Finite Group Databasebeta

← C37×#19489 #22640742

Subgroups — C37×#19489 #22640742

Order 9472.

646 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3227C211yesmaximal, characteristic, complemented
2C37×#3106C211yesmaximal, characteristic
3C37×#3039C211yesmaximal, characteristic, complemented
4C37×#2990C211yesmaximal, characteristic, complemented
5C37×#1702C212yesmaximal, complemented
6C37×#1692C212yesmaximal, complemented
7C37×#1681C212yesmaximal, complemented
8C37×#1671C212yesmaximal, complemented
9C37×#1574C211yesmaximal, characteristic, complemented
10C37×#1560C211yesmaximal, characteristic, complemented
11C37×#1549C211yesmaximal, characteristic, complemented
12C2×#137×C37—21no—
13C37×#532C2211yescharacteristic
14C2×C4⋊Q8×C37C2211yescharacteristic
15C4×#41×C37C2211yescharacteristic
16C37×#498C2212yes—
17C37×#486C2212yes—
18C37×#482—21no—
19C37×#481—22no—
20C37×#477C2211yescharacteristic
21C37×#476—21no—
22C37×#476—21no—
23C37×#476C2211yescharacteristic
24C37×#462—21no—
25C37×#462C2212yes—
26C37×#461—21no—
27C37×#461C2212yes—
28C37×#460C2211yescharacteristic
29C37×#459C2211yescharacteristic
30C37×#449—21no—
31C37×#446C2212yes—
32C4×SD16×C37—21no—
33C4×D8×C37—21no—
34C37×#435—22no—
35C8×D4×C37C2212yes—
36C37×#432—21no—
37C37×#431C2211yescharacteristic
38C37×#431C2211yescharacteristic
39C37×#423C2211yescharacteristic
40C37×#423C2211yescharacteristic
41C2×C4⋊C8×C37—21no—
42C37×#419—21no—
43C37×#335C2212yes—
44C37×#334C2212yes—
45C37×#333C2212yes—
46C37×#332C2212yes—
47C37×#332C2212yes—
48C37×#331C2212yes—
49C2×#41×C37—21no—
50C2×#41×C37D411yescharacteristic
51C22×Q8×C37—21no—
52#137×C37—44no—
53C2×Q16×C37—22no—
54C2×SD16×C37—21no—
55C2×SD16×C37—22no—
56C2×D8×C37—21no—
57C2×M16×C37—21no—
58C2×M16×C37—21no—
59C22×C8×C37—22no—
60C4⋊Q8×C37—21no—
61C4⋊Q8×C37—21no—
62C4⋊Q8×C37—21no—
63C4⋊Q8×C37C2312yes—
64C4⋊Q8×C37C2311yescharacteristic
65#127×C37C2311yescharacteristic
66#124×C37—21no—
67#121×C37—21no—
68#121×C37—21no—
69C4×Q8×C37D411yescharacteristic
70C4×Q8×C37C2311yescharacteristic
71C4×D4×C37—21no—
72C4×D4×C37—21no—
73C4×D4×C37—21no—
74C4×D4×C37—21no—
75C4×D4×C37D411yescharacteristic
76C4×D4×C37C2311yescharacteristic
77#117×C37—21no—
78#117×C37D411yescharacteristic
79C2×C4⋊C4×C37—21no—
80C2×C4⋊C4×C37—21no—
81C2×C42×C37—21no—
82C2×C42×C37C2311yescharacteristic
83#107×C37—21no—
84#106×C37—22no—
85#106×C37—22no—
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×C37C2312yes—
94C4⋊C8×C37C2311yescharacteristic
95C4⋊C8×C37C2311yescharacteristic
96#103×C37—21no—
97#103×C37—22no—
98#103×C37—22no—
99#102×C37—21no—
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—
110#41×C37—22no—
111#41×C37—41no—
112#41×C37—82no—
113C2×Q8×C37—22no—
114C2×Q8×C37—21no—
115C2×Q8×C37—42no—
116C2×Q8×C37—42no—
117C2×Q8×C37—41no—
118C2×Q8×C37C2×D411yescharacteristic
119C2×D4×C37—21no—
120C2×D4×C37—21no—
121C2×D4×C37—21no—
122C2×D4×C37—21no—
123C2×D4×C37—41no—
124C2×D4×C37C2×D411yescharacteristic
125C22×C4×C37—21no—
126C22×C4×C37—21no—
127C22×C4×C37—21no—
128C22×C4×C37—41no—
129C22×C4×C37—41no—
130C22×C4×C37C2×D411yescharacteristic
131C22×C4×C37C2×D411yescharacteristic
132C22×C4×C37#4111yescharacteristic
133Q16×C37—44no—
134SD16×C37—42no—
135SD16×C37—44no—
136D8×C37—42no—
137M16×C37—42no—
138M16×C37—81no—
139C2×C8×C37—21no—
140C2×C8×C37—21no—
141C2×C8×C37—22no—
142C2×C8×C37—22no—
143C2×C8×C37—82no—
144C2×C8×C37C2×D412yes—
145C2×C8×C37C2×D412yes—
146C4⋊C4×C37—21no—
147C4⋊C4×C37—21no—
148C4⋊C4×C37—22no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—22no—
152C4⋊C4×C37—41no—
153C4⋊C4×C37—41no—
154C4⋊C4×C37C2×D411yescharacteristic
155C4⋊C4×C37C2×D411yescharacteristic
156C22⋊C4×C37—21no—
157C22⋊C4×C37—21no—
158C22⋊C4×C37—21no—
159C22⋊C4×C37—41no—
160C22⋊C4×C37—41no—
161C42×C37—21no—
162C42×C37—21no—
163C42×C37—21no—
164C42×C37C2×D411yescharacteristic
165C42×C37C2×D411yescharacteristic
166C42×C37#4111yescharacteristic
167C42×C37C2411yescharacteristic
168C23×C37—21no—
169C23×C37—41no—
170C23×C37#12111yescharacteristic
171Q8×C37—21no—
172Q8×C37—21no—
173Q8×C37—42no—
174Q8×C37—42no—
175Q8×C37—81no—
176Q8×C37—82no—
177D4×C37—21no—
178D4×C37—42no—
179D4×C37—41no—
180D4×C37—41no—
181D4×C37—41no—
182D4×C37—41no—
183D4×C37—81no—
184D4×C37—82no—
185D4×C37AGL(1,ℤ/8)12yes—
186C2×C4×C37—21no—
187C2×C4×C37—21no—
188C2×C4×C37—21no—
189C2×C4×C37—21no—
190C2×C4×C37—22no—
191C2×C4×C37—21no—
192C2×C4×C37—21no—
193C2×C4×C37—21no—
194C2×C4×C37—42no—
195C2×C4×C37—41no—
196C2×C4×C37—41no—
197C2×C4×C37—42no—
198C2×C4×C37—41no—
199C2×C4×C37—42no—
200C2×C4×C37—82no—
201C2×C4×C37—82no—
202C2×C4×C37#12111yescharacteristic
203C2×C4×C37#12111yescharacteristic
204C2×C4×C37#12111yescharacteristic
205C2×C4×C37C22×D411yescharacteristic
206C2×C4×C37C22×D411yescharacteristic
207C2×C4×C37C2×#4111yescharacteristic
208C8×C37—22no—
209C8×C37—22no—
210C8×C37—42no—
211C8×C37—41no—
212C8×C37—41no—
213C8×C37—42no—
214#19489C3711yesmaximal, characteristic, direct product factor, Sylow
215C22×C37—21no—
216C22×C37—21no—
217C22×C37—22no—
218C22×C37—21no—
219C22×C37—41no—
220C22×C37—41no—
221C22×C37—81no—
222C22×C37—81no—
223C22×C37—81no—
224C22×C37C2×#12111yescharacteristic
225C4×C37—21no—
226C4×C37—21no—
227C4×C37—21no—
228C4×C37—41no—
229C4×C37—41no—
230C4×C37—41no—
231C4×C37—82no—
232C4×C37—81no—
233C4×C37#47112yes—
234C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
235C4×C37#57511yescharacteristic
236C4×C37#57711yescharacteristic
237C4×C37#57811yescharacteristic
238#3227C2×C3711yescharacteristic, complemented
239#3106C2×C3711yescharacteristic
240#3039C2×C3711yescharacteristic, complemented
241#2990C2×C3711yescharacteristic, complemented
242#1702C2×C3712yescomplemented
243#1692C2×C3712yescomplemented
244#1681C2×C3712yescomplemented
245#1671C2×C3712yescomplemented
246#1574C2×C3711yescharacteristic, complemented
247#1560C2×C3711yescharacteristic, complemented
248#1549C2×C3711yescharacteristic, complemented
249C2×C37—41no—
250C2×C37—42no—
251C2×C37—161no—
252C2×C37#304611yescharacteristic
253C2×C37#305511yescharacteristic
254C2×C37C2×#47111yescharacteristic
255C2×#137—21no—
256#532C22×C3711yescharacteristic
257C2×C4⋊Q8C22×C3711yescharacteristic
258C4×#41C22×C3711yescharacteristic
259#498C22×C3712yes—
260#486C22×C3712yes—
261#482—21no—
262#481—22no—
263#477C22×C3711yescharacteristic
264#476—21no—
265#476—21no—
266#476C22×C3711yescharacteristic
267#462—21no—
268#462C22×C3712yes—
269#461—21no—
270#461C22×C3712yes—
271#460C22×C3711yescharacteristic
272#459C22×C3711yescharacteristic
273#449—21no—
274#446C22×C3712yes—
275C4×SD16—21no—
276C4×D8—21no—
277#435—22no—
278C8×D4C22×C3712yes—
279#432—21no—
280#431C22×C3711yescharacteristic
281#431C22×C3711yescharacteristic
282#423C22×C3711yescharacteristic
283#423C22×C3711yescharacteristic
284C2×C4⋊C8—21no—
285#419—21no—
286#335C22×C3712yes—
287#334C22×C3712yes—
288#333C22×C3712yes—
289#332C22×C3712yes—
290#332C22×C3712yes—
291#331C22×C3712yes—
292C37#1948911yescharacteristic, direct product factor, Sylow
293C2×#41—21no—
294C2×#41D4×C3711yescharacteristic
295C22×Q8—21no—
296#137—44no—
297C2×Q16—22no—
298C2×SD16—21no—
299C2×SD16—22no—
300C2×D8—21no—
301C2×M16—21no—
302C2×M16—21no—
303C22×C8—22no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8C23×C3712yes—
308C4⋊Q8C23×C3711yescharacteristic
309#127C23×C3711yescharacteristic
310#124—21no—
311#121—21no—
312#121—21no—
313C4×Q8D4×C3711yescharacteristic
314C4×Q8C23×C3711yescharacteristic
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4D4×C3711yescharacteristic
320C4×D4C23×C3711yescharacteristic
321#117—21no—
322#117D4×C3711yescharacteristic
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C42—21no—
326C2×C42C23×C3711yescharacteristic
327#107—21no—
328#106—22no—
329#106—22no—
330#106—21no—
331C4⋊C8—22no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334C4⋊C8D4×C3711yescharacteristic
335C4⋊C8D4×C3711yescharacteristic
336C4⋊C8C23×C3712yes—
337C4⋊C8C23×C3712yes—
338C4⋊C8C23×C3711yescharacteristic
339C4⋊C8C23×C3711yescharacteristic
340#103—21no—
341#103—22no—
342#103—22no—
343#102—21no—
344#102—22no—
345#102—22no—
346#102—21no—
347#102—21no—
348C22⋊C8—21no—
349C22⋊C8—22no—
350C22⋊C8D4×C3712yes—
351#97—22no—
352C4×C8—21no—
353C4×C8C23×C3712yes—
354#41—22no—
355#41—41no—
356#41—82no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8—41no—
362C2×Q8C2×D4×C3711yescharacteristic
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4C2×D4×C3711yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4C2×D4×C3711yescharacteristic
375C22×C4C2×D4×C3711yescharacteristic
376C22×C4#41×C3711yescharacteristic
377Q16—44no—
378SD16—42no—
379SD16—44no—
380D8—42no—
381M16—42no—
382M16—81no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—82no—
388C2×C8C2×D4×C3712yes—
389C2×C8C2×D4×C3712yes—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
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—41no—
404C22⋊C4—41no—
405C42—21no—
406C42—21no—
407C42—21no—
408C42C2×D4×C3711yescharacteristic
409C42C2×D4×C3711yescharacteristic
410C42#41×C3711yescharacteristic
411C42C24×C3711yescharacteristic
412C23—21no—
413C23—41no—
414C23#121×C3711yescharacteristic
415Q8—21no—
416Q8—21no—
417Q8—42no—
418Q8—42no—
419Q8—81no—
420Q8—82no—
421D4—21no—
422D4—42no—
423D4—41no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—81no—
428D4—82no—
429D4AGL(1,ℤ/8)×C3712yes—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4#121×C3711yescharacteristic
447C2×C4#121×C3711yescharacteristic
448C2×C4#121×C3711yescharacteristic
449C2×C4C22×D4×C3711yescharacteristic
450C2×C4C22×D4×C3711yescharacteristic
451C2×C4C2×#41×C3711yescharacteristic
452C8—22no—
453C8—22no—
454C8—42no—
455C8—41no—
456C8—41no—
457C8—42no—
458C22—21no—
459C22—21no—
460C22—22no—
461C22—21no—
462C22—41no—
463C22—41no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22C2×#121×C3711yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—82no—
475C4—81no—
476C4C37×#47112yes—
477C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
478C4C37×#57511yescharacteristic
479C4C37×#57711yescharacteristic
480C4C37×#57811yescharacteristic
481C2—41no—
482C2—42no—
483C2—161no—
484C2C37×#304611yescharacteristic
485C2C37×#305511yescharacteristic
486C2C2×C37×#47111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3106C2
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×#3227C2semidirect
3. C37×#3039C2semidirect
4. C37×#2990C2semidirect
5. C37×#1702C2semidirect
6. C37×#1692C2semidirect
7. C37×#1681C2semidirect
8. C37×#1671C2semidirect
9. C37×#1574C2semidirect
10. C37×#1560C2semidirect
11. C37×#1549C2semidirect
214. #19489C37direct (N × H)
238. #3227C2×C37semidirect
240. #3039C2×C37semidirect
241. #2990C2×C37semidirect
242. #1702C2×C37semidirect
243. #1692C2×C37semidirect
244. #1681C2×C37semidirect
245. #1671C2×C37semidirect
246. #1574C2×C37semidirect
247. #1560C2×C37semidirect
248. #1549C2×C37semidirect
292. C37#19489direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32272
C37×#31062
C37×#30392
C37×#29902
C37×#17022
C37×#16922
C37×#16812
C37×#16712
C37×#15742
C37×#15602
C37×#15492
#1948937