Finite Group Databasebeta

← C37×#18131 #22639384

Subgroups — C37×#18131 #22639384

Order 9472.

932 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C37×#3461C211yesmaximal, characteristic
2C37×#3108C212yesmaximal, complemented
3C37×#2399C211yesmaximal, characteristic, complemented
4C37×#1611C211yesmaximal, characteristic, complemented
5C37×#1610C211yesmaximal, characteristic
6C37×#1609C212yesmaximal, complemented
7C37×#1605C211yesmaximal, characteristic, complemented
8C37×#1604C211yesmaximal, characteristic
9C37×#1603C212yesmaximal, complemented
10C37×#1500C212yesmaximal, complemented
11C37×#1461C211yesmaximal, characteristic, complemented
12C37×#544C2211yescharacteristic
13C37×#542—22no—
14C37×#541—22no—
15C37×#539—21no—
16C37×#539C2212yes—
17C37×#537C2211yescharacteristic
18C37×#536—21no—
19C37×#533—22no—
20C37×#529—22no—
21C37×#529—21no—
22C37×#529C2212yes—
23C4×#41×C37—21no—
24C2×C4×Q8×C37C2211yescharacteristic
25C2×C4×Q8×C37C2211yescharacteristic
26C37×#483C2212yes—
27C37×#480C2212yes—
28C37×#479—22no—
29C37×#464—22no—
30C37×#451C2212yes—
31C37×#448C2212yes—
32C4×Q16×C37—22no—
33C4×SD16×C37—22no—
34C37×#431C2212yes—
35C37×#398—21no—
36C37×#398C2211yescharacteristic
37C37×#398C2211yescharacteristic
38C37×#395—21no—
39C37×#395C2211yescharacteristic
40C37×#395C2211yescharacteristic
41C4×C4⋊C4×C37—21no—
42C4×C4⋊C4×C37—21no—
43C37×#376C2211yescharacteristic
44C37×#328C2212yes—
45C37×#328C2212yes—
46C37×#327C2212yes—
47C37×#327C2212yes—
48C37×#324C2212yes—
49C37×#324C2211yescharacteristic
50C37×#324C2211yescharacteristic
51C2×#41×C37—21no—
52C22×Q8×C37D411yescharacteristic
53C22×Q8×C37C2311yescharacteristic
54C2×Q16×C37—22no—
55C2×SD16×C37—22no—
56C4⋊Q8×C37—22no—
57C4⋊Q8×C37—22no—
58#126×C37—22no—
59#126×C37—22no—
60#126×C37—22no—
61#126×C37—22no—
62#125×C37—21no—
63#125×C37—22no—
64#125×C37—22no—
65#125×C37—22no—
66#125×C37D412yes—
67#124×C37—22no—
68#124×C37—21no—
69#124×C37D412yes—
70#123×C37—22no—
71#123×C37—22no—
72#123×C37—22no—
73#123×C37—22no—
74C22⋊Q8×C37—22no—
75C22⋊Q8×C37—22no—
76C22⋊Q8×C37—22no—
77C22⋊Q8×C37—22no—
78C22⋊Q8×C37—21no—
79C22⋊Q8×C37—22no—
80C22⋊Q8×C37C2312yes—
81#121×C37—22no—
82#121×C37—21no—
83#121×C37C2312yes—
84C4×Q8×C37—21no—
85C4×Q8×C37—21no—
86C4×Q8×C37—21no—
87C4×Q8×C37—22no—
88C4×Q8×C37—22no—
89C4×Q8×C37—22no—
90C4×Q8×C37—22no—
91C4×Q8×C37D412yes—
92C4×D4×C37—21no—
93C4×D4×C37—21no—
94C4×D4×C37—21no—
95C4×D4×C37—22no—
96C4×D4×C37—22no—
97C4×D4×C37D412yes—
98#117×C37—22no—
99#117×C37—22no—
100#117×C37—21no—
101#117×C37—22no—
102C2×C4⋊C4×C37—21no—
103C2×C4⋊C4×C37—21no—
104C2×C4⋊C4×C37—21no—
105C2×C4⋊C4×C37—21no—
106C2×C4⋊C4×C37—21no—
107C2×C4⋊C4×C37D411yescharacteristic
108C2×C4⋊C4×C37C2311yescharacteristic
109C2×C4⋊C4×C37C2311yescharacteristic
110C2×C4⋊C4×C37C2311yescharacteristic
111C2×C42×C37—22no—
112C2×C42×C37—21no—
113C2×C42×C37—21no—
114C2×C42×C37D411yescharacteristic
115C2×C42×C37D411yescharacteristic
116C2×C42×C37C2311yescharacteristic
117#107×C37—22no—
118#106×C37—22no—
119C4⋊C8×C37—22no—
120#103×C37—22no—
121#103×C37—22no—
122#103×C37—22no—
123#102×C37—22no—
124C22⋊C8×C37C2312yes—
125C22⋊C8×C37C2312yes—
126C4×C8×C37—22no—
127#95×C37—21no—
128#95×C37—21no—
129#95×C37—21no—
130#95×C37—21no—
131#95×C37—21no—
132#95×C37C2311yescharacteristic
133#95×C37C2311yescharacteristic
134#41×C37—42no—
135#41×C37—42no—
136C2×Q8×C37—21no—
137C2×Q8×C37—21no—
138C2×Q8×C37—22no—
139C2×Q8×C37—22no—
140C2×Q8×C37—22no—
141C2×Q8×C37—41no—
142C2×Q8×C37—42no—
143C2×Q8×C37C2×D412yes—
144C2×D4×C37—21no—
145C2×D4×C37—22no—
146C2×D4×C37—21no—
147C2×D4×C37C2×D412yes—
148C22×C4×C37—22no—
149C22×C4×C37—21no—
150C22×C4×C37—21no—
151C22×C4×C37—21no—
152C22×C4×C37—22no—
153C22×C4×C37—22no—
154C22×C4×C37—21no—
155C22×C4×C37C2×D411yescharacteristic
156C22×C4×C37C2×D411yescharacteristic
157C22×C4×C37C2×D411yescharacteristic
158C22×C4×C37C2×D411yescharacteristic
159C22×C4×C37C2×D411yescharacteristic
160C22×C4×C37C2×D411yescharacteristic
161C22×C4×C37C2411yescharacteristic
162Q16×C37—44no—
163SD16×C37—44no—
164C2×C8×C37—22no—
165C2×C8×C37—22no—
166C4⋊C4×C37—21no—
167C4⋊C4×C37—22no—
168C4⋊C4×C37—21no—
169C4⋊C4×C37—22no—
170C4⋊C4×C37—22no—
171C4⋊C4×C37—21no—
172C4⋊C4×C37—21no—
173C4⋊C4×C37—22no—
174C4⋊C4×C37—22no—
175C4⋊C4×C37—22no—
176C4⋊C4×C37—22no—
177C4⋊C4×C37—22no—
178C4⋊C4×C37—22no—
179C4⋊C4×C37—22no—
180C4⋊C4×C37—22no—
181C4⋊C4×C37—22no—
182C4⋊C4×C37—42no—
183C4⋊C4×C37—42no—
184C4⋊C4×C37—42no—
185C4⋊C4×C37—42no—
186C4⋊C4×C37—42no—
187C4⋊C4×C37C2×D412yes—
188C4⋊C4×C37C2×D412yes—
189C22⋊C4×C37—22no—
190C22⋊C4×C37—22no—
191C22⋊C4×C37—22no—
192C22⋊C4×C37—22no—
193C22⋊C4×C37—22no—
194C22⋊C4×C37—22no—
195C22⋊C4×C37—22no—
196C22⋊C4×C37—22no—
197C22⋊C4×C37—22no—
198C42×C37—24no—
199C42×C37—22no—
200C42×C37—22no—
201C42×C37—21no—
202C42×C37—21no—
203C42×C37—21no—
204C42×C37—22no—
205C42×C37—21no—
206C42×C37—41no—
207C42×C37—41no—
208C42×C37C2×D412yes—
209C42×C37C2×D412yes—
210C23×C37—22no—
211C23×C37C22×D411yescharacteristic
212Q8×C37—24no—
213Q8×C37—44no—
214Q8×C37—42no—
215Q8×C37—42no—
216Q8×C37—42no—
217Q8×C37—81no—
218D4×C37—42no—
219D4×C37—42no—
220D4×C37—42no—
221D4×C37—42no—
222D4×C37—81no—
223C2×C4×C37—21no—
224C2×C4×C37—21no—
225C2×C4×C37—21no—
226C2×C4×C37—21no—
227C2×C4×C37—22no—
228C2×C4×C37—22no—
229C2×C4×C37—22no—
230C2×C4×C37—22no—
231C2×C4×C37—21no—
232C2×C4×C37—22no—
233C2×C4×C37—22no—
234C2×C4×C37—21no—
235C2×C4×C37—21no—
236C2×C4×C37—22no—
237C2×C4×C37—21no—
238C2×C4×C37—21no—
239C2×C4×C37—41no—
240C2×C4×C37—44no—
241C2×C4×C37—41no—
242C2×C4×C37—41no—
243C2×C4×C37—41no—
244C2×C4×C37—41no—
245C2×C4×C37—41no—
246C2×C4×C37—41no—
247C2×C4×C37—44no—
248C2×C4×C37—41no—
249C2×C4×C37—41no—
250C2×C4×C37—41no—
251C2×C4×C37—41no—
252C2×C4×C37—41no—
253C2×C4×C37—82no—
254C2×C4×C37#12011yescharacteristic
255C2×C4×C37#12012yes—
256C2×C4×C37#12011yescharacteristic
257C2×C4×C37#13512yes—
258C2×C4×C37C22×D412yes—
259C8×C37—42no—
260C8×C37—42no—
261#18131C3711yesmaximal, characteristic, direct product factor, Sylow
262C22×C37—21no—
263C22×C37—21no—
264C22×C37—42no—
265C22×C37—42no—
266C22×C37—42no—
267C22×C37C2×#12011yescharacteristic
268C22×C37C2×#13511yescharacteristic
269C22×C37#57511yescharacteristic
270C4×C37—22no—
271C4×C37—22no—
272C4×C37—21no—
273C4×C37—22no—
274C4×C37—42no—
275C4×C37—42no—
276C4×C37—41no—
277C4×C37—42no—
278C4×C37—42no—
279C4×C37—42no—
280C4×C37—41no—
281C4×C37—41no—
282C4×C37—42no—
283C4×C37—81no—
284C4×C37#45612yes—
285#3461C2×C3711yescharacteristic
286#3108C2×C3712yescomplemented
287#2399C2×C3711yescharacteristic, complemented
288#1611C2×C3711yescharacteristic, complemented
289#1610C2×C3711yescharacteristic
290#1609C2×C3712yescomplemented
291#1605C2×C3711yescharacteristic, complemented
292#1604C2×C3711yescharacteristic
293#1603C2×C3712yescomplemented
294#1500C2×C3712yescomplemented
295#1461C2×C3711yescharacteristic, complemented
296C2×C37—21no—
297C2×C37—21no—
298C2×C37—82no—
299C2×C37#300211yescharacteristic
300C2×C37C2×#45611yescharacteristic
301C2×C37#302511yescharacteristic
302#544C22×C3711yescharacteristic
303#542—22no—
304#541—22no—
305#539—21no—
306#539C22×C3712yes—
307#537C22×C3711yescharacteristic
308#536—21no—
309#533—22no—
310#529—22no—
311#529—21no—
312#529C22×C3712yes—
313C4×#41—21no—
314C2×C4×Q8C22×C3711yescharacteristic
315C2×C4×Q8C22×C3711yescharacteristic
316#483C22×C3712yes—
317#480C22×C3712yes—
318#479—22no—
319#464—22no—
320#451C22×C3712yes—
321#448C22×C3712yes—
322C4×Q16—22no—
323C4×SD16—22no—
324#431C22×C3712yes—
325#398—21no—
326#398C22×C3711yescharacteristic
327#398C22×C3711yescharacteristic
328#395—21no—
329#395C22×C3711yescharacteristic
330#395C22×C3711yescharacteristic
331C4×C4⋊C4—21no—
332C4×C4⋊C4—21no—
333#376C22×C3711yescharacteristic
334#328C22×C3712yes—
335#328C22×C3712yes—
336#327C22×C3712yes—
337#327C22×C3712yes—
338#324C22×C3712yes—
339#324C22×C3711yescharacteristic
340#324C22×C3711yescharacteristic
341C37#1813111yescharacteristic, direct product factor, Sylow
342C2×#41—21no—
343C22×Q8D4×C3711yescharacteristic
344C22×Q8C23×C3711yescharacteristic
345C2×Q16—22no—
346C2×SD16—22no—
347C4⋊Q8—22no—
348C4⋊Q8—22no—
349#126—22no—
350#126—22no—
351#126—22no—
352#126—22no—
353#125—21no—
354#125—22no—
355#125—22no—
356#125—22no—
357#125D4×C3712yes—
358#124—22no—
359#124—21no—
360#124D4×C3712yes—
361#123—22no—
362#123—22no—
363#123—22no—
364#123—22no—
365C22⋊Q8—22no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—21no—
370C22⋊Q8—22no—
371C22⋊Q8C23×C3712yes—
372#121—22no—
373#121—21no—
374#121C23×C3712yes—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—22no—
379C4×Q8—22no—
380C4×Q8—22no—
381C4×Q8—22no—
382C4×Q8D4×C3712yes—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—22no—
387C4×D4—22no—
388C4×D4D4×C3712yes—
389#117—22no—
390#117—22no—
391#117—21no—
392#117—22no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4D4×C3711yescharacteristic
399C2×C4⋊C4C23×C3711yescharacteristic
400C2×C4⋊C4C23×C3711yescharacteristic
401C2×C4⋊C4C23×C3711yescharacteristic
402C2×C42—22no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42D4×C3711yescharacteristic
406C2×C42D4×C3711yescharacteristic
407C2×C42C23×C3711yescharacteristic
408#107—22no—
409#106—22no—
410C4⋊C8—22no—
411#103—22no—
412#103—22no—
413#103—22no—
414#102—22no—
415C22⋊C8C23×C3712yes—
416C22⋊C8C23×C3712yes—
417C4×C8—22no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95C23×C3711yescharacteristic
424#95C23×C3711yescharacteristic
425#41—42no—
426#41—42no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8—22no—
432C2×Q8—41no—
433C2×Q8—42no—
434C2×Q8C2×D4×C3712yes—
435C2×D4—21no—
436C2×D4—22no—
437C2×D4—21no—
438C2×D4C2×D4×C3712yes—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4C2×D4×C3711yescharacteristic
447C22×C4C2×D4×C3711yescharacteristic
448C22×C4C2×D4×C3711yescharacteristic
449C22×C4C2×D4×C3711yescharacteristic
450C22×C4C2×D4×C3711yescharacteristic
451C22×C4C2×D4×C3711yescharacteristic
452C22×C4C24×C3711yescharacteristic
453Q16—44no—
454SD16—44no—
455C2×C8—22no—
456C2×C8—22no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—42no—
477C4⋊C4—42no—
478C4⋊C4C2×D4×C3712yes—
479C4⋊C4C2×D4×C3712yes—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C42—24no—
490C42—22no—
491C42—22no—
492C42—21no—
493C42—22no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—41no—
498C42—41no—
499C42C2×D4×C3712yes—
500C42C2×D4×C3712yes—
501C23—22no—
502C23C22×D4×C3711yescharacteristic
503Q8—24no—
504Q8—44no—
505Q8—42no—
506Q8—42no—
507Q8—42no—
508Q8—81no—
509D4—42no—
510D4—42no—
511D4—42no—
512D4—42no—
513D4—81no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—41no—
531C2×C4—44no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—44no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—82no—
545C2×C4#120×C3711yescharacteristic
546C2×C4#120×C3712yes—
547C2×C4#120×C3711yescharacteristic
548C2×C4#135×C3712yes—
549C2×C4C22×D4×C3712yes—
550C8—42no—
551C8—42no—
552C22—21no—
553C22—21no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22C2×#120×C3711yescharacteristic
558C22C2×#135×C3711yescharacteristic
559C22C37×#57511yescharacteristic
560C4—22no—
561C4—22no—
562C4—21no—
563C4—22no—
564C4—42no—
565C4—42no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—42no—
573C4—81no—
574C4C37×#45612yes—
575C2—21no—
576C2—21no—
577C2—82no—
578C2C37×#300211yescharacteristic
579C2C2×C37×#45611yescharacteristic
580C2C37×#302511yescharacteristic
subgroupG/H
centerC2×C4×C37#120
commutator, Frattini, cosocleC22×C4C24×C37
socleC22×C37C2×#120
prime radicalC37×#537C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C37 ◁ C2×C42×C37 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C37×#3108C2semidirect
3. C37×#2399C2semidirect
4. C37×#1611C2semidirect
6. C37×#1609C2semidirect
7. C37×#1605C2semidirect
9. C37×#1603C2semidirect
10. C37×#1500C2semidirect
11. C37×#1461C2semidirect
261. #18131C37direct (N × H)
286. #3108C2×C37semidirect
287. #2399C2×C37semidirect
288. #1611C2×C37semidirect
290. #1609C2×C37semidirect
291. #1605C2×C37semidirect
293. #1603C2×C37semidirect
294. #1500C2×C37semidirect
295. #1461C2×C37semidirect
341. C37#18131direct (N × H)

Maximal subgroups

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

subgroupindex
C37×#34612
C37×#31082
C37×#23992
C37×#16112
C37×#16102
C37×#16092
C37×#16052
C37×#16042
C37×#16032
C37×#15002
C37×#14612
#1813137