Finite Group Databasebeta

← C37×#19339 #22640592

Subgroups — C37×#19339 #22640592

Order 9472.

658 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3254C211yesmaximal, characteristic, complemented
2C37×#3253C211yesmaximal, characteristic
3C37×#3167C211yesmaximal, characteristic, complemented
4C37×#2931C211yesmaximal, characteristic, complemented
5C37×#1691C212yesmaximal, complemented
6C37×#1685C212yesmaximal, complemented
7C37×#1683C212yesmaximal, complemented
8C37×#1681C212yesmaximal, complemented
9C37×#1567C211yesmaximal, characteristic, complemented
10C37×#1561C211yesmaximal, characteristic, complemented
11C37×#1560C211yesmaximal, characteristic, complemented
12C2×#131×C37—21no—
13C37×#533C2211yescharacteristic
14C37×#532C2211yescharacteristic
15C37×#532C2211yescharacteristic
16C37×#498C2211yescharacteristic
17C37×#492C2211yescharacteristic
18C37×#487C2211yescharacteristic
19C37×#486C2211yescharacteristic
20C37×#477—21no—
21C37×#476—21no—
22C37×#476C2212yes—
23C37×#474C2212yes—
24C37×#469—22no—
25C37×#468—22no—
26C37×#465—21no—
27C37×#465—21no—
28C37×#461C2212yes—
29C37×#460—21no—
30C37×#459—21no—
31C37×#459C2212yes—
32C4×SD16×C37—21no—
33C4×SD16×C37—21no—
34C37×#436—21no—
35C37×#436C2212yes—
36C8×D4×C37—21no—
37C8×D4×C37C2212yes—
38C37×#423C2211yescharacteristic
39C37×#423C2211yescharacteristic
40C37×#423C2211yescharacteristic
41C37×#408—21no—
42C2×C4×C8×C37C2211yescharacteristic
43C37×#335C2212yes—
44C37×#335C2212yes—
45C37×#333C2212yes—
46C37×#332C2212yes—
47C37×#332C2212yes—
48C37×#331C2212yes—
49C2×#41×C37—21no—
50C2×#41×C37—21no—
51C2×SD16×C37—22no—
52C2×SD16×C37—21no—
53C2×SD16×C37—21no—
54C2×D8×C37—22no—
55#131×C37—44no—
56C2×M16×C37—21no—
57C2×M16×C37—21no—
58C2×M16×C37—21no—
59C2×M16×C37—22no—
60C22×C8×C37—22no—
61C22×C8×C37D411yescharacteristic
62C22×C8×C37D411yescharacteristic
63C4⋊Q8×C37D411yescharacteristic
64C4⋊Q8×C37C2311yescharacteristic
65C4⋊Q8×C37C2311yescharacteristic
66C4⋊Q8×C37C2311yescharacteristic
67#127×C37D411yescharacteristic
68#127×C37C2311yescharacteristic
69#125×C37—21no—
70#124×C37—21no—
71#124×C37—21no—
72C22⋊Q8×C37—21no—
73C22⋊Q8×C37—21no—
74#121×C37—21no—
75#121×C37—21no—
76#121×C37—21no—
77#121×C37D412yes—
78C4×Q8×C37—21no—
79C4×Q8×C37—21no—
80C4×D4×C37—21no—
81C4×D4×C37—21no—
82C4×D4×C37—21no—
83C4×D4×C37C2312yes—
84#117×C37—21no—
85C2×C42×C37C2311yescharacteristic
86#107×C37—22no—
87#106×C37—21no—
88#106×C37—21no—
89#106×C37—22no—
90C4⋊C8×C37—21no—
91C4⋊C8×C37—21no—
92C4⋊C8×C37—21no—
93C4⋊C8×C37C2312yes—
94C4⋊C8×C37C2312yes—
95C4⋊C8×C37C2312yes—
96#103×C37—21no—
97#103×C37—21no—
98#103×C37—22no—
99#102×C37—22no—
100#102×C37—22no—
101#102×C37—21no—
102#102×C37—21no—
103#102×C37—22no—
104C22⋊C8×C37—22no—
105C22⋊C8×C37—22no—
106C4×C8×C37D411yescharacteristic
107C4×C8×C37D411yescharacteristic
108C4×C8×C37C2311yescharacteristic
109C4×C8×C37C2311yescharacteristic
110#41×C37—42no—
111#41×C37—42no—
112#41×C37—82no—
113C2×Q8×C37—21no—
114C2×Q8×C37—21no—
115C2×Q8×C37—21no—
116C2×Q8×C37—21no—
117C2×D4×C37—22no—
118C2×D4×C37—21no—
119C2×D4×C37—21no—
120C2×D4×C37—21no—
121C2×D4×C37—21no—
122C2×D4×C37—21no—
123C2×D4×C37—41no—
124C2×D4×C37C2×D412yes—
125C22×C4×C37—22no—
126C22×C4×C37—41no—
127C22×C4×C37C2×D411yescharacteristic
128C22×C4×C37C2×D411yescharacteristic
129C22×C4×C37#4111yescharacteristic
130SD16×C37—42no—
131SD16×C37—42no—
132SD16×C37—82no—
133D8×C37—82no—
134M16×C37—42no—
135M16×C37—44no—
136M16×C37—81no—
137M16×C37—81no—
138C2×C8×C37—22no—
139C2×C8×C37—22no—
140C2×C8×C37—22no—
141C2×C8×C37—22no—
142C2×C8×C37—41no—
143C2×C8×C37—44no—
144C2×C8×C37C2×D411yescharacteristic
145C2×C8×C37C2×D411yescharacteristic
146C2×C8×C37C2×D411yescharacteristic
147C2×C8×C37C2×D411yescharacteristic
148C4⋊C4×C37—21no—
149C4⋊C4×C37—21no—
150C4⋊C4×C37—21no—
151C4⋊C4×C37—21no—
152C4⋊C4×C37—21no—
153C4⋊C4×C37—21no—
154C4⋊C4×C37—21no—
155C4⋊C4×C37—41no—
156C4⋊C4×C37—41no—
157C4⋊C4×C37C2×D412yes—
158C22⋊C4×C37—22no—
159C22⋊C4×C37—22no—
160C22⋊C4×C37—41no—
161C22⋊C4×C37—41no—
162C22⋊C4×C37—41no—
163C42×C37—41no—
164C42×C37C2×D411yescharacteristic
165C42×C37C2×D411yescharacteristic
166C42×C37#4111yescharacteristic
167C42×C37C2411yescharacteristic
168C23×C37—22no—
169C23×C37—41no—
170C23×C37#12111yescharacteristic
171Q8×C37—42no—
172Q8×C37—41no—
173Q8×C37—41no—
174Q8×C37—41no—
175Q8×C37—41no—
176Q8×C37—81no—
177D4×C37—22no—
178D4×C37—22no—
179D4×C37—42no—
180D4×C37—44no—
181D4×C37—41no—
182D4×C37—41no—
183D4×C37—41no—
184D4×C37—41no—
185D4×C37—42no—
186D4×C37—81no—
187D4×C37—82no—
188C2×C4×C37—21no—
189C2×C4×C37—21no—
190C2×C4×C37—21no—
191C2×C4×C37—21no—
192C2×C4×C37—22no—
193C2×C4×C37—22no—
194C2×C4×C37—42no—
195C2×C4×C37—42no—
196C2×C4×C37—41no—
197C2×C4×C37—41no—
198C2×C4×C37—41no—
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—21no—
207C8×C37—21no—
208C8×C37—21no—
209C8×C37—42no—
210C8×C37—42no—
211C8×C37—42no—
212C8×C37AGL(1,ℤ/8)12yes—
213#19339C3711yesmaximal, characteristic, direct product factor, Sylow
214C22×C37—21no—
215C22×C37—21no—
216C22×C37—21no—
217C22×C37—42no—
218C22×C37—42no—
219C22×C37—42no—
220C22×C37—81no—
221C22×C37—81no—
222C22×C37—81no—
223C22×C37C2×#12111yescharacteristic
224C4×C37—21no—
225C4×C37—21no—
226C4×C37—21no—
227C4×C37—42no—
228C4×C37—81no—
229C4×C37—81no—
230C4×C37—81no—
231C4×C37#47112yes—
232C4×C37C2×AGL(1,ℤ/8)11yescharacteristic
233C4×C37#57511yescharacteristic
234C4×C37#57611yescharacteristic
235C4×C37#57811yescharacteristic
236#3254C2×C3711yescharacteristic, complemented
237#3253C2×C3711yescharacteristic
238#3167C2×C3711yescharacteristic, complemented
239#2931C2×C3711yescharacteristic, complemented
240#1691C2×C3712yescomplemented
241#1685C2×C3712yescomplemented
242#1683C2×C3712yescomplemented
243#1681C2×C3712yescomplemented
244#1567C2×C3711yescharacteristic, complemented
245#1561C2×C3711yescharacteristic, complemented
246#1560C2×C3711yescharacteristic, complemented
247C2×C37—41no—
248C2×C37—82no—
249C2×C37—161no—
250C2×C37#303611yescharacteristic
251C2×C37#306111yescharacteristic
252C2×C37C2×#47111yescharacteristic
253C2×#131—21no—
254#533C22×C3711yescharacteristic
255#532C22×C3711yescharacteristic
256#532C22×C3711yescharacteristic
257#498C22×C3711yescharacteristic
258#492C22×C3711yescharacteristic
259#487C22×C3711yescharacteristic
260#486C22×C3711yescharacteristic
261#477—21no—
262#476—21no—
263#476C22×C3712yes—
264#474C22×C3712yes—
265#469—22no—
266#468—22no—
267#465—21no—
268#465—21no—
269#461C22×C3712yes—
270#460—21no—
271#459—21no—
272#459C22×C3712yes—
273C4×SD16—21no—
274C4×SD16—21no—
275#436—21no—
276#436C22×C3712yes—
277C8×D4—21no—
278C8×D4C22×C3712yes—
279#423C22×C3711yescharacteristic
280#423C22×C3711yescharacteristic
281#423C22×C3711yescharacteristic
282#408—21no—
283C2×C4×C8C22×C3711yescharacteristic
284#335C22×C3712yes—
285#335C22×C3712yes—
286#333C22×C3712yes—
287#332C22×C3712yes—
288#332C22×C3712yes—
289#331C22×C3712yes—
290C37#1933911yescharacteristic, direct product factor, Sylow
291C2×#41—21no—
292C2×#41—21no—
293C2×SD16—22no—
294C2×SD16—21no—
295C2×SD16—21no—
296C2×D8—22no—
297#131—44no—
298C2×M16—21no—
299C2×M16—21no—
300C2×M16—21no—
301C2×M16—22no—
302C22×C8—22no—
303C22×C8D4×C3711yescharacteristic
304C22×C8D4×C3711yescharacteristic
305C4⋊Q8D4×C3711yescharacteristic
306C4⋊Q8C23×C3711yescharacteristic
307C4⋊Q8C23×C3711yescharacteristic
308C4⋊Q8C23×C3711yescharacteristic
309#127D4×C3711yescharacteristic
310#127C23×C3711yescharacteristic
311#125—21no—
312#124—21no—
313#124—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121D4×C3712yes—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4C23×C3712yes—
326#117—21no—
327C2×C42C23×C3711yescharacteristic
328#107—22no—
329#106—21no—
330#106—21no—
331#106—22no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334C4⋊C8—21no—
335C4⋊C8C23×C3712yes—
336C4⋊C8C23×C3712yes—
337C4⋊C8C23×C3712yes—
338#103—21no—
339#103—21no—
340#103—22no—
341#102—22no—
342#102—22no—
343#102—21no—
344#102—21no—
345#102—22no—
346C22⋊C8—22no—
347C22⋊C8—22no—
348C4×C8D4×C3711yescharacteristic
349C4×C8D4×C3711yescharacteristic
350C4×C8C23×C3711yescharacteristic
351C4×C8C23×C3711yescharacteristic
352#41—42no—
353#41—42no—
354#41—82no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—41no—
366C2×D4C2×D4×C3712yes—
367C22×C4—22no—
368C22×C4—41no—
369C22×C4C2×D4×C3711yescharacteristic
370C22×C4C2×D4×C3711yescharacteristic
371C22×C4#41×C3711yescharacteristic
372SD16—42no—
373SD16—42no—
374SD16—82no—
375D8—82no—
376M16—42no—
377M16—44no—
378M16—81no—
379M16—81no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—41no—
385C2×C8—44no—
386C2×C8C2×D4×C3711yescharacteristic
387C2×C8C2×D4×C3711yescharacteristic
388C2×C8C2×D4×C3711yescharacteristic
389C2×C8C2×D4×C3711yescharacteristic
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—41no—
398C4⋊C4—41no—
399C4⋊C4C2×D4×C3712yes—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C42—41no—
406C42C2×D4×C3711yescharacteristic
407C42C2×D4×C3711yescharacteristic
408C42#41×C3711yescharacteristic
409C42C24×C3711yescharacteristic
410C23—22no—
411C23—41no—
412C23#121×C3711yescharacteristic
413Q8—42no—
414Q8—41no—
415Q8—41no—
416Q8—41no—
417Q8—41no—
418Q8—81no—
419D4—22no—
420D4—22no—
421D4—42no—
422D4—44no—
423D4—41no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—42no—
428D4—81no—
429D4—82no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—82no—
442C2×C4#121×C3711yescharacteristic
443C2×C4#121×C3711yescharacteristic
444C2×C4#121×C3711yescharacteristic
445C2×C4C22×D4×C3711yescharacteristic
446C2×C4C22×D4×C3711yescharacteristic
447C2×C4C2×#41×C3711yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8—42no—
452C8—42no—
453C8—42no—
454C8AGL(1,ℤ/8)×C3712yes—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—81no—
462C22—81no—
463C22—81no—
464C22C2×#121×C3711yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—42no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4C37×#47112yes—
473C4C2×AGL(1,ℤ/8)×C3711yescharacteristic
474C4C37×#57511yescharacteristic
475C4C37×#57611yescharacteristic
476C4C37×#57811yescharacteristic
477C2—41no—
478C2—82no—
479C2—161no—
480C2C37×#303611yescharacteristic
481C2C37×#306111yescharacteristic
482C2C2×C37×#47111yescharacteristic
subgroupG/H
center, socleC22×C37C2×#121
commutator, Frattini, cosocleC42C24×C37
prime radicalC37×#3253C2
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×#3254C2semidirect
3. C37×#3167C2semidirect
4. C37×#2931C2semidirect
5. C37×#1691C2semidirect
6. C37×#1685C2semidirect
7. C37×#1683C2semidirect
8. C37×#1681C2semidirect
9. C37×#1567C2semidirect
10. C37×#1561C2semidirect
11. C37×#1560C2semidirect
213. #19339C37direct (N × H)
236. #3254C2×C37semidirect
238. #3167C2×C37semidirect
239. #2931C2×C37semidirect
240. #1691C2×C37semidirect
241. #1685C2×C37semidirect
242. #1683C2×C37semidirect
243. #1681C2×C37semidirect
244. #1567C2×C37semidirect
245. #1561C2×C37semidirect
246. #1560C2×C37semidirect
290. C37#19339direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#32542
C37×#32532
C37×#31672
C37×#29312
C37×#16912
C37×#16852
C37×#16832
C37×#16812
C37×#15672
C37×#15612
C37×#15602
#1933937