Finite Group Databasebeta

← C37×#19484 #22640737

Subgroups — C37×#19484 #22640737

Order 9472.

710 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3205C211yesmaximal, characteristic, complemented
2C37×#3106C211yesmaximal, characteristic, complemented
3C37×#3038C211yesmaximal, characteristic, complemented
4C37×#2990C211yesmaximal, characteristic, complemented
5C37×#1698C212yesmaximal, complemented
6C37×#1688C212yesmaximal, complemented
7C37×#1677C212yesmaximal, complemented
8C37×#1667C212yesmaximal, complemented
9C37×#1574C211yesmaximal, characteristic, complemented
10C37×#1560C211yesmaximal, characteristic, complemented
11C37×#1545C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C37—21no—
13C37×#532C2211yescharacteristic
14C2×#127×C37C2211yescharacteristic
15C4×#41×C37C2211yescharacteristic
16C37×#493C2212yes—
17C37×#486C2212yes—
18C37×#482—21no—
19C37×#477C2211yescharacteristic, complemented
20C37×#476C2211yescharacteristic, complemented
21C37×#460—21no—
22C37×#460C2212yes—
23C37×#460C2211yescharacteristic, complemented
24C37×#459—21no—
25C37×#459—21no—
26C37×#459—21no—
27C37×#459C2212yes—
28C37×#459C2211yescharacteristic, complemented
29C37×#449—21no—
30C37×#447—22no—
31C37×#446C2212yescomplemented
32C4×SD16×C37—21no—
33C4×D8×C37—21no—
34C37×#435—22no—
35C8×D4×C37C2212yescomplemented
36C37×#432—21no—
37C37×#431C2211yescharacteristic
38C37×#431C2211yescharacteristic
39C37×#423C2211yescharacteristic
40C37×#423C2211yescharacteristic
41C2×C4⋊C8×C37—21no—
42C37×#418—21no—
43C37×#335C2212yescomplemented
44C37×#334C2212yescomplemented
45C37×#333C2212yescomplemented
46C37×#331C2212yes—
47C37×#331C2212yes—
48C37×#331C2212yescomplemented
49C2×#41×C37—21no—
50C2×#41×C37D411yescharacteristic
51C22×D4×C37—21no—
52C22×D4×C37—21no—
53C22×D4×C37—21no—
54AGL(1,ℤ/8)×C37—44no—
55C2×SD16×C37—22no—
56C2×SD16×C37—21no—
57C2×D8×C37—22no—
58C2×D8×C37—21no—
59C2×D8×C37—22no—
60C2×D8×C37—22no—
61C2×M16×C37—21no—
62C2×M16×C37—21no—
63C22×C8×C37—22no—
64C4⋊Q8×C37C2311yescharacteristic
65#127×C37—21no—
66#127×C37—21no—
67#127×C37—21no—
68#127×C37C2312yes—
69#127×C37C2311yescharacteristic
70#124×C37—21no—
71#121×C37—21no—
72#121×C37—21no—
73C4×Q8×C37D411yescharacteristic
74C4×Q8×C37C2311yescharacteristic
75C4×D4×C37—21no—
76C4×D4×C37—21no—
77C4×D4×C37—21no—
78C4×D4×C37—21no—
79C4×D4×C37D411yescharacteristic
80C4×D4×C37C2311yescharacteristic
81#117×C37—21no—
82#117×C37D411yescharacteristic
83C2×C42×C37—21no—
84C2×C42×C37C2311yescharacteristic
85#107×C37—21no—
86#106×C37—21no—
87C4⋊C8×C37—22no—
88C4⋊C8×C37—21no—
89C4⋊C8×C37—21no—
90C4⋊C8×C37D411yescharacteristic
91C4⋊C8×C37D411yescharacteristic
92C4⋊C8×C37C2312yes—
93C4⋊C8×C37C2311yescharacteristic
94C4⋊C8×C37C2311yescharacteristic
95C4⋊C8×C37C2312yes—
96#103×C37—21no—
97#102×C37—21no—
98#102×C37—22no—
99#102×C37—22no—
100#102×C37—22no—
101#102×C37—22no—
102#102×C37—21no—
103#102×C37—21no—
104C22⋊C8×C37—21no—
105C22⋊C8×C37—22no—
106C22⋊C8×C37D412yes—
107#97×C37—22no—
108C4×C8×C37—21no—
109C4×C8×C37C2312yes—
110C24×C37—41no—
111#41×C37—22no—
112#41×C37—41no—
113#41×C37—82no—
114C2×Q8×C37—21no—
115C2×Q8×C37C2×D411yescharacteristic
116C2×D4×C37—21no—
117C2×D4×C37—21no—
118C2×D4×C37—22no—
119C2×D4×C37—22no—
120C2×D4×C37—21no—
121C2×D4×C37—21no—
122C2×D4×C37—22no—
123C2×D4×C37—42no—
124C2×D4×C37—42no—
125C2×D4×C37—41no—
126C2×D4×C37—41no—
127C2×D4×C37—41no—
128C2×D4×C37—41no—
129C2×D4×C37—81no—
130C2×D4×C37—81no—
131C2×D4×C37—82no—
132C2×D4×C37C2×D411yescharacteristic
133C22×C4×C37—21no—
134C22×C4×C37—21no—
135C22×C4×C37—21no—
136C22×C4×C37—41no—
137C22×C4×C37C2×D411yescharacteristic
138C22×C4×C37C2×D411yescharacteristic
139C22×C4×C37#4111yescharacteristic
140SD16×C37—42no—
141SD16×C37—44no—
142D8×C37—42no—
143D8×C37—44no—
144D8×C37—82no—
145D8×C37—82no—
146M16×C37—42no—
147M16×C37—81no—
148C2×C8×C37—21no—
149C2×C8×C37—21no—
150C2×C8×C37—22no—
151C2×C8×C37—22no—
152C2×C8×C37—82no—
153C2×C8×C37C2×D412yes—
154C2×C8×C37C2×D412yes—
155C4⋊C4×C37—21no—
156C4⋊C4×C37—21no—
157C4⋊C4×C37—21no—
158C4⋊C4×C37—21no—
159C4⋊C4×C37C2×D411yescharacteristic
160C4⋊C4×C37C2×D411yescharacteristic
161C22⋊C4×C37—21no—
162C22⋊C4×C37—21no—
163C22⋊C4×C37—21no—
164C22⋊C4×C37—41no—
165C22⋊C4×C37—41no—
166C42×C37—21no—
167C42×C37—21no—
168C42×C37—21no—
169C42×C37C2×D411yescharacteristic
170C42×C37C2×D411yescharacteristic
171C42×C37#4111yescharacteristic
172C42×C37C2411yescharacteristic
173C23×C37—21no—
174C23×C37—41no—
175C23×C37—42no—
176C23×C37—82no—
177C23×C37—82no—
178C23×C37—82no—
179C23×C37#12111yescharacteristic
180Q8×C37—21no—
181Q8×C37—21no—
182Q8×C37—81no—
183D4×C37—21no—
184D4×C37—42no—
185D4×C37—42no—
186D4×C37—41no—
187D4×C37—41no—
188D4×C37—42no—
189D4×C37—41no—
190D4×C37—42no—
191D4×C37—41no—
192D4×C37—42no—
193D4×C37—82no—
194D4×C37—81no—
195D4×C37—82no—
196D4×C37—82no—
197D4×C37—82no—
198D4×C37—82no—
199D4×C37AGL(1,ℤ/8)12yes—
200C2×C4×C37—21no—
201C2×C4×C37—21no—
202C2×C4×C37—21no—
203C2×C4×C37—21no—
204C2×C4×C37—22no—
205C2×C4×C37—21no—
206C2×C4×C37—21no—
207C2×C4×C37—21no—
208C2×C4×C37—42no—
209C2×C4×C37—41no—
210C2×C4×C37—41no—
211C2×C4×C37—42no—
212C2×C4×C37—41no—
213C2×C4×C37—82no—
214C2×C4×C37#12111yescharacteristic
215C2×C4×C37#12111yescharacteristic
216C2×C4×C37#12111yescharacteristic
217C2×C4×C37C22×D411yescharacteristic
218C2×C4×C37C22×D411yescharacteristic
219C2×C4×C37C2×#4111yescharacteristic
220C8×C37—22no—
221C8×C37—22no—
222C8×C37—42no—
223C8×C37—41no—
224C8×C37—41no—
225C8×C37—42no—
226#19484C3711yesmaximal, characteristic, direct product factor, Sylow
227C22×C37—21no—
228C22×C37—21no—
229C22×C37—22no—
230C22×C37—21no—
231C22×C37—41no—
232C22×C37—41no—
233C22×C37—82no—
234C22×C37—81no—
235C22×C37—82no—
236C22×C37—81no—
237C22×C37—81no—
238C22×C37—82no—
239C22×C37—164no—
240C22×C37C2×#12111yescharacteristic
241C4×C37—21no—
242C4×C37—21no—
243C4×C37—21no—
244C4×C37—41no—
245C4×C37—41no—
246C4×C37—41no—
247C4×C37—81no—
248C4×C37#47212yes—
249C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
250C4×C37#57511yescharacteristic
251C4×C37#57611yescharacteristic
252C4×C37#57711yescharacteristic
253#3205C2×C3711yescharacteristic, complemented
254#3106C2×C3711yescharacteristic, complemented
255#3038C2×C3711yescharacteristic, complemented
256#2990C2×C3711yescharacteristic, complemented
257#1698C2×C3712yescomplemented
258#1688C2×C3712yescomplemented
259#1677C2×C3712yescomplemented
260#1667C2×C3712yescomplemented
261#1574C2×C3711yescharacteristic, complemented
262#1560C2×C3711yescharacteristic, complemented
263#1545C2×C3711yescharacteristic, complemented
264C2×C37—41no—
265C2×C37—42no—
266C2×C37—161no—
267C2×C37—162no—
268C2×C37#304511yescharacteristic
269C2×C37#305511yescharacteristic
270C2×C37C2×#47211yescharacteristic
271C2×AGL(1,ℤ/8)—21no—
272#532C22×C3711yescharacteristic
273C2×#127C22×C3711yescharacteristic
274C4×#41C22×C3711yescharacteristic
275#493C22×C3712yes—
276#486C22×C3712yes—
277#482—21no—
278#477C22×C3711yescharacteristic, complemented
279#476C22×C3711yescharacteristic, complemented
280#460—21no—
281#460C22×C3712yes—
282#460C22×C3711yescharacteristic, complemented
283#459—21no—
284#459—21no—
285#459—21no—
286#459C22×C3712yes—
287#459C22×C3711yescharacteristic, complemented
288#449—21no—
289#447—22no—
290#446C22×C3712yescomplemented
291C4×SD16—21no—
292C4×D8—21no—
293#435—22no—
294C8×D4C22×C3712yescomplemented
295#432—21no—
296#431C22×C3711yescharacteristic
297#431C22×C3711yescharacteristic
298#423C22×C3711yescharacteristic
299#423C22×C3711yescharacteristic
300C2×C4⋊C8—21no—
301#418—21no—
302#335C22×C3712yescomplemented
303#334C22×C3712yescomplemented
304#333C22×C3712yescomplemented
305#331C22×C3712yes—
306#331C22×C3712yes—
307#331C22×C3712yescomplemented
308C37#1948411yescharacteristic, direct product factor, Sylow
309C2×#41—21no—
310C2×#41D4×C3711yescharacteristic
311C22×D4—21no—
312C22×D4—21no—
313C22×D4—21no—
314AGL(1,ℤ/8)—44no—
315C2×SD16—22no—
316C2×SD16—21no—
317C2×D8—22no—
318C2×D8—21no—
319C2×D8—22no—
320C2×D8—22no—
321C2×M16—21no—
322C2×M16—21no—
323C22×C8—22no—
324C4⋊Q8C23×C3711yescharacteristic
325#127—21no—
326#127—21no—
327#127—21no—
328#127C23×C3712yes—
329#127C23×C3711yescharacteristic
330#124—21no—
331#121—21no—
332#121—21no—
333C4×Q8D4×C3711yescharacteristic
334C4×Q8C23×C3711yescharacteristic
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—21no—
339C4×D4D4×C3711yescharacteristic
340C4×D4C23×C3711yescharacteristic
341#117—21no—
342#117D4×C3711yescharacteristic
343C2×C42—21no—
344C2×C42C23×C3711yescharacteristic
345#107—21no—
346#106—21no—
347C4⋊C8—22no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8D4×C3711yescharacteristic
351C4⋊C8D4×C3711yescharacteristic
352C4⋊C8C23×C3712yes—
353C4⋊C8C23×C3711yescharacteristic
354C4⋊C8C23×C3711yescharacteristic
355C4⋊C8C23×C3712yes—
356#103—21no—
357#102—21no—
358#102—22no—
359#102—22no—
360#102—22no—
361#102—22no—
362#102—21no—
363#102—21no—
364C22⋊C8—21no—
365C22⋊C8—22no—
366C22⋊C8D4×C3712yes—
367#97—22no—
368C4×C8—21no—
369C4×C8C23×C3712yes—
370C24—41no—
371#41—22no—
372#41—41no—
373#41—82no—
374C2×Q8—21no—
375C2×Q8C2×D4×C3711yescharacteristic
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—81no—
390C2×D4—81no—
391C2×D4—82no—
392C2×D4C2×D4×C3711yescharacteristic
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—41no—
397C22×C4C2×D4×C3711yescharacteristic
398C22×C4C2×D4×C3711yescharacteristic
399C22×C4#41×C3711yescharacteristic
400SD16—42no—
401SD16—44no—
402D8—42no—
403D8—44no—
404D8—82no—
405D8—82no—
406M16—42no—
407M16—81no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—82no—
413C2×C8C2×D4×C3712yes—
414C2×C8C2×D4×C3712yes—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4C2×D4×C3711yescharacteristic
420C4⋊C4C2×D4×C3711yescharacteristic
421C22⋊C4—21no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C42—21no—
427C42—21no—
428C42—21no—
429C42C2×D4×C3711yescharacteristic
430C42C2×D4×C3711yescharacteristic
431C42#41×C3711yescharacteristic
432C42C24×C3711yescharacteristic
433C23—21no—
434C23—41no—
435C23—42no—
436C23—82no—
437C23—82no—
438C23—82no—
439C23#121×C3711yescharacteristic
440Q8—21no—
441Q8—21no—
442Q8—81no—
443D4—21no—
444D4—42no—
445D4—42no—
446D4—41no—
447D4—41no—
448D4—42no—
449D4—41no—
450D4—42no—
451D4—41no—
452D4—42no—
453D4—82no—
454D4—81no—
455D4—82no—
456D4—82no—
457D4—82no—
458D4—82no—
459D4AGL(1,ℤ/8)×C3712yes—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—82no—
474C2×C4#121×C3711yescharacteristic
475C2×C4#121×C3711yescharacteristic
476C2×C4#121×C3711yescharacteristic
477C2×C4C22×D4×C3711yescharacteristic
478C2×C4C22×D4×C3711yescharacteristic
479C2×C4C2×#41×C3711yescharacteristic
480C8—22no—
481C8—22no—
482C8—42no—
483C8—41no—
484C8—41no—
485C8—42no—
486C22—21no—
487C22—21no—
488C22—22no—
489C22—21no—
490C22—41no—
491C22—41no—
492C22—82no—
493C22—81no—
494C22—82no—
495C22—81no—
496C22—81no—
497C22—82no—
498C22—164no—
499C22C2×#121×C3711yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—41no—
504C4—41no—
505C4—41no—
506C4—81no—
507C4C37×#47212yes—
508C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
509C4C37×#57511yescharacteristic
510C4C37×#57611yescharacteristic
511C4C37×#57711yescharacteristic
512C2—41no—
513C2—42no—
514C2—162no—
515C2—161no—
516C2C37×#304511yescharacteristic
517C2C37×#305511yescharacteristic
518C2C2×C37×#47211yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
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×#3205C2semidirect
2. C37×#3106C2semidirect
3. C37×#3038C2semidirect
4. C37×#2990C2semidirect
5. C37×#1698C2semidirect
6. C37×#1688C2semidirect
7. C37×#1677C2semidirect
8. C37×#1667C2semidirect
9. C37×#1574C2semidirect
10. C37×#1560C2semidirect
11. C37×#1545C2semidirect
19. C37×#477C22semidirect
20. C37×#476C22semidirect
23. C37×#460C22semidirect
28. C37×#459C22semidirect
31. C37×#446C22semidirect
35. C8×D4×C37C22semidirect
43. C37×#335C22semidirect
44. C37×#334C22semidirect
45. C37×#333C22semidirect
48. C37×#331C22semidirect
226. #19484C37direct (N × H)
253. #3205C2×C37semidirect
254. #3106C2×C37semidirect
255. #3038C2×C37semidirect
256. #2990C2×C37semidirect
257. #1698C2×C37semidirect
258. #1688C2×C37semidirect
259. #1677C2×C37semidirect
260. #1667C2×C37semidirect
261. #1574C2×C37semidirect
262. #1560C2×C37semidirect
263. #1545C2×C37semidirect
278. #477C22×C37semidirect
279. #476C22×C37semidirect
282. #460C22×C37semidirect
287. #459C22×C37semidirect
290. #446C22×C37semidirect
294. C8×D4C22×C37semidirect
302. #335C22×C37semidirect
303. #334C22×C37semidirect
304. #333C22×C37semidirect
307. #331C22×C37semidirect
308. C37#19484direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32052
C37×#31062
C37×#30382
C37×#29902
C37×#16982
C37×#16882
C37×#16772
C37×#16672
C37×#15742
C37×#15602
C37×#15452
#1948437