Finite Group Databasebeta

← C37×#19456 #22640709

Subgroups — C37×#19456 #22640709

Order 9472.

722 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3208C211yesmaximal, characteristic, complemented
2C37×#3110C211yesmaximal, characteristic, complemented
3C2×C37×#459C211yesmaximal, characteristic
4C37×#2974C211yesmaximal, characteristic, complemented
5C37×#1701C212yesmaximal, complemented
6C37×#1685C212yesmaximal, complemented
7C37×#1681C212yesmaximal, complemented
8C37×#1665C212yesmaximal, complemented
9C37×#1573C211yesmaximal, characteristic, complemented
10C37×#1555C211yesmaximal, characteristic, complemented
11C37×#1552C211yesmaximal, characteristic, complemented
12C22×D8×C37—21no—
13C37×#533C2211yescharacteristic
14C2×#127×C37C2211yescharacteristic
15C2×C4×D4×C37C2211yescharacteristic
16C37×#492C2212yescomplemented
17C37×#486C2212yescomplemented
18C37×#484—21no—
19C37×#474C2211yescharacteristic, complemented
20C37×#474C2211yescharacteristic, complemented
21C37×#461C2211yescharacteristic, complemented
22C37×#461C2211yescharacteristic, complemented
23C37×#460—22no—
24C37×#459—21no—
25C37×#459—21no—
26C37×#459C2212yes—
27C37×#459C2212yes—
28C37×#450—21no—
29C37×#450—21no—
30C37×#450—21no—
31C37×#440—21no—
32C37×#440—21no—
33C37×#436C2212yescomplemented
34C37×#435—22no—
35C8×D4×C37C2212yescomplemented
36C37×#432C2211yescharacteristic
37C37×#432C2211yescharacteristic
38C37×#431C2211yescharacteristic
39C2×C4⋊C8×C37C2211yescharacteristic
40C2×#102×C37—21no—
41C37×#407—21no—
42C2×C22⋊C8×C37—21no—
43C37×#335C2212yescomplemented
44C37×#334C2212yescomplemented
45C37×#332C2212yescomplemented
46C37×#332C2212yescomplemented
47C37×#331C2212yescomplemented
48C37×#331C2212yescomplemented
49C22×D4×C37—21no—
50C22×D4×C37—21no—
51C22×D4×C37—21no—
52C22×D4×C37D411yescharacteristic
53C23×C4×C37—21no—
54C2×SD16×C37—21no—
55C2×SD16×C37—21no—
56C2×SD16×C37—22no—
57C2×SD16×C37—22no—
58C2×D8×C37—22no—
59C2×D8×C37—22no—
60C2×D8×C37—44no—
61C2×M16×C37—22no—
62C22×C8×C37—21no—
63C22×C8×C37—22no—
64C4⋊Q8×C37C2311yescharacteristic
65C4⋊Q8×C37C2311yescharacteristic
66#127×C37—21no—
67#127×C37—21no—
68#127×C37—21no—
69#127×C37C2312yes—
70#125×C37—21no—
71C22⋊Q8×C37—21no—
72C22⋊Q8×C37—21no—
73C4×Q8×C37—21no—
74C4×Q8×C37—21no—
75C4×D4×C37—21no—
76C4×D4×C37—21no—
77C4×D4×C37D411yescharacteristic
78C4×D4×C37D411yescharacteristic
79C4×D4×C37C2311yescharacteristic
80C4×D4×C37C2311yescharacteristic
81#117×C37—21no—
82C2×C4⋊C4×C37D411yescharacteristic
83C2×C22⋊C4×C37—21no—
84C2×C42×C37C2311yescharacteristic
85#107×C37—21no—
86#107×C37—21no—
87C4⋊C8×C37—21no—
88C4⋊C8×C37D412yes—
89C4⋊C8×C37C2312yes—
90C4⋊C8×C37C2311yescharacteristic
91C4⋊C8×C37C2311yescharacteristic
92C4⋊C8×C37C2312yes—
93#103×C37—21no—
94#103×C37—21no—
95#102×C37—21no—
96#102×C37—21no—
97#102×C37—22no—
98#102×C37—22no—
99#102×C37—22no—
100#102×C37—22no—
101C22⋊C8×C37—21no—
102C22⋊C8×C37—21no—
103C22⋊C8×C37—22no—
104C22⋊C8×C37—22no—
105C22⋊C8×C37D411yescharacteristic
106C22⋊C8×C37D411yescharacteristic
107#97×C37—21no—
108#97×C37—21no—
109C4×C8×C37C2312yes—
110C24×C37—21no—
111C24×C37—41no—
112C2×Q8×C37—21no—
113C2×Q8×C37—21no—
114C2×D4×C37—22no—
115C2×D4×C37—21no—
116C2×D4×C37—22no—
117C2×D4×C37—22no—
118C2×D4×C37—22no—
119C2×D4×C37—41no—
120C2×D4×C37—42no—
121C2×D4×C37—42no—
122C2×D4×C37—41no—
123C2×D4×C37—41no—
124C2×D4×C37—41no—
125C2×D4×C37—82no—
126C2×D4×C37—82no—
127C2×D4×C37C2×D411yescharacteristic
128C2×D4×C37C2×D411yescharacteristic
129C22×C4×C37—21no—
130C22×C4×C37—21no—
131C22×C4×C37—21no—
132C22×C4×C37—21no—
133C22×C4×C37—21no—
134C22×C4×C37—82no—
135C22×C4×C37C2×D411yescharacteristic
136C22×C4×C37C2×D411yescharacteristic
137C22×C4×C37#4111yescharacteristic
138SD16×C37—42no—
139SD16×C37—42no—
140SD16×C37—82no—
141SD16×C37—82no—
142D8×C37—44no—
143D8×C37—44no—
144M16×C37—82no—
145C2×C8×C37—22no—
146C2×C8×C37—21no—
147C2×C8×C37—21no—
148C2×C8×C37—22no—
149C2×C8×C37—42no—
150C2×C8×C37—82no—
151C2×C8×C37C2×D412yes—
152C2×C8×C37C2×D412yes—
153C4⋊C4×C37—21no—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—21no—
156C4⋊C4×C37—21no—
157C4⋊C4×C37—21no—
158C4⋊C4×C37—41no—
159C4⋊C4×C37—41no—
160C4⋊C4×C37C2×D411yescharacteristic
161C4⋊C4×C37C2×D411yescharacteristic
162C22⋊C4×C37—21no—
163C22⋊C4×C37—21no—
164C22⋊C4×C37—21no—
165C22⋊C4×C37—21no—
166C22⋊C4×C37—41no—
167C42×C37—41no—
168C42×C37C2×D411yescharacteristic
169C42×C37C2×D411yescharacteristic
170C42×C37#4111yescharacteristic
171C42×C37C2411yescharacteristic
172C23×C37—21no—
173C23×C37—21no—
174C23×C37—42no—
175C23×C37—42no—
176C23×C37—42no—
177C23×C37—81no—
178C23×C37—82no—
179C23×C37—82no—
180C23×C37—82no—
181C23×C37#12111yescharacteristic
182Q8×C37—41no—
183Q8×C37—41no—
184Q8×C37—42no—
185D4×C37—21no—
186D4×C37—21no—
187D4×C37—21no—
188D4×C37—42no—
189D4×C37—42no—
190D4×C37—42no—
191D4×C37—42no—
192D4×C37—42no—
193D4×C37—82no—
194D4×C37—82no—
195D4×C37—82no—
196D4×C37—82no—
197D4×C37AGL(1,ℤ/8)12yes—
198C2×C4×C37—22no—
199C2×C4×C37—21no—
200C2×C4×C37—21no—
201C2×C4×C37—22no—
202C2×C4×C37—21no—
203C2×C4×C37—21no—
204C2×C4×C37—42no—
205C2×C4×C37—42no—
206C2×C4×C37—41no—
207C2×C4×C37—41no—
208C2×C4×C37—81no—
209C2×C4×C37—81no—
210C2×C4×C37—81no—
211C2×C4×C37#12111yescharacteristic
212C2×C4×C37#12111yescharacteristic
213C2×C4×C37#12111yescharacteristic
214C2×C4×C37C22×D411yescharacteristic
215C2×C4×C37C22×D411yescharacteristic
216C2×C4×C37C2×#4111yescharacteristic
217C8×C37—22no—
218C8×C37—22no—
219C8×C37—42no—
220C8×C37—41no—
221C8×C37—41no—
222C8×C37—42no—
223#19456C3711yesmaximal, characteristic, direct product factor, Sylow
224C22×C37—21no—
225C22×C37—21no—
226C22×C37—22no—
227C22×C37—41no—
228C22×C37—41no—
229C22×C37—41no—
230C22×C37—41no—
231C22×C37—41no—
232C22×C37—84no—
233C22×C37—82no—
234C22×C37—82no—
235C22×C37—82no—
236C22×C37—164no—
237C22×C37#47112yes—
238C22×C37C2×#12111yescharacteristic
239C4×C37—21no—
240C4×C37—21no—
241C4×C37—21no—
242C4×C37—21no—
243C4×C37—41no—
244C4×C37—41no—
245C4×C37—81no—
246C4×C37—81no—
247C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
248C4×C37#57511yescharacteristic
249C4×C37#57612yes—
250#3208C2×C3711yescharacteristic, complemented
251#3110C2×C3711yescharacteristic, complemented
252C2×#459C2×C3711yescharacteristic
253#2974C2×C3711yescharacteristic, complemented
254#1701C2×C3712yescomplemented
255#1685C2×C3712yescomplemented
256#1681C2×C3712yescomplemented
257#1665C2×C3712yescomplemented
258#1573C2×C3711yescharacteristic, complemented
259#1555C2×C3711yescharacteristic, complemented
260#1552C2×C3711yescharacteristic, complemented
261C2×C37—22no—
262C2×C37—42no—
263C2×C37—81no—
264C2×C37—162no—
265C2×C37#304111yescharacteristic
266C2×C37#305511yescharacteristic
267C2×C37C2×#47111yescharacteristic
268C22×D8—21no—
269#533C22×C3711yescharacteristic
270C2×#127C22×C3711yescharacteristic
271C2×C4×D4C22×C3711yescharacteristic
272#492C22×C3712yescomplemented
273#486C22×C3712yescomplemented
274#484—21no—
275#474C22×C3711yescharacteristic, complemented
276#474C22×C3711yescharacteristic, complemented
277#461C22×C3711yescharacteristic, complemented
278#461C22×C3711yescharacteristic, complemented
279#460—22no—
280#459—21no—
281#459—21no—
282#459C22×C3712yes—
283#459C22×C3712yes—
284#450—21no—
285#450—21no—
286#450—21no—
287#440—21no—
288#440—21no—
289#436C22×C3712yescomplemented
290#435—22no—
291C8×D4C22×C3712yescomplemented
292#432C22×C3711yescharacteristic
293#432C22×C3711yescharacteristic
294#431C22×C3711yescharacteristic
295C2×C4⋊C8C22×C3711yescharacteristic
296C2×#102—21no—
297#407—21no—
298C2×C22⋊C8—21no—
299#335C22×C3712yescomplemented
300#334C22×C3712yescomplemented
301#332C22×C3712yescomplemented
302#332C22×C3712yescomplemented
303#331C22×C3712yescomplemented
304#331C22×C3712yescomplemented
305C37#1945611yescharacteristic, direct product factor, Sylow
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—21no—
309C22×D4D4×C3711yescharacteristic
310C23×C4—21no—
311C2×SD16—21no—
312C2×SD16—21no—
313C2×SD16—22no—
314C2×SD16—22no—
315C2×D8—22no—
316C2×D8—22no—
317C2×D8—44no—
318C2×M16—22no—
319C22×C8—21no—
320C22×C8—22no—
321C4⋊Q8C23×C3711yescharacteristic
322C4⋊Q8C23×C3711yescharacteristic
323#127—21no—
324#127—21no—
325#127—21no—
326#127C23×C3712yes—
327#125—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C4×Q8—21no—
331C4×Q8—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4D4×C3711yescharacteristic
335C4×D4D4×C3711yescharacteristic
336C4×D4C23×C3711yescharacteristic
337C4×D4C23×C3711yescharacteristic
338#117—21no—
339C2×C4⋊C4D4×C3711yescharacteristic
340C2×C22⋊C4—21no—
341C2×C42C23×C3711yescharacteristic
342#107—21no—
343#107—21no—
344C4⋊C8—21no—
345C4⋊C8D4×C3712yes—
346C4⋊C8C23×C3712yes—
347C4⋊C8C23×C3711yescharacteristic
348C4⋊C8C23×C3711yescharacteristic
349C4⋊C8C23×C3712yes—
350#103—21no—
351#103—21no—
352#102—21no—
353#102—21no—
354#102—22no—
355#102—22no—
356#102—22no—
357#102—22no—
358C22⋊C8—21no—
359C22⋊C8—21no—
360C22⋊C8—22no—
361C22⋊C8—22no—
362C22⋊C8D4×C3711yescharacteristic
363C22⋊C8D4×C3711yescharacteristic
364#97—21no—
365#97—21no—
366C4×C8C23×C3712yes—
367C24—21no—
368C24—41no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×D4—22no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—41no—
377C2×D4—42no—
378C2×D4—42no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—82no—
383C2×D4—82no—
384C2×D4C2×D4×C3711yescharacteristic
385C2×D4C2×D4×C3711yescharacteristic
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—82no—
392C22×C4C2×D4×C3711yescharacteristic
393C22×C4C2×D4×C3711yescharacteristic
394C22×C4#41×C3711yescharacteristic
395SD16—42no—
396SD16—42no—
397SD16—82no—
398SD16—82no—
399D8—44no—
400D8—44no—
401M16—82no—
402C2×C8—22no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—22no—
406C2×C8—42no—
407C2×C8—82no—
408C2×C8C2×D4×C3712yes—
409C2×C8C2×D4×C3712yes—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4C2×D4×C3711yescharacteristic
418C4⋊C4C2×D4×C3711yescharacteristic
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—21no—
423C22⋊C4—41no—
424C42—41no—
425C42C2×D4×C3711yescharacteristic
426C42C2×D4×C3711yescharacteristic
427C42#41×C3711yescharacteristic
428C42C24×C3711yescharacteristic
429C23—21no—
430C23—21no—
431C23—42no—
432C23—42no—
433C23—42no—
434C23—81no—
435C23—82no—
436C23—82no—
437C23—82no—
438C23#121×C3711yescharacteristic
439Q8—41no—
440Q8—41no—
441Q8—42no—
442D4—21no—
443D4—21no—
444D4—21no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—42no—
450D4—82no—
451D4—82no—
452D4—82no—
453D4—82no—
454D4AGL(1,ℤ/8)×C3712yes—
455C2×C4—22no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—81no—
466C2×C4—81no—
467C2×C4—81no—
468C2×C4#121×C3711yescharacteristic
469C2×C4#121×C3711yescharacteristic
470C2×C4#121×C3711yescharacteristic
471C2×C4C22×D4×C3711yescharacteristic
472C2×C4C22×D4×C3711yescharacteristic
473C2×C4C2×#41×C3711yescharacteristic
474C8—22no—
475C8—22no—
476C8—42no—
477C8—41no—
478C8—41no—
479C8—42no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—84no—
489C22—82no—
490C22—82no—
491C22—82no—
492C22—164no—
493C22C37×#47112yes—
494C22C2×#121×C3711yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—41no—
500C4—41no—
501C4—81no—
502C4—81no—
503C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
504C4C37×#57511yescharacteristic
505C4C37×#57612yes—
506C2—22no—
507C2—42no—
508C2—81no—
509C2—162no—
510C2C37×#304111yescharacteristic
511C2C37×#305511yescharacteristic
512C2C2×C37×#47111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC2×C37×#459C2
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×#3208C2semidirect
2. C37×#3110C2semidirect
4. C37×#2974C2semidirect
5. C37×#1701C2semidirect
6. C37×#1685C2semidirect
7. C37×#1681C2semidirect
8. C37×#1665C2semidirect
9. C37×#1573C2semidirect
10. C37×#1555C2semidirect
11. C37×#1552C2semidirect
16. C37×#492C22semidirect
17. C37×#486C22semidirect
19. C37×#474C22semidirect
20. C37×#474C22semidirect
21. C37×#461C22semidirect
22. C37×#461C22semidirect
33. C37×#436C22semidirect
35. C8×D4×C37C22semidirect
43. C37×#335C22semidirect
44. C37×#334C22semidirect
45. C37×#332C22semidirect
46. C37×#332C22semidirect
47. C37×#331C22semidirect
48. C37×#331C22semidirect
223. #19456C37direct (N × H)
250. #3208C2×C37semidirect
251. #3110C2×C37semidirect
253. #2974C2×C37semidirect
254. #1701C2×C37semidirect
255. #1685C2×C37semidirect
256. #1681C2×C37semidirect
257. #1665C2×C37semidirect
258. #1573C2×C37semidirect
259. #1555C2×C37semidirect
260. #1552C2×C37semidirect
272. #492C22×C37semidirect
273. #486C22×C37semidirect
275. #474C22×C37semidirect
276. #474C22×C37semidirect
277. #461C22×C37semidirect
278. #461C22×C37semidirect
289. #436C22×C37semidirect
291. C8×D4C22×C37semidirect
299. #335C22×C37semidirect
300. #334C22×C37semidirect
301. #332C22×C37semidirect
302. #332C22×C37semidirect
303. #331C22×C37semidirect
304. #331C22×C37semidirect
305. C37#19456direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32082
C37×#31102
C2×C37×#4592
C37×#29742
C37×#17012
C37×#16852
C37×#16812
C37×#16652
C37×#15732
C37×#15552
C37×#15522
#1945637