Finite Group Databasebeta

← C37×#19091 #22640344

Subgroups — C37×#19091 #22640344

Order 9472.

854 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3561C211yesmaximal, characteristic
2C37×#3240C211yesmaximal, characteristic, complemented
3C37×#3237C211yesmaximal, characteristic, complemented
4C37×#3215C211yesmaximal, characteristic, complemented
5C37×#1664C212yesmaximal, complemented
6C37×#1662C212yesmaximal, complemented
7C37×#1661C212yesmaximal, complemented
8C37×#1660C212yesmaximal, complemented
9C37×#1537C211yesmaximal, characteristic, complemented
10C37×#1535C211yesmaximal, characteristic, complemented
11C37×#1533C211yesmaximal, 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×#501C2211yescharacteristic, complemented
31C37×#497C2212yes—
32C37×#491C2212yescomplemented
33C37×#489C2212yes—
34C37×#489C2211yescharacteristic, complemented
35C37×#489C2211yescharacteristic, complemented
36C37×#485—21no—
37C37×#485—22no—
38C37×#482—21no—
39C37×#479—21no—
40C37×#478—21no—
41C37×#477—21no—
42C37×#475—21no—
43C37×#464—22no—
44C37×#451—21no—
45C37×#450—21no—
46C37×#432C2211yescharacteristic
47C37×#432C2211yescharacteristic
48C37×#432C2211yescharacteristic
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—22no—
60C2×SD16×C37—22no—
61C4⋊Q8×C37—21no—
62C4⋊Q8×C37—22no—
63C4⋊Q8×C37D411yescharacteristic
64C4⋊Q8×C37D411yescharacteristic
65C4⋊Q8×C37C2311yescharacteristic
66C4⋊Q8×C37C2311yescharacteristic
67#126×C37—22no—
68#126×C37—22no—
69#126×C37—22no—
70#126×C37—21no—
71#125×C37—21no—
72#125×C37C2311yescharacteristic
73#125×C37C2312yes—
74#124×C37—21no—
75#124×C37—22no—
76#124×C37—22no—
77#124×C37—21no—
78#124×C37—21no—
79#124×C37D412yes—
80#124×C37C2312yes—
81#124×C37C2311yescharacteristic
82#123×C37—22no—
83#123×C37—22no—
84#123×C37—21no—
85#123×C37—22no—
86#123×C37—22no—
87C22⋊Q8×C37—22no—
88C22⋊Q8×C37—22no—
89C22⋊Q8×C37—21no—
90C22⋊Q8×C37—22no—
91C22⋊Q8×C37—22no—
92C22⋊Q8×C37—22no—
93C22⋊Q8×C37—21no—
94C22⋊Q8×C37—21no—
95C22⋊Q8×C37—22no—
96C22⋊Q8×C37—22no—
97C22⋊Q8×C37—21no—
98C22⋊Q8×C37—21no—
99C22⋊Q8×C37D411yescharacteristic
100#121×C37—21no—
101#121×C37—22no—
102#121×C37—22no—
103#121×C37D411yescharacteristic
104#120×C37—22no—
105C4×Q8×C37—21no—
106C4×Q8×C37—21no—
107C4×Q8×C37—21no—
108C4×Q8×C37—21no—
109C4×Q8×C37—21no—
110C4×Q8×C37D411yescharacteristic
111C4×D4×C37—22no—
112C4×D4×C37—21no—
113C4×D4×C37—22no—
114C4×D4×C37—21no—
115C4×D4×C37D411yescharacteristic
116#117×C37—22no—
117#117×C37—21no—
118#117×C37—21no—
119#117×C37D412yes—
120C2×C22⋊C4×C37—22no—
121C2×C22⋊C4×C37—21no—
122C2×C22⋊C4×C37—21no—
123C2×C42×C37C2311yescharacteristic
124#107×C37—22no—
125#107×C37—21no—
126#107×C37—21no—
127#106×C37—22no—
128#106×C37—21no—
129#106×C37—21no—
130C4⋊C8×C37—21no—
131C4⋊C8×C37—21no—
132C4⋊C8×C37—21no—
133#103×C37—22no—
134#103×C37—21no—
135#103×C37—21no—
136#103×C37—22no—
137#103×C37—22no—
138#102×C37—22no—
139#102×C37—21no—
140#102×C37—21no—
141C22⋊C8×C37—21no—
142C22⋊C8×C37—21no—
143C22⋊C8×C37—21no—
144#97×C37C2312yes—
145#97×C37C2311yescharacteristic
146#97×C37C2311yescharacteristic
147#97×C37C2312yes—
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—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—81no—
165C2×D4×C37C2×D411yescharacteristic
166C2×D4×C37C2×D412yes—
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—82no—
176SD16×C37—82no—
177C2×C8×C37—21no—
178C2×C8×C37—21no—
179C2×C8×C37—22no—
180C2×C8×C37—22no—
181C4⋊C4×C37—22no—
182C4⋊C4×C37—22no—
183C4⋊C4×C37—22no—
184C4⋊C4×C37—22no—
185C4⋊C4×C37—21no—
186C4⋊C4×C37—21no—
187C4⋊C4×C37—21no—
188C4⋊C4×C37—21no—
189C4⋊C4×C37—21no—
190C4⋊C4×C37—21no—
191C4⋊C4×C37—22no—
192C4⋊C4×C37—22no—
193C4⋊C4×C37—21no—
194C4⋊C4×C37—21no—
195C4⋊C4×C37—21no—
196C4⋊C4×C37—21no—
197C4⋊C4×C37—41no—
198C4⋊C4×C37—41no—
199C4⋊C4×C37C2×D412yes—
200C4⋊C4×C37C2×D412yes—
201C4⋊C4×C37C2×D411yescharacteristic
202C4⋊C4×C37C2×D411yescharacteristic
203C22⋊C4×C37—22no—
204C22⋊C4×C37—22no—
205C22⋊C4×C37—22no—
206C22⋊C4×C37—22no—
207C22⋊C4×C37—22no—
208C22⋊C4×C37—21no—
209C22⋊C4×C37—22no—
210C22⋊C4×C37—22no—
211C22⋊C4×C37—22no—
212C22⋊C4×C37—21no—
213C22⋊C4×C37—21no—
214C22⋊C4×C37—22no—
215C22⋊C4×C37—22no—
216C22⋊C4×C37—21no—
217C22⋊C4×C37—21no—
218C22⋊C4×C37—41no—
219C42×C37—22no—
220C42×C37—22no—
221C42×C37—21no—
222C42×C37—41no—
223C42×C37C2×D411yescharacteristic
224C42×C37C2×D411yescharacteristic
225C42×C37C2×D411yescharacteristic
226C42×C37C2411yescharacteristic
227C23×C37—22no—
228C23×C37—21no—
229C23×C37—42no—
230C23×C37—81no—
231C23×C37—81no—
232C23×C37#12011yescharacteristic
233Q8×C37—42no—
234Q8×C37—41no—
235Q8×C37—42no—
236Q8×C37—42no—
237Q8×C37—42no—
238Q8×C37—42no—
239Q8×C37—81no—
240Q8×C37—82no—
241D4×C37—42no—
242D4×C37—41no—
243D4×C37—42no—
244D4×C37—42no—
245D4×C37—82no—
246D4×C37—82no—
247C2×C4×C37—21no—
248C2×C4×C37—22no—
249C2×C4×C37—21no—
250C2×C4×C37—22no—
251C2×C4×C37—22no—
252C2×C4×C37—21no—
253C2×C4×C37—41no—
254C2×C4×C37—41no—
255C2×C4×C37—41no—
256C2×C4×C37—42no—
257C2×C4×C37—41no—
258C2×C4×C37—41no—
259C2×C4×C37—81no—
260C2×C4×C37—82no—
261C2×C4×C37—82no—
262C2×C4×C37—82no—
263C2×C4×C37#12011yescharacteristic
264C2×C4×C37#12011yescharacteristic
265C2×C4×C37#12011yescharacteristic
266C2×C4×C37C22×D411yescharacteristic
267C2×C4×C37C22×D411yescharacteristic
268C2×C4×C37C22×D411yescharacteristic
269C8×C37—42no—
270C8×C37—41no—
271C8×C37—41no—
272C8×C37—42no—
273#19091C3711yesmaximal, characteristic, direct product factor, Sylow
274C22×C37—21no—
275C22×C37—21no—
276C22×C37—21no—
277C22×C37—41no—
278C22×C37—42no—
279C22×C37—41no—
280C22×C37—42no—
281C22×C37—42no—
282C22×C37—41no—
283C22×C37—162no—
284C22×C37C2×#12011yescharacteristic
285C4×C37—21no—
286C4×C37—21no—
287C4×C37—21no—
288C4×C37—21no—
289C4×C37—21no—
290C4×C37—21no—
291C4×C37—41no—
292C4×C37—42no—
293C4×C37—42no—
294C4×C37—41no—
295C4×C37—41no—
296C4×C37—42no—
297C4×C37—81no—
298C4×C37—81no—
299#3561C2×C3711yescharacteristic
300#3240C2×C3711yescharacteristic, complemented
301#3237C2×C3711yescharacteristic, complemented
302#3215C2×C3711yescharacteristic, complemented
303#1664C2×C3712yescomplemented
304#1662C2×C3712yescomplemented
305#1661C2×C3712yescomplemented
306#1660C2×C3712yescomplemented
307#1537C2×C3711yescharacteristic, complemented
308#1535C2×C3711yescharacteristic, complemented
309#1533C2×C3711yescharacteristic, complemented
310C2×C37—41no—
311C2×C37—81no—
312C2×C37—82no—
313C2×C37#301911yescharacteristic
314C2×C37#302011yescharacteristic
315C2×C37#302211yescharacteristic
316#563C22×C3712yes—
317#562C22×C3712yes—
318#556—21no—
319#551—22no—
320D4×Q8—21no—
321#548—21no—
322#546—21no—
323#543—21no—
324#542—21no—
325#542—22no—
326#538—21no—
327#536—21no—
328#533C22×C3711yescharacteristic
329#533C22×C3711yescharacteristic
330#529C22×C3711yescharacteristic
331C2×#124C22×C3711yescharacteristic
332#501C22×C3711yescharacteristic, complemented
333#501C22×C3712yescomplemented
334#501C22×C3711yescharacteristic, complemented
335#497C22×C3712yes—
336#491C22×C3712yescomplemented
337#489C22×C3712yes—
338#489C22×C3711yescharacteristic, complemented
339#489C22×C3711yescharacteristic, complemented
340#485—21no—
341#485—22no—
342#482—21no—
343#479—21no—
344#478—21no—
345#477—21no—
346#475—21no—
347#464—22no—
348#451—21no—
349#450—21no—
350#432C22×C3711yescharacteristic
351#432C22×C3711yescharacteristic
352#432C22×C3711yescharacteristic
353#330C22×C3712yescomplemented
354#330C22×C3712yescomplemented
355#330C22×C3712yescomplemented
356#329C22×C3712yes—
357#329C22×C3712yes—
358#329C22×C3712yescomplemented
359C37#1909111yescharacteristic, direct product factor, Sylow
360C2×#41—21no—
361C22×Q8—21no—
362C22×Q8D4×C3711yescharacteristic
363C22×D4D4×C3711yescharacteristic
364C2×Q16—22no—
365C2×SD16—22no—
366C4⋊Q8—21no—
367C4⋊Q8—22no—
368C4⋊Q8D4×C3711yescharacteristic
369C4⋊Q8D4×C3711yescharacteristic
370C4⋊Q8C23×C3711yescharacteristic
371C4⋊Q8C23×C3711yescharacteristic
372#126—22no—
373#126—22no—
374#126—22no—
375#126—21no—
376#125—21no—
377#125C23×C3711yescharacteristic
378#125C23×C3712yes—
379#124—21no—
380#124—22no—
381#124—22no—
382#124—21no—
383#124—21no—
384#124D4×C3712yes—
385#124C23×C3712yes—
386#124C23×C3711yescharacteristic
387#123—22no—
388#123—22no—
389#123—21no—
390#123—22no—
391#123—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—21no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8D4×C3711yescharacteristic
405#121—21no—
406#121—22no—
407#121—22no—
408#121D4×C3711yescharacteristic
409#120—22no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8D4×C3711yescharacteristic
416C4×D4—22no—
417C4×D4—21no—
418C4×D4—22no—
419C4×D4—21no—
420C4×D4D4×C3711yescharacteristic
421#117—22no—
422#117—21no—
423#117—21no—
424#117D4×C3712yes—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C42C23×C3711yescharacteristic
429#107—22no—
430#107—21no—
431#107—21no—
432#106—22no—
433#106—21no—
434#106—21no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438#103—22no—
439#103—21no—
440#103—21no—
441#103—22no—
442#103—22no—
443#102—22no—
444#102—21no—
445#102—21no—
446C22⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8—21no—
449#97C23×C3712yes—
450#97C23×C3711yescharacteristic
451#97C23×C3711yescharacteristic
452#97C23×C3712yes—
453C24—21no—
454#41—82no—
455C2×Q8—22no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—82no—
462C2×Q8—81no—
463C2×Q8C2×D4×C3711yescharacteristic
464C2×Q8C2×D4×C3712yes—
465C2×D4—21no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—81no—
470C2×D4C2×D4×C3711yescharacteristic
471C2×D4C2×D4×C3712yes—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4C2×D4×C3711yescharacteristic
478C22×C4C2×D4×C3711yescharacteristic
479C22×C4C2×D4×C3711yescharacteristic
480Q16—82no—
481SD16—82no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—22no—
485C2×C8—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4C2×D4×C3712yes—
505C4⋊C4C2×D4×C3712yes—
506C4⋊C4C2×D4×C3711yescharacteristic
507C4⋊C4C2×D4×C3711yescharacteristic
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—21no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C42—22no—
525C42—22no—
526C42—21no—
527C42—41no—
528C42C2×D4×C3711yescharacteristic
529C42C2×D4×C3711yescharacteristic
530C42C2×D4×C3711yescharacteristic
531C42C24×C3711yescharacteristic
532C23—22no—
533C23—21no—
534C23—42no—
535C23—81no—
536C23—81no—
537C23#120×C3711yescharacteristic
538Q8—42no—
539Q8—41no—
540Q8—42no—
541Q8—42no—
542Q8—42no—
543Q8—42no—
544Q8—81no—
545Q8—82no—
546D4—42no—
547D4—41no—
548D4—42no—
549D4—42no—
550D4—82no—
551D4—82no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—42no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—81no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4#120×C3711yescharacteristic
569C2×C4#120×C3711yescharacteristic
570C2×C4#120×C3711yescharacteristic
571C2×C4C22×D4×C3711yescharacteristic
572C2×C4C22×D4×C3711yescharacteristic
573C2×C4C22×D4×C3711yescharacteristic
574C8—42no—
575C8—42no—
576C8—41no—
577C8—41no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—41no—
582C22—42no—
583C22—41no—
584C22—42no—
585C22—42no—
586C22—41no—
587C22—162no—
588C22C2×#120×C3711yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—21no—
593C4—21no—
594C4—21no—
595C4—41no—
596C4—42no—
597C4—42no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—81no—
602C4—81no—
603C2—41no—
604C2—82no—
605C2—81no—
606C2C37×#301911yescharacteristic
607C2C37×#302011yescharacteristic
608C2C37×#302211yescharacteristic
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×#3240C2semidirect
3. C37×#3237C2semidirect
4. C37×#3215C2semidirect
5. C37×#1664C2semidirect
6. C37×#1662C2semidirect
7. C37×#1661C2semidirect
8. C37×#1660C2semidirect
9. C37×#1537C2semidirect
10. C37×#1535C2semidirect
11. C37×#1533C2semidirect
28. C37×#501C22semidirect
29. C37×#501C22semidirect
30. C37×#501C22semidirect
32. C37×#491C22semidirect
34. C37×#489C22semidirect
35. C37×#489C22semidirect
49. C37×#330C22semidirect
50. C37×#330C22semidirect
51. C37×#330C22semidirect
54. C37×#329C22semidirect
273. #19091C37direct (N × H)
300. #3240C2×C37semidirect
301. #3237C2×C37semidirect
302. #3215C2×C37semidirect
303. #1664C2×C37semidirect
304. #1662C2×C37semidirect
305. #1661C2×C37semidirect
306. #1660C2×C37semidirect
307. #1537C2×C37semidirect
308. #1535C2×C37semidirect
309. #1533C2×C37semidirect
332. #501C22×C37semidirect
333. #501C22×C37semidirect
334. #501C22×C37semidirect
336. #491C22×C37semidirect
338. #489C22×C37semidirect
339. #489C22×C37semidirect
353. #330C22×C37semidirect
354. #330C22×C37semidirect
355. #330C22×C37semidirect
358. #329C22×C37semidirect
359. C37#19091direct (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×#32402
C37×#32372
C37×#32152
C37×#16642
C37×#16622
C37×#16612
C37×#16602
C37×#15372
C37×#15352
C37×#15332
#1909137