Finite Group Databasebeta

← C37×#19165 #22640418

Subgroups — C37×#19165 #22640418

Order 9472.

674 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3165C211yesmaximal, characteristic, complemented
2C37×#3101C211yesmaximal, characteristic
3C2×C37×#476C211yesmaximal, characteristic
4D4×M16×C37C211yesmaximal, characteristic
5C37×#1695C212yesmaximal, complemented
6C37×#1691C212yesmaximal, complemented
7C37×#1675C212yesmaximal, complemented
8C37×#1671C212yesmaximal, complemented
9C37×#1565C211yesmaximal, characteristic, complemented
10C37×#1550C211yesmaximal, characteristic, complemented
11C37×#1548C211yesmaximal, characteristic, complemented
12C22×M16×C37—21no—
13C37×#533C2211yescharacteristic
14C2×C4⋊Q8×C37C2211yescharacteristic
15C2×C4×D4×C37C2211yescharacteristic
16C37×#501—22no—
17C37×#500C2212yescomplemented
18C37×#498C2212yescomplemented
19C37×#483—21no—
20C37×#476—21no—
21C37×#476—21no—
22C37×#476C2212yes—
23C37×#476C2211yescharacteristic
24C37×#476C2212yes—
25C37×#476C2211yescharacteristic
26C37×#461C2211yescharacteristic
27C37×#461C2211yescharacteristic
28C37×#450—21no—
29C4×SD16×C37—21no—
30C4×SD16×C37—21no—
31C37×#436C2212yes—
32C37×#435—22no—
33C8×D4×C37C2212yes—
34C37×#431C2211yescharacteristic
35C37×#428—21no—
36C37×#428—21no—
37C2×#106×C37—21no—
38C37×#423C2211yescharacteristic
39C2×C4⋊C8×C37C2211yescharacteristic
40C2×#102×C37—21no—
41C37×#407—21no—
42C4×M16×C37C2211yescharacteristic
43C37×#335C2212yescomplemented
44C37×#334C2212yescomplemented
45C37×#333C2212yescomplemented
46C37×#333C2212yescomplemented
47C37×#333C2212yescomplemented
48C37×#332C2212yescomplemented
49C22×Q8×C37—21no—
50C22×D4×C37D411yescharacteristic
51C23×C4×C37—21no—
52C2×SD16×C37—21no—
53C2×SD16×C37—21no—
54C2×M16×C37—21no—
55C2×M16×C37—22no—
56C2×M16×C37—44no—
57C2×M16×C37D411yescharacteristic
58C2×M16×C37D411yescharacteristic
59C22×C8×C37—21no—
60C22×C8×C37—22no—
61C4⋊Q8×C37—21no—
62C4⋊Q8×C37—21no—
63C4⋊Q8×C37—21no—
64C4⋊Q8×C37C2312yes—
65C4⋊Q8×C37C2311yescharacteristic
66C4⋊Q8×C37C2311yescharacteristic
67#125×C37—21no—
68C22⋊Q8×C37—21no—
69C22⋊Q8×C37—21no—
70C4×Q8×C37—21no—
71C4×Q8×C37—21no—
72C4×D4×C37—21no—
73C4×D4×C37—21no—
74C4×D4×C37D411yescharacteristic
75C4×D4×C37D411yescharacteristic
76C4×D4×C37C2311yescharacteristic
77C4×D4×C37C2311yescharacteristic
78#117×C37—21no—
79C2×C4⋊C4×C37—21no—
80C2×C4⋊C4×C37—21no—
81C2×C4⋊C4×C37D411yescharacteristic
82C2×C22⋊C4×C37—21no—
83C2×C42×C37C2311yescharacteristic
84#107×C37—22no—
85#107×C37—22no—
86#106×C37—22no—
87#106×C37—22no—
88#106×C37—22no—
89#106×C37—22no—
90#106×C37—21no—
91#106×C37—21no—
92C4⋊C8×C37—21no—
93C4⋊C8×C37—21no—
94C4⋊C8×C37C2312yes—
95C4⋊C8×C37C2312yes—
96C4⋊C8×C37C2311yescharacteristic
97C4⋊C8×C37C2311yescharacteristic
98#103×C37—21no—
99#103×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×C37—22no—
107#97×C37D412yes—
108C4×C8×C37—21no—
109C4×C8×C37C2312yes—
110C24×C37—21no—
111C2×Q8×C37—21no—
112C2×Q8×C37—21no—
113C2×Q8×C37—22no—
114C2×Q8×C37—41no—
115C2×Q8×C37—82no—
116C2×D4×C37—22no—
117C2×D4×C37—21no—
118C2×D4×C37—41no—
119C2×D4×C37C2×D411yescharacteristic
120C2×D4×C37C2×D411yescharacteristic
121C22×C4×C37—21no—
122C22×C4×C37—21no—
123C22×C4×C37—21no—
124C22×C4×C37—21no—
125C22×C4×C37—21no—
126C22×C4×C37—42no—
127C22×C4×C37—42no—
128C22×C4×C37—41no—
129C22×C4×C37C2×D411yescharacteristic
130C22×C4×C37C2×D411yescharacteristic
131C22×C4×C37#4111yescharacteristic
132SD16×C37—42no—
133SD16×C37—42no—
134M16×C37—22no—
135M16×C37—42no—
136M16×C37—44no—
137M16×C37SD1614yescomplemented
138C2×C8×C37—21no—
139C2×C8×C37—21no—
140C2×C8×C37—22no—
141C2×C8×C37—22no—
142C2×C8×C37—42no—
143C2×C8×C37—44no—
144C2×C8×C37C2×D412yes—
145C2×C8×C37C2×D412yes—
146C4⋊C4×C37—21no—
147C4⋊C4×C37—22no—
148C4⋊C4×C37—21no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—22no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—21no—
153C4⋊C4×C37—41no—
154C4⋊C4×C37—41no—
155C4⋊C4×C37—41no—
156C4⋊C4×C37—41no—
157C4⋊C4×C37C2×D411yescharacteristic
158C4⋊C4×C37C2×D411yescharacteristic
159C22⋊C4×C37—21no—
160C22⋊C4×C37—21no—
161C22⋊C4×C37—21no—
162C22⋊C4×C37—21no—
163C22⋊C4×C37—41no—
164C42×C37—41no—
165C42×C37C2×D411yescharacteristic
166C42×C37C2×D411yescharacteristic
167C42×C37#4111yescharacteristic
168C42×C37C2411yescharacteristic
169C23×C37—21no—
170C23×C37—21no—
171C23×C37—42no—
172C23×C37—42no—
173C23×C37—81no—
174C23×C37#12111yescharacteristic
175Q8×C37—41no—
176Q8×C37—41no—
177Q8×C37—81no—
178Q8×C37—82no—
179Q8×C37—82no—
180D4×C37—21no—
181D4×C37—21no—
182D4×C37—21no—
183D4×C37—42no—
184D4×C37#13712yes—
185C2×C4×C37—21no—
186C2×C4×C37—21no—
187C2×C4×C37—21no—
188C2×C4×C37—21no—
189C2×C4×C37—41no—
190C2×C4×C37—42no—
191C2×C4×C37—41no—
192C2×C4×C37—41no—
193C2×C4×C37—41no—
194C2×C4×C37—41no—
195C2×C4×C37—42no—
196C2×C4×C37—42no—
197C2×C4×C37—41no—
198C2×C4×C37—41no—
199C2×C4×C37—42no—
200C2×C4×C37—82no—
201C2×C4×C37#12111yescharacteristic
202C2×C4×C37#12111yescharacteristic
203C2×C4×C37#12111yescharacteristic
204C2×C4×C37C2×SD1612yes—
205C2×C4×C37#13712yes—
206C2×C4×C37C22×D411yescharacteristic
207C2×C4×C37C22×D411yescharacteristic
208C2×C4×C37C2×#4111yescharacteristic
209C8×C37—22no—
210C8×C37—42no—
211C8×C37—41no—
212C8×C37—42no—
213C8×C37—41no—
214C8×C37C2×SD1614yes—
215#19165C3711yesmaximal, characteristic, direct product factor, Sylow
216C22×C37—21no—
217C22×C37—21no—
218C22×C37—22no—
219C22×C37—41no—
220C22×C37—41no—
221C22×C37—41no—
222C22×C37—41no—
223C22×C37—41no—
224C22×C37—84no—
225C22×C37#46112yes—
226C22×C37C2×#12111yescharacteristic
227C4×C37—21no—
228C4×C37—21no—
229C4×C37—21no—
230C4×C37—41no—
231C4×C37—41no—
232C4×C37—81no—
233C4×C37—82no—
234C4×C37—81no—
235C4×C37#46112yes—
236C4×C37C22×SD1611yescharacteristic
237C4×C37C2×#13711yescharacteristic
238C4×C37C2×#13711yescharacteristic
239C4×C37#57511yescharacteristic
240#3165C2×C3711yescharacteristic, complemented
241#3101C2×C3711yescharacteristic
242C2×#476C2×C3711yescharacteristic
243D4×M16C2×C3711yescharacteristic
244#1695C2×C3712yescomplemented
245#1691C2×C3712yescomplemented
246#1675C2×C3712yescomplemented
247#1671C2×C3712yescomplemented
248#1565C2×C3711yescharacteristic, complemented
249#1550C2×C3711yescharacteristic, complemented
250#1548C2×C3711yescharacteristic, complemented
251C2×C37—22no—
252C2×C37—42no—
253C2×C37—81no—
254C2×C37C2×#46111yescharacteristic
255C2×C37#305611yescharacteristic
256C2×C37#306811yescharacteristic
257C22×M16—21no—
258#533C22×C3711yescharacteristic
259C2×C4⋊Q8C22×C3711yescharacteristic
260C2×C4×D4C22×C3711yescharacteristic
261#501—22no—
262#500C22×C3712yescomplemented
263#498C22×C3712yescomplemented
264#483—21no—
265#476—21no—
266#476—21no—
267#476C22×C3711yescharacteristic
268#476C22×C3711yescharacteristic
269#476C22×C3712yes—
270#476C22×C3712yes—
271#461C22×C3711yescharacteristic
272#461C22×C3711yescharacteristic
273#450—21no—
274C4×SD16—21no—
275C4×SD16—21no—
276#436C22×C3712yes—
277#435—22no—
278C8×D4C22×C3712yes—
279#431C22×C3711yescharacteristic
280#428—21no—
281#428—21no—
282C2×#106—21no—
283#423C22×C3711yescharacteristic
284C2×C4⋊C8C22×C3711yescharacteristic
285C2×#102—21no—
286#407—21no—
287C4×M16C22×C3711yescharacteristic
288#335C22×C3712yescomplemented
289#334C22×C3712yescomplemented
290#333C22×C3712yescomplemented
291#333C22×C3712yescomplemented
292#333C22×C3712yescomplemented
293#332C22×C3712yescomplemented
294C37#1916511yescharacteristic, direct product factor, Sylow
295C22×Q8—21no—
296C22×D4D4×C3711yescharacteristic
297C23×C4—21no—
298C2×SD16—21no—
299C2×SD16—21no—
300C2×M16—21no—
301C2×M16—22no—
302C2×M16—44no—
303C2×M16D4×C3711yescharacteristic
304C2×M16D4×C3711yescharacteristic
305C22×C8—21no—
306C22×C8—22no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8C23×C3712yes—
311C4⋊Q8C23×C3711yescharacteristic
312C4⋊Q8C23×C3711yescharacteristic
313#125—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4D4×C3711yescharacteristic
321C4×D4D4×C3711yescharacteristic
322C4×D4C23×C3711yescharacteristic
323C4×D4C23×C3711yescharacteristic
324#117—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4D4×C3711yescharacteristic
328C2×C22⋊C4—21no—
329C2×C42C23×C3711yescharacteristic
330#107—22no—
331#107—22no—
332#106—22no—
333#106—22no—
334#106—22no—
335#106—22no—
336#106—21no—
337#106—21no—
338C4⋊C8—21no—
339C4⋊C8—21no—
340C4⋊C8C23×C3712yes—
341C4⋊C8C23×C3712yes—
342C4⋊C8C23×C3711yescharacteristic
343C4⋊C8C23×C3711yescharacteristic
344#103—21no—
345#103—21no—
346#102—22no—
347#102—22no—
348#102—21no—
349#102—21no—
350C22⋊C8—21no—
351C22⋊C8—22no—
352C22⋊C8—22no—
353#97D4×C3712yes—
354C4×C8—21no—
355C4×C8C23×C3712yes—
356C24—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—41no—
361C2×Q8—82no—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—41no—
365C2×D4C2×D4×C3711yescharacteristic
366C2×D4C2×D4×C3711yescharacteristic
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—41no—
375C22×C4C2×D4×C3711yescharacteristic
376C22×C4C2×D4×C3711yescharacteristic
377C22×C4#41×C3711yescharacteristic
378SD16—42no—
379SD16—42no—
380M16—22no—
381M16—42no—
382M16—44no—
383M16SD16×C3714yescomplemented
384C2×C8—21no—
385C2×C8—21no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—42no—
389C2×C8—44no—
390C2×C8C2×D4×C3712yes—
391C2×C8C2×D4×C3712yes—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4C2×D4×C3711yescharacteristic
404C4⋊C4C2×D4×C3711yescharacteristic
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—21no—
408C22⋊C4—21no—
409C22⋊C4—41no—
410C42—41no—
411C42C2×D4×C3711yescharacteristic
412C42C2×D4×C3711yescharacteristic
413C42#41×C3711yescharacteristic
414C42C24×C3711yescharacteristic
415C23—21no—
416C23—21no—
417C23—42no—
418C23—42no—
419C23—81no—
420C23#121×C3711yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—82no—
424Q8—81no—
425Q8—82no—
426D4—21no—
427D4—21no—
428D4—21no—
429D4—42no—
430D4#137×C3712yes—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—82no—
447C2×C4#121×C3711yescharacteristic
448C2×C4#121×C3711yescharacteristic
449C2×C4#121×C3711yescharacteristic
450C2×C4C2×SD16×C3712yes—
451C2×C4#137×C3712yes—
452C2×C4C22×D4×C3711yescharacteristic
453C2×C4C22×D4×C3711yescharacteristic
454C2×C4C2×#41×C3711yescharacteristic
455C8—22no—
456C8—42no—
457C8—41no—
458C8—42no—
459C8—41no—
460C8C2×SD16×C3714yes—
461C22—21no—
462C22—21no—
463C22—22no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—84no—
470C22C37×#46112yes—
471C22C2×#121×C3711yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—82no—
479C4—81no—
480C4C37×#46112yes—
481C4C22×SD16×C3711yescharacteristic
482C4C2×#137×C3711yescharacteristic
483C4C2×#137×C3711yescharacteristic
484C4C37×#57511yescharacteristic
485C2—22no—
486C2—42no—
487C2—81no—
488C2C2×C37×#46111yescharacteristic
489C2C37×#305611yescharacteristic
490C2C37×#306811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC22×D4×C37D4
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×#3165C2semidirect
5. C37×#1695C2semidirect
6. C37×#1691C2semidirect
7. C37×#1675C2semidirect
8. C37×#1671C2semidirect
9. C37×#1565C2semidirect
10. C37×#1550C2semidirect
11. C37×#1548C2semidirect
17. C37×#500C22semidirect
18. C37×#498C22semidirect
43. C37×#335C22semidirect
44. C37×#334C22semidirect
45. C37×#333C22semidirect
46. C37×#333C22semidirect
47. C37×#333C22semidirect
48. C37×#332C22semidirect
137. M16×C37SD16semidirect
215. #19165C37direct (N × H)
240. #3165C2×C37semidirect
244. #1695C2×C37semidirect
245. #1691C2×C37semidirect
246. #1675C2×C37semidirect
247. #1671C2×C37semidirect
248. #1565C2×C37semidirect
249. #1550C2×C37semidirect
250. #1548C2×C37semidirect
262. #500C22×C37semidirect
263. #498C22×C37semidirect
288. #335C22×C37semidirect
289. #334C22×C37semidirect
290. #333C22×C37semidirect
291. #333C22×C37semidirect
292. #333C22×C37semidirect
293. #332C22×C37semidirect
294. C37#19165direct (N × H)
383. M16SD16×C37semidirect

Maximal subgroups

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

subgroupindex
C37×#31652
C37×#31012
C2×C37×#4762
D4×M16×C372
C37×#16952
C37×#16912
C37×#16752
C37×#16712
C37×#15652
C37×#15502
C37×#15482
#1916537