Finite Group Databasebeta

← C37×#19465 #22640718

Subgroups — C37×#19465 #22640718

Order 9472.

648 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3226C211yesmaximal, characteristic, complemented
2C37×#3109C211yesmaximal, characteristic
3C2×C37×#476C211yesmaximal, characteristic, complemented
4C37×#2974C211yesmaximal, characteristic, complemented
5C37×#1697C212yesmaximal, complemented
6C37×#1695C212yesmaximal, complemented
7C37×#1677C212yesmaximal, complemented
8C37×#1675C212yesmaximal, complemented
9C37×#1573C211yesmaximal, characteristic, complemented
10C37×#1558C211yesmaximal, characteristic, complemented
11C37×#1551C211yesmaximal, characteristic, complemented
12C37×#532C2211yescharacteristic
13C2×C4⋊Q8×C37C2211yescharacteristic
14C2×C4×D4×C37C2211yescharacteristic
15C37×#500C2212yescomplemented
16C37×#486C2212yescomplemented
17C37×#481—21no—
18C37×#480—21no—
19C37×#480—21no—
20C37×#476—21no—
21C37×#476—21no—
22C37×#476C2211yescharacteristic
23C37×#476C2212yes—
24C37×#476C2211yescharacteristic
25C37×#476C2212yes—
26C37×#474—22no—
27C37×#459C2211yescharacteristic
28C37×#459C2211yescharacteristic
29C37×#447—21no—
30C37×#442—21no—
31C37×#442—21no—
32C37×#436C2212yes—
33C37×#435—22no—
34C8×D4×C37C2212yes—
35C37×#432C2211yescharacteristic
36C37×#432C2211yescharacteristic
37C37×#431C2211yescharacteristic
38C2×#106×C37—21no—
39C2×C4⋊C8×C37C2211yescharacteristic
40C2×#102×C37—21no—
41C37×#407—21no—
42C2×C22⋊C8×C37—21no—
43C37×#335C2212yescomplemented
44C37×#334C2212yescomplemented
45C37×#333C2212yescomplemented
46C37×#333C2212yescomplemented
47C37×#333C2212yescomplemented
48C37×#331C2212yescomplemented
49C2×#41×C37—21no—
50C22×Q8×C37—21no—
51C22×D4×C37D411yescharacteristic
52C23×C4×C37—21no—
53C2×D8×C37—21no—
54C2×D8×C37—21no—
55C2×M16×C37—22no—
56C22×C8×C37—21no—
57C22×C8×C37—22no—
58C4⋊Q8×C37—21no—
59C4⋊Q8×C37—21no—
60C4⋊Q8×C37—21no—
61C4⋊Q8×C37C2312yes—
62C4⋊Q8×C37C2311yescharacteristic
63#127×C37C2311yescharacteristic
64#124×C37—21no—
65#121×C37—21no—
66#121×C37—21no—
67C4×D4×C37—21no—
68C4×D4×C37—21no—
69C4×D4×C37—21no—
70C4×D4×C37—21no—
71C4×D4×C37D411yescharacteristic
72C4×D4×C37D411yescharacteristic
73C4×D4×C37C2311yescharacteristic
74C4×D4×C37C2311yescharacteristic
75C2×C4⋊C4×C37—21no—
76C2×C4⋊C4×C37—21no—
77C2×C4⋊C4×C37D411yescharacteristic
78C2×C22⋊C4×C37—21no—
79C2×C42×C37C2311yescharacteristic
80#107×C37—22no—
81#107×C37—22no—
82#106×C37—22no—
83#106×C37—22no—
84#106×C37—21no—
85#106×C37—21no—
86C4⋊C8×C37—21no—
87C4⋊C8×C37D412yes—
88C4⋊C8×C37C2312yes—
89C4⋊C8×C37C2312yes—
90C4⋊C8×C37C2311yescharacteristic
91C4⋊C8×C37C2311yescharacteristic
92#102×C37—22no—
93#102×C37—22no—
94#102×C37—21no—
95#102×C37—21no—
96#102×C37—22no—
97#102×C37—22no—
98#102×C37—21no—
99#102×C37—21no—
100C22⋊C8×C37—21no—
101C22⋊C8×C37—21no—
102C22⋊C8×C37—22no—
103C22⋊C8×C37—22no—
104C22⋊C8×C37D411yescharacteristic
105C22⋊C8×C37D411yescharacteristic
106#97×C37—21no—
107#97×C37—21no—
108C4×C8×C37C2312yes—
109C24×C37—21no—
110#41×C37—82no—
111C2×Q8×C37—21no—
112C2×Q8×C37—22no—
113C2×Q8×C37—41no—
114C2×Q8×C37—82no—
115C2×D4×C37—22no—
116C2×D4×C37—21no—
117C2×D4×C37—21no—
118C2×D4×C37—21no—
119C2×D4×C37—21no—
120C2×D4×C37—41no—
121C2×D4×C37—41no—
122C2×D4×C37C2×D411yescharacteristic
123C2×D4×C37C2×D411yescharacteristic
124C22×C4×C37—21no—
125C22×C4×C37—21no—
126C22×C4×C37—21no—
127C22×C4×C37—21no—
128C22×C4×C37—21no—
129C22×C4×C37—41no—
130C22×C4×C37—41no—
131C22×C4×C37—82no—
132C22×C4×C37C2×D411yescharacteristic
133C22×C4×C37C2×D411yescharacteristic
134C22×C4×C37#4111yescharacteristic
135D8×C37—42no—
136D8×C37—42no—
137M16×C37—82no—
138C2×C8×C37—22no—
139C2×C8×C37—21no—
140C2×C8×C37—21no—
141C2×C8×C37—22no—
142C2×C8×C37—42no—
143C2×C8×C37—82no—
144C2×C8×C37C2×D412yes—
145C2×C8×C37C2×D412yes—
146C4⋊C4×C37—21no—
147C4⋊C4×C37—22no—
148C4⋊C4×C37—21no—
149C4⋊C4×C37—22no—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—41no—
152C4⋊C4×C37—41no—
153C4⋊C4×C37C2×D411yescharacteristic
154C4⋊C4×C37C2×D411yescharacteristic
155C22⋊C4×C37—21no—
156C22⋊C4×C37—21no—
157C22⋊C4×C37—21no—
158C22⋊C4×C37—21no—
159C22⋊C4×C37—41no—
160C22⋊C4×C37—41no—
161C42×C37C2×D411yescharacteristic
162C42×C37C2×D411yescharacteristic
163C42×C37#4111yescharacteristic
164C42×C37C2411yescharacteristic
165C23×C37—21no—
166C23×C37—21no—
167C23×C37—42no—
168C23×C37—42no—
169C23×C37—41no—
170C23×C37—81no—
171C23×C37#12111yescharacteristic
172Q8×C37—82no—
173Q8×C37—81no—
174Q8×C37—82no—
175D4×C37—21no—
176D4×C37—21no—
177D4×C37—21no—
178D4×C37—42no—
179D4×C37—41no—
180D4×C37—41no—
181D4×C37—42no—
182D4×C37—81no—
183D4×C37—82no—
184D4×C37#13712yes—
185C2×C4×C37—22no—
186C2×C4×C37—21no—
187C2×C4×C37—21no—
188C2×C4×C37—22no—
189C2×C4×C37—21no—
190C2×C4×C37—21no—
191C2×C4×C37—42no—
192C2×C4×C37—42no—
193C2×C4×C37—41no—
194C2×C4×C37—42no—
195C2×C4×C37—81no—
196C2×C4×C37—81no—
197C2×C4×C37—82no—
198C2×C4×C37—81no—
199C2×C4×C37—82no—
200C2×C4×C37#12111yescharacteristic
201C2×C4×C37#12111yescharacteristic
202C2×C4×C37#12111yescharacteristic
203C2×C4×C37C22×D411yescharacteristic
204C2×C4×C37C22×D411yescharacteristic
205C2×C4×C37C2×#4111yescharacteristic
206C8×C37—22no—
207C8×C37—22no—
208C8×C37—41no—
209C8×C37—42no—
210C8×C37—41no—
211C8×C37—42no—
212#19465C3711yesmaximal, characteristic, direct product factor, Sylow
213C22×C37—21no—
214C22×C37—21no—
215C22×C37—22no—
216C22×C37—41no—
217C22×C37—41no—
218C22×C37—41no—
219C22×C37—41no—
220C22×C37—41no—
221C22×C37—84no—
222C22×C37—81no—
223C22×C37—81no—
224C22×C37—81no—
225C22×C37#47212yes—
226C22×C37C2×#12111yescharacteristic
227C4×C37—21no—
228C4×C37—21no—
229C4×C37—21no—
230C4×C37—21no—
231C4×C37—41no—
232C4×C37—41no—
233C4×C37—81no—
234C4×C37—82no—
235C4×C37C2×#13711yescharacteristic
236C4×C37#57511yescharacteristic
237C4×C37#57712yes—
238#3226C2×C3711yescharacteristic, complemented
239#3109C2×C3711yescharacteristic
240C2×#476C2×C3711yescharacteristic, complemented
241#2974C2×C3711yescharacteristic, complemented
242#1697C2×C3712yescomplemented
243#1695C2×C3712yescomplemented
244#1677C2×C3712yescomplemented
245#1675C2×C3712yescomplemented
246#1573C2×C3711yescharacteristic, complemented
247#1558C2×C3711yescharacteristic, complemented
248#1551C2×C3711yescharacteristic, complemented
249C2×C37—22no—
250C2×C37—42no—
251C2×C37—81no—
252C2×C37—161no—
253C2×C37#304211yescharacteristic
254C2×C37#305611yescharacteristic
255C2×C37C2×#47211yescharacteristic
256#532C22×C3711yescharacteristic
257C2×C4⋊Q8C22×C3711yescharacteristic
258C2×C4×D4C22×C3711yescharacteristic
259#500C22×C3712yescomplemented
260#486C22×C3712yescomplemented
261#481—21no—
262#480—21no—
263#480—21no—
264#476—21no—
265#476—21no—
266#476C22×C3711yescharacteristic
267#476C22×C3711yescharacteristic
268#476C22×C3712yes—
269#476C22×C3712yes—
270#474—22no—
271#459C22×C3711yescharacteristic
272#459C22×C3711yescharacteristic
273#447—21no—
274#442—21no—
275#442—21no—
276#436C22×C3712yes—
277#435—22no—
278C8×D4C22×C3712yes—
279#432C22×C3711yescharacteristic
280#432C22×C3711yescharacteristic
281#431C22×C3711yescharacteristic
282C2×#106—21no—
283C2×C4⋊C8C22×C3711yescharacteristic
284C2×#102—21no—
285#407—21no—
286C2×C22⋊C8—21no—
287#335C22×C3712yescomplemented
288#334C22×C3712yescomplemented
289#333C22×C3712yescomplemented
290#333C22×C3712yescomplemented
291#333C22×C3712yescomplemented
292#331C22×C3712yescomplemented
293C37#1946511yescharacteristic, direct product factor, Sylow
294C2×#41—21no—
295C22×Q8—21no—
296C22×D4D4×C3711yescharacteristic
297C23×C4—21no—
298C2×D8—21no—
299C2×D8—21no—
300C2×M16—22no—
301C22×C8—21no—
302C22×C8—22no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8C23×C3712yes—
307C4⋊Q8C23×C3711yescharacteristic
308#127C23×C3711yescharacteristic
309#124—21no—
310#121—21no—
311#121—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4D4×C3711yescharacteristic
317C4×D4D4×C3711yescharacteristic
318C4×D4C23×C3711yescharacteristic
319C4×D4C23×C3711yescharacteristic
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4D4×C3711yescharacteristic
323C2×C22⋊C4—21no—
324C2×C42C23×C3711yescharacteristic
325#107—22no—
326#107—22no—
327#106—22no—
328#106—22no—
329#106—21no—
330#106—21no—
331C4⋊C8—21no—
332C4⋊C8D4×C3712yes—
333C4⋊C8C23×C3712yes—
334C4⋊C8C23×C3712yes—
335C4⋊C8C23×C3711yescharacteristic
336C4⋊C8C23×C3711yescharacteristic
337#102—22no—
338#102—22no—
339#102—21no—
340#102—21no—
341#102—22no—
342#102—22no—
343#102—21no—
344#102—21no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—22no—
348C22⋊C8—22no—
349C22⋊C8D4×C3711yescharacteristic
350C22⋊C8D4×C3711yescharacteristic
351#97—21no—
352#97—21no—
353C4×C8C23×C3712yes—
354C24—21no—
355#41—82no—
356C2×Q8—21no—
357C2×Q8—22no—
358C2×Q8—41no—
359C2×Q8—82no—
360C2×D4—22no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4C2×D4×C3711yescharacteristic
368C2×D4C2×D4×C3711yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—82no—
377C22×C4C2×D4×C3711yescharacteristic
378C22×C4C2×D4×C3711yescharacteristic
379C22×C4#41×C3711yescharacteristic
380D8—42no—
381D8—42no—
382M16—82no—
383C2×C8—22no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—22no—
387C2×C8—42no—
388C2×C8—82no—
389C2×C8C2×D4×C3712yes—
390C2×C8C2×D4×C3712yes—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4C2×D4×C3711yescharacteristic
399C4⋊C4C2×D4×C3711yescharacteristic
400C22⋊C4—21no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—21no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C42C2×D4×C3711yescharacteristic
407C42C2×D4×C3711yescharacteristic
408C42#41×C3711yescharacteristic
409C42C24×C3711yescharacteristic
410C23—21no—
411C23—21no—
412C23—42no—
413C23—42no—
414C23—41no—
415C23—81no—
416C23#121×C3711yescharacteristic
417Q8—82no—
418Q8—81no—
419Q8—82no—
420D4—21no—
421D4—21no—
422D4—21no—
423D4—42no—
424D4—41no—
425D4—41no—
426D4—42no—
427D4—81no—
428D4—82no—
429D4#137×C3712yes—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—82no—
443C2×C4—81no—
444C2×C4—82no—
445C2×C4#121×C3711yescharacteristic
446C2×C4#121×C3711yescharacteristic
447C2×C4#121×C3711yescharacteristic
448C2×C4C22×D4×C3711yescharacteristic
449C2×C4C22×D4×C3711yescharacteristic
450C2×C4C2×#41×C3711yescharacteristic
451C8—22no—
452C8—22no—
453C8—41no—
454C8—42no—
455C8—41no—
456C8—42no—
457C22—21no—
458C22—21no—
459C22—22no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—84no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22C37×#47212yes—
470C22C2×#121×C3711yescharacteristic
471C4—21no—
472C4—21no—
473C4—21no—
474C4—21no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—82no—
479C4C2×#137×C3711yescharacteristic
480C4C37×#57511yescharacteristic
481C4C37×#57712yes—
482C2—22no—
483C2—42no—
484C2—81no—
485C2—161no—
486C2C37×#304211yescharacteristic
487C2C37×#305611yescharacteristic
488C2C2×C37×#47211yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3109C2
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×#3226C2semidirect
3. C2×C37×#476C2semidirect
4. C37×#2974C2semidirect
5. C37×#1697C2semidirect
6. C37×#1695C2semidirect
7. C37×#1677C2semidirect
8. C37×#1675C2semidirect
9. C37×#1573C2semidirect
10. C37×#1558C2semidirect
11. C37×#1551C2semidirect
15. C37×#500C22semidirect
16. C37×#486C22semidirect
43. C37×#335C22semidirect
44. C37×#334C22semidirect
45. C37×#333C22semidirect
46. C37×#333C22semidirect
47. C37×#333C22semidirect
48. C37×#331C22semidirect
212. #19465C37direct (N × H)
238. #3226C2×C37semidirect
240. C2×#476C2×C37semidirect
241. #2974C2×C37semidirect
242. #1697C2×C37semidirect
243. #1695C2×C37semidirect
244. #1677C2×C37semidirect
245. #1675C2×C37semidirect
246. #1573C2×C37semidirect
247. #1558C2×C37semidirect
248. #1551C2×C37semidirect
259. #500C22×C37semidirect
260. #486C22×C37semidirect
287. #335C22×C37semidirect
288. #334C22×C37semidirect
289. #333C22×C37semidirect
290. #333C22×C37semidirect
291. #333C22×C37semidirect
292. #331C22×C37semidirect
293. C37#19465direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32262
C37×#31092
C2×C37×#4762
C37×#29742
C37×#16972
C37×#16952
C37×#16772
C37×#16752
C37×#15732
C37×#15582
C37×#15512
#1946537