Finite Group Databasebeta

← C37×#19470 #22640723

Subgroups — C37×#19470 #22640723

Order 9472.

694 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3205C211yesmaximal, characteristic
2C37×#3112C211yesmaximal, characteristic, complemented
3C2×C37×#460C211yesmaximal, characteristic, complemented
4C37×#2984C211yesmaximal, characteristic, complemented
5C37×#1698C212yesmaximal, complemented
6C37×#1688C212yesmaximal, complemented
7C37×#1678C212yesmaximal, complemented
8C37×#1668C212yesmaximal, complemented
9C37×#1573C211yesmaximal, characteristic, complemented
10C37×#1555C211yesmaximal, characteristic, complemented
11C37×#1551C211yesmaximal, characteristic, complemented
12C22×SD16×C37—21no—
13C37×#532C2211yescharacteristic
14C2×#127×C37C2211yescharacteristic
15C2×C4×Q8×C37C2211yescharacteristic
16C37×#493C2212yes—
17C37×#486C2212yes—
18C37×#480—21no—
19C37×#477C2211yescharacteristic, complemented
20C37×#477C2211yescharacteristic, complemented
21C37×#460—21no—
22C37×#460—21no—
23C37×#460C2212yes—
24C37×#460C2212yes—
25C37×#460C2211yescharacteristic, complemented
26C37×#460C2211yescharacteristic, complemented
27C37×#459—22no—
28C37×#448—21no—
29C37×#447—21no—
30C37×#447—21no—
31C37×#446—22no—
32C37×#446C2212yescomplemented
33C8×Q8×C37C2212yescomplemented
34C37×#440—21no—
35C37×#440—21no—
36C37×#432—21no—
37C37×#432C2211yescharacteristic
38C37×#432C2211yescharacteristic
39C37×#431—21no—
40C37×#431C2211yescharacteristic
41C2×C4⋊C8×C37C2211yescharacteristic
42C2×#102×C37—21no—
43C37×#335C2212yescomplemented
44C37×#334C2212yescomplemented
45C37×#333C2212yescomplemented
46C37×#331C2212yes—
47C37×#331C2212yes—
48C37×#331C2212yescomplemented
49C2×#41×C37—21no—
50C22×Q8×C37D411yescharacteristic
51C22×D4×C37—21no—
52C22×D4×C37—21no—
53C22×D4×C37—21no—
54C2×SD16×C37—22no—
55C2×SD16×C37—22no—
56C2×SD16×C37—21no—
57C2×SD16×C37—21no—
58C2×SD16×C37—44no—
59C2×D8×C37—22no—
60C2×D8×C37—22no—
61C22×C8×C37—21no—
62C4⋊Q8×C37C2311yescharacteristic
63#127×C37—21no—
64#127×C37—21no—
65#127×C37—21no—
66#127×C37C2312yes—
67#127×C37C2311yescharacteristic
68#124×C37—21no—
69#121×C37—21no—
70#121×C37—21no—
71C4×Q8×C37—21no—
72C4×Q8×C37—21no—
73C4×Q8×C37D411yescharacteristic
74C4×Q8×C37D411yescharacteristic
75C4×Q8×C37C2311yescharacteristic
76C4×Q8×C37C2311yescharacteristic
77C4×D4×C37—21no—
78C4×D4×C37—21no—
79C2×C4⋊C4×C37—21no—
80C2×C4⋊C4×C37D411yescharacteristic
81C2×C42×C37—21no—
82C2×C42×C37C2311yescharacteristic
83#107×C37—21no—
84#107×C37—21no—
85C4⋊C8×C37—22no—
86C4⋊C8×C37—22no—
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—22no—
96#102×C37—22no—
97#102×C37—22no—
98#102×C37—22no—
99#102×C37—21no—
100#102×C37—21no—
101C22⋊C8×C37—21no—
102C22⋊C8×C37—21no—
103C22⋊C8×C37D411yescharacteristic
104C22⋊C8×C37D411yescharacteristic
105#97×C37—22no—
106#97×C37—21no—
107#97×C37—21no—
108C4×C8×C37—22no—
109C4×C8×C37C2312yes—
110C24×C37—41no—
111#41×C37—82no—
112C2×Q8×C37—21no—
113C2×Q8×C37—22no—
114C2×Q8×C37—21no—
115C2×Q8×C37—41no—
116C2×Q8×C37C2×D411yescharacteristic
117C2×Q8×C37C2×D411yescharacteristic
118C2×D4×C37—21no—
119C2×D4×C37—22no—
120C2×D4×C37—22no—
121C2×D4×C37—21no—
122C2×D4×C37—21no—
123C2×D4×C37—22no—
124C2×D4×C37—42no—
125C2×D4×C37—42no—
126C2×D4×C37—41no—
127C2×D4×C37—41no—
128C2×D4×C37—41no—
129C2×D4×C37—41no—
130C2×D4×C37—82no—
131C2×D4×C37—82no—
132C22×C4×C37—21no—
133C22×C4×C37—21no—
134C22×C4×C37—41no—
135C22×C4×C37C2×D411yescharacteristic
136C22×C4×C37C2×D411yescharacteristic
137C22×C4×C37#4111yescharacteristic
138SD16×C37—42no—
139SD16×C37—44no—
140SD16×C37—42no—
141SD16×C37—44no—
142D8×C37—82no—
143D8×C37—82no—
144C2×C8×C37—22no—
145C2×C8×C37—21no—
146C2×C8×C37—21no—
147C2×C8×C37—22no—
148C2×C8×C37—42no—
149C2×C8×C37C2×D412yes—
150C2×C8×C37C2×D412yes—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—21no—
153C4⋊C4×C37—21no—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—21no—
156C4⋊C4×C37—21no—
157C4⋊C4×C37—21no—
158C4⋊C4×C37C2×D411yescharacteristic
159C4⋊C4×C37C2×D411yescharacteristic
160C22⋊C4×C37—41no—
161C22⋊C4×C37—41no—
162C42×C37—21no—
163C42×C37—21no—
164C42×C37—21no—
165C42×C37—21no—
166C42×C37C2×D411yescharacteristic
167C42×C37C2×D411yescharacteristic
168C42×C37#4111yescharacteristic
169C42×C37C2411yescharacteristic
170C23×C37—41no—
171C23×C37—42no—
172C23×C37—82no—
173C23×C37—82no—
174C23×C37—82no—
175C23×C37#12111yescharacteristic
176Q8×C37—21no—
177Q8×C37—21no—
178Q8×C37—21no—
179Q8×C37—42no—
180Q8×C37—81no—
181Q8×C37AGL(1,ℤ/8)12yes—
182D4×C37—42no—
183D4×C37—41no—
184D4×C37—41no—
185D4×C37—42no—
186D4×C37—42no—
187D4×C37—42no—
188D4×C37—42no—
189D4×C37—82no—
190D4×C37—81no—
191D4×C37—82no—
192D4×C37—82no—
193D4×C37—82no—
194D4×C37—82no—
195C2×C4×C37—21no—
196C2×C4×C37—22no—
197C2×C4×C37—21no—
198C2×C4×C37—21no—
199C2×C4×C37—22no—
200C2×C4×C37—21no—
201C2×C4×C37—21no—
202C2×C4×C37—21no—
203C2×C4×C37—42no—
204C2×C4×C37—42no—
205C2×C4×C37—41no—
206C2×C4×C37—82no—
207C2×C4×C37#12111yescharacteristic
208C2×C4×C37#12111yescharacteristic
209C2×C4×C37#12111yescharacteristic
210C2×C4×C37C22×D411yescharacteristic
211C2×C4×C37C22×D411yescharacteristic
212C2×C4×C37C2×#4111yescharacteristic
213C8×C37—22no—
214C8×C37—22no—
215C8×C37—42no—
216C8×C37—41no—
217C8×C37—41no—
218C8×C37—42no—
219#19470C3711yesmaximal, characteristic, direct product factor, Sylow
220C22×C37—21no—
221C22×C37—21no—
222C22×C37—82no—
223C22×C37—81no—
224C22×C37—82no—
225C22×C37—81no—
226C22×C37—81no—
227C22×C37—82no—
228C22×C37—164no—
229C22×C37#47212yes—
230C22×C37C2×#12111yescharacteristic
231C4×C37—21no—
232C4×C37—21no—
233C4×C37—22no—
234C4×C37—21no—
235C4×C37—21no—
236C4×C37—41no—
237C4×C37—41no—
238C4×C37—41no—
239C4×C37—81no—
240C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
241C4×C37#57511yescharacteristic
242C4×C37#57712yes—
243#3205C2×C3711yescharacteristic
244#3112C2×C3711yescharacteristic, complemented
245C2×#460C2×C3711yescharacteristic, complemented
246#2984C2×C3711yescharacteristic, complemented
247#1698C2×C3712yescomplemented
248#1688C2×C3712yescomplemented
249#1678C2×C3712yescomplemented
250#1668C2×C3712yescomplemented
251#1573C2×C3711yescharacteristic, complemented
252#1555C2×C3711yescharacteristic, complemented
253#1551C2×C3711yescharacteristic, complemented
254C2×C37—22no—
255C2×C37—161no—
256C2×C37—162no—
257C2×C37#304311yescharacteristic
258C2×C37#305511yescharacteristic
259C2×C37C2×#47211yescharacteristic
260C22×SD16—21no—
261#532C22×C3711yescharacteristic
262C2×#127C22×C3711yescharacteristic
263C2×C4×Q8C22×C3711yescharacteristic
264#493C22×C3712yes—
265#486C22×C3712yes—
266#480—21no—
267#477C22×C3711yescharacteristic, complemented
268#477C22×C3711yescharacteristic, complemented
269#460—21no—
270#460—21no—
271#460C22×C3712yes—
272#460C22×C3712yes—
273#460C22×C3711yescharacteristic, complemented
274#460C22×C3711yescharacteristic, complemented
275#459—22no—
276#448—21no—
277#447—21no—
278#447—21no—
279#446—22no—
280#446C22×C3712yescomplemented
281C8×Q8C22×C3712yescomplemented
282#440—21no—
283#440—21no—
284#432—21no—
285#432C22×C3711yescharacteristic
286#432C22×C3711yescharacteristic
287#431—21no—
288#431C22×C3711yescharacteristic
289C2×C4⋊C8C22×C3711yescharacteristic
290C2×#102—21no—
291#335C22×C3712yescomplemented
292#334C22×C3712yescomplemented
293#333C22×C3712yescomplemented
294#331C22×C3712yes—
295#331C22×C3712yes—
296#331C22×C3712yescomplemented
297C37#1947011yescharacteristic, direct product factor, Sylow
298C2×#41—21no—
299C22×Q8D4×C3711yescharacteristic
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303C2×SD16—22no—
304C2×SD16—22no—
305C2×SD16—21no—
306C2×SD16—21no—
307C2×SD16—44no—
308C2×D8—22no—
309C2×D8—22no—
310C22×C8—21no—
311C4⋊Q8C23×C3711yescharacteristic
312#127—21no—
313#127—21no—
314#127—21no—
315#127C23×C3712yes—
316#127C23×C3711yescharacteristic
317#124—21no—
318#121—21no—
319#121—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8D4×C3711yescharacteristic
323C4×Q8D4×C3711yescharacteristic
324C4×Q8C23×C3711yescharacteristic
325C4×Q8C23×C3711yescharacteristic
326C4×D4—21no—
327C4×D4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4D4×C3711yescharacteristic
330C2×C42—21no—
331C2×C42C23×C3711yescharacteristic
332#107—21no—
333#107—21no—
334C4⋊C8—22no—
335C4⋊C8—22no—
336C4⋊C8—21no—
337C4⋊C8D4×C3712yes—
338C4⋊C8C23×C3712yes—
339C4⋊C8C23×C3711yescharacteristic
340C4⋊C8C23×C3711yescharacteristic
341C4⋊C8C23×C3712yes—
342#103—21no—
343#103—21no—
344#102—22no—
345#102—22no—
346#102—22no—
347#102—22no—
348#102—21no—
349#102—21no—
350C22⋊C8—21no—
351C22⋊C8—21no—
352C22⋊C8D4×C3711yescharacteristic
353C22⋊C8D4×C3711yescharacteristic
354#97—22no—
355#97—21no—
356#97—21no—
357C4×C8—22no—
358C4×C8C23×C3712yes—
359C24—41no—
360#41—82no—
361C2×Q8—21no—
362C2×Q8—22no—
363C2×Q8—21no—
364C2×Q8—41no—
365C2×Q8C2×D4×C3711yescharacteristic
366C2×Q8C2×D4×C3711yescharacteristic
367C2×D4—21no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—42no—
374C2×D4—42no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—82no—
380C2×D4—82no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—41no—
384C22×C4C2×D4×C3711yescharacteristic
385C22×C4C2×D4×C3711yescharacteristic
386C22×C4#41×C3711yescharacteristic
387SD16—42no—
388SD16—44no—
389SD16—42no—
390SD16—44no—
391D8—82no—
392D8—82no—
393C2×C8—22no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—22no—
397C2×C8—42no—
398C2×C8C2×D4×C3712yes—
399C2×C8C2×D4×C3712yes—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4C2×D4×C3711yescharacteristic
408C4⋊C4C2×D4×C3711yescharacteristic
409C22⋊C4—41no—
410C22⋊C4—41no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42C2×D4×C3711yescharacteristic
416C42C2×D4×C3711yescharacteristic
417C42#41×C3711yescharacteristic
418C42C24×C3711yescharacteristic
419C23—41no—
420C23—42no—
421C23—82no—
422C23—82no—
423C23—82no—
424C23#121×C3711yescharacteristic
425Q8—21no—
426Q8—21no—
427Q8—21no—
428Q8—42no—
429Q8—81no—
430Q8AGL(1,ℤ/8)×C3712yes—
431D4—42no—
432D4—41no—
433D4—41no—
434D4—42no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—82no—
439D4—81no—
440D4—82no—
441D4—82no—
442D4—82no—
443D4—82no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—82no—
456C2×C4#121×C3711yescharacteristic
457C2×C4#121×C3711yescharacteristic
458C2×C4#121×C3711yescharacteristic
459C2×C4C22×D4×C3711yescharacteristic
460C2×C4C22×D4×C3711yescharacteristic
461C2×C4C2×#41×C3711yescharacteristic
462C8—22no—
463C8—22no—
464C8—42no—
465C8—41no—
466C8—41no—
467C8—42no—
468C22—21no—
469C22—21no—
470C22—82no—
471C22—81no—
472C22—82no—
473C22—81no—
474C22—81no—
475C22—82no—
476C22—164no—
477C22C37×#47212yes—
478C22C2×#121×C3711yescharacteristic
479C4—21no—
480C4—21no—
481C4—22no—
482C4—21no—
483C4—21no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—81no—
488C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
489C4C37×#57511yescharacteristic
490C4C37×#57712yes—
491C2—22no—
492C2—162no—
493C2—161no—
494C2C37×#304311yescharacteristic
495C2C37×#305511yescharacteristic
496C2C2×C37×#47211yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3205C2
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×#3112C2semidirect
3. C2×C37×#460C2semidirect
4. C37×#2984C2semidirect
5. C37×#1698C2semidirect
6. C37×#1688C2semidirect
7. C37×#1678C2semidirect
8. C37×#1668C2semidirect
9. C37×#1573C2semidirect
10. C37×#1555C2semidirect
11. C37×#1551C2semidirect
19. C37×#477C22semidirect
20. C37×#477C22semidirect
25. C37×#460C22semidirect
26. C37×#460C22semidirect
32. C37×#446C22semidirect
33. C8×Q8×C37C22semidirect
43. C37×#335C22semidirect
44. C37×#334C22semidirect
45. C37×#333C22semidirect
48. C37×#331C22semidirect
219. #19470C37direct (N × H)
244. #3112C2×C37semidirect
245. C2×#460C2×C37semidirect
246. #2984C2×C37semidirect
247. #1698C2×C37semidirect
248. #1688C2×C37semidirect
249. #1678C2×C37semidirect
250. #1668C2×C37semidirect
251. #1573C2×C37semidirect
252. #1555C2×C37semidirect
253. #1551C2×C37semidirect
267. #477C22×C37semidirect
268. #477C22×C37semidirect
273. #460C22×C37semidirect
274. #460C22×C37semidirect
280. #446C22×C37semidirect
281. C8×Q8C22×C37semidirect
291. #335C22×C37semidirect
292. #334C22×C37semidirect
293. #333C22×C37semidirect
296. #331C22×C37semidirect
297. C37#19470direct (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×#31122
C2×C37×#4602
C37×#29842
C37×#16982
C37×#16882
C37×#16782
C37×#16682
C37×#15732
C37×#15552
C37×#15512
#1947037