Finite Group Databasebeta

← C37×#18139 #22639392

Subgroups — C37×#18139 #22639392

Order 9472.

962 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C37×#539C211yesmaximal, characteristic
2C37×#3095C211yesmaximal, characteristic, complemented
3C37×#3094C211yesmaximal, characteristic
4C37×#2484C211yesmaximal, characteristic, complemented
5C37×#1615C214yesmaximal, complemented
6C37×#1609C214yesmaximal, complemented
7C37×#1511C211yesmaximal, characteristic, complemented
8C37×#1510C211yesmaximal, characteristic
9C37×#1463C211yesmaximal, characteristic, complemented
10C37×#539—22no—
11C37×#539—22no—
12C37×#539—22no—
13C37×#539C2214yes—
14C2×#126×C37—21no—
15C2×#125×C37—21no—
16C2×#123×C37—21no—
17C2×#123×C37—21no—
18C2×C22⋊Q8×C37—21no—
19C2×C22⋊Q8×C37C2211yescharacteristic
20C2×#121×C37C2211yescharacteristic
21C2×C4×D4×C37—21no—
22C2×#117×C37C2211yescharacteristic
23C22×C4⋊C4×C37C2211yescharacteristic
24C37×#485—22no—
25C37×#484C2212yescomplemented
26C37×#483C2212yescomplemented
27C37×#482—22no—
28C37×#481C2212yes—
29C37×#480C2212yes—
30C37×#428—21no—
31C37×#428—21no—
32C37×#419—21no—
33C37×#418—21no—
34C37×#407C2211yescharacteristic
35C37×#407C2211yescharacteristic
36C37×#400C2212yescomplemented
37C37×#398C2212yescomplemented
38C37×#387—22no—
39C37×#385—21no—
40C37×#381—21no—
41C37×#381C2211yescharacteristic
42C37×#328C2214yescomplemented
43C37×#327C2214yes—
44C37×#324C2214yescomplemented
45C22×Q8×C37D411yescharacteristic
46C22×D4×C37—21no—
47C22×D4×C37D411yescharacteristic
48C23×C4×C37—21no—
49C23×C4×C37D411yescharacteristic
50C23×C4×C37D411yescharacteristic
51C23×C4×C37C2311yescharacteristic
52C2×M16×C37—21no—
53C2×M16×C37—21no—
54#126×C37—24no—
55#126×C37—24no—
56#125×C37—24no—
57#125×C37—24no—
58#123×C37—24no—
59#123×C37—24no—
60#123×C37—24no—
61#123×C37—24no—
62C22⋊Q8×C37—24no—
63C22⋊Q8×C37—24no—
64C22⋊Q8×C37—21no—
65C22⋊Q8×C37—21no—
66C22⋊Q8×C37D412yes—
67C22⋊Q8×C37C2312yes—
68#121×C37—21no—
69#121×C37—21no—
70#121×C37D412yes—
71#121×C37C2312yes—
72C4×D4×C37—24no—
73C4×D4×C37—24no—
74#117×C37—21no—
75#117×C37—21no—
76#117×C37—21no—
77#117×C37—21no—
78C2×C4⋊C4×C37—21no—
79C2×C4⋊C4×C37—21no—
80C2×C4⋊C4×C37—21no—
81C2×C4⋊C4×C37—21no—
82C2×C4⋊C4×C37—21no—
83C2×C4⋊C4×C37—21no—
84C2×C4⋊C4×C37—21no—
85C2×C4⋊C4×C37—21no—
86C2×C4⋊C4×C37—22no—
87C2×C4⋊C4×C37D412yes—
88C2×C4⋊C4×C37D411yescharacteristic
89C2×C4⋊C4×C37D411yescharacteristic
90C2×C4⋊C4×C37C2311yescharacteristic
91C2×C4⋊C4×C37C2311yescharacteristic
92C2×C4⋊C4×C37C2312yes—
93C2×C22⋊C4×C37—21no—
94C2×C22⋊C4×C37—21no—
95C2×C22⋊C4×C37—21no—
96C2×C22⋊C4×C37—21no—
97C2×C22⋊C4×C37—21no—
98C2×C22⋊C4×C37—21no—
99C2×C22⋊C4×C37—21no—
100C2×C42×C37—21no—
101C2×C42×C37—21no—
102#107×C37—22no—
103#107×C37—22no—
104#106×C37—22no—
105#106×C37—22no—
106#103×C37—22no—
107#103×C37—22no—
108#102×C37—22no—
109#102×C37—22no—
110C22⋊C8×C37—21no—
111C22⋊C8×C37—21no—
112C22⋊C8×C37C2312yes—
113C22⋊C8×C37C2312yes—
114#95×C37—22no—
115#95×C37—22no—
116#95×C37—21no—
117#95×C37—22no—
118#95×C37C2312yes—
119C24×C37—21no—
120C24×C37C2×D411yescharacteristic
121C2×Q8×C37—21no—
122C2×Q8×C37—42no—
123C2×Q8×C37C2×D412yes—
124C2×D4×C37—22no—
125C2×D4×C37—22no—
126C2×D4×C37—21no—
127C2×D4×C37—42no—
128C2×D4×C37—44no—
129C2×D4×C37C2×D412yes—
130C22×C4×C37—21no—
131C22×C4×C37—21no—
132C22×C4×C37—21no—
133C22×C4×C37—21no—
134C22×C4×C37—21no—
135C22×C4×C37—21no—
136C22×C4×C37—24no—
137C22×C4×C37—21no—
138C22×C4×C37—22no—
139C22×C4×C37—21no—
140C22×C4×C37—21no—
141C22×C4×C37—42no—
142C22×C4×C37—42no—
143C22×C4×C37—42no—
144C22×C4×C37—82no—
145C22×C4×C37C2×D412yes—
146C22×C4×C37C2×D411yescharacteristic
147C22×C4×C37C2×D411yescharacteristic
148C22×C4×C37C2×D412yes—
149C22×C4×C37C2×D411yescharacteristic
150C22×C4×C37C2×D411yescharacteristic
151C22×C4×C37C2×D411yescharacteristic
152C22×C4×C37C2411yescharacteristic
153M16×C37—42no—
154M16×C37—42no—
155C2×C8×C37—22no—
156C2×C8×C37—22no—
157C4⋊C4×C37—24no—
158C4⋊C4×C37—24no—
159C4⋊C4×C37—24no—
160C4⋊C4×C37—22no—
161C4⋊C4×C37—22no—
162C4⋊C4×C37—22no—
163C4⋊C4×C37—21no—
164C4⋊C4×C37—21no—
165C4⋊C4×C37—22no—
166C4⋊C4×C37—22no—
167C4⋊C4×C37—22no—
168C4⋊C4×C37—21no—
169C4⋊C4×C37—21no—
170C4⋊C4×C37—21no—
171C4⋊C4×C37—21no—
172C4⋊C4×C37—44no—
173C4⋊C4×C37C2×D412yes—
174C4⋊C4×C37C2×D412yes—
175C22⋊C4×C37—24no—
176C22⋊C4×C37—24no—
177C22⋊C4×C37—24no—
178C22⋊C4×C37—22no—
179C22⋊C4×C37—22no—
180C22⋊C4×C37—22no—
181C22⋊C4×C37—22no—
182C22⋊C4×C37—42no—
183C22⋊C4×C37—41no—
184C22⋊C4×C37—41no—
185C42×C37—24no—
186C42×C37—41no—
187C42×C37—41no—
188C23×C37—22no—
189C23×C37—22no—
190C23×C37—22no—
191C23×C37—41no—
192C23×C37—42no—
193C23×C37—42no—
194C23×C37—42no—
195C23×C37#12011yescharacteristic
196C23×C37#12011yescharacteristic
197C23×C37C22×D411yescharacteristic
198Q8×C37—42no—
199Q8×C37—81no—
200D4×C37—42no—
201D4×C37—44no—
202D4×C37—44no—
203D4×C37—81no—
204C2×C4×C37—22no—
205C2×C4×C37—22no—
206C2×C4×C37—22no—
207C2×C4×C37—22no—
208C2×C4×C37—22no—
209C2×C4×C37—22no—
210C2×C4×C37—22no—
211C2×C4×C37—22no—
212C2×C4×C37—22no—
213C2×C4×C37—41no—
214C2×C4×C37—41no—
215C2×C4×C37—41no—
216C2×C4×C37—41no—
217C2×C4×C37—42no—
218C2×C4×C37—42no—
219C2×C4×C37—42no—
220C2×C4×C37—42no—
221C2×C4×C37—42no—
222C2×C4×C37—42no—
223C2×C4×C37—42no—
224C2×C4×C37—42no—
225C2×C4×C37—42no—
226C2×C4×C37—42no—
227C2×C4×C37—41no—
228C2×C4×C37—41no—
229C2×C4×C37—42no—
230C2×C4×C37—42no—
231C2×C4×C37—81no—
232C2×C4×C37—84no—
233C2×C4×C37#12011yescharacteristic
234C2×C4×C37#12011yescharacteristic
235C2×C4×C37C22×D411yescharacteristic
236C2×C4×C37C22×D411yescharacteristic
237C8×C37—42no—
238C8×C37—42no—
239#18139C3711yesmaximal, characteristic, direct product factor, Sylow
240C22×C37—21no—
241C22×C37—21no—
242C22×C37—21no—
243C22×C37—21no—
244C22×C37—21no—
245C22×C37—21no—
246C22×C37—21no—
247C22×C37—44no—
248C22×C37—42no—
249C22×C37—42no—
250C22×C37—42no—
251C22×C37—84no—
252C22×C37#45812yes—
253C22×C37C2×#12011yescharacteristic
254C22×C37#57512yes—
255C4×C37—21no—
256C4×C37—21no—
257C4×C37—21no—
258C4×C37—21no—
259C4×C37—42no—
260C4×C37—42no—
261C4×C37—42no—
262C4×C37—42no—
263C4×C37—42no—
264C4×C37—82no—
265C4×C37—81no—
266C4×C37—81no—
267C2×#539C2×C3711yescharacteristic
268#3095C2×C3711yescharacteristic, complemented
269#3094C2×C3711yescharacteristic
270#2484C2×C3711yescharacteristic, complemented
271#1615C2×C3714yescomplemented
272#1609C2×C3714yescomplemented
273#1511C2×C3711yescharacteristic, complemented
274#1510C2×C3711yescharacteristic
275#1463C2×C3711yescharacteristic, complemented
276C2×C37—22no—
277C2×C37—22no—
278C2×C37—41no—
279C2×C37—82no—
280C2×C37#300511yescharacteristic
281C2×C37#302011yescharacteristic
282C2×C37C2×#45811yescharacteristic
283#539—22no—
284#539—22no—
285#539—22no—
286#539C22×C3714yes—
287C2×#126—21no—
288C2×#125—21no—
289C2×#123—21no—
290C2×#123—21no—
291C2×C22⋊Q8—21no—
292C2×C22⋊Q8C22×C3711yescharacteristic
293C2×#121C22×C3711yescharacteristic
294C2×C4×D4—21no—
295C2×#117C22×C3711yescharacteristic
296C22×C4⋊C4C22×C3711yescharacteristic
297#485—22no—
298#484C22×C3712yescomplemented
299#483C22×C3712yescomplemented
300#482—22no—
301#481C22×C3712yes—
302#480C22×C3712yes—
303#428—21no—
304#428—21no—
305#419—21no—
306#418—21no—
307#407C22×C3711yescharacteristic
308#407C22×C3711yescharacteristic
309#400C22×C3712yescomplemented
310#398C22×C3712yescomplemented
311#387—22no—
312#385—21no—
313#381—21no—
314#381C22×C3711yescharacteristic
315#328C22×C3714yescomplemented
316#327C22×C3714yes—
317#324C22×C3714yescomplemented
318C37#1813911yescharacteristic, direct product factor, Sylow
319C22×Q8D4×C3711yescharacteristic
320C22×D4—21no—
321C22×D4D4×C3711yescharacteristic
322C23×C4—21no—
323C23×C4D4×C3711yescharacteristic
324C23×C4D4×C3711yescharacteristic
325C23×C4C23×C3711yescharacteristic
326C2×M16—21no—
327C2×M16—21no—
328#126—24no—
329#126—24no—
330#125—24no—
331#125—24no—
332#123—24no—
333#123—24no—
334#123—24no—
335#123—24no—
336C22⋊Q8—24no—
337C22⋊Q8—24no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8D4×C3712yes—
341C22⋊Q8C23×C3712yes—
342#121—21no—
343#121—21no—
344#121D4×C3712yes—
345#121C23×C3712yes—
346C4×D4—24no—
347C4×D4—24no—
348#117—21no—
349#117—21no—
350#117—21no—
351#117—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4D4×C3712yes—
362C2×C4⋊C4D4×C3711yescharacteristic
363C2×C4⋊C4D4×C3711yescharacteristic
364C2×C4⋊C4C23×C3711yescharacteristic
365C2×C4⋊C4C23×C3711yescharacteristic
366C2×C4⋊C4C23×C3712yes—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C42—21no—
375C2×C42—21no—
376#107—22no—
377#107—22no—
378#106—22no—
379#106—22no—
380#103—22no—
381#103—22no—
382#102—22no—
383#102—22no—
384C22⋊C8—21no—
385C22⋊C8—21no—
386C22⋊C8C23×C3712yes—
387C22⋊C8C23×C3712yes—
388#95—22no—
389#95—22no—
390#95—21no—
391#95—22no—
392#95C23×C3712yes—
393C24—21no—
394C24C2×D4×C3711yescharacteristic
395C2×Q8—21no—
396C2×Q8—42no—
397C2×Q8C2×D4×C3712yes—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—21no—
401C2×D4—42no—
402C2×D4—44no—
403C2×D4C2×D4×C3712yes—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—24no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—82no—
419C22×C4C2×D4×C3712yes—
420C22×C4C2×D4×C3711yescharacteristic
421C22×C4C2×D4×C3711yescharacteristic
422C22×C4C2×D4×C3712yes—
423C22×C4C2×D4×C3711yescharacteristic
424C22×C4C2×D4×C3711yescharacteristic
425C22×C4C2×D4×C3711yescharacteristic
426C22×C4C24×C3711yescharacteristic
427M16—42no—
428M16—42no—
429C2×C8—22no—
430C2×C8—22no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—44no—
447C4⋊C4C2×D4×C3712yes—
448C4⋊C4C2×D4×C3712yes—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—42no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C42—24no—
460C42—41no—
461C42—41no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—41no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23#120×C3711yescharacteristic
470C23#120×C3711yescharacteristic
471C23C22×D4×C3711yescharacteristic
472Q8—42no—
473Q8—81no—
474D4—42no—
475D4—44no—
476D4—44no—
477D4—81no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—81no—
506C2×C4—84no—
507C2×C4#120×C3711yescharacteristic
508C2×C4#120×C3711yescharacteristic
509C2×C4C22×D4×C3711yescharacteristic
510C2×C4C22×D4×C3711yescharacteristic
511C8—42no—
512C8—42no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—44no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—84no—
525C22C37×#45812yes—
526C22C2×#120×C3711yescharacteristic
527C22C37×#57512yes—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—42no—
536C4—42no—
537C4—82no—
538C4—81no—
539C4—81no—
540C2—22no—
541C2—22no—
542C2—41no—
543C2—82no—
544C2C37×#300511yescharacteristic
545C2C37×#302011yescharacteristic
546C2C2×C37×#45811yescharacteristic
subgroupG/H
center, socleC22×C37C2×#120
commutator, Frattini, cosocleC22×C4C24×C37
prime radicalC2×#121×C37C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C37 ◁ C23×C4×C37 ◁ G

Complements

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

NH ≅ G/Ntype
2. C37×#3095C2semidirect
4. C37×#2484C2semidirect
5. C37×#1615C2semidirect
6. C37×#1609C2semidirect
7. C37×#1511C2semidirect
9. C37×#1463C2semidirect
25. C37×#484C22semidirect
26. C37×#483C22semidirect
36. C37×#400C22semidirect
37. C37×#398C22semidirect
42. C37×#328C22semidirect
44. C37×#324C22semidirect
239. #18139C37direct (N × H)
268. #3095C2×C37semidirect
270. #2484C2×C37semidirect
271. #1615C2×C37semidirect
272. #1609C2×C37semidirect
273. #1511C2×C37semidirect
275. #1463C2×C37semidirect
298. #484C22×C37semidirect
299. #483C22×C37semidirect
309. #400C22×C37semidirect
310. #398C22×C37semidirect
315. #328C22×C37semidirect
317. #324C22×C37semidirect
318. C37#18139direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C37×#5392
C37×#30952
C37×#30942
C37×#24842
C37×#16152
C37×#16092
C37×#15112
C37×#15102
C37×#14632
#1813937