Finite Group Databasebeta

← C37×#19483 #22640736

Subgroups — C37×#19483 #22640736

Order 9472.

688 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3208C211yesmaximal, characteristic, complemented
2C37×#3107C211yesmaximal, characteristic, complemented
3C37×#3038C211yesmaximal, characteristic
4C37×#2990C211yesmaximal, characteristic, complemented
5C37×#1702C212yesmaximal, complemented
6C37×#1686C212yesmaximal, complemented
7C37×#1681C212yesmaximal, complemented
8C37×#1665C212yesmaximal, complemented
9C37×#1574C211yesmaximal, characteristic, complemented
10C37×#1561C211yesmaximal, characteristic, complemented
11C37×#1545C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C37—21no—
13C37×#533C2211yescharacteristic
14C2×#127×C37C2211yescharacteristic
15C4×#41×C37C2211yescharacteristic
16C37×#492C2212yes—
17C37×#486C2212yes—
18C37×#485—21no—
19C37×#475C2211yescharacteristic, complemented
20C37×#474C2211yescharacteristic, complemented
21C37×#462C2211yescharacteristic, complemented
22C37×#461C2211yescharacteristic, complemented
23C37×#460—21no—
24C37×#460—21no—
25C37×#460—21no—
26C37×#460C2212yes—
27C37×#459—21no—
28C37×#459C2212yes—
29C37×#452—21no—
30C37×#450—22no—
31C37×#446C2212yescomplemented
32C4×Q16×C37—21no—
33C4×SD16×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×#332C2212yescomplemented
46C37×#332C2212yescomplemented
47C37×#331C2212yes—
48C37×#331C2212yes—
49C2×#41×C37D411yescharacteristic
50C22×D4×C37—21no—
51C22×D4×C37—21no—
52C22×D4×C37—21no—
53AGL(1,ℤ/8)×C37—44no—
54C2×Q16×C37—21no—
55C2×SD16×C37—22no—
56C2×SD16×C37—21no—
57C2×SD16×C37—22no—
58C2×SD16×C37—22no—
59C2×D8×C37—22no—
60C2×M16×C37—21no—
61C2×M16×C37—21no—
62C22×C8×C37—22no—
63C4⋊Q8×C37C2311yescharacteristic
64C4⋊Q8×C37C2311yescharacteristic
65#127×C37—21no—
66#127×C37—21no—
67#127×C37—21no—
68#127×C37C2312yes—
69#125×C37—21no—
70C22⋊Q8×C37—21no—
71C22⋊Q8×C37—21no—
72C4×Q8×C37—21no—
73C4×Q8×C37—21no—
74C4×Q8×C37D411yescharacteristic
75C4×Q8×C37C2311yescharacteristic
76C4×D4×C37—21no—
77C4×D4×C37—21no—
78C4×D4×C37D411yescharacteristic
79C4×D4×C37C2311yescharacteristic
80#117×C37—21no—
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#103×C37—21no—
98#103×C37—21no—
99#102×C37—21no—
100#102×C37—22no—
101#102×C37—22no—
102#102×C37—22no—
103#102×C37—22no—
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—
113C2×Q8×C37—21no—
114C2×Q8×C37—21no—
115C2×Q8×C37C2×D411yescharacteristic
116C2×D4×C37—21no—
117C2×D4×C37—22no—
118C2×D4×C37—22no—
119C2×D4×C37—22no—
120C2×D4×C37—42no—
121C2×D4×C37—42no—
122C2×D4×C37—41no—
123C2×D4×C37—41no—
124C2×D4×C37—41no—
125C2×D4×C37—81no—
126C2×D4×C37—81no—
127C2×D4×C37—82no—
128C2×D4×C37C2×D411yescharacteristic
129C22×C4×C37—21no—
130C22×C4×C37—21no—
131C22×C4×C37—21no—
132C22×C4×C37C2×D411yescharacteristic
133C22×C4×C37C2×D411yescharacteristic
134C22×C4×C37#4111yescharacteristic
135Q16×C37—42no—
136SD16×C37—44no—
137SD16×C37—42no—
138SD16×C37—82no—
139SD16×C37—82no—
140D8×C37—44no—
141M16×C37—42no—
142M16×C37—81no—
143C2×C8×C37—21no—
144C2×C8×C37—21no—
145C2×C8×C37—22no—
146C2×C8×C37—22no—
147C2×C8×C37—82no—
148C2×C8×C37C2×D412yes—
149C2×C8×C37C2×D412yes—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—21no—
153C4⋊C4×C37—21no—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—21no—
156C4⋊C4×C37—41no—
157C4⋊C4×C37—41no—
158C4⋊C4×C37C2×D411yescharacteristic
159C4⋊C4×C37C2×D411yescharacteristic
160C22⋊C4×C37—21no—
161C22⋊C4×C37—21no—
162C22⋊C4×C37—21no—
163C22⋊C4×C37—41no—
164C42×C37—21no—
165C42×C37—21no—
166C42×C37—21no—
167C42×C37—41no—
168C42×C37C2×D411yescharacteristic
169C42×C37C2×D411yescharacteristic
170C42×C37#4111yescharacteristic
171C42×C37C2411yescharacteristic
172C23×C37—21no—
173C23×C37—42no—
174C23×C37—82no—
175C23×C37—82no—
176C23×C37—82no—
177C23×C37#12111yescharacteristic
178Q8×C37—21no—
179Q8×C37—21no—
180Q8×C37—41no—
181Q8×C37—41no—
182Q8×C37—41no—
183Q8×C37—41no—
184D4×C37—21no—
185D4×C37—42no—
186D4×C37—42no—
187D4×C37—42no—
188D4×C37—42no—
189D4×C37—42no—
190D4×C37—82no—
191D4×C37—82no—
192D4×C37—82no—
193D4×C37—82no—
194D4×C37AGL(1,ℤ/8)12yes—
195C2×C4×C37—21no—
196C2×C4×C37—21no—
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—41no—
205C2×C4×C37—41no—
206C2×C4×C37—42no—
207C2×C4×C37—41no—
208C2×C4×C37—41no—
209C2×C4×C37#12111yescharacteristic
210C2×C4×C37#12111yescharacteristic
211C2×C4×C37#12111yescharacteristic
212C2×C4×C37C22×D411yescharacteristic
213C2×C4×C37C22×D411yescharacteristic
214C2×C4×C37C2×#4111yescharacteristic
215C8×C37—22no—
216C8×C37—22no—
217C8×C37—42no—
218C8×C37—41no—
219C8×C37—41no—
220C8×C37—42no—
221#19483C3711yesmaximal, characteristic, direct product factor, Sylow
222C22×C37—21no—
223C22×C37—21no—
224C22×C37—22no—
225C22×C37—21no—
226C22×C37—41no—
227C22×C37—41no—
228C22×C37—82no—
229C22×C37—82no—
230C22×C37—82no—
231C22×C37—164no—
232C22×C37C2×#12111yescharacteristic
233C4×C37—21no—
234C4×C37—21no—
235C4×C37—21no—
236C4×C37—41no—
237C4×C37—41no—
238C4×C37—41no—
239C4×C37—81no—
240C4×C37—81no—
241C4×C37#47112yes—
242C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
243C4×C37#57511yescharacteristic
244C4×C37#57611yescharacteristic
245C4×C37#57711yescharacteristic
246#3208C2×C3711yescharacteristic, complemented
247#3107C2×C3711yescharacteristic, complemented
248#3038C2×C3711yescharacteristic
249#2990C2×C3711yescharacteristic, complemented
250#1702C2×C3712yescomplemented
251#1686C2×C3712yescomplemented
252#1681C2×C3712yescomplemented
253#1665C2×C3712yescomplemented
254#1574C2×C3711yescharacteristic, complemented
255#1561C2×C3711yescharacteristic, complemented
256#1545C2×C3711yescharacteristic, complemented
257C2×C37—41no—
258C2×C37—42no—
259C2×C37—162no—
260C2×C37#304511yescharacteristic
261C2×C37#305511yescharacteristic
262C2×C37C2×#47111yescharacteristic
263C2×AGL(1,ℤ/8)—21no—
264#533C22×C3711yescharacteristic
265C2×#127C22×C3711yescharacteristic
266C4×#41C22×C3711yescharacteristic
267#492C22×C3712yes—
268#486C22×C3712yes—
269#485—21no—
270#475C22×C3711yescharacteristic, complemented
271#474C22×C3711yescharacteristic, complemented
272#462C22×C3711yescharacteristic, complemented
273#461C22×C3711yescharacteristic, complemented
274#460—21no—
275#460—21no—
276#460—21no—
277#460C22×C3712yes—
278#459—21no—
279#459C22×C3712yes—
280#452—21no—
281#450—22no—
282#446C22×C3712yescomplemented
283C4×Q16—21no—
284C4×SD16—21no—
285#435—22no—
286C8×D4C22×C3712yescomplemented
287#432—21no—
288#431C22×C3711yescharacteristic
289#431C22×C3711yescharacteristic
290#423C22×C3711yescharacteristic
291#423C22×C3711yescharacteristic
292C2×C4⋊C8—21no—
293#418—21no—
294#335C22×C3712yescomplemented
295#334C22×C3712yescomplemented
296#332C22×C3712yescomplemented
297#332C22×C3712yescomplemented
298#331C22×C3712yes—
299#331C22×C3712yes—
300C37#1948311yescharacteristic, direct product factor, Sylow
301C2×#41D4×C3711yescharacteristic
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305AGL(1,ℤ/8)—44no—
306C2×Q16—21no—
307C2×SD16—22no—
308C2×SD16—21no—
309C2×SD16—22no—
310C2×SD16—22no—
311C2×D8—22no—
312C2×M16—21no—
313C2×M16—21no—
314C22×C8—22no—
315C4⋊Q8C23×C3711yescharacteristic
316C4⋊Q8C23×C3711yescharacteristic
317#127—21no—
318#127—21no—
319#127—21no—
320#127C23×C3712yes—
321#125—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8D4×C3711yescharacteristic
327C4×Q8C23×C3711yescharacteristic
328C4×D4—21no—
329C4×D4—21no—
330C4×D4D4×C3711yescharacteristic
331C4×D4C23×C3711yescharacteristic
332#117—21no—
333#117—21no—
334#117D4×C3711yescharacteristic
335C2×C42—21no—
336C2×C42C23×C3711yescharacteristic
337#107—21no—
338#106—21no—
339C4⋊C8—22no—
340C4⋊C8—21no—
341C4⋊C8—21no—
342C4⋊C8D4×C3711yescharacteristic
343C4⋊C8D4×C3711yescharacteristic
344C4⋊C8C23×C3712yes—
345C4⋊C8C23×C3711yescharacteristic
346C4⋊C8C23×C3711yescharacteristic
347C4⋊C8C23×C3712yes—
348#103—21no—
349#103—21no—
350#103—21no—
351#102—21no—
352#102—22no—
353#102—22no—
354#102—22no—
355#102—22no—
356C22⋊C8—21no—
357C22⋊C8—22no—
358C22⋊C8D4×C3712yes—
359#97—22no—
360C4×C8—21no—
361C4×C8C23×C3712yes—
362C24—41no—
363#41—22no—
364#41—41no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8C2×D4×C3711yescharacteristic
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—42no—
373C2×D4—42no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—81no—
378C2×D4—81no—
379C2×D4—82no—
380C2×D4C2×D4×C3711yescharacteristic
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4C2×D4×C3711yescharacteristic
385C22×C4C2×D4×C3711yescharacteristic
386C22×C4#41×C3711yescharacteristic
387Q16—42no—
388SD16—44no—
389SD16—42no—
390SD16—82no—
391SD16—82no—
392D8—44no—
393M16—42no—
394M16—81no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—22no—
398C2×C8—22no—
399C2×C8—82no—
400C2×C8C2×D4×C3712yes—
401C2×C8C2×D4×C3712yes—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4C2×D4×C3711yescharacteristic
411C4⋊C4C2×D4×C3711yescharacteristic
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—21no—
415C22⋊C4—41no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42—41no—
420C42C2×D4×C3711yescharacteristic
421C42C2×D4×C3711yescharacteristic
422C42#41×C3711yescharacteristic
423C42C24×C3711yescharacteristic
424C23—21no—
425C23—42no—
426C23—82no—
427C23—82no—
428C23—82no—
429C23#121×C3711yescharacteristic
430Q8—21no—
431Q8—21no—
432Q8—41no—
433Q8—41no—
434Q8—41no—
435Q8—41no—
436D4—21no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4—42no—
441D4—42no—
442D4—82no—
443D4—82no—
444D4—82no—
445D4—82no—
446D4AGL(1,ℤ/8)×C3712yes—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4#121×C3711yescharacteristic
462C2×C4#121×C3711yescharacteristic
463C2×C4#121×C3711yescharacteristic
464C2×C4C22×D4×C3711yescharacteristic
465C2×C4C22×D4×C3711yescharacteristic
466C2×C4C2×#41×C3711yescharacteristic
467C8—22no—
468C8—22no—
469C8—42no—
470C8—41no—
471C8—41no—
472C8—42no—
473C22—21no—
474C22—21no—
475C22—22no—
476C22—21no—
477C22—41no—
478C22—41no—
479C22—82no—
480C22—82no—
481C22—82no—
482C22—164no—
483C22C2×#121×C3711yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—41no—
488C4—41no—
489C4—41no—
490C4—81no—
491C4—81no—
492C4C37×#47112yes—
493C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
494C4C37×#57511yescharacteristic
495C4C37×#57611yescharacteristic
496C4C37×#57711yescharacteristic
497C2—41no—
498C2—42no—
499C2—162no—
500C2C37×#304511yescharacteristic
501C2C37×#305511yescharacteristic
502C2C2×C37×#47111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3038C2
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×#3107C2semidirect
4. C37×#2990C2semidirect
5. C37×#1702C2semidirect
6. C37×#1686C2semidirect
7. C37×#1681C2semidirect
8. C37×#1665C2semidirect
9. C37×#1574C2semidirect
10. C37×#1561C2semidirect
11. C37×#1545C2semidirect
19. C37×#475C22semidirect
20. C37×#474C22semidirect
21. C37×#462C22semidirect
22. C37×#461C22semidirect
31. C37×#446C22semidirect
35. C8×D4×C37C22semidirect
43. C37×#335C22semidirect
44. C37×#334C22semidirect
45. C37×#332C22semidirect
46. C37×#332C22semidirect
221. #19483C37direct (N × H)
246. #3208C2×C37semidirect
247. #3107C2×C37semidirect
249. #2990C2×C37semidirect
250. #1702C2×C37semidirect
251. #1686C2×C37semidirect
252. #1681C2×C37semidirect
253. #1665C2×C37semidirect
254. #1574C2×C37semidirect
255. #1561C2×C37semidirect
256. #1545C2×C37semidirect
270. #475C22×C37semidirect
271. #474C22×C37semidirect
272. #462C22×C37semidirect
273. #461C22×C37semidirect
282. #446C22×C37semidirect
286. C8×D4C22×C37semidirect
294. #335C22×C37semidirect
295. #334C22×C37semidirect
296. #332C22×C37semidirect
297. #332C22×C37semidirect
300. C37#19483direct (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×#31072
C37×#30382
C37×#29902
C37×#17022
C37×#16862
C37×#16812
C37×#16652
C37×#15742
C37×#15612
C37×#15452
#1948337