Finite Group Databasebeta

← C37×#25669 #22646922

Subgroups — C37×#25669 #22646922

Order 9472.

992 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3511C211yesmaximal, characteristic
2C37×#3142C211yesmaximal, characteristic, complemented
3C37×#3080C211yesmaximal, characteristic, complemented
4C37×#2660C211yesmaximal, characteristic, complemented
5C37×#2040C212yesmaximal, complemented
6C37×#2039C212yesmaximal, complemented
7C37×#1997C211yesmaximal, characteristic, complemented
8C37×#1963C211yesmaximal, characteristic, complemented
9C37×#1860C212yesmaximal, complemented
10C37×#1859C212yesmaximal, complemented
11C37×#1759C211yesmaximal, characteristic, complemented
12C37×#556—21no—
13C37×#555—21no—
14C37×#554—21no—
15C37×#553—22no—
16C37×#548—22no—
17C37×#547—21no—
18C37×#542—22no—
19C37×#537C2212yes—
20C37×#533—21no—
21C37×#532—21no—
22C37×#532C2211yescharacteristic
23C2×C4⋊Q8×C37C2211yescharacteristic
24C2×#125×C37C2211yescharacteristic
25C37×#520C2212yes—
26C4×#41×C37C2211yescharacteristic
27C37×#491—21no—
28C37×#490—21no—
29C37×#488—22no—
30C37×#479—21no—
31C37×#479—21no—
32C37×#478—21no—
33C37×#478—21no—
34C37×#428C2211yescharacteristic
35C37×#428C2211yescharacteristic
36C37×#423C2211yescharacteristic
37C2×#104×C37C2212yes—
38C2×#104×C37C2212yes—
39C2×#104×C37C2212yes—
40C37×#417C2212yes—
41C37×#417C2212yes—
42C37×#417C2211yescharacteristic
43C37×#417C2211yescharacteristic
44C4×M16×C37C2211yescharacteristic
45C37×#398—22no—
46C37×#395—22no—
47C37×#384C2212yes—
48C37×#382C2212yes—
49C37×#376C2211yescharacteristic
50C37×#343C2212yes—
51C37×#343C2212yes—
52C37×#339C2212yes—
53C2×#41×C37—22no—
54C2×#41×C37C2312yes—
55C2×#41×C37C2311yescharacteristic
56C22×Q8×C37D412yes—
57C2×M16×C37C2312yes—
58C2×M16×C37C2311yescharacteristic
59C2×M16×C37C2311yescharacteristic
60C4⋊Q8×C37—21no—
61C4⋊Q8×C37—21no—
62C4⋊Q8×C37—21no—
63C4⋊Q8×C37—21no—
64C4⋊Q8×C37D411yescharacteristic
65#127×C37D411yescharacteristic
66#126×C37—24no—
67#125×C37—22no—
68#125×C37—21no—
69#125×C37—21no—
70#125×C37—21no—
71#125×C37—21no—
72#124×C37—22no—
73#124×C37—24no—
74#124×C37D412yes—
75#123×C37—24no—
76C22⋊Q8×C37—22no—
77C22⋊Q8×C37—24no—
78C22⋊Q8×C37—22no—
79C22⋊Q8×C37—22no—
80#121×C37—22no—
81#121×C37—22no—
82#121×C37—22no—
83#121×C37—21no—
84#121×C37—21no—
85#121×C37—24no—
86C4×Q8×C37—22no—
87C4×Q8×C37—22no—
88C4×Q8×C37D411yescharacteristic
89C4×Q8×C37D411yescharacteristic
90C4×D4×C37—22no—
91C4×D4×C37—22no—
92C4×D4×C37—24no—
93C4×D4×C37—21no—
94C4×D4×C37—21no—
95C4×D4×C37—21no—
96C4×D4×C37—21no—
97C4×D4×C37D411yescharacteristic
98C4×D4×C37D411yescharacteristic
99#117×C37—22no—
100#117×C37—22no—
101#117×C37—21no—
102#117×C37C2311yescharacteristic
103C2×C4⋊C4×C37—22no—
104C2×C4⋊C4×C37—21no—
105C2×C4⋊C4×C37—21no—
106C2×C4⋊C4×C37—24no—
107C2×C4⋊C4×C37D412yes—
108C2×C4⋊C4×C37C2311yescharacteristic
109C2×C4⋊C4×C37C2311yescharacteristic
110C2×C4⋊C4×C37C2312yes—
111C2×C42×C37—21no—
112C2×C42×C37C2312yes—
113C2×C42×C37C2311yescharacteristic
114#107×C37—21no—
115#107×C37—21no—
116#106×C37—21no—
117#106×C37—21no—
118C4⋊C8×C37—21no—
119C4⋊C8×C37—21no—
120#104×C37—24no—
121#104×C37—24no—
122#104×C37—24no—
123#103×C37—21no—
124#103×C37—21no—
125#103×C37—22no—
126#103×C37—22no—
127#102×C37—21no—
128#102×C37—21no—
129#102×C37—22no—
130#102×C37—22no—
131#97×C37—21no—
132C4×C8×C37—21no—
133#95×C37—21no—
134#95×C37—21no—
135#95×C37—24no—
136#41×C37—22no—
137#41×C37—22no—
138#41×C37—22no—
139#41×C37—22no—
140#41×C37—22no—
141#41×C37—22no—
142#41×C37—84no—
143C2×Q8×C37—22no—
144C2×Q8×C37—22no—
145C2×Q8×C37—82no—
146C2×Q8×C37C2×D412yes—
147C2×Q8×C37C2×D411yescharacteristic
148C2×D4×C37—22no—
149C2×D4×C37—21no—
150C2×D4×C37—24no—
151C2×D4×C37—21no—
152C2×D4×C37—21no—
153C2×D4×C37C2×D412yes—
154C2×D4×C37C2×D411yescharacteristic
155C22×C4×C37—22no—
156C22×C4×C37—24no—
157C22×C4×C37—21no—
158C22×C4×C37—21no—
159C22×C4×C37—21no—
160C22×C4×C37—22no—
161C22×C4×C37—21no—
162C22×C4×C37—21no—
163C22×C4×C37C2×D414yes—
164C22×C4×C37C2×D411yescharacteristic
165C22×C4×C37C2×D411yescharacteristic
166C22×C4×C37C2411yescharacteristic
167M16×C37—22no—
168M16×C37—22no—
169M16×C37—22no—
170M16×C37—22no—
171C2×C8×C37—22no—
172C2×C8×C37—21no—
173C2×C8×C37—21no—
174C4⋊C4×C37—24no—
175C4⋊C4×C37—24no—
176C4⋊C4×C37—22no—
177C4⋊C4×C37—22no—
178C4⋊C4×C37—21no—
179C4⋊C4×C37—21no—
180C4⋊C4×C37—21no—
181C4⋊C4×C37—21no—
182C4⋊C4×C37—22no—
183C4⋊C4×C37—22no—
184C4⋊C4×C37—21no—
185C4⋊C4×C37—21no—
186C4⋊C4×C37—21no—
187C4⋊C4×C37—21no—
188C4⋊C4×C37—41no—
189C4⋊C4×C37—41no—
190C4⋊C4×C37—41no—
191C4⋊C4×C37—41no—
192C4⋊C4×C37—84no—
193C4⋊C4×C37C2×D411yescharacteristic
194C4⋊C4×C37C2×D411yescharacteristic
195C22⋊C4×C37—24no—
196C22⋊C4×C37—24no—
197C22⋊C4×C37—24no—
198C22⋊C4×C37—21no—
199C22⋊C4×C37—21no—
200C22⋊C4×C37—21no—
201C22⋊C4×C37—22no—
202C22⋊C4×C37—22no—
203C42×C37—24no—
204C42×C37—21no—
205C42×C37—21no—
206C42×C37—21no—
207C42×C37—22no—
208C42×C37C2×D411yescharacteristic
209C42×C37C2×D411yescharacteristic
210C42×C37C2×D411yescharacteristic
211C42×C37C2×D411yescharacteristic
212C42×C37#4114yescomplemented
213C23×C37—21no—
214C23×C37—22no—
215C23×C37C22×D411yescharacteristic
216Q8×C37—21no—
217Q8×C37—21no—
218Q8×C37—22no—
219Q8×C37—22no—
220Q8×C37—44no—
221Q8×C37—82no—
222D4×C37—21no—
223D4×C37—21no—
224D4×C37—22no—
225D4×C37—22no—
226D4×C37—42no—
227D4×C37—42no—
228D4×C37—42no—
229D4×C37—42no—
230D4×C37—42no—
231D4×C37—84no—
232C2×C4×C37—21no—
233C2×C4×C37—22no—
234C2×C4×C37—21no—
235C2×C4×C37—21no—
236C2×C4×C37—24no—
237C2×C4×C37—24no—
238C2×C4×C37—41no—
239C2×C4×C37—41no—
240C2×C4×C37—42no—
241C2×C4×C37—42no—
242C2×C4×C37—42no—
243C2×C4×C37—42no—
244C2×C4×C37—42no—
245C2×C4×C37—42no—
246C2×C4×C37—42no—
247C2×C4×C37—44no—
248C2×C4×C37—42no—
249C2×C4×C37—42no—
250C2×C4×C37—41no—
251C2×C4×C37—41no—
252C2×C4×C37—84no—
253C2×C4×C37#12011yescharacteristic
254C2×C4×C37#12011yescharacteristic
255C2×C4×C37#12011yescharacteristic
256C2×C4×C37#12011yescharacteristic
257C2×C4×C37C22×D411yescharacteristic
258C2×C4×C37C22×D411yescharacteristic
259C2×C4×C37C2×#4112yes—
260C2×C4×C372−1+412yes—
261C8×C37—41no—
262C8×C37—41no—
263C8×C37—42no—
264#25669C3711yesmaximal, characteristic, direct product factor, Sylow
265C22×C37—21no—
266C22×C37—21no—
267C22×C37—42no—
268C22×C37—41no—
269C22×C37—41no—
270C22×C37—42no—
271C22×C37—41no—
272C22×C37—42no—
273C22×C37C2×#12011yescharacteristic
274C22×C37#54812yes—
275C4×C37—21no—
276C4×C37—21no—
277C4×C37—21no—
278C4×C37—21no—
279C4×C37—44no—
280C4×C37—42no—
281C4×C37—41no—
282C4×C37—41no—
283C4×C37—44no—
284C4×C37—41no—
285C4×C37—81no—
286C4×C37—81no—
287C4×C37#53211yescharacteristic
288C4×C37#53611yescharacteristic
289C4×C37#54712yes—
290#3511C2×C3711yescharacteristic
291#3142C2×C3711yescharacteristic, complemented
292#3080C2×C3711yescharacteristic, complemented
293#2660C2×C3711yescharacteristic, complemented
294#2040C2×C3712yescomplemented
295#2039C2×C3712yescomplemented
296#1997C2×C3711yescharacteristic, complemented
297#1963C2×C3711yescharacteristic, complemented
298#1860C2×C3712yescomplemented
299#1859C2×C3712yescomplemented
300#1759C2×C3711yescharacteristic, complemented
301C2×C37—22no—
302C2×C37—81no—
303C2×C37—82no—
304C2×C37#243211yescharacteristic
305C2×C37#301911yescharacteristic
306C2×C37#302011yescharacteristic
307#556—21no—
308#555—21no—
309#554—21no—
310#553—22no—
311#548—22no—
312#547—21no—
313#542—22no—
314#537C22×C3712yes—
315#533—21no—
316#532—21no—
317#532C22×C3711yescharacteristic
318C2×C4⋊Q8C22×C3711yescharacteristic
319C2×#125C22×C3711yescharacteristic
320#520C22×C3712yes—
321C4×#41C22×C3711yescharacteristic
322#491—21no—
323#490—21no—
324#488—22no—
325#479—21no—
326#479—21no—
327#478—21no—
328#478—21no—
329#428C22×C3711yescharacteristic
330#428C22×C3711yescharacteristic
331#423C22×C3711yescharacteristic
332C2×#104C22×C3712yes—
333C2×#104C22×C3712yes—
334C2×#104C22×C3712yes—
335#417C22×C3711yescharacteristic
336#417C22×C3711yescharacteristic
337#417C22×C3712yes—
338#417C22×C3712yes—
339C4×M16C22×C3711yescharacteristic
340#398—22no—
341#395—22no—
342#384C22×C3712yes—
343#382C22×C3712yes—
344#376C22×C3711yescharacteristic
345#343C22×C3712yes—
346#343C22×C3712yes—
347#339C22×C3712yes—
348C37#2566911yescharacteristic, direct product factor, Sylow
349C2×#41—22no—
350C2×#41C23×C3711yescharacteristic
351C2×#41C23×C3712yes—
352C22×Q8D4×C3712yes—
353C2×M16C23×C3712yes—
354C2×M16C23×C3711yescharacteristic
355C2×M16C23×C3711yescharacteristic
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8D4×C3711yescharacteristic
361#127D4×C3711yescharacteristic
362#126—24no—
363#125—22no—
364#125—21no—
365#125—21no—
366#125—21no—
367#125—21no—
368#124—22no—
369#124—24no—
370#124D4×C3712yes—
371#123—24no—
372C22⋊Q8—22no—
373C22⋊Q8—24no—
374C22⋊Q8—22no—
375C22⋊Q8—22no—
376#121—22no—
377#121—22no—
378#121—22no—
379#121—21no—
380#121—21no—
381#121—24no—
382C4×Q8—22no—
383C4×Q8—22no—
384C4×Q8D4×C3711yescharacteristic
385C4×Q8D4×C3711yescharacteristic
386C4×D4—22no—
387C4×D4—22no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—24no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4D4×C3711yescharacteristic
394C4×D4D4×C3711yescharacteristic
395#117—22no—
396#117—22no—
397#117—21no—
398#117C23×C3711yescharacteristic
399C2×C4⋊C4—22no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4D4×C3712yes—
404C2×C4⋊C4C23×C3711yescharacteristic
405C2×C4⋊C4C23×C3711yescharacteristic
406C2×C4⋊C4C23×C3712yes—
407C2×C42—21no—
408C2×C42C23×C3712yes—
409C2×C42C23×C3711yescharacteristic
410#107—21no—
411#107—21no—
412#106—21no—
413#106—21no—
414C4⋊C8—21no—
415C4⋊C8—21no—
416#104—24no—
417#104—24no—
418#104—24no—
419#103—21no—
420#103—21no—
421#103—22no—
422#103—22no—
423#102—21no—
424#102—21no—
425#102—22no—
426#102—22no—
427#97—21no—
428C4×C8—21no—
429#95—21no—
430#95—21no—
431#95—24no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—22no—
436#41—22no—
437#41—22no—
438#41—84no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—82no—
442C2×Q8C2×D4×C3712yes—
443C2×Q8C2×D4×C3711yescharacteristic
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—24no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4C2×D4×C3712yes—
450C2×D4C2×D4×C3711yescharacteristic
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4C2×D4×C3714yes—
460C22×C4C2×D4×C3711yescharacteristic
461C22×C4C2×D4×C3711yescharacteristic
462C22×C4C24×C3711yescharacteristic
463M16—22no—
464M16—22no—
465M16—22no—
466M16—22no—
467C2×C8—22no—
468C2×C8—21no—
469C2×C8—21no—
470C4⋊C4—24no—
471C4⋊C4—24no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—84no—
489C4⋊C4C2×D4×C3711yescharacteristic
490C4⋊C4C2×D4×C3711yescharacteristic
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—22no—
499C42—24no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—22no—
504C42C2×D4×C3711yescharacteristic
505C42C2×D4×C3711yescharacteristic
506C42C2×D4×C3711yescharacteristic
507C42C2×D4×C3711yescharacteristic
508C42#41×C3714yescomplemented
509C23—21no—
510C23—22no—
511C23C22×D4×C3711yescharacteristic
512Q8—21no—
513Q8—21no—
514Q8—22no—
515Q8—22no—
516Q8—44no—
517Q8—82no—
518D4—21no—
519D4—21no—
520D4—22no—
521D4—22no—
522D4—42no—
523D4—42no—
524D4—42no—
525D4—42no—
526D4—42no—
527D4—84no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—84no—
549C2×C4#120×C3711yescharacteristic
550C2×C4#120×C3711yescharacteristic
551C2×C4#120×C3711yescharacteristic
552C2×C4#120×C3711yescharacteristic
553C2×C4C22×D4×C3711yescharacteristic
554C2×C4C22×D4×C3711yescharacteristic
555C2×C4C2×#41×C3712yes—
556C2×C42−1+4×C3712yes—
557C8—41no—
558C8—41no—
559C8—42no—
560C22—21no—
561C22—21no—
562C22—42no—
563C22—41no—
564C22—41no—
565C22—42no—
566C22—41no—
567C22—42no—
568C22C2×#120×C3711yescharacteristic
569C22C37×#54812yes—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—44no—
575C4—42no—
576C4—41no—
577C4—41no—
578C4—44no—
579C4—41no—
580C4—81no—
581C4—81no—
582C4C37×#53211yescharacteristic
583C4C37×#53611yescharacteristic
584C4C37×#54712yes—
585C2—22no—
586C2—81no—
587C2—82no—
588C2C37×#243211yescharacteristic
589C2C37×#301911yescharacteristic
590C2C37×#302011yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC37×#3511C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C37 ◁ C2×C42×C37 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C37×#3142C2semidirect
3. C37×#3080C2semidirect
4. C37×#2660C2semidirect
5. C37×#2040C2semidirect
6. C37×#2039C2semidirect
7. C37×#1997C2semidirect
8. C37×#1963C2semidirect
9. C37×#1860C2semidirect
10. C37×#1859C2semidirect
11. C37×#1759C2semidirect
212. C42×C37#41semidirect
264. #25669C37direct (N × H)
291. #3142C2×C37semidirect
292. #3080C2×C37semidirect
293. #2660C2×C37semidirect
294. #2040C2×C37semidirect
295. #2039C2×C37semidirect
296. #1997C2×C37semidirect
297. #1963C2×C37semidirect
298. #1860C2×C37semidirect
299. #1859C2×C37semidirect
300. #1759C2×C37semidirect
348. C37#25669direct (N × H)
508. C42#41×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#35112
C37×#31422
C37×#30802
C37×#26602
C37×#20402
C37×#20392
C37×#19972
C37×#19632
C37×#18602
C37×#18592
C37×#17592
#2566937