37—22no—
130C4⋊C8×C37—21no—
131#103×C37—22no—
132#103×C37—22no—
133#103×C37—21no—
134#103×C37—21no—
135#103×C37—21no—
136#103×C37—22no—
137#103×C37—22no—
138#102×C37—22no—
139#102×C37—22no—
140#102×C37—21no—
141C22⋊C8×C37—21no—
142#97×C37C2312yes—
143#97×C37C2311yescharacteristic
144#97×C37C2311yescharacteristic
145#97×C37C2312yes—
146C4×C8×C37—21no—
147C4×C8×C37—21no—
148C24×C37—21no—
149#41×C37—82no—
150C2×Q8×C37—22no—
151C2×Q8×C37—21no—
152C2×Q8×C37—21no—
153C2×Q8×C37—21no—
154C2×Q8×C37—21no—
155C2×Q8×C37—21no—
156C2×Q8×C37—42no—
157C2×Q8×C37—82no—
158C2×Q8×C37C2×D412yes—
159C2×Q8×C37C2×D411yescharacteristic
160C2×D4×C37—21no—
161C2×D4×C37—22no—
162C2×D4×C37—22no—
163C2×D4×C37—21no—
164C2×D4×C37—42no—
165C2×D4×C37C2×D412yes—
166C2×D4×C37C2×D411yescharacteristic
167C22×C4×C37—22no—
168C22×C4×C37—22no—
169C22×C4×C37—22no—
170C22×C4×C37—21no—
171C22×C4×C37—21no—
172C22×C4×C37C2×D411yescharacteristic
173C22×C4×C37C2×D411yescharacteristic
174C22×C4×C37C2×D411yescharacteristic
175Q16×C37—42no—
176SD16×C37—42no—
177M16×C37—42no—
178M16×C37—42no—
179C2×C8×C37—21no—
180C2×C8×C37—22no—
181C2×C8×C37—21no—
182C2×C8×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—21no—
191C4⋊C4×C37—21no—
192C4⋊C4×C37—21no—
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—41no—
200C4⋊C4×C37—41no—
201C4⋊C4×C37C2×D412yes—
202C4⋊C4×C37C2×D411yescharacteristic
203C4⋊C4×C37C2×D412yes—
204C4⋊C4×C37C2×D411yescharacteristic
205C22⋊C4×C37—22no—
206C22⋊C4×C37—22no—
207C22⋊C4×C37—22no—
208C22⋊C4×C37—22no—
209C22⋊C4×C37—22no—
210C22⋊C4×C37—21no—
211C22⋊C4×C37—22no—
212C22⋊C4×C37—22no—
213C22⋊C4×C37—22no—
214C22⋊C4×C37—21no—
215C22⋊C4×C37—21no—
216C22⋊C4×C37—22no—
217C22⋊C4×C37—22no—
218C22⋊C4×C37—21no—
219C22⋊C4×C37—21no—
220C22⋊C4×C37—41no—
221C42×C37—22no—
222C42×C37—22no—
223C42×C37—21no—
224C42×C37—41no—
225C42×C37C2×D411yescharacteristic
226C42×C37C2×D411yescharacteristic
227C42×C37C2×D411yescharacteristic
228C42×C37C2411yescharacteristic
229C23×C37—22no—
230C23×C37—21no—
231C23×C37—42no—
232C23×C37—81no—
233C23×C37—81no—
234C23×C37#12011yescharacteristic
235Q8×C37—41no—
236Q8×C37—42no—
237Q8×C37—41no—
238Q8×C37—41no—
239Q8×C37—42no—
240Q8×C37—42no—
241Q8×C37—42no—
242Q8×C37—81no—
243Q8×C37—82no—
244D4×C37—41no—
245D4×C37—42no—
246D4×C37—42no—
247D4×C37—42no—
248D4×C37—82no—
249D4×C37—82no—
250C2×C4×C37—22no—
251C2×C4×C37—21no—
252C2×C4×C37—22no—
253C2×C4×C37—21no—
254C2×C4×C37—22no—
255C2×C4×C37—22no—
256C2×C4×C37—21no—
257C2×C4×C37—41no—
258C2×C4×C37—41no—
259C2×C4×C37—42no—
260C2×C4×C37—41no—
261C2×C4×C37—41no—
262C2×C4×C37—81no—
263C2×C4×C37—82no—
264C2×C4×C37—82no—
265C2×C4×C37—82no—
266C2×C4×C37#12011yescharacteristic
267C2×C4×C37#12011yescharacteristic
268C2×C4×C37#12011yescharacteristic
269C2×C4×C37C22×D411yescharacteristic
270C2×C4×C37C22×D411yescharacteristic
271C2×C4×C37C22×D411yescharacteristic
272C8×C37—22no—
273C8×C37—42no—
274C8×C37—42no—
275C8×C37—41no—
276#19025C3711yesmaximal, characteristic, direct product factor, Sylow
277C22×C37—21no—
278C22×C37—21no—
279C22×C37—21no—
280C22×C37—41no—
281C22×C37—42no—
282C22×C37—42no—
283C22×C37—41no—
284C22×C37—41no—
285C22×C37—42no—
286C22×C37—162no—
287C22×C37C2×#12011yescharacteristic
288C4×C37—21no—
289C4×C37—21no—
290C4×C37—21no—
291C4×C37—21no—
292C4×C37—21no—
293C4×C37—41no—
294C4×C37—42no—
295C4×C37—42no—
296C4×C37—41no—
297C4×C37—42no—
298C4×C37—41no—
299C4×C37—81no—
300C4×C37—81no—
301C4×C37#45512yes—
302#3561C2×C3711yescharacteristic
303#3237C2×C3711yescharacteristic, complemented
304#3172C2×C3711yescharacteristic, complemented
305#3140C2×C3711yescharacteristic, complemented
306#1664C2×C3712yescomplemented
307#1664C2×C3712yescomplemented
308#1662C2×C3712yescomplemented
309#1661C2×C3712yescomplemented
310#1529C2×C3711yescharacteristic, complemented
311#1527C2×C3711yescharacteristic, complemented
312#1526C2×C3711yescharacteristic, complemented
313C2×C37—41no—
314C2×C37—81no—
315C2×C37—82no—
316C2×C37C2×#45511yescharacteristic
317C2×C37#301811yescharacteristic
318C2×C37#302011yescharacteristic
319#563C22×C3712yes—
320#562C22×C3712yes—
321#556—21no—
322#551—22no—
323D4×Q8—21no—
324#548—21no—
325#546—21no—
326#543—21no—
327#542—21no—
328#542—22no—
329#538—21no—
330#536—21no—
331#533C22×C3711yescharacteristic
332#533C22×C3711yescharacteristic
333#529C22×C3711yescharacteristic
334C2×#124C22×C3711yescharacteristic
335#501C22×C3711yescharacteristic, complemented
336#501C22×C3712yescomplemented
337#497C22×C3711yescharacteristic, complemented
338#491C22×C3711yescharacteristic, complemented
339#491C22×C3712yescomplemented
340#489C22×C3712yes—
341#489C22×C3712yes—
342#489C22×C3711yescharacteristic, complemented
343#488—22no—
344#485—22no—
345#477—21no—
346#475—21no—
347#470—21no—
348#468—21no—
349C4×Q16—21no—
350C4×SD16—21no—
351#432C22×C3711yescharacteristic
352#419—21no—
353#418—21no—
354C4×M16C22×C3711yescharacteristic
355C4×M16C22×C3711yescharacteristic
356#330C22×C3712yescomplemented
357#330C22×C3712yescomplemented
358#330C22×C3712yescomplemented
359#329C22×C3712yes—
360#329C22×C3712yes—
361#329C22×C3712yescomplemented
362C37#1902511yescharacteristic, direct product factor, Sylow
363C2×#41—21no—
364C22×Q8—21no—
365C22×Q8D4×C3711yescharacteristic
366C22×D4D4×C3711yescharacteristic
367C2×Q16—21no—
368C2×SD16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C4⋊Q8—21no—
372C4⋊Q8—22no—
373C4⋊Q8D4×C3711yescharacteristic
374C4⋊Q8D4×C3711yescharacteristic
375C4⋊Q8C23×C3711yescharacteristic
376C4⋊Q8C23×C3711yescharacteristic
377#126—22no—
378#126—22no—
379#126—22no—
380#126—21no—
381#125—21no—
382#125C23×C3711yescharacteristic
383#125C23×C3712yes—
384#124—21no—
385#124—22no—
386#124—22no—
387#124—21no—
388#124—21no—
389#124D4×C3712yes—
390#124C23×C3712yes—
391#124C23×C3711yescharacteristic
392#123—22no—
393#123—22no—
394#123—21no—
395#123—22no—
396#123—22no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—21no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8D4×C3711yescharacteristic
410#121—21no—
411#121—22no—
412#121—22no—
413#121D4×C3711yescharacteristic
414#120—22no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8D4×C3711yescharacteristic
421C4×D4—22no—
422C4×D4—21no—
423C4×D4—22no—
424C4×D4—21no—
425C4×D4D4×C3711yescharacteristic
426#117—22no—
427#117—21no—
428#117—21no—
429#117D4×C3712yes—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C42C23×C3711yescharacteristic
434#107—21no—
435#107—22no—
436#106—21no—
437#106—22no—
438C4⋊C8—21no—
439#103—22no—
440#103—22no—
441#103—21no—
442#103—21no—
443#103—21no—
444#103—22no—
445#103—22no—
446#102—22no—
447#102—22no—
448#102—21no—
449C22⋊C8—21no—
450#97C23×C3712yes—
451#97C23×C3711yescharacteristic
452#97C23×C3711yescharacteristic
453#97C23×C3712yes—
454C4×C8—21no—
455C4×C8—21no—
456C24—21no—
457#41—82no—
458C2×Q8—22no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—42no—
465C2×Q8—82no—
466C2×Q8C2×D4×C3712yes—
467C2×Q8C2×D4×C3711yescharacteristic
468C2×D4—21no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—42no—
473C2×D4C2×D4×C3712yes—
474C2×D4C2×D4×C3711yescharacteristic
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4C2×D4×C3711yescharacteristic
481C22×C4C2×D4×C3711yescharacteristic
482C22×C4C2×D4×C3711yescharacteristic
483Q16—42no—
484SD16—42no—
485M16—42no—
486M16—42no—
487C2×C8—21no—
488C2×C8—22no—
489C2×C8—21no—
490C2×C8—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4C2×D4×C3712yes—
510C4⋊C4C2×D4×C3711yescharacteristic
511C4⋊C4C2×D4×C3712yes—
512C4⋊C4C2×D4×C3711yescharacteristic
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—21no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—41no—
529C42—22no—
530C42—22no—
531C42—21no—
532C42—41no—
533C42C2×D4×C3711yescharacteristic
534C42C2×D4×C3711yescharacteristic
535C42C2×D4×C3711yescharacteristic
536C42C24×C3711yescharacteristic
537C23—22no—
538C23—21no—
539C23—42no—
540C23—81no—
541C23—81no—
542C23#120×C3711yescharacteristic
543Q8—41no—
544Q8—42no—
545Q8—41no—
546Q8—41no—
547Q8—42no—
548Q8—42no—
549Q8—42no—
550Q8—81no—
551Q8—82no—
552D4—41no—
553D4—42no—
554D4—42no—
555D4—42no—
556D4—82no—
557D4—82no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—81no—
571C2×C4—82no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4#120×C3711yescharacteristic
575C2×C4#120×C3711yescharacteristic
576C2×C4#120×C3711yescharacteristic
577C2×C4C22×D4×C3711yescharacteristic
578C2×C4C22×D4×C3711yescharacteristic
579C2×C4C22×D4×C3711yescharacteristic
580C8—22no—
581C8—42no—
582C8—41no—
583C8—42no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—41no—
588C22—42no—
589C22—42no—
590C22—41no—
591C22—41no—
592C22—42no—
593C22—162no—
594C22C2×#120×C3711yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—42no—
602C4—42no—
603C4—41no—
604C4—42no—
605C4—41no—
606C4—81no—
607C4—81no—
608C4C37×#45512yes—
609C2—41no—
610C2—82no—
611C2—81no—
612C2C2×C37×#45511yescharacteristic
613C2C37×#301811yescharacteristic
614C2C37×#302011yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3561C2
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
2. C37×#3237C2semidirect
3. C37×#3172C2semidirect
4. C37×#3140C2semidirect
5. C37×#1664C2semidirect
6. C37×#1664C2semidirect
7. C37×#1662C2semidirect
8. C37×#1661C2semidirect
9. C37×#1529C2semidirect
10. C37×#1527C2semidirect
11. C37×#1526C2semidirect
28. C37×#501C22semidirect
29. C37×#501C22semidirect
30. C37×#497C22semidirect
31. C37×#491C22semidirect
32. C37×#491C22semidirect
35. C37×#489C22semidirect
49. C37×#330C22semidirect
50. C37×#330C22semidirect
51. C37×#330C22semidirect
54. C37×#329C22semidirect
276. #19025C37direct (N × H)
303. #3237C2×C37semidirect
304. #3172C2×C37semidirect
305. #3140C2×C37semidirect
306. #1664C2×C37semidirect
307. #1664C2×C37semidirect
308. #1662C2×C37semidirect
309. #1661C2×C37semidirect
310. #1529C2×C37semidirect
311. #1527C2×C37semidirect
312. #1526C2×C37semidirect
335. #501C22×C37semidirect
336. #501C22×C37semidirect
337. #497C22×C37semidirect
338. #491C22×C37semidirect
339. #491C22×C37semidirect
342. #489C22×C37semidirect
356. #330C22×C37semidirect
357. #330C22×C37semidirect
358. #330C22×C37semidirect
361. #329C22×C37semidirect
362. C37#19025direct (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×#32372
C37×#31722
C37×#31402
C37×#16642
C37×#16622
C37×#16612
C37×#15292
C37×#15272
C37×#15262
#1902537