Finite Group Databasebeta

← C37×#19308 #22640561

Subgroups — C37×#19308 #22640561

Order 9472.

632 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3182C211yesmaximal, characteristic
2C37×#3113C211yesmaximal, characteristic, complemented
3C37×#3037C211yesmaximal, characteristic
4Q8×M16×C37C211yesmaximal, characteristic, complemented
5C37×#1702C211yesmaximal, characteristic, complemented
6C37×#1700C211yesmaximal, characteristic, complemented
7C37×#1694C211yesmaximal, characteristic, complemented
8C37×#1686C211yesmaximal, characteristic, complemented
9C37×#1682C211yesmaximal, characteristic, complemented
10C37×#1680C211yesmaximal, characteristic, complemented
11C37×#1674C211yesmaximal, characteristic, complemented
12C37×#1666C211yesmaximal, characteristic, complemented
13C37×#1569C211yesmaximal, characteristic, complemented
14C37×#1561C211yesmaximal, characteristic, complemented
15C37×#1557C211yesmaximal, characteristic
16C2×#137×C37—21no—
17C37×#533C2211yescharacteristic
18C37×#532C2211yescharacteristic
19C2×C4×Q8×C37C2211yescharacteristic
20C37×#500C2211yescharacteristic
21C37×#492C2211yescharacteristic
22C37×#487C2211yescharacteristic
23C37×#486C2211yescharacteristic
24C37×#483—21no—
25C37×#475C2211yescharacteristic
26C37×#475C2211yescharacteristic
27C37×#468—21no—
28C37×#468—21no—
29C37×#464—21no—
30C37×#464—21no—
31C37×#462C2211yescharacteristic
32C37×#462C2211yescharacteristic
33C37×#462C2211yescharacteristic
34C37×#462C2211yescharacteristic
35C37×#460C2211yescharacteristic
36C37×#460C2211yescharacteristic
37C37×#451—21no—
38C37×#446—21no—
39C37×#446—21no—
40C37×#446C2211yescharacteristic
41C37×#446C2211yescharacteristic
42C8×Q8×C37C2211yescharacteristic
43C8×Q8×C37C2211yescharacteristic
44C37×#441—21no—
45C37×#441—21no—
46C37×#440—21no—
47C37×#440—21no—
48C37×#432C2211yescharacteristic
49C37×#423—21no—
50C37×#423C2211yescharacteristic
51C37×#423C2211yescharacteristic
52C37×#417—21no—
53C4×M16×C37—21no—
54C4×M16×C37C2211yescharacteristic
55C37×#335C2211yescharacteristic
56C37×#335C2211yescharacteristic
57C37×#334C2211yescharacteristic
58C37×#334C2211yescharacteristic
59C37×#332C2211yescharacteristic
60C37×#332C2211yescharacteristic
61C37×#332C2211yescharacteristic
62C37×#332C2211yescharacteristic
63C37×#332C2211yescharacteristic
64C37×#332C2211yescharacteristic
65C37×#331C2211yescharacteristic
66C37×#331C2211yescharacteristic
67C2×#41×C37—21no—
68C22×Q8×C37D411yescharacteristic
69#137×C37—44no—
70C2×Q16×C37—21no—
71C2×Q16×C37—21no—
72C2×Q16×C37—21no—
73C2×Q16×C37—21no—
74C2×SD16×C37—21no—
75C2×SD16×C37—21no—
76C2×SD16×C37—21no—
77C2×SD16×C37—21no—
78C2×M16×C37—21no—
79C2×M16×C37—21no—
80C2×M16×C37D411yescharacteristic
81C2×M16×C37D411yescharacteristic
82C4⋊Q8×C37C2311yescharacteristic
83C4⋊Q8×C37C2311yescharacteristic
84C4⋊Q8×C37C2311yescharacteristic
85#127×C37C2311yescharacteristic
86#125×C37—21no—
87#124×C37—21no—
88C22⋊Q8×C37—21no—
89C22⋊Q8×C37—21no—
90#121×C37—21no—
91#121×C37—21no—
92C4×Q8×C37—21no—
93C4×Q8×C37—21no—
94C4×Q8×C37—21no—
95C4×Q8×C37—21no—
96C4×Q8×C37D411yescharacteristic
97C4×Q8×C37D411yescharacteristic
98C4×Q8×C37C2311yescharacteristic
99C4×Q8×C37C2311yescharacteristic
100C4×D4×C37—21no—
101C4×D4×C37—21no—
102#117×C37—21no—
103C2×C4⋊C4×C37—21no—
104C2×C4⋊C4×C37D411yescharacteristic
105C2×C42×C37—21no—
106C2×C42×C37C2311yescharacteristic
107#107×C37—21no—
108#107×C37—21no—
109#106×C37—21no—
110#106×C37—21no—
111C4⋊C8×C37—21no—
112C4⋊C8×C37—21no—
113C4⋊C8×C37—21no—
114C4⋊C8×C37—21no—
115C4⋊C8×C37—21no—
116C4⋊C8×C37—21no—
117C4⋊C8×C37C2311yescharacteristic
118C4⋊C8×C37C2311yescharacteristic
119C4⋊C8×C37C2311yescharacteristic
120C4⋊C8×C37C2311yescharacteristic
121C4⋊C8×C37C2311yescharacteristic
122C4⋊C8×C37C2311yescharacteristic
123#103×C37—21no—
124#103×C37—21no—
125#103×C37—21no—
126#103×C37—21no—
127#103×C37—21no—
128#103×C37—21no—
129#103×C37—21no—
130#103×C37—21no—
131#102×C37—21no—
132#102×C37—21no—
133#102×C37—21no—
134#102×C37—21no—
135C22⋊C8×C37—21no—
136#97×C37—21no—
137#97×C37—21no—
138#97×C37—21no—
139#97×C37D411yescharacteristic
140#97×C37D411yescharacteristic
141C4×C8×C37—21no—
142C4×C8×C37—21no—
143C4×C8×C37C2311yescharacteristic
144C4×C8×C37C2311yescharacteristic
145#41×C37—42no—
146#41×C37—42no—
147C2×Q8×C37—21no—
148C2×Q8×C37—22no—
149C2×Q8×C37—21no—
150C2×Q8×C37—21no—
151C2×Q8×C37—21no—
152C2×Q8×C37—41no—
153C2×Q8×C37C2×D411yescharacteristic
154C2×Q8×C37C2×D411yescharacteristic
155C2×D4×C37—21no—
156C2×D4×C37—21no—
157C2×D4×C37—21no—
158C2×D4×C37—41no—
159C22×C4×C37—21no—
160C22×C4×C37—21no—
161C22×C4×C37—41no—
162C22×C4×C37C2×D411yescharacteristic
163C22×C4×C37C2×D411yescharacteristic
164C22×C4×C37#4111yescharacteristic
165Q16×C37—42no—
166Q16×C37—42no—
167Q16×C37—42no—
168Q16×C37—42no—
169SD16×C37—42no—
170SD16×C37—42no—
171SD16×C37—42no—
172SD16×C37—42no—
173M16×C37—22no—
174M16×C37—41no—
175M16×C37—42no—
176M16×C37—42no—
177C2×C8×C37—21no—
178C2×C8×C37—21no—
179C2×C8×C37—21no—
180C2×C8×C37—21no—
181C2×C8×C37—21no—
182C2×C8×C37—21no—
183C2×C8×C37C2×D411yescharacteristic
184C2×C8×C37C2×D411yescharacteristic
185C2×C8×C37C2×D411yescharacteristic
186C2×C8×C37C2×D411yescharacteristic
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—21no—
194C4⋊C4×C37—21no—
195C4⋊C4×C37—21no—
196C4⋊C4×C37—21no—
197C4⋊C4×C37—21no—
198C4⋊C4×C37—41no—
199C4⋊C4×C37—41no—
200C4⋊C4×C37C2×D411yescharacteristic
201C4⋊C4×C37C2×D411yescharacteristic
202C22⋊C4×C37—41no—
203C22⋊C4×C37—41no—
204C22⋊C4×C37—41no—
205C42×C37—21no—
206C42×C37—21no—
207C42×C37—21no—
208C42×C37—21no—
209C42×C37—41no—
210C42×C37C2×D411yescharacteristic
211C42×C37C2×D411yescharacteristic
212C42×C37#4111yescharacteristic
213C42×C37C2411yescharacteristic
214C23×C37—41no—
215C23×C37#12111yescharacteristic
216Q8×C37—21no—
217Q8×C37—21no—
218Q8×C37—21no—
219Q8×C37—42no—
220Q8×C37—41no—
221Q8×C37—41no—
222Q8×C37—41no—
223Q8×C37—41no—
224Q8×C37—41no—
225Q8×C37—41no—
226Q8×C37AGL(1,ℤ/8)12yes—
227D4×C37—41no—
228D4×C37—41no—
229D4×C37—41no—
230D4×C37—41no—
231D4×C37—81no—
232D4×C37—82no—
233C2×C4×C37—21no—
234C2×C4×C37—21no—
235C2×C4×C37—21no—
236C2×C4×C37—21no—
237C2×C4×C37—21no—
238C2×C4×C37—21no—
239C2×C4×C37—21no—
240C2×C4×C37—21no—
241C2×C4×C37—41no—
242C2×C4×C37—42no—
243C2×C4×C37—41no—
244C2×C4×C37—41no—
245C2×C4×C37—41no—
246C2×C4×C37—82no—
247C2×C4×C37—81no—
248C2×C4×C37#12111yescharacteristic
249C2×C4×C37#12111yescharacteristic
250C2×C4×C37#12111yescharacteristic
251C2×C4×C37C22×D411yescharacteristic
252C2×C4×C37C22×D411yescharacteristic
253C2×C4×C37C2×#4111yescharacteristic
254C8×C37—21no—
255C8×C37—21no—
256C8×C37—21no—
257C8×C37—41no—
258C8×C37—41no—
259C8×C37—41no—
260C8×C37—41no—
261C8×C37—41no—
262C8×C37—41no—
263C8×C37#13712yescomplemented
264#19308C3711yesmaximal, characteristic, direct product factor, Sylow
265C22×C37—21no—
266C22×C37—21no—
267C22×C37—21no—
268C22×C37—81no—
269C22×C37—81no—
270C22×C37—81no—
271C22×C37C2×#12111yescharacteristic
272C4×C37—21no—
273C4×C37—21no—
274C4×C37—22no—
275C4×C37—21no—
276C4×C37—21no—
277C4×C37—41no—
278C4×C37—41no—
279C4×C37—41no—
280C4×C37—81no—
281C4×C37—81no—
282C4×C37—81no—
283C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
284C4×C37C2×#13711yescharacteristic
285C4×C37#57511yescharacteristic
286C4×C37#57511yescharacteristic
287#3182C2×C3711yescharacteristic
288#3113C2×C3711yescharacteristic, complemented
289#3037C2×C3711yescharacteristic
290Q8×M16C2×C3711yescharacteristic, complemented
291#1702C2×C3711yescharacteristic, complemented
292#1700C2×C3711yescharacteristic, complemented
293#1694C2×C3711yescharacteristic, complemented
294#1686C2×C3711yescharacteristic, complemented
295#1682C2×C3711yescharacteristic, complemented
296#1680C2×C3711yescharacteristic, complemented
297#1674C2×C3711yescharacteristic, complemented
298#1666C2×C3711yescharacteristic, complemented
299#1569C2×C3711yescharacteristic, complemented
300#1561C2×C3711yescharacteristic, complemented
301#1557C2×C3711yescharacteristic
302C2×C37—41no—
303C2×C37—161no—
304C2×C37#303711yescharacteristic
305C2×C37#305511yescharacteristic
306C2×C37#306911yescharacteristic
307C2×#137—21no—
308#533C22×C3711yescharacteristic
309#532C22×C3711yescharacteristic
310C2×C4×Q8C22×C3711yescharacteristic
311#500C22×C3711yescharacteristic
312#492C22×C3711yescharacteristic
313#487C22×C3711yescharacteristic
314#486C22×C3711yescharacteristic
315#483—21no—
316#475C22×C3711yescharacteristic
317#475C22×C3711yescharacteristic
318#468—21no—
319#468—21no—
320#464—21no—
321#464—21no—
322#462C22×C3711yescharacteristic
323#462C22×C3711yescharacteristic
324#462C22×C3711yescharacteristic
325#462C22×C3711yescharacteristic
326#460C22×C3711yescharacteristic
327#460C22×C3711yescharacteristic
328#451—21no—
329#446—21no—
330#446—21no—
331#446C22×C3711yescharacteristic
332#446C22×C3711yescharacteristic
333C8×Q8C22×C3711yescharacteristic
334C8×Q8C22×C3711yescharacteristic
335#441—21no—
336#441—21no—
337#440—21no—
338#440—21no—
339#432C22×C3711yescharacteristic
340#423—21no—
341#423C22×C3711yescharacteristic
342#423C22×C3711yescharacteristic
343#417—21no—
344C4×M16—21no—
345C4×M16C22×C3711yescharacteristic
346#335C22×C3711yescharacteristic
347#335C22×C3711yescharacteristic
348#334C22×C3711yescharacteristic
349#334C22×C3711yescharacteristic
350#332C22×C3711yescharacteristic
351#332C22×C3711yescharacteristic
352#332C22×C3711yescharacteristic
353#332C22×C3711yescharacteristic
354#332C22×C3711yescharacteristic
355#332C22×C3711yescharacteristic
356#331C22×C3711yescharacteristic
357#331C22×C3711yescharacteristic
358C37#1930811yescharacteristic, direct product factor, Sylow
359C2×#41—21no—
360C22×Q8D4×C3711yescharacteristic
361#137—44no—
362C2×Q16—21no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×Q16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16D4×C3711yescharacteristic
373C2×M16D4×C3711yescharacteristic
374C4⋊Q8C23×C3711yescharacteristic
375C4⋊Q8C23×C3711yescharacteristic
376C4⋊Q8C23×C3711yescharacteristic
377#127C23×C3711yescharacteristic
378#125—21no—
379#124—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382#121—21no—
383#121—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×Q8D4×C3711yescharacteristic
389C4×Q8D4×C3711yescharacteristic
390C4×Q8C23×C3711yescharacteristic
391C4×Q8C23×C3711yescharacteristic
392C4×D4—21no—
393C4×D4—21no—
394#117—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4D4×C3711yescharacteristic
397C2×C42—21no—
398C2×C42C23×C3711yescharacteristic
399#107—21no—
400#107—21no—
401#106—21no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8C23×C3711yescharacteristic
410C4⋊C8C23×C3711yescharacteristic
411C4⋊C8C23×C3711yescharacteristic
412C4⋊C8C23×C3711yescharacteristic
413C4⋊C8C23×C3711yescharacteristic
414C4⋊C8C23×C3711yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427C22⋊C8—21no—
428#97—21no—
429#97—21no—
430#97—21no—
431#97D4×C3711yescharacteristic
432#97D4×C3711yescharacteristic
433C4×C8—21no—
434C4×C8—21no—
435C4×C8C23×C3711yescharacteristic
436C4×C8C23×C3711yescharacteristic
437#41—42no—
438#41—42no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—41no—
445C2×Q8C2×D4×C3711yescharacteristic
446C2×Q8C2×D4×C3711yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4C2×D4×C3711yescharacteristic
455C22×C4C2×D4×C3711yescharacteristic
456C22×C4#41×C3711yescharacteristic
457Q16—42no—
458Q16—42no—
459Q16—42no—
460Q16—42no—
461SD16—42no—
462SD16—42no—
463SD16—42no—
464SD16—42no—
465M16—22no—
466M16—41no—
467M16—42no—
468M16—42no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8C2×D4×C3711yescharacteristic
476C2×C8C2×D4×C3711yescharacteristic
477C2×C8C2×D4×C3711yescharacteristic
478C2×C8C2×D4×C3711yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C3711yescharacteristic
493C4⋊C4C2×D4×C3711yescharacteristic
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42C2×D4×C3711yescharacteristic
503C42C2×D4×C3711yescharacteristic
504C42#41×C3711yescharacteristic
505C42C24×C3711yescharacteristic
506C23—41no—
507C23#121×C3711yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—42no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8AGL(1,ℤ/8)×C3712yes—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—82no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—81no—
540C2×C4#121×C3711yescharacteristic
541C2×C4#121×C3711yescharacteristic
542C2×C4#121×C3711yescharacteristic
543C2×C4C22×D4×C3711yescharacteristic
544C2×C4C22×D4×C3711yescharacteristic
545C2×C4C2×#41×C3711yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8#137×C3712yescomplemented
556C22—21no—
557C22—21no—
558C22—21no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22C2×#121×C3711yescharacteristic
563C4—21no—
564C4—21no—
565C4—22no—
566C4—21no—
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
575C4C2×#137×C3711yescharacteristic
576C4C37×#57511yescharacteristic
577C4C37×#57511yescharacteristic
578C2—41no—
579C2—161no—
580C2C37×#303711yescharacteristic
581C2C37×#305511yescharacteristic
582C2C37×#306911yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#532C22
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×#3113C2semidirect
4. Q8×M16×C37C2semidirect
5. C37×#1702C2semidirect
6. C37×#1700C2semidirect
7. C37×#1694C2semidirect
8. C37×#1686C2semidirect
9. C37×#1682C2semidirect
10. C37×#1680C2semidirect
11. C37×#1674C2semidirect
12. C37×#1666C2semidirect
13. C37×#1569C2semidirect
14. C37×#1561C2semidirect
263. C8×C37#137semidirect
264. #19308C37direct (N × H)
288. #3113C2×C37semidirect
290. Q8×M16C2×C37semidirect
291. #1702C2×C37semidirect
292. #1700C2×C37semidirect
293. #1694C2×C37semidirect
294. #1686C2×C37semidirect
295. #1682C2×C37semidirect
296. #1680C2×C37semidirect
297. #1674C2×C37semidirect
298. #1666C2×C37semidirect
299. #1569C2×C37semidirect
300. #1561C2×C37semidirect
358. C37#19308direct (N × H)
555. C8#137×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#31822
C37×#31132
C37×#30372
Q8×M16×C372
C37×#17022
C37×#17002
C37×#16942
C37×#16862
C37×#16822
C37×#16802
C37×#16742
C37×#16662
C37×#15692
C37×#15612
C37×#15572
#1930837